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Interface Method And Greens Function Based Poisson Boltzmann Equation Solver And Interface Technique Based Molecular Dynamics
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Book Synopsis Interface Method and Green's Function Based Poisson Boltzmann Equation Solver and Interface Technique Based Molecular Dynamics by : Weihua Geng
Download or read book Interface Method and Green's Function Based Poisson Boltzmann Equation Solver and Interface Technique Based Molecular Dynamics written by Weihua Geng and published by . This book was released on 2008 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Poisson-Boltzmann Methods by : Qin Cai
Download or read book Poisson-Boltzmann Methods written by Qin Cai and published by . This book was released on 2013 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implicit solvent models based on the Poisson-Boltzmann theory have enjoyed numerous successes in a variety of biological applications where electrostatic interactions are crucial, especially in efficient modeling of solvation and protein-ligand binding free energies. The protein-ligand binding free energy can be used to assess the binding affinity of organic small molecules with a protein during the virtual screening stage of the computer-aided drug design. The reliability of the prediction depends heavily on the accuracy in the modeling of protein-ligand interactions. To improve the accuracy of the Poisson-Boltzmann implicit solvent model, I have developed a number of numerical strategies, including singularity removal, nonlinear solvers of the Poisson-Boltzmann equation, molecular surface refinement, grid dependence reduction, molecular surface integration, and charge-view energy and force computation. In addition, these numerical methods can lead to stable molecular dynamics simulations in the Poisson-Boltzmann implicit solvent framework, which is also beneficial for the virtual screening because implicit solvent molecular dynamics have the potential to sample the configurations of proteins more efficiently, thus expediting the binding free energy calculation. Furthermore, I explore to extend the classical Poisson-Boltzmann model by explicitly tracking the molecule-water interface based on the solution of the Navier-Stokes equation.
Book Synopsis Regularization Methods on Solving Poisson's Equation and Poisson Boltzmann Equation with Singular Charge Sources and Diffuse Interfaces by : Siwen Wang
Download or read book Regularization Methods on Solving Poisson's Equation and Poisson Boltzmann Equation with Singular Charge Sources and Diffuse Interfaces written by Siwen Wang and published by . This book was released on 2021 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical treatment of singular charges is a grand challenge in solving Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. For diffuse interface models in which solute and solvent are separated by a smooth boundary, no effective algorithm for singular charges has been developed, because the fundamental solution with a space dependent dielectric function is intractable. In this research work, regularization formulations are introduced to capture the singularity analytically, which are the first of their kind for diffuse interface Poisson's equation and PB models. The success lies in a dual decomposition -- besides decomposing the potential into Coulomb and reaction field components, the dielectric function is also split into a constant base plus space changing part. Using the constant dielectric base, the Coulomb potential is represented analytically via Green's functions. After removing the singularity, the reaction field potential satisfies a regularized PB equation with a smooth source. Some diffuse interface models including a Gaussian convolution surface (GCS) are also introduced. The GCS efficiently generates a diffuse interface for three-dimensional realistic biomolecules. The performance of the proposed regularization is examined by considering both analytical and GCS diffuse interfaces, and compared with the trilinear method. Moreover, the proposed GCS-regularization algorithm is validated by calculating electrostatic free energies for a set of proteins and by estimating salt affinities for seven protein complexes. The results are consistent with experimental data and estimates of sharp interface PB models.
Book Synopsis Green's Function Integral Equation Methods in Nano-Optics by : Thomas M. Søndergaard
Download or read book Green's Function Integral Equation Methods in Nano-Optics written by Thomas M. Søndergaard and published by CRC Press. This book was released on 2019-01-30 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to Green’s function integral equation methods (GFIEMs) for scattering problems in the field of nano-optics. First, a brief review is given of the most important theoretical foundations from electromagnetics, optics, and scattering theory, including theory of waveguides, Fresnel reflection, and scattering, extinction, and absorption cross sections. This is followed by a presentation of different types of GFIEMs of increasing complexity for one-, two-, and three-dimensional scattering problems. In GFIEMs, the electromagnetic field at any position is directly related to the field at either the inside or the surface of a scattering object placed in a reference structure. The properties of the reference structure, and radiating or periodic boundary conditions, are automatically taken care of via the choice of Green’s function. This book discusses in detail how to solve the integral equations using either simple or higher-order finite-element-based methods; how to calculate the relevant Green’s function for different reference structures and choices of boundary conditions; and how to calculate near-fields, optical cross sections, and the power emitted by a local source. Solution strategies for large structures are discussed based on either transfer-matrix-approaches or the conjugate gradient algorithm combined with the Fast Fourier Transform. Special attention is given to reducing the computational problem for three-dimensional structures with cylindrical symmetry by using cylindrical harmonic expansions. Each presented method is accompanied by examples from nano-optics, including: resonant metal nano-particles placed in a homogeneous medium or on a surface or waveguide; a microstructured gradient-index-lens; the Purcell effect for an emitter in a photonic crystal; the excitation of surface plasmon polaritons by second-harmonic generation in a polymer fiber placed on a thin metal film; and anti-reflective, broadband absorbing or resonant surface microstructures. Each presented method is also accompanied by guidelines for software implementation and exercises. Features Comprehensive introduction to Green’s function integral equation methods for scattering problems in the field of nano-optics Detailed explanation of how to discretize and solve integral equations using simple and higher-order finite-element approaches Solution strategies for large structures Guidelines for software implementation and exercises Broad selection of examples of scattering problems in nano-optics
Book Synopsis Computational Methods for Electromagnetic Phenomena by : Wei Cai
Download or read book Computational Methods for Electromagnetic Phenomena written by Wei Cai and published by Cambridge University Press. This book was released on 2013-01-03 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind to cover a wide range of computational methods for electromagnetic phenomena, from atomistic to continuum scales, this integrated and balanced treatment of mathematical formulations, algorithms and the underlying physics enables us to engage in innovative and advanced interdisciplinary computational research.
