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Critical dynamics in multicomponent lipid membranes

Physical Review E 2009年第2期80卷 020902(R)-020902(R)页

作者： Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes both in vivo and in vitro lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, the roles of membrane and exterior fluid hydrodynamics on domain formation kinetics have received less attention. A case in point is the impact of hydrodynamics on the dynamics of compositional heterogeneities in lipid membranes in the vicinity of a critical point. In this Rapid Communication it is argued that the asymptotic dynamic behavior of a lipid membrane system in the vicinity of a critical point is strongly influenced by hydrodynamic interactions. More specifically, a mode-coupling argument is developed which predicts a scaling behavior of lipid transport coefficients near the critical point for both symmetric and asymmetric bilayers immersed in a bulk fluid.

关键词： Hydrodynamics

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Parallel domain decomposition for simulation of large-scale power grids

Parallel domain decomposition for simulation of large-scale ...

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IEEE International Conference on Computer-Aided Design

作者： Kai Sun Quming Zhou Kartik Mohanram Danny C. Sorensen Department of Computational and Applied Mathematics Rice University Houston USA Department of Electrical and Computer Engineering Rice University Houston USA

This paper presents fully parallel domain decomposition (DO) techniques for efficient simulation of large-scale linear circuits such as power grids. DD techniques that use non-overlapping and overlapping partitioning of power grids are described in this paper. Simulation results show that with the proposed parallel DD framework, existing linear circuit simulators can be extended to handle large-scale power grids. Results for circuits with more than four million nodes indicate that parallel DD with LU factorization is most suitable for power grid simulation. However, for densely connected power grids, parallel DD with additive Schwarz preconditioning offers maximum scalability and best performance.

关键词： Large-scale systems Power grids computational modeling Circuit simulation Concurrent computing Linear circuits Power systems Grid computing Scalability Computer simulation

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Unified Variational Approach Description of Ground-State Phases of the Two-Dimensional Electron Gas

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Physical Review Letters 2024年第26期133卷 266504-266504页

作者： Conor Smith Yixiao Chen (陈一潇) Ryan Levy Yubo Yang (杨煜波) Miguel A. Morales Shiwei Zhang Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Electrical and Computer Engineering University of New Mexico Albuquerque New Mexico 87131 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different Ansätze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs=37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.

关键词： Wave functions

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Machine learning based non-Newtonian fluid model with molecular fidelity

arXiv

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arXiv 2020年

作者： Lei, Huan Wu, Lei Weinan, E. Department of Computational Mathematics Science & Engineering Department of Statistics & Probability Michigan State University MI48824 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Polymer solution is used as an example to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a new form of the objective tensor derivative. Numerical results demonstrate the accuracy of DeePN2. Copyright © 2020, The Authors. All rights reserved.

关键词： Viscous flow

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Local timestepping techniques using taylor expansion for modeling electromagnetic wave propagation with discontinuous galerkin-FEM

Local timestepping techniques using taylor expansion for mod...

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作者： Schomann, S. Gödel, N. Warburton, T. Clemens, M. Department for Theory of Electrical Engineering and Computational Electromagnetics Helmut-Schmidt-University University of the Federal Armed Forces Hamburg Hamburg 22008 Germany Department of Computational and Applied Mathematics Rice University Houston TX 77005-1892 United States Department for Electromagnetic Theory Bergische Universität Wuppertal Wuppertal 42119 Germany

A time integration scheme based on Taylor expansion using the higher order discontinuous Galerkin finite element method (DG-FEM) is presented. The special properties of the scheme allow for using explicit time integration. Local timestepping techniques are proposed, which are efficient whenever large ratios in element size affect the performance of global explicit time integration schemes. The algorithm is introduced, its characteristics are analyzed, and benchmarks are presented. © 2006 IEEE.

关键词： Time domain analysis

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Minimum time control of helicopter UAVs using computational dynamic optimization

Minimum time control of helicopter UAVs using computational ...

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9th IEEE International Conference on Control and Automation, ICCA 2011

作者： Tang, K. Wang, B. Kang, W. Chen, B. Internship Program Naval Postgraduate School Monterey CA 93943 United States Department of Electrical and Computer Engineering National University of Singapore Singapore 117576 Singapore Department of Applied Mathematics Naval Postgraduate School Monterey CA 93943 United States

ISBN: (纸本)9781457714757

This paper focuses on the problem of minimum time trajectory planning for helicopter UAVs. It is formulated as a nonlinear optimal control subject to the dynamics and limitations of helicopter UAVs. The dynamical system is defined by a set of fifteen states nonlinear differential equations developed for HeLion, a UAV helicopter constructed in National University of Singapore (NUS). The problem is then solved numerically using pseudospectral method for dynamic optimization. The results show that minimum time trajectories are highly nonlinear that require complicated maneuvering. © 2011 IEEE.

