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Micro-Macro Stochastic Galerkin Methods for Nonlinear Fokker–Planck Equations with Random Inputs Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-03-13 Giacomo Dimarco, Lorenzo Pareschi, Mattia Zanella
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 527-560, March 2024. Abstract. Nonlinear Fokker–Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and biological dynamics. Their mathematical formulation often has to face physical
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Upscaling an Extended Heterogeneous Stefan Problem from the Pore-Scale to the Darcy Scale in Permafrost Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-03-06 Malgorzata Peszynska, Naren Vohra, Lisa Bigler
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 436-475, March 2024. Abstract. In this paper we upscale thermal models from the pore–scale to the Darcy scale for applications in permafrost. We incorporate thawing and freezing of water at the pore-scale and adapt rigorous homogenization theory from [A. Visintin, SIAM J. Math. Anal., 39 (2007), pp. 987–1017] to the original nonlinear multivalued
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Fano Resonances in All-Dielectric Electromagnetic Metasurfaces Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-03-06 Habib Ammari, Bowen Li, Hongjie Li, Jun Zou
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 476-526, March 2024. Abstract. We are interested in the resonant electromagnetic scattering by all-dielectric metasurfaces made of a two-dimensional lattice of nanoparticles with high refractive indices. In [Ammari, Li, and Zou, Trans. Amer. Math. Soc., 376 (2023), pp. 39–90], it has been shown that a single high-index nanoresonator can couple
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Dynamical Properties of Coarse-Grained Linear SDEs Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-02-27 Thomas Hudson, Xingjie Helen Li
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 406-435, March 2024. Abstract. Coarse-graining or model reduction is a term describing a range of approaches used to extend the timescale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard coarse-graining approaches approximate the potential of mean force and use this to drive
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On the Compatibility of Sharp and Diffuse Interfaces Out of Equilibrium Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-02-26 Václav Klika, Hans Christian Öttinger
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 369-405, March 2024. Abstract. There are two main approaches to modelling interfaces within nonequilibrium thermodynamics, the so-called sharp and diffuse interface models. Both of them are based on the local equilibrium assumption (LEA) in the bulk, but the latter additionally assumes the validity of this concept also within the interface itself
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Generalized Multiscale Finite Element Treatment of a Heterogeneous Nonlinear Strain-limiting Elastic Model Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-02-06 Maria Vasilyeva, S. M. Mallikarjunaiah
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 334-368, March 2024. Abstract. In this work, we consider a nonlinear strain-limiting elastic model in heterogeneous domains. We investigate heterogeneous material with soft and stiff inclusions and perforations that are important to understand an elastic solid’s behavior and crack-tip fields. Numerical solutions of problems in computational
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Quantum Mechanics for Closure of Dynamical Systems Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-02-05 David C. Freeman, Dimitrios Giannakis, Joanna Slawinska
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 283-333, March 2024. Abstract. We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state are unknown, this method involves defining a surrogate system in a time-dependent
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Exponential Convergence of a Generalized FEM for Heterogeneous Reaction-Diffusion Equations Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-02-05 Chupeng Ma, J. M. Melenk
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 256-282, March 2024. Abstract. A generalized finite element method (FEM) is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter [math], based on locally approximating the solution on each subdomain by solution of a local reaction-diffusion equation and eigenfunctions of a local eigenproblem
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Particle-Continuum Multiscale Modeling of Sea Ice Floes Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-30 Quanling Deng, Samuel N. Stechmann, Nan Chen
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 230-255, March 2024. Abstract. Sea ice profoundly influences the polar environment and the global climate. Traditionally, sea ice has been modeled as a continuum under Eulerian coordinates to describe its large-scale features, using, for instance, viscous-plastic rheology. Recently, Lagrangian particle models, also known as the discrete element
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Localized Orthogonal Decomposition for a Multiscale Parabolic Stochastic Partial Differential Equation Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-18 Annika Lang, Per Ljung, Axel Målqvist
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 204-229, March 2024. Abstract. A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a coarse-scale representation of the elliptic operator, enriched by fine-scale
