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arXiv 2020年

作者： Schleuss, Julia Smetana, Kathrin Institute for Computational and Applied Mathematics University of Münster Einsteinstr. 62 Münster48149 Germany Department of Mathematical Sciences Stevens Institute of Technology 1 Castle Point Terrace HobokenNJ07030 United States

We propose local space-time approximation spaces for parabolic problems that are optimal in the sense of Kolmogorov and may be employed in multiscale and domain decomposition methods. The diffusion coefficient can be arbitrarily rough in space and time. To construct local approximation spaces we consider a compact transfer operator that acts on the space of local solutions and covers the full time dimension. The optimal local spaces are then given by the left singular vectors of the transfer operator. To prove compactness of the latter we combine a suitable parabolic Caccioppoli inequality with the compactness theorem of Aubin-Lions. In contrast to the elliptic setting [I. Babuška and R. Lipton, Multiscale Model. Simul., 9 (2011), pp. 373-406] we need an additional regularity result to combine the two results. Furthermore, we employ the generalized finite element method to couple local spaces and construct an approximation of the global solution. Since our approach yields reduced space-time bases, the computation of the global approximation does not require a time stepping method and is thus computationally efficient. Moreover, we derive rigorous local and global a priori error bounds. In detail, we bound the global approximation error in a graph norm by the local errors in the L2(H1)-norm, noting that the space the transfer operator maps to is equipped with this norm. Numerical experiments demonstrate an exponential decay of the singular values of the transfer operator and the local and global approximation errors for problems with high contrast or multiscale structure regarding space and *** Codes 65M12, 65M15, 65M55, 65M60 Copyright © 2020, The Authors. All rights reserved.

关键词： Vector spaces

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PDE model for multi-patch epidemic models with migration and infection-age dependent infectivity

arXiv

引用

arXiv 2023年

作者： Pang, Guodong Pardoux, Étienne Department of Computational Applied Mathematics and Operations Research George R. Brown School of Engineering Rice University HoustonTX77005 United States Aix-Marseille Université CNRS I2M Marseille France

We study a stochastic epidemic model with multiple patches (locations), where individuals in each patch are categorized into three compartments, Susceptible, Infected and Recovered/Removed, and may migrate from one patch to another in any of the compartments. Each individual is associated with a random infectivity function which dictates the force of infection depending upon the age of infection (elapsed time since infection). We prove a functional law of large number for the epidemic evolution dynamics including the aggregate infectivity process, the numbers of susceptible and recovered individuals as well as the number of infected individuals at each time that have been infected for a certain amount of time. From the limits, we derive a PDE model for the density of the number of infected individuals with respect to the infection age, which is a system of linear PDE equations with a boundary condition that is determined by a set of integral equations. Copyright © 2023, The Authors. All rights reserved.

关键词： Integral equations

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Near-field simulations of pellet ablation for disruptions mitigation in tokamaks

arXiv

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arXiv 2020年

作者： Bosviel, Nicolas Parks, Paul B. Samulyak, Roman Department of Applied Mathematics and Statistics Stony Brook University Stony BrookNY United States General Atomics San DiegoCA United States Computational Science Initiative Brookhaven National Laboratory UptownNY United States

Detailed numerical studies of the ablation of a single neon pellet in the plasma disruption mitigation parameter space have been performed. Simulations were carried out using FronTier, a hydrodynamic and low magnetic Reynolds number MHD code with explicit tracking of material interfaces. FronTier’s physics models resolve the pellet surface ablation and the formation of a dense, cold cloud of ablated material, the deposition of energy from hot plasma electrons passing through the ablation cloud, expansion of the ablation cloud along magnetic field lines and the radiation losses. A local thermodynamic equilibrium model based on Saha equations has been used to resolve atomic processes in the cloud and Redlich-Kwong corrections to the ideal gas equation of state for cold and dense gases have been used near the pellet surface. The FronTier pellet code is the next generation of the code described in [R. Samulyak, T. Lu, P. Parks, Nuclear Fusion, (47) 2007, 103–118]. It has been validated against the semi-analytic improved Neutral Gas Shielding model in the 1D spherically symmetric approximation. Main results include quantification of the influence of atomic processes and Redlich-Kwong corrections on the pellet ablation in spherically symmetric approximation and verification of analytic scaling laws in a broad range of pellet and plasma parameters. Using axially symmetric MHD simulations, properties of ablation channels and the reduction of pellet ablation rates in magnetic fields of increasing strength have been studied. While the main emphasis has been given to neon pellets for the plasma disruption mitigation, selected results on deuterium fueling pellets have also been presented. Copyright © 2020, The Authors. All rights reserved.

