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arXiv 2023年

作者： Barrett, Aaron Fogelson, Aaron L. Gregory Forest, M. Gruninger, Cole Lim, Sookkyung Griffith, Boyce E. Department of Mathematics University of Utah Salt Lake CityUT United States Departments of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Department of Mathematical Sciences University of Cincinnati CincinnatiOH United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear-thinning of the viscoelastic environment. Copyright © 2023, The Authors. All rights reserved.

关键词： Shear thinning

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On the Particle Approximation of Lagged Feynman-Kac Formulae

arXiv

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arXiv 2024年

作者： Awadelkarim, Elsiddig Caffarel, Michel Moral, Pierre Del Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence33405 France School of Data Science The Chinese University Hong Kong Shenzhen China

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel lagged approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman-Kac marginals associated with a positive operator iterated l ∈ N times;a lagged Feynman-Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) have been extensively employed in the physics literature. In short, DMC is an iterative algorithm involving N ∈ N particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman-Kac formula, one has an almost sure characterization of the L1-error as the time parameter (iteration) goes to infinity and this is at most of O(exp{−κl}/N), for_ κ > 0. In addition a non-asymptotic in time, and time uniform L1−bound is proved which is O(l/√N). We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with N and l small and, for long time enough, is mathematically justified. Our results also suggest how one should choose N and l in practice. We emphasize that these results are not restricted to physical applications;they have broad relevance to the general problem of particle simulation of the Feynman-Kac formula, which is utilized in a great variety of scientific and engineering fields. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

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THE COMPLEX INTERPLAY BETWEEN RISK TOLERANCE AND THE SPREAD OF INFECTIOUS DISEASES

arXiv

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arXiv 2024年

作者： Nguyen, Maximilian Freedman, Ari Cheung, Matthew Saad-Roy, Chadi Espinoza, Baltazar Grenfell, Bryan Levin, Simon Lewis-Sigler Institute Princeton University PrincetonNJ08544 United States Department of Ecology and Evolutionary Biology Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Miller Institute for Basic Research in Science Department of Integrative Biology University of California Berkeley BerkeleyCA United States Biocomplexity Institute University of Virginia CharlottesvilleVA United States

Risk-driven behavior provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regards to risk tolerance. The interplay between behavior and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioral composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behavior, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the number of risk-averse people in the population, and the duration of intervention usage reduces the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold. Lastly, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse. Copyright © 2024, The Authors. All rights reserved.

关键词： Epidemiology

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Inversion problems for fourier transforms of particle distributions

arXiv

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arXiv 2018年

作者： Kim, Jaeuk Zhang, Ge Stillinger, Frank H. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Physics and Astronomy University of Pennsylvania PhiladelphiaPA19104-6396 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Collective coordinates in a many-particle system are complex Fourier components of the particle density n(x) ≡ PNj=1 δ(x − rj), and often provide useful physical insights. However, given collective coordinates, it is desirable to infer the particle coordinates via inverse transformations. In principle, a sufficiently large set of collective coordinates are equivalent to particle coordinates, but the nonlinear relation between collective and particle coordinates makes the inversion procedure highly nontrivial. Given a "target" configuration in one-dimensional Euclidean space, we investigate the minimal set of its collective coordinates that can be uniquely inverted into particle coordinates. For this purpose, we treat a finite number M of the real and/or the imaginary parts of collective coordinates of the target configuration as constraints, and then reconstruct "solution" configurations whose collective coordinates satisfy these constraints. Both theoretical and numerical investigations reveal that the number of numerically distinct solutions depends sensitively on the chosen collective-coordinate constraints and target configurations. From detailed analysis, we conclude that collective coordinates at the dN2 e smallest wavevectors is the minimal set of constraints for unique inversion, where d·e represents the ceiling function. This result provides useful groundwork to the inverse transform of collective coordinates in higher-dimensional systems. Copyright © 2018, The Authors. All rights reserved.

关键词： Inverse transforms

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Liquid-liquid transition in water from first principles

arXiv

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arXiv 2022年

作者： Gartner, Thomas E. Piaggi, Pablo M. Car, Roberto Panagiotopoulos, Athanassios Z. Debenedetti, Pablo G. Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States

A longstanding question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles. Copyright © 2022, The Authors. All rights reserved.

关键词： Density functional theory

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Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order-disorder transitions in LixCoO2

arXiv

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arXiv 2023年

作者： Teichert, G.H. Das, S. Shojaei, M. Faghih Holber, J. Mueller, T. Hung, L. Gavini, V. Garikipati, K. Department of Mechanical Engineering University of Michigan United States Toyota Research Institute Los AltosCA United States Department of Materials Science & Engineering University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States Applied Physics Program University of Michigan United States Materials Science & Engineering Johns Hopkins University United States

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order-disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarsegraining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes’ phase evolution in terms of temperature, morphology, charge cycling and particle size. © 2023, CC BY-NC-SA.

