Showing 1–50 of 93 results for abstract: "self-intersection" AND simulation

A Magnetic Unification of Merging Supermassive Black Hole Binaries

Authors: Mark J. Avara, David O'Neill, Zoltán Haiman

Abstract: …an electromagnetic (EM) transient from a supermassive black hole binary (SMBHB) merging within a gaseous environment will constitute a multi-messenger milestone. Numerical simulations of these systems have mostly been performed in 2D with a constant viscosity parameter representing turbulent and magnetic stresses. These… ▽ More The detection of an electromagnetic (EM) transient from a supermassive black hole binary (SMBHB) merging within a gaseous environment will constitute a multi-messenger milestone. Numerical simulations of these systems have mostly been performed in 2D with a constant viscosity parameter representing turbulent and magnetic stresses. These simulations predict a steep drop in accretion rate and X-ray luminosity at merger, followed by a slow recovery. However, 3D-GRMHD and 3D-MHD simulations have shown only a modest reduction in accretion rate and a fast post-merger recovery. We present a new 2D pseudo-Newtonian framework with physically motivated prescriptions for stochastic viscosity, relativistic apsidal precession, and large-scale magnetic fields. When suitably calibrated, this 2D framework accurately captures key 3D-GRMHD behavior, demonstrating that it can be used to explore binary accretion without the high computational cost of 3D-GRMHD simulations. We find that the merger signatures are most sensitive to the strength of the magnetic field, with a drop in the accretion rate at merger progressively less pronounced for stronger fields. Post-merger evolution is determined by both magnetization and relativistic precession of orbiting gas, yielding rapid recovery of accretion. For low-magnetization disks, recovery is driven by self-intersection shocks, and the dip at merger is followed by a distinct second dimming. Large-scale magnetic fields of increasing magnitude lead to magnetically arrested disk (MAD) behavior which disturbs the merging system progressively earlier before merger, and longer after. Our results unify the EM signatures of the merger of embedded coplanar SMBHBs, and provide novel observational constraints on their intrinsic magnetization. △ Less

Submitted 21 September, 2026; originally announced September 2026.

Comments: 34 pages, 19 figures

Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields

Authors: Zhouru Xiao, Sha Luo, Yang Lu, Mingliang Xiao, Weijia Yao, Bohuan Lin, Xianzhe Cheng, Yaonan Wang

Abstract: …can eliminate singular points (i.e., points where the vector field vanishes) inherent in conventional GVFs and guarantee global convergence of robot trajectories to closed and self-… ▽ More The existing singularity-free guiding vector field (SF-GVF) with an additional virtual coordinate can eliminate singular points (i.e., points where the vector field vanishes) inherent in conventional GVFs and guarantee global convergence of robot trajectories to closed and self-intersecting desired paths. However, the desired speed given by the GVF along the desired path in the original lower-dimensional space cannot be arbitrarily specified but depends on path parameterizations. One possible workaround is to partially normalize the physical projection of the SF-GVF and assign a user-designed speed. However, we show that this workaround may introduce new singularities since the normalization denominator can become zero. To address this issue, we propose a new SF-GVF with prescribed physical speed (PPS). The integral curves of the new SF-GVF converge exponentially to the desired path from any initial condition in the higher-dimensional space (including virtual dimension); more importantly, the robot's physical speed converges to the PPS, while the path-error dynamics remain invariant under regular reparameterizations of the desired path. We further develop a saturated acceleration control law for second-order kinematic models. Finally, comparative simulations and 3D path-following experiments with a quadrotor under different PPS profiles validate the theoretical results and demonstrate the effectiveness of the proposed approach. △ Less

Submitted 17 September, 2026; originally announced September 2026.

Singularity-Free Guiding Vector Fields on SO(3) with Designer-Specified Progression Behavior

Authors: Jesus Bautista, Hector Garcia de Marina

Abstract: …results are established under a bi-invariant Riemannian metric and hold uniformly across choices of path, progression, and Lyapunov gain. The framework is illustrated in simulation on self-intersecting paths under both constant and point-convergence progression behaviors. ▽ More This paper develops a singularity-free guiding vector field (SF-GVF) for path following on the special orthogonal group SO(3). First, we lift the Euclidean SF-GVF construction to SO(3), integrating the augmented-state approach with the intrinsic Lie-group geometry and obtaining a closed-form geometric guidance law whose integral curves converge to a designer-specified attitude path. The field is defined on a dense open subset of SO(3), excluding only the measure-zero antipodal set - a manifestation of the topological obstruction to continuous global stabilization on SO(3). The construction requires no per-step optimization and produces a control input intrinsically in so(3) as body angular rates. Second, we formalize the progression behavior along the path as a designer-supplied function ν(ξ), promoting the parametric speed from an implicitly resolved degree of freedom to a first-class design specification. In contrast to the Euclidean condition v = 0, which excludes vehicles with minimum-speed constraints, the corresponding condition ω= 0 on SO(3) is physically admissible for most platforms with active attitude control, making the progression behavior a design freedom structurally available on SO(3) but absent in the Euclidean setting. The framework's structural results are established under a bi-invariant Riemannian metric and hold uniformly across choices of path, progression, and Lyapunov gain. The framework is illustrated in simulation on self-intersecting paths under both constant and point-convergence progression behaviors. △ Less

Submitted 7 September, 2026; originally announced September 2026.

Comments: 12 pages, submitted to Automatica

X-ray Variability and Photosphere Evolution during Accretion Disk Formation in Tidal Disruption Events

Authors: Xiaoshan Huang, Maria Renee Meza, Sol Bin Yun, Brenna Mockler, Shane W. Davis, Yan-fei Jiang

Abstract: …(TDEs) originates from both accretion and shocks, producing photons that eventually emerge from an inhomogeneous photosphere. We model disk formation following debris stream self-… ▽ More The early time emission in tidal disruption events (TDEs) originates from both accretion and shocks, producing photons that eventually emerge from an inhomogeneous photosphere. We model disk formation following debris stream self-intersection in a TDE using three-dimensional, frequency-integrated and multi-group radiation hydrodynamic simulations. We find a more circularized disk forms about 24 days following the stream-stream collision, once the mass fallback rate passes its peak and the debris stream density decreases. Despite the absence of a circularized disk at early times, various shocks and the asymmetric photosphere are sufficient to drive a wide range of x-ray-to-optical ratios and soft-X-ray variability. We find that with strong apsidal precession, the first light is from the stream-stream collision. It launches an optically-thick outflow, but only produces modest prompt emission. The subsequent optical and ultraviolet (UV) light curve rise is mainly powered by shocks in the turbulent accretion flow close to the black hole. The optical-UV luminosity peaks roughly when the disk forms and shock-driven outflows subside. Radiation pressure clears the polar region and creates optically-thin channels. We obtain the broadband spectral energy distribution (SED) by post-processing multi-group simulations with 16-20 frequency groups. The SED has a black body component that peaks in the extreme UV. The soft X-ray component either resembles a thermal tail, or can be described by a power law associated with bulk Compton scattering. The blackbody parameters are broadly consistent with observed optical TDEs and vary weakly with viewing angle, but the soft X-ray emission is highly angle-dependent. △ Less

Submitted 25 August, 2026; v1 submitted 15 December, 2025; originally announced December 2025.

Comments: 18 figures, 27 pages

Dynamic Optimal Transport with Optimal Preferential Paths

Authors: Marcello Carioni, Juliane Krautz, Jan-F. Pietschmann

Abstract: …the main interest in this paper. To this end, the Tangent-Point energy is added to the action functional in order to preserve the regularity properties of the curve and prevent self-intersections. Also in this case, by relying on suitable compactness estimates both for the time-dependent measures and the curve $Γ$, the… ▽ More We study a dynamic optimal transport type problem on a domain that consists of two parts: a compact set $Ω\subset \mathbb{R}^d$ (bulk) and a non-intersecting and sufficiently regular curve $Γ\subset Ω$. On each of them, a Benamou-Brenier type dynamic optimal transport problem is considered, yet with an additional mechanism that allows the exchange (at a cost) of mass between bulk and curve. In the respective actions, we also allow for non-linear mobilities. We first ensure the existence of minimizers by relying on the direct method of calculus of variations and we study the asymptotic properties of the minimizers under changes in the parameters regulating the dynamics in $Ω$ and $Γ$. Then, we study the case when the curve $Γ$ is also allowed to change, being the main interest in this paper. To this end, the Tangent-Point energy is added to the action functional in order to preserve the regularity properties of the curve and prevent self-intersections. Also in this case, by relying on suitable compactness estimates both for the time-dependent measures and the curve $Γ$, the existence of optimizers is shown. We extend these analytical findings by numerical simulations based on a primal-dual approach that illustrate the behaviour of geodesics, for fixed and varying curves. △ Less

Submitted 30 July, 2026; v1 submitted 4 April, 2025; originally announced April 2025.

MSC Class: 49Q22; 35R01; 60B05; 49M41

Geometric Shape Optimization for Limbless Locomotion

Authors: Utpal Khanal, Avirup Mandal

Abstract: The simulation of locomotion in limbless, deformable organisms remains a challenging problem across computer graphics, soft robotics, and computational modeling. In this work, we present a novel differential-geometric framework for modeling the motion of slender soft bodies, such as snakes. The body is represented as a three-dimensional parametric curve usin… ▽ More The simulation of locomotion in limbless, deformable organisms remains a challenging problem across computer graphics, soft robotics, and computational modeling. In this work, we present a novel differential-geometric framework for modeling the motion of slender soft bodies, such as snakes. The body is represented as a three-dimensional parametric curve using a Fourier-Chebyshev polynomial basis. Motion is computed by solving an optimization problem that determines the interaction between the curve and its environment by estimating polynomial coefficients. To ensure physically plausible and non-self-intersecting behavior, bending and torsional energy terms are incorporated into the formulation. The resulting curve is then used to drive a surface representation via interpolation, enabling realistic visualization analogous to skinning techniques. We evaluate the proposed approach across a range of complex scenarios and parameter settings to demonstrate its robustness and versatility. Comparative analysis with state-of-the-art methods indicates that our approach achieves improved simulation quality and generates more physically realistic motion. △ Less

Submitted 1 July, 2026; originally announced July 2026.

