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CONVERGENCE OF A TIME-STEPPING SCHEME TO THE FREE BOUNDARY IN THE SUPERCOOLED STEFAN PROBLEM

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arXiv 2020年

作者： Kaushansky, Vadim Reisinger, Christoph Shkolnikov, Mykhaylo Song, Zhuo Qun Department of Mathematics University of California Los AngelesCA90095 United States Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter OxfordOX2 6GG United Kingdom ORFE Department Bendheim Center for Finance and Program in Applied & Computational Mathematics Princeton University Princeton NJ08544 United States Department of Mathematics Princeton University Princeton NJ08544 United States

The supercooled Stefan problem and its variants describe the freezing of a supercooled liquid in physics, as well as the large system limits of systemic risk models in finance and of integrate-and-fire models in neuroscience. Adopting the physics terminology, the supercooled Stefan problem is known to feature a finite-time blow-up of the freezing rate for a wide range of initial temperature distributions in the liquid. Such a blow-up can result in a discontinuity of the liquid-solid boundary. In this paper, we prove that the natural Euler time-stepping scheme applied to a probabilistic formulation of the supercooled Stefan problem converges to the liquid-solid boundary of its physical solution globally in time, in the Skorokhod M1 topology. In the course of the proof, we give an explicit bound on the rate of local convergence for the time-stepping scheme. We also run numerical tests to compare our theoretical results to the practically observed convergence *** Codes 80A22, 35B44, 65N20, 60H30 Copyright © 2020, The Authors. All rights reserved.

关键词： Supercooling

DeePN2: A deep learning-based non-Newtonian hydrodynamic model

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arXiv 2021年

作者： Fang, Lidong Ge, Pei Zhang, Lei Weinan, E. Lei, Huan Department of Computational Mathematics Science and Engineering Michigan State University MI48824 United States School of Mathematical Sciences Institute of Natural Sciences and MOE-LSC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing100080 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States Department of Statistics and Probability Michigan State University MI48824 United States

A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying micro-scale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure and heterogeneous interaction. DeePN2, a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN2 using more complex micro-structural models. We show that DeePN2 can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention. © 2021, CC BY.

关键词： Non Newtonian flow

Simultaneous tracking of movement and gene expression in multiple Drosophila melanogaster flies using GFP and DsRED fluorescent reporter transgenes

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BMC Research Notes 2009年第1期2卷 58-58页

作者： Grover, Dhruv Yang, Junsheng Ford, Daniel Tavaré, Simon Tower, John Molecular and Computational Biology Program Department of Biological Sciences University of Southern California Los Angeles CA 90089-2910 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge CB3 0WA United Kingdom

Background. Fluorescent proteins such as GFP (Green Fluorescent Protein) and DsRED (Discosoma *** Fluorescent Protein) are often used as reporter molecules for transgene expression in Drosophila and other species. We have recently reported methods that allow simultaneous tracking of animal movement and GFP expression in real time, however the assay was limited to single animals and a single transgene. Numerous studies would be facilitated by methods that allow for assay of multiple animals and multiple transgenes. Findings. Here we report an improved fly video tracking system that allows multiple transgenic flies to be tracked simultaneously using visible light, GFP fluorescence and DsRED fluorescence. The movement of multiple flies could be accurately tracked at real time rates, while simultaneously assaying the expression level of two different transgenes marked with GFP and DsRED. The individual flies could be accurately tracked and distinguished even during periods when transgene fluorescence was undetected. For example, characteristic patterns of hsp70 and hsp22 transgene induction could be simultaneously quantified and correlated with animal movement in aging flies, and as groups of flies died due to dessication/starvation. Conclusion. The improved methods allow for more efficient assay of the correlation between gene expression, behavior, aging and mortality: multiple animals can be assayed with simultaneous quantification of multiple transgenes using GFP and DsRED fluorescence. These methods should allow for increased flexibility in experimental designs. For example, in the future it should be possible to use gene expression levels to predict remaining life span more accurately, and to quantify gene expression changes caused by interactions between animals in real time. © 2009 Tower et al.

