APBSmem: A Graphical Interface for Electrostatic Calculations at the Membrane

PubMed Central

Callenberg, Keith M.; Choudhary, Om P.; de Forest, Gabriel L.; Gohara, David W.; Baker, Nathan A.; Grabe, Michael

2010-01-01

Electrostatic forces are one of the primary determinants of molecular interactions. They help guide the folding of proteins, increase the binding of one protein to another and facilitate protein-DNA and protein-ligand binding. A popular method for computing the electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation, and there are several easy-to-use software packages available that solve the PB equation for soluble proteins. Here we present a freely available program, called APBSmem, for carrying out these calculations in the presence of a membrane. The Adaptive Poisson-Boltzmann Solver (APBS) is used as a back-end for solving the PB equation, and a Java-based graphical user interface (GUI) coordinates a set of routines that introduce the influence of the membrane, determine its placement relative to the protein, and set the membrane potential. The software Jmol is embedded in the GUI to visualize the protein inserted in the membrane before the calculation and the electrostatic potential after completing the computation. We expect that the ease with which the GUI allows one to carry out these calculations will make this software a useful resource for experimenters and computational researchers alike. Three examples of membrane protein electrostatic calculations are carried out to illustrate how to use APBSmem and to highlight the different quantities of interest that can be calculated. PMID:20949122

APBSmem: a graphical interface for electrostatic calculations at the membrane.

PubMed

Callenberg, Keith M; Choudhary, Om P; de Forest, Gabriel L; Gohara, David W; Baker, Nathan A; Grabe, Michael

2010-09-29

Electrostatic forces are one of the primary determinants of molecular interactions. They help guide the folding of proteins, increase the binding of one protein to another and facilitate protein-DNA and protein-ligand binding. A popular method for computing the electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation, and there are several easy-to-use software packages available that solve the PB equation for soluble proteins. Here we present a freely available program, called APBSmem, for carrying out these calculations in the presence of a membrane. The Adaptive Poisson-Boltzmann Solver (APBS) is used as a back-end for solving the PB equation, and a Java-based graphical user interface (GUI) coordinates a set of routines that introduce the influence of the membrane, determine its placement relative to the protein, and set the membrane potential. The software Jmol is embedded in the GUI to visualize the protein inserted in the membrane before the calculation and the electrostatic potential after completing the computation. We expect that the ease with which the GUI allows one to carry out these calculations will make this software a useful resource for experimenters and computational researchers alike. Three examples of membrane protein electrostatic calculations are carried out to illustrate how to use APBSmem and to highlight the different quantities of interest that can be calculated.

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

NASA Technical Reports Server (NTRS)

Kaup, D. J.; Hansen, P. J.; Choudhury, S. Roy; Thomas, Gary E.

1986-01-01

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate.

PubMed

Fellner, Klemens; Kovtunenko, Victor A

2016-01-01

A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.

Electrostatic similarity of proteins: Application of three dimensional spherical harmonic decomposition

PubMed Central

Długosz, Maciej; Trylska, Joanna

2008-01-01

We present a method for describing and comparing global electrostatic properties of biomolecules based on the spherical harmonic decomposition of electrostatic potential data. Unlike other approaches our method does not require any prior three dimensional structural alignment. The electrostatic potential, given as a volumetric data set from a numerical solution of the Poisson or Poisson–Boltzmann equation, is represented with descriptors that are rotation invariant. The method can be applied to large and structurally diverse sets of biomolecules enabling to cluster them according to their electrostatic features. PMID:18624502

cDPD: A new dissipative particle dynamics method for modeling electrokinetic phenomena at the mesoscale

NASA Astrophysics Data System (ADS)

Deng, Mingge; Li, Zhen; Borodin, Oleg; Karniadakis, George Em

2016-10-01

We develop a "charged" dissipative particle dynamics (cDPD) model for simulating mesoscopic electrokinetic phenomena governed by the stochastic Poisson-Nernst-Planck and the Navier-Stokes equations. Specifically, the transport equations of ionic species are incorporated into the DPD framework by introducing extra degrees of freedom and corresponding evolution equations associated with each DPD particle. Diffusion of ionic species driven by the ionic concentration gradient, electrostatic potential gradient, and thermal fluctuations is captured accurately via pairwise fluxes between DPD particles. The electrostatic potential is obtained by solving the Poisson equation on the moving DPD particles iteratively at each time step. For charged surfaces in bounded systems, an effective boundary treatment methodology is developed for imposing both the correct hydrodynamic and electrokinetics boundary conditions in cDPD simulations. To validate the proposed cDPD model and the corresponding boundary conditions, we first study the electrostatic structure in the vicinity of a charged solid surface, i.e., we perform cDPD simulations of the electrostatic double layer and show that our results are in good agreement with the well-known mean-field theoretical solutions. We also simulate the electrostatic structure and capacity densities between charged parallel plates in salt solutions with different salt concentrations. Moreover, we employ the proposed methodology to study the electro-osmotic and electro-osmotic/pressure-driven flows in a micro-channel. In the latter case, we simulate the dilute poly-electrolyte solution drifting by electro-osmotic flow in a micro-channel, hence demonstrating the flexibility and capability of this method in studying complex fluids with electrostatic interactions at the micro- and nano-scales.

A quantum mechanical-Poisson-Boltzmann equation approach for studying charge flow between ions and a dielectric continuum

NASA Astrophysics Data System (ADS)

Gogonea, Valentin; Merz, Kenneth M.

2000-02-01

This paper presents a theoretical model for the investigation of charge transfer between ions and a solvent treated as a dielectric continuum media. The method is a combination of a semiempirical effective Hamiltonian with a modified Poisson-Boltzmann equation which includes charge transfer in the form of a surface charge density positioned at the dielectric interface. The new Poisson-Boltzmann equation together with new boundary conditions results in a new set of equations for the electrostatic potential (or polarization charge densities). Charge transfer adds a new free energy component to the solvation free energy term, which accounts for all interactions between the transferred charge at the dielectric interface, the solute wave function and the solvent polarization charges. Practical calculations on a set of 19 anions and 17 cations demonstrate that charge exchange with a dielectric is present and it is in the range of 0.06-0.4 eu. Furthermore, the pattern of the magnitudes of charge transfer can be related to the acid-base properties of the ions in many cases, but exceptions are also found. Finally, we show that the method leads to an energy decomposition scheme of the total electrostatic energy, which can be used in mechanistic studies on protein and DNA interaction with water.

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations

NASA Astrophysics Data System (ADS)

Vergara-Perez, Sandra; Marucho, Marcelo

2016-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson-Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post-analysis of structural and electrical properties of biomolecules.

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations

PubMed Central

Vergara-Perez, Sandra; Marucho, Marcelo

2015-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post- analysis of structural and electrical properties of biomolecules. PMID:26924848

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations.

PubMed

Vergara-Perez, Sandra; Marucho, Marcelo

2016-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post- analysis of structural and electrical properties of biomolecules.

New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics

NASA Astrophysics Data System (ADS)

Xie, Dexuan

2014-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package.

Dendritic polyelectrolytes as seen by the Poisson-Boltzmann-Flory theory.

PubMed

Kłos, J S; Milewski, J

2018-06-20

G3-G9 dendritic polyelectrolytes accompanied by counterions are investigated using the Poisson-Boltzmann-Flory theory. Within this approach we solve numerically the Poisson-Boltzmann equation for the mean electrostatic potential and minimize the Poisson-Boltzmann-Flory free energy with respect to the size of the molecules. Such a scheme enables us to inspect the conformational and electrostatic properties of the dendrimers in equilibrium based on their response to varying the dendrimer generation. The calculations indicate that the G3-G6 dendrimers exist in the polyelectrolyte regime where absorption of counterions into the volume of the molecules is minor. Trapping of ions in the interior region becomes significant for the G7-G9 dendrimers and signals the emergence of the osmotic regime. We find that the behavior of the dendritic polyelectrolytes corresponds with the degree of ion trapping. In particular, in both regimes the polyelectrolytes are swollen as compared to their neutral counterparts and the expansion factor is maximal at the crossover generation G7.

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media.

PubMed

Ma, Manman; Xu, Zhenli

2014-12-28

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.

Beyond the continuum: how molecular solvent structure affects electrostatics and hydrodynamics at solid-electrolyte interfaces.

PubMed

Bonthuis, Douwe Jan; Netz, Roland R

2013-10-03

Standard continuum theory fails to predict several key experimental results of electrostatic and electrokinetic measurements at aqueous electrolyte interfaces. In order to extend the continuum theory to include the effects of molecular solvent structure, we generalize the equations for electrokinetic transport to incorporate a space dependent dielectric profile, viscosity profile, and non-electrostatic interaction potential. All necessary profiles are extracted from atomistic molecular dynamics (MD) simulations. We show that the MD results for the ion-specific distribution of counterions at charged hydrophilic and hydrophobic interfaces are accurately reproduced using the dielectric profile of pure water and a non-electrostatic repulsion in an extended Poisson-Boltzmann equation. The distributions of Na(+) at both surface types and Cl(-) at hydrophilic surfaces can be modeled using linear dielectric response theory, whereas for Cl(-) at hydrophobic surfaces it is necessary to apply nonlinear response theory. The extended Poisson-Boltzmann equation reproduces the experimental values of the double-layer capacitance for many different carbon-based surfaces. In conjunction with a generalized hydrodynamic theory that accounts for a space dependent viscosity, the model captures the experimentally observed saturation of the electrokinetic mobility as a function of the bare surface charge density and the so-called anomalous double-layer conductivity. The two-scale approach employed here-MD simulations and continuum theory-constitutes a successful modeling scheme, providing basic insight into the molecular origins of the static and kinetic properties of charged surfaces, and allowing quantitative modeling at low computational cost.

Differential geometry-based solvation and electrolyte transport models for biomolecular modeling: a review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Guowei; Baker, Nathan A.

2016-11-11

This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the major physical observables of interest, for example, biomolecular surface area, enclosed volume, electrostatic potential, ion density, electron density, etc. Recently, differential geometry theory has been used to define the surfaces that separate the microscopic (solute) domains for biomolecules from the macroscopic (solvent) domains. In thesemore » approaches, the microscopic domains are modeled with atomistic or quantum mechanical descriptions, while continuum mechanics models (including fluid mechanics, elastic mechanics, and continuum electrostatics) are applied to the macroscopic domains. This multiphysics description is integrated through an energy functional formalism and the resulting Euler-Lagrange equation is employed to derive a variety of governing partial differential equations for different solvation and transport processes; e.g., the Laplace-Beltrami equation for the solvent-solute interface, Poisson or Poisson-Boltzmann equations for electrostatic potentials, the Nernst-Planck equation for ion densities, and the Kohn-Sham equation for solute electron density. Extensive validation of these models has been carried out over hundreds of molecules, including proteins and ion channels, and the experimental data have been compared in terms of solvation energies, voltage-current curves, and density distributions. We also propose a new quantum model for electrolyte transport.« less

Improvements to the APBS biomolecular solvation software suite: Improvements to the APBS Software Suite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jurrus, Elizabeth; Engel, Dave; Star, Keith

The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suitemore » of accompanying software since its release in 2001. In this manuscript, we discuss the models and capabilities that have recently been implemented within the APBS software package including: a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory based algorithm for determining pKa values, and an improved web-based visualization tool for viewing electrostatics.« less

Improvements to the APBS biomolecular solvation software suite.

PubMed

Jurrus, Elizabeth; Engel, Dave; Star, Keith; Monson, Kyle; Brandi, Juan; Felberg, Lisa E; Brookes, David H; Wilson, Leighton; Chen, Jiahui; Liles, Karina; Chun, Minju; Li, Peter; Gohara, David W; Dolinsky, Todd; Konecny, Robert; Koes, David R; Nielsen, Jens Erik; Head-Gordon, Teresa; Geng, Weihua; Krasny, Robert; Wei, Guo-Wei; Holst, Michael J; McCammon, J Andrew; Baker, Nathan A

2018-01-01

The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that have provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses the three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this article, we discuss the models and capabilities that have recently been implemented within the APBS software package including a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory-based algorithm for determining pK a values, and an improved web-based visualization tool for viewing electrostatics. © 2017 The Protein Society.

A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces

PubMed Central

Zhou, Y. C.; Holst, Michael; McCammon, J. Andrew

2008-01-01

In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic potential is analyzed in a domain varying with the elastic deformation of molecules, and a new continuous model of the electrostatic forces is developed to ensure solvability of the nonlinear elasticity equations. We derive the estimates of electrostatic forces corresponding to four types of perturbations to an electrostatic potential field, and establish the existance of an equilibrium configuration using a fixed-point argument, under the assumption that the change in the ionic strength and charges due to the additional molecules causing the deformation are sufficiently small. The results are valid for elastic models with arbitrarily complex dielectric interfaces and cavities, and can be generalized to large elastic deformation caused by high ionic strength, large charges, and strong external fields by using continuation methods. PMID:19461946

Self consistent solution of Schrödinger Poisson equations and some electronic properties of ZnMgO/ZnO hetero structures

NASA Astrophysics Data System (ADS)

Uslu, Salih; Yarar, Zeki

2017-02-01

The epitaxial growth of quantum wells composed of high quality allows the production and application to their device of new structures in low dimensions. The potential profile at the junction is determined by free carriers and by the level of doping. Therefore, the shape of potential is obtained by the electron density. Energy level determines the number of electrons that can be occupied at every level. Energy levels and electron density values of each level must be calculated self consistently. Starting with V(z) test potential, wave functions and electron densities for each energy levels can be calculated to solve Schrödinger equation. If Poisson's equation is solved with the calculated electron density, the electrostatic potential can be obtained. The new V(z) potential can be calculated with using electrostatic potential found beforehand. Thus, the obtained values are calculated self consistently to a certain error criterion. In this study, the energy levels formed in the interfacial potential, electron density in each level and the wave function dependence of material parameters were investigated self consistently.

Low-frequency surface waves on semi-bounded magnetized quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moradi, Afshin, E-mail: a.moradi@kut.ac.ir

2016-08-15

The propagation of low-frequency electrostatic surface waves on the interface between a vacuum and an electron-ion quantum plasma is studied in the direction perpendicular to an external static magnetic field which is parallel to the interface. A new dispersion equation is derived by employing both the quantum magnetohydrodynamic and Poisson equations. It is shown that the dispersion equations for forward and backward-going surface waves are different from each other.

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution.

PubMed

Womack, James C; Anton, Lucian; Dziedzic, Jacek; Hasnip, Phil J; Probert, Matt I J; Skylaris, Chris-Kriton

2018-03-13

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10 9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field. PMID:25382892

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Quasi-electrostatic twisted waves in Lorentzian dusty plasmas

NASA Astrophysics Data System (ADS)

Arshad, Kashif; Lazar, M.; Poedts, S.

2018-07-01

The quasi electrostatic modes are investigated in non thermal dusty plasma using non-gyrotropic Kappa distribution in the presence of helical electric field. The Laguerre Gaussian (LG) mode function is employed to decompose the perturbed distribution function and helical electric field. The modified dielectric function is obtained for the dust ion acoustic (DIA) and dust acoustic (DA) twisted modes from the solution of Vlasov-Poisson equation. The threshold conditions for the growing modes is also illustrated.

Modeling salt-mediated electrostatics of macromolecules: the discrete surface charge optimization algorithm and its application to the nucleosome.

PubMed

Beard, D A; Schlick, T

2001-01-01

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels. Copyright 2000 John Wiley & Sons, Inc.

Particle flows to shape and voltage surface discontinuities in the electron sheath surrounding a high voltage solar array in LEO

NASA Technical Reports Server (NTRS)

Metz, Roger N.

1991-01-01

This paper discusses the numerical modeling of electron flows from the sheath surrounding high positively biased objects in LEO (Low Earth Orbit) to regions of voltage or shape discontinuity on the biased surfaces. The sheath equations are derived from the Two-fluid, Warm Plasma Model. An equipotential corner and a plane containing strips of alternating voltage bias are treated in two dimensions. A self-consistent field solution of the sheath equations is outlined and is pursued through one cycle. The electron density field is determined by numerical solution of Poisson's equation for the electrostatic potential in the sheath using the NASCAP-LEO relation between electrostatic potential and charge density. Electron flows are calculated numerically from the electron continuity equation. Magnetic field effects are not treated.

A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation

NASA Astrophysics Data System (ADS)

Geng, Weihua; Zhao, Shan

2017-12-01

We present a new Matched Interface and Boundary (MIB) regularization method for treating charge singularity in solvated biomolecules whose electrostatics are described by the Poisson-Boltzmann (PB) equation. In a regularization method, by decomposing the potential function into two or three components, the singular component can be analytically represented by the Green's function, while other components possess a higher regularity. Our new regularization combines the efficiency of two-component schemes with the accuracy of the three-component schemes. Based on this regularization, a new MIB finite difference algorithm is developed for solving both linear and nonlinear PB equations, where the nonlinearity is handled by using the inexact-Newton's method. Compared with the existing MIB PB solver based on a three-component regularization, the present algorithm is simpler to implement by circumventing the work to solve a boundary value Poisson equation inside the molecular interface and to compute related interface jump conditions numerically. Moreover, the new MIB algorithm becomes computationally less expensive, while maintains the same second order accuracy. This is numerically verified by calculating the electrostatic potential and solvation energy on the Kirkwood sphere on which the analytical solutions are available and on a series of proteins with various sizes.

Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biswas, Debabrata; Singh, Gaurav; Kumar, Raghwendra

2015-09-15

Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations, such as high power microwave or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary conditions is best suited for large aspect ratios, while a proposed non-local matching method, based on the solution of the Laplace equation,more » scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.« less

On push-forward representations in the standard gyrokinetic model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyato, N., E-mail: miyato.naoaki@jaea.go.jp; Yagi, M.; Scott, B. D.

2015-01-15

Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This ismore » true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.« less

Continuum simulations of acetylcholine consumption by acetylcholinesterase: a Poisson-Nernst-Planck approach.

PubMed

Zhou, Y C; Lu, Benzhuo; Huber, Gary A; Holst, Michael J; McCammon, J Andrew

2008-01-17

The Poisson-Nernst-Planck (PNP) equation provides a continuum description of electrostatic-driven diffusion and is used here to model the diffusion and reaction of acetylcholine (ACh) with acetylcholinesterase (AChE) enzymes. This study focuses on the effects of ion and substrate concentrations on the reaction rate and rate coefficient. To this end, the PNP equations are numerically solved with a hybrid finite element and boundary element method at a wide range of ion and substrate concentrations, and the results are compared with the partially coupled Smoluchowski-Poisson-Boltzmann model. The reaction rate is found to depend strongly on the concentrations of both the substrate and ions; this is explained by the competition between the intersubstrate repulsion and the ionic screening effects. The reaction rate coefficient is independent of the substrate concentration only at very high ion concentrations, whereas at low ion concentrations the behavior of the rate depends strongly on the substrate concentration. Moreover, at physiological ion concentrations, variations in substrate concentration significantly affect the transient behavior of the reaction. Our results offer a reliable estimate of reaction rates at various conditions and imply that the concentrations of charged substrates must be coupled with the electrostatic computation to provide a more realistic description of neurotransmission and other electrodiffusion and reaction processes.

PDB_Hydro: incorporating dipolar solvents with variable density in the Poisson-Boltzmann treatment of macromolecule electrostatics.

PubMed

Azuara, Cyril; Lindahl, Erik; Koehl, Patrice; Orland, Henri; Delarue, Marc

2006-07-01

We describe a new way to calculate the electrostatic properties of macromolecules which eliminates the assumption of a constant dielectric value in the solvent region, resulting in a Generalized Poisson-Boltzmann-Langevin equation (GPBLE). We have implemented a web server (http://lorentz.immstr.pasteur.fr/pdb_hydro.php) that both numerically solves this equation and uses the resulting water density profiles to place water molecules at preferred sites of hydration. Surface atoms with high or low hydration preference can be easily displayed using a simple PyMol script, allowing for the tentative prediction of the dimerization interface in homodimeric proteins, or lipid binding regions in membrane proteins. The web site includes options that permit mutations in the sequence as well as reconstruction of missing side chain and/or main chain atoms. These tools are accessible independently from the electrostatics calculation, and can be used for other modeling purposes. We expect this web server to be useful to structural biologists, as the knowledge of solvent density should prove useful to get better fits at low resolution for X-ray diffraction data and to computational biologists, for whom these profiles could improve the calculation of interaction energies in water between ligands and receptors in docking simulations.

Nonlinear waves in electron-positron-ion plasmas including charge separation

NASA Astrophysics Data System (ADS)

Mugemana, A.; Moolla, S.; Lazarus, I. J.

2017-02-01

Nonlinear low-frequency electrostatic waves in a magnetized, three-component plasma consisting of hot electrons, hot positrons and warm ions have been investigated. The electrons and positrons are assumed to have Boltzmann density distributions while the motion of the ions are governed by fluid equations. The system is closed with the Poisson equation. This set of equations is numerically solved for the electric field. The effects of the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle are investigated. It is shown that depending on the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle, the numerical solutions exhibit waveforms that are sinusoidal, sawtooth and spiky. The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E 0 was reduced. The results are compared with satellite observations.

Complex wet-environments in electronic-structure calculations

NASA Astrophysics Data System (ADS)

Fisicaro, Giuseppe; Genovese, Luigi; Andreussi, Oliviero; Marzari, Nicola; Goedecker, Stefan

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of an applied electrochemical potentials, including complex electrostatic screening coming from the solvent. In the present work we present a solver to handle both the Generalized Poisson and the Poisson-Boltzmann equation. A preconditioned conjugate gradient (PCG) method has been implemented for the Generalized Poisson and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations. On the other hand, a self-consistent procedure enables us to solve the Poisson-Boltzmann problem. The algorithms take advantage of a preconditioning procedure based on the BigDFT Poisson solver for the standard Poisson equation. They exhibit very high accuracy and parallel efficiency, and allow different boundary conditions, including surfaces. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and it will be released as a independent program, suitable for integration in other codes. We present test calculations for large proteins to demonstrate efficiency and performances. This work was done within the PASC and NCCR MARVEL projects. Computer resources were provided by the Swiss National Supercomputing Centre (CSCS) under Project ID s499. LG acknowledges also support from the EXTMOS EU project.

Membrane protein properties revealed through data-rich electrostatics calculations

PubMed Central

Guerriero, Christopher J.; Brodsky, Jeffrey L.; Grabe, Michael

2015-01-01

SUMMARY The electrostatic properties of membrane proteins often reveal many of their key biophysical characteristics, such as ion channel selectivity and the stability of charged membrane-spanning segments. The Poisson-Boltzmann (PB) equation is the gold standard for calculating protein electrostatics, and the software APBSmem enables the solution of the PB equation in the presence of a membrane. Here, we describe significant advances to APBSmem including: full automation of system setup, per-residue energy decomposition, incorporation of PDB2PQR, calculation of membrane induced pKa shifts, calculation of non-polar energies, and command-line scripting for large scale calculations. We highlight these new features with calculations carried out on a number of membrane proteins, including the recently solved structure of the ion channel TRPV1 and a large survey of 1,614 membrane proteins of known structure. This survey provides a comprehensive list of residues with large electrostatic penalties for being embedded in the membrane potentially revealing interesting functional information. PMID:26118532

Membrane Protein Properties Revealed through Data-Rich Electrostatics Calculations.

PubMed

Marcoline, Frank V; Bethel, Neville; Guerriero, Christopher J; Brodsky, Jeffrey L; Grabe, Michael

2015-08-04

The electrostatic properties of membrane proteins often reveal many of their key biophysical characteristics, such as ion channel selectivity and the stability of charged membrane-spanning segments. The Poisson-Boltzmann (PB) equation is the gold standard for calculating protein electrostatics, and the software APBSmem enables the solution of the PB equation in the presence of a membrane. Here, we describe significant advances to APBSmem, including full automation of system setup, per-residue energy decomposition, incorporation of PDB2PQR, calculation of membrane-induced pKa shifts, calculation of non-polar energies, and command-line scripting for large-scale calculations. We highlight these new features with calculations carried out on a number of membrane proteins, including the recently solved structure of the ion channel TRPV1 and a large survey of 1,614 membrane proteins of known structure. This survey provides a comprehensive list of residues with large electrostatic penalties for being embedded in the membrane, potentially revealing interesting functional information. Copyright © 2015 Elsevier Ltd. All rights reserved.

Calculation of ionized fields in DC electrostatic precipitators in the presence of dust and electric wind

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cristina, S.; Feliziani, M.

1995-11-01

This paper describes a new procedure for the numerical computation of the electric field and current density distributions in a dc electrostatic precipitator in the presence of dust, taking into account the particle-size distribution. Poisson`s and continuity equations are numerically solved by supposing that the coronating conductors satisfy Kaptzov`s assumption on the emitter surfaces. Two iterative numerical procedures, both based on the finite element method (FEM), are implemented for evaluating, respectively, the unknown ionic charge density and the particle charge density distributions. The V-I characteristic and the precipitation efficiencies for the individual particle-size classes, calculated with reference to the pilotmore » precipitator installed by ENEL (Italian Electricity Board) at its Marghera (Venice) coal-fired power station, are found to be very close to those measured experimentally.« less

Green's function enriched Poisson solver for electrostatics in many-particle systems

NASA Astrophysics Data System (ADS)

Sutmann, Godehard

2016-06-01

A highly accurate method is presented for the construction of the charge density for the solution of the Poisson equation in particle simulations. The method is based on an operator adjusted source term which can be shown to produce exact results up to numerical precision in the case of a large support of the charge distribution, therefore compensating the discretization error of finite difference schemes. This is achieved by balancing an exact representation of the known Green's function of regularized electrostatic problem with a discretized representation of the Laplace operator. It is shown that the exact calculation of the potential is possible independent of the order of the finite difference scheme but the computational efficiency for higher order methods is found to be superior due to a faster convergence to the exact result as a function of the charge support.

Are electrostatic potentials between regions of different chemical composition measurable? The Gibbs-Guggenheim Principle reconsidered, extended and its consequences revisited.

PubMed

Pethica, Brian A

2007-12-21

As indicated by Gibbs and made explicit by Guggenheim, the electrical potential difference between two regions of different chemical composition cannot be measured. The Gibbs-Guggenheim Principle restricts the use of classical electrostatics in electrochemical theories as thermodynamically unsound with some few approximate exceptions, notably for dilute electrolyte solutions and concomitant low potentials where the linear limit for the exponential of the relevant Boltzmann distribution applies. The Principle invalidates the widespread use of forms of the Poisson-Boltzmann equation which do not include the non-electrostatic components of the chemical potentials of the ions. From a thermodynamic analysis of the parallel plate electrical condenser, employing only measurable electrical quantities and taking into account the chemical potentials of the components of the dielectric and their adsorption at the surfaces of the condenser plates, an experimental procedure to provide exceptions to the Principle has been proposed. This procedure is now reconsidered and rejected. No other related experimental procedures circumvent the Principle. Widely-used theoretical descriptions of electrolyte solutions, charged surfaces and colloid dispersions which neglect the Principle are briefly discussed. MD methods avoid the limitations of the Poisson-Bolzmann equation. Theoretical models which include the non-electrostatic components of the inter-ion and ion-surface interactions in solutions and colloid systems assume the additivity of dispersion and electrostatic forces. An experimental procedure to test this assumption is identified from the thermodynamics of condensers at microscopic plate separations. The available experimental data from Kelvin probe studies are preliminary, but tend against additivity. A corollary to the Gibbs-Guggenheim Principle is enunciated, and the Principle is restated that for any charged species, neither the difference in electrostatic potential nor the sum of the differences in the non-electrostatic components of the thermodynamic potential difference between regions of different chemical compositions can be measured.

Two-dimensional computer simulation of EMVJ and grating solar cells under AMO illumination

NASA Technical Reports Server (NTRS)

Gray, J. L.; Schwartz, R. J.

1984-01-01

A computer program, SCAP2D (Solar Cell Analysis Program in 2-Dimensions), is used to evaluate the Etched Multiple Vertical Junction (EMVJ) and grating solar cells. The aim is to demonstrate how SCAP2D can be used to evaluate cell designs. The cell designs studied are by no means optimal designs. The SCAP2D program solves the three coupled, nonlinear partial differential equations, Poisson's Equation and the hole and electron continuity equations, simultaneously in two-dimensions using finite differences to discretize the equations and Newton's Method to linearize them. The variables solved for are the electrostatic potential and the hole and electron concentrations. Each linear system of equations is solved directly by Gaussian Elimination. Convergence of the Newton Iteration is assumed when the largest correction to the electrostatic potential or hole or electron quasi-potential is less than some predetermined error. A typical problem involves 2000 nodes with a Jacobi matrix of order 6000 and a bandwidth of 243.

Role of electrostatic interactions during protein ultrafiltration.

PubMed

Rohani, Mahsa M; Zydney, Andrew L

2010-10-15

A number of studies over the last decade have clearly demonstrated the importance of electrostatic interactions on the transport of charged proteins through semipermeable ultrafiltration membranes. This paper provides a review of recent developments in this field with a focus on the role of both protein and membrane charge on the rate of protein transport. Experimental results are analyzed using available theoretical models developed from the solution of the Poisson-Boltzmann equation for the partitioning of a charged particle into a charged pore. The potential of exploiting these electrostatic interactions for selective protein separations and for the development of ultrafiltration membranes with enhanced performance characteristics is also examined. Copyright © 2010 Elsevier B.V. All rights reserved.

On the equilibrium charge density at tilt grain boundaries

NASA Astrophysics Data System (ADS)

Srikant, V.; Clarke, D. R.

1998-05-01

The equilibrium charge density and free energy of tilt grain boundaries as a function of their misorientation is computed using a Monte Carlo simulation that takes into account both the electrostatic and configurational energies associated with charges at the grain boundary. The computed equilibrium charge density increases with the grain-boundary angle and approaches a saturation value. The equilibrium charge density at large-angle grain boundaries compares well with experimental values for large-angle tilt boundaries in GaAs. The computed grain-boundary electrostatic energy is in agreement with the analytical solution to a one-dimensional Poisson equation at high donor densities but indicates that the analytical solution overestimates the electrostatic energy at lower donor densities.