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Multiscale Motion and Deformation of Bumps in Stochastic Neural Fields with Dynamic Connectivity Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-17 Heather L. Cihak, Zachary P. Kilpatrick
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 178-203, March 2024. Abstract. The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain’s learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and stimulus-encoding spatiotemporal patterns of neural activity. Neural activity
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An Adaptive Preconditioner for Three-Dimensional Single-Phase Compressible Flow in Highly Heterogeneous Porous Media Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-17 Shubin Fu, Eric Chung, Lina Zhao
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 155-177, March 2024. Abstract. In this paper, we study two-grid preconditioners for three-dimensional single-phase nonlinear compressible flow in highly heterogeneous porous media arising from reservoir simulation. Our goal is to develop robust and efficient preconditioners that converge independently of the contrast of the media and types of
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Improved Self-consistent Field Iteration for Kohn–Sham Density Functional Theory Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-12 Fei Xu, Qiumei Huang
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 142-154, March 2024. Abstract. In this article, an improved self-consistent field iteration scheme is introduced. The proposed method has essential applications in Kohn–Sham density functional theory and relies on an extrapolation scheme and the least squares method. Moreover, the proposed solution is easy to implement and can accelerate the
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Metadynamics for Transition Paths in Irreversible Dynamics Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-12 Tobias Grafke, Alessandro Laio
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 125-141, March 2024. Abstract. Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic systems, these transitions can happen via multiple physical mechanisms
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Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-10 Pingbing Ming, Siqi Song
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 106-124, March 2024. Abstract. We derive the optimal energy error estimate for a multiscale finite element method with oversampling technique applied to an elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a byproduct
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Semiclassical Propagation Along Curved Domain Walls Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-10 Guillaume Bal
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 66-105, March 2024. Abstract. We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set [math] of a slowly varying domain wall modeling the interface separating two insulating media. We propose a semiclassical oscillatory representation of the propagating wavepackets
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Three-Dimensional Random Wave Coupling Along a Boundary and an Associated Inverse Problem Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-09 Maarten V. de Hoop, Josselin Garnier, Knut Sølna
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 39-65, March 2024. Abstract. We consider random wave coupling along a flat boundary in dimension three, where the coupling is between surface and body modes and is induced by scattering by a randomly heterogeneous medium. In an appropriate scaling regime we obtain a system of radiative transfer equations which are satisfied by the mean Wigner
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A New Class of Uniformly Stable Time-Domain Foldy–Lax Models for Scattering by Small Particles. Acoustic Sound-Soft Scattering by Circles Multiscale Modeling Simul. (IF 1.6) Pub Date : 2024-01-03 Maryna Kachanovska
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 1-38, March 2024. Abstract. In this work we study time-domain sound-soft scattering by small circles. Our goal is to derive an asymptotic model for this problem that is valid when the size of the particles tends to zero. We present a systematic approach to constructing such models based on a well-chosen Galerkin discretization of a boundary
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Bottom-Up Transient Time Models in Coarse-Graining Molecular Systems Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-12-06 Georgia Baxevani, Vagelis Harmandaris, Evangelia Kalligiannaki, Ivi Tsantili
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1746-1774, December 2023. Abstract. This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential depends explicitly on time to efficiently approximate the transient coarse-grained
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A Bending-Torsion Theory for Thin and Ultrathin Rods as a [math]-Limit of Atomistic Models Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-12-06 Bernd Schmidt, Jiří Zeman
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1717-1745, December 2023. Abstract. The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as [math]-limits of three-dimensional atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness [math] and interatomic distance [math]. First, we set up a novel
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Analysis and Simulation of Optimal Control for a Two-Time-Scale Fractional Advection-Diffusion-Reaction Equation with Space-Time-Dependent Order and Coefficients Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-12-06 Yiqun Li, Hong Wang, Xiangcheng Zheng