关键词： Cathodes

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Publisher’s Note: “Enhanced damping of ion acoustic waves in dense plasmas” [Phys. Plasmas 18, 014505 (2011)]

引用

Physics of Plasmas 2011年第3期18卷

作者： S. Son Sung Joon Moon 118 Caleb Lane Princeton New Jersey 08540 USA 2Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

This article was originally published online on 11 January 2011 with an error in S. Son’s affiliation. AIP apologizes for this error.

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Phase equilibrium of water with hexagonal and cubic ice using the SCAN functional

arXiv

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arXiv 2021年

作者： Piaggi, Pablo Miguel Panagiotopoulos, Athanassios Z. Debenedetti, Pablo G. Car, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models are rapidly becoming widely used to simulate complex physicochemical phenomena with ab initio accuracy. Here, we use one such model as well as direct density functional theory (DFT) calculations to investigate the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an eye towards studying ice nucleation. The machine learning model is based on deep neural networks and has been trained on DFT data obtained using the SCAN exchange and correlation functional. We use this model to drive enhanced sampling simulations aimed at calculating a number of complex properties that are out of reach of DFT-driven simulations and then employ an appropriate reweighting procedure to compute the corresponding properties for the SCAN functional. This approach allows us to calculate the melting temperature of both ice polymorphs, the driving force for nucleation, the heat of fusion, the densities at the melting temperature, the relative stability of ice Ih and Ic, and other properties. We find a correct qualitative prediction of all properties of interest. In some cases, quantitative agreement with experiment is better than for state-of-the-art semiempirical potentials for water. Our results also show that SCAN correctly predicts that ice Ih is more stable than ice Ic. Copyright © 2021, The Authors. All rights reserved.

关键词： Ice

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Viscosity in water from first-principles and deep-neural-network simulations

arXiv

引用

arXiv 2022年

作者： Malosso, Cesare Zhang, Linfeng Car, Roberto Baroni, Stefano Tisi, Davide SISSA - Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States DP Technology Beijing100080 China Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States CNR Istituto Officina dei Materiali SISSA Unit Trieste34136 Italy

We report on an extensive study of the viscosity of liquid water at near-ambient conditions, performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics (AIMD), based on density-functional theory (DFT). In order to cope with the long simulation times necessary to achieve an acceptable statistical accuracy, our ab initio approach is enhanced with deep-neural-network potentials (NNP). This approach is first validated against AIMD results, obtained by using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and paying careful attention to crucial, yet often overlooked, aspects of the statistical data analysis. Then, we train a second NNP to a dataset generated from the Strongly Constrained and Appropriately Normed (SCAN) functional. Once the error resulting from the imperfect prediction of the melting line is offset by referring the simulated temperature to the theoretical melting one, our SCAN predictions of the shear viscosity of water are in very good agreement with experiments. Copyright © 2022, The Authors. All rights reserved.

关键词： Deep neural networks

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Quality of internal representation shapes learning performance in feedback neural networks

arXiv

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arXiv 2020年

作者： Susman, Lee Mastrogiuseppe, Francesca Brenner, Naama Barak, Omri Interdisciplinary Program in Applied Mathematics Technion Israel Institute of Technology Haifa32000 Israel Network Biology Research Laboratories Technion Israel Institute of Technology Haifa32000 Israel Gatsby Computational Neuroscience Unit University College London London United Kingdom Dept. of Chemical Engineering Technion Israel Institute of Technology Haifa32000 Israel Rappaport Faculty of Medicine Technion Israel Institute of Technology Haifa32000 Israel

A fundamental feature of complex biological systems is the ability to form feedback interactions with their environment. A prominent model for studying such interactions is reservoir computing, where learning acts on low-dimensional bottlenecks. Despite the simplicity of this learning scheme, the factors contributing to or hindering the success of training in reservoir networks are in general not well understood. In this work, we study non-linear feedback networks trained to generate a sinusoidal signal, and analyze how learning performance is shaped by the interplay between internal network dynamics and target properties. By performing exact mathematical analysis of linearized networks, we predict that learning performance is maximized when the target is characterized by an optimal, intermediate frequency which monotonically decreases with the strength of the internal reservoir connectivity. At the optimal frequency, the reservoir representation of the target signal is high-dimensional, de-synchronized, and thus maximally robust to noise. We show that our predictions successfully capture the qualitative behaviour of performance in non-linear networks. Moreover, we find that the relationship between internal representations and performance can be further exploited in trained non-linear networks to explain behaviours which do not have a linear counterpart. Our results indicate that a major determinant of learning success is the quality of the internal representation of the target, which in turn is shaped by an interplay between parameters controlling the internal network and those defining the task. © 2020, CC BY.

关键词： Quality control

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