Electrostatic Interactions Between Glycosaminoglycan Molecules

NASA Astrophysics Data System (ADS)

Song, Fan; Moyne, Christian; Bai, Yi-Long

2005-02-01

The electrostatic interactions between nearest-neighbouring chondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains are obtained on the bottle brush conformation of proteoglycan aggrecan based on an asymptotic solution of the Poisson-Boltzmann equation the CS-GAGs satisfy under the physiological conditions of articular cartilage. The present results show that the interactions are associated intimately with the minimum separation distance and mutual angle between the molecular chains themselves. Further analysis indicates that the electrostatic interactions are not only expressed to be purely exponential in separation distance and decrease with the increasing mutual angle but also dependent sensitively on the saline concentration in the electrolyte solution within the tissue, which is in agreement with the existed relevant conclusions.

On the theory of electric double layer with explicit account of a polarizable co-solvent.

PubMed

Budkov, Yu A; Kolesnikov, A L; Kiselev, M G

2016-05-14

We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the grand thermodynamic potential with respect to the electrostatic potential. We apply present modified Poisson-Boltzmann equation to the electric double layer theory, showing that accounting for the excluded volume of co-solvent molecules and ions slightly changes the main result of our previous simplified theory. Namely, in the case of small co-solvent polarizability with its increase under the enough small surface potentials of electrode, the differential capacitance undergoes the significant growth. Oppositely, when the surface potential exceeds some threshold value (which is slightly smaller than the saturation potential), the increase in the co-solvent polarizability results in a differential capacitance decrease. However, when the co-solvent polarizability exceeds some threshold value, its increase generates a considerable enhancement of the differential capacitance in a wide range of surface potentials. We demonstrate that two qualitatively different behaviors of the differential capacitance are related to the depletion and adsorption of co-solvent molecules at the charged electrode. We show that an additive of the strongly polarizable co-solvent to an electrolyte solution can shift significantly the saturation potential in two qualitatively different manners. Namely, a small additive of strongly polarizable co-solvent results in a shift of saturation potential to higher surface potentials. On the contrary, a sufficiently large additive of co-solvent shifts the saturation potential to lower surface potentials. We obtain that an increase in the co-solvent polarizability makes the electrostatic potential profile longer-ranged. However, increase in the co-solvent concentration in the bulk leads to non-monotonic behavior of the electrostatic potential profile. An increase in the co-solvent concentration in the bulk at its sufficiently small values makes the electrostatic potential profile longer-ranged. Oppositely, when the co-solvent concentration in the bulk exceeds some threshold value, its further increase leads to decrease in electrostatic potential at all distances from the electrode.

Electro-osmosis over inhomogeneously charged surfaces in presence of non-electrostatic ion-ion interactions

NASA Astrophysics Data System (ADS)

Ghosh, Uddipta; Chakraborty, Suman

2016-06-01

In this study, we attempt to bring out a generalized formulation for electro-osmotic flows over inhomogeneously charged surfaces in presence of non-electrostatic ion-ion interactions. To this end, we start with modified electro-chemical potential of the individual species and subsequently use it to derive modified Nernst-Planck equation accounting for the ionic fluxes generated because of the presence of non-electrostatic potential. We establish what we refer to as the Poisson-Helmholtz-Nernst-Planck equations, coupled with the Navier-Stokes equations, to describe the complete transport process. Our analysis shows that the presence of non-electrostatic interactions between the ions results in an excess body force on the fluid, and modifies the osmotic pressure as well, which has hitherto remained unexplored. We further apply our analysis to a simple geometry, in an effort to work out the Smoluchowski slip velocity for thin electrical double layer limits. To this end, we employ singular perturbation and develop a general framework for the asymptotic analysis. Our calculations reveal that the final expression for slip velocity remains the same as that without accounting for non-electrostatic interactions. However, the presence of non-electrostatic interactions along with ion specificity can significantly change the quantitative behavior of Smoluchowski slip velocity. We subsequently demonstrate that the presence of non-electrostatic interactions may significantly alter the effective interfacial potential, also termed as the "Zeta potential." Our analysis can potentially act as a guide towards the prediction and possibly quantitative determination of the implications associated with the existence of non-electrostatic potential, in an electrokinetic transport process.

Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Wang, Jun; Luo, Ray

2009-01-01

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

On the Electrostatic Born-Infeld Equation with Extended Charges

NASA Astrophysics Data System (ADS)

Bonheure, Denis; d'Avenia, Pietro; Pomponio, Alessio

2016-09-01

In this paper, we deal with the electrostatic Born-Infeld equation -operatorname{div} (nablaφ/√{1-|nabla φ|^2} )= ρ quad{in} {R}^N, lim_{|x|to ∞} φ(x)= 0,. quad quad quad quad ({{BI}}) where {ρ} is an assigned extended charge density. We are interested in the existence and uniqueness of the potential {φ} and finiteness of the energy of the electrostatic field {-nabla φ}. We first relax the problem and treat it with the direct method of the Calculus of Variations for a broad class of charge densities. Assuming {ρ} is radially distributed, we recover the weak formulation of {({{BI}})} and the regularity of the solution of the Poisson equation (under the same smoothness assumptions). In the case of a locally bounded charge, we also recover the weak formulation without assuming any symmetry. The solution is even classical if {ρ} is smooth. Then we analyze the case where the density {ρ} is a superposition of point charges and discuss the results in (Kiessling, Commun Math Phys 314:509-523, 2012). Other models are discussed, as for instance a system arising from the coupling of the nonlinear Klein-Gordon equation with the Born-Infeld theory.

Electrostatic energy and screened charge interaction near the surface of metals with different Fermi surface shape

NASA Astrophysics Data System (ADS)

Gabovich, A. M.; Il'chenko, L. G.; Pashitskii, E. A.; Romanov, Yu. A.

1980-04-01

Using the Poisson equation Green function for a self-consistent field in a spatially inhomogeneous system, expressions for the electrostatic energy and screened charge interaction near the surface of a semi-infinite metal and a thin quantizing film are derived. It is shown that the decrease law and Friedel oscillation amplitude of adsorbed atom indirect interaction are determined by the electron spectrum character and the Fermi surface shape. The results obtained enable us to explain, in particular, the submonolayer adsorbed film structure on the W and Mo surfaces.

PBEQ-Solver for online visualization of electrostatic potential of biomolecules.

PubMed

Jo, Sunhwan; Vargyas, Miklos; Vasko-Szedlar, Judit; Roux, Benoît; Im, Wonpil

2008-07-01

PBEQ-Solver provides a web-based graphical user interface to read biomolecular structures, solve the Poisson-Boltzmann (PB) equations and interactively visualize the electrostatic potential. PBEQ-Solver calculates (i) electrostatic potential and solvation free energy, (ii) protein-protein (DNA or RNA) electrostatic interaction energy and (iii) pKa of a selected titratable residue. All the calculations can be performed in both aqueous solvent and membrane environments (with a cylindrical pore in the case of membrane). PBEQ-Solver uses the PBEQ module in the biomolecular simulation program CHARMM to solve the finite-difference PB equation of molecules specified by users. Users can interactively inspect the calculated electrostatic potential on the solvent-accessible surface as well as iso-electrostatic potential contours using a novel online visualization tool based on MarvinSpace molecular visualization software, a Java applet integrated within CHARMM-GUI (http://www.charmm-gui.org). To reduce the computational time on the server, and to increase the efficiency in visualization, all the PB calculations are performed with coarse grid spacing (1.5 A before and 1 A after focusing). PBEQ-Solver suggests various physical parameters for PB calculations and users can modify them if necessary. PBEQ-Solver is available at http://www.charmm-gui.org/input/pbeqsolver.

A spectral Poisson solver for kinetic plasma simulation

NASA Astrophysics Data System (ADS)

Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf

2011-10-01

Plasma resonance spectroscopy is a well established plasma diagnostic method, realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In this contribution we concentrate on the specialized Poisson solver for that tool. The plasma is represented by an ensemble of point charges. By expanding both the charge density and the potential into spherical harmonics, a largely analytical solution of the Poisson problem can be employed. For a practical implementation, the expansion must be appropriately truncated. With this spectral solver we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.

A modified Poisson-Boltzmann equation applied to protein adsorption.

PubMed

Gama, Marlon de Souza; Santos, Mirella Simões; Lima, Eduardo Rocha de Almeida; Tavares, Frederico Wanderley; Barreto, Amaro Gomes Barreto

2018-01-05

Ion-exchange chromatography has been widely used as a standard process in purification and analysis of protein, based on the electrostatic interaction between the protein and the stationary phase. Through the years, several approaches are used to improve the thermodynamic description of colloidal particle-surface interaction systems, however there are still a lot of gaps specifically when describing the behavior of protein adsorption. Here, we present an improved methodology for predicting the adsorption equilibrium constant by solving the modified Poisson-Boltzmann (PB) equation in bispherical coordinates. By including dispersion interactions between ions and protein, and between ions and surface, the modified PB equation used can describe the Hofmeister effects. We solve the modified Poisson-Boltzmann equation to calculate the protein-surface potential of mean force, treated as spherical colloid-plate system, as a function of process variables. From the potential of mean force, the Henry constants of adsorption, for different proteins and surfaces, are calculated as a function of pH, salt concentration, salt type, and temperature. The obtained Henry constants are compared with experimental data for several isotherms showing excellent agreement. We have also performed a sensitivity analysis to verify the behavior of different kind of salts and the Hofmeister effects. Copyright © 2017 Elsevier B.V. All rights reserved.

Ion strength limit of computed excess functions based on the linearized Poisson-Boltzmann equation.

PubMed

Fraenkel, Dan

2015-12-05

The linearized Poisson-Boltzmann (L-PB) equation is examined for its κ-range of validity (κ, Debye reciprocal length). This is done for the Debye-Hückel (DH) theory, i.e., using a single ion size, and for the SiS treatment (D. Fraenkel, Mol. Phys. 2010, 108, 1435), which extends the DH theory to the case of ion-size dissimilarity (therefore dubbed DH-SiS). The linearization of the PB equation has been claimed responsible for the DH theory's failure to fit with experiment at > 0.1 m; but DH-SiS fits with data of the mean ionic activity coefficient, γ± (molal), against m, even at m > 1 (κ > 0.33 Å(-1) ). The SiS expressions combine the overall extra-electrostatic potential energy of the smaller ion, as central ion-Ψa>b (κ), with that of the larger ion, as central ion-Ψb>a (κ); a and b are, respectively, the counterion and co-ion distances of closest approach. Ψa>b and Ψb>a are derived from the L-PB equation, which appears to conflict with their being effective up to moderate electrolyte concentrations (≈1 m). However, the L-PB equation can be valid up to κ ≥ 1.3 Å(-1) if one abandons the 1/κ criterion for its effectiveness and, instead, use, as criterion, the mean-field electrostatic interaction potential of the central ion with its ion cloud, at a radial distance dividing the cloud charge into two equal parts. The DH theory's failure is, thus, not because of using the L-PB equation; the lethal approximation is assigning a single size to the positive and negative ions. © 2015 Wiley Periodicals, Inc.

Nonlocal Poisson-Fermi model for ionic solvent.

PubMed

Xie, Dexuan; Liu, Jinn-Liang; Eisenberg, Bob

2016-07-01

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Hou, Tingjun; McCammon, J. Andrew

2005-08-01

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM.

Including diverging electrostatic potential in 3D-RISM theory: The charged wall case.

PubMed

Vyalov, Ivan; Rocchia, Walter

2018-03-21

Although three-dimensional site-site molecular integral equations of liquids are a powerful tool of the modern theoretical chemistry, their applications to the problem of characterizing the electrical double layer originating at the solid-liquid interface with a macroscopic substrate are severely limited by the fact that an infinitely extended charged plane generates a divergent electrostatic potential. Such potentials cannot be treated within the standard 3D-Reference Interaction Site Model equation solution framework since it leads to functions that are not Fourier transformable. In this paper, we apply a renormalization procedure to overcome this obstacle. We then check the validity and numerical accuracy of the proposed computational scheme on the prototypical gold (111) surface in contact with water/alkali chloride solution. We observe that despite the proposed method requires, to achieve converged charge densities, a higher spatial resolution than that suited to the estimation of biomolecular solvation with either 3D-RISM or continuum electrostatics approaches, it still is computationally efficient. Introducing the electrostatic potential of an infinite wall, which is periodic in 2 dimensions, we avoid edge effects, permit a robust integration of Poisson's equation, and obtain the 3D electrostatic potential profile for the first time in such calculations. We show that the potential within the electrical double layer presents oscillations which are not grasped by the Debye-Hückel and Gouy-Chapman theories. This electrostatic potential deviates from its average of up to 1-2 V at small distances from the substrate along the lateral directions. Applications of this theoretical development are relevant, for example, for liquid scanning tunneling microscopy imaging.

Including diverging electrostatic potential in 3D-RISM theory: The charged wall case

NASA Astrophysics Data System (ADS)

Vyalov, Ivan; Rocchia, Walter

2018-03-01

Although three-dimensional site-site molecular integral equations of liquids are a powerful tool of the modern theoretical chemistry, their applications to the problem of characterizing the electrical double layer originating at the solid-liquid interface with a macroscopic substrate are severely limited by the fact that an infinitely extended charged plane generates a divergent electrostatic potential. Such potentials cannot be treated within the standard 3D-Reference Interaction Site Model equation solution framework since it leads to functions that are not Fourier transformable. In this paper, we apply a renormalization procedure to overcome this obstacle. We then check the validity and numerical accuracy of the proposed computational scheme on the prototypical gold (111) surface in contact with water/alkali chloride solution. We observe that despite the proposed method requires, to achieve converged charge densities, a higher spatial resolution than that suited to the estimation of biomolecular solvation with either 3D-RISM or continuum electrostatics approaches, it still is computationally efficient. Introducing the electrostatic potential of an infinite wall, which is periodic in 2 dimensions, we avoid edge effects, permit a robust integration of Poisson's equation, and obtain the 3D electrostatic potential profile for the first time in such calculations. We show that the potential within the electrical double layer presents oscillations which are not grasped by the Debye-Hückel and Gouy-Chapman theories. This electrostatic potential deviates from its average of up to 1-2 V at small distances from the substrate along the lateral directions. Applications of this theoretical development are relevant, for example, for liquid scanning tunneling microscopy imaging.

Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

PubMed Central

Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

2012-01-01

The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

Poisson-Boltzmann-Nernst-Planck model

NASA Astrophysics Data System (ADS)

Zheng, Qiong; Wei, Guo-Wei

2011-05-01

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Poisson-Boltzmann-Nernst-Planck model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng Qiong; Wei Guowei; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species inmore » the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.« less

Poisson-Boltzmann-Nernst-Planck model.

PubMed

Zheng, Qiong; Wei, Guo-Wei

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. © 2011 American Institute of Physics.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions

NASA Astrophysics Data System (ADS)

Netz, R. R.; Orland, H.

2000-02-01

We formulate the exact non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point of the field-theoretic action, and the effects of counter-ion fluctuations are included by a loop-wise expansion around this saddle point. The Poisson equation is obeyed at each order in this loop expansion. We explicitly give the expansion of the Gibbs potential up to two loops. We then apply our field-theoretic formalism to the case of a single impenetrable wall with counter ions only (in the absence of salt ions). We obtain the fluctuation corrections to the electrostatic potential and the counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. The effective interactions and correlation functions between charged particles close to the charged wall are obtained on the one-loop level.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

PubMed Central

Botello-Smith, Wesley M.; Luo, Ray

2016-01-01

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966

Hydration effects on the electrostatic potential around tuftsin.

PubMed

Valdeavella, C V; Blatt, H D; Yang, L; Pettitt, B M

1999-08-01

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr-Lys-Pro-Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson-Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed.

Possible influence of the Kuramoto length in a photo-catalytic water splitting reaction revealed by Poisson-Nernst-Planck equations involving ionization in a weak electrolyte

NASA Astrophysics Data System (ADS)

Suzuki, Yohichi; Seki, Kazuhiko

2018-03-01

We studied ion concentration profiles and the charge density gradient caused by electrode reactions in weak electrolytes by using the Poisson-Nernst-Planck equations without assuming charge neutrality. In weak electrolytes, only a small fraction of molecules is ionized in bulk. Ion concentration profiles depend on not only ion transport but also the ionization of molecules. We considered the ionization of molecules and ion association in weak electrolytes and obtained analytical expressions for ion densities, electrostatic potential profiles, and ion currents. We found the case that the total ion density gradient was given by the Kuramoto length which characterized the distance over which an ion diffuses before association. The charge density gradient is characterized by the Debye length for 1:1 weak electrolytes. We discuss the role of these length scales for efficient water splitting reactions using photo-electrocatalytic electrodes.

A 2D electrostatic PIC code for the Mark III Hypercube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferraro, R.D.; Liewer, P.C.; Decyk, V.K.

We have implemented a 2D electrostastic plasma particle in cell (PIC) simulation code on the Caltech/JPL Mark IIIfp Hypercube. The code simulates plasma effects by evolving in time the trajectories of thousands to millions of charged particles subject to their self-consistent fields. Each particle`s position and velocity is advanced in time using a leap frog method for integrating Newton`s equations of motion in electric and magnetic fields. The electric field due to these moving charged particles is calculated on a spatial grid at each time by solving Poisson`s equation in Fourier space. These two tasks represent the largest part ofmore » the computation. To obtain efficient operation on a distributed memory parallel computer, we are using the General Concurrent PIC (GCPIC) algorithm previously developed for a 1D parallel PIC code.« less

Electrostatics of proteins in dielectric solvent continua. II. First applications in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Stork, Martina; Tavan, Paul

2007-04-01

In the preceding paper by Stork and Tavan, [J. Chem. Phys. 126, 165105 (2007)], the authors have reformulated an electrostatic theory which treats proteins surrounded by dielectric solvent continua and approximately solves the associated Poisson equation [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)]. The resulting solution comprises analytical expressions for the electrostatic reaction field (RF) and potential, which are generated within the protein by the polarization of the surrounding continuum. Here the field and potential are represented in terms of Gaussian RF dipole densities localized at the protein atoms. Quite like in a polarizable force field, also the RF dipole at a given protein atom is induced by the partial charges and RF dipoles at the other atoms. Based on the reformulated theory, the authors have suggested expressions for the RF forces, which obey Newton's third law. Previous continuum approaches, which were also built on solutions of the Poisson equation, used to violate the reactio principle required by this law, and thus were inapplicable to molecular dynamics (MD) simulations. In this paper, the authors suggest a set of techniques by which one can surmount the few remaining hurdles still hampering the application of the theory to MD simulations of soluble proteins and peptides. These techniques comprise the treatment of the RF dipoles within an extended Lagrangian approach and the optimization of the atomic RF polarizabilities. Using the well-studied conformational dynamics of alanine dipeptide as the simplest example, the authors demonstrate the remarkable accuracy and efficiency of the resulting RF-MD approach.

AN EFFICIENT HIGHER-ORDER FAST MULTIPOLE BOUNDARY ELEMENT SOLUTION FOR POISSON-BOLTZMANN BASED MOLECULAR ELECTROSTATICS

PubMed Central

Bajaj, Chandrajit; Chen, Shun-Chuan; Rand, Alexander

2011-01-01

In order to compute polarization energy of biomolecules, we describe a boundary element approach to solving the linearized Poisson-Boltzmann equation. Our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface. State of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation. We perform a variety of computational experiments, testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy. PMID:21660123

Modeling the Electrostatics of Hollow Shell Suspensions: Ion Distribution, Pair Interactions, and Many-Body Effects.

PubMed

Hallez, Yannick; Meireles, Martine

2016-10-11

Electrostatic interactions play a key role in hollow shell suspensions as they determine their structure, stability, thermodynamics, and rheology and also the loading capacity of small charged species for nanoreservoir applications. In this work, fast, reliable modeling strategies aimed at predicting the electrostatics of hollow shells for one, two, and many colloids are proposed and validated. The electrostatic potential inside and outside a hollow shell with a finite thickness and a specific permittivity is determined analytically in the Debye-Hückel (DH) limit. An expression for the interaction potential between two such hollow shells is then derived and validated numerically. It follows a classical Yukawa form with an effective charge depending on the shell geometry, permittivity, and inner and outer surface charge densities. The predictions of the Ornstein-Zernike (OZ) equation with this pair potential to determine equations of state are then evaluated by comparison to results obtained with a Brownian dynamics algorithm coupled to the resolution of the linearized Poisson-Boltzmann and Laplace equations (PB-BD simulations). The OZ equation based on the DLVO-like potential performs very well in the dilute regime as expected, but also quite well, and more surprisingly, in the concentrated regime in which full spheres exhibit significant many-body effects. These effects are shown to vanish for shells with small thickness and high permittivity. For highly charged hollow shells, we propose and validate a charge renormalization procedure. Finally, using PB-BD simulations, we show that the cell model predicts the ion distribution inside and outside hollow shells accurately in both electrostatically dilute and concentrated suspensions. We then determine the shell loading capacity as a function of salt concentration, volume fraction, and surface charge density for nanoreservoir applications such as drug delivery, sensing, or smart coatings.

Counterion accumulation effects on a suspension of DNA molecules: Equation of state and pressure-driven denaturation

NASA Astrophysics Data System (ADS)

Nicasio-Collazo, Luz Adriana; Delgado-González, Alexandra; Hernández-Lemus, Enrique; Castañeda-Priego, Ramón

2017-04-01

The study of the effects associated with the electrostatic properties of DNA is of fundamental importance to understand both its molecular properties at the single molecule level, like the rigidity of the chain, and its interaction with other charged bio-molecules, including other DNA molecules; such interactions are crucial to maintain the thermodynamic stability of the intra-cellular medium. In the present work, we combine the Poisson-Boltzmann mean-field theory with an irreversible thermodynamic approximation to analyze the effects of counterion accumulation inside DNA on both the denaturation profile of the chain and the equation of state of the suspension. To this end, we model the DNA molecule as a porous charged cylinder immersed in an aqueous solution. These thermo-electrostatic effects are explicitly studied in the particular case of some genes for which damage in their sequence is associated with diffuse large B-cell lymphoma.

Electrostatic Rate Enhancement and Transient Complex of Protein-Protein Association

PubMed Central

Alsallaq, Ramzi; Zhou, Huan-Xiang

2012-01-01

The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to ~105 – 106 M−1s−1. Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys. J. 1997;73:2441–2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by kD = kD0 exp(−*/ kBT), where kD and kD0 are the rates in the presence and absence of electrostatic interactions, respectively, * is the average electrostatic interaction energy in a “transient-complex” ensemble, and kBT is thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007, 15:215–224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations. PMID:17932929

Generation of low-emittance electron beams in electrostatic accelerators for FEL applications

NASA Astrophysics Data System (ADS)

Chen, Teng; Elias, Luis R.

1995-02-01

This paper reports results of transverse emittance studies and beam propagation in electrostatic accelerators for free electron laser applications. In particular, we discuss emittance growth analysis of a low current electron beam system consisting of a miniature thermoionic electron gun and a National Electrostatics Accelerator (NEC) tube. The emittance growth phenomenon is discussed in terms of thermal effects in the electron gun cathode and aberrations produced by field gradient changes occurring inside the electron gun and throughout the accelerator tube. A method of reducing aberrations using a magnetic solenoidal field is described. Analysis of electron beam emittance was done with the EGUN code. Beam propagation along the accelerator tube was studied using a cylindrically symmetric beam envelope equation that included beam self-fields and the external accelerator fields which were derived from POISSON simulations.

Progress in developing Poisson-Boltzmann equation solvers

PubMed Central

Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil

2013-01-01

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185

AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

2010-06-01

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summaryProgram title: AFMPB: Adaptive fast multipole Poisson-Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson-Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix-vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids

PubMed Central

Boschitsch, Alexander H.; Fenley, Marcia O.

2011-01-01

An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent – analytical solutions are available for this case, thus allowing rigorous assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities – obtained with both linear and nonlinear Poisson-Boltzmann equation – for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers. PMID:21984876

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

NASA Astrophysics Data System (ADS)

Cherstvy, A. G.; Winkler, R. G.

2006-08-01

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthén potential, which is used as an approximation for the screened Debye-Hückel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

The impact of electrostatic correlations on Dielectrophoresis of Non-conducting Particles

NASA Astrophysics Data System (ADS)

Alidoosti, Elaheh; Zhao, Hui

2017-11-01

The dipole moment of a charged, dielectric, spherical particle under the influence of a uniform alternating electric field is computed theoretically and numerically by solving the modified continuum Poisson-Nernst-Planck (PNP) equations accounting for ion-ion electrostatic correlations that is important at concentrated electrolytes (Phys. Rev. Lett. 106, 2011). The dependence on the frequency, zeta potential, electrostatic correlation lengths, and double layer thickness is thoroughly investigated. In the limit of thin double layers, we carry out asymptotic analysis to develop simple models which are in good agreement with the modified PNP model. Our results suggest that the electrostatic correlations have a complicated impact on the dipole moment. As the electrostatic correlations length increases, the dipole moment decreases, initially, reach a minimum, and then increases since the surface conduction first decreases and then increases due to the ion-ion correlations. The modified PNP model can improve the theoretical predictions particularly at low frequencies where the simple model can't qualitatively predict the dipole moment. This work was supported, in part, by NIH R15GM116039.

Electrostatic rate enhancement and transient complex of protein-protein association.

PubMed

Alsallaq, Ramzi; Zhou, Huan-Xiang

2008-04-01

The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to approximately 10(5)-10(6) M(-1) s(-1). Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys J 1997;73:2441-2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by $k_{\\bf D}$ = $k_{D}0\\ {exp} ( - \\langle U_{el} \\rangle;{\\star}/k_{B} T),$ where k(D) and k(D0) are the rates in the presence and absence of electrostatic interactions, respectively, U(el) is the average electrostatic interaction energy in a "transient-complex" ensemble, and k(B)T is the thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with the experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007;15:215-224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations. (c) 2007 Wiley-Liss, Inc.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Optimizing electrostatic field calculations with the Adaptive Poisson-Boltzmann Solver to predict electric fields at protein-protein interfaces II: explicit near-probe and hydrogen-bonding water molecules.

PubMed

Ritchie, Andrew W; Webb, Lauren J

2014-07-17

We have examined the effects of including explicit, near-probe solvent molecules in a continuum electrostatics strategy using the linear Poisson-Boltzmann equation with the Adaptive Poisson-Boltzmann Solver (APBS) to calculate electric fields at the midpoint of a nitrile bond both at the surface of a monomeric protein and when docked at a protein-protein interface. Results were compared to experimental vibrational absorption energy measurements of the nitrile oscillator. We examined three methods for selecting explicit water molecules: (1) all water molecules within 5 Å of the nitrile nitrogen; (2) the water molecule closest to the nitrile nitrogen; and (3) any single water molecule hydrogen-bonding to the nitrile. The correlation between absolute field strengths with experimental absorption energies were calculated and it was observed that method 1 was only an improvement for the monomer calculations, while methods 2 and 3 were not significantly different from the purely implicit solvent calculations for all protein systems examined. Upon taking the difference in calculated electrostatic fields and comparing to the difference in absorption frequencies, we typically observed an increase in experimental correlation for all methods, with method 1 showing the largest gain, likely due to the improved absolute monomer correlations using that method. These results suggest that, unlike with quantum mechanical methods, when calculating absolute fields using entirely classical models, implicit solvent is typically sufficient and additional work to identify hydrogen-bonding or nearest waters does not significantly impact the results. Although we observed that a sphere of solvent near the field of interest improved results for relative field calculations, it should not be consider a panacea for all situations.

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes.

PubMed

Ubbink, Job; Khokhlov, Alexei R

2004-03-15

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)]. (c) 2004 American Institute of Physics.

Protein-ion binding process on finite macromolecular concentration. A Poisson-Boltzmann and Monte Carlo study.

PubMed

de Carvalho, Sidney Jurado; Fenley, Márcia O; da Silva, Fernando Luís Barroso

2008-12-25

Electrostatic interactions are one of the key driving forces for protein-ligands complexation. Different levels for the theoretical modeling of such processes are available on the literature. Most of the studies on the Molecular Biology field are performed within numerical solutions of the Poisson-Boltzmann Equation and the dielectric continuum models framework. In such dielectric continuum models, there are two pivotal questions: (a) how the protein dielectric medium should be modeled, and (b) what protocol should be used when solving this effective Hamiltonian. By means of Monte Carlo (MC) and Poisson-Boltzmann (PB) calculations, we define the applicability of the PB approach with linear and nonlinear responses for macromolecular electrostatic interactions in electrolyte solution, revealing some physical mechanisms and limitations behind it especially due the raise of both macromolecular charge and concentration out of the strong coupling regime. A discrepancy between PB and MC for binding constant shifts is shown and explained in terms of the manner PB approximates the excess chemical potentials of the ligand, and not as a consequence of the nonlinear thermal treatment and/or explicit ion-ion interactions as it could be argued. Our findings also show that the nonlinear PB predictions with a low dielectric response well reproduce the pK shifts calculations carried out with an uniform dielectric model. This confirms and completes previous results obtained by both MC and linear PB calculations.

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

Multiscale modeling and computation of nano-electronic transistors and transmembrane proton channels

NASA Astrophysics Data System (ADS)

Chen, Duan

The miniaturization of nano-scale electronic transistors, such as metal oxide semiconductor field effect transistors (MOSFETs), has given rise to a pressing demand in the new theoretical understanding and practical tactic for dealing with quantum mechanical effects in integrated circuits. In biology, proton dynamics and transport across membrane proteins are of paramount importance to the normal function of living cells. Similar physical characteristics are behind the two subjects, and model simulations share common mathematical interests/challenges. In this thesis work, multiscale and multiphysical models are proposed to study the mechanisms of nanotransistors and proton transport in transmembrane at the atomic level. For nano-electronic transistors, we introduce a unified two-scale energy functional to describe the electrons and the continuum electrostatic potential. This framework enables us to put microscopic and macroscopic descriptions on an equal footing at nano-scale. Additionally, this model includes layered structures and random doping effect of nano-transistors. For transmembrane proton channels, we describe proton dynamics quantum mechanically via a density functional approach while implicitly treat numerous solvent molecules as a dielectric continuum. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered in atomic details. We formulate a total free energy functional to include kinetic and potential energies of protons, as well as electrostatic energy of all other ions on an equal footing. For both nano-transistors and proton channels systems, the variational principle is employed to derive nonlinear governing equations. The Poisson-Kohn-Sham equations are derived for nano-transistors while the generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained for proton channels. Related numerical challenges in simulations are addressed: the matched interface and boundary (MIB) method, the Dirichlet-to-Neumann mapping (DNM) technique, and the Krylov subspace and preconditioner theory are introduced to improve the computational efficiency of the Poisson-type equation. The quantum transport theory is employed to solve the Kohn-Sham equation. The Gummel iteration and relaxation technique are utilized for overall self-consistent iterations. Finally, applications are considered and model validations are verified by realistic nano-transistors and transmembrane proteins. Two distinct device configurations, a double-gate MOSFET and a four-gate MOSFET, are considered in our threedimensional numerical simulations. For these devices, the current uctuation and voltage threshold lowering effect induced by discrete dopants are explored. For proton transport, a realistic channel protein, the Gramicidin A (GA) is used to demonstrate the performance of the proposed proton channel model and validate the efficiency of the proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. Proton channel conductances are studied over a number of applied voltages and reference concentrations. Comparisons with experimental data are utilized to verify our model predictions.

