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arXiv 2021年

作者： Chini, Gregory P. Michel, Guillaume Julien, Keith Rocha, Cesar B. Caulfield, Colm-Cille P. Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Institut Jean Le Rond d’Alembert Sorbonne Université CNRS UMR 7190 ParisF-75005 France Department of Applied Mathematics University of Colorado BoulderCO80309 United States Department of Marine Sciences University of Connecticut StorrsCT06269 United States BP Institute Department of Applied Mathematics & Theoretical Physics Cambridge University CambridgeCB3 0WA United Kingdom

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly-varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow-fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly-evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. Algorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parameterizations. Copyright © 2021, The Authors. All rights reserved.

关键词： Asymptotic analysis

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Correction: Unbiased and multilevel methods for a class of diffusions partially observed via marked point processes

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Statistics and Computing 2024年第6期34卷 1-1页

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

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Prediction and Prevention of Pandemics via Graphical Model Inference and Convex programming

arXiv

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arXiv 2021年

作者： Krechetov, Mikhail Sikaroudi, Amir Mohammad Esmaieeli Efrat, Alon Polishchuk, Valentin Chertkov, Michael Skolkovo Institute of Science and Technology Moscow121205 Russia University of Arizona Department of Computer Science TucsonAZ85721 United States University of Arizona Program in Applied Mathematics TucsonAZ85721 United States Linköping Univeristy Communications and Transport Systems Norrkoping60174 Sweden University of Arizona Department of Mathematics TucsonAZ85721 United States

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges of immense social impact which have not been adequately addressed (1) Inference Challenge: assuming that there are N census blocks (nodes) in the city, and given an initial infection at any set of nodes, e.g. any N of possible single node infections, any N(N-1)=2 of possible two node infections, etc, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge: What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census tract and each edge factor represents the strength of the pairwise interaction between a pair of nodes, e.g. representing the inter-node travel, road closure and related, and each local bias/field represents the community level of immunization, acceptance of the social distance and mask wearing practice, etc. Resolving the Inference Challenge requires finding the Maximum-A-Posteriory (MAP), i.e. most probable, state of the Ising Model constrained to the set of initially infected nodes. (An infected node is in the +1 state and a node which remained safe is in the-1 state.) We show that almost all attractive Ising Models on dense graphs result in either of the two possibilities (modes) for the MAP state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected (susceptible). This bi-modal solution of the Inference Challenge allows us to re-sta

关键词： Ising model

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Flexibility and rigidity in steady fluid motion

arXiv

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arXiv 2020年

作者： Constantin, Peter Drivas, Theodore D. Ginsberg, Daniel Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Stony Brook University Stony BrookNY11794 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol'd stable solutions are shown to be structurally stable. Copyright © 2020, The Authors. All rights reserved.

关键词： Rigidity

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mechanoChemML: A software library for machine learning in computational materials physics

arXiv

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arXiv 2021年

作者： Zhang, X. Teichert, G.H. Wang, Z. Duschenes, M. Srivastava, Siddhartha Livingston, E. Holber, J. Shojaei, M. Faghih Sundararajan, A. Garikipati, K. Department of Mechanical Engineering University of Michigan United States Applied Physics Program University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States

We present mechanoChemML, a machine learning software library for computational materials physics. mechanoChemML is designed to function as an interface between platforms that are widely used for machine learning on one hand, and others for solution of partial differential equations-based models of physics. Of special interest here, and the focus of mechanoChemML, are applications to computational materials physics. These typically feature the coupled solution of material transport, reaction, phase transformation, mechanics, heat transport and electrochemistry. Central to the organization of mechanoChemML are machine learning workflows that arise in the context of data-driven computational materials physics. The mechanoChemML code structure is described, the machine learning workflows are laid out and their application to the solution of several problems in materials physics is outlined. © 2021, CC BY-NC-SA.

关键词： Partial differential equations

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Understanding degeneracy of two-point correlation functions via debye random media

arXiv

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arXiv 2021年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 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 PrincetonNJ08544 United States

It is well-known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function S2(r) is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media, which are entirely defined by a purely exponentially decaying two-point correlation function S2(r). In this work, we consider three different classes of Debye random media. First, we generate the "most probable" class using the Yeong-Torquato construction algorithm [Yeong and Torquato, Phys. Rev. E, 57, 495 (1998)]. A second class of Debye random media is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized in the first three space dimensions by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct Debye random media that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of Debye random media from one another by ascertaining their other statistical descriptors, including the pore-size, surface correlation, chordlength probability density, and lineal-path functions. We also compare and contrast the percolation thresholds as well as the diffusion and fluid transport properties of these degenerate Debye random media. We find that these three classes of Debye random media are generally distinguished by the aforementioned descriptors and their microstructures are also visually distinct from one another. Our work further confirms the well-known fact that scattering information is insufficient to determine the effective physical properties of two-phase media. Additionally, our findings demonstrate the importance of the other two-point descriptors considered here in the design of materials with a spectrum of physical properties. © 2021, CC BY-SA.

