We study the traveling wave solutions of a lattice Boltzmann model for the planar streamer fronts that appear in the transport of electrons through a gas in a strong electrical field. To mimic the physical properties of the impact ionization reaction, we introduce a reaction matrix containing reaction rates that depend on the electron velocities. Via a Chapman--Enskog expansion, one is able to find only a rough approximation for a macroscopic evolution law that describes the traveling wave solution. We propose to compute these solutions with the help of a coarse-grained time-stepper, which is an effective evolution law for the macroscopic fields that only uses appropriately initialized simulations of the lattice Boltzmann model over short time intervals. The traveling wave solution is found as a fixed point of the sequential application of the coarse-grained time-stepper and a shift-back operator. The fixed point is then computed with a Newton-Krylov Solver. We compare the resulting solutions with those of the approximate PDE model, and propose a method to find the minimal physical wave speed.
The success of lattice Boltzmann methods has been attributed to their mesoscopic nature as a method derivable from a physically consistent microscopic model. Original lattice Boltzmann methods were Boltzmann averages of an underlying lattice gas. In the transition to modern lattice Boltzmann method, this link was broken, and the frequently used over-relaxation to achieve high Reynolds numbers has been seen as lacking physical motivation. While this approach has undeniable utility, it appeared to break the link to any underlying physical reality putting into question the special place of lattic…
For many complex dynamical systems, a separation of scales prevails between the (microscopic) level of description of the available model, and the (macroscopic) level at which one would like to observe and analyze the system. For this type of problems, an ``equation-free'' framework has recently been proposed. Using appropriately initialized microscopic simulations, one can build a coarse-grained time-stepper to approximate a time-stepper for the unavailable macroscopic model. Here, we show how one can use this coarse-grained time-stepper to compute coarse-grained traveling wave solutions of a…
A upscaled lattice Boltzmann method (LBM) for flow simulations in heterogeneous porous media, at both pore and Darcy scales, is proposed in this paper. In the micro-scale simulations, we model flows using LBM with the modified Guo et al. algorithm where we replace the force model with a simple Shan-Chen force model. The proposed upscaled LBM uses coarser grids to represent the effects of the fine-grid (pore-scale) simulations. For the upscaled LBM, effective properties and reduced-order models are proposed as we coarsen the grid. The effective properties are computed using solutions of local p…
We present a simple technique for the computation of coarse-scale steady states of dynamical systems with time scale separation in the form of a "wrapper" around a fine-scale simulator. We discuss how this approach alleviates certain problems encountered by comparable existing approaches, and illustrate its use by computing coarse-scale steady states of a lattice Boltzmann fine scale code. Interestingly, in the same context of multiple time scale problems, the approach can be slightly modified to provide initial conditions (on the slow manifold) with prescribed coarse-scale observables. The ap…
Constructing atom-resolved states from low-resolution data is of practical importance in many areas of science and engineering. This problem is addressed in this paper in the context of multiscale factorization methods for molecular dynamics. These methods capture the crosstalk between atomic and coarse-grained scales arising in macromolecular systems. This crosstalk is accounted for by Trotter factorization, which is used to separate the all-atom from the coarse-grained phases of the computation. In this approach, short molecular dynamics runs are used to advance in time the coarse-grained va…
In a recent work [A. De Rosis, R. Huang, and C. Coreixas, "Universal formulation of central-moments-based lattice Boltzmann method with external forcing for the simulation of multiphysics phenomena", Phys. Fluids 31, 117102 (2019)], a multiple-relaxation-time lattice Boltzmann method (LBM) has been proposed by means of the D3Q27 discretization, where the collision stage is performed in the space of central moments (CMs). These quantities relax towards an elegant Galilean invariant equilibrium, and can also include the effect of external accelerations. Here, we investigate the possibility to ad…
The molecular dynamics lattice gas method maps a molecular dynamics simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method by taking a Boltzmann average over the molecular dynamics lattice gas. A key property of the lattice Boltzmann method is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the molecular dynamics simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient…
At first glance the definition of mass and momentum appears to be uniquely defined. We show here, however, that this certainty can be misleading for many coarse grained systems. We show that particularly the fluctuating properties of common definitions of momentum in coarse grained methods like lattice gas and lattice Boltzmann do not agree with a fundamental definition of momentum. In the case of lattice gases, the definition of momentum will even disagree in the limit of large wavelength. For short times we can give analytical representations for the distribution of different momentum measur…
We introduce a lattice gas implementation that is based on coarse-graining a Molecular Dynamics (MD) simulation. Such a lattice gas is similar to standard lattice gases, but its collision operator is informed by an underlying MD simulation. This can be considered an optimal lattice gas implementation because it allows for the representation of any system that can be simulated with MD. We show here that equilibrium behavior of the popular lattice Boltzmann algorithm is consistent with this optimal lattice gas. This comparison allows us to make a more accurate identification of the expressions f…