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1690-1716, December 2023. Abstract. We investigate an optimal control model with pointwise constraints governed by a two-time-scale time-fractional advection-diffusion-reaction equation with space-time-dependent fractional order and coefficients, which describes, e.g., the contaminant in groundwater under various transport scales or miscible
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Preconditioned Algorithm for Difference of Convex Functions with Applications to Graph Ginzburg–Landau Model Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-12-04 Xinhua Shen, Hongpeng Sun, Xuecheng Tai
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1667-1689, December 2023. Abstract. In this work, we propose and study a preconditioned framework with a graphic Ginzburg–Landau functional for image segmentation and data clustering by parallel computing. Solving nonlocal models is usually challenging due to the huge computation burden. For the nonconvex and nonlocal variational functional
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High-order Contrast Bounds for Piezoelectric Constants of Two-phase Fibrous Composites Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-11-27 Vladimir Mityushev
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1644-1666, December 2023. Abstract. The constructive theory of analytical higher-order contrast bounds for the effective constants of dispersed conducting and piezoelectric fibrous composites is developed. The lower-order bounds, e.g., Wiener and Hashin–Shtrikman bounds, are universal for composites but do not take into account interactions
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Extending the Regime of Linear Response with Synthetic Forcings Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-11-14 Renato Spacek, Gabriel Stoltz
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1602-1643, December 2023. Abstract. Transport coefficients, such as the mobility, thermal conductivity, and shear viscosity, are quantities of prime interest in statistical physics. At the macroscopic level, transport coefficients relate an external forcing of magnitude [math], with [math], acting on the system to an average response expressed
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FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-11-03 Daria Sushnikova, Leslie Greengard, Michael O’Neil, Manas Rachh
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1570-1601, December 2023. Abstract. We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an [math]-like hierarchical factorization of the
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Large Deviation Principle and Thermodynamic Limit of Chemical Master Equation via Nonlinear Semigroup Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-24 Yuan Gao, Jian-Guo Liu
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1534-1569, December 2023. Abstract. Chemical reactions can be modeled by a random time-changed Poisson process on countable states. The macroscopic behaviors, such as large fluctuations, can be studied via the WKB reformulation. The WKB reformulation for the backward equation is Varadhan’s discrete nonlinear semigroup and is also a monotone
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Homogenization and Dimension Reduction of the Stokes Problem with Navier-Slip Condition in Thin Perforated Layers Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-24 John Fabricius, Markus Gahn
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1502-1533, December 2023. Abstract. We study a Stokes system posed in a thin perforated layer with a Navier-slip condition on the internal oscillating boundary from two viewpoints: (1) dimensional reduction of the layer and (2) homogenization of the perforated structure. Assuming the perforations are periodic, both aspects can be described through
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On the Periodic Homogenization of Elliptic Equations in Nondivergence Form with Large Drifts Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-20 Wenjia Jing, Yiping Zhang
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1486-1501, December 2023. Abstract. We study the quantitative homogenization of linear second order elliptic equations in nondivergence form with highly oscillating periodic diffusion coefficients and with large drifts, in the so-called centered setting where homogenization occurs and the large drifts contribute to the effective diffusivity
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Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-20 Fabian Kröpfl, Roland Maier, Daniel Peterseim
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1457-1485, December 2023. Abstract. Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale subproblems on local subdomains whose solutions are then employed to deduce appropriate coarse contributions to the surrogate
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An Effective Fractional Paraxial Wave Equation for Wave-Fronts in Randomly Layered Media with Long-Range Correlations Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-18 Christophe Gomez
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1410-1456, December 2023. Abstract. This work concerns the asymptotic analysis of high-frequency wave propagation in randomly layered media with fast variations and long-range correlations. The analysis takes place in the three-dimensional physical space and weak-coupling regime. The role played by the slow decay of the correlations on a propagating
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Elastic Far-Field Decay from Dislocations in Multilattices Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-12 Derek Olson, Christoph Ortner, Yangshuai Wang, Lei Zhang