Computational time analysis of the numerical solution of 3D electrostatic Poisson's equation

NASA Astrophysics Data System (ADS)

Kamboh, Shakeel Ahmed; Labadin, Jane; Rigit, Andrew Ragai Henri; Ling, Tech Chaw; Amur, Khuda Bux; Chaudhary, Muhammad Tayyab

2015-05-01

3D Poisson's equation is solved numerically to simulate the electric potential in a prototype design of electrohydrodynamic (EHD) ion-drag micropump. Finite difference method (FDM) is employed to discretize the governing equation. The system of linear equations resulting from FDM is solved iteratively by using the sequential Jacobi (SJ) and sequential Gauss-Seidel (SGS) methods, simulation results are also compared to examine the difference between the results. The main objective was to analyze the computational time required by both the methods with respect to different grid sizes and parallelize the Jacobi method to reduce the computational time. In common, the SGS method is faster than the SJ method but the data parallelism of Jacobi method may produce good speedup over SGS method. In this study, the feasibility of using parallel Jacobi (PJ) method is attempted in relation to SGS method. MATLAB Parallel/Distributed computing environment is used and a parallel code for SJ method is implemented. It was found that for small grid size the SGS method remains dominant over SJ method and PJ method while for large grid size both the sequential methods may take nearly too much processing time to converge. Yet, the PJ method reduces computational time to some extent for large grid sizes.

Continuum description of ionic and dielectric shielding for molecular-dynamics simulations of proteins in solution

NASA Astrophysics Data System (ADS)

Egwolf, Bernhard; Tavan, Paul

2004-01-01

We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)], which has provided an efficient and accurate solution of the Poisson equation, to ionic solvents as described by the linearized Poisson-Boltzmann (LPB) equation. We start with the formulation of a general theory for the electrostatics of an arbitrarily shaped molecular system, which consists of partially charged atoms and is embedded in a LPB continuum. This theory represents the reaction field induced by the continuum in terms of charge and dipole densities localized within the molecular system. Because these densities cannot be calculated analytically for systems of arbitrary shape, we introduce an atom-based discretization and a set of carefully designed approximations. This allows us to represent the densities by charges and dipoles located at the atoms. Coupled systems of linear equations determine these multipoles and can be rapidly solved by iteration during a MD simulation. The multipoles yield the reaction field forces and energies. Finally, we scrutinize the quality of our approach by comparisons with an analytical solution restricted to perfectly spherical systems and with results of a finite difference method.

Long-ranged electrostatic repulsion and crystallization of emulsion droplets in an ultralow dielectric medium supercritical carbon dioxide.

PubMed

Ryoo, Won; Webber, Stephen E; Bonnecaze, Roger T; Johnston, Keith P

2006-01-31

Electrostatic repulsion stabilizes micrometer-sized water droplets with spacings greater than 10 microm in an ultralow dielectric medium, CO2 (epsilon = 1.5), at elevated pressures. The morphology of the water/CO2 emulsion is characterized by optical microscopy and laser diffraction as a function of height. The counterions, stabilized with a nonionic, highly branched, stubby hydrocarbon surfactant, form an extremely thick double layer with a Debye screening length of 8.9 microm. As a result of the balance between electrostatic repulsion and the downward force due to gravity, the droplets formed a hexagonal crystalline lattice at the bottom of the high-pressure cell with spacings of over 10 microm. The osmotic pressure, calculated by solving the Poisson-Boltzmann equation in the framework of the Wigner-Seitz cell model, is in good agreement with that determined from the sedimentation profile measured by laser diffraction. Thus, the long-ranged stabilization of the emulsion may be attributed to electrostatic stabilization. The ability to form new types of colloids in CO2 with electrostatic stabilization is beneficial because steric stabilization is often unsatisfactory because of poor solvation of the stabilizers.

Modeling electrokinetics in ionic liquids: General

DOE PAGES

Wang, Chao; Bao, Jie; Pan, Wenxiao; ...

2017-04-01

Using direct numerical simulations, we provide a thorough study regarding the electrokinetics of ionic liquids. In particular, modified Poisson–Nernst–Planck equations are solved to capture the crowding and overscreening effects characteristic of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the modified Poisson-Nernst-Planck equations are coupled with Navier–Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel charged surfaces, charging dynamics in a nanopore, capacitance of electric double-layer capacitors, electroosmotic flow in a nanochannel, electroconvective instability on a plane ion-selective surface, and electroconvective flow on amore » curved ionselective surface. Lastly, we also discuss how crowding and overscreening and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.« less

THREE-DIMENSIONAL NON-VACUUM PULSAR OUTER-GAP MODEL: LOCALIZED ACCELERATION ELECTRIC FIELD IN THE HIGHER ALTITUDES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hirotani, Kouichi

2015-01-10

We investigate the particle accelerator that arises in a rotating neutron-star magnetosphere. Simultaneously solving the Poisson equation for the electro-static potential, the Boltzmann equations for relativistic electrons and positrons, and the radiative transfer equation, we demonstrate that the electric field is substantially screened along the magnetic field lines by pairs that are created and separated within the accelerator. As a result, the magnetic-field-aligned electric field is localized in higher altitudes near the light cylinder and efficiently accelerates the positrons created in the lower altitudes outward but does not accelerate the electrons inward. The resulting photon flux becomes predominantly outward, leadingmore » to typical double-peak light curves, which are commonly observed from many high-energy pulsars.« less

ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION

PubMed Central

HOLST, MICHAEL; MCCAMMON, JAMES ANDREW; YU, ZEYUN; ZHOU, YOUNGCHENG; ZHU, YUNRONG

2011-01-01

We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein. PMID:21949541

Biomolecular surface construction by PDE transform

PubMed Central

Zheng, Qiong; Yang, Siyang; Wei, Guo-Wei

2011-01-01

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high order PDEs. As a consequence, the time integration of high order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and the MSMS approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, i.e., surface area, surface enclosed volume, solvation free energy and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform based surface method, we solve the Poisson-Nernst-Planck (PNP) equations with a PDE transform surface of a protein. Second order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable and efficient approach for biomolecular surface generation in Cartesian meshes. PMID:22582140

Stern potential and Debye length measurements in dilute ionic solutions with electrostatic force microscopy.

PubMed

Kumar, Bharat; Crittenden, Scott R

2013-11-01

We demonstrate the ability to measure Stern potential and Debye length in dilute ionic solution with atomic force microscopy. We develop an analytic expression for the second harmonic force component of the capacitive force in an ionic solution from the linearized Poisson-Boltzmann equation. This allows us to calibrate the AFM tip potential and, further, obtain the Stern potential of sample surfaces. In addition, the measured capacitive force is independent of van der Waals and double layer forces, thus providing a more accurate measure of Debye length.

Poisson-Boltzmann model for protein-surface electrostatic interactions and grid-convergence study using the PyGBe code

NASA Astrophysics Data System (ADS)

Cooper, Christopher D.; Barba, Lorena A.

2016-05-01

Interactions between surfaces and proteins occur in many vital processes and are crucial in biotechnology: the ability to control specific interactions is essential in fields like biomaterials, biomedical implants and biosensors. In the latter case, biosensor sensitivity hinges on ligand proteins adsorbing on bioactive surfaces with a favorable orientation, exposing reaction sites to target molecules. Protein adsorption, being a free-energy-driven process, is difficult to study experimentally. This paper develops and evaluates a computational model to study electrostatic interactions of proteins and charged nanosurfaces, via the Poisson-Boltzmann equation. We extended the implicit-solvent model used in the open-source code PyGBe to include surfaces of imposed charge or potential. This code solves the boundary integral formulation of the Poisson-Boltzmann equation, discretized with surface elements. PyGBe has at its core a treecode-accelerated Krylov iterative solver, resulting in O(N log N) scaling, with further acceleration on hardware via multi-threaded execution on GPUs. It computes solvation and surface free energies, providing a framework for studying the effect of electrostatics on adsorption. We derived an analytical solution for a spherical charged surface interacting with a spherical dielectric cavity, and used it in a grid-convergence study to build evidence on the correctness of our approach. The study showed the error decaying with the average area of the boundary elements, i.e., the method is O(1 / N) , which is consistent with our previous verification studies using PyGBe. We also studied grid-convergence using a real molecular geometry (protein G B1 D4‧), in this case using Richardson extrapolation (in the absence of an analytical solution) and confirmed the O(1 / N) scaling. With this work, we can now access a completely new family of problems, which no other major bioelectrostatics solver, e.g. APBS, is capable of dealing with. PyGBe is open-source under an MIT license and is hosted under version control at https://github.com/barbagroup/pygbe. To supplement this paper, we prepared ;reproducibility packages; consisting of running and post-processing scripts in Python for replicating the grid-convergence studies, all the way to generating the final plots, with a single command.

Modeling and simulation of electronic structure, material interface and random doping in nano electronic devices

PubMed Central

Chen, Duan; Wei, Guo-Wei

2010-01-01

The miniaturization of nano-scale electronic devices, such as metal oxide semiconductor field effect transistors (MOSFETs), has given rise to a pressing demand in the new theoretical understanding and practical tactic for dealing with quantum mechanical effects in integrated circuits. Modeling and simulation of this class of problems have emerged as an important topic in applied and computational mathematics. This work presents mathematical models and computational algorithms for the simulation of nano-scale MOSFETs. We introduce a unified two-scale energy functional to describe the electrons and the continuum electrostatic potential of the nano-electronic device. This framework enables us to put microscopic and macroscopic descriptions in an equal footing at nano scale. By optimization of the energy functional, we derive consistently-coupled Poisson-Kohn-Sham equations. Additionally, layered structures are crucial to the electrostatic and transport properties of nano transistors. A material interface model is proposed for more accurate description of the electrostatics governed by the Poisson equation. Finally, a new individual dopant model that utilizes the Dirac delta function is proposed to understand the random doping effect in nano electronic devices. Two mathematical algorithms, the matched interface and boundary (MIB) method and the Dirichlet-to-Neumann mapping (DNM) technique, are introduced to improve the computational efficiency of nano-device simulations. Electronic structures are computed via subband decomposition and the transport properties, such as the I-V curves and electron density, are evaluated via the non-equilibrium Green's functions (NEGF) formalism. Two distinct device configurations, a double-gate MOSFET and a four-gate MOSFET, are considered in our three-dimensional numerical simulations. For these devices, the current fluctuation and voltage threshold lowering effect induced by the discrete dopant model are explored. Numerical convergence and model well-posedness are also investigated in the present work. PMID:20396650

Modeling electrokinetics in ionic liquids: General

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Chao; Bao, Jie; Pan, Wenxiao

2017-04-07

Using direct numerical simulations we provide a thorough study on the electrokinetics of ionic liquids. In particular, the modfied Poisson-Nernst-Planck (MPNP) equations are solved to capture the crowding and overscreening effects that are the characteristics of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the MPNP equations are coupled with the Navier-Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel plates, charging dynamics in a 2D straight-walled pore, electro-osmotic ow in a nano-channel, electroconvective instability on a plane ion-selective surface, and electroconvective ow onmore » a curved ion-selective surface. We discuss how the crowding and overscreening effects and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.« less

Understanding the physical basis of the salt dependence of the electrostatic binding free energy of mutated charged ligand-nucleic acid complexes.

PubMed

Harris, Robert C; Bredenberg, Johan H; Silalahi, Alexander R J; Boschitsch, Alexander H; Fenley, Marcia O

2011-06-01

The predictions of the derivative of the electrostatic binding free energy of a biomolecular complex, ΔG(el), with respect to the logarithm of the 1:1 salt concentration, d(ΔG(el))/d(ln[NaCl]), SK, by the Poisson-Boltzmann equation, PBE, are very similar to those of the simpler Debye-Hückel equation, DHE, because the terms in the PBE's predictions of SK that depend on the details of the dielectric interface are small compared to the contributions from long-range electrostatic interactions. These facts allow one to obtain predictions of SK using a simplified charge model along with the DHE that are highly correlated with both the PBE and experimental binding data. The DHE-based model developed here, which was derived from the generalized Born model, explains the lack of correlation between SK and ΔG(el) in the presence of a dielectric discontinuity, which conflicts with the popular use of this supposed correlation to parse experimental binding free energies into electrostatic and nonelectrostatic components. Moreover, the DHE model also provides a clear justification for the correlations between SK and various empirical quantities, like the number of ion pairs, the ligand charge on the interface, the Coulomb binding free energy, and the product of the charges on the complex's components, but these correlations are weak, questioning their usefulness. Copyright © 2011 Elsevier B.V. All rights reserved.

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J.

2009-11-01

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie-Poisson bracket and its Casimir invariants are presented. The model describes the evolution of the density, the electrostatic potential, and the component of the vector potential along a strong background field. This makes it suitable for describing such phenomena as the propagation of kinetic-Alfv'en modons, the nonlinear saturation of drift-tearing modes, and the diamagnetic stabilization of the internal kink. The invariants are used to obtain a set of coupled Grad-Shafranov equations describing equilibria and propagating coherent structures. They also lead to a Lagrangian formulation of the equations of motion that is well suited to solution with the PIC method.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Theoretical and computational studies of the sheath of a planar wall

NASA Astrophysics Data System (ADS)

Giraudo, Martina; Camporeale, Enrico; Delzanno, Gian Luca; Lapenta, Giovanni

2012-03-01

We present an investigation of the stability and nonlinear evolution of the sheath of a planar wall. We focus on the electrostatic limit. The stability analysis is conducted with a fluid model where continuity and momentum equations for the electrons and ions are coupled through Poisson's equation. The effect of electron emission from the wall is studied parametrically. Our results show that a sheath instability associated with the emitted electrons can exist. Following Ref. [1], it is interpreted as a Rayleigh-Taylor instability driven by the favorable combination of the sheath electron density gradient and electric field. Fully kinetic Particle-In-Cell (PIC) simulations will also be presented to investigate whether this instability indeed exists and to study the nonlinear effect of electron emission on the sheath profiles. The simulations will be conducted with CPIC, a new electrostatic PIC code that couples the standard PIC algorithm with strategies for generation and adaptation of the computational grid. [4pt] [1] G.L. Delzanno, ``A paradigm for the stability of the plasma sheath against fluid perturbations,'' Phys. Plasmas 18, 103508 (2011).

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

PubMed

Koehl, Patrice; Delarue, Marc

2010-02-14

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.

Hydrodynamic model of temperature change in open ionic channels.

PubMed Central

Chen, D P; Eisenberg, R S; Jerome, J W; Shu, C W

1995-01-01

Most theories of open ionic channels ignore heat generated by current flow, but that heat is known to be significant when analogous currents flow in semiconductors, so a generalization of the Poisson-Nernst-Planck theory of channels, called the hydrodynamic model, is needed. The hydrodynamic theory is a combination of the Poisson and Euler field equations of electrostatics and fluid dynamics, conservation laws that describe diffusive and convective flow of mass, heat, and charge (i.e., current), and their coupling. That is to say, it is a kinetic theory of solute and solvent flow, allowing heat and current flow as well, taking into account density changes, temperature changes, and electrical potential gradients. We integrate the equations with an essentially nonoscillatory shock-capturing numerical scheme previously shown to be stable and accurate. Our calculations show that 1) a significant amount of electrical energy is exchanged with the permeating ions; 2) the local temperature of the ions rises some tens of degrees, and this temperature rise significantly alters for ionic flux in a channel 25 A long, such as gramicidin-A; and 3) a critical parameter, called the saturation velocity, determines whether ionic motion is overdamped (Poisson-Nernst-Planck theory), is an intermediate regime (called the adiabatic approximation in semiconductor theory), or is altogether unrestricted (requiring the full hydrodynamic model). It seems that significant temperature changes are likely to accompany current flow in the open ionic channel. PMID:8599638

Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Wei

Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equationsmore » such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.« less

Multipolar Ewald methods, 1: theory, accuracy, and performance.

PubMed

Giese, Timothy J; Panteva, Maria T; Chen, Haoyuan; York, Darrin M

2015-02-10

The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.

Real-Space Multiple-Scattering Theory and Its Applications at Exascale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eisenbach, Markus; Wang, Yang

In recent decades, the ab initio methods based on density functional theory (DFT) (Hohenberg and Kohn 1964, Kohn and Sham 1965) have become a widely used tool in computational materials science, which allows theoretical prediction of physical properties of materials from the first principles and theoretical interpretation of new physical phenomena found in experiments. In the framework of DFT, the original problem that requires solving a quantum mechanical equation for a many-electron system is reduced to a one-electron problem that involves an electron moving in an effective field, while the effective field potential is made up of an electrostatic potential,more » also known as Hartree potential, arising from the electronic and ion charge distribution in space and an exchange–correlation potential, which is a function of the electron density and encapsulates the exchange and correlation effects of the many-electron system. Even though the exact functional form of the exchange-correlation potential is formally unknown, a local density approximation (LDA) or a generalized gradient approximation (GGA) is usually applied so that the calculation of the exchange–correlation potential, as well as the exchange–correlation energy, becomes tractable while a required accuracy is retained. Based on DFT, ab initio electronic structure calculations for a material generally involve a self-consistent process that iterates between two computational tasks: (1) solving an one-electron Schrödinger equation, also known as Kohn–Sham equation, to obtain the electron density and, if needed, the magnetic moment density, and (2) solving the Poisson equation to obtain the electrostatic potential corresponding to the electron density and constructing the effective potential by adding the exchange–correlation potential to the electrostatic potential. This self-consistent process proceeds until a convergence criteria is reached.« less

The double-layer of penetrable ions: an alternative route to charge reversal.

PubMed

Frydel, Derek; Levin, Yan

2013-05-07

We investigate a double-layer of penetrable ions near a charged wall. We find a new mechanism for charge reversal that occurs in the weak-coupling regime and, accordingly, the system is suitable for the mean-field analysis. The penetrability is achieved by smearing-out the ionic charge inside a sphere, so there is no need to introduce non-electrostatic forces and the system in the low coupling limit can be described by a modified version of the Poisson-Boltzmann equation. The predictions of the theory are compared with the Monte Carlo simulations.

Variational multiscale models for charge transport.

PubMed

Wei, Guo-Wei; Zheng, Qiong; Chen, Zhan; Xia, Kelin

2012-01-01

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field.

Variational multiscale models for charge transport

PubMed Central

Wei, Guo-Wei; Zheng, Qiong; Chen, Zhan; Xia, Kelin

2012-01-01

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field. PMID:23172978

STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS.

PubMed

Li, B O; Sun, Hui; Zhou, Shenggao

The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.

AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation

DOE PAGES

Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin; ...

2016-04-19

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes ofmore » computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Here, simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.« less

AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov–Poisson equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Xingyu; Samulyak, Roman, E-mail: roman.samulyak@stonybrook.edu; Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes ofmore » computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.« less

AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes ofmore » computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Here, simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.« less

On the nature of liquid junction and membrane potentials.

PubMed

Perram, John W; Stiles, Peter J

2006-09-28

Whenever a spatially inhomogeneous electrolyte, composed of ions with different mobilities, is allowed to diffuse, charge separation and an electric potential difference is created. Such potential differences across very thin membranes (e.g. biomembranes) are often interpreted using the steady state Goldman equation, which is usually derived by assuming a spatially constant electric field. Through the fundamental Poisson equation of electrostatics, this implies the absence of free charge density that must provide the source of any such field. A similarly paradoxical situation is encountered for thick membranes (e.g. in ion-selective electrodes) for which the diffusion potential is normally interpreted using the Henderson equation. Standard derivations of the Henderson equation appeal to local electroneutrality, which is also incompatible with sources of electric fields, as these require separated charges. We analyse self-consistent solutions of the Nernst-Planck-Poisson equations for a 1 : 1-univalent electrolyte to show that the Goldman and Henderson steady-state membrane potentials are artefacts of extraneous charges created in the reservoirs of electrolyte solution on either side of the membrane, due to the unphysical nature of the usual (Dirichlet) boundary conditions assumed to apply at the membrane-electrolyte interfaces. We also show, with the aid of numerical simulations, that a transient electric potential difference develops in any confined, but initially non-uniform, electrolyte solution. This potential difference ultimately decays to zero in the real steady state of the electrolyte, which corresponds to thermodynamic equilibrium. We explain the surprising fact that such transient potential differences are well described by the Henderson equation by using a computer algebra system to extend previous steady-state singular perturbation theories to the time-dependent case. Our work therefore accounts for the success of the Henderson equation in analysing experimental liquid-junction potentials.

Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

PubMed Central

Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce

2009-01-01

We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry, such as charge optimization or component analysis, can be computed to high accuracy using the presented BEM approach, in compute times comparable to traditional finite-difference methods. PMID:18567005

Biomolecular surface construction by PDE transform.

PubMed

Zheng, Qiong; Yang, Siyang; Wei, Guo-Wei

2012-03-01

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high-order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high-order PDEs. As a consequence, the time integration of high-order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two-dimensional and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and a standard approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, that is, surface area, surface-enclosed volume, solvation free energy, and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform-based surface method, we solve the Poisson-Nernst-Planck equations with a PDE transform surface of a protein. Second-order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform-based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable, and efficient approach for biomolecular surface generation in Cartesian meshes. Copyright © 2012 John Wiley & Sons, Ltd.

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

Three-dimensional structural modelling and calculation of electrostatic potentials of HLA Bw4 and Bw6 epitopes to explain the molecular basis for alloantibody binding: toward predicting HLA antigenicity and immunogenicity.

PubMed

Mallon, Dermot H; Bradley, J Andrew; Winn, Peter J; Taylor, Craig J; Kosmoliaptsis, Vasilis

2015-02-01

We have previously shown that qualitative assessment of surface electrostatic potential of HLA class I molecules helps explain serological patterns of alloantibody binding. We have now used a novel computational approach to quantitate differences in surface electrostatic potential of HLA B-cell epitopes and applied this to explain HLA Bw4 and Bw6 antigenicity. Protein structure models of HLA class I alleles expressing either the Bw4 or Bw6 epitope (defined by sequence motifs at positions 77 to 83) were generated using comparative structure prediction. The electrostatic potential in 3-dimensional space encompassing the Bw4/Bw6 epitope was computed by solving the Poisson-Boltzmann equation and quantitatively compared in a pairwise, all-versus-all fashion to produce distance matrices that cluster epitopes with similar electrostatics properties. Quantitative comparison of surface electrostatic potential at the carboxyl terminal of the α1-helix of HLA class I alleles, corresponding to amino acid sequence motif 77 to 83, produced clustering of HLA molecules in 3 principal groups according to Bw4 or Bw6 epitope expression. Remarkably, quantitative differences in electrostatic potential reflected known patterns of serological reactivity better than Bw4/Bw6 amino acid sequence motifs. Quantitative assessment of epitope electrostatic potential allowed the impact of known amino acid substitutions (HLA-B*07:02 R79G, R82L, G83R) that are critical for antibody binding to be predicted. We describe a novel approach for quantitating differences in HLA B-cell epitope electrostatic potential. Proof of principle is provided that this approach enables better assessment of HLA epitope antigenicity than amino acid sequence data alone, and it may allow prediction of HLA immunogenicity.

Study of Ion Beam Forming Process in Electric Thruster Using 3D FEM Simulation

NASA Astrophysics Data System (ADS)

Huang, Tao; Jin, Xiaolin; Hu, Quan; Li, Bin; Yang, Zhonghai

2015-11-01

There are two algorithms to simulate the process of ion beam forming in electric thruster. The one is electrostatic steady state algorithm. Firstly, an assumptive surface, which is enough far from the accelerator grids, launches the ion beam. Then the current density is calculated by theory formula. Secondly these particles are advanced one by one according to the equations of the motions of ions until they are out of the computational region. Thirdly, the electrostatic potential is recalculated and updated by solving Poisson Equation. At the end, the convergence is tested to determine whether the calculation should continue. The entire process will be repeated until the convergence is reached. Another one is time-depended PIC algorithm. In a global time step, we assumed that some new particles would be produced in the simulation domain and its distribution of position and velocity were certain. All of the particles that are still in the system will be advanced every local time steps. Typically, we set the local time step low enough so that the particle needs to be advanced about five times to move the distance of the edge of the element in which the particle is located.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

PubMed Central

Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

2013-01-01

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599

Protein dielectric constants determined from NMR chemical shift perturbations.

PubMed

Kukic, Predrag; Farrell, Damien; McIntosh, Lawrence P; García-Moreno E, Bertrand; Jensen, Kristine Steen; Toleikis, Zigmantas; Teilum, Kaare; Nielsen, Jens Erik

2013-11-13

Understanding the connection between protein structure and function requires a quantitative understanding of electrostatic effects. Structure-based electrostatic calculations are essential for this purpose, but their use has been limited by a long-standing discussion on which value to use for the dielectric constants (ε(eff) and ε(p)) required in Coulombic and Poisson-Boltzmann models. The currently used values for ε(eff) and ε(p) are essentially empirical parameters calibrated against thermodynamic properties that are indirect measurements of protein electric fields. We determine optimal values for ε(eff) and ε(p) by measuring protein electric fields in solution using direct detection of NMR chemical shift perturbations (CSPs). We measured CSPs in 14 proteins to get a broad and general characterization of electric fields. Coulomb's law reproduces the measured CSPs optimally with a protein dielectric constant (ε(eff)) from 3 to 13, with an optimal value across all proteins of 6.5. However, when the water-protein interface is treated with finite difference Poisson-Boltzmann calculations, the optimal protein dielectric constant (ε(p)) ranged from 2 to 5 with an optimum of 3. It is striking how similar this value is to the dielectric constant of 2-4 measured for protein powders and how different it is from the ε(p) of 6-20 used in models based on the Poisson-Boltzmann equation when calculating thermodynamic parameters. Because the value of ε(p) = 3 is obtained by analysis of NMR chemical shift perturbations instead of thermodynamic parameters such as pK(a) values, it is likely to describe only the electric field and thus represent a more general, intrinsic, and transferable ε(p) common to most folded proteins.

Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors

NASA Astrophysics Data System (ADS)

Zoete, V.; Michielin, O.; Karplus, M.

2003-12-01

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SAS bur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, ΔGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC 50 without reparametrization.

Simulations of Coulomb systems confined by polarizable surfaces using periodic Green functions.

PubMed

Dos Santos, Alexandre P; Girotto, Matheus; Levin, Yan

2017-11-14

We present an efficient approach for simulating Coulomb systems confined by planar polarizable surfaces. The method is based on the solution of the Poisson equation using periodic Green functions. It is shown that the electrostatic energy arising from the surface polarization can be decoupled from the energy due to the direct Coulomb interaction between the ions. This allows us to combine an efficient Ewald summation method, or any other fast method for summing over the replicas, with the polarization contribution calculated using Green function techniques. We apply the method to calculate density profiles of ions confined between the charged dielectric and metal surfaces.

Electrostatic potential calculation for biomolecules--creating a database of pre-calculated values reported on a per residue basis for all PDB protein structures.

PubMed

Rocchia, W; Neshich, G

2007-10-05

STING and Java Protein Dossier provide a collection of physical-chemical parameters, describing protein structure, stability, function, and interaction, considered one of the most comprehensive among the available protein databases of similar type. Particular attention in STING is paid to the electrostatic potential. It makes use of DelPhi, a well-known tool that calculates this physical-chemical quantity for biomolecules by solving the Poisson Boltzmann equation. In this paper, we describe a modification to the DelPhi program aimed at integrating it within the STING environment. We also outline how the "amino acid electrostatic potential" and the "surface amino acid electrostatic potential" are calculated (over all Protein Data Bank (PDB) content) and how the corresponding values are made searchable in STING_DB. In addition, we show that the STING and Java Protein Dossier are also capable of providing these particular parameter values for the analysis of protein structures modeled in computers or being experimentally solved, but not yet deposited in the PDB. Furthermore, we compare the calculated electrostatic potential values obtained by using the earlier version of DelPhi and those by STING, for the biologically relevant case of lysozyme-antibody interaction. Finally, we describe the STING capacity to make queries (at both residue and atomic levels) across the whole PDB, by looking at a specific case where the electrostatic potential parameter plays a crucial role in terms of a particular protein function, such as ligand binding. BlueStar STING is available at http://www.cbi.cnptia.embrapa.br.

Transient electrokinetic transport in a finite length microchannel: currents, capacitance, and an electrical analogy.

PubMed

Mansouri, Ali; Bhattacharjee, Subir; Kostiuk, Larry W

2007-11-08

Numerical simulations with the fluid mechanics based on the unsteady Navier-Stokes equations and the Poisson-Nernst-Planck formulation of electrostatics and ion transport were used to explore the transient transport of charge through a finite length cylindrical microchannel that is driven by a pressure difference. The evolution of the transcapillary potential from a no-flow equilibrium to the steady-state-steady-flow streaming potential was analyzed by following the convection, migration, and net currents. Observations of the unsteady characteristics of the streaming current, electrical resistance, and capacitance led to an electrical analogy. This electrical analogy was made from a current source (to represent convection current), which was placed in parallel with a capacitor (to allow the accumulation of charge) and a resistor (to permit a migration current). A parametric study involving a range of geometries, fluid mechanics, electrostatics, and mass transfer states allowed predictive submodels for the current source, capacitor, and resistor to be developed based on a dimensional analysis.

