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Reduced basis methods for numerical room acoustic simulations with parametrized boundaries

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arXiv 2021年

作者： Llopis, Hermes Sampedro Engsig-Karup, Allan P. Jeong, Cheol-Ho Pind, Finnur Hesthaven, Jan S. Rambøll Denmark Copenhagen Denmark Acoustic Technology Group Department of Electrical Engineering Technical University of Denmark Kongens Lyngby Denmark Scientific Computing Section Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark Treble Technologies Reykjavík Iceland Computational Mathematics and Simulation Science Ecole Polytechnique Federale de Lausanne Lausanne Switzerland

The use of model-based numerical simulation of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively and this is computationally expensive. We present a reduced basis methods (RBM) to achieve a computational cost reduction relative to a traditional full order model (FOM), for wave-based room acoustic simulations with parametrized boundary conditions. In this study, the FOM solver is based on the spectral element method, however other numerical methods could be applied. The RBM reduces the computational burden by solving the problem in a low-dimensional subspace for parametrized frequency-independent and frequency-dependent boundary conditions. The problem is formulated and solved in the Laplace domain, which ensures the stability of the reduced order model based on the RBM approach. We study the potential of the proposed RBM framework in terms of computational efficiency, accuracy and storage requirements and we show that the RBM leads to 100-fold speed-ups for a 2D case with an upper frequency of 2kHz and around 1000-fold speed-ups for an analogous 3D case with an upper frequency of 1kHz. While the FOM simulations needed to construct the ROM are expensive, we demonstrate that despite this cost, the ROM has a potential of three orders of magnitude faster than the FOM when four different boundary conditions are simulated per room surface. Moreover, results show that the storage model for the ROM is relatively high but affordable for the presented 2D and 3D cases. © 2021, CC BY-NC-ND.

关键词： Boundary conditions

Critical mass effect in evolutionary games triggered by zealots

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arXiv 2019年

作者： Cardillo, Alessio Masuda, Naoki Department of Engineering Mathematics University of Bristol BristolBS8 1UB United Kingdom Department of Computer Science and Mathematics University Rovira i Virgili TarragonaE-43007 Spain University of Zaragoza ZaragozaE-50018 Spain Department of Mathematics University at Buffalo BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program University at Buffalo State University of New York BuffaloNY14260-5030 United States

Tiny perturbations may trigger large responses in systems near criticality, shifting them across equilibria. Committed minorities are suggested to be responsible for the emergence of collective behaviors in many physical, social, and biological systems. Using evolutionary game theory, we address the question whether a finite fraction of zealots can drive the system to large-scale coordination. We find that a tipping point exists in coordination games, whereas the same phenomenon depends on the selection pressure, update rule, and network structure in other types of games. Our study paves the way to understand social systems driven by the individuals’ benefit in presence of zealots, such as human vaccination behavior or cooperative transports in animal groups. Copyright © 2019, The Authors. All rights reserved.

关键词： Game theory

On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model

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arXiv 2019年

作者： Ho, Lam Si Tung Dinh, Vu Matsen, Frederick A. Suchard, Marc A. Department of Mathematics and Statistics Dalhousie University HalifaxNS Canada Department of Mathematical Sciences University of Delaware Program in Computational Biology Fred Hutchinson Cancer Research Center Departments of Biomathematics Biostatistics and Human Genetics University of California Los Angeles United States

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we cannot appeal to this result because trait values of different species are correlated due to shared evolutionary history. In this paper, we consider a 2-state symmetric model for a single binary trait and investigate the theoretical properties of the MLE for the transition rate in the large-tree limit. Here, the large-tree limit is a theoretical scenario where the number of taxa increases to infinity and we can observe the trait values for all species. Specifically, we prove that the MLE converges to the true value under some regularity conditions. These conditions ensure that the tree shape is not too irregular, and holds for many practical scenarios such as trees with bounded edges, trees generated from the Yule (pure birth) process, and trees generated from the coalescent point process. Our result also provides an upper bound for the distance between the MLE and the true value. Copyright © 2019, The Authors. All rights reserved.