Comments: 19 pages, 15 figures

Coupled integrated photonic quantum memristors using a single photon source made of a colour center

Authors: Alessio Baldazzi, Roy Philip George Konnoth Ancel, Sebastiano Guaraldo, Ivan Fattori, Xuan Chen, Ziad Abi Akar, Regis Deturche, Stefano Azzini, Christophe Couteau, Lorenzo Pavesi

Abstract: …enhanced memristive behaviour compared to single devices. In particular, we report inter-memristor input-output hysteresis curves exhibiting larger form factors and displaying self-… ▽ More Photonic quantum memristors provide a measurement-induced route to nonlinear and history-dependent quantum dynamics. Experimental demonstrations have so far focused on isolated devices or simple cascaded devices configurations. Here, we experimentally realize and characterize a network of two coupled photonic quantum memristors with crossed feedback, implemented on a silicon nitride photonic integrated circuit and fed by a room-temperature single-photon source based on a silicon-vacancy color center SiV$^-$ in a nanodiamond. Each memristor consists of an integrated Mach-Zehnder interferometer whose transfer function is adaptively updated by photon detection events on another memristor, thus generating novel non-Markovian input-output dynamics with an enhanced memristive behaviour compared to single devices. In particular, we report inter-memristor input-output hysteresis curves exhibiting larger form factors and displaying self-intersecting loops, respectively revealing marked bistability and self-intersecting hysteresis geometry. Furthermore, numerical simulations show how these features emerge from the interplay between memory depth and relative input phase, for both intra- and inter-memristor input-output relations. We experimentally test the performance of our system in the NARMA task. Our results establish coupled integrated photonic quantum memristors as scalable nonlinear building blocks and highlight their potential for implementing compact quantum neuromorphic and reservoir computing architectures. △ Less

Submitted 10 June, 2026; v1 submitted 16 February, 2026; originally announced February 2026.

Comments: 30 pages, 11 figures, 3 tables

Resolving the (Debate About) Nozzle Shocks in Tidal Disruption Events

Authors: Zachary L. Andalman, Eliot Quataert, Eric R. Coughlin, C. J. Nixon

Abstract: …the debris stream, but its role is the subject of ongoing debate. We develop an idealized model for the debris stream evolution combining 3D smoothed-particle hydrodynamics simulations, the semi-analytic affine model, and 1D finite-volume hydrodynamic simulations. Because our model is computationally cheap, we can unam… ▽ More When a star passes within the Roche limit of a supermassive black hole (SMBH), it is pulled apart by the BH's tidal field in a tidal disruption event (TDE). The resulting flare is powered by the circularization and accretion of bound stellar debris, which initially returns to the BH on eccentric orbits in a thin debris stream. The returning fluid elements follow inclined orbits that converge near pericenter, resulting in extreme vertical compression to scales $10^{-4}~R_\odot$ and the formation of a nozzle shock. Dissipation at the nozzle shock may affect circularization by altering the properties of the debris stream, but its role is the subject of ongoing debate. We develop an idealized model for the debris stream evolution combining 3D smoothed-particle hydrodynamics simulations, the semi-analytic affine model, and 1D finite-volume hydrodynamic simulations. Because our model is computationally cheap, we can unambiguously resolve the nozzle shock, use a realistic equation of state, and follow the debris stream evolution at many different times. Near peak fallback, Hydrogen recombination and molecular Hydrogen formation broaden the stream by a factor $\sim 5$, enhancing dissipation at the nozzle. However, the dissipation is still insufficient to directly circularize the debris by in-plane pressure gradients. Instead, the thicker stream substantially increases the likelihood that the stream self-intersects on the second orbit, despite relativistic nodal precession. The stream properties at self-intersection are sensitive to dissipation at the nozzle and the timing of focal points where the ballistic trajectories of the debris converge. Our results clarify the nozzle shock's role in circularization in TDEs, providing a foundation for more realistic circularization and emission models. △ Less

Submitted 1 June, 2026; v1 submitted 9 December, 2025; originally announced December 2025.

Comments: 19 pages main body, 23 pages total, 17 figures. Accepted by OJA on June 1st, 2026. Resubmitted for 2nd review on May 8th, 2026. Originally submitted to OJA on Dec 10th, 2025. Comments welcome. The code to generate our EOS tables is available at https://zandalman.com/publications/Andalman+2026a/

SDFStent: Real-time interactive virtual stenting via SDF deformation fields

Authors: Bohan J. Li, Nicholas C. Dorn, Andras Lasso, Matthew A. Jolley, Jeffrey A. Feinstein, Doug L. James, Alison L. Marsden

Abstract: Stenting is among the most common transcatheter interventions for congenital heart disease (CHD). Patient-specific computational fluid dynamics (CFD) simulations can predict hemodynamic outcomes of intervention scenarios but require post-operative vascular geometries that reflect stent-induced shape changes, which existing tools either model inadequately or… ▽ More Stenting is among the most common transcatheter interventions for congenital heart disease (CHD). Patient-specific computational fluid dynamics (CFD) simulations can predict hemodynamic outcomes of intervention scenarios but require post-operative vascular geometries that reflect stent-induced shape changes, which existing tools either model inadequately or require extensive time or manual effort to generate. We present SDFStent, a signed distance function (SDF) based mesh deformation method for virtual stenting that operates in real time, maintains mesh integrity, and preserves junction geometry. The stent is modeled as a pipe surface composed of piecewise-capsule SDFs joined by a smooth-minimum operator. Mesh vertices near the expanding SDF surface are displaced along the SDF gradient with a compactly supported fall-off function and an alpha blending mask. SDFStent was benchmarked against three existing approaches and validated on three tetralogy of Fallot (ToF) patients and three coarctation of the aorta (CoA) patients using rigid-wall steady-state CFD simulations against clinical catheterization measurements. Against a prescribed diameter of 6.0 mm, the method produced a mean stented diameter of 5.92 $\pm$ 0.08 mm in 1.5 s, over 100$\times$ faster than the best stenting-specific comparator. All output meshes were watertight and self-intersection-free. CFD-simulated post-operative pressure drops agreed with clinical measurements within 4 mmHg (mean error 2 mmHg). SDFStent produces simulation-ready post-stent models that match prescribed stent dimensions at interactive speeds, from pre-operative anatomy and catheterization data alone. The implementation is open-source and available in 3D Slicer. Its scriptable architecture enables automated generation of large synthetic cohorts for data-driven surrogate modeling. △ Less

Submitted 21 May, 2026; originally announced May 2026.

Comments: 39 pages, 12 figures, 4 tables. Under review at Computer Methods and Programs in Biomedicine

On the origin of anomalous dissipation in simulations of tidal disruption events

Authors: Chris Nixon, Eric R. Coughlin, Zachary L. Andalman

Abstract: …orbits, and a longstanding question in TDE theory is: How does the stellar debris circularize into a disc and accrete? The originally proposed answer to this question is self-… ▽ More In a tidal disruption event (TDE), a star is destroyed by the tidal field of a supermassive black hole. The stellar debris is initially placed on highly elliptical orbits, and a longstanding question in TDE theory is: How does the stellar debris circularize into a disc and accrete? The originally proposed answer to this question is self-intersection shocks, where relativistic apsidal precession results in a strong collision between the incoming and outgoing material. However, global simulations of TDEs tend to find enhanced hydrodynamical dissipation prior to any intersections of the debris orbits, with the material ``fanning out'' into a wide-angle and partially-unbound outflow upon passing through pericenter. We show that this dissipation is numerical in origin and arises from a combination of 1) the change in the kinematics of the debris as it passes through pericenter, with its velocity profile along the stream transitioning from strongly diverging pre-pericenter to strongly converging post-pericenter, and 2) the dependence of numerical algorithms (viscosity switches for particle-based methods and Riemann solvers for Godunov-based schemes) on the diverging vs. converging nature of the fluid. We support this conclusion with analytical and numerical modeling. We discuss possible resolutions to these issues as well as the implications of our findings in the context of observations. △ Less

Submitted 19 May, 2026; originally announced May 2026.

Comments: 22 pages, 13 figures, 1 appendix, submitted

RopeDreamer: A Kinematic Recurrent State Space Model for Dynamics of Flexible Deformable Linear Objects

Authors: Tim Missal, Lucas Domingues, Berk Guler, Simon Manschitz, Jan Peters, Paula Dornhofer Paro Costa

Abstract: …integrity during contact-rich tasks. While recent data-driven methods have utilized Recurrent and Graph Neural Networks for dynamics modeling, they often struggle with self-… ▽ More The robotic manipulation of Deformable Linear Objects (DLOs) is a fundamental challenge due to the high-dimensional, non-linear dynamics of flexible structures and the complexity of maintaining topological integrity during contact-rich tasks. While recent data-driven methods have utilized Recurrent and Graph Neural Networks for dynamics modeling, they often struggle with self-intersections and non-physical deformations, such as tangling and link stretching. In this paper, we propose a latent dynamics framework that combines a Recurrent State Space Model with a Quaternionic Kinematic Chain representation to enable robust, long-term forecasting of DLO states. By encoding the DLO as a sequence of relative rotations (quaternions) rather than independent Cartesian positions, we inherently constrain the model to a physically valid manifold that preserves link-length constancy. Furthermore, we introduce a dual-decoder architecture that decouples state reconstruction from future-state prediction, forcing the latent space to capture the underlying physics of deformation. We evaluate our approach on a large-scale simulated dataset of complex pick-and-place trajectories involving self-intersections. Our results demonstrate that the proposed model achieves a 40.52% reduction in open-loop prediction error over 50-step horizons compared to the state-of-the-art baseline, while reducing inference time by 31.17%. Our model further maintains superior topological consistency in scenarios with multiple crossings, proving its efficacy as a compositional primitive for long-horizon manipulation planning. △ Less

Submitted 30 April, 2026; originally announced April 2026.