Book Synopsis Adaptive Pseudo-time Methods for the Poisson-Boltzmann Equation with Eulerian Solvent Excluded Surface by : Benjamin Daniel Jones
Download or read book Adaptive Pseudo-time Methods for the Poisson-Boltzmann Equation with Eulerian Solvent Excluded Surface written by Benjamin Daniel Jones and published by . This book was released on 2021 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work further improves the pseudo-transient approach for the Poisson Boltzmann equation (PBE) in the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is known to involve many difficulties, such as exponential nonlinear term, strong singularity by the source terms, and complex dielectric interface. Recently, a pseudo-time ghost-fluid method (GFM) has been developed in [S. Ahmed Ullah and S. Zhao, Applied Mathematics and Computation, 380, 125267, (2020)], by analytically handling both nonlinearity and singular sources. The GFM interface treatment not only captures the discontinuity in the regularized potential and its flux across the molecular surface, but also guarantees the stability and efficiency of the time integration. However, the molecular surface definition based on the MSMS package is known to induce instability in some cases, and a nontrivial Lagrangian-to-Eulerian conversion is indispensable for the GFM finite difference discretization. In this paper, an Eulerian Solvent Excluded Surface (ESES) is implemented to replace the MSMS for defining the dielectric interface. The electrostatic analysis shows that the ESES free energy is more accurate than that of the MSMS, while being free of instability issues. Moreover, this work explores, for the first time in the PBE literature, adaptive time integration techniques for the pseudo-transient simulations. A major finding is that the time increment Delta t should become smaller as the time increases, in order to maintain the temporal accuracy. This is opposite to the common practice for the steady state convergence, and is believed to be due to the PBE nonlinearity and its time splitting treatment. Effective adaptive schemes have been constructed so that the pseudo-time GFM methods become more efficient than the constant Delta t ones.
Book Synopsis Numerical Solution of the Poisson Interface Problem Using the Correction Function Method Framework by : Philippe Blain
Download or read book Numerical Solution of the Poisson Interface Problem Using the Correction Function Method Framework written by Philippe Blain and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this work we study the Poisson interface problem and a numerical method for its solution, the Correction Function Method. The Poisson interface problem complements the classical Poisson problem, a partial differential equation given in terms of the Laplacian operator, with jump conditions on the solution and its normal derivative along a co-dimension one interface inside the domain. Interface problems arise whenever materials with different properties come into contact, and thus have important applications in many fields of physics and engineering. The Correction Function Method (CFM) is a general framework to solve the Poisson interface problem in the wider context of finite difference methods. In essence, it modifies the finite difference stencils for nodes near the interface in order to take into account the jump conditions. However, these modifications are incorporated, using correction terms, to the right-hand side of the linear system deriving from the finite difference approximation of the partial differential equation, leaving the coefficient matrix identical to the one resulting from the regular Poisson problem. This is essential as many efficient linear solvers, termed "Fast Poisson solvers", are specifically designed to solve this system; by keeping the same matrix we can use them with no modification. In order to account for the multiple possible geometric configurations of the interface with respect to the finite difference stencil, we compute the correction terms locally using a functional minimization approach. Our specific implementation of the CFM is shown to be fourth-order accurate. We also present preliminary work towards a CFM-based Navier-Stokes solver for higher-order numerical simulation of multiphase flow." --
Book Synopsis Certified Reduced Basis Methods for Parametrized Partial Differential Equations by : Jan S Hesthaven
Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
Book Synopsis Reduced Basis Methods for Partial Differential Equations by : Alfio Quarteroni
Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni and published by Springer. This book was released on 2015-08-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
Book Synopsis Parallel Multigrid-based Methods for Calculating Electrostatic Potentials by Solving the Full Nonlinear Poisson-Boltzmann Equation by : Dong Zeng
Download or read book Parallel Multigrid-based Methods for Calculating Electrostatic Potentials by Solving the Full Nonlinear Poisson-Boltzmann Equation written by Dong Zeng and published by . This book was released on 2000 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reviews in Computational Chemistry, Volume 26 by : Kenny B. Lipkowitz
Download or read book Reviews in Computational Chemistry, Volume 26 written by Kenny B. Lipkowitz and published by John Wiley & Sons. This book was released on 2008-11-19 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational chemistry is increasingly used in conjunction with organic, inorganic, medicinal, biological, physical, and analytical chemistry, biotechnology, materials science, and chemical physics. This series is essential in keeping those individuals involved in these fields abreast of recent developments in computational chemistry.