关键词： Maximum likelihood estimation

Effective-range approximation for surface states in one dimension

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Physical Review B 1986年第8期34卷 5205-5205页

作者： M. Steslicka M. Radny S. G. Davison Quantum Theory Group Department of Applied Mathematics and Department of Physics University of Waterloo Waterloo Ontario Canada N2L?1 and Guelph-Waterloo Program for Graduate Work in Physics University of Guelph Guelph Ontario Canada N1G?1

The effective-range approximation is adopted to study surface states of a linear array of scattering centers. It is shown that, depending on the values of the scattering length and effective range for the surface atom, two, one, or zero surface states can exist in the forbidden energy gap. The possibility of a smooth transition from true (stationary) surface states to virtual (decaying) states is discussed. A comparison is also made with the crystal-potential approach.

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Atomic stick-slip friction as a two-dimensional thermally activated process

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Physical Review B 2022年第16期105卷 165429-165429页

作者： Quanzhou Yao Jiawei Sun Xiaoying Zhuang Peter Wriggers Xi-Qiao Feng Qunyang Li Applied Mechanics Laboratory Department of Engineering Mechanics Tsinghua University Beijing 100084 China Chair of Computational Science and Simulation Technology Institute of Photonics Department of Mathematics and Physics Leibniz University Hannover 30167 Hannover Germany Institute for Continuum Mechanics Leibniz University Hannover Garbsen Germany State Key Laboratory of Tribology Tsinghua University Beijing 100084 China

Widely recognized as a thermally activated process, atomic stick-slip friction has been typically explained by Prandtl-Tomlinson model with thermal activation. Despite the limited success, theoretical predictions from the classic model are primarily based on a one-dimensional (1D) assumption, which is generally not compatible with real experiments that are two-dimensional (2D) in nature. In this letter, a theoretical model based on 2D transition state theory has been derived and confirmed to be able to capture the 2D slip kinetics in atomic-scale friction experiments on crystalline surface with a hexagonal energy landscape. Moreover, we propose a reduced scheme that enables extraction of intrinsic interfacial parameters from 2D experiments approximately using the traditional 1D model. The 2D model provides a theoretical tool for understanding the rich kinetics of atomic-scale friction or other phenomena involving higher dimensional transitions.

关键词： Friction Atomic force microscopy Thermal & statistical models

Isostables for stochastic oscillators

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arXiv 2021年

作者： Pérez-Cervera, Alberto Lindner, Benjamin Thomas, Peter J. National Research University Higher School of Economics Moscow Russia Instituto de Matemática Interdisciplinar Universidad Complutense de Madrid Madrid28040 Spain Bernstein Center for Computational Neuroscience Berlin Berlin Germany Department of Physics Humboldt University Berlin Germany Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University ClevelandOH44106 United States

Thomas and Lindner (2014, Phys. Rev. Lett.) defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having complex eigenvalue with least negative real part, of the backward Kolmogorov (or stochastic Koopman) operator. We complete the phase-amplitude description of noisy oscillators by defining the stochastic isostable coordinate as the eigenfunction with the least negative nontrivial real eigenvalue. Our results suggest a framework for stochastic limit cycle dynamics that encompasses noise-induced oscillations. Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Adsorption and dissociation of O2 at Be(0001): First-principles prediction of an energy barrier on the adiabatic potential energy surface

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Physical Review B 2009年第16期79卷 165416-165416页

作者： Ping Zhang Bo Sun Yu Yang LCP Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 People’s Republic of China Center for Applied Physics and Technology Peking University Beijing 100871 People’s Republic of China Department of Physics and Center for Advanced Study Tsinghua University Beijing 100084 People’s Republic of China

