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A new phase-field approach to variational implicit solvation of charged molecules with the coulomb-field approximation

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arXiv 2017年

作者： Zhao, Yanxiang Ma, Yanping Sun, Hui Li, Bo Du, Qiang Department of Mathematics George Washington University 801 22nd St. NW Phillips 739 WashingtonDC20052 United States Department of Mathematics Loyola Marymount University 1 LMU drive Los AngelesCA90045 United States Department of Mathematics and Statistics California State University Long BeachCA90840-1001 United States Department of Mathematics and Quantitative Biology Graduate Program University of California San Diego 9500 Gilman Drive Mail code: 0112 La JollaCA92093-0112 United States Department of Applied Physics and Applied Mathematics Columbia University NY10027 United States

We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and electrostatic interaction energy that is described by the Coulomb-field approximation, all coupled together self-consistently through a phase field. By introducing a new phase-field term in the description of the solute-solvent van der Waals and electrostatic interactions, we can keep the phase-field values closer to those describing the solute and solvent regions, respectively, making it more accurate in the free-energy estimate. We first prove that our phase-field functionals Γ-converge to the corresponding sharp-interface limit. We then develop and implement an efficient and stable numerical method to solve the resulting gradient-flow equation to obtain equilibrium conformations and their associated free energies of the underlying charged molecular system. Our numerical method combines a linear splitting scheme, spectral discretization, and exponential time differencing Runge-Kutta approximations. Applications to the solvation of single ions and a two-plate system demonstrate that our new phase-field implementation improves the previous ones by achieving the localization of the system forces near the solute-solvent interface and maintaining more robustly the desirable hyperbolic tangent profile for even larger interfacial width. This work provides a scheme to resolve the possible unphysical feature of negative values in the phase-field function found in the previous phase-field modeling (cf. H. Sun, et al. J. Chem. Phys., 2015) of charged molecules with the Poisson-Boltzmann equation for the electrostatic interaction. Copyright © 2017, The Authors. All rights reserved.

关键词： Free energy

Coarse-grained descriptions of dynamics for networks with both intrinsic and structural heterogeneities

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arXiv 2017年

作者： Bertalan, Tom Wu, Yan Laing, Carlo William Gear, C. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University PrincetonNJ United States Department of Bioengineering University of California San DiegoCA United States Institute of Natural and Mathematical Sciences Massey University Auckland New Zealand Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and, ultimately, design. Here we propose and illustrate a systematic and powerful approach to obtaining good collective coarse-grained observables-variables successfully summarizing the detailed state of such networks. Finding such variables can naturally lead to successful reduced dynamic models for the networks. The main premise enabling our approach is the assumption that the behavior of a node in the network depends (after a short initial transient) on the node identity: a set of descriptors that quantify the node properties, whether intrinsic (e.g. parameters in the node evolution equations) or structural (imparted to the node by its connectivity in the particular network structure). The approach creates a natural link with modeling and "computational enabling technology" developed in the context of Uncertainty Quantification. In our case, however, we will not focus on ensembles of different realizations of a problem, each with parameters randomly selected from a distribution. We will instead study many coupled heterogeneous units, each characterized by randomly assigned (heterogeneous) parameter value(s). One could then coin the term Heterogeneity Quantification for this approach, which we illustrate through a model dynamic network consisting of coupled oscillators with one intrinsic heterogeneity (oscillator individual frequency) and one structural heterogeneity (oscillator degree in the undirected network). The computational implementation of the approach, its shortcomings and possible extensions are also discussed. Copyright © 2017, The Authors. All rights reserved.