Book Synopsis Mathematical Methods for Implicit Solvation Models in Quantum Chemistry by : Chaoyu Quan
Download or read book Mathematical Methods for Implicit Solvation Models in Quantum Chemistry written by Chaoyu Quan and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is devoted to study and improve the mathematical models and methods used in implicit solvation models in quantum chemistry. The manuscript is composed of two parts. In the first part where we analyze the solute-solvent interface, we give, for the first time, a complete characterization of the so-called “smooth” molecular surface, i.e., the solvent excluded surface (SES). Based on this characterization, we develop a piecewise meshing algorithm for different molecular surfaces, especially the SES, using the advancing-front triangulation. Further, it has been pointed out in the literature that the SES-cavity (the region enclosed by the SES) is a more accurate description of the solute cavity. In the second part, we therefore construct an SES-based polarizable continuum model (PCM), in which the dielectric permittivity parameter is continuous. The electrostatic problem of this model involves solving a Poisson equation defined in R3. We then develop a particular Schwarz domain decomposition method where only local equations restricted to balls need to be solved. Finally, the Poisson-Boltzmann solvation model, another implicit solvation model, is also investigated, which takes into account both the dielectric permittivity and the ionic strength of the solvent. A similar Schwarz domain decomposition method is proposed to solve the associated Poisson-Boltzmann equation by solving local equations restricted to balls as it is for the SES-based PCM.
Book Synopsis A Novel Stochastic Poisson-boltzmann Solver and Incorporation of Finite Ion Sizes by : Alexander R. J. Silalahi
Download or read book A Novel Stochastic Poisson-boltzmann Solver and Incorporation of Finite Ion Sizes written by Alexander R. J. Silalahi and published by . This book was released on 2011 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Electrostatic interactions play an important role in many aspects of the structural and functional properties of biomolecules because of their long-range behavior. The nonlinear Poisson-Boltzmann equation (NLPBE) theory has long been used as a standard tool for modeling non-specific electrostatic interactions of biomolecules in aqueous salt solution. In the NLPBE framework, ions are treated as point-like charged particles and their size effects are neglected. A major contribution in this dissertation is the incorporation of the ion sizes effect into the NLPBE framework. In this dissertation we developed a non-uniform ion size modified Poisson-Boltzmann equation (SMPBE) to study the distribution of ions around an A-form ribonucleic acid (RNA) duplex and compare it with predictions obtained with molecular dynamics (MD) simulations.
Book Synopsis Atomistic Modeling of Materials Failure by : Markus J. Buehler
Download or read book Atomistic Modeling of Materials Failure written by Markus J. Buehler and published by Springer Science & Business Media. This book was released on 2008-08-07 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to molecular and atomistic modeling techniques applied to fracture and deformation of solids, focusing on a variety of brittle, ductile, geometrically confined and biological materials. The overview includes computational methods and techniques operating at the atomic scale, and describes how these techniques can be used to model cracks and other deformation mechanisms. The book aims to make new molecular modeling techniques available to a wider community.
Book Synopsis Level Set Methods and Dynamic Implicit Surfaces by : Stanley Osher
Download or read book Level Set Methods and Dynamic Implicit Surfaces written by Stanley Osher and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and Fedkiw; Osher and Fedkiw are internationally well-known researchers in this area
Book Synopsis Continuum Solvation Models in Chemical Physics by : Benedetta Mennucci
Download or read book Continuum Solvation Models in Chemical Physics written by Benedetta Mennucci and published by John Wiley & Sons. This book was released on 2008-02-28 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the theory and applications of continuum solvation models. The main focus is on the quantum-mechanical version of these models, but classical approaches and combined or hybrid techniques are also discussed. Devoted to solvation models in which reviews of the theory, the computational implementation Solvation continuum models are treated using the different points of view from experts belonging to different research fields Can be read at two levels: one, more introductive, and the other, more detailed (and more technical), on specific physical and numerical aspects involved in each issue and/or application Possible limitations or incompleteness of models is pointed out with, if possible, indications of future developments Four-colour representation of the computational modeling throughout.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