Electrostatic attraction of charged drops of water inside dropwise cluster

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shavlov, A. V.; Tyumen State Oil and Gas University, 38, Volodarskogo Str., Tyumen 625000; Dzhumandzhi, V. A.

2013-08-15

Based on the analytical solution of the Poisson-Boltzmann equation, we demonstrate that inside the electrically neutral system of charges an electrostatic attraction can occur between the like-charged particles, where charge Z ≫ 1 (in terms of elementary charge) and radius R > 0, whereas according to the literature, only repulsion is possible inside non-electrically neutral systems. We calculate the free energy of the charged particles of water inside a cluster and demonstrate that its minimum is when the interdroplet distance equals several Debye radii defined based on the light plasma component. The deepest minimum depth is in a cluster withmore » close spatial packing of drops by type, in a face-centered cubic lattice, if almost all the electric charge of one sign is concentrated on the drops and that of the other sign is concentrated on the light compensation carriers of charge, where the charge moved by equilibrium carriers is rather small.« less

Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels.

PubMed

Park, H M; Lee, J S; Kim, T W

2007-11-15

In the analysis of electroosmotic flows, the internal electric potential is usually modeled by the Poisson-Boltzmann equation. The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distributions are not affected by fluid flows. Although this is a reasonable assumption for steady electroosmotic flows through straight microchannels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. In the present work, the predictions of the Nernst-Planck equation are compared with those of the Poisson-Boltzmann equation for electroosmotic flows in various microchannels where the convective transport of ions is not negligible.

Prediction of Protein-Protein Interaction Sites Using Electrostatic Desolvation Profiles

PubMed Central

Fiorucci, Sébastien; Zacharias, Martin

2010-01-01

Abstract Protein-protein complex formation involves removal of water from the interface region. Surface regions with a small free energy penalty for water removal or desolvation may correspond to preferred interaction sites. A method to calculate the electrostatic free energy of placing a neutral low-dielectric probe at various protein surface positions has been designed and applied to characterize putative interaction sites. Based on solutions of the finite-difference Poisson equation, this method also includes long-range electrostatic contributions and the protein solvent boundary shape in contrast to accessible-surface-area-based solvation energies. Calculations on a large set of proteins indicate that in many cases (>90%), the known binding site overlaps with one of the six regions of lowest electrostatic desolvation penalty (overlap with the lowest desolvation region for 48% of proteins). Since the onset of electrostatic desolvation occurs even before direct protein-protein contact formation, it may help guide proteins toward the binding region in the final stage of complex formation. It is interesting that the probe desolvation properties associated with residue types were found to depend to some degree on whether the residue was outside of or part of a binding site. The probe desolvation penalty was on average smaller if the residue was part of a binding site compared to other surface locations. Applications to several antigen-antibody complexes demonstrated that the approach might be useful not only to predict protein interaction sites in general but to map potential antigenic epitopes on protein surfaces. PMID:20441756

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

Inter-subunit electrostatic interactions in ferritin molecule: comparison with inter-molecular interactions in crystals

NASA Astrophysics Data System (ADS)

Takahashi, Takuya; Hogyoku, Michiru; Nagayama, Kuniaki

1996-10-01

We evaluated the contribution of electrostatic interactions to the stability of macromolecular assembly in a horse L ferritin molecule composed of 24 subunits and the three-dimensional crystal of the ferritin molecules with numerical calculation of Poisson-Boltzmann equation based on dielectric model. The calculation showed that the electrostatic energy both favors the assembly of the 24 subunits and the crystalline assembly of the ferritin molecules (i.e., 24-mers). Short-range interactions less than 5 Å such as salt bridges and hydrogen bonds were important for both the subunit assembly and the crystalline assembly. To elucidate the strong stabilization by electrostatic interactions in both the ferritin 24-mer and its crystal, we analyzed the contribution of individual atoms. It revealed that the stabilization was arising from buried salt bridges or hydrogen bonds, which yielded more than 5 kcal/mol in some interactions. These large electrostatic stabilization and also the unexpected small ionic strength dependence was different from those of bovine pancreatic trypsin inhibitor (BPTI) orthorhombic and pig-insulin cubic crystals previously calculated. We also evaluated changes of the accessible surface area (ASA) and hydration free energy in accordance with the process of the subunit assembly. The change of hydration free energy, which was very large (i.e. ˜ + 100 kcal/mol/subunit) and unfavorable for the assembly, was proportional to the electrostatic hydration energy (i.e. Born energy change in hydration process). Hydrophobic groups were likely to appear more frequently than hydrophilic groups at the subunit interfaces. These results suggest that the molecular structure of the ferritin 24-mer and the crystal structure of the 24-mers were both stabilized by local electrostatic interactions, in particular. We view protein crystals as an extension of the protein oligomer to an infinite number of subunits association.

Comparison of three-dimensional poisson solution methods for particle-based simulation and inhomogeneous dielectrics.

PubMed

Berti, Claudio; Gillespie, Dirk; Bardhan, Jaydeep P; Eisenberg, Robert S; Fiegna, Claudio

2012-07-01

Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the two methods are essentially equivalent; i.e., they have comparable accuracies for the same number of elements. We find that ions in water--charges embedded in a high-dielectric medium--are harder to compute accurately than charges in a low-dielectric medium.

A Gibbs point field model for the spatial pattern of coronary capillaries

NASA Astrophysics Data System (ADS)

Karch, R.; Neumann, M.; Neumann, F.; Ullrich, R.; Neumüller, J.; Schreiner, W.

2006-09-01

We propose a Gibbs point field model for the pattern of coronary capillaries in transverse histologic sections from human hearts, based on the physiology of oxygen supply from capillaries to tissue. To specify the potential energy function of the Gibbs point field, we draw on an analogy between the equation of steady-state oxygen diffusion from an array of parallel capillaries to the surrounding tissue and Poisson's equation for the electrostatic potential of a two-dimensional distribution of identical point charges. The influence of factors other than diffusion is treated as a thermal disturbance. On this basis, we arrive at the well-known two-dimensional one-component plasma, a system of identical point charges exhibiting a weak (logarithmic) repulsive interaction that is completely characterized by a single dimensionless parameter. By variation of this parameter, the model is able to reproduce many characteristics of real capillary patterns.

KEEN Wave Simulations: Comparing various PIC to various fixed grid Vlasov to Phase-Space Adaptive Sparse Tiling & Effective Lagrangian (PASTEL) Techniques

NASA Astrophysics Data System (ADS)

Afeyan, Bedros; Larson, David; Shadwick, Bradley; Sydora, Richard

2017-10-01

We compare various ways of solving the Vlasov-Poisson and Vlasov-Maxwell equations on rather demanding nonlinear kinetic phenomena associated with KEEN and KEEPN waves. KEEN stands for Kinetic, Electrostatic, Electron Nonlinear, and KEEPN, for electron-positron or pair plasmas analogs. Because these self-organized phase space structures are not steady-state, or single mode, or fluid or low order moment equation limited, typical techniques with low resolution or too much noise will distort the answer too much, too soon, and fail. This will be shown via Penrose criteria triggers for instability at the formation stage as well as particle orbit statistics in fully formed KEEN waves and KEEN-KEEN and KEEN-EPW interacting states. We will argue that PASTEL is a viable alternative to traditional methods with reasonable chances of success in higher dimensions. Work supported by a Grant from AFOSR PEEP.

5D Tempest simulations of kinetic edge turbulence

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Cohen, B. I.; Cohen, R. H.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G. D.; Nevins, W. M.; Rognlien, T. D.; Umansky, M. V.; Qin, H.

2006-10-01

Results are presented from the development and application of TEMPEST, a nonlinear five dimensional (3d2v) gyrokinetic continuum code. The simulation results and theoretical analysis include studies of H-mode edge plasma neoclassical transport and turbulence in real divertor geometry and its relationship to plasma flow generation with zero external momentum input, including the important orbit-squeezing effect due to the large electric field flow-shear in the edge. In order to extend the code to 5D, we have formulated a set of fully nonlinear electrostatic gyrokinetic equations and a fully nonlinear gyrokinetic Poisson's equation which is valid for both neoclassical and turbulence simulations. Our 5D gyrokinetic code is built on 4D version of Tempest neoclassical code with extension to a fifth dimension in binormal direction. The code is able to simulate either a full torus or a toroidal segment. Progress on performing 5D turbulence simulations will be reported.

Modeling pH-Responsive Adsorption of Polyelectrolytes at Oil-Water Interfaces

NASA Astrophysics Data System (ADS)

Qin, Shiyi; Yong, Xin

We use dissipative particle dynamics (DPD) to discover the interfacial adsorption of pH-responsive polyelectrolytes in oil-water binary systems under different pH values. The electrostatic interactions between charged beads and the dielectric discontinuity across the interface are modeled by exploiting a modified Particle-Particle-Particle-Mesh (PPPM) method, which uses an iterative method to solve the Poisson equation on a uniform grid. We first model the adsorption behavior of a single linear polyelectrolyte from the aqueous phase. The Henderson-Hasselbalch equation describes the relation between pH and the degree of ionization of the modeled polyelectrolytes. Through changing the degree of ionization, we explore the influence of pH on the adsorption behavior and show that the electrostatic interactions significantly modulate the adsorption. Time evolutions of the position and conformation of the polyelectrolytes and the variation in the oil-water surface tension will be measured to characterize the adsorption behavior. Furthermore, we model the pH-dependent adsorption behavior of polyelectrolytes with more complicated structures, namely, branched polyelectrolytes with hydrophobic backbones and hydrophilic side chains. We also find that the addition of salts in the medium and the lengths of the backbone and ionized side chain affect the adsorption. This research supported by the American Chemical Society Petroleum Research Fund (Award 56884-DNI9).

An implicit boundary integral method for computing electric potential of macromolecules in solvent

NASA Astrophysics Data System (ADS)

Zhong, Yimin; Ren, Kui; Tsai, Richard

2018-04-01

A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equation that arises in mathematical models for the electrostatics of molecules in solvent. The proposed method uses an implicit boundary integral formulation to derive a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separates the molecule and the solvent. The needed implicit surface is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.

Electrostatics of electron-hole interactions in van der Waals heterostructures

NASA Astrophysics Data System (ADS)

Cavalcante, L. S. R.; Chaves, A.; Van Duppen, B.; Peeters, F. M.; Reichman, D. R.

2018-03-01

The role of dielectric screening of electron-hole interaction in van der Waals heterostructures is theoretically investigated. A comparison between models available in the literature for describing these interactions is made and the limitations of these approaches are discussed. A simple numerical solution of Poisson's equation for a stack of dielectric slabs based on a transfer matrix method is developed, enabling the calculation of the electron-hole interaction potential at very low computational cost and with reasonable accuracy. Using different potential models, direct and indirect exciton binding energies in these systems are calculated within Wannier-Mott theory, and a comparison of theoretical results with recent experiments on excitons in two-dimensional materials is discussed.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

The electrostatic interaction between interfacial colloidal particles

NASA Astrophysics Data System (ADS)

Hurd, A. J.

1985-11-01

The electrostatic interaction between charged, colloidal particles trapped at an air-water interface is considered using linearised Poisson-Boltzmann results for point particles. In addition to the expected screened-Coulomb contribution, which decays exponentially, an algebraic dipole-dipole interaction occurs that may account for long-range interactions in interfacial colloidal systems.

Extending the Diffuse Layer Model of Surface Acidity Constant Behavior: IV. Diffuse Layer Charge/Potential Relationships

EPA Science Inventory

Most current electrostatic surface complexation models describing ionic binding at the particle/water interface rely on the use of Poisson - Boltzmann (PB) theory for relating diffuse layer charge densities to diffuse layer electrostatic potentials. PB theory is known to contain ...

MIBPB: a software package for electrostatic analysis.

PubMed

Chen, Duan; Chen, Zhan; Chen, Changjun; Geng, Weihua; Wei, Guo-Wei

2011-03-01

The Poisson-Boltzmann equation (PBE) is an established model for the electrostatic analysis of biomolecules. The development of advanced computational techniques for the solution of the PBE has been an important topic in the past two decades. This article presents a matched interface and boundary (MIB)-based PBE software package, the MIBPB solver, for electrostatic analysis. The MIBPB has a unique feature that it is the first interface technique-based PBE solver that rigorously enforces the solution and flux continuity conditions at the dielectric interface between the biomolecule and the solvent. For protein molecular surfaces, which may possess troublesome geometrical singularities, the MIB scheme makes the MIBPB by far the only existing PBE solver that is able to deliver the second-order convergence, that is, the accuracy increases four times when the mesh size is halved. The MIBPB method is also equipped with a Dirichlet-to-Neumann mapping technique that builds a Green's function approach to analytically resolve the singular charge distribution in biomolecules in order to obtain reliable solutions at meshes as coarse as 1 Å--whereas it usually takes other traditional PB solvers 0.25 Å to reach similar level of reliability. This work further accelerates the rate of convergence of linear equation systems resulting from the MIBPB by using the Krylov subspace (KS) techniques. Condition numbers of the MIBPB matrices are significantly reduced by using appropriate KS solver and preconditioner combinations. Both linear and nonlinear PBE solvers in the MIBPB package are tested by protein-solvent solvation energy calculations and analysis of salt effects on protein-protein binding energies, respectively. Copyright © 2010 Wiley Periodicals, Inc.

MIBPB: A software package for electrostatic analysis

PubMed Central

Chen, Duan; Chen, Zhan; Chen, Changjun; Geng, Weihua; Wei, Guo-Wei

2010-01-01

The Poisson-Boltzmann equation (PBE) is an established model for the electrostatic analysis of biomolecules. The development of advanced computational techniques for the solution of the PBE has been an important topic in the past two decades. This paper presents a matched interface and boundary (MIB) based PBE software package, the MIBPB solver, for electrostatic analysis. The MIBPB has a unique feature that it is the first interface technique based PBE solver that rigorously enforces the solution and flux continuity conditions at the dielectric interface between the biomolecule and the solvent. For protein molecular surfaces which may possess troublesome geometrical singularities, the MIB scheme makes the MIBPB by far the only existing PBE solver that is able to deliver the second order convergence, i.e., the accuracy increases four times when the mesh size is halved. The MIBPB method is also equipped with a Dirichlet-to-Neumann mapping (DNM) technique, that builds a Green's function approach to analytically resolve the singular charge distribution in biomolecules in order to obtain reliable solutions at meshes as coarse as 1Å — while it usually takes other traditional PB solvers 0.25Å to reach similar level of reliability. The present work further accelerates the rate of convergence of linear equation systems resulting from the MIBPB by utilizing the Krylov subspace (KS) techniques. Condition numbers of the MIBPB matrices are significantly reduced by using appropriate Krylov subspace solver and preconditioner combinations. Both linear and nonlinear PBE solvers in the MIBPB package are tested by protein-solvent solvation energy calculations and analysis of salt effects on protein-protein binding energies, respectively. PMID:20845420

Accurate, robust and reliable calculations of Poisson-Boltzmann binding energies

PubMed Central

Nguyen, Duc D.; Wang, Bao

2017-01-01

Poisson-Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, ΔGel, and binding free energy, ΔΔGel, is important to computational biophysics and biochemistry. In this work, we investigate the grid dependence of our PB solver (MIBPB) with SESs for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of ΔGel obtained at the grid spacing of 1.0 Å compared to ΔGel at 0.2 Å averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in ΔΔGel calculation. In fact, the grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. PMID:28211071

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

PubMed

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

Fractional Poisson Fields and Martingales

NASA Astrophysics Data System (ADS)

Aletti, Giacomo; Leonenko, Nikolai; Merzbach, Ely

2018-02-01

We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.

Prediction of protein-protein interaction sites using electrostatic desolvation profiles.

PubMed

Fiorucci, Sébastien; Zacharias, Martin

2010-05-19

Protein-protein complex formation involves removal of water from the interface region. Surface regions with a small free energy penalty for water removal or desolvation may correspond to preferred interaction sites. A method to calculate the electrostatic free energy of placing a neutral low-dielectric probe at various protein surface positions has been designed and applied to characterize putative interaction sites. Based on solutions of the finite-difference Poisson equation, this method also includes long-range electrostatic contributions and the protein solvent boundary shape in contrast to accessible-surface-area-based solvation energies. Calculations on a large set of proteins indicate that in many cases (>90%), the known binding site overlaps with one of the six regions of lowest electrostatic desolvation penalty (overlap with the lowest desolvation region for 48% of proteins). Since the onset of electrostatic desolvation occurs even before direct protein-protein contact formation, it may help guide proteins toward the binding region in the final stage of complex formation. It is interesting that the probe desolvation properties associated with residue types were found to depend to some degree on whether the residue was outside of or part of a binding site. The probe desolvation penalty was on average smaller if the residue was part of a binding site compared to other surface locations. Applications to several antigen-antibody complexes demonstrated that the approach might be useful not only to predict protein interaction sites in general but to map potential antigenic epitopes on protein surfaces. Copyright (c) 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

A new approach to implement absorbing boundary condition in biomolecular electrostatics.

PubMed

Goni, Md Osman

2013-01-01

This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.

Density functional study on the structural and thermodynamic properties of aqueous DNA-electrolyte solution in the framework of cell model.

PubMed

Wang, Ke; Yu, Yang-Xin; Gao, Guang-Hua

2008-05-14

A density functional theory (DFT) in the framework of cell model is proposed to calculate the structural and thermodynamic properties of aqueous DNA-electrolyte solution with finite DNA concentrations. The hard-sphere contribution to the excess Helmholtz energy functional is derived from the modified fundamental measure theory, and the electrostatic interaction is evaluated through a quadratic functional Taylor expansion around a uniform fluid. The electroneutrality in the cell leads to a variational equation with a constraint. Since the reference fluid is selected to be a bulk phase, the Lagrange multiplier proves to be the potential drop across the cell boundary (Donnan potential). The ion profiles and electrostatic potential profiles in the cell are calculated from the present DFT-cell model. Our DFT-cell model gives better prediction of ion profiles than the Poisson-Boltzmann (PB)- or modified PB-cell models when compared to the molecular simulation data. The effects of polyelectrolyte concentration, ion size, and added-salt concentration on the electrostatic potential difference between the DNA surface and the cell boundary are investigated. The expression of osmotic coefficient is derived from the general formula of grand potential. The osmotic coefficients predicted by the DFT are lower than the PB results and are closer to the simulation results and experimental data.

Finite element solution of torsion and other 2-D Poisson equations

NASA Technical Reports Server (NTRS)

Everstine, G. C.

1982-01-01

The NASTRAN structural analysis computer program may be used, without modification, to solve two dimensional Poisson equations such as arise in the classical Saint Venant torsion problem. The nonhomogeneous term (the right-hand side) in the Poisson equation can be handled conveniently by specifying a gravitational load in a "structural" analysis. The use of an analogy between the equations of elasticity and those of classical mathematical physics is summarized in detail.

Simulation of Charged Systems in Heterogeneous Dielectric Media via a True Energy Functional

NASA Astrophysics Data System (ADS)

Jadhao, Vikram; Solis, Francisco J.; de la Cruz, Monica Olvera

2012-11-01

For charged systems in heterogeneous dielectric media, a key obstacle for molecular dynamics (MD) simulations is the need to solve the Poisson equation in the media. This obstacle can be bypassed using MD methods that treat the local polarization charge density as a dynamic variable, but such approaches require access to a true free energy functional, one that evaluates to the equilibrium electrostatic energy at its minimum. In this Letter, we derive the needed functional. As an application, we develop a Car-Parrinello MD method for the simulation of free charges present near a spherical emulsion droplet separating two immiscible liquids with different dielectric constants. Our results show the presence of nonmonotonic ionic profiles in the dielectric with a lower dielectric constant.

pKa values in proteins determined by electrostatics applied to molecular dynamics trajectories.

PubMed

Meyer, Tim; Knapp, Ernst-Walter

2015-06-09

For a benchmark set of 194 measured pKa values in 13 proteins, electrostatic energy computations are performed in which pKa values are computed by solving the Poisson-Boltzmann equation. In contrast to the previous approach of Karlsberg(+) (KB(+)) that essentially used protein crystal structures with variations in their side chain conformations, the present approach (KB2(+)MD) uses protein conformations from four molecular dynamics (MD) simulations of 10 ns each. These MD simulations are performed with different specific but fixed protonation patterns, selected to sample the conformational space for the different protonation patterns faithfully. The root-mean-square deviation between computed and measured pKa values (pKa RMSD) is shown to be reduced from 1.17 pH units using KB(+) to 0.96 pH units using KB2(+)MD. The pKa RMSD can be further reduced to 0.79 pH units, if each conformation is energy-minimized with a dielectric constant of εmin = 4 prior to calculating the electrostatic energy. The electrostatic energy expressions upon which the computations are based have been reformulated such that they do not involve terms that mix protein and solvent environment contributions and no thermodynamic cycle is needed. As a consequence, conformations of the titratable residues can be treated independently in the protein and solvent environments. In addition, the energy terms used here avoid the so-called intrinsic pKa and can therefore be interpreted without reference to arbitrary protonation states and conformations.

Accurate solution of the Poisson equation with discontinuities

NASA Astrophysics Data System (ADS)

Nave, Jean-Christophe; Marques, Alexandre; Rosales, Rodolfo

2017-11-01

Solving the Poisson equation in the presence of discontinuities is of great importance in many applications of science and engineering. In many cases, the discontinuities are caused by interfaces between different media, such as in multiphase flows. These interfaces are themselves solutions to differential equations, and can assume complex configurations. For this reason, it is convenient to embed the interface into a regular triangulation or Cartesian grid and solve the Poisson equation in this regular domain. We present an extension of the Correction Function Method (CFM), which was developed to solve the Poisson equation in the context of embedded interfaces. The distinctive feature of the CFM is that it uses partial differential equations to construct smooth extensions of the solution in the vicinity of interfaces. A consequence of this approach is that it can achieve high order of accuracy while maintaining compact discretizations. The extension we present removes the restrictions of the original CFM, and yields a method that can solve the Poisson equation when discontinuities are present in the solution, the coefficients of the equation (material properties), and the source term. We show results computed to fourth order of accuracy in two and three dimensions. This work was partially funded by DARPA, NSF, and NSERC.

Probing lipid membrane electrostatics

NASA Astrophysics Data System (ADS)

Yang, Yi

The electrostatic properties of lipid bilayer membranes play a significant role in many biological processes. Atomic force microscopy (AFM) is highly sensitive to membrane surface potential in electrolyte solutions. With fully characterized probe tips, AFM can perform quantitative electrostatic analysis of lipid membranes. Electrostatic interactions between Silicon nitride probes and supported zwitterionic dioleoylphosphatidylcholine (DOPC) bilayer with a variable fraction of anionic dioleoylphosphatidylserine (DOPS) were measured by AFM. Classical Gouy-Chapman theory was used to model the membrane electrostatics. The nonlinear Poisson-Boltzmann equation was numerically solved with finite element method to provide the potential distribution around the AFM tips. Theoretical tip-sample electrostatic interactions were calculated with the surface integral of both Maxwell and osmotic stress tensors on tip surface. The measured forces were interpreted with theoretical forces and the resulting surface charge densities of the membrane surfaces were in quantitative agreement with the Gouy-Chapman-Stern model of membrane charge regulation. It was demonstrated that the AFM can quantitatively detect membrane surface potential at a separation of several screening lengths, and that the AFM probe only perturbs the membrane surface potential by <2%. One important application of this technique is to estimate the dipole density of lipid membrane. Electrostatic analysis of DOPC lipid bilayers with the AFM reveals a repulsive force between the negatively charged probe tips and the zwitterionic lipid bilayers. This unexpected interaction has been analyzed quantitatively to reveal that the repulsion is due to a weak external field created by the internai membrane dipole moment. The analysis yields a dipole moment of 1.5 Debye per lipid with a dipole potential of +275 mV for supported DOPC membranes. This new ability to quantitatively measure the membrane dipole density in a noninvasive manner will be useful in identifying the biological effects of the dipole potential. Finally, heterogeneous model membranes were studied with fluid electric force microscopy (FEFM). Electrostatic mapping was demonstrated with 50 nm resolution. The capabilities of quantitative electrostatic measurement and lateral charge density mapping make AFM a unique and powerful probe of membrane electrostatics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ali, S.; Bukhari, S.; Department of Physics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Azad Kashmir

Keeping in view the kinetic treatment for plasma particles, the electrostatic twisted dust-acoustic (DA) and dust-ion-acoustic (DIA) waves are investigated in a collisionless unmagnetized multi-component dusty plasma, whose constituents are the electrons, singly ionized positive ions, and negatively charged massive dust particulates. With this background, the Vlasov–Poisson equations are coupled together to derive a generalized dielectric constant by utilizing the Laguerre-Gaussian perturbed distribution function and electrostatic potential in the paraxial limit. The dispersion and damping rates of twisted DA and DIA waves are analyzed with finite orbital angular momentum states in a multi-component dusty plasma. Significant modifications concerning the realmore » wave frequencies and damping rates appeared with varying twisted dimensionless parameter and dust concentration. In particular, it is shown that dust concentration enhances the phase speed of the DIA waves in contrary to DA waves, whereas the impact of twisted parameter reduces the frequencies of both DA and DIA waves. The results should be useful for the understanding of particle transport and trapping phenomena caused by wave excitation in laboratory dusty plasmas.« less

Truncated Painlevé expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

NASA Astrophysics Data System (ADS)

Ibrahim, R. S.; El-Kalaawy, O. H.

2006-10-01

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painlevé expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.

Complexes of native Ubiquitin and dodecyl sulfate illustrate the nature of hydrophobic and electrostatic interactions in the binding of proteins and surfactants

PubMed Central

Shaw, Bryan F.; Schneider, Grégory F.; Arthanari, Haribabu; Narovlyansky, Max; Moustakas, Demetri; Durazo, Armando; Wagner, Gerhard; Whitesides, George M.

2011-01-01

A previous study, using capillary electrophoresis (CE), reported that six discrete complexes of ubiquitin (UBI) and sodium dodecyl sulfate (SDS) form at different concentrations of SDS along the pathway to unfolding of UBI in solutions of SDS. One complex (which formed between 0.8 and 1.8 mM SDS) consisted of native UBI associated with approximately 11 molecules of SDS. The current study used CE and 15N/13C-1H heteronuclear single quantum coherence (HSQC) NMR spectroscopy to identify residues in folded UBI that associate specifically with SDS at 0.8-1.8 mM SDS, and to correlate these associations with established biophysical and structural properties of this well-characterized protein. The ability of the surface charge and hydrophobicity of folded UBI to affect the association with SDS (at concentrations below the CMC) was studied, using CE, by converting lys-ε-NH3+ to lys-ε-NHCOCH3 groups. According to CE, the acetylation of lysine residues inhibited the binding of 11 SDS ([SDS] < 2 mM) and decreased the number of complexes of composition UBI-(NHAc)8·SDSn that formed on the pathway of unfolding of UBI-(NHAc)8 in SDS. A comparison of 15N-1H HSQC spectra at 0 mM and 1 mM SDS with calculated electrostatic surface potentials of folded UBI (e.g., solutions to the non-linear Poisson-Boltzmann (PB) equation) suggested, however, that SDS binds preferentially to native UBI at hydrophobic residues that are formally neutral (i.e., Leu and Ile), but that have positive electrostatic surface potential (as predicted from solutions to non-linear Poisson-Boltzmann equations); SDS did not uniformly interact with residues that have formal positive charge (e.g., Lys or Arg). Cationic functional groups, therefore, promote the binding of SDS to folded UBI because these groups exert long-range effects on the positive electrostatic surface potential (which extend beyond their own van der Waal’s radii, as predicted from PB theory), and not because cationic groups are necessarily the site of ionic interactions with sulfate groups. Moreover, SDS associated with residues in native UBI without regard to their location in α-helix or β-sheet structure (although residues in hydrogen-bonded loops did not bind SDS). No correlation was observed between the association of an amino acid with SDS and the solvent accessibility of the residue or its rate of amide H/D exchange. This study establishes a few (of perhaps several) factors that control the simultaneous molecular recognition of multiple anionic amphiphiles by a folded cytosolic protein. PMID:21939262

Schrödinger-Poisson-Vlasov-Poisson correspondence

NASA Astrophysics Data System (ADS)

Mocz, Philip; Lancaster, Lachlan; Fialkov, Anastasia; Becerra, Fernando; Chavanis, Pierre-Henri

2018-04-01

The Schrödinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As ℏ/m →0 , m being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as ℏ/m →0 due to interference and the uncertainty principle, the potential field converges to the classical answer as (ℏ/m )2. Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as ℏ/m →0 . The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schrödinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultralight axions, which in the classical limit (ℏ/m →0 ) is expected to manifest itself as collisionless cold dark matter.

Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations

NASA Astrophysics Data System (ADS)

Blossey, R.; Maggs, A. C.; Podgornik, R.

2017-06-01

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

Numerical Investigation of Two-Phase Flows With Charged Droplets in Electrostatic Field

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1996-01-01

A numerical method to solve two-phase turbulent flows with charged droplets in an electrostatic field is presented. The ensemble-averaged Navier-Stokes equations and the electrostatic potential equation are solved using a finite volume method. The transitional turbulence field is described using multiple-time-scale turbulence equations. The equations of motion of droplets are solved using a Lagrangian particle tracking scheme, and the inter-phase momentum exchange is described by the Particle-In-Cell scheme. The electrostatic force caused by an applied electrical potential is calculated using the electrostatic field obtained by solving a Laplacian equation and the force exerted by charged droplets is calculated using the Coulombic force equation. The method is applied to solve electro-hydrodynamic sprays. The calculated droplet velocity distributions for droplet dispersions occurring in a stagnant surrounding are in good agreement with the measured data. For droplet dispersions occurring in a two-phase flow, the droplet trajectories are influenced by aerodynamic forces, the Coulombic force, and the applied electrostatic potential field.

The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Chiun-Chang, E-mail: chlee@mail.nhcue.edu.tw

2014-05-15

The present article is concerned with the charge conserving Poisson-Boltzmann (CCPB) equation in high-dimensional bounded smooth domains. The CCPB equation is a Poisson-Boltzmann type of equation with nonlocal coefficients. First, under the Robin boundary condition, we get the existence of weak solutions to this equation. The main approach is variational, based on minimization of a logarithm-type energy functional. To deal with the regularity of weak solutions, we establish a maximum modulus estimate for the standard Poisson-Boltzmann (PB) equation to show that weak solutions of the CCPB equation are essentially bounded. Then the classical solutions follow from the elliptic regularity theorem.more » Second, a maximum principle for the CCPB equation is established. In particular, we show that in the case of global electroneutrality, the solution achieves both its maximum and minimum values at the boundary. However, in the case of global non-electroneutrality, the solution may attain its maximum value at an interior point. In addition, under certain conditions on the boundary, we show that the global non-electroneutrality implies pointwise non-electroneutrality.« less

Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions.

