Article
Physics, Mathematical
Mitia Duerinckx
Summary: This study analyzes a system of classical particles and provides sharp estimates on many-particle correlation functions. By proposing a novel non-hierarchical approach, the BBGKY hierarchy can be truncated to any precision on the mean-field timescale, thereby justifying the Bogolyubov corrections to mean field. As a result, a quantitative central limit theorem for fluctuations of the empirical measure is derived, and the Lenard-Balescu limit for a spatially homogeneous system away from thermal equilibrium is discussed.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Petar Mitric, Veljko Jankovic, Nenad Vukmirovic, Darko Tanaskovic
Summary: The dynamical mean field theory is an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model even in one dimension, as revealed by detailed comparisons with other methods and literature results.
PHYSICAL REVIEW LETTERS
(2022)
Article
Operations Research & Management Science
Fabio Bagagiolo, Silvia Faggian, Rosario Maggistro, Raffaele Pesenti
Summary: This paper addresses the issue of modeling and studying tourist flow in the narrow alleys of historic heritage cities. It introduces a mean field game model and an optimization problem to study the existence of mean field equilibrium.
NETWORKS & SPATIAL ECONOMICS
(2022)
Article
Automation & Control Systems
Benoit Bonnet, Francesco Rossi
Summary: In this article, sufficient conditions for the Lipschitz regularity of the controlled vector fields solution of optimal control problems formulated on continuity equations are provided. The approach involves mean-field approximations and a careful extension of the existence result of locally optimal Lipschitz feedbacks.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Physics, Fluids & Plasmas
Asher Baram, Azi Lipshtat
Summary: This study examines the rate of convergence of two types of random sequential adsorption (RSA) processes on a d-dimensional cubic lattice to their asymptotic high-dimensional tree approximation. It shows that for the N1 model, the deviation of jamming density from its asymptotic high d value vanishes with a certain rate, while for the N2 model the convergence rate is slower. The results also indicate that the generalized Palasti approximation is a better fit for 2 <= d <= 4, but for higher d values the convergence rate to the asymptotic limits is faster than predicted by the approximation.
Article
Chemistry, Physical
Cristina Caruso, Annalisa Cardellini, Martina Crippa, Daniele Rapetti, Giovanni M. Pavan
Summary: Many molecular systems and physical phenomena are controlled by difficult-to-detect local fluctuations and microscopic dynamical rearrangements. In this study, a SOAP-based descriptor called tSOAP is developed to track time variations in local atomic environments and detect dynamic domains in molecular systems. This simple and general approach is expected to shed light on complex dynamical phenomena.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Engineering, Mechanical
Lin He, Chunqiu Wei, Jiang Sha, Delong Mao, Kangshuo Wang
Summary: This paper presents a general numerical scheme for the optimal control problem of fractional Birkhoffian systems. The scheme derives the fractional forced Birkhoff equations and directly discretizes the fractional Pfaff-Birkhoff-d'Alembert principle to convert the original problem into a nonlinear optimization problem. An illustrative example demonstrates the efficiency and simplicity of the proposed method.
NONLINEAR DYNAMICS
(2022)
Article
Materials Science, Multidisciplinary
Paolo Gazzaneo, Tommaso Maria Mazzocchi, Jan Lotze, Enrico Arrigoni
Summary: We study a model of photovoltaic energy collection where a Mott-insulating layer interacts with acoustic phonons and is coupled to two wide-band fermion leads. This system is driven into a nonequilibrium steady state by a periodic electric field. We find that the driving frequency has a peak effect on the photocurrent, which can be attributed to impact ionization processes. The hybridization strength between the layer and the leads affects the suppression of impact ionization. Acoustic phonons slightly enhance the photocurrent at low driving frequencies and suppress it around the main peak at all hybridization strengths.
