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The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…

Computational Physics · Physics 2026-04-20 Mauricio Guerrero-Montero , Michal Bosy , Christopher D. Cooper

In transport theory, physical phenomena are well described using the Boltzmann equation, which is efficiently simulated and discretized with the lattice Boltzmann method. The collision step defines the microscopic molecules behavior, and…

We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the…

Quantum Physics · Physics 2023-04-13 Wael Itani , Katepalli R. Sreenivasan , Sauro Succi

The Burton-Miller method is a widely used approach in acoustics to enhance the stability of the boundary element method for exterior Helmholtz problems at so-called critical frequencies. This method depends on a coupling parameter $\eta$…

Numerical Analysis · Mathematics 2024-08-02 Wolfgang Kreuzer

The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…

Analysis of PDEs · Mathematics 2019-01-08 Ricardo Alonso , Yoshinori Morimoto , Weiran Sun , Tong Yang

We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by…

Computational Physics · Physics 2017-12-11 D. A. Konovalov , D. G. Cocks , R. D. White

An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we…

Computational Physics · Physics 2017-04-20 I. A. Ender , L. A. Bakaleinikov , E. Yu. Flegontova , A. B. Gerasimenko

A non-linear Boltzmann equation describing the time evolution of a partonic system in the central rapidity region after a heavy ion collision is solved numerically. A particular model of the collinear logarithmic divergences due to small…

High Energy Physics - Phenomenology · Physics 2017-08-23 Jefferson Bjoraker , Raju Venugopalan

We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known…

Statistical Mechanics · Physics 2025-10-03 Jakob Mihatsch , Thomas Ihle

In this paper, we apply projective integration methods to hyperbolic moment models of the Boltzmann equation and the BGK equation, and investigate the numerical properties of the resulting scheme. Projective integration is an explicit,…

Computational Physics · Physics 2021-01-06 Julian Koellermeier , Giovanni Samaey

The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…

Numerical Analysis · Mathematics 2020-09-25 Vicente Ramm , Jehanzeb H. Chaudhry , Christopher D. Cooper

One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availability of efficient tools, it is an obvious idea to try to…

Computational Physics · Physics 2021-07-28 Tianbai Xiao , Martin Frank

This paper proposes a collocation boundary element method based on the Burton--Miller method for solving transmission problems, which is rapidly convergent within the Krylov subspace solver framework. Our study enhances Burton--Miller-type…

Numerical Analysis · Mathematics 2025-01-17 Yasuhiro Matsumoto , Akihiro Yoshiki , Hiroshi Isakari

In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…

Statistical Mechanics · Physics 2016-08-31 A. N. Gorban , I. V. Karlin

Time harmonic inverse scattering using accurate forward models is often computationally expensive. On the other hand, the use of computationally efficient solvers, such as the Born approximation, may fail if the targets do not satisfy the…

Computational Physics · Physics 2019-07-05 Jari P. Kaipio , Tomi Huttunen , Teemu Luostari , Timo Lähivaara , Peter B. Monk

We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an…

Strongly Correlated Electrons · Physics 2017-11-30 Yusuke Nomura , Andrew S. Darmawan , Youhei Yamaji , Masatoshi Imada

We present an algorithm for solving the one-dimensional space collisional Boltzmann transport equation (BTE) for electrons in low-temperature plasmas (LTPs). Modeling LTPs is useful in many applications, including advanced manufacturing,…

Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…

Computational Physics · Physics 2025-12-24 Longqing Ge , Qingdong Cai , Yonghao Zhang , Tianbai Xiao

At higher altitudes, for high temperature gases, for instance near space shuttles moving at hypersonic speed, not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In…

Analysis of PDEs · Mathematics 2024-08-16 Niclas Bernhoff

We compute the moments of the nonlinear binary collision integral in the ultrarelativistic hard-sphere approximation for an arbitrary anisotropic distribution function in the local rest frame. This anisotropic distribution function has an…

Nuclear Theory · Physics 2025-07-03 Etele Molnár