PubMed

Marenich, Aleksandr V; Cramer, Christopher J; Truhlar, Donald G

2009-05-07

We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the "D" stands for "density" to denote that the full solute electron density is used without defining partial atomic charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calculation are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality constants called atomic surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aqueous ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and dimethyl sulfoxide, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaqueous organic solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic atomic Coulomb radii and atomic surface tension coefficients) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G, M05-2X/6-31+G, M05-2X/cc-pVTZ, B3LYP/6-31G, and HF/6-31G. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calculations in which the solute is represented by its electron density in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions with either Gaussian03 or GAMESS.

Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marenich, Aleksandr; Cramer, Christopher J; Truhlar, Donald G

2009-04-30

We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the “D” stands for “density” to denote that the full solute electron density is used without defining partial atomic charges. “Continuum” denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where “universal” denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which amore » few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calculation are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality constants called atomic surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aqueous ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and dimethyl sulfoxide, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaqueous organic solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic atomic Coulomb radii and atomic surface tension coefficients) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calculations in which the solute is represented by its electron density in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions with either Gaussian03 or GAMESS.« less

Broken degeneracy of low frequency surface waves in semi-bounded quantum plasmas including the quantum recoil effect

NASA Astrophysics Data System (ADS)

Lee, Myoung-Jae; Jung, Young-Dae

2018-02-01

We present a derivation of the dispersion relation for electrostatic waves propagating at the interface of semi-bounded quantum plasma in which degenerate electrons are governed by the Wigner-Poisson system, while non-degenerate ions follow the classical fluid equations. We consider parameters for metallic plasmas in terms of the ratio of plasmon energy to Fermi energy. The dispersion relation is solved numerically and analyzed for various plasmon energies. The result shows that two-mode of waves can be possible: high- and low-mode. We have found that the degeneracy for high-mode wave would be broken when the plasmon energy is larger than the Fermi energy. We also discuss the characteristics of group velocities for high- and low-mode waves.

Comparison of calculation and experiment implicates significant electrostatic contributions to the binding stability of barnase and barstar.

PubMed

Dong, Feng; Vijayakumar, M; Zhou, Huan-Xiang

2003-07-01

The contributions of electrostatic interactions to the binding stability of barnase and barstar were studied by the Poisson-Boltzmann model with three different protocols: a), the dielectric boundary specified as the van der Waals (vdW) surface of the protein along with a protein dielectric constant (epsilon (p)) of 4; b), the dielectric boundary specified as the molecular (i.e., solvent-exclusion (SE)) surface along with epsilon (p) = 4; and c), "SE + epsilon (p) = 20." The "vdW + epsilon (p) = 4" and "SE + epsilon (p) = 20" protocols predicted an overall electrostatic stabilization whereas the "SE + epsilon (p) = 4" protocol predicted an overall electrostatic destabilization. The "vdW + epsilon (p) = 4" protocol was most consistent with experiment. It quantitatively reproduced the observed effects of 17 mutations neutralizing charged residues lining the binding interface and the measured coupling energies of six charge pairs across the interface and reasonably rationalized the experimental ionic strength and pH dependences of the binding constant. In contrast, the "SE + epsilon (p) = 4" protocol predicted significantly larger coupling energies of charge pairs whereas the "SE + epsilon (p) = 20" protocol did not predict any pH dependence. This study calls for further scrutiny of the different Poisson-Boltzmann protocols and demonstrates potential danger in drawing conclusions on electrostatic contributions based on a particular calculation protocol.

Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

NASA Astrophysics Data System (ADS)

Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

2018-04-01

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

Predicting Nonspecific Ion Binding Using DelPhi

PubMed Central

Petukh, Marharyta; Zhenirovskyy, Maxim; Li, Chuan; Li, Lin; Wang, Lin; Alexov, Emil

2012-01-01

Ions are an important component of the cell and affect the corresponding biological macromolecules either via direct binding or as a screening ion cloud. Although some ion binding is highly specific and frequently associated with the function of the macromolecule, other ions bind to the protein surface nonspecifically, presumably because the electrostatic attraction is strong enough to immobilize them. Here, we test such a scenario and demonstrate that experimentally identified surface-bound ions are located at a potential that facilitates binding, which indicates that the major driving force is the electrostatics. Without taking into consideration geometrical factors and structural fluctuations, we show that ions tend to be bound onto the protein surface at positions with strong potential but with polarity opposite to that of the ion. This observation is used to develop a method that uses a DelPhi-calculated potential map in conjunction with an in-house-developed clustering algorithm to predict nonspecific ion-binding sites. Although this approach distinguishes only the polarity of the ions, and not their chemical nature, it can predict nonspecific binding of positively or negatively charged ions with acceptable accuracy. One can use the predictions in the Poisson-Boltzmann approach by placing explicit ions in the predicted positions, which in turn will reduce the magnitude of the local potential and extend the limits of the Poisson-Boltzmann equation. In addition, one can use this approach to place the desired number of ions before conducting molecular-dynamics simulations to neutralize the net charge of the protein, because it was shown to perform better than standard screened Coulomb canned routines, or to predict ion-binding sites in proteins. This latter is especially true for proteins that are involved in ion transport, because such ions are loosely bound and very difficult to detect experimentally. PMID:22735539

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Transport of Multivalent Electrolyte Mixtures in Micro- and Nanochannels

DTIC Science & Technology

2013-11-08

equations for this process are the unsteady Navier-Stokes equations along with continuity and the Poisson- Nernst -Planck system for the electro- static part...about five times the Debye screening length D (the 1/e lengthscale for the potential from the solution of the linearized Poisson- Boltzmann equation

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Full particle simulations of quasi-perpendicular shocks

NASA Astrophysics Data System (ADS)

Lembège, B.

This tutorial-style review is dedicated to the different strategies and constraints used for analysing the dynamics of a collisionless shocks with full particle simulations. Main results obtained with such simulations can be found in published materials (recent references are provided in this text); these will be only quoted herein in order to illustrate a few aspects of these simulations. Thanks to the large improvement of super computers, full particle simulations reveal to be quite helpful for analyzing in details the dynamics of collisionless shocks. The main characteristics of such codes can be shortly reminded as follows: one resolves the full set of Poisson and Maxwell's equations without any approximation. Two approaches are commonly used for resolving this equation's set, more precisely the space derivatives: (i) the finite difference approach and (ii) the use of FFT's (Fast Fourier Transform). Two advantages of approach (ii) are that FFT's are highly optimized in supercomputers libraries, and these allow to separate all fields components into two groups: the longitudinal electrostatic component El (solution of Poisson equation) and the transverse electromagnetic components Et and Bt solutions of the Maxwell's equations (so called "fields pusher"). Such a separation is quite helpful in the post processing stage necessary for the data analysis, as will be explained in the presentation. both ions and electrons populations are treated as individual finite-size particles and suffer the effects of all fields via the Lorentz force, so called "particle pusher", which is applied to each particle. Because of the large number of particles commonly used, the particle pusher represents the most expensive part of the calculations on which most efforts of optimisation needs to be performed (in terms of "vectorisation" or of "parallelism"). Relativistic effects may be included in this force via the use of particle momemtum. Each particle has three velocity components (vx, vy, vz), but may have 1, 2 or 3 space coordinates (x, y, z) according to the dimension of the code of concern.

The Electric Potential of a Macromolecule in a Solvent: A Fundamental Approach

NASA Astrophysics Data System (ADS)

Juffer, André H.; Botta, Eugen F. F.; van Keulen, Bert A. M.; van der Ploeg, Auke; Berendsen, Herman J. C.

1991-11-01

A general numerical method is presented to compute the electric potential for a macromolecule of arbitrary shape in a solvent with nonzero ionic strength. The model is based on a continuum description of the dielectric and screening properties of the system, which consists of a bounded internal region with discrete charges and an infinite external region. The potential obeys the Poisson equation in the internal region and the linearized Poisson-Boltzmann equation in the external region, coupled through appropriate boundary conditions. It is shown how this three-dimensional problem can be presented as a pair of coupled integral equations for the potential and the normal component of the electric field at the dielectric interface. These equations can be solved by a straightforward application of boundary element techniques. The solution involves the decomposition of a matrix that depends only on the geometry of the surface and not on the positions of the charges. With this approach the number of unknowns is reduced by an order of magnitude with respect to the usual finite difference methods. Special attention is given to the numerical inaccuracies resulting from charges which are located close to the interface; an adapted formulation is given for that case. The method is tested both for a spherical geometry, for which an exact solution is available, and for a realistic problem, for which a finite difference solution and experimental verification is available. The latter concerns the shift in acid strength (pK-values) of histidines in the copper-containing protein azurin on oxidation of the copper, for various values of the ionic strength. A general method is given to triangulate a macromolecular surface. The possibility is discussed to use the method presented here for a correct treatment of long-range electrostatic interactions in simulations of solvated macromolecules, which form an essential part of correct potentials of mean force.

Computational study of graphene-based vertical field effect transistor

NASA Astrophysics Data System (ADS)

Chen, Wenchao; Rinzler, Andrew; Guo, Jing

2013-03-01

Poisson and drift-diffusion equations are solved in a three-dimensional device structure to simulate graphene-based vertical field effect transistors (GVFETs). Operation mechanisms of the GVFET with and without punched holes in the graphene source contact are presented and compared. The graphene-channel Schottky barrier can be modulated by gate electric field due to graphene's low density of states. For the graphene contact with punched holes, the contact barrier thinning and lowering around punched hole edge allow orders of magnitude higher tunneling current compared to the region away from the punched hole edge, which is responsible for significant performance improvement as already verified by experiments. Small hole size is preferred due to less electrostatic screening from channel inversion layer, which gives large electric field around the punched hole edge, thus, leading to a thinner and lower barrier. Bilayer and trilayer graphenes as the source contact degrade the performance improvement because stronger electrostatic screening leads to smaller contact barrier lowering and thinning. High punched hole area percentage improves current performance by allowing more gate electric field to modulate the graphene-channel barrier. Low effective mass channel material gives better on-off current ratio.

The influence of screening of the polyion electrostatic potential on the counterion dynamics in polyelectrolyte solutions

NASA Astrophysics Data System (ADS)

Schipper, F. J. M.; Hollander, J. G.; Leyte, J. C.

1998-10-01

The self-diffusion coefficient of tetra-methylammonium counterion in solutions of polymethacrylic acid in 0953-8984/10/41/004/img1 has been measured over a broad polyion concentration range at a constant degree of neutralization and at different ratios of added monovalent or bivalent salt to polyions. A maximum counterion self-diffusion coefficient was observed as a function of polyion concentration. The value of the self-diffusion coefficient at the maximum did not depend on the valency of the added salt. The maximum was found at lower polymer concentrations and with a higher value, when the ratio of added salt to polyions was increased, as predicted by the Poisson-Boltzmann-Smoluchowski equation in the cylindrical cell model for polyelectrolytes. At higher polyion concentrations a maximum counterion self-diffusion coefficient against the ratio of added salt and polyions was observed, which has not been reported before. Upon increasing this ratio the electrostatic potential of the polyelectrolyte gets screened, leading to an increase of the counterion self-diffusion coefficient. Concentration effects of the added salt on the other hand ultimately lead to a decrease of the counterion self-diffusion coefficient, which explains the occurrence of a maximum.

Exact solution for the Poisson field in a semi-infinite strip.

PubMed

Cohen, Yossi; Rothman, Daniel H

2017-04-01

The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

Comparison of Calculation and Experiment Implicates Significant Electrostatic Contributions to the Binding Stability of Barnase and Barstar

PubMed Central

Dong, Feng; Vijayakumar, M.; Zhou, Huan-Xiang

2003-01-01

The contributions of electrostatic interactions to the binding stability of barnase and barstar were studied by the Poisson-Boltzmann model with three different protocols: a), the dielectric boundary specified as the van der Waals (vdW) surface of the protein along with a protein dielectric constant (ɛp) of 4; b), the dielectric boundary specified as the molecular (i.e., solvent-exclusion (SE)) surface along with ɛp = 4; and c), “SE + ɛp = 20.” The “vdW + ɛp = 4” and “SE + ɛp = 20” protocols predicted an overall electrostatic stabilization whereas the “SE + ɛp = 4” protocol predicted an overall electrostatic destabilization. The “vdW + ɛp = 4” protocol was most consistent with experiment. It quantitatively reproduced the observed effects of 17 mutations neutralizing charged residues lining the binding interface and the measured coupling energies of six charge pairs across the interface and reasonably rationalized the experimental ionic strength and pH dependences of the binding constant. In contrast, the “SE + ɛp = 4” protocol predicted significantly larger coupling energies of charge pairs whereas the “SE + ɛp = 20” protocol did not predict any pH dependence. This study calls for further scrutiny of the different Poisson-Boltzmann protocols and demonstrates potential danger in drawing conclusions on electrostatic contributions based on a particular calculation protocol. PMID:12829463

Ion-Conserving Modified Poisson-Boltzmann Theory Considering a Steric Effect in an Electrolyte

NASA Astrophysics Data System (ADS)

Sugioka, Hideyuki

2016-12-01

The modified Poisson-Nernst-Planck (MPNP) and modified Poisson-Boltzmann (MPB) equations are well known as fundamental equations that consider a steric effect, which prevents unphysical ion concentrations. However, it is unclear whether they are equivalent or not. To clarify this problem, we propose an improved free energy formulation that considers a steric limit with an ion-conserving condition and successfully derive the ion-conserving modified Poisson-Boltzmann (IC-MPB) equations that are equivalent to the MPNP equations. Furthermore, we numerically examine the equivalence by comparing between the IC-MPB solutions obtained by the Newton method and the steady MPNP solutions obtained by the finite-element finite-volume method. A surprising aspect of our finding is that the MPB solutions are much different from the MPNP (IC-MPB) solutions in a confined space. We consider that our findings will significantly contribute to understanding the surface science between solids and liquids.

Electrostatic charge on a dust size distribution in a plasma. [in interplanetary space

NASA Technical Reports Server (NTRS)

Houpis, Harry L. F.; Whipple, Elden C., Jr.

1987-01-01

The capacitance of a grain immersed in a steady state plasma containing a size distribution of dust particles is studied. The grain charge is determined by assuming the equilibrium potential has been obtained by a simple balance of electron and ion collection currents. It is shown that the validity of the analytical treatment given here for the linearized Poisson equation is confined to a certain region of space. Within this region and starting at very small plasma Debye length lambda(D), the capacitance at first exhibits a monotonic increase with increasing lambda(D). The capacitance eventually reaches a maximum, followed by a monotonic decrease. The charge density of the dust in the plasma is found to be only a function of the lambda(D); there is no significant dependence on the interparticle spacing.

NASCAP user's manual

NASA Technical Reports Server (NTRS)

Mandell, M. J.; Harvey, J. M.; Katz, I.

1977-01-01

The NASCAP (NASA Charging Analyzer Program) code simulates the charging process for a complex object in either tenuous plasma or ground test environment. Detailed specifications needed to run the code are presented. The object definition section, OBJDEF, allows the test object to be easily defined in the cubic mesh. The test object is composed of conducting sections which may be wholly or partially covered with thin dielectric coatings. The potential section, POTENT, obtains the electrostatic potential in the space surrounding the object. It uses the conjugate gradient method to solve the finite element formulation of Poisson's equation. The CHARGE section of NASCAP treats charge redistribution among the surface cells of the object as well as charging through radiation bombardment. NASCAP has facilities for extensive graphical output, including several types of object display plots, potential contour plots, space charge density contour plots, current density plots, and particle trajectory plots.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.

Here, five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currentsmore » to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.« less

Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels.

PubMed Central

Nonner, W; Eisenberg, B

1998-01-01

L-type Ca channels contain a cluster of four charged glutamate residues (EEEE locus), which seem essential for high Ca specificity. To understand how this highly charged structure might produce the currents and selectivity observed in this channel, a theory is needed that relates charge to current. We use an extended Poisson-Nernst-Planck (PNP2) theory to compute (mean) Coulombic interactions and thus to examine the role of the mean field electrostatic interactions in producing current and selectivity. The pore was modeled as a central cylinder with tapered atria; the cylinder (i.e., "pore proper") contained a uniform volume density of fixed charge equivalent to that of one to four carboxyl groups. The pore proper was assigned ion-specific, but spatially uniform, diffusion coefficients and excess chemical potentials. Thus electrostatic selection by valency was computed self-consistently, and selection by other features was also allowed. The five external parameters needed for a system of four ionic species (Na, Ca, Cl, and H) were determined analytically from published measurements of thre limiting conductances and two critical ion concentrations, while treating the pore as a macroscopic ion-exchange system in equilibrium with a uniform bath solution. The extended PNP equations were solved with these parameters, and the predictions were compared to currents measured in a variety of solutions over a range of transmembrane voltages. The extended PNP theory accurately predicted current-voltage relations, anomalous mole fraction effects in the observed current, saturation effects of varied Ca and Na concentrations, and block by protons. Pore geometry, dielectric permittivity, and the number of carboxyl groups had only weak effects. The successful prediction of Ca fluxes in this paper demonstrates that ad hoc electrostatic parameters, multiple discrete binding sites, and logistic assumptions of single-file movement are all unnecessary for the prediction of permeation in Ca channels over a wide range of conditions. Further work is needed, however, to understand the atomic origin of the fixed charge, excess chemical potentials, and diffusion coefficients of the channel. The Appendix uses PNP2 theory to predict ionic currents for published "barrier-and-well" energy profiles of this channel. PMID:9726931

Quantum dynamics in continuum for proton transport—Generalized correlation

NASA Astrophysics Data System (ADS)

Chen, Duan; Wei, Guo-Wei

2012-04-01

As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and boundary method, the Dirichlet to Neumann mapping, Gummel iteration, and Krylov space techniques, is employed to improve the accuracy, efficiency, and robustness of model simulations. Finally, comparisons between the present model predictions and experimental data of current-voltage curves, as well as current-concentration curves of the Gramicidin A channel, verify our new model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Yang; Xiao, Jianyuan; Zhang, Ruili

Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.

A multichannel model for the self-consistent analysis of coherent transport in graphene nanoribbons.

PubMed

Mencarelli, Davide; Pierantoni, Luca; Farina, Marco; Di Donato, Andrea; Rozzi, Tullio

2011-08-23

In this contribution, we analyze the multichannel coherent transport in graphene nanoribbons (GNRs) by a scattering matrix approach. We consider the transport properties of GNR devices of a very general form, involving multiple bands and multiple leads. The 2D quantum transport over the whole GNR surface, described by the Schrödinger equation, is strongly nonlinear as it implies calculation of self-generated and externally applied electrostatic potentials, solutions of the 3D Poisson equation. The surface charge density is computed as a balance of carriers traveling through the channel at all of the allowed energies. Moreover, formation of bound charges corresponding to a discrete modal spectrum is observed and included in the model. We provide simulation examples by considering GNR configurations typical for transistor devices and GNR protrusions that find an interesting application as cold cathodes for X-ray generation. With reference to the latter case, a unified model is required in order to couple charge transport and charge emission. However, to a first approximation, these could be considered as independent problems, as in the example. © 2011 American Chemical Society

A simple model for electrical charge in globular macromolecules and linear polyelectrolytes in solution

NASA Astrophysics Data System (ADS)

Krishnan, M.

2017-05-01

We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule's interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an "interaction charge" for the molecule which we demonstrate agrees closely with the "effective charge" discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of pKa shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or rapid, reliable predictions are desired.

Long-pore Electrostatics in Inward-rectifier Potassium Channels

PubMed Central

Robertson, Janice L.; Palmer, Lawrence G.; Roux, Benoît

2008-01-01

Inward-rectifier potassium (Kir) channels differ from the canonical K+ channel structure in that they possess a long extended pore (∼85 Å) for ion conduction that reaches deeply into the cytoplasm. This unique structural feature is presumably involved in regulating functional properties specific to Kir channels, such as conductance, rectification block, and ligand-dependent gating. To elucidate the underpinnings of these functional roles, we examine the electrostatics of an ion along this extended pore. Homology models are constructed based on the open-state model of KirBac1.1 for four mammalian Kir channels: Kir1.1/ROMK, Kir2.1/IRK, Kir3.1/GIRK, and Kir6.2/KATP. By solving the Poisson-Boltzmann equation, the electrostatic free energy of a K+ ion is determined along each pore, revealing that mammalian Kir channels provide a favorable environment for cations and suggesting the existence of high-density regions in the cytoplasmic domain and cavity. The contribution from the reaction field (the self-energy arising from the dielectric polarization induced by the ion's charge in the complex geometry of the pore) is unfavorable inside the long pore. However, this is well compensated by the electrostatic interaction with the static field arising from the protein charges and shielded by the dielectric surrounding. Decomposition of the static field provides a list of residues that display remarkable correspondence with existing mutagenesis data identifying amino acids that affect conduction and rectification. Many of these residues demonstrate interactions with the ion over long distances, up to 40 Å, suggesting that mutations potentially affect ion or blocker energetics over the entire pore. These results provide a foundation for understanding ion interactions in Kir channels and extend to the study of ion permeation, block, and gating in long, cation-specific pores. PMID:19001143

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

NASA Technical Reports Server (NTRS)

Sohn, J. L.; Heinrich, J. C.

1990-01-01

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

Electrostatic Solvation Free Energy of Amino Acid Side Chain Analogs: Implications for the Validity of Electrostatic Linear Response in Water

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Bin; Pettitt, Bernard M.

Electrostatic free energies of solvation for 15 neutral amino acid side chain analogs are computed. We compare three methods of varying computational complexity and accuracy for three force fields: free energy simulations, Poisson-Boltzmann (PB), and linear response approximation (LRA) using AMBER, CHARMM, and OPLSAA force fields. We find that deviations from simulation start at low charges for solutes. The approximate PB and LRA produce an overestimation of electrostatic solvation free energies for most of molecules studied here. These deviations are remarkably systematic. The variations among force fields are almost as large as the variations found among methods. Our study confirmsmore » that success of the approximate methods for electrostatic solvation free energies comes from their ability to evaluate free energy differences accurately.« less

Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

NASA Astrophysics Data System (ADS)

Campos-García, Manuel; Granados-Agustín, Fermín.; Cornejo-Rodríguez, Alejandro; Estrada-Molina, Amilcar; Avendaño-Alejo, Maximino; Moreno-Oliva, Víctor Iván.

2013-11-01

In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).

Vibrational Stark effect spectroscopy at the interface of Ras and Rap1A bound to the Ras binding domain of RalGDS reveals an electrostatic mechanism for protein-protein interaction.

PubMed

Stafford, Amy J; Ensign, Daniel L; Webb, Lauren J

2010-11-25

Electrostatic fields at the interface of the Ras binding domain of the protein Ral guanine nucleotide dissociation stimulator (RalGDS) with the structurally analogous GTPases Ras and Rap1A were measured with vibrational Stark effect (VSE) spectroscopy. Eleven residues on the surface of RalGDS that participate in this protein-protein interaction were systematically mutated to cysteine and subsequently converted to cyanocysteine in order to introduce a nitrile VSE probe in the form of the thiocyanate (SCN) functional group. The measured SCN absorption energy on the monomeric protein was compared with solvent-accessible surface area (SASA) calculations and solutions to the Poisson-Boltzmann equation using Boltzmann-weighted structural snapshots from molecular dynamics simulations. We found a weak negative correlation between SASA and measured absorption energy, indicating that water exposure of protein surface amino acids can be estimated from experimental measurement of the magnitude of the thiocyanate absorption energy. We found no correlation between calculated field and measured absorption energy. These results highlight the complex structural and electrostatic nature of the protein-water interface. The SCN-labeled RalGDS was incubated with either wild-type Ras or wild-type Rap1A, and the formation of the docked complex was confirmed by measurement of the dissociation constant of the interaction. The change in absorption energy of the thiocyanate functional group due to complex formation was related to the change in electrostatic field experienced by the nitrile functional group when the protein-protein interface forms. At some locations, the nitrile experiences the same shift in field when bound to Ras and Rap1A, but at others, the change in field is dramatically different. These differences identify residues on the surface of RalGDS that direct the specificity of RalGDS binding to its in vivo binding partner, Rap1A, through an electrostatic mechanism.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Symplectic discretization for spectral element solution of Maxwell's equations

NASA Astrophysics Data System (ADS)

Zhao, Yanmin; Dai, Guidong; Tang, Yifa; Liu, Qinghuo

2009-08-01

Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.

Massively Parallel Solution of Poisson Equation on Coarse Grain MIMD Architectures

NASA Technical Reports Server (NTRS)

Fijany, A.; Weinberger, D.; Roosta, R.; Gulati, S.

1998-01-01

In this paper a new algorithm, designated as Fast Invariant Imbedding algorithm, for solution of Poisson equation on vector and massively parallel MIMD architectures is presented. This algorithm achieves the same optimal computational efficiency as other Fast Poisson solvers while offering a much better structure for vector and parallel implementation. Our implementation on the Intel Delta and Paragon shows that a speedup of over two orders of magnitude can be achieved even for moderate size problems.

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

Center of Excellence in Theoretical Geoplasma Research

DTIC Science & Technology

1989-11-10

iii) First results of closed-form solutions of the3 Balescu -Lenard-Poisson equations for collisional plasmas were reported I REPORT November 10, 1989...Basu, "Solutions of the Linearized Balescu -Lenard-Poisson Equations for a Weakly-Collisional Plasma: Some New Results". [511 American Geophysical Union

Numerical model of the plasma formation at electron beam welding

NASA Astrophysics Data System (ADS)

Trushnikov, D. N.; Mladenov, G. M.

2015-01-01

The model of plasma formation in the keyhole in liquid metal as well as above the electron beam welding zone is described. The model is based on solution of two equations for the density of electrons and the mean electron energy. The mass transfer of heavy plasma particles (neutral atoms, excited atoms, and ions) is taken into account in the analysis by the diffusion equation for a multicomponent mixture. The electrostatic field is calculated using the Poisson equation. Thermionic electron emission is calculated for the keyhole wall. The ionization intensity of the vapors due to beam electrons and high-energy secondary and backscattered electrons is calibrated using the plasma parameters when there is no polarized collector electrode above the welding zone. The calculated data are in good agreement with experimental data. Results for the plasma parameters for excitation of a non-independent discharge are given. It is shown that there is a need to take into account the effect of a strong electric field near the keyhole walls on electron emission (the Schottky effect) in the calculation of the current for a non-independent discharge (hot cathode gas discharge). The calculated electron drift velocities are much bigger than the velocity at which current instabilities arise. This confirms the hypothesis for ion-acoustic instabilities, observed experimentally in previous research.

Calculations of the binding affinities of protein-protein complexes with the fast multipole method

NASA Astrophysics Data System (ADS)

Kim, Bongkeun; Song, Jiming; Song, Xueyu

2010-09-01

In this paper, we used a coarse-grained model at the residue level to calculate the binding free energies of three protein-protein complexes. General formulations to calculate the electrostatic binding free energy and the van der Waals free energy are presented by solving linearized Poisson-Boltzmann equations using the boundary element method in combination with the fast multipole method. The residue level model with the fast multipole method allows us to efficiently investigate how the mutations on the active site of the protein-protein interface affect the changes in binding affinities of protein complexes. Good correlations between the calculated results and the experimental ones indicate that our model can capture the dominant contributions to the protein-protein interactions. At the same time, additional effects on protein binding due to atomic details are also discussed in the context of the limitations of such a coarse-grained model.

The electrostatics of a dusty plasma

NASA Technical Reports Server (NTRS)

Whipple, E. C.; Mendis, D. A.; Northrop, T. G.

1986-01-01

The potential distribution in a plasma containing dust grains were derived where the Debye length can be larger or smaller than the average intergrain spacing. Three models were treated for the grain-plasma system, with the assumption that the system of dust and plasma is charge-neutral: a permeable grain model, an impermeable grain model, and a capacitor model that does not require the nearest neighbor approximation of the other two models. A gauge-invariant form of Poisson's equation was used which is linearized about the average potential in the system. The charging currents to a grain are functions of the difference between the grain potential and this average potential. Expressions were obtained for the equilibrium potential of the grain and for the gauge-invariant capacitance between the grain and the plasma. The charge on a grain is determined by the product of this capacitance and the grain-plasma potential difference.

Self-consistent simulation of radio frequency multipactor on micro-grooved dielectric surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Libing; Wang, Jianguo, E-mail: wanguiuc@mail.xjtu.edu.cn; Northwest Institute of Nuclear Technology, Xi'an, Shaanxi 710024

2015-02-07

The multipactor plays a key role in the surface breakdown on the feed dielectric window irradiated by high power microwave. To study the suppression of multipactor, a 2D electrostatic PIC-MCC simulation code was developed. The space charge field, including surface deposited charge and multipactor electron charge field, is obtained by solving 2D Poisson's equation in time. Therefore, the simulation is self-consistent and does not require presetting a fixed space charge field. By using this code, the self-consistent simulation of the RF multipactor on the periodic micro-grooved dielectric surface is realized. The 2D space distributions of the multipactor electrons and spacemore » charge field are presented. From the simulation results, it can be found that only half slopes have multipactor discharge when the slope angle exceeds a certain value, and the groove presents a pronounced suppression effect on the multipactor.« less

Effect of Surfaces on Amyloid Fibril Formation

PubMed Central

Moores, Bradley; Drolle, Elizabeth; Attwood, Simon J.; Simons, Janet; Leonenko, Zoya

2011-01-01

Using atomic force microscopy (AFM) we investigated the interaction of amyloid beta (Aβ) (1–42) peptide with chemically modified surfaces in order to better understand the mechanism of amyloid toxicity, which involves interaction of amyloid with cell membrane surfaces. We compared the structure and density of Aβ fibrils on positively and negatively charged as well as hydrophobic chemically-modified surfaces at physiologically relevant conditions. We report that due to the complex distribution of charge and hydrophobicity amyloid oligomers bind to all types of surfaces investigated (CH3, COOH, and NH2) although the charge and hydrophobicity of surfaces affected the structure and size of amyloid deposits as well as surface coverage. Hydrophobic surfaces promote formation of spherical amorphous clusters, while charged surfaces promote protofibril formation. We used the nonlinear Poisson-Boltzmann equation (PBE) approach to analyze the electrostatic interactions of amyloid monomers and oligomers with modified surfaces to complement our AFM data. PMID:22016789

Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma

DOE PAGES

Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.; ...

