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arXiv 2020年

作者： Kim, Jaeuk Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 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

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform heterogeneous two-phase media, which include composites, porous media, foams, cellular solids, colloidal suspensions and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σV2 (R) and the associated hyperuniformity order metrics BV . This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered/irregular packings, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have the minimal value of the hyperuniformity order metrics BV across all volume fractions. On the other hand, among all packings considered, the triangular-lattice packings have the smallest values of BV for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing has the minimal order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems by inverse design procedures. Copyright © 2020, The Authors. All rights reserved.

关键词： Wireless networks

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Critical pore radius and transport properties of disordered hard- And overlapping-sphere models

arXiv

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arXiv 2021年

作者： Klatt, Michael A. Ziff, Robert M. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 Erlangen91058 Germany Center for the Study of Complex Systems Department of Chemical Engineering University of Michigan Ann ArborMI48109 United States Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δc. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, "quantizer" sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δc is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato. Adv. Wat. Resour. 140,103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size hδ2i, which is easier to determine than δc. Here, we compare δc to the second moment of the pore size hδ2i, and indeed confirm that, for all porosities and all models considered, δc2 is to a good approximation proportional to hδ2i. However, unlike hδ2i, the permeability estimate based on δc2 does not predict the correct ranking of k for our models. Thus, we confirm hδ2i to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via target

关键词： Porous materials

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Localization transition in three-dimensional stealthy hyperuniform disordered systems

arXiv

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arXiv 2021年

作者： Sgrignuoli, F. Torquato, S. Dal Negro, L. Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary’s Street BostonMA02215 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Division of Material Science and Engineering Boston University 15 Saint Mary’s Street BrooklineMA02446 United States Department of Physics Boston University 590 Commonwealth Avenue BostonMA02215 United States

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems (3D-SHDS) are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green’s matrix spectral method, we establish a transport phase diagram that demonstrates a clear delocalization-localization transition beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed sub-radiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and localization properties of light in stealthy hyperuniform structures and motivates the engineering of novel photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices. Copyright © 2021, The Authors. All rights reserved.

关键词： Phase diagrams

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The unseen invaders: Tracking phylogeographic dynamics and genetic diversity of cryptic Pomacea canaliculata and P. maculata (Golden apple snails) across Taiwan

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Ecology and Evolution 2024年第4期14卷 e11268页

作者： Banerjee, Pritam Dey, Gobinda Maity, Jyoti Prakash Stewart, Kathryn A. Sharma, Raju Kumar Chan, Michael W. Y. Lee, Kuanhsuen Chen, Chien-Yen Department of Environmental Science Policy and Management University of California Berkeley CA United States Department of Biomedical Sciences Graduate Institute of Molecular Biology National Chung Cheng University Chiayi County Min-Hsiung Taiwan Department of Agricultural Chemistry National Taiwan University Taipei Taiwan Environmental Science Laboratory Department of Chemistry Biological Laboratory School of Applied Sciences KIIT Deemed to be University Odisha Bhubaneswar India Institute of Environmental Sciences Leiden University Leiden Netherlands Doctoral Program in Science Technology Environment and Mathematics Department of Earth and Environmental Sciences National Chung Cheng University Chiayi County Min-Hsiung Taiwan Department of Earth and Environmental Sciences National Chung Cheng University Chiayi County Min-Hsiung Taiwan Department of Emergency Medicine Ditmanson Medical Foundation Chia-Yi Christian Hospital Chiayi Taiwan Center for Nano Bio-Detection Center for Innovative Research on Aging Society AIM-HI National Chung Cheng University Chiayi Taiwan

The cryptic invasion of golden apple snails (Pomacea canaliculata and P. maculata) in Taiwan has caused significant ecological and economical damage over the last few decades, however, their management remains difficult due to inadequate taxonomic identification, complex phylogeny, and limited population genetic information. We aim to understand the current distribution, putative population of origin, genetic diversity, and potential path of cryptic invasion of Pomacea canaliculata and P. maculata across Taiwan to aid in improved mitigation approaches. The present investigation conducted a nationwide survey with 254 samples collected from 41 locations in 14 counties or cities across Taiwan. We identified P. canaliculata and P. maculata based on mitochondrial COI and compared their genetic diversity across Taiwan, as well as other introduced and native countries (based on publicly available COI data) to understand the possible paths of invasion to Taiwan. Based on mitochondrial COI barcoding, sympatric and heterogeneous distributions of invasive P. canaliculata and P. maculata were noted. Our haplotype analysis and mismatch distribution results suggested multiple introductions of P. canaliculata in Taiwan was likely originated directly from Argentina, whereas P. maculata was probably introduced from a single, or a few, introduction event(s) from Argentina and Brazil. Our population genetic data further demonstrated a higher haplotype and genetic diversity for P. canaliculata and P. maculata in Taiwan compared to other introduced regions. Based on our current understanding, the establishment of P. canaliculata and P. maculata is alarming and widespread beyond geopolitical borders, requiring a concerted and expedited national and international invasive species mitigation program. © 2024 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.