关键词： Random processes

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Sensitivity Analysis of Wind Energy Resources with Bayesian non-Gaussian and nonstationary Functional ANOVA

arXiv

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arXiv 2021年

作者： Zhang, Jiachen Crippa, Paola Genton, Marc G. Castruccio, Stefano Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Civid and Environmental Engineering and Geoscience University of Notre Dame United States Statistics Program King Abdullah University of Science and Technology Saudi Arabia

The transition from non-renewable to renewable energies represents a global societal challenge, and developing a sustainable energy portfolio is an especially daunting task for developing countries where little to no information is available regarding the abundance of renewable resources such as wind. Weather model simulations are key to obtain such information when observational data are scarce and sparse over a country as large and geographically diverse as Saudi Arabia. However, output from such models is uncertain, as it depends on inputs such as the parametrization of the physical processes and the spatial resolution of the simulated domain. In such situations, a sensitivity analysis must be performed and the input may have a spatially heterogeneous influence of wind. In this work, we propose a latent Gaussian functional analysis of variance (ANOVA) model that relies on a nonstationary Gaussian Markov random field approximation of a continuous latent process. The proposed approach is able to capture the local sensitivity of Gaussian and non-Gaussian wind characteristics such as speed and threshold exceedances over a large simulation domain, and a continuous underlying process also allows us to assess the effect of different spatial resolutions. Our results indicate that (1) the non-local planetary boundary layer scheme and high spatial resolution are both instrumental in capturing wind speed and energy (especially over complex mountainous terrain), and (2) the impact of planetary boundary layer scheme and resolution on Saudi Arabia’s planned wind farms is small (at most 1.4%). Thus, our results lend support for the construction of these wind farms in the next decade. © 2021, CC BY-NC-ND.

关键词： Sensitivity analysis

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Ecumenical modal logic

arXiv

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arXiv 2020年

作者： Marin, Sonia Pereira, Luiz Carlos Pimentel, Elaine Sales, Emerson Department of Computer Science University College London United Kingdom Philosophy Department PUC-Rio Brazil Department of Mathematics UFRN Brazil Graduate Program of Applied Mathematics and Statistics UFRN Brazil

The discussion about how to put together Gentzen's systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called Ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz' system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz' main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In a recent work, Ecumenical sequent calculi and a nested system were presented, and some very interesting proof theoretical properties of the systems were established. In this work we extend Prawitz' Ecumenical idea to alethic *** Codes 03B45, 03F03 Copyright © 2020, The Authors. All rights reserved.

关键词： Computer circuits

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Assessment of Gamma and Neutron Dose of Optimizing the Radiation Protection in TRIGA 2000 BATAN Bandung. 6

Assessment of Gamma and Neutron Dose of Optimizing the Radia...

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6th International Conference on Advances in Nuclear Science and Engineering, ICANSE 2018

作者： Oméga, Rakotovao Lovanantenaina Permana, Sidik Oetami, Rini Heroe Rasito Master Program of Physics Department Faculty of Mathematics and Natural Science Bandung Institute of Technology Jalan Ganesha 10 Bandung40132 Indonesia Nuclear Physics Laboratory Physics Department Faculty of Mathematics and Natural Science Bandung Institute of Technology Jalan Ganesha 10 Bandung40132 Indonesia Center for Science and Applied Nuclear Technology National Nuclear Energy Agency Jl. Tamansari 71 Bandung Indonesia

The TRIGA 2000 reactor is a nuclear installation which is operated at 1000 kW. Gamma and neutron radiation exposure will contribute to occupational doses that will be received by operators and other radiation workers. To maintain the safety of radiation workers, assessment of gamma and neutron radiation is needed in the TRIGA 2000 reactor. survey in the hall reactor using the RTD 30 and RadEye NL detectors. In addition to the direct measurement, calculations are also carried out with simulation data dose using Monte Carlo MCNPX for the calculation and followed by PHITS to get the graphical dose distribution of gamma and neutron. The study will focus on the assessment of the diffusion Gamma and neutron doses by doing the measurement and simulation data collect for the aim of the optimization of the Radiation protection policy in the reactor TRIGA 2000 Bandung. The result of the measurement is shown with graph in different power taken during the measurement and the simulation is the graphical distribution dose of gamma and neutron using PHITS code. A preventive dose reduction technique, worker and publics protection elaborate to optimise the Radiation protection program. © 2020 Published under licence by IOP Publishing Ltd.

关键词： Monte Carlo methods

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Simulating Cardiac Fluid Dynamics in the Human Heart

arXiv

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arXiv 2023年

作者： Davey, Marshall Puelz, Charles Rossi, Simone Smith, Margaret Anne Wells, David R. Sturgeon, Gregory M. Segars, W. Paul Vavalle, John P. Peskin, Charles S. Griffith, Boyce E. University of North Carolina Chapel HillNC United States Department of Pediatrics-Cardiology Baylor College of Medicine Texas Children’s Hospital HoustonTX United States Department of Mathematics University North Carolina Chapel HillNC United States Department of Radiology Duke University Medical Center DurhamNC United States Division of Cardiology Department of Medicine University of North Carolina School of Medicine Chapel HillNC United States Courant Institute of Mathematical Sciences New York University New YorkNY United States Departments of Mathematics and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC 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

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions. However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the cardiac valves are limited in their abilities to predict valve performance, resolve fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac fluid dynamics in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart’s microstructure. Further, it is the first fluid-structure interaction model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and predicts fine-scale flow features. None of these outputs are prescribed;instead, they emerge from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical devices or clinical interventions. They also can serve as platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients. Copyright © 2023, The Authors. All rights reserved.

关键词： Heart

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