The strange mechanics of an elastic rod under null-resultant transverse loads

Authors: Davide Bigoni, Diego Misseroni, Andrea Piccolroaz

Abstract: …For this reason, instability induced by transverse loading persists even when the rod thickness tends to zero. These theoretical predictions are confirmed by numerical simulations of a slender elastic layer, which show that increasing transverse load can induce buckling and drive the layer along a deformation path that closely follows that predicted by the… ▽ More Two equal and opposite distributed dead loads are applied orthogonally to the axis of an elastic rod in its rectilinear reference configuration, one at the extrados and the other at the intrados, such that the resultant applied force per unit length is uniformly zero. In this configuration, the rod is subjected to a transverse (tensile or compressive) stress, which is usually believed to have no significant effect on the structural response and has therefore not been considered so far. Contrary to this common belief, the asymptotic behavior of an incrementally deformed elastic layer and three different rod models (the first derived as an asymptotic approximation of the elastic layer; the second based on Euler elastica; and the third obtained by homogenization of a discrete model) reveal that this loading condition produces the same deformation in the rod as an axial load. In particular, the transverse load adds to the axial load in a generalized version of the Euler elastica, leading to buckling and nontrivial postcritical deformations when compressive. The critical transverse stress for buckling is found to have the same form as the Euler critical stress under axial force and tends to zero in the limit of vanishing rod inertia. For this reason, instability induced by transverse loading persists even when the rod thickness tends to zero. These theoretical predictions are confirmed by numerical simulations of a slender elastic layer, which show that increasing transverse load can induce buckling and drive the layer along a deformation path that closely follows that predicted by the generalized Euler elastica throughout the entire postcritical regime, even beyond self-intersection. To show that this behavior can be realized in practice, a dedicated experimental setup is developed, and the experimental results fully confirm the theoretical and numerical predictions. △ Less

Submitted 20 April, 2026; originally announced April 2026.

Comments: 20 pages, 12 figures

Journal ref: Journal of the Mechanics and Physics of Solids, Volume 212, 2026, 106590

Curvature-induced bound states in quantum wires

Authors: Tim Bergmann, Benjamin Schwager, Jamal Berakdar

Abstract: …states and the dynamics of the particle. For particles constrained to different spaces, such as structures hosting sharp bents, vertices, wedges, conical apices, tips, or self-… ▽ More A classical particle under spatial constraints is strictly confined to live on a specific space manifold or path, but this assumption is incompatible with the zero-point fluctuations of a quantum particle. One way to describe quantum mechanics under constraints is the confinement potential approach (CPA). For a non-relativistic particle, the CPA maps the problem onto the solution of a Schrödinger-type equation in an isometrically embedded Riemannian submanifold of Euclidean space while the motion along orthogonal directions are decoupled and spatially confined. This approach respects quantum uncertainty, and one of its key results is the appearance of geometry- and metric-induced potentials that affect the stationary states and the dynamics of the particle. For particles constrained to different spaces, such as structures hosting sharp bents, vertices, wedges, conical apices, tips, or self-intersections, a formalism beyond the CPA is needed. Here, a step towards a CPA extension for irregular spaces is presented. After classifying the possible geometric irregularities concerning the CPA formalism, the presentation is focused on a sharply bent quantum wire modeled as an embedded curve with singular (but absolute integrable) curvature. For a subclass fulfilling the additional requirement that the geometric potential is a distribution of first order, a solution scheme for the confined Schrödinger equation is presented based on singular Sturm-Liouville theory and operator theoretic methods. The analytical considerations and numerical simulations evidence the existence of curvature-induced bound states with non-differentiable wave functions localized around the singular point, with an extension well beyond the singularity. Furthermore, a multitude of scattering states appear that may affect the transport and optical properties of the system. △ Less

Submitted 2 April, 2026; originally announced April 2026.

Comments: 21 pages, 5 figures, submitted to Phys. Rev. Research

Journal ref: Phys. Rev. Research 8, 033228 (2026)

Vector-field guided constraint-following control for path following of uncertain mechanical systems

Authors: Hui Yin, Xiang Li, Yifan Liu, Weijia Yao

Abstract: …both fully-actuated and underactuated mechanical systems, heterogeneous (possibly fast) time-varying uncertainties with unknown bounds, and geometric desired paths that may be self-intersecting. Simulations are conducted to demonstrate the effectiveness of the approach. ▽ More This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it operates at the dynamics level and can handle both fully-actuated and underactuated mechanical systems, heterogeneous (possibly fast) time-varying uncertainties with unknown bounds, and geometric desired paths that may be self-intersecting. Simulations are conducted to demonstrate the effectiveness of the approach. △ Less

Submitted 16 March, 2026; v1 submitted 10 March, 2026; originally announced March 2026.

KidMesh: Computational Mesh Reconstruction for Pediatric Congenital Hydronephrosis Using Deep Neural Networks

Authors: Haoran Sun, Zhanpeng Zhu, Anguo Zhang, Bo Liu, Zhaohua Lin, Liqin Huang, Mingjing Yang, Lei Liu, Shan Lin, Wangbin Ding

Abstract: …However, these segmentation methods predominantly focus on morphological features, such as size, shape, and structure. To enable functional assessments, such as urodynamic simulations, external complex post-processing steps are required to convert these results into mesh-level representations. To address this limitation, we propose an end-to-end method base… ▽ More Pediatric congenital hydronephrosis (CH) is a common urinary tract disorder, primarily caused by obstruction at the renal pelvis-ureter junction. Magnetic resonance urography (MRU) can visualize hydronephrosis, including renal pelvis and calyces, by utilizing the natural contrast provided by water. Existing voxel-based segmentation approaches can extract CH regions from MRU, facilitating disease diagnosis and prognosis. However, these segmentation methods predominantly focus on morphological features, such as size, shape, and structure. To enable functional assessments, such as urodynamic simulations, external complex post-processing steps are required to convert these results into mesh-level representations. To address this limitation, we propose an end-to-end method based on deep neural networks, namely KidMesh, which could automatically reconstruct CH meshes directly from MRU. Generally, KidMesh extracts feature maps from MRU images and converts them into feature vertices through grid sampling. It then deforms a template mesh according to these feature vertices to generate the specific CH meshes of MRU images. Meanwhile, we develop a novel schema to train KidMesh without relying on accurate mesh-level annotations, which are difficult to obtain due to the sparsely sampled MRU slices. Experimental results show that KidMesh could reconstruct CH meshes in an average of 0.4 seconds, and achieve comparable performance to conventional methods without requiring post-processing. The reconstructed meshes exhibited no self-intersections, with only 3.7% and 0.2% of the vertices having error distances exceeding 3.2mm and 6.4mm, respectively. After rasterization, these meshes achieved a Dice score of 0.86 against manually delineated CH masks. Furthermore, these meshes could be used in renal urine flow simulations, providing valuable urodynamic information for clinical practice. △ Less

Submitted 9 February, 2026; originally announced February 2026.

Rings around irregular bodies. II. Numerical simulations of the 1/3 spin-orbit resonance confinement and applications to Chariklo

Authors: Heikki Salo, Bruno Sicardy

Abstract: …an active confinement mechanism by these resonances. Our goal is to understand how collisional rings can be confined near second-order SORs in spite of the fact that they force self-… ▽ More Rings have been found around Chariklo, Haumea and Quaoar, three small objects of the Solar System. All these rings are observed near the second-order spin-orbit resonances (SORs) 1/3 or 5/7 with the central body, suggesting an active confinement mechanism by these resonances. Our goal is to understand how collisional rings can be confined near second-order SORs in spite of the fact that they force self-intersecting streamlines.We use full 3D numerical simulations that treat rings of inelastically colliding particles orbiting non-axisymmetric central bodies, characterized by a dimensionless mass anomaly parameter mu. While most of our simulations ignore self-gravity, a few runs include gravitational interactions between particles, providing preliminary results on the effect of self-gravity on the ring confinement. The 1/3 SOR can confine ring material, by transferring the forced resonant mode into free Lindblad modes. We derive a criterion ensuring that the 1/3 SOR counteracts viscous spreading. Assuming meter-sized ring particles, and tau~1, this requires a threshold value mu > 1e-3 in Chariklo's case. The confinement is not permanent as a slow outward leakage of particles is observed in our simulations. This leakage can be halted by an outside moonlet with a mass of ~1e-7 - 1e-6 relative to Chariklo, corresponding to subkilometer-sized objects. With self-gravity, the ring viscosity nu increases by a factor of few in low-tau rings due to gravitational encounters. For large tau, self-gravity wakes enhance nu by a factor of ~100 compared to a non-gravitating ring, requiring ~10-fold larger mu since the threshold value increases proportional to square-root of nu. △ Less

Submitted 11 January, 2026; originally announced January 2026.

Comments: 26 pages, 26 figures. Accepted to Astronomy & Astrophysics

Journal ref: A&A 708, A9 (2026)

Connectivity-Preserving Cortical Surface Tetrahedralization

Authors: Besm Osman, Ruben Vink, Andrei Jalba, Maxime Chamberland

Abstract: A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface… ▽ More A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface simulations, preserving input surface connectivity is critical. However, automated surface extraction often yields meshes containing self-intersections, small holes, and faulty geometry, which prevents existing constrained and unconstrained meshers from preserving this connectivity. We address this issue by developing a novel tetrahedralization method that maintains input surface connectivity in the presence of such defects. We also present a metric to quantify the preservation of surface connectivity and demonstrate that our method correctly maintains connectivity compared to existing solutions. △ Less

Submitted 9 December, 2025; originally announced December 2025.