关键词： Data mining

Fluctuating hydrodynamics of reactive liquid mixtures

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arXiv 2018年

作者： Kim, Changho Nonaka, Andy Bell, John B. Garcia, Alejandro L. Donev, Aleksandar Computational Research Division Lawrence Berkeley National Laboratory 1 Cyclotron Road BerkeleyCA94720 United States Applied Mathematics University of California Merced 5200 North Lake Road MercedqCA95343 United States Department of Physics and Astronomy San Jose State University 1 Washington Square San JoseCA95192 United States Courant Institute of Mathematical Sciences New York University 251 Mercer Street New YorkNY10012 United States

Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively-driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominate the initial growth of the instability. Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

Interactions between coherent twin boundaries and phase transition of iron under dynamic loading and unloading

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arXiv 2017年

作者： Wang, Kun Chen, Jun Zhang, Xueyang Zhu, Wenjun Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China Center for Applied Physics and Technology Peking University Beijing100071 China Department of Applied Physics School of Physics and Electronics Hunan University Changsha410082 China National Key Laboratory of Shock Wave and Detonation Physics Institute of Fluid Physics Mianyang621900 China

Under high pressures, phase transition, as well as deformation twins, are constantly reported in many BCC metals, whose interactions are of fundamental importance to understand strengthen mechanism of these metals under extreme conditions. However, the interactions between twins and phase transition in BCC metals are remain largely unexplored. In this work, interactions between coherent twin boundaries and α↔Ε phase transition of iron are investigated using both non- equilibrium molecular dynamics simulations and nudge elastic band method. Mechanisms of both twin-assisted phase transition and reverse phase transition are studied and orientation relationships between BCC and HCP phase are found to be 〈111¯〉BCC||〈1¯21¯0〉HCP and 〈11¯0〉BCC||〈0001〉HCP for both cases. The twin boundary corresponds to {101¯0}HCP after the phase transition. It is amazing that the reverse transition seems to be able to "memory" and recover the initial BCC twins. The memory would partly loss when plastic slips take place in the HCP phase before the reverse transition. In the recovered initial BCC twins, three major twin spacing are observed, which are well explained in terms of energy barriers of the transition from HCP phase to BCC twin. Besides, variant selection rule of the twin assisted phase transition is also discussed. The results of present work could be expected to give some clues for producing ultra-fine grain structure in materials exhibiting martensitic phase transition. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecular dynamics

On the one-dimensional nonlinear monodomain equations with moving controls

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arXiv 2017年

作者： Kunisch, Karl Souza, Diego A. Institut für Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universität Heinrichstraße 36 Graz8010 Austria Johann Radon Institute for Computational and Applied Mathematics Österreichische Akademieder Wissenschaften Department of Mathematics Federal University of Pernambuco Ufpe RecifePECEP 50740-545 Brazil

In this paper local exact controllability to the trajectories for the one-dimensional monodomain equations with the FitzHugh-Nagumo and Rogers-McCulloch ionic models using distributed controls with a moving support is investigated. In a first step a new Carleman inequality for the adjoint of the linearized monodomain equations, under assumptions on the movement of the control region, is presented. It leads to null controllability at any positive time. Subsequently, a local result concerning the exact controllability to the trajectories for the nonlinear monodomain equations is deduced. Copyright © 2017, The Authors. All rights reserved.

关键词： Trajectories

Multi-patch and multi-group epidemic models: A new framework

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arXiv 2017年

作者： Bichara, Derdei Iggidr, Abderrahman Department of Mathematics Center for Computational and Applied Mathematics California State University FullertonCA92831 United States Inria Université de Lorraine CNRS Institut Elie Cartan de Lorraine UMR 7502 ISGMP Bat. A Ile du Saulcy Metz Cedex 0157045 France

We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of groups and interacts into an arbitrary number of patches where the infection takes place. In this framework, we model host mobility that depends on its epidemiological status, by a Lagrangian approach. This framework is applied to a general SEIRS model and the basic reproduction number R0 is derived. The effects of heterogeneity in groups, patches and mobility patterns on R0 and disease prevalence are explored. Our results show that for a fixed number of groups, the basic reproduction number increases with respect to the number of patches and the host mobility patterns. Moreover, when the mobility matrix of susceptible individuals is of rank one, the basic reproduction number is explicitly determined and was found to be independent of the latter if the matrix is also stochastic. The cases where mobility matrices are of rank one capture important modeling scenarios. Additionally, we study the global analysis of equilibria for some special cases. Numerical simulations are carried out to showcase the ramifications of mobility pattern matrices on disease prevalence and basic reproduction *** Codes 92D25, 92D30 Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