2017-05-29

Here, five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currentsmore » to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.« less

The interplay between screening properties and colloid anisotropy: towards a reliable pair potential for disc-like charged particles.

PubMed

Agra, R; Trizac, E; Bocquet, L

2004-12-01

The electrostatic potential of a highly charged disc (clay platelet) in an electrolyte is investigated in detail. The corresponding non-linear Poisson-Boltzmann (PB) equation is solved numerically, and we show that the far-field behaviour (relevant for colloidal interactions in dilute suspensions) is exactly that obtained within linearized PB theory, with the surface boundary condition of a uniform potential. The latter linear problem is solved by a new semi-analytical procedure and both the potential amplitude (quantified by an effective charge) and potential anisotropy coincide closely within PB and linearized PB, provided the disc bare charge is high enough. This anisotropy remains at all scales; it is encoded in a function that may vary over several orders of magnitude depending on the azimuthal angle under which the disc is seen. The results allow to construct a pair potential for discs interaction, that is strongly orientation dependent.

A vectorized Poisson solver over a spherical shell and its application to the quasi-geostrophic omega-equation

NASA Technical Reports Server (NTRS)

Mullenmeister, Paul

1988-01-01

The quasi-geostrophic omega-equation in flux form is developed as an example of a Poisson problem over a spherical shell. Solutions of this equation are obtained by applying a two-parameter Chebyshev solver in vector layout for CDC 200 series computers. The performance of this vectorized algorithm greatly exceeds the performance of its scalar analog. The algorithm generates solutions of the omega-equation which are compared with the omega fields calculated with the aid of the mass continuity equation.

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm.

PubMed

Zhang, Qing; Beard, Daniel A; Schlick, Tamar

2003-12-01

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 2063-2074, 2003

AESOP: A Python Library for Investigating Electrostatics in Protein Interactions.

PubMed

Harrison, Reed E S; Mohan, Rohith R; Gorham, Ronald D; Kieslich, Chris A; Morikis, Dimitrios

2017-05-09

Electric fields often play a role in guiding the association of protein complexes. Such interactions can be further engineered to accelerate complex association, resulting in protein systems with increased productivity. This is especially true for enzymes where reaction rates are typically diffusion limited. To facilitate quantitative comparisons of electrostatics in protein families and to describe electrostatic contributions of individual amino acids, we previously developed a computational framework called AESOP. We now implement this computational tool in Python with increased usability and the capability of performing calculations in parallel. AESOP utilizes PDB2PQR and Adaptive Poisson-Boltzmann Solver to generate grid-based electrostatic potential files for protein structures provided by the end user. There are methods within AESOP for quantitatively comparing sets of grid-based electrostatic potentials in terms of similarity or generating ensembles of electrostatic potential files for a library of mutants to quantify the effects of perturbations in protein structure and protein-protein association. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Electrostatic and dispersion interactions during protein adsorption on topographic nanostructures.

PubMed

Elter, Patrick; Lange, Regina; Beck, Ulrich

2011-07-19

Recently, biomaterials research has focused on developing functional implant surfaces with well-defined topographic nanostructures in order to influence protein adsorption and cellular behavior. To enhance our understanding of how proteins interact with such surfaces, we analyze the adsorption of lysozyme on an oppositely charged nanostructure using a computer simulation. We present an algorithm that combines simulated Brownian dynamics with numerical field calculation methods to predict the preferred adsorption sites for arbitrarily shaped substrates. Either proteins can be immobilized at their initial adsorption sites or surface diffusion can be considered. Interactions are analyzed on the basis of Derjaguin-Landau-Verway-Overbeek (DLVO) theory, including electrostatic and London dispersion forces, and numerical solutions are derived using the Poisson-Boltzmann and Hamaker equations. Our calculations show that for a grooved nanostructure (i.e., groove and plateau width 8 nm, height 4 nm), proteins first contact the substrate primarily near convex edges because of better geometric accessibility and increased electric field strengths. Subsequently, molecules migrate by surface diffusion into grooves and concave corners, where short-range dispersion interactions are maximized. In equilibrium, this mechanism leads to an increased surface protein concentration in the grooves, demonstrating that the total amount of protein per surface area can be increased if substrates have concave nanostructures.

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

PubMed

Pan, Zhao; Whitehead, Jared; Thomson, Scott; Truscott, Tadd

2016-08-01

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Vlasov-Maxwell and Vlasov-Poisson equations as models of a one-dimensional electron plasma

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Cooper, J.

1983-01-01

The Vlasov-Maxwell and Vlasov-Poisson systems of equations for a one-dimensional electron plasma are defined and discussed. A method for transforming a solution of one system which is periodic over a bounded or unbounded spatial interval to a similar solution of the other is constructed.

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

DNA-lipid complexes: stability of honeycomb-like and spaghetti-like structures.

PubMed Central

May, S; Ben-Shaul, A

1997-01-01

A molecular level theory is presented for the thermodynamic stability of two (similar) types of structural complexes formed by (either single strand or supercoiled) DNA and cationic liposomes, both involving a monolayer-coated DNA as the central structural unit. In the "spaghetti" complex the central unit is surrounded by another, oppositely curved, monolayer, thus forming a bilayer mantle. The "honeycomb" complex is a bundle of hexagonally packed DNA-monolayer units. The formation free energy of these complexes, starting from a planar cationic/neutral lipid bilayer and bare DNA, is expressed as a sum of electrostatic, bending, mixing, and (for the honeycomb) chain frustration contributions. The electrostatic free energy is calculated using the Poisson-Boltzmann equation. The bending energy of the mixed lipid layers is treated in the quadratic curvature approximation with composition-dependent bending rigidity and spontaneous curvature. Ideal lipid mixing is assumed within each lipid monolayer. We found that the most stable monolayer-coated DNA units are formed when the charged/neutral lipid composition corresponds (nearly) to charge neutralization; the optimal monolayer radius corresponds to close DNA-monolayer contact. These conclusions are also valid for the honeycomb complex, as the chain frustration energy is found to be negligible. Typically, the stabilization energies for these structures are on the order of 1 k(B)T/A of DNA length, reflecting mainly the balance between the electrostatic and bending energies. The spaghetti complexes are less stable due to the additional bending energy of the external monolayer. A thermodynamic analysis is presented for calculating the equilibrium lipid compositions when the complexes coexist with excess bilayer. PMID:9370436

A strategy for reducing gross errors in the generalized Born models of implicit solvation

PubMed Central

Onufriev, Alexey V.; Sigalov, Grigori

2011-01-01

The “canonical” generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ΔGel of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2kBT relative to numerical Poisson equation reference) in pairwise interactions between individual atomic charges. Analysis of exact analytical solutions of the Poisson equation (PE) for several idealized nonspherical geometries reveals two distinct spatial modes of the PE solution; these modes are also found in realistic biomolecular shapes. The canonical GB Green function misses one of two modes seen in the exact PE solution, which explains the observed gross errors. To address the problem and reduce gross errors of the GB formalism, we have used exact PE solutions for idealized nonspherical geometries to suggest an alternative analytical Green function to replace the canonical GB formula. The proposed functional form is mathematically nearly as simple as the original, but depends not only on the effective Born radii but also on their gradients, which allows for better representation of details of nonspherical molecular shapes. In particular, the proposed functional form captures both modes of the PE solution seen in nonspherical geometries. Tests on realistic biomolecular structures ranging from small peptides to medium size proteins show that the proposed functional form reduces gross pairwise errors in all cases, with the amount of reduction varying from more than an order of magnitude for small structures to a factor of 2 for the largest ones. PMID:21528947

Charged Substrate and Product Together Contribute Like a Nonreactive Species to the Overall Electrostatic Steering in Diffusion-Reaction Processes.

PubMed

Xu, Jingjie; Xie, Yan; Lu, Benzhuo; Zhang, Linbo

2016-08-25

The Debye-Hückel limiting law is used to study the binding kinetics of substrate-enzyme system as well as to estimate the reaction rate of a electrostatically steered diffusion-controlled reaction process. It is based on a linearized Poisson-Boltzmann model and known for its accurate predictions in dilute solutions. However, the substrate and product particles are in nonequilibrium states and are possibly charged, and their contributions to the total electrostatic field cannot be explicitly studied in the Poisson-Boltzmann model. Hence the influences of substrate and product on reaction rate coefficient were not known. In this work, we consider all the charged species, including the charged substrate, product, and mobile salt ions in a Poisson-Nernst-Planck model, and then compare the results with previous work. The results indicate that both the charged substrate and product can significantly influence the reaction rate coefficient with different behaviors under different setups of computational conditions. It is interesting to find that when substrate and product are both considered, under an overall neutral boundary condition for all the bulk charged species, the computed reaction rate kinetics recovers a similar Debye-Hückel limiting law again. This phenomenon implies that the charged product counteracts the influence of charged substrate on reaction rate coefficient. Our analysis discloses the fact that the total charge concentration of substrate and product, though in a nonequilibrium state individually, obeys an equilibrium Boltzmann distribution, and therefore contributes as a normal charged ion species to ionic strength. This explains why the Debye-Hückel limiting law still works in a considerable range of conditions even though the effects of charged substrate and product particles are not specifically and explicitly considered in the theory.

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation.

PubMed

Chen, Duan; Wei, Guo-Wei

2013-01-01

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data.

PubMed

Yelland, Lisa N; Salter, Amy B; Ryan, Philip

2011-10-15

Modified Poisson regression, which combines a log Poisson regression model with robust variance estimation, is a useful alternative to log binomial regression for estimating relative risks. Previous studies have shown both analytically and by simulation that modified Poisson regression is appropriate for independent prospective data. This method is often applied to clustered prospective data, despite a lack of evidence to support its use in this setting. The purpose of this article is to evaluate the performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data, by using generalized estimating equations to account for clustering. A simulation study is conducted to compare log binomial regression and modified Poisson regression for analyzing clustered data from intervention and observational studies. Both methods generally perform well in terms of bias, type I error, and coverage. Unlike log binomial regression, modified Poisson regression is not prone to convergence problems. The methods are contrasted by using example data sets from 2 large studies. The results presented in this article support the use of modified Poisson regression as an alternative to log binomial regression for analyzing clustered prospective data when clustering is taken into account by using generalized estimating equations.

New superfield extension of Boussinesq and its (x,t) interchanged equation from odd Poisson bracket

NASA Astrophysics Data System (ADS)

Palit, S.; Chowdhury, A. Roy

1995-08-01

A new superfield extension of the Boussinesq equation and its corresponding (x,t) interchanged variant are deduced from the odd Poisson-bracket-formalism, which is similar to the antibracket of Batalin and Vilkovisky. In the former case we obtain the equation deduced by Figueroa-O'Farrill et al from a different approach. In each case we have deduced the bi-Hamiltonian structure and some basic symmetries associated with them.

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

ERIC Educational Resources Information Center

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

Dynamics of a prey-predator system under Poisson white noise excitation

NASA Astrophysics Data System (ADS)

Pan, Shan-Shan; Zhu, Wei-Qiu

2014-10-01

The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

Steady-State Ion Beam Modeling with MICHELLE

NASA Astrophysics Data System (ADS)

Petillo, John

2003-10-01

There is a need to efficiently model ion beam physics for ion implantation, chemical vapor deposition, and ion thrusters. Common to all is the need for three-dimensional (3D) simulation of volumetric ion sources, ion acceleration, and optics, with the ability to model charge exchange of the ion beam with a background neutral gas. The two pieces of physics stand out as significant are the modeling of the volumetric source and charge exchange. In the MICHELLE code, the method for modeling the plasma sheath in ion sources assumes that the electron distribution function is a Maxwellian function of electrostatic potential over electron temperature. Charge exchange is the process by which a neutral background gas with a "fast" charged particle streaming through exchanges its electron with the charged particle. An efficient method for capturing this is essential, and the model presented is based on semi-empirical collision cross section functions. This appears to be the first steady-state 3D algorithm of its type to contain multiple generations of charge exchange, work with multiple species and multiple charge state beam/source particles simultaneously, take into account the self-consistent space charge effects, and track the subsequent fast neutral particles. The solution used by MICHELLE is to combine finite element analysis with particle-in-cell (PIC) methods. The basic physics model is based on the equilibrium steady-state application of the electrostatic particle-in-cell (PIC) approximation employing a conformal computational mesh. The foundation stems from the same basic model introduced in codes such as EGUN. Here, Poisson's equation is used to self-consistently include the effects of space charge on the fields, and the relativistic Lorentz equation is used to integrate the particle trajectories through those fields. The presentation will consider the complexity of modeling ion thrusters.

Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2013-12-01

The structure and properties of families of critical points for classes of functions W(z,{\\overline{z}}) obeying the elliptic Euler-Poisson-Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(\\beta ,{\\overline{\\beta }};1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed.

A generalized Poisson solver for first-principles device simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch; Brück, Sascha

2016-01-28

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative methodmore » in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.« less

Computations of Wall Distances Based on Differential Equations

NASA Technical Reports Server (NTRS)

Tucker, Paul G.; Rumsey, Chris L.; Spalart, Philippe R.; Bartels, Robert E.; Biedron, Robert T.

2004-01-01

The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne

2011-11-01

We present a coarse-grid projection (CGP) algorithm for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. Here, we investigate a particular CGP method for the vorticity-stream function formulation that uses the full weighting operation for mapping from fine to coarse grids, the third-order Runge-Kutta method for time stepping, and finite differences for the spatial discretization. After solving the Poisson equation on a coarsened grid, bilinear interpolation is used to obtain the fine data for consequent time stepping on the full grid. We compute several benchmark flows: the Taylor-Green vortex, a vortex pair merging, a double shear layer, decaying turbulence and the Taylor-Green vortex on a distorted grid. In all cases we use either FFT-based or V-cycle multigrid linear-cost Poisson solvers. Reducing the number of degrees of freedom of the Poisson solver by powers of two accelerates these computations while, for the first level of coarsening, retaining the same level of accuracy in the fine resolution vorticity field.

Complete synchronization of the global coupled dynamical network induced by Poisson noises.

PubMed

Guo, Qing; Wan, Fangyi

2017-01-01

The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

1992-01-01

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Relaxation in two dimensions and the 'sinh-Poisson' equation

NASA Technical Reports Server (NTRS)

Montgomery, D.; Matthaeus, W. H.; Stribling, W. T.; Martinez, D.; Oughton, S.

1992-01-01

Long-time states of a turbulent, decaying, two-dimensional, Navier-Stokes flow are shown numerically to relax toward maximum-entropy configurations, as defined by the "sinh-Poisson" equation. The large-scale Reynolds number is about 14,000, the spatial resolution is (512)-squared, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large-scale eddy-turnover times.

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

NASA Technical Reports Server (NTRS)

Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

1986-01-01

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

Numerical model of the plasma formation at electron beam welding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trushnikov, D. N., E-mail: trdimitr@yandex.ru; The Department for Welding Production and Technology of Constructional Materials, Perm National Research Polytechnic University, Perm 614990; Mladenov, G. M., E-mail: gmmladenov@abv.bg

2015-01-07

The model of plasma formation in the keyhole in liquid metal as well as above the electron beam welding zone is described. The model is based on solution of two equations for the density of electrons and the mean electron energy. The mass transfer of heavy plasma particles (neutral atoms, excited atoms, and ions) is taken into account in the analysis by the diffusion equation for a multicomponent mixture. The electrostatic field is calculated using the Poisson equation. Thermionic electron emission is calculated for the keyhole wall. The ionization intensity of the vapors due to beam electrons and high-energy secondarymore » and backscattered electrons is calibrated using the plasma parameters when there is no polarized collector electrode above the welding zone. The calculated data are in good agreement with experimental data. Results for the plasma parameters for excitation of a non-independent discharge are given. It is shown that there is a need to take into account the effect of a strong electric field near the keyhole walls on electron emission (the Schottky effect) in the calculation of the current for a non-independent discharge (hot cathode gas discharge). The calculated electron drift velocities are much bigger than the velocity at which current instabilities arise. This confirms the hypothesis for ion-acoustic instabilities, observed experimentally in previous research.« less

Differential geometry based solvation model II: Lagrangian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface (MMS) and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature. PMID:21279359

Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified Stern layer.

PubMed

Lim, Jongil; Whitcomb, John; Boyd, James; Varghese, Julian

2007-01-01

A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.

Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

PubMed

Schuss, Z; Nadler, B; Eisenberg, R S

2001-09-01

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.

Gyrofluid theory and simulation of electromagnetic turbulence and transport in tokamak plasmas

NASA Astrophysics Data System (ADS)

Snyder, Philip Benjamin

1999-11-01

Turbulence and transport in toroidal plasmas is studied via the development of an electromagnetic gyrofluid model, and its implementation in realistic nonlinear simulations. This work extends earlier electrostatic gyrofluid models to include magnetic fluctuations and non-adiabatic passing electron dynamics. A new set of electron fluid equations is derived from the drift kinetic equation, via an expansion in the electron-ion mass ratio. These electron equations include descriptions of linear and nonlinear drift motion, Landau damping, and electron-ion collisions. Ion moment equations are derived from the electromagnetic gyrokinetic equation, and the gyrokinetic Poisson's Equation and Ampere's Law close the system. The model is benchmarked with linear gyrokinetic calculations, and good agreement is found for both the finite-β ion temperature gradient (ITG) and kinetic Alfvén ballooning (KBM) instabilities. Nonlinear simulations of ITG and KBM-driven turbulence are performed in toroidal flux tube geometry at a range of values of plasma β, and electromagnetic effects are found to significantly impact turbulent heat and particle transport. At low values of β, transport is reduced, as expected due to the finite-β stabilization of the ITG mode. However, as β approaches the Ideal-MHD stability threshold, transport can increase. In the presence of dissipation provided by a model of electron Landau damping and electron-ion collisions, this transport increase can be quite dramatic. Finally, the results of the simulations are compared to tokamak experiments, and encouraging agreement is found with measured density and temperature fluctuation spectra. Direct comparisons of transport fluxes reveal that electromagnetic effects are important at characteristic edge parameters, bringing predicted fluxes more closely in line with observations.

Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye-Hückel approximation and Deryagin formulation.

PubMed

Duval, Jérôme F L; Merlin, Jenny; Narayana, Puranam A L

2011-01-21

We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may dramatically change depending on the interplay between characteristic Debye length, thickness of ion-permeable layers and their respective protolytic features (e.g. location, magnitude and sign of charge density). This formalism extends a recent model by Ohshima which is strictly limited to interaction between soft mono-shell particles within Deryagin and Debye-Hückel approximations under conditions where ionizable sites are completely dissociated.

Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations.

PubMed

Kilic, Mustafa Sabri; Bazant, Martin Z; Ajdari, Armand

2007-02-01

In situations involving large potentials or surface charges, the Poisson-Boltzman (PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations," which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these modified PNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari [Phys. Rev. E 70, 021506 (2004)] for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I [Kilic, Bazant, and Ajdari, Phys. Rev. E 75, 021502 (2007)] for such problems.

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions

NASA Astrophysics Data System (ADS)

Gavish, Nir

2018-04-01

We study the existence and stability of stationary solutions of Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) with two counter-charged species. We show that within a range of parameters, steric effects give rise to multiple solutions of the corresponding stationary equation that are smooth. The PNP-steric equation, however, is found to be ill-posed at the parameter regime where multiple solutions arise. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, show that it is well-posed and that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

Calculations of the electrostatic potential adjacent to model phospholipid bilayers.

PubMed

Peitzsch, R M; Eisenberg, M; Sharp, K A; McLaughlin, S

1995-03-01

We used the nonlinear Poisson-Boltzmann equation to calculate electrostatic potentials in the aqueous phase adjacent to model phospholipid bilayers containing mixtures of zwitterionic lipids (phosphatidylcholine) and acidic lipids (phosphatidylserine or phosphatidylglycerol). The aqueous phase (relative permittivity, epsilon r = 80) contains 0.1 M monovalent salt. When the bilayers contain < 11% acidic lipid, the -25 mV equipotential surfaces are discrete domes centered over the negatively charged lipids and are approximately twice the value calculated using Debye-Hückel theory. When the bilayers contain > 25% acidic lipid, the -25 mV equipotential profiles are essentially flat and agree well with the values calculated using Gouy-Chapman theory. When the bilayers contain 100% acidic lipid, all of the equipotential surfaces are flat and agree with Gouy-Chapman predictions (including the -100 mV surface, which is located only 1 A from the outermost atoms). Even our model bilayers are not simple systems: the charge on each lipid is distributed over several atoms, these partial charges are non-coplanar, there is a 2 A ion-exclusion region (epsilon r = 80) adjacent to the polar headgroups, and the molecular surface is rough. We investigated the effect of these four factors using smooth (or bumpy) epsilon r = 2 slabs with embedded point charges: these factors had only minor effects on the potential in the aqueous phase.

Evolutionary conservativeness of electric field in the Cu,Zn superoxide dismutase active site. Evidence for co-ordinated mutation of charged amino acid residues.

PubMed

Desideri, A; Falconi, M; Polticelli, F; Bolognesi, M; Djinovic, K; Rotilio, G

1992-01-05

Equipotential lines were calculated, using the Poisson-Boltzmann equation, for six Cu,Zn superoxide dismutases with different protein electric charge and various degrees of sequence homology, namely those from ox, pig, sheep, yeast, and the isoenzymes A and B from the amphibian Xenopus laevis. The three-dimensional structures of the porcine and ovine superoxide dismutases were obtained by molecular modelling reconstruction using the structure of the highly homologous bovine enzyme as a template. The three-dimensional structure of the evolutionary distant yeast Cu,Zn superoxide dismutase was recently resolved by us, while computer-modelled structures are available for X. laevis isoenzymes. The six proteins display large differences in the net protein charge and distribution of electrically charged surface residues but the trend of the equipotential lines in the proximity of the active sites was found to be constant in all cases. These results are in line with the very similar catlytic rate constants experimentally measured for the corresponding enzyme activities. This analysis shows that electrostatic guidance for the enzyme-substrate interaction in Cu,Zn superoxide dismutases is related to a spatial distribution of charges, arranged so as to maintain, in the area surrounding the active sites, an identical electrostatic potential distribution, which is conserved in the evolution of this protein family.

Calculations of the electrostatic potential adjacent to model phospholipid bilayers.

PubMed Central

Peitzsch, R M; Eisenberg, M; Sharp, K A; McLaughlin, S

1995-01-01

We used the nonlinear Poisson-Boltzmann equation to calculate electrostatic potentials in the aqueous phase adjacent to model phospholipid bilayers containing mixtures of zwitterionic lipids (phosphatidylcholine) and acidic lipids (phosphatidylserine or phosphatidylglycerol). The aqueous phase (relative permittivity, epsilon r = 80) contains 0.1 M monovalent salt. When the bilayers contain < 11% acidic lipid, the -25 mV equipotential surfaces are discrete domes centered over the negatively charged lipids and are approximately twice the value calculated using Debye-Hückel theory. When the bilayers contain > 25% acidic lipid, the -25 mV equipotential profiles are essentially flat and agree well with the values calculated using Gouy-Chapman theory. When the bilayers contain 100% acidic lipid, all of the equipotential surfaces are flat and agree with Gouy-Chapman predictions (including the -100 mV surface, which is located only 1 A from the outermost atoms). Even our model bilayers are not simple systems: the charge on each lipid is distributed over several atoms, these partial charges are non-coplanar, there is a 2 A ion-exclusion region (epsilon r = 80) adjacent to the polar headgroups, and the molecular surface is rough. We investigated the effect of these four factors using smooth (or bumpy) epsilon r = 2 slabs with embedded point charges: these factors had only minor effects on the potential in the aqueous phase. Images FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 PMID:7756540

Interaction of the BKCa channel gating ring with dendrotoxins

PubMed Central

Takacs, Zoltan; Imredy, John P; Bingham, Jon-Paul; Zhorov, Boris S; Moczydlowski, Edward G

2014-01-01

Two classes of small homologous basic proteins, mamba snake dendrotoxins (DTX) and bovine pancreatic trypsin inhibitor (BPTI), block the large conductance Ca2+-activated K+ channel (BKCa, KCa1.1) by production of discrete subconductance events when added to the intracellular side of the membrane. This toxin-channel interaction is unlikely to be pharmacologically relevant to the action of mamba venom, but as a fortuitous ligand-protein interaction, it has certain biophysical implications for the mechanism of BKCa channel gating. In this work we examined the subconductance behavior of 9 natural dendrotoxin homologs and 6 charge neutralization mutants of δ-dendrotoxin in the context of current structural information on the intracellular gating ring domain of the BKCa channel. Calculation of an electrostatic surface map of the BKCa gating ring based on the Poisson-Boltzmann equation reveals a predominantly electronegative surface due to an abundance of solvent-accessible side chains of negatively charged amino acids. Available structure-activity information suggests that cationic DTX/BPTI molecules bind by electrostatic attraction to site(s) on the gating ring located in or near the cytoplasmic side portals where the inactivation ball peptide of the β2 subunit enters to block the channel. Such an interaction may decrease the apparent unitary conductance by altering the dynamic balance of open versus closed states of BKCa channel activation gating. PMID:25483585

Treatment of geometric singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Yu, Sining; Geng, Weihua; Wei, G. W.

2007-06-01

Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces. Moreover, the matrix of the MIBPB-I is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPB-II, to address the aforementioned problems. The present MIBPB-II solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPB-II matrix optimally symmetrical and diagonally dominant. The MIBPB-II solver is extensively validated by the molecular surfaces of few-atom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5Å and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings.

A Multifluid Numerical Algorithm for Interpenetrating Plasma Dynamics

NASA Astrophysics Data System (ADS)

Ghosh, Debojyoti; Kavouklis, Christos; Berger, Richard; Chapman, Thomas; Hittinger, Jeffrey

2017-10-01

Interpenetrating plasmas occur in situations including inertial confinement fusion experiments, where plasmas ablate off the hohlraum and capsule surfaces and interact with each other, and in high-energy density physics experiments that involve the collision of plasma streams ablating off discs irradiated by laser beams. Single-fluid, multi-species hydrodynamic models are not well-suited to study this interaction because they cannot support more than a single fluid velocity; this results in unphysical solutions. Though kinetic models yield accurate solutions for multi-fluid interactions, they are prohibitively expensive for at-scale three-dimensional (3D) simulations. In this study, we propose a multifluid approach where the compressible fluid equations are solved for each ion species and the electrons. Electrostatic forces and inter-species friction and thermal equilibration couple the species. A high-order finite-volume algorithm with explicit time integration is used to solve on a 3D Cartesian domain, and a high-order Poisson solver is used to compute the electrostatic potential. We present preliminary results for the interpenetration of two plasma streams in vacuum and in the presence of a gas fill. This work was performed under the auspices of the U.S. DOE by Lawrence Livermore National Laboratory under Contract No. DE-AC52- 07NA27344 and funded by the LDRD Program at LLNL under project tracking code 17-ERD-081.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne E.

2013-01-01

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.

Molecular simulations of the pairwise interaction of monoclonal antibodies.

PubMed

Lapelosa, Mauro; Patapoff, Thomas W; Zarraga, Isidro E

2014-11-20

Molecular simulations are employed to compute the free energy of pairwise monoclonal antibodies (mAbs) association using a conformational sampling algorithm with a scoring function. The work reported here is aimed at investigating the mAb-mAb association driven by weak interactions with a computational method capable of predicting experimental observations of low binding affinity. The simulations are able to explore the free energy landscape. A steric interaction component, electrostatic interactions, and a nonpolar component of the free energy form the energy scoring function. Electrostatic interactions are calculated by solving the Poisson-Boltzmann equation. The nonpolar component is derived from the van der Waals interactions upon close contact of the protein surfaces. Two mAbs with similar IgG1 framework but with small sequence differences, mAb1 and mAb2, are considered for their different viscosity and propensity to form a weak interacting dimer. mAb1 presents favorable free energy of association at pH 6 with 15 mM of ion concentration reproducing experimental trends of high viscosity and dimer formation at high concentration. Free energy landscape and minimum free energy configurations of the dimer, as well as the second virial coefficient (B22) values are calculated. The energy distributions for mAb1 are obtained, and the most probable configurations are seen to be consistent with experimental measurements. In contrast, mAb2 shows an unfavorable average free energy at the same buffer conditions due to poor electrostatic complementarity, and reversible dimer configurations with favorable free energy are found to be unlikely. Finally, the simulations of the mAb association dynamics provide insights on the self-association responsible for bulk solution behavior and aggregation, which are important to the processing and the quality of biopharmaceuticals.

Non-Poisson Processes: Regression to Equilibrium Versus Equilibrium Correlation Functions

DTIC Science & Technology

2004-07-07

ARTICLE IN PRESSPhysica A 347 (2005) 268–2880378-4371/$ - doi:10.1016/j Correspo E-mail adwww.elsevier.com/locate/physaNon- Poisson processes : regression...05.40.a; 89.75.k; 02.50.Ey Keywords: Stochastic processes; Non- Poisson processes ; Liouville and Liouville-like equations; Correlation function...which is not legitimate with renewal non- Poisson processes , is a correct property if the deviation from the exponential relaxation is obtained by time

Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Fairén, Víctor

1998-11-01

This work is devoted to the establishment of a Poisson structure for a format of equations known as generalized Lotka-Volterra systems. These equations, which include the classical Lotka-Volterra systems as a particular case, have been deeply studied in the literature. They have been shown to constitute a whole hierarchy of systems, the characterization of which is made in the context of simple algebra. Our main result is to show that this algebraic structure is completely translatable into the Poisson domain. Important Poisson structures features, such as the symplectic foliation and the Darboux canonical representation, rise as a result of rather simple matrix manipulations.

Poisson equations of rotational motion for a rigid triaxial body with application to a tumbling artificial satellite

NASA Technical Reports Server (NTRS)

Liu, J. J. F.; Fitzpatrick, P. M.