关键词： agricultural pest biological invasion DNA barcoding golden apple snails mitochondrial COI Pomacea population genetics

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Warm dense matter simulation via electron temperature dependent deep potential molecular dynamics

arXiv

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arXiv 2019年

作者： Zhang, Yuzhi Gao, Chang Zhang, Linfeng Wang, Han Chen, Mohan Center for Applied Physics and Technology HEDPS College of Engineering Peking University Beijing100871 China Beijing Institute of Big Data Research Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China

Simulating warm dense matter that undergoes a wide range of temperatures and densities is challenging. Predictive theoretical models, such as quantum-mechanics-based first-principles molecular dynamics (FPMD), require a huge amount of computational resources. Herein, we propose a deep learning based scheme, called electron temperature dependent deep potential molecular dynamics (TDDPMD), for efficiently simulating warm dense matter with the accuracy of FPMD. The TDDPMD simulation is several orders of magnitudes faster than FPMD, and, unlike FPMD, its efficiency is not affected by the electron temperature. We apply the TDDPMD scheme to beryllium (Be) in a wide range of temperatures (0.4 to 2500 eV) and densities (3.50 to 8.25 g/cm3). Our results demonstrate that the TDDPMD method not only accurately reproduces the structural properties of Be along the principal Hugoniot curve at the FPMD level, but also yields even more reliable diffusion coefficients than typical FPMD simulations due to its ability to simulate larger systems with longer time. Copyright © 2019, The Authors. All rights reserved.

关键词： Molecular dynamics

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GLOBAL SOLUTIONS TO THE SUPERCOOLED STEFAN PROBLEM WITH BLOW-UPS: REGULARITY AND UNIQUENESS

arXiv

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arXiv 2019年

作者： Delarue, François Nadtochiy, Sergey Shkolnikov, Mykhaylo Université Côte d’Azur CNRS Laboratoire J.A. Dieudonné Nice France Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States ORFE Department Bendheim Center for Finance and Program in Applied & Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the freezing rate. We provide a complete description of such solutions, by relating the temperature distribution in the liquid to the regularity of the ice growth process. The latter is shown to transition between (i) continuous differentiability, (ii) Hölder continuity, and (iii) discontinuity. In particular, in the second regime we rediscover the square root behavior of the growth process pointed out by Stefan in his seminal paper [Ste89] from 1889 for the ordinary Stefan problem. In our second main theorem, we establish the uniqueness of the global solutions, a first result of this kind in the context of growth processes with singular self-excitation when blow-ups are *** Codes 80A22, 35B44, 60H30, 35B05 Copyright © 2019, The Authors. All rights reserved.

关键词： Supercooling

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Exploring Modified Gravity: Constraints on the μ and Σ Parametrization with WMAP, ACT, and SPT

arXiv

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arXiv 2023年

作者： Andrade, Uendert Capistrano, Abraão J.S. Di Valentino, Eleonora Nunes, Rafael C. Leinweber Center for Theoretical Physics University of Michigan 450 Church Street Ann ArborMI48109-1040 United States Department of Physics College of Literature Science and the Arts University of Michigan 450 Church Street Ann ArborMI48109-1040 United States Observatório Nacional RJ Rio de Janeiro20921-400 Brazil Universidade Federal do Paraná PR Palotina85950-000 Brazil Applied physics graduation program UNILA PR Foz do Iguaçu85867-670 Brazil School of Mathematics and Statistics University of Sheffield United Kingdom Instituto de Física Universidade Federal do Rio Grande do Sul Porto Alegre RS 91501-970 Brazil Divisão de Astrofísica Instituto Nacional de Pesquisas Espaciais Avenida dos Astronautas 1758 SP São José dos Campos12227-010 Brazil