Article
Mathematics, Interdisciplinary Applications
Eduardo Velasco Stock, Roberto da Silva
Summary: In this study, a simple stochastic agent-based model is proposed to explain the revenue dynamics of a nightclub venue based on the relationship between profit and spatial occupation. The model consists of a square lattice representing the nightclub's dance floor, where attendees can move to neighboring cells. Each attendee has a specific time interval between drinks, denoted as τ, and will move towards the bar when feeling thirsty. After leaving the bar area, τ time steps should pass before feeling thirsty again. The model highlights the importance of optimization rather than simply filling the bar to maximize profit, taking into account the income and ticket cost ratio.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Jan Peszek, David Poyato
Summary: In this article, we introduce an optimal transport topology on the space of probability measures over a fiber bundle, which penalizes the transport cost between different fibers. We illustrate this construction in the Euclidean case and show that even though the cost is infinitely valued and discontinuous, the space of probability measures with fixed marginal conditions is still a Polish space with a weak Riemannian structure. The article also explores the abstract theory of gradient flows with respect to the new topology, applications to evolution PDEs with heterogeneities, and the long-time behavior and global-in-time mean-field limits in a specific alignment model.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Francois Golse, Thierry Paul
Summary: We propose a time-dependent quantum perturbation result that is applicable to a potential with bounded gradient almost everywhere, with the perturbation being independent of the Planck constant. We demonstrate that the perturbed quantum dynamics in the classical limit remains in a tubular neighborhood of the unperturbed classical dynamics, with the size of the neighborhood proportional to the square root of the perturbation. We consider both the Schrodinger and von Neumann-Heisenberg equations.
INDIANA UNIVERSITY MATHEMATICS JOURNAL
(2023)
Article
Chemistry, Physical
Ajay Muralidharan, Arun Yethiraj
Summary: Ion-pairing plays a crucial role in electrolyte solutions, and accurately estimating ion-pairing is valuable for designing and screening new electrolytes. In this study, we propose an efficient cluster model to estimate the ion-pair potential-of-mean-force between ionic solutes in electrolytes, utilizing an enhanced sampling approach to achieve high efficiency and accuracy.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Andrew Akerson
Summary: Designing for impact resistance is challenging due to the complex physics and failure modes involved. Recent advances in 3D printing and additive manufacturing techniques allow for tailored geometries and multi-material structures. This study applies gradient-based topology optimization to design such structures, and presents efficient methods for computing their transient dynamic evolution. By studying the optimal design of solid-void structures and spall-resistant structures, the trade-offs between strength and toughness are explored.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Guosheng Fu, Siting Liu, Stanley Osher, Wuchen Li
Summary: This work explores the application of general high-order numerical schemes with finite element methods in the space-time domain for computing optimal transport, mean-field planning, and potential MFG problems. Several experiments are conducted to validate the convergence rate of the high-order method numerically, demonstrating the efficiency and effectiveness of the approach.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Qiancheng Xu, Mohcine Chraibi, Armin Seyfried
Summary: This study investigates clogging phenomena using a velocity-based model for pedestrian dynamics. It identifies prolonged clogs in bottleneck simulations and analyzes the factors causing this phenomenon. Results show that prolonged clogs are closely linked to parameters of spatial boundaries and movement model, rather than algorithmic factors.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
Judith Berendsen, Martin Burger, Virginie Ehrlacher, Jan-Frederik Pietschmann
JOURNAL OF EVOLUTION EQUATIONS
(2020)
Article
Mathematics, Applied
Leon Bungert, Martin Burger, Yury Korolev, Carola-Bibiane Schonlieb
Article
Mathematics
Martin Burger, Philippe Laurencot, Ariane Trescases
Summary: This paper analyzes a chemotaxis model based on local sensing mechanism, different from the traditional gradient sensing mechanism, where the delay of explosion in the supercritical mass case is observed to be infinite time. Through mathematical proof, the global existence of weak solutions is established, and the regularity and uniqueness of solutions are studied. The key difference is the (H1)'-bound in the equation structure, leading to a lower bound on entropy, contrasting with the minimal Keller-Segel model.
