Related papers: On the single-Hessian Gaussian wavepacket dynamics
3D Gaussian Splatting is a recognized method for 3D scene representation, known for its high rendering quality and speed. However, its substantial data requirements present challenges for practical applications. In this paper, we introduce…
We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs Ensembles (GEs) with unequal temperatures…
A version of the Gaussian self-consistent (GSC) method, which avoids the use of the Edwards' virial expansion, is presented. Instead, the mean energy is evaluated directly via a convolution of the attractive part of the pair-wise non-bonded…
We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of…
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the…
Efficient hybrid DFT simulations of solid state materials would be extremely beneficial for computational chemistry and materials science, but is presently bottlenecked by difficulties in computing Hartree-Fock (HF) exchange with plane wave…
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…
The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally…
We apply the approximate dynamics derived from the Gaussian time-dependent variational principle to the Hamiltonian $ \hat H= {1/2}(\hat p_x ^2+ \hat p_y ^2)+ {1/2}\hat x^2\hat y^2$, which is strongly chaotic in the classical limit. We are…
Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a…
The detection of gravitational waves has opened a new era for astronomy, allowing for the combined use of gravitational wave and electromagnetic emissions to directly probe the physics of compact objects, still poorly understood. So far,…
The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address…
In this paper, we present two Hermite polynomial based approaches to derive one-step numerical integrators for mechanical systems. These methods are based on discretizing the configuration using Hermite polynomials which leads to numerical…
A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using using both canonical and non-canonical Hamiltonian formulations. Our…
We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation for compressible flow problems. The aim is to provide a critical assessment of the computational…
This paper presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian-Eulerian (ALE)…
The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
This paper develops and analyzes some interior penalty discontinuous Galerkin methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in the two and three dimensions. It is…
3D Gaussian Splatting (GS) demonstrates excellent rendering quality and generation speed in novel view synthesis. However, substantial data size poses challenges for storage and transmission, making 3D GS compression an essential…