关键词： Nonlinear equations

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Cryptocurrency Analysis using Machine Learning and Deep Learning

Cryptocurrency Analysis using Machine Learning and Deep Lear...

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2021 IEEE Signal Processing in Medicine and Biology Symposium, SPMB 2021

作者： Thomas, C. Watson, Z. Kim, M. Baidya, A. Lamsal, M. Chowdhury, M.H. Basnet, M. Poudel, K.N. East Central University Department of Mathematics and Computer Science AdaOK United States Middle Tennessee State University Computational Science Program MurfreesboroTN United States University of Memphis Department of Electrical and Computer Engineering MemphisTN United States Embry-Riddle Aeronautical University Department of Mathematics and Data Science FL United States

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A Family of Second-Order Energy-Stable Schemes for Cahn-Hilliard Type Equations

arXiv

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arXiv 2018年

作者： Dong, Suchuan Yang, Zhiguo Lin, Lianlei Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States School of Electrical Engineering and Automation Harbin Institute of Technology China

We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary variable, we approximate the system at the time step (n + θ) (n denoting the time step index and θ is a real-valued parameter), and devise a family of corresponding approximations that are second-order accurate and unconditionally energy stable. This family of approximations contains the often-used Crank-Nicolson scheme and the second-order backward differentiation formula as particular cases. We further develop an efficient solution algorithm for the resultant discrete system of equations to overcome the difficulty caused by the unknown scalar auxiliary variable. The final algorithm requires only the solution of four de-coupled individual Helmholtz type equations within each time step, which involve only constant and time-independent coefficient matrices that can be pre-computed. A number of numerical examples are presented to demonstrate the performance of the family of schemes developed herein. We note that this family of second-order approximations can be readily applied to devise energy-stable schemes for other types of gradient flows when combined with the auxiliary variable approaches. Copyright © 2018, The Authors. All rights reserved.

关键词： Free energy

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Numerical approximation of incompressible navier-stokes equations based on an auxiliary energy variable

arXiv

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arXiv 2018年

作者： Lin, Lianlei Dong, Suchuan Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States School of Electrical Engineering and Automation Harbin Institute of Technology China

We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and reformulating the Navier-Stokes equations into an equivalent system, the scheme satisfies a discrete energy stability property in terms of a modified energy and it allows for an efficient solution algorithm and implementation. Within each time step, the algorithm involves the computations of two pressure fields and two velocity fields by solving several de-coupled individual linear algebraic systems with constant coefficient matrices, together with the solution of a nonlinear algebraic equation about a scalar number involving a negligible cost. A number of numerical experiments are presented to demonstrate the accuracy and the performance of the presented algorithm. Copyright © 2018, The Authors. All rights reserved.

关键词： Viscous flow

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Predicting the friction angle of clays using a multi-layer perceptron neural network enhanced by yeo-johnson transformation and coral reefs optimization

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Journal of Rock Mechanics and Geotechnical engineering 2024年第10期16卷 3982-4003页

作者： Libing Yang Trung Nguyen-Thoi Trung-Tin Tran College of Civil Engineering and Architecture Hunan Institute of Science and TechnologyYueyang414006China Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh CityViet Nam Faculty of Mechanical-Electrical and Computer Engineering School of TechnologyVan Lang UniversityHo Chi Minh CityViet Nam Department of Information Technology Greenwich VietnamFPT UniversityDa Nang550000Viet Nam

The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering *** study addresses the importance of estimating the friction angle and presents the development of four soft computing models:YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and *** of all,the Yeo-Johnson(YJ)transformation technique was used to stabilize the variance of data and make it more suitable for parametric statistical models that assume normality and equal *** technique is expected to improve the accuracy of friction angle prediction *** friction angle prediction models then utilized multi-layer perceptron neural networks(MLPnet)and metaheuristic optimization algorithms to further enhance performance,including flower pollination algorithm(FPA),coral reefs optimization(CRO),ant colony optimization continuous(ACOC),and cuckoo search algorithm(CSA).The prediction models without the YJ technique,***-MLPnet,CRO-MLPnet,ACOC-MLPnet,and CSA-MLPnet,were then compared to those with the YJ technique,***-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and *** these,the YJ-CRO-MLPnet model demonstrated superior reliability,achieving an accuracy of up to 83%in predicting the friction angle of clay in practical engineering *** improvement is significant,as it represents an increase from 1.3%to approximately 20%compared to the models that did not utilize the YJ transformation technique.

关键词： Natural hazards Slope stability Friction angle Clay Soft computing models Geotechnical engineering

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