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1379-1409, December 2023. Abstract. We precisely and rigorously characterize the decay of elastic fields generated by dislocations in crystalline materials, focusing specifically on the role of multilattices. Concretely, we establish that the elastic field generated by a dislocation in a multilattice can be decomposed into a continuum field
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Electronic Observables for Relaxed Bilayer Two-Dimensional Heterostructures in Momentum Space Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-11 Daniel Massatt, Stephen Carr, Mitchell Luskin
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1344-1378, December 2023. Abstract. Momentum space transformations for incommensurate two-dimensional electronic structure calculations are fundamental for reducing computational cost and for representing the data in a more physically motivating format, as exemplified in the Bistritzer–MacDonald model [Proc. Natl. Acad. Sci. USA, 108 (2011)
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Stochastic Continuum Models for High-Entropy Alloys with Short-range Order Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-10-10 Yahong Yang, Luchan Zhang, Yang Xiang
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1323-1343, December 2023. Abstract. High entropy alloys (HEAs) are a class of novel materials that exhibit superb engineering properties. It has been demonstrated by extensive experiments and first principles/atomistic simulations that short-range order in the atomic level randomness strongly influences the properties of HEAs. In this paper
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Boundary Effects in Radiative Transfer of Acoustic Waves in a Randomly Fluctuating Half-space Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-09-25 Adel Messaoudi, Regis Cottereau, Christophe Gomez
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1299-1321, September 2023. Abstract. This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations
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The 3D Narrow Capture Problem for Traps with Semipermeable Interfaces Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-09-22 Paul C. Bressloff
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1268-1298, September 2023. Abstract. In this paper we analyze the narrow capture problem for a single Brownian particle diffusing in a three-dimensional (3D) bounded domain containing a set of small, spherical traps. The boundary surface of each trap is taken to be a semipermeable membrane. That is, the continuous flux across the interface is
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Multiscale Constitutive Framework of One-Dimensional Blood Flow Modeling: Asymptotic Limits and Numerical Methods Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-09-15 Giulia Bertaglia, Lorenzo Pareschi
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1237-1267, September 2023. Abstract. In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice
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Multiscale Numerical Schemes for the Collisional Vlasov Equation in the Finite Larmor Radius Approximation Regime Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-09-14 Anaïs Crestetto, Nicolas Crouseilles, Damien Prel
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1210-1236, September 2023. Abstract. This work is devoted to the construction of multiscale numerical schemes efficient in the finite Larmor radius approximation of the collisional Vlasov equation. Following the paper of Bostan and Finot [Commun. Contemp. Math., 22 (2020), 1950047], the system involves two different regimes, a highly oscillatory
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Aggregation Methods for Computing Steady States in Statistical Physics Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-09-08 Gabriel Earle, Brian Van Koten
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1170-1209, September 2023. Abstract. We give a new proof of local convergence of a multigrid method called iterative aggregation/disaggregation (IAD) for computing steady states of Markov chains. Our proof leads naturally to precise and interpretable estimates of the asymptotic rate of convergence. We study IAD as a model of more complex methods
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Double Dirac Cones in Band Structures of Periodic Schroedinger Operators Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-08-17 Ying Cao, Yi Zhu
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1147-1169, September 2023. Abstract. Dirac cones are conical singularities that occur near the degenerate points in band structures. Such singularities result in enormous unusual phenomena of the corresponding physical systems. This work investigates double Dirac cones that occur in the vicinity of a fourfold degenerate point in the band structures
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GANs and Closures: Micro-Macro Consistency in Multiscale Modeling Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-08-14 Ellis R. Crabtree, Juan M. Bello-Rivas, Andrew L. Ferguson, Ioannis G. Kevrekidis
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1122-1146, September 2023. Abstract. Sampling the phase space of molecular systems—and, more generally, of complex systems effectively modeled by stochastic differential equations (SDEs)—is a crucial modeling step in many fields, from protein folding to materials discovery. These problems are often multiscale in nature: they can be described
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Mathematical Models of Topologically Protected Transport in Twisted Bilayer Graphene Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-08-11 Guillaume Bal, Paul Cazeaux, Daniel Massatt, Solomon Quinn