1975-01-01

A mathematical model is developed for studying the effects of gravity gradient torque on the attitude stability of a tumbling triaxial rigid satellite. Poisson equations are used to investigate the rotation of the satellite (which is in elliptical orbit about an attracting point mass) about its center of mass. An averaging method is employed to obtain an intermediate set of differential equations for the nonresonant, secular behavior of the osculating elements which describe the rotational motions of the satellite, and the averaged equations are then integrated to obtain long-term secular solutions for the osculating elements.

Comment on: Accurate and fast numerical solution of Poisson s equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gonis, Antonios; Zhang, Xiaoguang

2012-01-01

This is a comment on the paper by Aftab Alam, Brian G. Wilson, and D. D. Johnson [1], proposing the solution of the near-field corrections (NFC s) problem for the Poisson equation for extended, e.g., space filling, charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, while their method does not address the genuine problem of NFC s that arises when the solution of the Poisson equation is attempted within multiple scattering theory. We also point out a flaw in their line ofmore » reasoning leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable to certain geometries.« less

Tensorial Basis Spline Collocation Method for Poisson's Equation

NASA Astrophysics Data System (ADS)

Plagne, Laurent; Berthou, Jean-Yves

2000-01-01

This paper aims to describe the tensorial basis spline collocation method applied to Poisson's equation. In the case of a localized 3D charge distribution in vacuum, this direct method based on a tensorial decomposition of the differential operator is shown to be competitive with both iterative BSCM and FFT-based methods. We emphasize the O(h4) and O(h6) convergence of TBSCM for cubic and quintic splines, respectively. We describe the implementation of this method on a distributed memory parallel machine. Performance measurements on a Cray T3E are reported. Our code exhibits high performance and good scalability: As an example, a 27 Gflops performance is obtained when solving Poisson's equation on a 2563 non-uniform 3D Cartesian mesh by using 128 T3E-750 processors. This represents 215 Mflops per processors.

Comment on ``Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited''

NASA Astrophysics Data System (ADS)

Gonis, A.; Zhang, X.-G.

2012-09-01

This is a Comment on the paper by Alam, Wilson, and Johnson [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.84.205106 84, 205106 (2011)], proposing the solution of the near-field corrections (NFCs) problem for the Poisson equation for extended, e.g., space-filling charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, whereas, their method does not address the genuine problem of NFCs that arises when the solution of the Poisson equation is attempted within multiple-scattering theory. We also point out a flaw in their line of reasoning, leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable for certain geometries.

Salt dependence of compression normal forces of quenched polyelectrolyte brushes

NASA Astrophysics Data System (ADS)

Hernandez-Zapata, Ernesto; Tamashiro, Mario N.; Pincus, Philip A.

2001-03-01

We obtained mean-field expressions for the compression normal forces between two identical opposing quenched polyelectrolyte brushes in the presence of monovalent salt. The brush elasticity is modeled using the entropy of ideal Gaussian chains, while the entropy of the microions and the electrostatic contribution to the grand potential is obtained by solving the non-linear Poisson-Boltzmann equation for the system in contact with a salt reservoir. For the polyelectrolyte brush we considered both a uniformly charged slab as well as an inhomogeneous charge profile obtained using a self-consistent field theory. Using the Derjaguin approximation, we related the planar-geometry results to the realistic two-crossed cylinders experimental set up. Theoretical predictions are compared to experimental measurements(Marc Balastre's abstract, APS March 2001 Meeting.) of the salt dependence of the compression normal forces between two quenched polyelectrolyte brushes formed by the adsorption of diblock copolymers poly(tert-butyl styrene)-sodium poly(styrene sulfonate) [PtBs/NaPSS] onto an octadecyltriethoxysilane (OTE) hydrophobically modified mica, as well as onto bare mica.

WAKES: Wavelet Adaptive Kinetic Evolution Solvers

NASA Astrophysics Data System (ADS)

Mardirian, Marine; Afeyan, Bedros; Larson, David

2016-10-01

We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.

Expansion of Non-Quasi-Neutral Limited Plasmas Driven by Two-Temperature Electron Clouds

NASA Astrophysics Data System (ADS)

Murakami, Masakatsu; Honrubia, Javier

2017-10-01

Fast heating of an isolated solid mass, under irradiation of ultra-intense ultra-short laser pulse, to averaged temperatures of order of keV is theoretically studied. Achievable maximum ion temperatures are determined as a consequence of the interplay of the electron-to-ion energy deposition and nonrelativistic plasma expansion, where fast ion emission plays an important role in the energy balance. To describe the plasma expansion, we develop a self-similar solution, in which the plasma is composed of three fluids, i.e., ions and two-temperature electrons. Under the condition of isothermal electron expansion in cylindrical geometry, such a fluid system, self-consistently incorporated with the Poisson equation, is fully solved. The charge separation and resultant accelerated ion population due to the induced electrostatic field are quantitatively presented. The analytical model is compared with two-dimensional hydrodynamic simulations to provide practical working windows for the target and laser parameters for the fast heating.

2D modeling based comprehensive analysis of short channel effects in DMG strained VSTB FET

NASA Astrophysics Data System (ADS)

Saha, Priyanka; Banerjee, Pritha; Sarkar, Subir Kumar

2018-06-01

The paper aims to develop two dimensional analytical model of the proposed dual material (DM) Vertical Super Thin Body (VSTB) strained Field Effect Transistor (FET) with focus on its short channel behaviour in nanometer regime. Electrostatic potential across gate/channel and dielectric wall/channel interface is derived by solving 2D Poisson's equation with parabolic approximation method by applying appropriate boundary conditions. Threshold voltage is then calculated by using the criteria of minimum surface potential considering both gate and dielectric wall side potential. Performance analysis of the present structure is demonstrated in terms of potential, electric field, threshold voltage characteristics and subthreshold behaviour by varying various device parameters and applied biases. Effect of application of strain in channel is further explored to establish the superiority of the proposed device in comparison to conventional VSTB FET counterpart. All analytical results are compared with Silvaco ATLAS device simulated data to substantiate the accuracy of our derived model.

Generalized master equations for non-Poisson dynamics on networks.

PubMed

Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Generalized master equations for non-Poisson dynamics on networks

NASA Astrophysics Data System (ADS)

Hoffmann, Till; Porter, Mason A.; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Clinical characterization of 2D pressure field in human left ventricles

NASA Astrophysics Data System (ADS)

Borja, Maria; Rossini, Lorenzo; Martinez-Legazpi, Pablo; Benito, Yolanda; Alhama, Marta; Yotti, Raquel; Perez Del Villar, Candelas; Gonzalez-Mansilla, Ana; Barrio, Alicia; Fernandez-Aviles, Francisco; Bermejo, Javier; Khan, Andrew; Del Alamo, Juan Carlos

2014-11-01

The evaluation of left ventricle (LV) function in the clinical setting remains a challenge. Pressure gradient is a reliable and reproducible indicator of the LV function. We obtain 2D relative pressure field in the LV using in-vivo measurements obtained by processing Doppler-echocardiography images of healthy and dilated hearts. Exploiting mass conservation, we solve the Poisson pressure equation (PPE) dropping the time derivatives and viscous terms. The flow acceleration appears only in the boundary conditions, making our method weakly sensible to the time resolution of in-vivo acquisitions. To ensure continuity with respect to the discrete operator and grid used, a potential flow correction is applied beforehand, which gives another Poisson equation. The new incompressible velocity field ensures that the compatibility equation for the PPE is satisfied. Both Poisson equations are efficiently solved on a Cartesian grid using a multi-grid method and immersed boundary for the LV wall. The whole process is computationally inexpensive and could play a diagnostic role in the clinical assessment of LV function.

Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2015-04-05

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.

On the Geometry of the Hamilton-Jacobi Equation and Generating Functions

NASA Astrophysics Data System (ADS)

Ferraro, Sebastián; de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David; Vaquero, Miguel

2017-10-01

In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results about symplectic groupoids, in particular cotangent groupoids, as a keystone for the construction of our framework. Our methodology follows the ambitious program proposed by Weinstein (In Mechanics day (Waterloo, ON, 1992), volume 7 of fields institute communications, American Mathematical Society, Providence, 1996) in order to develop geometric formulations of the dynamical behavior of Lagrangian and Hamiltonian systems on Lie algebroids and Lie groupoids. This procedure allows us to take symmetries into account, and, as a by-product, we recover results from Channell and Scovel (Phys D 50(1):80-88, 1991), Ge (Indiana Univ. Math. J. 39(3):859-876, 1990), Ge and Marsden (Phys Lett A 133(3):134-139, 1988), but even in these situations our approach is new. A theory of generating functions for the Poisson structures considered here is also developed following the same pattern, solving a longstanding problem of the area: how to obtain a generating function for the identity transformation and the nearby Poisson automorphisms of Poisson manifolds. A direct application of our results gives the construction of a family of Poisson integrators, that is, integrators that conserve the underlying Poisson geometry. These integrators are implemented in the paper in benchmark problems. Some conclusions, current and future directions of research are shown at the end of the paper.

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnich, Glenn; Troessaert, Cedric

2009-04-15

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

Alternative Derivations for the Poisson Integral Formula

ERIC Educational Resources Information Center

Chen, J. T.; Wu, C. S.

2006-01-01

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

Graphic Simulations of the Poisson Process.

DTIC Science & Technology

1982-10-01

RANDOM NUMBERS AND TRANSFORMATIONS..o......... 11 Go THE RANDOM NUMBERGENERATOR....... .oo..... 15 III. POISSON PROCESSES USER GUIDE....oo.ooo ......... o...again. In the superimposed mode, two Poisson processes are active, each with a different rate parameter, (call them Type I and Type II with respective...occur. The value ’p’ is generated by the following equation where ’Li’ and ’L2’ are the rates of the two Poisson processes ; p = Li / (Li + L2) The value

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

The polarized Debye sheath effect on Kadomtsev-Petviashvili electrostatic structures in strongly coupled dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shahmansouri, M.; Alinejad, H.

2015-04-15

We give a theoretical investigation on the dynamics of nonlinear electrostatic waves in a strongly coupled dusty plasma with strong electrostatic interaction between dust grains in the presence of the polarization force (i.e., the force due to the polarized Debye sheath). Adopting a reductive perturbation method, we derived a three-dimensional Kadomtsev-Petviashvili equation that describes the evolution of weakly nonlinear electrostatic localized waves. The energy integral equation is used to study the existence domains of the localized structures. The analysis provides the localized structure existence region, in terms of the effects of strong interaction between the dust particles and polarization force.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson-Boltzmann Solvent.

PubMed

Molavi Tabrizi, Amirhossein; Goossens, Spencer; Mehdizadeh Rahimi, Ali; Cooper, Christopher D; Knepley, Matthew G; Bardhan, Jaydeep P

2017-06-13

We extend the linearized Poisson-Boltzmann (LPB) continuum electrostatic model for molecular solvation to address charge-hydration asymmetry. Our new solvation-layer interface condition (SLIC)/LPB corrects for first-shell response by perturbing the traditional continuum-theory interface conditions at the protein-solvent and the Stern-layer interfaces. We also present a GPU-accelerated treecode implementation capable of simulating large proteins, and our results demonstrate that the new model exhibits significant accuracy improvements over traditional LPB models, while reducing the number of fitting parameters from dozens (atomic radii) to just five parameters, which have physical meanings related to first-shell water behavior at an uncharged interface. In particular, atom radii in the SLIC model are not optimized but uniformly scaled from their Lennard-Jones radii. Compared to explicit-solvent free-energy calculations of individual atoms in small molecules, SLIC/LPB is significantly more accurate than standard parametrizations (RMS error 0.55 kcal/mol for SLIC, compared to RMS error of 3.05 kcal/mol for standard LPB). On parametrizing the electrostatic model with a simple nonpolar component for total molecular solvation free energies, our model predicts octanol/water transfer free energies with an RMS error 1.07 kcal/mol. A more detailed assessment illustrates that standard continuum electrostatic models reproduce total charging free energies via a compensation of significant errors in atomic self-energies; this finding offers a window into improving the accuracy of Generalized-Born theories and other coarse-grained models. Most remarkably, the SLIC model also reproduces positive charging free energies for atoms in hydrophobic groups, whereas standard PB models are unable to generate positive charging free energies regardless of the parametrized radii. The GPU-accelerated solver is freely available online, as is a MATLAB implementation.

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics

NASA Astrophysics Data System (ADS)

Sun, Hui; Wen, Jiayi; Zhao, Yanxiang; Li, Bo; McCammon, J. Andrew

2015-12-01

Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics.

PubMed

Sun, Hui; Wen, Jiayi; Zhao, Yanxiang; Li, Bo; McCammon, J Andrew

2015-12-28

Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.

Dispersion equation for electrostatic ion cyclotron instability under the effect of ionization in a dusty plasma

NASA Astrophysics Data System (ADS)

Singh, Sukhmander

2018-05-01

In the present paper we derive the plasma dispersion equation under the effect of ionization rate in a dust plasma to investigate the electrostatic ion cyclotron instability, where dust charge fluctuation is absent. It has one of the lowest threshold drift velocities among all the current-driven instabilities in isothermal plasma. The Electrostatic ion cyclotron instability in a dusty plasma containing electrons, light ions, and massive negatively charged dust grains which can be investigated both experimentally and theoretically.

Integración automatizada de las ecuaciones de Lagrange en el movimiento orbital.

NASA Astrophysics Data System (ADS)

Abad, A.; San Juan, J. F.

The new techniques of algebraic manipulation, especially the Poisson Series Processor, permit the analytical integration of the more and more complex problems of celestial mechanics. The authors are developing a new Poisson Series Processor, PSPC, and they use it to solve the Lagrange equation of the orbital motion. They integrate the Lagrange equation by using the stroboscopic method, and apply it to the main problem of the artificial satellite theory.

Poisson equation for the three-loop ladder diagram in string theory at genus one

NASA Astrophysics Data System (ADS)

Basu, Anirban

2016-11-01

The three-loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D12ℛ4 amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet and the links represent scalar Green functions connecting them. By using the properties of the Green function and manipulating the various expressions, we obtain a modular invariant Poisson equation satisfied by this diagram, with source terms involving one-, two- and three-loop diagrams. Unlike the source terms in the Poisson equations for diagrams at lower orders in the momentum expansion or the Mercedes diagram, a particular source term involves a five-point function containing a holomorphic and a antiholomorphic worldsheet derivative acting on different Green functions. We also obtain simple equalities between topologically distinct diagrams, and consider some elementary examples.

A physically based compact I-V model for monolayer TMDC channel MOSFET and DMFET biosensor.

PubMed

Rahman, Ehsanur; Shadman, Abir; Ahmed, Imtiaz; Khan, Saeed Uz Zaman; Khosru, Quazi D M

2018-06-08

In this work, a compact transport model has been developed for monolayer transition metal dichalcogenide (TMDC) channel MOSFET. The analytical model solves the Poisson's equation for the inversion charge density to get the electrostatic potential in the channel. Current is then calculated by solving the drift-diffusion equation. The model makes gradual channel approximation to simplify the solution procedure. The appropriate density of states obtained from the first principle density functional theory simulation has been considered to keep the model physically accurate for monolayer TMDC channel FET. The outcome of the model has been benchmarked against both experimental and numerical quantum simulation results with the help of a few fitting parameters. Using the compact model, detailed output and transfer characteristics of monolayer WSe 2 FET have been studied, and various performance parameters have been determined. The study confirms excellent ON and OFF state performances of monolayer WSe 2 FET which could be viable for the next generation high-speed, low power applications. Also, the proposed model has been extended to study the operation of a biosensor. A monolayer MoS 2 channel based dielectric modulated FET is investigated using the compact model for detection of a biomolecule in a dry environment.

Electrostatic and Quantum Transport Simulations of Quantum Point Contacts in the Integer Quantum Hall Regime

NASA Astrophysics Data System (ADS)

Sahasrabudhe, Harshad; Fallahi, Saeed; Nakamura, James; Povolotskyi, Michael; Novakovic, Bozidar; Rahman, Rajib; Manfra, Michael; Klimeck, Gerhard

Quantum Point Contacts (QPCs) are extensively used in semiconductor devices for charge sensing, tunneling and interference experiments. Fabry-Pérot interferometers containing 2 QPCs have applications in quantum computing, in which electrons/quasi-particles undergo interference due to back-scattering from the QPCs. Such experiments have turned out to be difficult because of the complex structure of edge states near the QPC boundary. We present realistic simulations of the edge states in QPCs based on GaAs/AlGaAs heterostructures, which can be used to predict conductance and edge state velocities. Conduction band profile is obtained by solving decoupled effective mass Schrödinger and Poisson equations self-consistently on a finite element mesh of a realistic geometry. In the integer quantum Hall regime, we obtain compressible and in-compressible regions near the edges. We then use the recursive Green`s function algorithm to solve Schrödinger equation with open boundary conditions for calculating transmission and local current density in the QPCs. Impurities are treated by inserting bumps in the potential with a Gaussian distribution. We compare observables with experiments for fitting some adjustable parameters. The authors would like to thank Purdue Research Foundation and Purdue Center for Topological Materials for their support.

Four-dimensional gravity as an almost-Poisson system

NASA Astrophysics Data System (ADS)

Ita, Eyo Eyo

2015-04-01

In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.

Deterministic multidimensional nonuniform gap sampling.

PubMed

Worley, Bradley; Powers, Robert

2015-12-01

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities. Copyright © 2015 Elsevier Inc. All rights reserved.

Electrostatics of lipid bilayer bending.

PubMed Central

Chou, T; Jarić, M V; Siggia, E D

1997-01-01

The electrostatic contribution to spontaneous membrane curvature is calculated within Poisson-Boltzmann theory under a variety of assumptions and emphasizing parameters in the physiological range. Asymmetrical surface charges can be fixed with respect to bilayer midplane area or with respect to the lipid-water area, but induce curvatures of opposite signs. Unequal screening layers on the two sides of a vesicle (e.g., multivalent cationic proteins on one side and monovalent salt on the other) also induce bending. For reasonable parameters, tubules formed by electrostatically induced bending can have radii in the 50-100-nm range, often seen in many intracellular organelles. Thus membrane associated proteins may induce curvature and subsequent budding, without themselves being intrinsically curved. Furthermore, we derive the previously unexplored effects of respecting the strict conservation of charge within the interior of a vesicle. The electrostatic component of the bending modulus is small under most of our conditions and is left as an experimental parameter. The large parameter space of conditions is surveyed in an array of graphs. Images FIGURE 1 FIGURE 10 PMID:9129807

Low Mach-number collisionless electrostatic shocks and associated ion acceleration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pusztai, Istvan; TenBarge, Jason; Csapó, Aletta N.

The existence and properties of low Mach-number (M >~ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. By using this semi-analytical model, we also study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock propertiesmore » significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.« less

Low Mach-number collisionless electrostatic shocks and associated ion acceleration

DOE PAGES

Pusztai, Istvan; TenBarge, Jason; Csapó, Aletta N.; ...

2017-12-19

The existence and properties of low Mach-number (M >~ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. By using this semi-analytical model, we also study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock propertiesmore » significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sackett, S.J.

JASON solves general electrostatics problems having either slab or cylindrical symmetry. More specifically, it solves the self-adjoint elliptic equation, div . (KgradV) - ..gamma..V + rho = 0 in an aritrary two-dimensional domain. For electrostatics, V is the electrostatic potential, K is the dielectric tensor, and rho is the free-charge density. The parameter ..gamma.. is identically zero for electrostatics but may have a positive nonzero value in other cases (e.g., capillary surface problems with gravity loading). The system of algebraic equations used in JASON is generated by the finite element method. Four-node quadrilateral elements are used for most of themore » mesh. Triangular elements, however, are occasionally used on boundaries to avoid severe mesh distortions. 15 figures. (RWR)« less

Marginal Stability of Ion-Acoustic Waves in a Weakly Collisional Two-Temperature Plasma without a Current.

DTIC Science & Technology

1987-08-06

ABSTRACT (Continue on reverse if necessary and identify by block number) The linearized Balescu -Lenard-Poisson equations are solved in the weakly...free plasma is . unresolved. The purpose of this report is to present a resolution based upon the Balescu -Lenard-Poisson equations. The Balescu -Lenard...acoustic waves become marginally stable. Gur re- sults are based on the closed form solution for the dielectric function for the line- arized Balescu -Lenard

Inflation without inflaton: A model for dark energy

NASA Astrophysics Data System (ADS)

Falomir, H.; Gamboa, J.; Méndez, F.; Gondolo, P.

2017-10-01

The interaction between two initially causally disconnected regions of the Universe is studied using analogies of noncommutative quantum mechanics and the deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lemaître-Robertson-Walker (FLRW) metrics with scale factors a and b and cosmological constants Λa and Λb, respectively. The causality is turned on by positing a nontrivial Poisson bracket [Pα,Pβ]=ɛα βκ/G , where G is Newton's gravitational constant and κ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies, and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of κ . In this model, the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for κ ≪1 is also studied.

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

Poisson's ratio of fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Christiansson, Henrik; Helsing, Johan

1996-05-01

Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

Localization of intense electromagnetic waves in a relativistically hot plasma.

PubMed

Shukla, P K; Eliasson, B

2005-02-18

We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schro dinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.

Reference manual for the POISSON/SUPERFISH Group of Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1987-01-01

The POISSON/SUPERFISH Group codes were set up to solve two separate problems: the design of magnets and the design of rf cavities in a two-dimensional geometry. The first stage of either problem is to describe the layout of the magnet or cavity in a way that can be used as input to solve the generalized Poisson equation for magnets or the Helmholtz equations for cavities. The computer codes require that the problems be discretized by replacing the differentials (dx,dy) by finite differences ({delta}X,{delta}Y). Instead of defining the function everywhere in a plane, the function is defined only at a finitemore » number of points on a mesh in the plane.« less

Electron Density and Two-Channel Neutron Emission Measurements in Steady-State Spherical Inertial-Electrostatically Confined Plasmas, with Review of the 1-D Kinetic Model

NASA Technical Reports Server (NTRS)

Dobson, Chris C.; Hrbud, Ivana

2004-01-01

Electron density measurements have been made in steady-state plasmas in a spherical inertial electrostatic confinement (IEC) discharge using microwave interferometry. Plasma cores interior to two cathodes, having diameters of 15 and 23 cm, respectively, were probed over a transverse range of 10 cm with a spatial resolution of about 1.4 cm for buffer gas pressures from 0.2 to 6 Pa in argon and deuterium. The transverse profiles are generally flat, in some cases with eccentric symmetric minima, and give mean densities of from approx. = 0.4 to 7x 10(exp 10)/cu cm, the density generally increasing with the neutral gas pressure. Numerical solutions of the 1-D Poisson equation for EC plasmas are reviewed and energy distribution functions are identified which give flat transverse profiles. These functions are used with the plasma approximation to obtain solutions which also give densities consistent with the measurements, and a double potential well solution is obtained which has minima qualitatively similar to those observed. Explicit consideration is given to the compatibility of the solutions interior and exterior to the cathode, and to grid transparency. Deuterium fusion neutron emission rates were also measured and found to be isotropic, to within the measurement error, over two simultaneous directions. Anisotropy was observed in residual emissions during operation with non-fusing hydrogen-1. The deuterium rates are consistent with predictions from the model.

Brownian dynamics simulations of interactions between aldolase and G- or F-actin.

PubMed Central

Ouporov, I V; Knull, H R; Thomasson, K A

1999-01-01

Compartmentation of proteins in cells is important to proper cell function. Interactions of F-actin and glycolytic enzymes is one mechanism by which glycolytic enzymes can compartment. Brownian dynamics (BD) simulations of the binding of the muscle form of the glycolytic enzyme fructose-1,6-bisphosphate aldolase (aldolase) to F- or G-actin provide first-encounter snapshots of these interactions. Using x-ray structures of aldolase, G-actin, and three-dimensional models of F-actin, the electrostatic potential about each protein was predicted by solving the linearized Poisson-Boltzmann equation for use in BD simulations. The BD simulations provided solution complexes of aldolase with F- or G-actin. All complexes demonstrate the close contacts between oppositely charged regions of the protein surfaces. Positively charged surface regions of aldolase (residues Lys 13, 27, 288, 293, and 341 and Arg 257) are attracted to the negatively charged amino terminus (Asp 1 and Glu 2 and 4) and other patches (Asp 24, 25, and 363 and Glu 361, 364, 99, and 100) of actin subunits. According to BD results, the most important factor for aldolase binding to actin is the quaternary structure of aldolase and actin. Two pairs of adjacent aldolase subunits greatly add to the positive electrostatic potential of each other creating a region of attraction for the negatively charged subdomain 1 of the actin subunit that is exposed to solvent in the quaternary F-actin structure. PMID:9876119

Atomistic Molecular Dynamics Simulations of Charged Latex Particle Surfaces in Aqueous Solution.

PubMed

Li, Zifeng; Van Dyk, Antony K; Fitzwater, Susan J; Fichthorn, Kristen A; Milner, Scott T

2016-01-19

Charged particles in aqueous suspension form an electrical double layer at their surfaces, which plays a key role in suspension properties. For example, binder particles in latex paint remain suspended in the can because of repulsive forces between overlapping double layers. Existing models of the double layer assume sharp interfaces bearing fixed uniform charge, and so cannot describe aqueous binder particle surfaces, which are soft and diffuse, and bear mobile charge from ionic surfactants as well as grafted multivalent oligomers. To treat this industrially important system, we use atomistic molecular dynamics simulations to investigate a structurally realistic model of commercial binder particle surfaces, informed by extensive characterization of particle synthesis and surface properties. We determine the interfacial profiles of polymer, water, bound and free ions, from which the charge density and electrostatic potential can be calculated. We extend the traditional definitions of the inner and outer Helmholtz planes to our diffuse interfaces. Beyond the Stern layer, the simulated electrostatic potential is well described by the Poisson-Boltzmann equation. The potential at the outer Helmholtz plane compares well to the experimental zeta potential. We compare particle surfaces bearing two types of charge groups, ionic surfactant and multivalent oligomers, with and without added salt. Although the bare charge density of a surface bearing multivalent oligomers is much higher than that of a surfactant-bearing surface at realistic coverage, greater counterion condensation leads to similar zeta potentials for the two systems.

On the mass concentration of L^2-constrained minimizers for a class of Schrödinger-Poisson equations

NASA Astrophysics Data System (ADS)

Ye, Hongyu; Luo, Tingjian

2018-06-01

In this paper, we study the mass concentration behavior of positive solutions with prescribed L^2-norm for a class of Schrödinger-Poisson equations in R^3 -Δ u-μ u+φ _uu-|u|^{p-2}u=0, &{} x\\in R^3, μ \\in R, -Δ φ _u=|u|^2, where p\\in (2,6). We show that positive solutions with prescribed L^2-norm as which tends to 0 (in some cases) or to + ∞ (in others), behave like the positive solution of Schrödinger equation -Δ u+u=|u|^{p-2}u in R^3.

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

NASA Technical Reports Server (NTRS)

Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

1995-01-01

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Gao, Shan; Liu, Zaiming

2010-03-01

In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the nth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case that the claim size distribution is exponential is considered in some detail.

Beyond single-stream with the Schrödinger method

NASA Astrophysics Data System (ADS)

Uhlemann, Cora; Kopp, Michael

2016-10-01

We investigate large scale structure formation of collisionless dark matter in the phase space description based on the Vlasov-Poisson equation. We present the Schrödinger method, originally proposed by \\cite{WK93} as numerical technique based on the Schrödinger Poisson equation, as an analytical tool which is superior to the common standard pressureless fluid model. Whereas the dust model fails and develops singularities at shell crossing the Schrödinger method encompasses multi-streaming and even virialization.

Electrostatic contribution to the binding stability of protein-protein complexes.

PubMed

Dong, Feng; Zhou, Huan-Xiang

2006-10-01

To investigate roles of electrostatic interactions in protein binding stability, electrostatic calculations were carried out on a set of 64 mutations over six protein-protein complexes. These mutations alter polar interactions across the interface and were selected for putative dominance of electrostatic contributions to the binding stability. Three protocols of implementing the Poisson-Boltzmann model were tested. In vdW4 the dielectric boundary between the protein low dielectric and the solvent high dielectric is defined as the protein van der Waals surface and the protein dielectric constant is set to 4. In SE4 and SE20, the dielectric boundary is defined as the surface of the protein interior inaccessible to a 1.4-A solvent probe, and the protein dielectric constant is set to 4 and 20, respectively. In line with earlier studies on the barnase-barstar complex, the vdW4 results on the large set of mutations showed the closest agreement with experimental data. The agreement between vdW4 and experiment supports the contention of dominant electrostatic contributions for the mutations, but their differences also suggest van der Waals and hydrophobic contributions. The results presented here will serve as a guide for future refinement in electrostatic calculation and inclusion of nonelectrostatic effects. Proteins 2006. (c) 2006 Wiley-Liss, Inc.

On the Impact of Electrostatic Correlations on the Double-Layer Polarization of a Spherical Particle in an Alternating Current Field.

PubMed

Alidoosti, Elaheh; Zhao, Hui

2018-05-15

At concentrated electrolytes, the ion-ion electrostatic correlation effect is considered an important factor in electrokinetics. In this paper, we compute, in theory and simulation, the dipole moment for a spherical particle (charged, dielectric) under the action of an alternating electric field using the modified continuum Poisson-Nernst-Planck (PNP) model by Bazant et al. [ Double Layer in Ionic Liquids: Overscreening Versus Crowding . Phys. Rev. Lett. 2011 , 106 , 046102 ] We investigate the dependency of the dipole moment in terms of frequency and its variation with such quantities like ζ-potential, electrostatic correlation length, and double-layer thickness. With thin electric double layers, we develop simple models through performing an asymptotic analysis of the modified PNP model. We also present numerical results for an arbitrary Debye screening length and electrostatic correlation length. From the results, we find a complicated impact of electrostatic correlations on the dipole moment. For instance, with increasing the electrostatic correlation length, the dipole moment decreases and reaches a minimum and then it goes up. This is because of initially decreasing of surface conduction and finally increasing due to the impact of ion-ion electrostatic correlations on ion's convection and migration. Also, we show that in contrast to the standard PNP model, the modified PNP model can qualitatively explain the data from the experimental results in multivalent electrolytes.