关键词： Green Fluorescent Protein Extended Kalman Filter Green Fluorescent Protein Expression Green Fluorescent Protein Fluorescence Daily Activity Pattern

Coarse-graining conformational dynamics with multi-dimensional generalized Langevin equation: how, when, and why

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arXiv 2024年

作者： Xie, Pinchen Qiu, Yunrui Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry University of Wisconsin-Madison MadisonWI53706 United States AI for Science Institute Beijing100080 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100084 China

A data-driven ab initio generalized Langevin equation (AIGLE) approach is developed to learn and simulate high-dimensional, heterogeneous, coarse-grained conformational dynamics. Constrained by the fluctuation-dissipation theorem, the approach can build coarse-grained models in dynamical consistency with all-atom molecular dynamics. We also propose practical criteria for AIGLE to enforce long-term dynamical consistency. Case studies of a toy polymer, with 20 coarse-grained sites, and the alanine dipeptide, with two dihedral angles, elucidate why one should adopt AIGLE or its Markovian limit for modeling coarse-grained conformational dynamics in practice. © 2024, CC BY.

关键词： Coarse-grained modeling

A non-Gaussian spatio-temporal model for daily wind speeds based on a multivariate skew-t distribution

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arXiv 2017年

作者： Tagle, Felipe Castruccio, Stefano Crippa, Paola Genton, Marc G. Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre DameIN46556 United States Statistics Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

Facing increasing domestic energy consumption from population growth and industrialization, Saudi Arabia is aiming to reduce its reliance on fossil fuels and to broaden its energy mix by expanding investment in renewable energy sources, including wind energy. A preliminary task in the development of wind energy infrastructure is the assessment of wind energy potential, a key aspect of which is the characterization of its spatio-temporal behavior. In this study we examine the impact of internal climate variability on seasonal wind power density uctuations over Saudi Arabia using 30 simulations from the Large Ensemble Project (LENS) developed at the National Center for Atmospheric Research. Furthermore, a spatio-temporal model for daily wind speed is proposed with neighbor-based cross-temporal dependence, and a multivariate skewt distribution to capture the spatial patterns of higher order moments. The model can be used to generate synthetic time series over the entire spatial domain that adequately reproduce the internal variability of the LENS dataset. Copyright © 2017, The Authors. All rights reserved.

关键词： Wind power

Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime

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arXiv 2023年

作者： Kim, Jaeuk Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Torquato and Kim [Phys. Rev. X 11, 296 021002 (2021)] derived exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor Εe(kq, ω) that treat general three-dimensional (3D) two-phase composite microstructures, which are valid well beyond the long-wavelength regime. Here, we demonstrate that truncating this general rapidly converging expansion at the two- and three-point levels is a powerful theoretical tool from which one can extract accurate approximations suited for various microstructural symmetries. Among other results, we show that such truncations yield closed-form formulas applicable to transverse polarization in layered media and transverse magnetic polarization in transversely isotropic media, respectively. We apply these formulas to estimate Εe(kq, ω) for models of 3D disordered hyperuniform layered and transversely isotropic media: nonstealthy hyperuniform media and stealthy hyperuniform media. In particular, we show that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (trivially implying no Anderson localization, in principle) within finite wave number intervals through the third-order terms. For all models considered here, we validate that the second-order formulas, which depend on the spectral density, are already very accurate well beyond the long-wavelength regime by showing very good agreement with the finite-difference time-domain (FDTD) simulations. The high predictive power of the second-order formula is due to the fact that higher-order contributions are negligibly small, implying that it very accurately approximates multiple scattering through all orders. This implies that there can be no Anderson localization within the predicted perfect transparency interval in stealthy hyperuniform layered and transversely isotropic media in practice because the localization length (associated with only possibly negligibly small higher-order contributions) should be very large compar

