Related papers: A Lagrangian Integrator for Planetary Accretion an…
We present a COMSOL Multiphysics implementation of a continuum model for directed cell migration, a key mechanism underlying tissue self-organization and morphogenesis. The model is formulated as a partial integro-differential equation…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
We have developed an adaptive multigrid code for solving the Poisson equation in gravitational simulations. Finer rectangular subgrids are adaptively created in locations where the density exceeds a local level-dependent threshold. We…
A planetary instability occurring at time $<100$ My after formation of the giant planets in our solar system can be responsible for some characteristics of the inner solar system. However, the actual influence of the instability on the…
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…
Context. Planet formation with pebbles has been proposed to solve a couple of long-standing issues in the classical formation model. Some sophisticated simulations have been done to confirm the efficiency of pebble accretion. However, there…
In this dissertation, a fully object-oriented, fully relativistic, multi-dimensional Particle-In-Cell code was developed and applied to answer key questions in plasma-based accelerator research. The simulations increase the understanding of…
We present TES, a new n-body integration code for the accurate and rapid propagation of planetary systems in the presence of close encounters. TES builds upon the classic Encke method and integrates only the perturbations to Keplerian…
We have newly developed a Parallelized Particle-Particle Particle-tree code for Planet formation, PENTACLE, which is a parallelized hybrid $N$-body integrator executed on a CPU-based (super)computer. PENTACLE uses a 4th-order Hermite…
Generative world models have become essential data engines for autonomous driving, yet most existing efforts focus on videos or occupancy grids, overlooking the unique LiDAR properties. Extending LiDAR generation to dynamic 4D world…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…
Cosmological N-Body simulations are used for a variety of applications. Indeed progress in the study of large scale structures and galaxy formation would have been very limited without this tool. For nearly twenty years the limitations…
The numerical simulations of massive collisional stellar systems, such as globular clusters (GCs), are very time-consuming. Until now, only a few realistic million-body simulations of GCs with a small fraction of binaries (5%) have been…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
A microphysics model to describe the photoionization and impact ionization processes in dielectric ablator materials like plastic has been implemented into the one-dimensional hydrodynamic code LILAC for planar and spherical targets. At…
Recently, 3D Gaussian Splatting (3DGS), an explicit scene representation technique, has shown significant promise for dynamic novel-view synthesis from monocular video input. However, purely data-driven 3DGS often struggles to capture the…
A computationally efficient model is introduced to account for the sub-grid scale velocities of tracer particles dispersed in statistically homogeneous and isotropic turbulent flows. The model embeds the multi-scale nature of turbulent…
It is well known that numerical errors grow exponentially in $N$-body simulations of gravitational bound stellar systems, but it is not well understood how the accuracy parameters of algorithms affect the physical evolution in simulations.…
We present a minimal model for simulating dynamics of assorted lipid assemblies in a computationally efficient manner. Our model is particle-based and consists of coarse-grained beads put together on a modular platform to give generic…
A second-order accurate divergence-conserving hybrid particle-in-cell code Maximus has been developed for microscopic modeling of collisionless plasmas. The main specifics of the code include a constrained transport algorithm for exact…