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
(2021)
Article
Multidisciplinary Sciences
Sargon Gross-Thebing, Lukasz Truszkowski, Daniel Tenbrinck, Hector Sanchez-Iranzo, Carolina Camelo, Kim J. Westerich, Amrita Singh, Paul Maier, Jonas Prengel, Pia Lange, Jan Huewel, Fjedor Gaede, Ramona Sasse, Bart E. Vos, Timo Betz, Maja Matis, Robert Prevedel, Stefan Luschnig, Alba Diz-Munoz, Martin Burger, Erez Raz
Article
Mathematics, Applied
Marco Di Francesco, Antonio Esposito, Markus Schmidtchen
Summary: This study investigates a one-dimensional discrete particle system comprising two species coupled through nonlocal interactions driven by the Newtonian potential, with repulsive self-interaction and attractive cross-interaction. The empirical measure associated with the particle system converges to the unique 2-Wasserstein gradient flow solution of a system of two partial differential equations with nonlocal interaction terms in a proper measure sense. The proof relies on uniform estimates of the L-m-norms of a piecewise constant reconstruction of density using the particle trajectories.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
M. Burger, A. Hauptmann, T. Helin, N. Hyvonen, J. P. Puska
Summary: This work applies Bayesian experimental design to select optimal projection geometries in (discretized) parallel beam x-ray tomography with Gaussian prior and additive noise. The introduced greedy exhaustive optimization algorithm proceeds sequentially, allowing redefining the region of interest after each projection and considering both A and D-optimality. Two-dimensional numerical experiments demonstrate the functionality of the approach.
Article
Mathematics
Martin Burger
Summary: This paper aims to study the appropriate meso- and macroscopic models for interactions in social processes, considering network structures and different roles of interacting agents. By deriving kinetic equations and obtaining macroscopic models from them, spatial phase separation phenomena can be explained.
VIETNAM JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Philipp Werner, Martin Burger, Florian Frank, Harald Garcke
Summary: The aim of this paper is to develop suitable models for cell blebbing phenomenon and predict the mechanical effects, including the interaction between cell membrane and actin cortex. A two-phase field model is employed, which uses diffuse descriptions of both membrane and cortex and allows for a proper description of interaction via linker protein densities. In addition to the detailed modeling, some energetic aspects of the models are discussed, and a numerical scheme is presented for computational studies. The results demonstrate that several effects found in experiments, particularly bleb formation by cortex rupture, can be reproduced, which was not possible with previous models lacking linker dynamics.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Katharina Hopf, Martin Burger
Summary: We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. This article aims at a systematic study of the question of existence of weak solutions and their long-time asymptotic behaviour, as well as provides a weak-strong stability estimate for a wide range of coefficients.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Maria Bruna, Martin Burger, Antonio Esposito, Simon M. Schulz
Summary: This paper discusses the mathematical modeling of Brownian active particle systems and presents four microscopic models and their associated macroscopic models obtained using different coarse-graining methods. It is found that models with short-range interactions can explain motility-induced phase separation, while the mean-field model with long-range repulsive interactions cannot.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Marco Di Francesco, Simone Fagioli, Valeria Iorio
Summary: We study a mathematical theory of second order systems with two species, considering the dynamics of interacting particles subject to linear damping, nonlocal forces, and external forces. Our results are limited to the one-dimensional case with initial data taken in a Wasserstein space of probability measures. We prove existence and uniqueness for smooth nonlocal interaction potentials, and convergence to solutions for large times and large damping scaled versions of the system.
ACTA APPLICANDAE MATHEMATICAE
(2023)
Article
Engineering, Electrical & Electronic
Protim Bhattacharjee, Martin Burger, Anko Boerner, Veniamin I. Morgenshtern
Summary: In this work, a RoI Prioritised Sampling algorithm is proposed to effectively utilize the limited resources of the imaging instrument on a space rover. The algorithm prioritizes Region-of-Interests (RoIs) based on an estimator that evaluates the change in information content at consecutive spatial scales. The algorithm's performance is compared with state-of-the-art multi-resolution reconstruction algorithms and shown to better utilize the system resources.
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
(2022)
Article
Engineering, Electrical & Electronic
Alexandra Koulouri, Pia Heins, Martin Burger
Summary: This study investigates superresolution in deconvolution driven by sparsity priors. By estimating the positions and amplitudes of peaks based on prior knowledge and solving finite dimensional convex problems on a computational grid, the study confirms observations on discrete reconstructions of sparse peaks using the l(1)-norm. The proposed self-driven adaptive grid approach allows for superresolution in one-dimensional and multi-dimensional spaces, contributing to the development of robust algorithms for single molecule detection in microscopy and characteristic frequency detection in spectroscopy.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Computer Science, Artificial Intelligence
Byung-Woo Hong, Ja-Keoung Koo, Martin Burger, Stefano Soatto
IEEE TRANSACTIONS ON IMAGE PROCESSING
(2020)
Article
Mathematics, Applied
Martin Burger, Ina Humpert, Jan-Frederik Pietschmann
KINETIC AND RELATED MODELS
(2020)