Comments: 13 pages, 3 figures

Simulations of Tidal Disruption of Supernova in Galaxy Nuclear Region: A Novel Model for Ambiguous Nuclear Transients

Authors: Xiangli Lei, Qingwen Wu, Ya-Ping Li, Wei-Hua Lei

Abstract: …slowly than typical tidal disruption events (TDEs), without the black hole mass limit as in TDEs. In this scenario, the SMBH capture the supernova ejecta, which subsequently self-intersects and circularizes into an accretion disk. Based on hydrodynamical simulations, we find that… ▽ More An increasing number of ambiguous nuclear transients, including some extreme nuclear transients with very shallow light-curve declines and weak AGN activity in their host galaxies, have been reported. Stars form in or are captured by AGN disks will grow and migrate inward, potentially exploding as supernovae once the inner cold accretion disk disappears in low-luminosity AGNs. We propose that the tidal disruption of a supernova (TDS) by a supermassive black hole (SMBH) can produce nuclear transients that are more energetic and evolve more slowly than typical tidal disruption events (TDEs), without the black hole mass limit as in TDEs. In this scenario, the SMBH capture the supernova ejecta, which subsequently self-intersects and circularizes into an accretion disk. Based on hydrodynamical simulations, we find that the accretion rate of the TDS disk exhibits a slow decline that can last for months to decades. The peak accretion rate of a typical core-collapse SN scenario can exceed the Eddington limit for SMBHs with $M_{\rm BH} \lesssim 10^{7.5}\,M_\odot$, while it remains sub-Eddington for more massive SMBHs. This model provides a mechanism for triggering an energetic TDE-like flare with luminosity \(\gtrsim10^{45}\,\mathrm{erg\,s^{-1}}\) in weak AGNs even with SMBH mass much larger than $10^{8}\,M_\odot$ or triggering turn-on changing-look AGNs. △ Less

Submitted 25 November, 2025; v1 submitted 14 September, 2025; originally announced September 2025.

Comments: submitted to ApJL

Numerical gravitational backreaction on cosmic string loops from simulation

Authors: Jeremy M. Wachter, Ken D. Olum, Jose J. Blanco-Pillado, Vishnu R. Gade, Kirthivarsha Sivakumar

Abstract: We report on the results of performing computational gravitational backreaction on cosmic string loops taken from a network simulation. The principal effect of backreaction is to smooth out small-scale structure on loops, which we demonstrate by various measures including the average loop power spectrum and the distribution of kink angles on the loops. Backr… ▽ More We report on the results of performing computational gravitational backreaction on cosmic string loops taken from a network simulation. The principal effect of backreaction is to smooth out small-scale structure on loops, which we demonstrate by various measures including the average loop power spectrum and the distribution of kink angles on the loops. Backreaction does lead to self-intersections in most cases, but these are typically small. An important effect discussed in prior work is the rounding off of kinks to form cusps, but we find that the cusps produced by that process are very weak and do not significantly contribute to the total gravitational-wave radiation of the loop. We comment briefly on extrapolating our results to loops as they would be found in nature. △ Less

Submitted 13 November, 2025; v1 submitted 15 November, 2024; originally announced November 2024.

Comments: 29 pages, 11 figures. Power spectrum data available via Zenodo: https://doi.org/10.5281/zenodo.17351106

Tidal disruption events with SPH-EXA: resolving the return of the stream

Authors: Noah Kubli, Alessia Franchini, Eric R. Coughlin, C. J. Nixon, Sebastian Keller, Pedro R. Capelo, Lucio Mayer

Abstract: …powers a luminous flare. Over the last few decades, several numerical studies have concluded that shock-induced dissipation occurs as the stream returns to pericentre (i.e., pre-self-… ▽ More In a tidal disruption event (TDE), a star is disrupted by the tidal field of a massive black hole, creating a debris stream that returns to the black hole, forms an accretion flow, and powers a luminous flare. Over the last few decades, several numerical studies have concluded that shock-induced dissipation occurs as the stream returns to pericentre (i.e., pre-self-intersection), resulting in efficient circularisation of the debris. However, the efficacy of these shocks is the subject of intense debate. We present high-resolution simulations (up to 10^10 particles) of the disruption of a solar-like star by a 10^6M_sun black hole with the new, GPU-based, smoothed-particle hydrodynamics code SPH-EXA, including the relativistic apsidal precession of the stellar debris orbits; our simulations run from initial disruption to the moment of stream self-intersection. With 10^8 particles - corresponding to the highest-resolution SPH simulations of TDEs in the pre-existing literature - we find significant, in-plane spreading of the debris as the stream returns through pericenter, in line with previous works that suggested this is a significant source of dissipation and luminous emission. However, with increasing resolution this effect is dramatically diminished, and with 10^10 particles there is effectively no change between the incoming and the outgoing stream widths. Our results demonstrate that the paradigm of significant dissipation of kinetic energy during pericentre passage is incorrect, and instead it is likely that debris circularisation is mediated by the originally proposed, stream-stream collision scenario. △ Less

Submitted 30 October, 2025; originally announced October 2025.

Comments: 10 pages, 4 figures, submitted to ApJL

Radiation-magnetohydrodynamic Simulations of Accretion Flow Formation After a Tidal Disruption Event

Authors: Maria Renee Meza, Xiaoshan Huang, Shane W. Davis, Yan-Fei Jiang

Abstract: We perform 3D radiation-magnetohydrodynamic simulations of the evolution of the fallback debris after a tidal disruption event. We focus on studying the effects of magnetic fields on the formation and early evolution of the accretion flow. We find that large magnetic fields can increase the debris stream thickness, moderately reducing the efficiency of the r… ▽ More We perform 3D radiation-magnetohydrodynamic simulations of the evolution of the fallback debris after a tidal disruption event. We focus on studying the effects of magnetic fields on the formation and early evolution of the accretion flow. We find that large magnetic fields can increase the debris stream thickness, moderately reducing the efficiency of the radiative acceleration of outflows during the first self-intersecting collisions. As gas accumulates and the collisions happen instead between the infalling stream and the accretion flow, magnetized and nonmagnetized systems evolve similarly at these early times: radiation-driven outflows dominate early after the initial stream-stream collision and a few days later, the accretion rate exceeds the mass outflow rate. We find that the MRI does not play a significant role in angular momentum transport and dissipation. Nor do we find evidence of a magnetocentrifugal driven outflow. Instead, collisions continue to dissipate kinetic energy into radiation that launches outflows and powers TDE luminosities reaching $L\sim4-6\times10^{44}$ erg s$^{-1}$. Shock-driven outflows and inflows redistribute angular momentum throughout the extent ($\sim50 r_s$) of the forming eccentric disk. Even in the presence of magnetic stresses, the accretion flow remains mostly eccentric with $e\sim0.2-0.3$ for $r\lesssim8r_s$ and $e\sim0.4-0.5$ for $10\lesssim r\,(r_s)\lesssim50$. Lastly, we find a polar angle-dependent density structure compatible with the viewing-angle effect, along with an additional azimuthal angle dependence established by the collisions. △ Less

Submitted 26 October, 2025; v1 submitted 30 May, 2025; originally announced June 2025.

Comments: 19 pages, 14 figures, 1 table. Submitted to ApJ. Comments are welcome. Update: 20 pages, 16 figures, 1 table. Published by ApJ

PaMO: Parallel Mesh Optimization for Intersection-Free Low-Poly Modeling on the GPU

Authors: Seonghun Oh, Xiaodi Yuan, Xinyue Wei, Ruoxi Shi, Fanbo Xiang, Minghua Liu, Hao Su

Abstract: …in graphics pipelines such as efficient rendering and interactive editing. However, most existing mesh simplification methods exhibit a few issues. Firstly, they often lead to self-… ▽ More Reducing the triangle count in complex 3D models is a basic geometry preprocessing step in graphics pipelines such as efficient rendering and interactive editing. However, most existing mesh simplification methods exhibit a few issues. Firstly, they often lead to self-intersections during decimation, a major issue for applications such as 3D printing and soft-body simulation. Second, to perform simplification on a mesh in the wild, one would first need to perform re-meshing, which often suffers from surface shifts and losses of sharp features. Finally, existing re-meshing and simplification methods can take minutes when processing large-scale meshes, limiting their applications in practice. To address the challenges, we introduce a novel GPU-based mesh optimization approach containing three key components: (1) a parallel re-meshing algorithm to turn meshes in the wild into watertight, manifold, and intersection-free ones, and reduce the prevalence of poorly shaped triangles; (2) a robust parallel simplification algorithm with intersection-free guarantees; (3) an optimization-based safe projection algorithm to realign the simplified mesh with the input, eliminating the surface shift introduced by re-meshing and recovering the original sharp features. The algorithm demonstrates remarkable efficiency, simplifying a 2-million-face mesh to 20k triangles in 3 seconds on RTX4090. We evaluated the approach on the Thingi10K dataset and showcased its exceptional performance in geometry preservation and speed. △ Less

Submitted 6 September, 2025; originally announced September 2025.

StructuredField: Unifying Structured Geometry and Radiance Field

Authors: Kaiwen Song, Jinkai Cui, Zherui Qiu, Juyong Zhang

Abstract: …to the unstructured nature of point-based representations, they are difficult to apply to modern graphics pipelines designed for structured meshes, as well as to a variety of simulation and editing algorithms that work well with structured mesh representations. To this end, we propose StructuredField, a novel representation that achieves both a structured ge… ▽ More Recent point-based differentiable rendering techniques have achieved significant success in high-fidelity reconstruction and fast rendering. However, due to the unstructured nature of point-based representations, they are difficult to apply to modern graphics pipelines designed for structured meshes, as well as to a variety of simulation and editing algorithms that work well with structured mesh representations. To this end, we propose StructuredField, a novel representation that achieves both a structured geometric representation of the reconstructed object and high-fidelity rendering reconstruction. We employ structured tetrahedral meshes to represent the reconstructed object. We reparameterize the geometric attributes of these tetrahedra into the parameters of 3D Gaussian primitives, thereby enabling differentiable, high-fidelity rendering directly from the mesh. Furthermore, a hierarchical implicit subdivision strategy is utilized to ensure a conformal mesh structure while empowering the representation to capture multi-scale details. To maintain geometric integrity during optimization, we propose a novel inversion-free homeomorphism that constrains the tetrahedral mesh, guaranteeing it remains both inversion-free and self-intersection-free during the optimization process and in the final result. Based on our proposed StructuredField, we achieve high-quality structured meshes that are completely inversion-free and conformal, while also attaining reconstruction results comparable to those of 3DGS. We also demonstrate the applicability of our representation to various applications such as physical simulation, deformation, and level-of-detail. △ Less

Submitted 11 August, 2025; v1 submitted 30 January, 2025; originally announced January 2025.