The cosmic acceleration problem remains one of the most significant challenges in cosmology. One of the proposed solutions to this problem is the modification of gravity on large scales. In this paper, we explore the well-known μ-Σ parametrization scenarios and confront them with observational data, including the cosmic microwave background (CMB) radiation from the Wilkinson Microwave Anisotropy Probe (WMAP), Atacama Cosmology Telescope (ACT), and South Pole Telescope (SPT), as well as large-scale structure data from the Sloan Digital Sky Survey (SDSS: BAO+RSD) and Pantheon Supernovae (SN) catalog. We employ a Bayesian framework to constrain the model parameters and discuss the implications of our results on the viability of modified gravity theories. Our analysis reveals the strengths and limitations of the μ-Σ parametrization and provides valuable insights into the nature of gravity on cosmological scales. From the joint analysis of the ACT + WMAP + SDSS + SN, we find μ0 − 1 = 0.02 ± 0.19 and Σ0 − 1 = 0.021 ± 0.068 at 68% CL. In light of the SPT + WMAP + SDSS + SN, we find μ0 − 1 = 0.07 ± 0.18 and Σ0 − 1 = −0.009+−0007811 at 68% CL. In all the analyses carried out, we do not find any deviations from the theory of general relativity. Our results represent an observational update on the well-known μ-Σ parameterization in view of current CMB data, independent and competitive with the constraints obtained with the Planck data. Copyright © 2023, The Authors. All rights reserved.

关键词： Telescopes

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Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations

arXiv

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arXiv 2019年

作者： Kobak, Dmitry Linderman, George Steinerberger, Stefan Kluger, Yuval Berens, Philipp Institute for Ophthalmic Research University of Tübingen Germany Applied Mathematics Program Yale University New Haven United States Department of Mathematics Yale University New Haven United States Department of Pathology Yale School of Medicine New Haven United States

T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient implementation of t-SNE for a t-distribution kernel with an arbitrary degree of freedom v, with v → ∞ corresponding to SNE and v = 1 corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that v Copyright © 2019, The Authors. All rights reserved.

关键词： Data visualization

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ON THE MOTION OF CURVED DISLOCATIONS IN THREE DIMENSIONS: SIMPLIFIED LINEARIZED ELASTICITY

arXiv

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arXiv 2020年

作者： Fonseca, Irene Ginster, Janusz Wojtowytsch, Stephan Department of Mathematical Sciences Carnegie-Mellon University 5000 Forbes Avenue PittsburghPA15213 United States Institut für Mathematik Humboldt-Universität zu Berlin Rudower Chaussee 25 Berlin12489 Germany Program in Applied and Computational Mathematics Princeton University 205 Fine Hall PrincetonNJ08544 United States

It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the negative gradient of the elastic energy asymptotically approaches the mean curvature of the curve as the cutoff radius converges to zero. Rigorous error bounds in Hölder spaces are provided. As an application, convergence of dislocations moving by the gradient flow of the elastic energy to dislocations moving by the gradient flow of the arclength functional, when the motion law is given by an H1-type dissipation, and convergence to curve shortening flow in co-dimension 2 for the usual L2-dissipation is established. In the second scenario, existence and regularity are assumed while the H1-gradient flow is treated in full generality (for short time). The methods developed here are a blueprint for the more physical setting of linearized isotropic *** Codes 35K93, 35Q74, 74N05 Copyright © 2020, The Authors. All rights reserved.

关键词： Elasticity

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The replicator dynamics for multilevel selection in evolutionary games

arXiv

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arXiv 2018年

作者： Cooney, Daniel B. Program in Applied and Computational Mathematics Princeton University

We consider a stochastic model for evolution of group-structured populations in which interactions between group members correspond to the Prisoner’s Dilemma or the Hawk-Dove game. Selection operates at two organization levels: individuals compete with peer group members based on individual payoff, while groups also compete with other groups based on average payoff of group members. In the Prisoner’s Dilemma, this creates a tension between the two levels of selection, as defectors are favored at the individual level, whereas groups with at least some cooperators outperform groups of defectors at the between-group level. In the limit of infinite group size and infinite number of groups, we derive a non-local PDE that describes the probability distribution of group compositions in the population. For special families of payoff matrices, we characterize the long-time behavior of solutions of our equation, finding a threshold intensity of between-group selection required to sustain density steady-states and the survival of cooperation. When all-cooperator groups are most fit, the average and most abundant group compositions at steady-state range from featuring all-defector groups when individual-level selection dominates to featuring all-cooperator groups when group-level selection dominates. When the most fit groups have a mix of cooperators and defectors, then the average and most abundant group compositions always feature a smaller fraction of cooperators than required for the optimal mix, even in the limit where group-level selection is infinitely stronger than individual-level selection. In such cases, the conflict between the two levels of selection cannot be decoupled, and cooperation cannot be sustained at all in the case where between-group competition favors an even mix of cooperators and *** Codes 92D25, 91A22, 35F20 Copyright © 2018, The Authors. All rights reserved.

关键词： Probability distributions

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