关键词： Neon

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Fast decisions reflect biases, slow decisions do not

arXiv

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arXiv 2023年

作者： Linn, Samantha Lawley, Sean D. Karamched, Bhargav R. Kilpatrick, Zachary P. Josić, Krešimir Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics Florida State University TallahasseeFL32306 United States Institute of Molecular Biophysics Florida State University TallahasseeFL32306 United States Program in Neuroscience Florida State University TallahasseeFL32306 United States Department of Applied Mathematics University of Colorado Boulder BoulderCO80309 United States Department of Mathematics University of Houston HoustonTX77004 United States Department of Biology and Biochemistry University of Houston HoustonTX77004 United States

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in large groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased, and hence make better choices. We obtain asymptotic expressions in the large population limit that quantify how agents’ initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in non-trivial ways to determine the reliability of decisions in a group. © 2023, CC BY.

关键词： Reliability analysis

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Free time optimal control problems with time delays

Free time optimal control problems with time delays

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IEEE Annual Conference on Decision and Control

作者： Andrea Boccia Paola Falugi Helmut Maurer Richard B. Vinter Department of Electrical and Electronic Engineering Imperial College London Exhibition Road London SW7 2BT UK Institute of Computational and Applied Mathematics University of Munster Einsteinstrasse 62 D-48149 Munster Germany

ISBN: (纸本)9781467357159

Solutions to optimal control problems for retarded systems, on a fixed time interval, satisfy a form of the Maximum Principle, in which the co-state equation is an advanced differential equation. In this paper we present an extension of this well-known necessary condition of optimality, to cover situations in which the data is non-smooth, and the final time is free. The fact that the end-time is a choice variable is accommodated by an extra transversality condition. A traditional approach to deriving this extra condition is to reduce the free end-time problem to a fixed end-time problem by a parameterized change of the time variable. This approach is problematic for time delay problems because it introduces a parameter dependent time-delay that is not readily amenable to analysis;to avoid this difficulty we instead base our analysis on direct perturbation of the end-time. Formulae are derived for the gradient of the minimum cost as a function of the end-time. It is shown how these formulae can be exploited to construct two-stage algorithms for the computation of solutions to optimal retarded control problems with free-time, in which a sequence of fixed time problems are solved by means of Guinn's transformation, and the end-time is adjusted according to a rule based on the earlier derived gradient formulae for the minimum cost function. Numerical examples are presented.

关键词： Time Delays Optimal Control Maximum Principle Free Time Problems maximum principle Optimal control formula unoccupied time time variable

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Model for dynamical coherence in thin films of self-propelled microorganisms

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Physical Review E 2007年第4期75卷 040901(R)-040901(R)页

作者： Igor S. Aranson Andrey Sokolov John O. Kessler Raymond E. Goldstein Argonne National Laboratory 9700 South Cass Avenue Argonne Illinois 60439 USA Illinois Institute of Technology 3101 South Dearborn Street Chicago Illinois 60616 USA Department of Physics University of Arizona Tucson Arizona 85721 USA Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA BIO5 Institute University of Arizona Tucson Arizona 85721 USA Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road Cambridge CB3 0WA United Kingdom

Concentrated bacterial suspensions spontaneously develop transient spatiotemporal patterns of coherent locomotion whose correlation lengths greatly exceed the size of individual organisms. Continuum models have indicated that a state of uniform swimming order is linearly unstable at finite wavelengths, but have not addressed the nonlinear dynamics of the coherent state, with its biological implications for mixing, transport, and intercellular communication. We investigate a specific model incorporating hydrodynamic interactions in thin-film geometries and show by numerical studies that it displays large scale persistently recurring vortices, as actually observed.

关键词： ORDER DIFFUSION CELLS

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Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

arXiv

引用

arXiv 2024年

作者： Weinberg, Daniel Hull, Olivia A. Clary, Jacob M. Sundararaman, Ravishankar Vigil-Fowler, Derek Del Ben, Mauro Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Materials Chemical and Computational Science Directorate National Renewable Energy Laboratory GoldenCO United States Department of Materials Science and Engineering Rensselaer Polytechnic Institute TroyNY United States

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation. Copyright © 2024, The Authors. All rights reserved.