Comments: Project page: https://structuredfield.github.io

Jet Tilt Instability from Stream-Disk Interactions in MAD Disks

Authors: Brandon Curd, Richard Anantua, Hayley West, Joaquin Duran

Abstract: …However, the stream and disk interact strongly at times, and this will lead to different dynamics than expected in the standard MAD model. Here we employ global GRMHD simulations of a MAD disk interacting with an injected stream with a penetrating pericenter $R_p\sim 10 r_g$ and a range of density contrasts $f_ρ\equiv ρ_d/ρ_s$, or how dense the disk is rela… ▽ More Magnetically arrested accretion disks (MADs) around a rapidly rotating black hole (BH) have been proposed as a model for jetted tidal disruption events (TDEs). However, the stream and disk interact strongly at times, and this will lead to different dynamics than expected in the standard MAD model. Here we employ global GRMHD simulations of a MAD disk interacting with an injected stream with a penetrating pericenter $R_p\sim 10 r_g$ and a range of density contrasts $f_ρ\equiv ρ_d/ρ_s$, or how dense the disk is relative to the stream. We demonstrate for the first time that a MAD or semi-MAD state can be sustained and jets powered by the BH spin can be produced even when the stream is much denser than the disk, i.e. in the first month(s) of a jetted TDE. We also demonstrate that the strength of the self-intersection shock decreases as $f_ρ$, and time, increases. The jet or funnel can become significantly tilted (by $10-30^\circ$) due to the self-intersection outflow when $f_ρ\leq 0.1$. In models with a powerful jet and $f_ρ\leq 0.01$, the tilted jet interacts with and ultimately tilts the disk by as much as 23 degrees from the incoming stream and this tilted state is stable for the duration of the simulation. As $f_ρ$ increases, the tilt of the jet and disk is expected to realign with the BH spin once $f_ρ\geq 0.1$. The jet tilt could rapidly realign due to outer disk collapse or the self-intersection radius increasing. Our results provide an alternative explanation for the observed X-ray jet shut-off in days-weeks in jetted TDEs. △ Less

Submitted 19 May, 2025; v1 submitted 31 October, 2023; originally announced October 2023.

Comments: 21 pages, 22 figures, videos available at https://www.youtube.com/playlist?list=PL6Na55ZD3RmoJl7Rjhn6gCeAE0HWYCI0b

GarmentX: Autoregressive Parametric Representations for High-Fidelity 3D Garment Generation

Authors: Jingfeng Guo, Jinnan Chen, Weikai Chen, Zhenyu Sun, Lanjiong Li, Baozhu Zhao, Lingting Zhu, Xin Wang, Qi Liu

Abstract: …input image. Traditional garment reconstruction methods directly predict 2D pattern edges and their connectivity, an overly unconstrained approach that often leads to severe self-… ▽ More This work presents GarmentX, a novel framework for generating diverse, high-fidelity, and wearable 3D garments from a single input image. Traditional garment reconstruction methods directly predict 2D pattern edges and their connectivity, an overly unconstrained approach that often leads to severe self-intersections and physically implausible garment structures. In contrast, GarmentX introduces a structured and editable parametric representation compatible with GarmentCode, ensuring that the decoded sewing patterns always form valid, simulation-ready 3D garments while allowing for intuitive modifications of garment shape and style. To achieve this, we employ a masked autoregressive model that sequentially predicts garment parameters, leveraging autoregressive modeling for structured generation while mitigating inconsistencies in direct pattern prediction. Additionally, we introduce GarmentX dataset, a large-scale dataset of 378,682 garment parameter-image pairs, constructed through an automatic data generation pipeline that synthesizes diverse and high-quality garment images conditioned on parametric garment representations. Through integrating our method with GarmentX dataset, we achieve state-of-the-art performance in geometric fidelity and input image alignment, significantly outperforming prior approaches. We will release GarmentX dataset upon publication. △ Less

Submitted 29 April, 2025; originally announced April 2025.

Cabbage: A Differential Growth Framework for Open Surfaces

Authors: Xiaoyi Liu, Hao Tang

Abstract: …growth framework to model buckling behavior in 3D open surfaces found in nature-like the curling of flower petals. Cabbage creates high-quality triangular meshes free of self-… ▽ More We propose Cabbage, a differential growth framework to model buckling behavior in 3D open surfaces found in nature-like the curling of flower petals. Cabbage creates high-quality triangular meshes free of self-intersection. Cabbage-Shell is driven by edge subdivision which differentially increases discretization resolution. Shell forces expands the surface, generating buckling over time. Feature-aware smoothing and remeshing ensures mesh quality. Corrective collision effectively prevents self-collision even in tight spaces. We additionally provide Cabbage-Collision, and approximate alternative, followed by CAD-ready surface generation. Cabbage is the first open-source effort with this calibre and robustness, outperforming SOTA methods in its morphological expressiveness, mesh quality, and stably generates large, complex patterns over hundreds of simulation steps. It is a source not only of computational modeling, digital fabrication, education, but also high-quality, annotated data for geometry processing and shape analysis. △ Less

Submitted 24 April, 2025; originally announced April 2025.

Generation of Conservative Dynamical Systems Based on Stiffness Encoding

Authors: Tengyu Hou, Hanming Bai, Ye Ding, Han Ding

Abstract: …behavior and a variable stiffness profile. The proposed method is applicable to demonstration trajectories belonging to different manifolds and types (e.g., closed and self-… ▽ More Dynamical systems (DSs) provide a framework for high flexibility, robustness, and control reliability and are widely used in motion planning and physical human-robot interaction. The properties of the DS directly determine the robot's specific motion patterns and the performance of the closed-loop control system. In this paper, we establish a quantitative relationship between stiffness properties and DS. We propose a stiffness encoding framework to modulate DS properties by embedding specific stiffnesses. In particular, from the perspective of the closed-loop control system's passivity, a conservative DS is learned by encoding a conservative stiffness. The generated DS has a symmetric attraction behavior and a variable stiffness profile. The proposed method is applicable to demonstration trajectories belonging to different manifolds and types (e.g., closed and self-intersecting trajectories), and the closed-loop control system is always guaranteed to be passive in different cases. For controllers tracking the general DS, the passivity of the system needs to be guaranteed by the energy tank. We further propose a generic vector field decomposition strategy based on conservative stiffness, which effectively slows down the decay rate of energy in the energy tank and improves the stability margin of the control system. Finally, a series of simulations in various scenarios and experiments on planar and curved motion tasks demonstrate the validity of our theory and methodology. △ Less

Submitted 1 November, 2024; originally announced November 2024.

Longitudinal Principal Manifold Estimation

Authors: Robert Zielinski, Kun Meng, Ani Eloyan

Abstract: …the effects of random disturbances to the manifold between time points. Additionally, we propose a novel data augmentation approach to enable principal manifold estimation on self-intersecting manifolds. Simulation studies demonstrate performance improvements over naive applicati… ▽ More Longitudinal magnetic resonance imaging data is used to model trajectories of change in brain regions of interest to identify areas susceptible to atrophy in those with neurodegenerative conditions like Alzheimer's disease. Most methods for extracting brain regions are applied to scans from study participants independently, resulting in wide variability in shape and volume estimates of these regions over time in longitudinal studies. To address this problem, we propose a longitudinal principal manifold estimation method, which seeks to recover smooth, longitudinally meaningful manifold estimates of shapes over time. The proposed approach uses a smoothing spline to smooth over the coefficients of principal manifold embedding functions estimated at each time point. This mitigates the effects of random disturbances to the manifold between time points. Additionally, we propose a novel data augmentation approach to enable principal manifold estimation on self-intersecting manifolds. Simulation studies demonstrate performance improvements over naive applications of principal manifold estimation and principal curve/surface methods. The proposed method improves the estimation of surfaces of hippocampuses and thalamuses using data from participants of the Alzheimer's Disease Neuroimaging Initiative. An analysis of magnetic resonance imaging data from 236 individuals shows the advantages of our proposed methods that leverage regional longitudinal trends for segmentation. △ Less

Submitted 24 July, 2024; originally announced July 2024.

Comments: 40 pages, 6 figures

Entropic sampling in frustrated magnets: role of self-intersecting spaces

Authors: Alwyn Jose Raja, R. Ganesh

Abstract: …this with two examples -- both clusters with four spins coupled by XY interactions. In the first, the classical ground states form a smooth space. In the second, they form a self-intersecting non-manifold space. Ground state sampling is very different in these two cases. We first consider the microcanonical ensemble pi… ▽ More Frustrated magnets typically possess a large space of classical ground states. If this degeneracy is not protected by symmetry, thermal fluctuations may `select' certain states via order-by-disorder. In this article, we examine a precursor effect where all ground states are sampled, but with different weights. Geometry plays a key role in determining the weight distribution and its behaviour. We demonstrate this with two examples -- both clusters with four spins coupled by XY interactions. In the first, the classical ground states form a smooth space. In the second, they form a self-intersecting non-manifold space. Ground state sampling is very different in these two cases. We first consider the microcanonical ensemble picture, where fluctuations conserve energy. Phase space arguments suggest that the first model exhibits energy-independent probabilities. The second shows a dramatic energy-dependence with relative probability increasing as $ε^{-1/2}$, where $ε$ is the energy of the system. We simulate low-energy dynamics in both models, confirming the expected behaviour. We next consider the canonical ensemble, where the first model produces temperature-independent probabilities. In the second, relative probability rises sharply as $T^{-1/2}$, where $T$ is the temperature. Our results bring out a classical analogue of order-by-singularity, a mechanism that has been recently proposed in the context of quantum spin clusters. The sampling of classical orders is qualitatively different in systems with self-intersecting ground state spaces. It grows at low energies and becomes singular as $ε\rightarrow 0$ (microcanonical ensemble) or $T\rightarrow 0$ (canonical ensemble). We discuss relevance for disordered phases in macroscopic magnets, particularly for spiral liquids. △ Less

Submitted 1 April, 2024; v1 submitted 29 July, 2023; originally announced July 2023.

Comments: 10 pages, 8 figures

Journal ref: Phys. Rev. B 109, 144401 (2024)

Which shapes can appear in a Curve Shortening Flow Singularity?