An improved discrete least-squares/reduced-basis method for parameterized elliptic PDEs

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arXiv 2017年

作者： Gunzburger, Max Schneier, Michael Webster, Clayton Zhang, Guannan Department of Scientific Computing Florida State University TallahasseeFL32306-4120 United States Computational and Applied Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831-6164 United States

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. In particular, we consider stochastic elliptic PDEs with an affine dependence on the random variable. The goal is to recover the entire solution map from the parameter space to the finite element space. To this end, first, a reduced-basis solution using a weak greedy algorithm is constructed, then a DLS approximation is determined by evaluating the reduced-basis approximation instead of the full finite element approximation. The main advantage of the new approach is that one only need apply the DLS operator to the coefficients of the reduced-basis expansion, resulting in huge savings in both the storage of the DLS coefficients and the online cost of evaluating the DLS approximation. In addition, the recently developed quasi-optimal polynomial space is also adopted in the new approach, resulting in superior convergence rates for a wider class of problems than previous analyzed. Numerical experiments are provided that illustrate the theoretical results. Copyright © 2017, The Authors. All rights reserved.

关键词： Least squares approximations

Analysis of Lead (Pb) and Zinc (Zn) Content in Sediments and Faunus ater at Bale Lhoknga Aceh Besar District

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Journal of Physics: Conference Series 2019年第1期1232卷

作者： Rahmi Agustina M. Ali Sarong Fredinan Yulianda Suhendrayatna Rahmadi Lelifajri Graduate School of Mathematics and Applied Sciences Syiah Kuala University Banda Aceh Indonesia 23111 Departement of Biology Faculty of Teacher Training and Education Jabal Ghafur University Sigli Indonesia 24171 Departement of Biology Faculty of Teacher Training and Education Syiah Kuala University Banda Aceh Indonesia 23111 Departement of Water Resources Management Faculty of Fisheries and Marine Sciences Bogor Agricultural University Bogor Indonesia 16680 Department of Chemical Engineering Faculty of Engineering Syiah Kuala University Banda Aceh Indonesia 23111 Department of Chemistry Faculty of Mathematics and Science Post Graduate Program Syiah Kuala University Banda Aceh Indonesia 23111

Faunus ater is a favoritemollusca that is often found on the Bale River. Local people use these snails as food for consumption along with their main food. Bale River itself is located adjacent to the cement factory, used water washing machines distributed to the river is feared to support the presence of lead (Pb) and zinc (Zn) metals in the river. This study aims to analyze the relationship of Pb and Zn content in sediments to the content of Pb and Zn in Faunus ater. Data collection was carried out in Februari until April 2018. The relationship between Pb and Zn content in sediments with Pb and Zn content in the body of Faunus ater was analyzed by correlation analysis. The results of the data analysis showed that the metal content of Pb and Zn in sediment and Faunus aterwere found to vary. The highest Pb content in sediment was found at station 2 in March, amounting to 32.87 mg / kg. while the highest Zn content was found at station 1 in March amounting to 84 mg / kg. The relationship of heavy metals Pb and Zn in sediments to the content of Pb and Zn in the body of Faunus ater showed a negative correlation. The conclusion of this study is that there is no correlation between the content of Pb and Zn heavy metals in sediments on the content of lead Pb and Zn in the body of Faunus ater at the Bale Lhoknga River in Aceh Besar District.

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Deep Potential: A general representation of a many-body potential energy surface

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arXiv 2017年

作者： Han, Jiequn Zhang, Linfeng Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that no ad hoc approximations or empirical fitting functions are required. The neural network structure naturally respects the underlying symmetries of the systems. When tested on a wide variety of examples, Deep Potential is able to reproduce the original model, either empirical or quantum mechanics based, within chemical accuracy. The computational cost of this new model is not substantially larger than that of empirical force fields. In addition, the method has promising scalability properties. This brings us one step closer to being able to carry out molecular simulations with accuracy comparable to that of quantum mechanics models and computational cost comparable to that of empirical potentials. Copyright © 2017, The Authors. All rights reserved.

关键词： Deep neural networks