We explore a novel simulation route for Plasma Wakefield Acceleration (PWFA) by using the computational method known as the Lattice Boltzmann Method (LBM). LBM is based on a discretization of the continuum kinetic theory while assuring the convergence towards hydrodynamics for coarse-grained fields (i.e., density, velocity, etc.). LBM is an established numerical analysis tool in computational fluid dynamics, able to efficiently bridge between kinetic theory and hydrodynamics, but its application in the context of PWFA has never been investigated so far. This paper aims at filling this gap. Res…
Force-Guided Bridge Matching for Full-Atom Time-Coarsened Dynamics of Peptides
Tsinghua University（清华大学）；Institute for AI Industry Research (AIR), Tsinghua University（清华大学人工智能产业研究院（AIR））；Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）
The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting these systems are a common set of symmetries and conservation laws, defining dry active fluids as a class of physical system. Many interesting behaviours have been observed at high densities, which remain difficult to simulate due to the computational demand. Here, we show how two-dimensional dry active fluids in a dense regime can be studied using a simple mo…
The study of the underlying physics of soft flowing materials depends heavily on numerical simulations, due to the complex structure of the governing equations reflecting the competition of concurrent mechanisms acting at widely disparate scales in space and time. A full-scale computational modelling remains a formidable challenge since it amounts to simultaneously handle six or more spatial decades in space and twice as many in time. Coarse-grained methods often provide a viable strategy to significantly mitigate this issue, through the implementation of mesoscale supramolecular forces design…
Here we present a systematic study of supercoil formation in DNA minicircles under varying linking number by using molecular dynamics simulations of a two-bead coarse-grained model. Our model is designed with the purpose of simulating long chains without sacrificing the characteristic structural properties of the DNA molecule, such as its helicity, backbone directionality and the presence of major and minor grooves. The model parameters are extracted directly from full-atomistic simulations of DNA oligomers via Boltzmann inversion, therefore our results can be interpreted as an extrapolation o…
We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite differenc…
The present study proposes a highly accurate lattice Boltzmann direct coupling cell-vertex algorithm, well suited for industrial purposes, making it highly valuable for aeroacoustic applications. It is indeed known that the convection of vortical structures across a grid refinement interface, where cell size is abruptly doubled, is likely to generate spurious noise that may corrupt the solution over the whole computational domain. This issue becomes critical in the case of aeroacoustic simulations, where accurate pressure estimations are of paramount importance. Consequently, any interfering n…
We present a framework based on the generalized lattice-Boltzmann equation using multiple relaxation times with forcing term for eddy capturing simulation of wall bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale turbulence effects are represented by the standard Smagorinsky eddy-viscosity model, which is modified by using the van Driest wall-damping function for near wall effects. For s…
We present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard Boltzmann device. The importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with alpha-helical and beta-sheet architecture. Extraction of the anisotropic interactions requires defining local reference frames for each amino acid that uniquely determine the coordinates of the neighboring residues. Using the local reference frames and histograms of the radial …
A tight and consistent link between resolutions is crucial to further expand the impact of multiscale modeling for complex materials. We herein tackle the generation of condensed molecular structures as a refinement -- backmapping -- of a coarse-grained structure. Traditional schemes start from a rough coarse-to-fine mapping and perform further energy minimization and molecular dynamics simulations to equilibrate the system. In this study we introduce DeepBackmap: A deep neural network based approach to directly predict equilibrated molecular structures for condensed-phase systems. We use gene…
Human blood flow is a multi-scale problem: in first approximation, blood is a dense suspension of plasma and deformable red cells. Physiological vessel diameters range from about one to thousands of cell radii. Current computational models either involve a homogeneous fluid and cannot track particulate effects or describe a relatively small number of cells with high resolution, but are incapable to reach relevant time and length scales. Our approach is to simplify much further than existing particulate models. We combine well established methods from other areas of physics in order to find the…
Scalable Generative Sampling and Multilevel Estimation for Lattice Field Theories Near Criticality
Berlin Institute for the Foundations of Learning and Data (BIFOLD)（柏林学习与数据基础研究所）；Technische Universität Berlin（柏林工业大学）；Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh（爱丁堡大学物理与天文学学院希格斯理论物理中心）；Deutsches Elektronen-Synchrotron (DESY)（德国电子同步加速器）；RIKEN Center for Advanced Intelligence Project (AIP)（理化学研究院先进智能项目中心）
Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials
Professorship of Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich（多尺度流体材料建模教授职位，工程物理与计算系，技术大学慕尼黑工程与设计学院）
Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators
Centre for Computational Science, University College London, UK；Institute for Mechanics, Computational Mechanics Group, Technical University of Darmstadt, Germany；Centre for Dynamic Systems, University College London, UK；Department of Statistical Science, University College London, UK；Department of Physics, Eindhoven University of Technology, Eindhoven, Netherlands；Centre d'Enseignement et de Recherche en Environnement Atmosphérique (CEREA), \' E cole des Ponts；Computational Science Laboratory, Institute for Informatics, University of Amsterdam, the Netherlands；Centre for Advanced Research Computing, University College London, UK
A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows
School of Mathematics and Computational Science, Xiangtan University（湘潭大学数学与计算科学学院）；National Center for Applied Mathematics in Hunan（湖南省应用数学中心）；Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University（湘潭大学计算与工程科学湖南省重点实验室）