Authors: Sigurd Angenent, Evan Patrick Davis, Ellie DeCleene, Paige Ellingson, Ziheng Feng, Edgar Gevorgyan, Aris Lemmenes, Alex Moon, Tyler Joseph Tommasi, Yamin Zhou

Abstract: We study possible tangles that can occur in singularities of solutions to plane Curve Shortening Flow. We exhibit solutions in which more complicated tangles with more than one self-intersection disappear into a singular point. It seems that there are many examples of this kind and that a complete classification presen… ▽ More We study possible tangles that can occur in singularities of solutions to plane Curve Shortening Flow. We exhibit solutions in which more complicated tangles with more than one self-intersection disappear into a singular point. It seems that there are many examples of this kind and that a complete classification presents a problem similar to the problem of classifying all knots in $\mathbb R^3$. As a particular example, we introduce the so-called $n$-loop curves, which generalize Matt Grayson's Figure-Eight curve, and we conjecture a generalization of the Coiculescu-Schwarz asymptotic bow-tie result, namely, a vanishing $n$-loop, when rescaled anisotropically to fit a square bounding box, converges to a "squeezed bow-tie," i.e. the curve $\{(x, y) : |x|\leq 1, y=\pm x^{n-1}\}\cup\{(\pm 1, y) : |y|\leq 1\}$. As evidence in support of the conjecture, we provide a formal asymptotic analysis on one hand, and a numerical simulation for the cases $n=3$ and $n=4$ on the other. △ Less

Submitted 14 March, 2024; originally announced March 2024.

Comments: 21 pages, 14 figures

MSC Class: 53E10; 35B40; 35K55

Peeling fingers in an elastic Hele-Shaw channel

Authors: J. V. Fontana, C. Cuttle, D. Pihler-Puzovic, A. L. Hazel, A. Juel

Abstract: …we extend the depth-averaged model introduced by Fontana et al. (J. Fluid Mech., vol. 916, 2021, A27) to include an artificial disjoining pressure which prevents the unphysical self-intersection of the interface. Using time simulations, we capture for the first time the majority… ▽ More Using experiments and a depth-averaged numerical model, we study instabilities of two-phase flows in a Hele-Shaw channel with an elastic upper boundary and a non-uniform cross-section prescribed by initial collapse. Experimentally, we find increasingly complex and unsteady modes of air-finger propagation as the dimensionless bubble speed, Ca, and level of collapse are increased, including pointed fingers, indented fingers and the feathered modes first identified by Cuttle et al.(J. Fluid Mech., vol. 886, 2020, A20). By introducing a measure of the viscous contribution to finger propagation, we identify a Ca threshold beyond which viscous forces are superseded by elastic effects. Quantitative prediction of this transition between 'viscous' and 'elastic' reopening regimes across levels of collapse establishes the fidelity of the numerical model. In the viscous regime, we recover the non-monotonic dependence on Ca of the finger pressure, which is characteristic of benchtop models of airway reopening. To explore the elastic regime numerically, we extend the depth-averaged model introduced by Fontana et al. (J. Fluid Mech., vol. 916, 2021, A27) to include an artificial disjoining pressure which prevents the unphysical self-intersection of the interface. Using time simulations, we capture for the first time the majority of experimental finger dynamics, including feathered modes. We show that these disordered states continually evolve, with no evidence of convergence to steady or periodic states. We find that the steady bifurcation structure satisfactorily predicts the bubble pressure as a function of Ca, but that it does not provide sufficient information to predict the transition to unsteady dynamics which appears strongly nonlinear. △ Less

Submitted 29 February, 2024; v1 submitted 19 October, 2023; originally announced October 2023.

Comments: 28 pages, 15 figures

LinFlo-Net: A two-stage deep learning method to generate simulation ready meshes of the heart

Authors: Arjun Narayanan, Fanwei Kong, Shawn Shadden

Abstract: …motion that penalizes surface contact and interpenetration. Our model demonstrates comparable accuracy with state-of-the-art methods while additionally producing meshes free of self-intersections. The resultant meshes are readily usable in physics based simulation, minimizing the… ▽ More We present a deep learning model to automatically generate computer models of the human heart from patient imaging data with an emphasis on its capability to generate thin-walled cardiac structures. Our method works by deforming a template mesh to fit the cardiac structures to the given image. Compared with prior deep learning methods that adopted this approach, our framework is designed to minimize mesh self-penetration, which typically arises when deforming surface meshes separated by small distances. We achieve this by using a two-stage diffeomorphic deformation process along with a novel loss function derived from the kinematics of motion that penalizes surface contact and interpenetration. Our model demonstrates comparable accuracy with state-of-the-art methods while additionally producing meshes free of self-intersections. The resultant meshes are readily usable in physics based simulation, minimizing the need for post-processing and cleanup. △ Less

Submitted 3 January, 2024; v1 submitted 30 October, 2023; originally announced October 2023.

Comments: Accepted manuscript in the Journal of Biomechanical Engineering

Efficient Incremental Potential Contact for Actuated Face Simulation

Authors: Bo Li, Lingchen Yang, Barbara Solenthaler

Abstract: We present a quasi-static finite element simulator for human face animation. We model the face as an actuated soft body, which can be efficiently… ▽ More We present a quasi-static finite element simulator for human face animation. We model the face as an actuated soft body, which can be efficiently simulated using Projective Dynamics (PD). We adopt Incremental Potential Contact (IPC) to handle self-intersection. However, directly integrating IPC into the simulation would impede the high efficiency of the PD solver, since the stiffness matrix in the global step is no longer constant and cannot be pre-factorized. We notice that the actual number of vertices affected by the collision is only a small fraction of the whole model, and by utilizing this fact we effectively decrease the scale of the linear system to be solved. With the proposed optimization method for collision, we achieve high visual fidelity at a relatively low performance overhead. △ Less

Submitted 3 December, 2023; originally announced December 2023.

Comments: SIGGRAPH Asia 2023 Technical Communications

Spontaneous-Ordering Platoon Control for Multirobot Path Navigation Using Guiding Vector Fields

Authors: Bin-Bin Hu, Hai-Tao Zhang, Weijia Yao, Jianing Ding, Ming Cao

Abstract: …additional virtual coordinate to each robot, the DGVF algorithm can eliminate the singular points where the vector fields vanish, and govern robots to approach a closed and even self-… ▽ More In this paper, we propose a distributed guiding-vector-field (DGVF) algorithm for a team of robots to form a spontaneous-ordering platoon moving along a predefined desired path in the n-dimensional Euclidean space. Particularly, by adding a path parameter as an additional virtual coordinate to each robot, the DGVF algorithm can eliminate the singular points where the vector fields vanish, and govern robots to approach a closed and even self-intersecting desired path. Then, the interactions among neighboring robots and a virtual target robot through their virtual coordinates enable the realization of the desired platoon; in particular, relative parametric displacements can be achieved with arbitrary ordering sequences. Rigorous analysis is provided to guarantee the global convergence to the spontaneous-ordering platoon on the common desired path from any initial positions. 2D experiments using three HUSTER-0.3 unmanned surface vessels (USVs) are conducted to validate the practical effectiveness of the proposed DGVF algorithm, and 3D numerical simulations are presented to demonstrate its effectiveness and robustness when tackling higher-dimensional multi-robot path-navigation missions and some robots breakdown. △ Less

Submitted 1 November, 2023; originally announced November 2023.

Journal ref: IEEE Transaction on Robotics, 2023

A comparison between the FENE-P and sPTT constitutive models in Large Amplitude Oscillatory Shear (LAOS)

Authors: Thomas P John, Robert J Poole, Adam Kowalski, Claudio P Fonte

Abstract: …non-linear region, there is a drastic difference between the responses of the two models, with the FENE-P model exhibiting strong shear stress overshoots which manifest as self-… ▽ More The FENE-P and sPTT viscoelastic models are widely used for modelling of complex fluids. Although they are derived from distinct micro-structural theories, these models can become mathematically identical in steady and homogeneous flows with a particular choice of the value of the model parameters. However, even with this choice of parameter values, the model responses are known to differ from each other in transient flows. In this work, we investigate the responses of the FENE-P and sPTT constitutive models in Large Amplitude Oscillatory Shear (LAOS). In steady-shear, the shear stress scales with the non-dimensional group $Wi/(aL) \ (Wi\sqrtε)$ for the FENE-P (sPTT) model, where $Wi$ is the Weissenberg number, $L^2$ is the limit of extensibility in the FENE-P model ($a$ being $L^2/(L^2-3)$) and $ε$ is the extensibility parameter in the sPTT model. Our numerical and analytical results show that, in LAOS, the FENE-P model only shows this universality for large values of $L^2$ whereas the sPTT model shows this universality for all values of$ε$. In the strongly non-linear region, there is a drastic difference between the responses of the two models, with the FENE-P model exhibiting strong shear stress overshoots which manifest as self-intersecting secondary loops in the viscous Lissajous curves. We quantify the non-linearity exhibited by each constitutive model using the Sequence of Physical Processes framework. Despite the high degree of non-linearity exhibited by the FENE-P model, we also show using fully non-linear 1D simulations that it does not shear band in LAOS within the range of conditions studied. △ Less

Submitted 1 September, 2023; v1 submitted 31 August, 2023; originally announced August 2023.

Comments: Submitted to Journal of Fluid Mechanics

Visual-Guided Mesh Repair

Authors: Zhongtian Zheng, Xifeng Gao, Zherong Pan, Wei Li, Peng-Shuai Wang, Guoping Wang, Kui Wu

Abstract: …in computer graphics and related fields. Converting defective meshes into watertight manifold meshes can greatly benefit downstream applications such as geometric processing, simulation, fabrication, learning, and synthesis. In this work, we first introduce three visual measures for visibility, orientation, and openness, based on ray-tracing. We then present… ▽ More Mesh repair is a long-standing challenge in computer graphics and related fields. Converting defective meshes into watertight manifold meshes can greatly benefit downstream applications such as geometric processing, simulation, fabrication, learning, and synthesis. In this work, we first introduce three visual measures for visibility, orientation, and openness, based on ray-tracing. We then present a novel mesh repair framework that incorporates visual measures with several critical steps, i.e., open surface closing, face reorientation, and global optimization, to effectively repair defective meshes, including gaps, holes, self-intersections, degenerate elements, and inconsistent orientations. Our method reduces unnecessary mesh complexity without compromising geometric accuracy or visual quality while preserving input attributes such as UV coordinates for rendering. We evaluate our approach on hundreds of models randomly selected from ShapeNet and Thingi10K, demonstrating its effectiveness and robustness compared to existing approaches. △ Less

Submitted 31 August, 2023; originally announced September 2023.

