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09/11/2023
Quantitative Convergence Analysis of Path Integral Representations for Quantum Thermal Average
The quantum thermal average is a central topic in quantum physics and ca...
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07/13/2023
Exact Calculation of Quantum Thermal Average from Continuous Loop Path Integral Molecular Dynamics
The quantum thermal average plays a central role in describing the therm...
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05/10/2023
A synchronization-capturing multi-scale solver to the noisy integrate-and-fire neuron networks
The noisy leaky integrate-and-fire (NLIF) model describes the voltage co...
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04/29/2023
A spectral method for a Fokker-Planck equation in neuroscience with applications in neural networks with learning rules
In this work, we consider the Fokker-Planck equation of the Nonlinear No...
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12/18/2022
A convergent numerical algorithm for the stochastic growth-fragmentation problem
The stochastic growth-fragmentation model describes the temporal evoluti...
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11/09/2022
Frozen Gaussian Sampling for Scalar Wave Equations
In this article, we introduce the frozen Gaussian sampling (FGS) algorit...
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06/05/2022
Efficient Frozen Gaussian Sampling Algorithms for Nonadiabatic Quantum Dynamics at Metal Surfaces
In this article, we propose a Frozen Gaussian Sampling (FGS) algorithm f...
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06/05/2022
Error Analysis of Time-Discrete Random Batch Method for Interacting Particle Systems and Associated Mean-Field Limits
The random batch method provides an efficient algorithm for computing st...
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12/10/2021
Frozen Gaussian Sampling: A Mesh-free Monte Carlo Method For Approximating Semiclassical Schrödinger Equations
In this paper, we develop a Monte Carlo algorithm named the Frozen Gauss...
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09/10/2021
A structure preserving numerical scheme for Fokker-Planck equations of structured neural networks with learning rules
In this work, we are concerned with a Fokker-Planck equation related to ...
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08/06/2021
Fast Algorithms and Error Analysis of Caputo Derivatives with Small Factional Orders
In this paper, we investigate fast algorithms to approximate the Caputo ...
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02/20/2021
A novel spectral method for the semi-classical Schrödinger equation based on the Gaussian wave-packet transform
In this article, we develop and analyse a new spectral method to solve t...
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06/30/2020
A unified structure preserving scheme for a multi-species model with a gradient flow structure and nonlocal interactions via singular kernels
In this paper, we consider a nonlinear and nonlocal parabolic model for ...
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06/16/2020
Multi-level Monte Carlo path integral molecular dynamics for thermal average calculation in the nonadiabatic regime
With the path integral approach, the thermal average in a multi-electron...
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12/19/2019
Field model for complex ionic fluids: analytical properties and numerical investigation
In this paper, we consider the field model for complex ionic fluids with...
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12/19/2019
Field model for complex ionic fluids
In this paper, we consider the field model for complex ionic fluids with...
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11/18/2019
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
In this work, we are concerned with the Fokker-Planck equations associat...
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10/25/2019
Towards understanding the boundary propagation speeds in tumor growth models
At the continuous level, we consider two types of tumor growth models: t...
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10/04/2019
The Bayesian Inversion Problem for Thermal Average Sampling of Quantum Systems
In this article, we propose a novel method for sampling potential functi...
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07/04/2019