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1081-1121, September 2023. Abstract. Twisted bilayer graphene gives rise to large moiré patterns that form a triangular network upon mechanical relaxation. If gating is included, each triangular region has gapped electronic Dirac points that behave as bulk topological insulators with topological indices depending on valley index and the type
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A Framework for a Generalization Analysis of Machine-Learned Interatomic Potentials Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-08-10 Christoph Ortner, Yangshuai Wang
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1053-1080, September 2023. Abstract. Machine-learned interatomic potentials (MLIPs) and force fields (i.e., interaction laws for atoms and molecules) are typically trained on limited data-sets that cover only a very small section of the full space of possible input structures. MLIPs are nevertheless capable of making accurate predictions of
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Mathematical Theory for Electromagnetic Scattering Resonances and Field Enhancement in a Subwavelength Annular Gap Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-08-08 Junshan Lin, Wangtao Lu, Hai Zhang
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 1012-1052, September 2023. Abstract. This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width [math]. The model is representative among many 3D subwavelength hole structures, which are able to induce resonant scattering of electromagnetic
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On Optimal Convergence Rates for Discrete Minimizers of the Gross–Pitaevskii Energy in Localized Orthogonal Decomposition Spaces Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-26 Patrick Henning, Anna Persson
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 993-1011, September 2023. Abstract. In this paper we revisit a two-level discretization based on localized orthogonal decomposition (LOD). It was originally proposed in [P. Henning, A. Målqvist, and D. Peterseim, SIAM J. Numer. Anal., 52 (2014), pp. 1525–1550] to compute ground states of Bose–Einstein condensates by finding discrete minimizers
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Edge Modes in Subwavelength Resonators in One Dimension Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-25 Habib Ammari, Silvio Barandun, Jinghao Cao, Florian Feppon
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 964-992, September 2023. Abstract. We present the mathematical theory of one-dimensional infinitely periodic chains of subwavelength resonators. We analyze both Hermitian and non-Hermitian systems. Subwavelength resonances and associated modes can be accurately predicted by a finite dimensional eigenvalue problem involving a capacitance matrix
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Radiative Decay of Edge States in Floquet Media Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-20 Sameh N. Hameedi, Amir Sagiv, Michael I. Weinstein
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 925-963, September 2023. Abstract. We consider the effect of time-periodic forcing on a one-dimensional Schrödinger equation with a topologically protected defect (edge) mode. The unforced system models a domain wall or dislocation defect in a periodic structure, and it supports a defect mode which bifurcates from the Dirac point (linear band
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Convergence of a Direct Simulation Monte Carlo Method for the Space Inhomogeneous Semiconductor Boltzmann Equations with Multi-valley Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-14 Jiachuan Cao, Li-qun Cao
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 884-924, September 2023. Abstract. This paper discusses the algorithm and error estimates for solving space inhomogeneous semiconductor Boltzmann equations with multi-valley, which describe the transport properties of carriers in semiconductor materials and devices. The high-dimensional feature and the singularity of the collision terms make
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Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-13 Yifan Chen, Thomas Y. Hou, Yixuan Wang
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 849-883, September 2023. Abstract. In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber [math] can be large. The main innovation is that our methods achieve a nearly exponential rate of convergence with respect
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Asymptotic Characterization of Localized Defect Modes: Su–Schrieffer–Heeger and Related Models Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-13 Richard V. Craster, Bryn Davies
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 827-848, September 2023. Abstract. Motivated by topologically protected states in wave physics, we study localized eigenmodes in one-dimensional periodic media with defects. The Su–Schrieffer–Heeger model (the canonical example of a one-dimensional system with topologically protected localized defect states) is used to demonstrate the method
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The Interaction Between Two Close-To-Touching Convex Acoustic Subwavelength Resonators Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-12 Haigang Li, Yan Zhao
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 804-826, September 2023. Abstract. The Minneart resonance is a low frequency resonance in which the wavelength is much larger than the size of the resonators. It is interesting to study the interaction between two adjacent bubbles when they are brought close together. Because the bubbles are usually compressible, in this paper we mainly investigate