Mass-stream trajectories with non-synchronously rotating donors

Authors: David Hendriks, Robert Izzard

Abstract: …of the accretor. To determine the trajectory of the mass-transfer stream, and whether it directly impacts the accretor, or forms an accretion disk, requires numerical simulations. The mass-transfer stream is approximately ballistic, and analytic approximations based on such trajectories are used in many binary population synthesis codes as well as in detaile… ▽ More Mass-transfer interactions in binary stars can lead to accretion disk formation, mass loss from the system and spin-up of the accretor. To determine the trajectory of the mass-transfer stream, and whether it directly impacts the accretor, or forms an accretion disk, requires numerical simulations. The mass-transfer stream is approximately ballistic, and analytic approximations based on such trajectories are used in many binary population synthesis codes as well as in detailed stellar evolution codes. We use binary population synthesis to explore the conditions under which mass transfer takes place. We then solve the reduced three-body equations to compute the trajectory of a particle in the stream for systems with varying system mass ratio, donor synchronicity and initial stream velocity. Our results show that on average both more mass and more time is spent during mass transfer from a sub-synchronous donor than from a synchronous donor. Moreover, we find that at low initial stream velocity the asynchronous rotation of the donor leads to self-accretion over a large range of mass ratios, especially for super-synchronous donors. The stream (self-)intersects in a narrow region of parameter space where it transitions between accreting onto the donor or the accretor. Increasing the initial stream velocity leads to larger areas of the parameter space where the stream accretes onto the accretor, but also more (self-)intersection. The radii of closest approach generally increase, but the range of specific angular momenta that these trajectories carry at the radius of closest approach gets broader. Our results are made publicly available. △ Less

Submitted 1 August, 2023; v1 submitted 10 July, 2023; originally announced July 2023.

Comments: 19 pages, 21 figures includings appendices. Published in MNRAS. Data available on https://zenodo.org/record/8204176

Journal ref: MNRAS, 524, 4315 (2023)

Metaheuristic conditional neural network for harvesting skyrmionic metastable states

Authors: Qichen Xu, I. P. Miranda, Manuel Pereiro, Filipp N. Rybakov, Danny Thonig, Erik Sjöqvist, Pavel Bessarab, Anders Bergman, Olle Eriksson, Pawel Herman, Anna Delin

Abstract: …are further analyzed using finite-temperature spin-dynamics simulations. We observe that for temperatures up to around 20\,K, lifetimes longer than 200\,ps are predicted, and that when these textures decay, new topological spin textures are formed. We also find that the relative stability of the spin textures depend linearly on the topological charge, but o… ▽ More We present a metaheuristic conditional neural-network-based method aimed at identifying physically interesting metastable states in a potential energy surface of high rugosity. To demonstrate how this method works, we identify and analyze spin textures with topological charge $Q$ ranging from 1 to $-13$ (where antiskyrmions have $Q<0$) in the Pd/Fe/Ir(111) system, which we model using a classical atomistic spin Hamiltonian based on parameters computed from density functional theory. To facilitate the harvest of relevant spin textures, we make use of the newly developed Segment Anything Model (SAM). Spin textures with $Q$ ranging from $-3$ to $-6$ are further analyzed using finite-temperature spin-dynamics simulations. We observe that for temperatures up to around 20\,K, lifetimes longer than 200\,ps are predicted, and that when these textures decay, new topological spin textures are formed. We also find that the relative stability of the spin textures depend linearly on the topological charge, but only when comparing the most stable antiskyrmions for each topological charge. In general, the number of holes (i.e., non-self-intersecting curves that define closed domain walls in the structure) in the spin texture is an important predictor of stability -- the more holes, the less stable is the texture. Methods for systematic identification and characterization of complex metastable skyrmionic textures -- such as the one demonstrated here -- are highly relevant for advancements in the field of topological spintronics. △ Less

Submitted 29 May, 2023; v1 submitted 5 March, 2023; originally announced March 2023.

Nambu-Goto Dynamics of Field Theory Cosmic String Loops

Authors: Jose J. Blanco-Pillado, Daniel Jiménez-Aguilar, Joanes Lizarraga, Asier Lopez-Eiguren, Ken D. Olum, Ander Urio, Jon Urrestilla

Abstract: We perform a detailed comparison of the dynamics of cosmic string loops obtained in cosmological field theory simulations with their expected motion according to the Nambu-Goto action. We demonstrate that these loops follow the trajectories predicted within the NG effective theory except in regions of high curvature where energy is emitted from the loop in t… ▽ More We perform a detailed comparison of the dynamics of cosmic string loops obtained in cosmological field theory simulations with their expected motion according to the Nambu-Goto action. We demonstrate that these loops follow the trajectories predicted within the NG effective theory except in regions of high curvature where energy is emitted from the loop in the form of massive radiation. This energy loss continues for all the loops studied in this simulation until they self-intersect or become small enough that they annihilate and disappear well before they complete a single oscillation. We comment on the relevance of this investigation to the interpretation of the results from cosmological field theory simulations as well as their extrapolation to a cosmological context. △ Less

Submitted 19 May, 2023; v1 submitted 7 February, 2023; originally announced February 2023.

Comments: 17 pages + appendix, 8 figures. Published version

Journal ref: JCAP 05 (2023) 035

Shortest Path to Boundary for Self-Intersecting Meshes

Authors: He Chen, Elie Diaz, Cem Yuksel

Abstract: We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-… ▽ More We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for self-intersecting objects and present a robust algorithm for computing the actual shortest boundary path. The resulting method offers an effective solution for collision and self-collision handling while simulating deformable volumetric objects, using fast simulation techniques that provide no guarantees on collision resolution. Our evaluation includes complex self-collision scenarios with a large number of active contacts, showing that our method can successfully handle them by introducing a relatively minor computational overhead. △ Less

Submitted 16 May, 2023; originally announced May 2023.

ACM Class: I.3.5

Neural Volumetric Blendshapes: Computationally Efficient Physics-Based Facial Blendshapes

Authors: Nicolas Wagner, Ulrich Schwanecke, Mario Botsch

Abstract: Computationally weak systems and demanding graphical applications are still mostly dependent on linear blendshapes for facial animations. The accompanying artifacts such as self-… ▽ More Computationally weak systems and demanding graphical applications are still mostly dependent on linear blendshapes for facial animations. The accompanying artifacts such as self-intersections, loss of volume, or missing soft tissue elasticity can be avoided by using physics-based animation models. However, these are cumbersome to implement and require immense computational effort. We propose neural volumetric blendshapes, an approach that combines the advantages of physics-based simulations with realtime runtimes even on consumer-grade CPUs. To this end, we present a neural network that efficiently approximates the involved volumetric simulations and generalizes across human identities as well as facial expressions. Our approach can be used on top of any linear blendshape system and, hence, can be deployed straightforwardly. Furthermore, it only requires a single neutral face mesh as input in the minimal setting. Along with the design of the network, we introduce a pipeline for the challenging creation of anatomically and physically plausible training data. Part of the pipeline is a novel hybrid regressor that densely positions a skull within a skin surface while avoiding intersections. The fidelity of all parts of the data generation pipeline as well as the accuracy and efficiency of the network are evaluated in this work. Upon publication, the trained models and associated code will be released. △ Less

Submitted 20 January, 2023; v1 submitted 23 December, 2022; originally announced December 2022.

AutoPoly: Predicting a Polygonal Mesh Construction Sequence from a Silhouette Image

Authors: I-Chao Shen, Yu Ju Chen, Oliver van Kaick, Takeo Igarashi

Abstract: …using differentiable rendering can only handle a fixed topology. Our novel reward function encourages MCTS to select topological actions that lead to a simpler shape without self-… ▽ More Polygonal modeling is a core task of content creation in Computer Graphics. The complexity of modeling, in terms of the number and the order of operations and time required to execute them makes it challenging to learn and execute. Our goal is to automatically derive a polygonal modeling sequence for a given target. Then, one can learn polygonal modeling by observing the resulting sequence and also expedite the modeling process by starting from the auto-generated result. As a starting point for building a system for 3D modeling in the future, we tackle the 2D shape modeling problem and present AutoPoly, a hybrid method that generates a polygonal mesh construction sequence from a silhouette image. The key idea of our method is the use of the Monte Carlo tree search (MCTS) algorithm and differentiable rendering to separately predict sequential topological actions and geometric actions. Our hybrid method can alter topology, whereas the recently proposed inverse shape estimation methods using differentiable rendering can only handle a fixed topology. Our novel reward function encourages MCTS to select topological actions that lead to a simpler shape without self-intersection. We further designed two deep learning-based methods to improve the expansion and simulation steps in the MCTS search process: an $n$-step "future action prediction" network (nFAP-Net) to generate candidates for potential topological actions, and a shape warping network (WarpNet) to predict polygonal shapes given the predicted rendered images and topological actions. We demonstrate the efficiency of our method on 2D polygonal shapes of multiple man-made object categories. △ Less

Submitted 29 March, 2022; originally announced March 2022.

Comments: 8 pages

A Robust Grid-Based Meshing Algorithm for Embedding Self-Intersecting Surfaces

Authors: Steven W. Gagniere, Yushan Han, Yizhou Chen, David A. B. Hyde, Alan Marquez-Razon, Joseph Teran, Ronald Fedkiw

Abstract: …of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not self-… ▽ More The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not self-intersecting. However, due to numerical and/or user error, input surfaces are commonly self-intersecting to some degree. The removal of self-intersection is a burdensome task that complicates workflow and generally slows down the process of creating simulation-ready digital assets. We present a method for the creation of a volumetric embedding hexahedron mesh from a self-intersecting input triangle mesh. Our method is designed for efficiency by minimizing use of computationally expensive exact/adaptive precision arithmetic. Although our approach allows for nearly no limit on the degree of self-intersection in the input surface, our focus is on efficiency in the most common case: many minimal self-intersections. The embedding hexahedron mesh is created from a uniform background grid and consists of hexahedron elements that are geometrical copies of grid cells. Multiple copies of a single grid cell are used to resolve regions of self-intersection/overlap. Lastly, we develop a novel topology-aware embedding mesh coarsening technique to allow for user-specified mesh resolution as well as a topology-aware tetrahedralization of the hexahedron mesh. △ Less

Submitted 17 January, 2022; originally announced January 2022.