The adsorption and dissociation of O2 molecules at the Be(0001) surface is studied by using density-functional theory within the generalized gradient approximation and a supercell approach. The physisorbed and chemisorbed molecular precursor states are identified to be along the parallel and vertical channels, respectively. It is shown that the vertical channel with O2 being at the hcp hollow sites of the Be(0001) surface is the most stable channel for the molecular chemisorption. The electronic and magnetic properties of this most stable chemisorbed molecular state are studied, which show that the electrons transfer forth and back between the spin-resolved antibonding π∗ molecular orbitals and surface Be sp states. A distinct covalent weight in the molecule-metal bond is also shown. The dissociation of O2 is determined by calculating the adiabatic potential energy surfaces, wherein the T-Y channel is found to be the most stable and favorable for dissociative adsorption of O2. Remarkably, we predict that unlike other simple sp metal surfaces such as Al(111) and Mg(0001), the adiabatic dissociation process of O2 at Be(0001) is an activated type with a sizeable energy barrier.

关键词： adsorption aluminium beryllium charge exchange chemisorption density functional theory dissociation magnesium oxygen potential energy surfaces reaction kinetics theory surface chemistry

A new approach in image registration

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A new approach in image registration

IEEE International Workshop on Imaging Systems and Techniques (IST)

作者： Constantinos Spanakis Emmanuel Mathioudakis Nikos Kampanis Manolis Tsiknakis Kostas Marias Institute of Computer Science Foundation for Research and Technology Greece Technical University of Crete Chania Greece School of Mineral Resources Engineering Technical University of Crete Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Greece Department of Applied Informatics and Multimedia Technological Educational Institute of Crete

ISBN: (纸本)9781509018185

Evolutionary algorithms are metaheuristic algorithms that mimic biological mechanisms for the solution of optimization problems. They are widely used in many problems of engineering, including image analysis and pattern recognition. Such methods had shown added value in overcoming certain problems and limitations of more traditional methods and approaches. This is particularly interesting in Computer for designing faster and more accurate optimization methods. Despite recent advances in image registration, there is still room for improvement especially with the use of metaheuristic algorithms. In this paper, we present a novel method for solving the automated rigid registration problem by introducing a variant of the relatively new metaheuristic method called harmony search which shows promising results in difficult rigid registration cases.

关键词： Image registration Search problems Radiation detectors Mutual information Electronic mail Standards Optimization

Hard convex lens-shaped particles: Characterization of dense disordered packings

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Physical Review E 2019年第6期100卷 062902-062902页

作者： Giorgio Cinacchi Salvatore Torquato Departamento de Física Teórica de la Materia Condensada Instituto de Física de la Materia Condensada (IFIMAC) Instituto de Ciencias de Materiales “Nicolás Cabrera” Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco E-28049 Madrid Spain Department of Chemistry and Department of Physics Institute for the Science and Technology of Materials Program for Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is “optimal” in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction ϕMRJ≃0.73 [G. Cinacchi and S. Torquato, Soft Matter 14, 8205 (2018)]. This value is only a few percent lower than ϕDKP=0.76210⋯, the packing fraction of the corresponding densest-known crystalline (degenerate) packings [G. Cinacchi and S. Torquato, J. Chem. Phys. 143, 224506 (2015)]. By exploiting the appreciably reduced propensity that a system of such optimal lenses has to positionally and orientationally order, disordered packings of them are progressively generated by a Monte Carlo method–based procedure from the dilute equilibrium isotropic fluid phase to the dense nonequilibrium MRJ state. This allows us to closely monitor how the (micro)structure of these packings changes in the process of formation of the MRJ state. The gradual changes undergone by the many structural descriptors calculated here can coherently and consistently be traced back to the gradual increase in contacts between the hard particles until the isostatic mean value of ten contact neighbors per lens is reached at the effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres, the MRJ state of such optimal lenses is denser (less porous), more disordered, and rattler-free. This set of characteristics makes them good glass formers. It is possible that this conclusion may also hold for other hard convex uniaxial particles with a correspondingly similar aspect ratio, be they oblate or prolate, and that, by using suitable biaxial variants of them, that set of characteristics might further improve.

关键词： Granular packing Jamming Colloids Disordered systems Granular materials Lyotropic liquid crystals Monte Carlo methods