关键词： Supercomputers

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Optimizing Hammerstein-Wiener Model for Forecasting Confirmed Cases of Covid-19

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IAENG International Journal of applied mathematics 2022年第1期52卷 1页

作者： Abdullahi, Sunusi Bala Ibrahim, Abdulkarim Hassan Abubakar, Auwal Bala Kambheera, Abhiwat General Investigation Zonal Criminal Investigation Section Force Criminal Investigation and Intelligence Department Nigeria Police Abuja900211 Nigeria Department of Applied Mathematics King Mongkut’s University of Technology Thonburi Bangkok Thailand Department of Mathematical Sciences Faculty of Physical Sciences Bayero University Kano700241 Nigeria Mathematics and Computing Science Program Faculty of Science and Technology Phetchabun Rajabhat University Phetchabun 67000 Thailand

Noise poses challenge to nonlinear Hammerstein-Wiener (HW) subsystem model application, because HW subsystem need large number of parameter interactions. However, flexibility, soft computing, and automatic adjustment to dynamic observation for best model fitting make it potential for forecasting nonlinear data. In this article, we adopted improved HW inference from Levenberg-Marquardt optimization algorithm to optimize HW subsystem and to select best model parameters. Therefore, the adopted model is tested on COVID-19 confirmed reported cases, to estimate transmission rate of COVID-19 virus for period from 15th March 2020 to 29th April 2020. Model validation is carried out on small dataset, which outperforms some existing models. The adopted model is further evaluated using statistical metrics and reported best accuracy of 0.127 and 0.998 for Mean Absolute percentage error (MAPE) and coefficient of determination (R2) respectively, with best model complexity of 1.86. The obtained results are promising enough in predicting spread of COVID-19 virus and may inspire as guidance to relax lockdown restriction policies. © 2022, IAENG International Journal of applied mathematics. All Rights Reserved.

关键词： COVID-19

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The law x ≤ I(y, x) and the three main classes of fuzzy implications

The law x ≤ I(y, x) and the three main classes of fuzzy imp...

引用

IEEE International Conference on Fuzzy Systems

作者： Anderson P. Cruz Benjamin C. Bedregal Regivan H. N. Santiago Group of Computational Theory and Intelligence Rural Federal University of Semi-arid - UFERSA Group of Logic Language Information Theory and Applications - LoLITA Department of Informatics and Applied Mathematics - DIMAp Federal University of Rio Grande do Norte - UFRN

ISBN: (纸本)9781467315074

Properties valid on classical theory (Boolean laws) have been extended to fuzzy set theory. Such generalizations of Boolean laws (Boolean-like laws) are not always valid in any standard fuzzy set theory and this fact induced a wide investigation. In this paper we show the conditions that the Boolean-like law x ≤ I(y,x) holds in fuzzy logic. We focus the investigation on three main classes of fuzzy implications, namely: (S,N)-, R- and QL-implications. Further, we show that the operator I satisfies this Boolean-like law if, and only if, Φ-conjugate of I also satisfies it.

关键词： Fuzzy implication Boolean-like laws (S N)- R-and QL-implications Automorphisms fuzzy implication Fuzzy Set Theory Fuzzy If and only if Fuzzy logic Valid

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Spatial segregation in stage-structured populations with an application to Tribolium

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Journal of Biological Dynamics 2011年第5期5卷 398-409页

作者： Robertson, Suzanne L. Cushing, J.M. Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ 85721 United States Department of Mathematics University of Arizona Tucson AZ 85721 United States Mathematical Biosciences Institute The Ohio State University Columbus OH 43210 United States

Spatial segregation among life-cycle stages has been observed in many stage-structured species, including species of the flour beetle Tribolium. We investigate density-dependent dispersal of life-cycle stages as a possible mechanism responsible for this separation. We explore this hypothesis using stage-structured, integrodifference equation (IDE) models that incorporate density-dependent dispersal kernels. We first investigate mechanisms that can lead to spatial patterns in juvenile-adult IDE models. We show, via numerical simulation, that density-dependent dispersal can lead to the spatial segregation of life-cycle stages in the sense that each stage peaks in a different spatial location. We then construct a three-stage spatial model to describe the population dynamics of Tribolium castaneum and Tribolium confusum and assess density-dependent dispersal mechanisms that are able to explain spatial patterns that have been experimentally observed in these species. © 2011 Taylor & Francis.

关键词： Density-dependent dispersal Integrodifference equations Population dynamics Segregation of life-cycle stages Spatial patterns

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