Tidal Disruption Disks Formed and Fed by Stream-Stream and Stream-Disk Interactions in Global GRHD Simulations

Authors: Zachary L. Andalman, Matthew T. P. Liska, Alexander Tchekhovskoy, Eric R. Coughlin, Nicholas Stone

Abstract: …In this work, we study the post-disruption phase of TDEs in general relativistic hydrodynamics (GRHD) using our GPU-accelerated code H-AMR. We carry out the first grid-based simulation of a deep-penetration TDE ($β$=7) with realistic system parameters: a black-hole-to-star mass ratio of $10^6$, a parabolic stellar trajectory, and a nonzero BH spin. We also… ▽ More When a star passes close to a supermassive black hole (BH), the BH's tidal forces rip it apart into a thin stream, leading to a tidal disruption event (TDE). In this work, we study the post-disruption phase of TDEs in general relativistic hydrodynamics (GRHD) using our GPU-accelerated code H-AMR. We carry out the first grid-based simulation of a deep-penetration TDE ($β$=7) with realistic system parameters: a black-hole-to-star mass ratio of $10^6$, a parabolic stellar trajectory, and a nonzero BH spin. We also carry out a simulation of a tilted TDE whose stellar orbit is inclined relative to the BH midplane. We show that for our aligned TDE, an accretion disk forms due to the dissipation of orbital energy with $\sim$20 percent of the infalling material reaching the BH. The dissipation is initially dominated by violent self-intersections and later by stream-disk interactions near the pericenter. The self-intersections completely disrupt the incoming stream, resulting in five distinct self-intersection events separated by approximately 12 hours and a flaring in the accretion rate. We also find that the disk is eccentric with mean eccentricity e$\approx$0.88. For our tilted TDE, we find only partial self-intersections due to nodal precession near pericenter. Although these partial intersections eject gas out of the orbital plane, an accretion disk still forms with a similar accreted fraction of the material to the aligned case. These results have important implications for disk formation in realistic tidal disruptions. For instance, the periodicity in accretion rate induced by the complete stream disruption may explain the flaring events from Swift J1644+57. △ Less

Submitted 23 November, 2021; v1 submitted 11 August, 2020; originally announced August 2020.

Comments: Accepted to MNRAS on November 23rd, 2021, 23 pages, 25 figures, uses mnras.cls. Comments welcome. Movies available at https://www.youtube.com/playlist?list=PL7YbfRC6zxzAqIPXWbJgXpr4Wq_nwHiDu

gVOF: An open-source package for unsplit geometric volume of fluid methods on arbitrary grids

Authors: Joaquín López, Julio Hernández

Abstract: …110579]. The operations required during the advection step of unsplit geometric VOF methods in general involve handling of high-complex non-convex flux polyhedra, even with self-… ▽ More The gVOF package includes a complete and self-contained set of routines for volume of fluid initialization, interface reconstruction and fluid advection, which are used to implement several accurate and efficient geometric volume of fluid (VOF) methods on arbitrary grids, either structured or unstructured with convex or non-convex cells, based on multidimensional unsplit advection and piecewise linear interface calculation (PLIC) schemes. The package uses the non-convex analytical and geometrical tools developed by López et al. [J. Comput. Phys. 392 (2019) 666-693] and the isosurface extraction procedure proposed by López et al. [J. Comput. Phys. 444 (2021) 110579]. The operations required during the advection step of unsplit geometric VOF methods in general involve handling of high-complex non-convex flux polyhedra, even with self-intersecting faces, which are robustly and efficiently treated in this work without the need of costly techniques based on convex decomposition. Results for the accuracy, computational efficiency, and volume (local and global) conservation properties of different combinations of the implemented advection and reconstruction methods are presented for several numerical tests on structured and unstructured grids. An extensive comparison with results obtained by other authors using advanced geometric VOF methods shows the outstanding performance of the gVOF package in terms of efficiency and accuracy. To demonstrate the performance of the package in solving complex two-phase flow problems, the implemented methods are combined with an existing in-house code to simulate the impact of a water drop on a free surface. The package can be used in FORTRAN or C languages and will be publicly available for download. The OpenMP application programming interface is also used to improve computational efficiency. △ Less

Submitted 2 November, 2021; originally announced November 2021.

Comments: 76 pages, 30 figures

Singularity-free Guiding Vector Field for Robot Navigation

Authors: Weijia Yao, Hector Garcia de Marina, Bohuan Lin, Ming Cao

Abstract: Most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-… ▽ More Most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in vector-field guided path-following (VF-PF) navigation algorithms. These algorithms are based on a vector field, and the singular points are exactly where the vector field diminishes. In this paper, we show that it is mathematically impossible for conventional VF-PF algorithms to achieve global convergence to desired paths that are self-intersected or even just simple closed (precisely, homeomorphic to the unit circle). Motivated by this new impossibility result, we propose a novel method to transform self-intersected or simple closed desired paths to non-self-intersected and unbounded (precisely, homeomorphic to the real line) counterparts in a higher-dimensional space. Corresponding to this new desired path, we construct a singularity-free guiding vector field on a higher-dimensional space. The integral curves of this new guiding vector field is thus exploited to enable global convergence to the higher-dimensional desired path, and therefore the projection of the integral curves on a lower-dimensional subspace converge to the physical (lower-dimensional) desired path. Rigorous theoretical analysis is carried out for the theoretical results using dynamical systems theory. In addition, we show both by theoretical analysis and numerical simulations that our proposed method is an extension combining conventional VF-PF algorithms and trajectory tracking algorithms. Finally, to show the practical value of our proposed approach for complex engineering systems, we conduct outdoor experiments with a fixed-wing airplane in windy environment to follow both 2D and 3D desired paths. △ Less

Submitted 23 October, 2021; v1 submitted 3 December, 2020; originally announced December 2020.

Comments: Accepted for publication in IEEE Trransactions on Robotics (T-RO)

Simulating Self-Avoiding Isometric Plate Bending

Authors: Sören Bartels, Frank Meyer, Christian Palus

Abstract: Inspired by recent results on self-avoiding inextensible curves, we propose and experimentally investigate a numerical method for simulating isometric plate bending without… ▽ More Inspired by recent results on self-avoiding inextensible curves, we propose and experimentally investigate a numerical method for simulating isometric plate bending without self-intersections. We consider a nonlinear two-dimensional Kirchhoff plate model which is augmented via addition of a tangent-point energy. The resulting continuous model energy is finite if and only if the corresponding deformation is injective, i.e. neither includes self-intersections nor self-contact. We propose a finite element method method based on discrete Kirchhoff triangles for the spatial discretization and employ a semi-implicit gradient descent scheme for the minimization of the discretized energy functional. Practical properties of the proposed method are illustrated with numerous numerical simulations, exploring the model behavior in different settings and demonstrating that our method is capable of preventing non-injective deformations. △ Less

Submitted 10 August, 2021; originally announced August 2021.

Comments: 20 pages, 11 figures, 5 tables

MSC Class: 65N30; 74-10; 74K20

An Efficient Generation Method based on Dynamic Curvature of the Reference Curve for Robust Trajectory Planning

Authors: Yuchen Sun, Dongchun Ren, Shiqi Lian, Mingyu Fan, Xiangyi Teng

Abstract: …reference curve maybe discontinuous. Then, some segments on the reference curve are not the image of any part of the planned path. Another issue is that the planned path might self-… ▽ More Trajectory planning is a fundamental task on various autonomous driving platforms, such as social robotics and self-driving cars. Many trajectory planning algorithms use a reference curve based Frenet frame with time to reduce the planning dimension. However, there is a common implicit assumption in classic trajectory planning approaches, which is that the generated trajectory should follow the reference curve continuously. This assumption is not always true in real applications and it might cause some undesired issues in planning. One issue is that the projection of the planned trajectory onto the reference curve maybe discontinuous. Then, some segments on the reference curve are not the image of any part of the planned path. Another issue is that the planned path might self-intersect when following a simple reference curve continuously. The generated trajectories are unnatural and suboptimal ones when these issues happen. In this paper, we firstly demonstrate these issues and then introduce an efficient trajectory generation method which uses a new transformation from the Cartesian frame to Frenet frames. Experimental results on a simulated street scenario demonstrated the effectiveness of the proposed method. △ Less

Submitted 29 December, 2020; originally announced December 2020.

Comments: no comments

Dual perspective method for solving the point in a polygon problem

Authors: Karim M. Ali, Amr Guaily

Abstract: A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-… ▽ More A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-intersecting. The introduced method is independent of rounding off errors, which gives it a leverage over some methods prone to this problem. A brief summary of the methods used to solve this problem is presented and the introduced method is discussed. The introduced method is compared to other existing methods from the point of view of computational cost. This method was inspired from a Computational Fluid Dynamics (CFD) application using grids not fitted to the simulated objects. △ Less

Submitted 9 December, 2020; originally announced December 2020.

Comments: 5 pages, 4 figures, 1 table containing 6 images, 1 algorithm

Planning Folding Motion with Simulation in the Loop Using Laser Forming Origami and Thermal Behaviors as an Example

Authors: Yue Hao, Weilin Guan, Edwin A Peraza Hernandez, Jyh-Ming Lien

Abstract: …challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric and kinematic aspects to avoid self-… ▽ More Designing a robot or structure that can fold itself into a target shape is a process that involves challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric and kinematic aspects to avoid self-intersection and undesired deformations. Recent works have shown success in estimating foldability of a design using robot motion planners. However, many foldable structures are actuated using physically coupled reactions (i.e., folding originated from thermal, chemical, or electromagnetic loads). Therefore, a reliable foldability analysis must consider additional constraints that resulted from these critical phenomena. This work investigates the idea of efficiently incorporating computationally expensive physics simulation within the folding motion planner to provide a better estimation of the foldability. In this paper, we will use laser forming origami as an example to demonstrate the benefits of considering the properties beyond geometry. We show that the design produced by the proposed method can be folded more efficiently. △ Less

Submitted 20 November, 2020; originally announced November 2020.