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Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-07-12 Xiaoying Dai, Stefano de Gironcoli, Bin Yang, Aihui Zhou
Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 777-803, September 2023. Abstract. In this paper, we investigate the energy minimization model arising in the ensemble Kohn–Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance of the energy functional and the existence of the minimizer
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Reconstruction of Multiscale Electromagnetic Sources from Multifrequency Electric Far Field Patterns at Sparse Observation Directions Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-06-06 Jialei Li, Xiaodong Liu
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 753-775, June 2023. Abstract. We introduce a multistep scheme for reconstructing multiscale sources from multifrequency sparse electric far field patterns. The unknown source is a combination of electric dipoles, magnetic dipoles and extended sources. The dipoles are shown to be uniquely identified by the multifrequency electric far field patterns
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Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Convection Diffusion Equation Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-06-05 Lina Zhao, Eric Chung
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 735-752, June 2023. Abstract. In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equations. To define the multiscale basis functions, we first build an auxiliary multiscale space by solving local spectral problems motivated by analysis. Then a constraint energy
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A Neural Network Approach for Homogenization of Multiscale Problems Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-06-01 Jihun Han, Yoonsang Lee
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 716-734, June 2023. Abstract. We propose a neural network-based approach to the homogenization of multiscale problems. The proposed method uses a derivative-free formulation of a training loss, which incorporates Brownian walkers to find the macroscopic description of a multiscale PDE solution. Compared with other network-based approaches for
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Mobility Estimation for Langevin Dynamics Using Control Variates Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-06-01 Grigorios A. Pavliotis, Gabriel Stoltz, Urbain Vaes
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 680-715, June 2023. Abstract. The scaling of the mobility of two-dimensional Langevin dynamics in a periodic potential as the friction vanishes is not well understood for nonseparable potentials. Theoretical results are lacking, and numerical calculation of the mobility in the underdamped regime is challenging because the computational cost
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Learning Markovian Homogenized Models in Viscoelasticity Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-05-19 Kaushik Bhattacharya, Burigede Liu, Andrew Stuart, Margaret Trautner
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 641-679, June 2023. Abstract. Fully resolving dynamics of materials with rapidly varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach for deriving effective macroscopic equations which eliminates the small scales by exploiting scale separation
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Quasi-Convergence of an Implementation of Optimal Balance by Backward-Forward Nudging Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-05-19 Gökce Tuba Masur, Haidar Mohamad, Marcel Oliver
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 624-640, June 2023. Abstract. Optimal balance is a nonasymptotic numerical method for computing a point on an elliptic slow manifold for two-scale dynamical systems with strong gyroscopic forces. It works by solving a modified differential equation as a boundary value problem in time, where the nonlinear terms are adiabatically ramped up from
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Quasistatic Evolution with Unstable Forces Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-05-17 Debdeep Bhattacharya, Robert P. Lipton
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 598-623, June 2023. Abstract. We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating at stable critical points. These points can be associated with local energy
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Heat Generation Using Lorentzian Nanoparticles: Estimation via Time-Domain Techniques Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-05-12 Arpan Mukherjee, Mourad Sini
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 542-597, June 2023. Abstract. We analyze the mathematical model that describes the heat generated by electromagnetic nanoparticles. We use the known optical properties of the nanoparticles to control the support and amount of the heat needed around a nanoparticle. Precisely, we show that the dominant part of the heat around the nanoparticle
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An Elliptic Local Problem with Exponential Decay of the Resonance Error for Numerical Homogenization Multiscale Modeling Simul. (IF 1.6) Pub Date : 2023-05-08 Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
Multiscale Modeling &Simulation, Volume 21, Issue 2, Page 513-541, June 2023. Abstract. Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These effective data need to be computed by running local microscale