关键词： Spectral density

Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials

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arXiv 2024年

作者： Torquato, Salvatore Kim, Jaeuk Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Three-dimensional (3D) bicontinuous two-phase materials are increasingly gaining interest because of their unique multifunctional characteristics and advancements in techniques to fabricate them. Because of their complex topological and structural properties, it still has been nontrivial to develop explicit microstructure-dependent formulas to predict accurately their physical properties. A primary goal of the present paper is to ascertain various microstructural and transport characteristics of five different models of triply periodic bicontinuous porous materials at a porosity 1 = 1/2: those in which the two-phase interfaces are the Schwarz P, Schwarz D and Schoen G minimal surfaces as well as two different pore-channel structures. We ascertain their spectral densities, pore-size distribution functions, local volume-fraction variances, and hyperuniformity order metrics and then use this information to estimate certain effective steady-state as well as time-dependent transport properties via closed-form microstructure-property formulas. Specifically, the recently introduced time-dependent diffusion spreadability is determined exactly from the spectral density. Moreover, we accurately estimate the fluid permeability of such porous materials from a closed-form formula that depends on the second moment of the pore-size function and the formation factor, a measure of the tortuosity of the pore space, which is exactly obtained for the three minimal-surface structures. We also rigorously bound the permeability from above using the spectral density. For the five models with identical cubic unit cells, we find that the permeability, inverse of the specific surface, hyperuniformity order metric, pore-size second moment and long-time spreadability behavior are all positively correlated and rank order the structures in exactly the same way. We also conjecture what structures maximize the fluid permeability for arbitrary porosities and show that this conjecture must be true in

关键词： Pore size

Asymmetric profiles observed in the recombination of Bi79+: A benchmark for relativistic theories involving interference

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Physical Review A 2009年第1期80卷 014503-014503页

作者： Nobuyuki Nakamura Anthony P. Kavanagh Hirofumi Watanabe Hiroyuki A. Sakaue Yueming Li Daiji Kato Fred J. Currell Xiao-Min Tong Tsutomu Watanabe Shunsuke Ohtani Institute for Laser Science The University of Electro-Communications Chofu Tokyo 182-8585 Japan Queen’s University Belfast Belfast BT7 1NN United Kingdom Chubu University Kasugai-shi Aichi 487-8501 Japan National Institute for Fusion Science Toki Gifu 509-5292 Japan Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba Ibaraki 305-8573 Japan Center for Computational Sciences University of Tsukuba Tsukuba Ibaraki 305-8577 Japan

Asymmetric profiles have been observed in the recombination cross section of Be-like Bi obtained by measuring the electron energy dependence of the ion abundance ratio in an electron-beam ion trap. In contrast to the previous x-ray measurements, the present measurement gives the integrated recombination cross section with higher statistical quality, which provides a benchmark to test the relativistic theory involving the interference between the resonant and continuum states. The comparison with our theoretical study shows that the Breit interaction plays an important role in this case.

关键词： Benchmarking

Quantifying Phase Mixing and Separation Behaviors Across Length and Time Scales

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SSRN

SSRN 2024年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Phase mixing and separation phenomena abound in the formation of natural and synthetic material systems, including alloys, composites, granular media, geological media, complex fluids, and biological media. While characterizing phase mixing is critical to understanding material microstructure formation and physical properties, previous metrics that measure the degree of mixing in condensed phases often rely on empirical observation, are applicable only to certain microstructures, and/or fail to detect nontrivial changes in mixing with respect to length scale. To overcome these shortcomings, we introduce and study a mixing metric that is applicable to a broad spectrum of complex microstructures and leverages the hyperuniformity concept to provide a unifying framework to rank and classify mixing in materials across both length and time scales. Specifically, we employ the local phase volume-fraction/field-intensity variance [[EQUATION]] associated with a spherical sampling window of radius [[EQUATION]] at time [[EQUATION]] as our metric. We demonstrate that of [[EQUATION]] provides a sensitive measure of mixing across both length and time scales of a structurally diverse set of real and simulated material microstructures: exotic disordered multihyperuniform avian retina photoreceptor cell patterns, time-evolving spinodal decomposition patterns, and a model material mixed via the baker's transformation. We also describe how this metric can be used to guide future work on fabricating materials whose bulk properties can be controlled by tuning their mixing characteristics across length and time scales. © 2024, The Authors. All rights reserved.

关键词： Blending