Bounding the electrostatic free energies associated with linear continuum models of molecular solvation.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G; Anitescu, Mihai

2009-03-14

The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.

Bounding the electrostatic free energies associated with linear continuum models of molecular solvation

NASA Astrophysics Data System (ADS)

Bardhan, Jaydeep P.; Knepley, Matthew G.; Anitescu, Mihai

2009-03-01

The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.

Improving the treatment of coarse-grain electrostatics: CVCEL.

PubMed

Ceres, N; Lavery, R

2015-12-28

We propose an analytic approach for calculating the electrostatic energy of proteins or protein complexes in aqueous solution. This method, termed CVCEL (Circular Variance Continuum ELectrostatics), is fitted to Poisson calculations and is able to reproduce the corresponding energies for different choices of solute dielectric constant. CVCEL thus treats both solute charge interactions and charge self-energies, and it can also deal with salt solutions. Electrostatic damping notably depends on the degree of solvent exposure of the charges, quantified here in terms of circular variance, a measure that reflects the vectorial distribution of the neighbors around a given center. CVCEL energies can be calculated rapidly and have simple analytical derivatives. This approach avoids the need for calculating effective atomic volumes or Born radii. After describing how the method was developed, we present test results for coarse-grain proteins of different shapes and sizes, using different internal dielectric constants and different salt concentrations and also compare the results with those from simple distance-dependent models. We also show that the CVCEL approach can be used successfully to calculate the changes in electrostatic energy associated with changes in protein conformation or with protein-protein binding.

Accelerating Electrostatic Surface Potential Calculation with Multiscale Approximation on Graphics Processing Units

PubMed Central

Anandakrishnan, Ramu; Scogland, Tom R. W.; Fenley, Andrew T.; Gordon, John C.; Feng, Wu-chun; Onufriev, Alexey V.

2010-01-01

Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multiscale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone. PMID:20452792

Electrostatic Potential Energy within a Protein Monitored by Metal Charge-Dependent Hydrogen Exchange

PubMed Central

Anderson, Janet S.; LeMaster, David M.; Hernández, Griselda

2006-01-01

Hydrogen exchange measurements on Zn(II)-, Ga(III)-, and Ge(IV)-substituted Pyrococcus furiosus rubredoxin demonstrate that the log ratio of the base-catalyzed rate constants (Δ log kex) varies inversely with the distance out to at least 12 Å from the metal. This pattern is consistent with the variation of the amide nitrogen pK values with the metal charge-dependent changes in the electrostatic potential. Fifteen monitored amides lie within this range, providing an opportunity to assess the strength of electrostatic interactions simultaneously at numerous positions within the structure. Poisson-Boltzmann calculations predict an optimal effective internal dielectric constant of 6. The largest deviations between the experimentally estimated and the predicted ΔpK values appear to result from the conformationally mobile charged side chains of Lys-7 and Glu-48 and from differential shielding of the peptide units arising from their orientation relative to the metal site. PMID:17012322

Coarse-graining, Electrostatics and pH effects in phospholipid systems

NASA Astrophysics Data System (ADS)

Travesset, Alex; Vangaveti, Sweta

2010-03-01

We introduce a minimal free energy describing the interaction of charged groups and counterions including both classical electrostatic and specific interactions. The predictions of the model are compared against the standard model for describing ions next to charged interfaces, consisting of Poisson-Boltzmann theory with additional constants describing ion binding, which are specific to the counterion and the interfacial charge (``chemical binding''). It is shown that the ``chemical'' model can be appropriately described by an underlying ``physical'' model over several decades in concentration, but the extracted binding constants are not uniquely defined, as they differ depending on the particular observable quantity being studied. It is also shown that electrostatic correlations for divalent (or higher valence) ions enhance the surface charge by increasing deprotonation, an effect not properly accounted within chemical models. The model is applied to the charged phospholipids phosphatidylserine, Phosphatidc acid and Phosphoinositides and implications for different biological processes are discussed.

Origin of translocation barriers for polyelectrolyte chains.

PubMed

Kumar, Rajeev; Muthukumar, M

2009-11-21

For single-file translocations of a charged macromolecule through a narrow pore, the crucial step of arrival of an end at the pore suffers from free energy barriers, arising from changes in intrachain electrostatic interaction, distribution of ionic clouds and solvent molecules, and conformational entropy of the chain. All contributing factors to the barrier in the initial stage of translocation are evaluated by using the self-consistent field theory for the polyelectrolyte and the coupled Poisson-Boltzmann description for ions without radial symmetry. The barrier is found to be essentially entropic due to conformational changes. For moderate and high salt concentrations, the barriers for the polyelectrolyte chain are quantitatively equivalent to that of uncharged self-avoiding walks. Electrostatic effects are shown to increase the free energy barriers, but only slightly. The degree of ionization, electrostatic interaction strength, decreasing salt concentration, and the solvent quality all result in increases in the barrier.

A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics.

PubMed

Buschmann, M D; Grodzinsky, A J

1995-05-01

Measured values of the swelling pressure of charged proteoglycans (PG) in solution (Williams RPW, and Comper WD; Biophysical Chemistry 36:223, 1990) and the ionic strength dependence of the equilibrium modulus of PG-rich articular cartilage (Eisenberg SR, and Grodzinsky AJ; J Orthop Res 3: 148, 1985) are compared to the predictions of two models. Each model is a representation of electrostatic forces arising from charge present on spatially fixed macromolecules and spatially mobile micro-ions. The first is a macroscopic continuum model based on Donnan equilibrium that includes no molecular-level structure and assumes that the electrical potential is spatially invariant within the polyelectrolyte medium (i.e. zero electric field). The second model is based on a microstructural, molecular-level solution of the Poisson-Boltzmann (PB) equation within a unit cell containing a charged glycosaminoglycan (GAG) molecule and its surrounding atmosphere of mobile ions. This latter approach accounts for the space-varying electrical potential and electrical field between the GAG constituents of the PG. In computations involving no adjustable parameters, the PB-cell model agrees with the measured pressure of PG solutions to within experimental error (10%), whereas the ideal Donnan model overestimates the pressure by up to 3-fold. In computations involving one adjustable parameter for each model, the PB-cell model predicts the ionic strength dependence of the equilibrium modulus of articular cartilage. Near physiological ionic strength, the Donnan model overpredicts the modulus data by 2-fold, but the two models coincide for low ionic strengths (C0 < 0.025M) where the spatially invariant Donnan potential is a closer approximation to the PB potential distribution. The PB-cell model result indicates that electrostatic forces between adjacent GAGs predominate in determining the swelling pressure of PG in the concentration range found in articular cartilage (20-80 mg/ml). The PB-cell model is also consistent with data (Eisenberg and Grodzinsky, 1985, Lai WM, Hou JS, and Mow VC; J Biomech Eng 113: 245, 1991) showing that these electrostatic forces account for approximately 1/2 (290kPa) the equilibrium modulus of cartilage at physiological ionic strength while absolute swelling pressures may be as low as approximately 25-100kPa. This important property of electrostatic repulsion between GAGs that are highly charged but spaced a few Debye lengths apart allows cartilage to resist compression (high modulus) without generating excessive intratissue swelling pressures.

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

NASA Technical Reports Server (NTRS)

Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

2003-01-01

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

NASA Technical Reports Server (NTRS)

Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

2003-01-01

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Matrix decomposition graphics processing unit solver for Poisson image editing

NASA Astrophysics Data System (ADS)

Lei, Zhao; Wei, Li

2012-10-01

In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) solver (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid solver (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks.

PubMed

Reis, Matthias; Kromer, Justus A; Klipp, Edda

2018-01-20

Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription-translation network and Bateman's model from nuclear physics. For both examples, multimodality was previously not reported.

Kinetic Theory of quasi-electrostatic waves in non-gyrotropic plasmas

NASA Astrophysics Data System (ADS)

Arshad, K.; Poedts, S.; Lazar, M.

2017-12-01

The orbital angular momentum (OAM) is a trait of helically phased light or helical (twisted) electric field. Lasers carrying orbital angular momentum (OAM) revolutionized many scientific and technological paradigms like microscopy, imaging and ionospheric radar facility to analyze three dimensional plasma dynamics in ionosphere, ultra-intense twisted laser pulses, twisted gravitational waves and astrophysics. This trend has also been investigated in plasma physics. Laguerre-Gaussian type solutions are predicted for magnetic tornadoes and Alfvénic tornadoes which exhibit spiral, split and ring-like morphologies. The ring shape morphology is ideal to fit the observed solar corona, solar atmosphere and Earth's ionosphere. The orbital angular momentum indicates the mediation of electrostatic and electromagnetic waves in new phenomena like Raman and Brillouin scattering. A few years ago, some new effects have been included in studies of orbital angular momentum in plasma regimes such as wave-particle interaction in the presence of helical electric field. Therefore, kinetic studies are carried out to investigate the Landau damping of the waves and growth of the instabilities in the presence helical electric field carrying orbital angular momentum for the Maxwellian distributed plasmas. Recently, a well suited approach involving a kappa distribution function has been adopted to model the twisted space plasmas. This leads to the development of new theoretical grounds for the study of Lorentzian or kappa distributed twisted Langmuir, ion acoustic, dust ion acoustic and dust acoustic modes. The quasi-electrostatic twisted waves have been studied now for the non-gyrotropic dusty plasmas in the presence of the orbital angular momentum of the helical electric field using Generalized Lorentzian or kappa distribution function. The Laguerre-Gaussian (LG) mode function is employed to decompose the perturbed distribution function and electric field into planar (longitudinal) and non-planar (azimuthal) components. The modified Vlasov and Poisson equations are solved to obtain the dielectric function for quasi-electrostatic twisted modes the non-gyrotropic dusty plasmas. Some numerical and graphical analysis is also illustrated for the better understanding of the twisted non-gyrotropic plasmas.

Methylene blue binding to DNA with alternating AT base sequence: minor groove binding is favored over intercalation.

PubMed

Rohs, Remo; Sklenar, Heinz

2004-04-01

The results presented in this paper on methylene blue (MB) binding to DNA with AT alternating base sequence complement the data obtained in two former modeling studies of MB binding to GC alternating DNA. In the light of the large amount of experimental data for both systems, this theoretical study is focused on a detailed energetic analysis and comparison in order to understand their different behavior. Since experimental high-resolution structures of the complexes are not available, the analysis is based on energy minimized structural models of the complexes in different binding modes. For both sequences, four different intercalation structures and two models for MB binding in the minor and major groove have been proposed. Solvent electrostatic effects were included in the energetic analysis by using electrostatic continuum theory, and the dependence of MB binding on salt concentration was investigated by solving the non-linear Poisson-Boltzmann equation. We find that the relative stability of the different complexes is similar for the two sequences, in agreement with the interpretation of spectroscopic data. Subtle differences, however, are seen in energy decompositions and can be attributed to the change from symmetric 5'-YpR-3' intercalation to minor groove binding with increasing salt concentration, which is experimentally observed for the AT sequence at lower salt concentration than for the GC sequence. According to our results, this difference is due to the significantly lower non-electrostatic energy for the minor groove complex with AT alternating DNA, whereas the slightly lower binding energy to this sequence is caused by a higher deformation energy of DNA. The energetic data are in agreement with the conclusions derived from different spectroscopic studies and can also be structurally interpreted on the basis of the modeled complexes. The simple static modeling technique and the neglect of entropy terms and of non-electrostatic solute-solvent interactions, which are assumed to be nearly constant for the compared complexes of MB with DNA, seem to be justified by the results.

Nonlinear gyrokinetics: a powerful tool for the description of microturbulence in magnetized plasmas

NASA Astrophysics Data System (ADS)

Krommes, John A.

2010-12-01

Gyrokinetics is the description of low-frequency dynamics in magnetized plasmas. In magnetic-confinement fusion, it provides the most fundamental basis for numerical simulations of microturbulence; there are astrophysical applications as well. In this tutorial, a sketch of the derivation of the novel dynamical system comprising the nonlinear gyrokinetic (GK) equation (GKE) and the coupled electrostatic GK Poisson equation will be given by using modern Lagrangian and Lie perturbation methods. No background in plasma physics is required in order to appreciate the logical development. The GKE describes the evolution of an ensemble of gyrocenters moving in a weakly inhomogeneous background magnetic field and in the presence of electromagnetic perturbations with wavelength of the order of the ion gyroradius. Gyrocenters move with effective drifts, which may be obtained by an averaging procedure that systematically, order by order, removes gyrophase dependence. To that end, the use of the Lagrangian differential one-form as well as the content and advantages of Lie perturbation theory will be explained. The electromagnetic fields follow via Maxwell's equations from the charge and current density of the particles. Particle and gyrocenter densities differ by an important polarization effect. That is calculated formally by a 'pull-back' (a concept from differential geometry) of the gyrocenter distribution to the laboratory coordinate system. A natural truncation then leads to the closed GK dynamical system. Important properties such as GK energy conservation and fluctuation noise will be mentioned briefly, as will the possibility (and difficulties) of deriving nonlinear gyrofluid equations suitable for rapid numerical solution—although it is probably best to directly simulate the GKE. By the end of the tutorial, students should appreciate the GKE as an extremely powerful tool and will be prepared for later lectures describing its applications to physical problems.

Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit: General formalism and perturbations analysis

NASA Astrophysics Data System (ADS)

Suárez, Abril; Chavanis, Pierre-Henri

2015-07-01

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with a λ |φ |4 potential. We study the evolution of the spatially homogeneous background in the fluid representation and derive the linearized equations describing the evolution of small perturbations in a static and in an expanding Universe. We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrödinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c →+∞. We study the evolution of the perturbations in the matter era using the nonrelativistic limit of our formalism. Perturbations whose wavelength is below the Jeans length oscillate in time while perturbations whose wavelength is above the Jeans length grow linearly with the scale factor as in the cold dark matter model. The growth of perturbations in the scalar field model is substantially faster than in the cold dark matter model. When the wavelength of the perturbations approaches the cosmological horizon (Hubble length), a relativistic treatment is mandatory. In that case, we find that relativistic effects attenuate or even prevent the growth of perturbations. This paper exposes the general formalism and provides illustrations in simple cases. Other applications of our formalism will be considered in companion papers.

Center of Excellence in Theoretical Geoplasma Research

DTIC Science & Technology

1993-08-31

of the Balescu -Lenard-Poisson ecluations for collisional plasmas were reported by J.R. Jasperse of the Geophysics Directorate. Discussions at the...the Chairperson: W. Burke (AFGL) 15:00 - 16:30 1. "Solutions of the linearized Balescu -Lenard-Poisson Equations for a Weakly-Collisional Plasma: Some

Prescription-induced jump distributions in multiplicative Poisson processes.

PubMed

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Prescription-induced jump distributions in multiplicative Poisson processes

NASA Astrophysics Data System (ADS)

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

DOE PAGES

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; ...

2016-04-22

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

Electrostatics Explains the Position-Dependent Effect of G⋅U Wobble Base Pairs on the Affinity of RNA Kissing Complexes.

PubMed

Abi-Ghanem, Josephine; Rabin, Clémence; Porrini, Massimiliano; Dausse, Eric; Toulmé, Jean-Jacques; Gabelica, Valérie

2017-10-06

In the RNA realm, non-Watson-Crick base pairs are abundant and can affect both the RNA 3D structure and its function. Here, we investigated the formation of RNA kissing complexes in which the loop-loop interaction is modulated by non-Watson-Crick pairs. Mass spectrometry, surface plasmon resonance, and UV-melting experiments show that the G⋅U wobble base pair favors kissing complex formation only when placed at specific positions. We tried to rationalize this effect by molecular modeling, including molecular mechanics Poisson-Boltzmann surface area (MMPBSA) thermodynamics calculations and PBSA calculations of the electrostatic potential surfaces. Modeling reveals that the G⋅U stabilization is due to a specific electrostatic environment defined by the base pairs of the entire loop-loop region. The loop is not symmetric, and therefore the identity and position of each base pair matters. Predicting and visualizing the electrostatic environment created by a given sequence can help to design specific kissing complexes with high affinity, for potential therapeutic, nanotechnology or analytical applications. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

PCE: web tools to compute protein continuum electrostatics

PubMed Central

Miteva, Maria A.; Tufféry, Pierre; Villoutreix, Bruno O.

2005-01-01

PCE (protein continuum electrostatics) is an online service for protein electrostatic computations presently based on the MEAD (macroscopic electrostatics with atomic detail) package initially developed by D. Bashford [(2004) Front Biosci., 9, 1082–1099]. This computer method uses a macroscopic electrostatic model for the calculation of protein electrostatic properties, such as pKa values of titratable groups and electrostatic potentials. The MEAD package generates electrostatic energies via finite difference solution to the Poisson–Boltzmann equation. Users submit a PDB file and PCE returns potentials and pKa values as well as color (static or animated) figures displaying electrostatic potentials mapped on the molecular surface. This service is intended to facilitate electrostatics analyses of proteins and thereby broaden the accessibility to continuum electrostatics to the biological community. PCE can be accessed at . PMID:15980492

Current-voltage characteristics of molecular conductors: two versus three terminal

NASA Astrophysics Data System (ADS)

Damle, P.; Rakshit, T.; Paulsson, M.; Datta, S.

2002-09-01

This paper addresses the question of whether a ``rigid molecule'' (one which does not deform in an external field) used as the conducting channel in a standard three-terminal MOSFET configuration can offer any performance advantage relative to a standard silicon MOSFET. A self-consistent solution of coupled quantum transport and Poisson's equations shows that even for extremely small channel lengths (about 1 nm), a ``well-tempered'' molecular FET demands much the same electrostatic considerations as a ``well-tempered'' conventional MOSFET. In other words, we show that just as in a conventional MOSFET, the gate oxide thickness needs to be much smaller than the channel length (length of the molecule) for the gate control to be effective. Furthermore, we show that a rigid molecule with metallic source and drain contacts has a temperature independent subthreshold slope much larger than 60 mV/decade, because the metal-induced gap states in the channel prevent it from turning off abruptly. However, this disadvantage can be overcome by using semiconductor contacts because of their band-limited nature.

The effects of ion adsorption on the potential of zero charge and the differential capacitance of charged aqueous interfaces

NASA Astrophysics Data System (ADS)

Uematsu, Yuki; Netz, Roland R.; Bonthuis, Douwe Jan

2018-02-01

Using a box profile approximation for the non-electrostatic surface adsorption potentials of anions and cations, we calculate the differential capacitance of aqueous electrolyte interfaces from a numerical solution of the Poisson-Boltzmann equation, including steric interactions between the ions and an inhomogeneous dielectric profile. Preferential adsorption of the positive (negative) ion shifts the minimum of the differential capacitance to positive (negative) surface potential values. The trends are similar for the potential of zero charge; however, the potential of zero charge does not correspond to the minimum of the differential capacitance in the case of asymmetric ion adsorption, contrary to the assumption commonly used to determine the potential of zero charge. Our model can be used to obtain more accurate estimates of ion adsorption properties from differential capacitance or electrocapillary measurements. Asymmetric ion adsorption also affects the relative heights of the characteristic maxima in the differential capacitance curves as a function of the surface potential, but even for strong adsorption potentials the effect is small, making it difficult to reliably determine the adsorption properties from the peak heights.

Two-dimensional hybrid Monte Carlo–fluid modelling of dc glow discharges: Comparison with fluid models, reliability, and accuracy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eylenceoğlu, E.; Rafatov, I., E-mail: rafatov@metu.edu.tr; Kudryavtsev, A. A.

2015-01-15

Two-dimensional hybrid Monte Carlo–fluid numerical code is developed and applied to model the dc glow discharge. The model is based on the separation of electrons into two parts: the low energetic (slow) and high energetic (fast) electron groups. Ions and slow electrons are described within the fluid model using the drift-diffusion approximation for particle fluxes. Fast electrons, represented by suitable number of super particles emitted from the cathode, are responsible for ionization processes in the discharge volume, which are simulated by the Monte Carlo collision method. Electrostatic field is obtained from the solution of Poisson equation. The test calculations weremore » carried out for an argon plasma. Main properties of the glow discharge are considered. Current-voltage curves, electric field reversal phenomenon, and the vortex current formation are developed and discussed. The results are compared to those obtained from the simple and extended fluid models. Contrary to reports in the literature, the analysis does not reveal significant advantages of existing hybrid methods over the extended fluid model.« less

An experimental/theoretical method to measure the capacitive compactness of an aqueous electrolyte surrounding a spherical charged colloid

NASA Astrophysics Data System (ADS)

Moraila-Martínez, Carmen Lucía; Guerrero-García, Guillermo Iván; Chávez-Páez, Martín; González-Tovar, Enrique

2018-04-01

The capacitive compactness has been introduced very recently [G. I. Guerrero-García et al., Phys. Chem. Chem. Phys. 20, 262-275 (2018)] as a robust and accurate measure to quantify the thickness, or spatial extension, of the electrical double layer next to either an infinite charged electrode or a spherical macroion. We propose here an experimental/theoretical scheme to determine the capacitive compactness of a spherical electrical double layer that relies on the calculation of the electrokinetic charge and the associated mean electrostatic potential at the macroparticle's surface. This is achieved by numerically solving the non-linear Poisson-Boltzmann equation of point ions around a colloidal sphere and matching the corresponding theoretical mobility, predicted by the O'Brien and White theory [J. Chem. Soc., Faraday Trans. 2 74, 1607-1626 (1978)], with experimental measurements of the electrophoretic mobility under the same conditions. This novel method is used to calculate the capacitive compactness of NaCl and CaCl2 electrolytes surrounding a negatively charged polystyrene particle as a function of the salt concentration.

Quasi-neutral limit of Euler–Poisson system of compressible fluids coupled to a magnetic field

NASA Astrophysics Data System (ADS)

Yang, Jianwei

2018-06-01

In this paper, we consider the quasi-neutral limit of a three-dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field. We prove that, as Debye length tends to zero, periodic initial-value problems of the model have unique smooth solutions existing in the time interval where the ideal incompressible magnetohydrodynamic equations has smooth solution. Meanwhile, it is proved that smooth solutions converge to solutions of incompressible magnetohydrodynamic equations with a sharp convergence rate in the process of quasi-neutral limit.

Exploring the inter-molecular interactions in amyloid-β protofibril with molecular dynamics simulations and molecular mechanics Poisson-Boltzmann surface area free energy calculations.

PubMed

Liu, Fu-Feng; Liu, Zhen; Bai, Shu; Dong, Xiao-Yan; Sun, Yan

2012-04-14

Aggregation of amyloid-β (Aβ) peptides correlates with the pathology of Alzheimer's disease. However, the inter-molecular interactions between Aβ protofibril remain elusive. Herein, molecular mechanics Poisson-Boltzmann surface area analysis based on all-atom molecular dynamics simulations was performed to study the inter-molecular interactions in Aβ(17-42) protofibril. It is found that the nonpolar interactions are the important forces to stabilize the Aβ(17-42) protofibril, while electrostatic interactions play a minor role. Through free energy decomposition, 18 residues of the Aβ(17-42) are identified to provide interaction energy lower than -2.5 kcal/mol. The nonpolar interactions are mainly provided by the main chain of the peptide and the side chains of nine hydrophobic residues (Leu17, Phe19, Phe20, Leu32, Leu34, Met35, Val36, Val40, and Ile41). However, the electrostatic interactions are mainly supplied by the main chains of six hydrophobic residues (Phe19, Phe20, Val24, Met35, Val36, and Val40) and the side chains of the charged residues (Glu22, Asp23, and Lys28). In the electrostatic interactions, the overwhelming majority of hydrogen bonds involve the main chains of Aβ as well as the guanidinium group of the charged side chain of Lys28. The work has thus elucidated the molecular mechanism of the inter-molecular interactions between Aβ monomers in Aβ(17-42) protofibril, and the findings are considered critical for exploring effective agents for the inhibition of Aβ aggregation.

Exploring the inter-molecular interactions in amyloid-β protofibril with molecular dynamics simulations and molecular mechanics Poisson-Boltzmann surface area free energy calculations

NASA Astrophysics Data System (ADS)

Liu, Fu-Feng; Liu, Zhen; Bai, Shu; Dong, Xiao-Yan; Sun, Yan

2012-04-01

Aggregation of amyloid-β (Aβ) peptides correlates with the pathology of Alzheimer's disease. However, the inter-molecular interactions between Aβ protofibril remain elusive. Herein, molecular mechanics Poisson-Boltzmann surface area analysis based on all-atom molecular dynamics simulations was performed to study the inter-molecular interactions in Aβ17-42 protofibril. It is found that the nonpolar interactions are the important forces to stabilize the Aβ17-42 protofibril, while electrostatic interactions play a minor role. Through free energy decomposition, 18 residues of the Aβ17-42 are identified to provide interaction energy lower than -2.5 kcal/mol. The nonpolar interactions are mainly provided by the main chain of the peptide and the side chains of nine hydrophobic residues (Leu17, Phe19, Phe20, Leu32, Leu34, Met35, Val36, Val40, and Ile41). However, the electrostatic interactions are mainly supplied by the main chains of six hydrophobic residues (Phe19, Phe20, Val24, Met35, Val36, and Val40) and the side chains of the charged residues (Glu22, Asp23, and Lys28). In the electrostatic interactions, the overwhelming majority of hydrogen bonds involve the main chains of Aβ as well as the guanidinium group of the charged side chain of Lys28. The work has thus elucidated the molecular mechanism of the inter-molecular interactions between Aβ monomers in Aβ17-42 protofibril, and the findings are considered critical for exploring effective agents for the inhibition of Aβ aggregation.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

NASA Astrophysics Data System (ADS)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models.

PubMed

Evangelista, Luiz Roberto; Lenzi, Ervin Kaminski; Barbero, Giovanni

2013-11-20

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions.

PubMed

Yu, Yang-Xin; Wu, Jianzhong; Gao, Guang-Hua

2004-04-15

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high. (c) 2004 American Institute of Physics.

Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling

NASA Astrophysics Data System (ADS)

Koehl, Patrice; Orland, Henri; Delarue, Marc

2011-08-01

We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ1 for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.

Lie-Hamilton systems on the plane: Properties, classification and applications

NASA Astrophysics Data System (ADS)

Ballesteros, A.; Blasco, A.; Herranz, F. J.; de Lucas, J.; Sardón, C.

2015-04-01

We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian vector fields with respect to a Poisson structure. We start with the local classification of finite-dimensional real Lie algebras of vector fields on the plane obtained in González-López, Kamran, and Olver (1992) [23] and we interpret their results as a local classification of Lie systems. By determining which of these real Lie algebras consist of Hamiltonian vector fields relative to a Poisson structure, we provide the complete local classification of Lie-Hamilton systems on the plane. We present and study through our results new Lie-Hamilton systems of interest which are used to investigate relevant non-autonomous differential equations, e.g. we get explicit local diffeomorphisms between such systems. We also analyse biomathematical models, the Milne-Pinney equations, second-order Kummer-Schwarz equations, complex Riccati equations and Buchdahl equations.

Communication: Nanoscale electrostatic theory of epistructural fields at the protein-water interface

NASA Astrophysics Data System (ADS)

Fernández, Ariel

2012-12-01

Nanoscale solvent confinement at the protein-water interface promotes dipole orientations that are not aligned with the internal electrostatic field of a protein, yielding what we term epistructural polarization. To quantify this effect, an equation is derived from first principles relating epistructural polarization with the magnitude of local distortions in water coordination causative of interfacial tension. The equation defines a nanoscale electrostatic model of water and enables an estimation of protein denaturation free energies and the inference of hot spots for protein associations. The theoretical results are validated vis-à-vis calorimetric data, revealing the destabilizing effect of epistructural polarization and its molecular origin.

Communication: Nanoscale electrostatic theory of epistructural fields at the protein-water interface.

PubMed

Fernández, Ariel

2012-12-21

Nanoscale solvent confinement at the protein-water interface promotes dipole orientations that are not aligned with the internal electrostatic field of a protein, yielding what we term epistructural polarization. To quantify this effect, an equation is derived from first principles relating epistructural polarization with the magnitude of local distortions in water coordination causative of interfacial tension. The equation defines a nanoscale electrostatic model of water and enables an estimation of protein denaturation free energies and the inference of hot spots for protein associations. The theoretical results are validated vis-à-vis calorimetric data, revealing the destabilizing effect of epistructural polarization and its molecular origin.

Electrostatic Similarity Analysis of Human β-Defensin Binding in the Melanocortin System

PubMed Central

Nix, Matthew A.; Kaelin, Christopher B.; Palomino, Rafael; Miller, Jillian L.; Barsh, Gregory S.; Millhauser, Glenn L.

2015-01-01

Summary The β-defensins are a class of small cationic proteins that serve as components of numerous systems in vertebrate biology, including the immune and melanocortin systems. Human β-defensin 3 (HBD3), which is produced in the skin, has been found to bind to melanocortin receptors 1 and 4 through complementary electrostatics, a unique mechanism of ligand-receptor interaction. This finding indicates that electrostatics alone, and not specific amino acid contact points, could be sufficient for function in this ligand-receptor system, and further suggests that other small peptide ligands could interact with these receptors in a similar fashion. Here, we conducted molecular-similarity analyses and functional studies of additional members of the human β-defensin family, examining their potential as ligands of melanocortin-1 receptor, through selection based on their electrostatic similarity to HBD3. Using Poisson-Boltzmann electrostatic calculations and molecular-similarity analysis, we identified members of the human β-defensin family that are both similar and dissimilar to HBD3 in terms of electrostatic potential. Synthesis and functional testing of a subset of these β-defensins showed that peptides with an HBD3-like electrostatic character bound to melanocortin receptors with high affinity, whereas those that were anticorrelated to HBD3 showed no binding affinity. These findings expand on the central role of electrostatics in the control of this ligand-receptor system and further demonstrate the utility of employing molecular-similarity analysis. Additionally, we identified several new potential ligands of melanocortin-1 receptor, which may have implications for our understanding of the role defensins play in melanocortin physiology. PMID:26536271

Counterion-induced swelling of ionic microgels

NASA Astrophysics Data System (ADS)

Denton, Alan R.; Tang, Qiyun

2016-10-01

Ionic microgel particles, when dispersed in a solvent, swell to equilibrium sizes that are governed by a balance between electrostatic and elastic forces. Tuning of particle size by varying external stimuli, such as pH, salt concentration, and temperature, has relevance for drug delivery, microfluidics, and filtration. To model swelling of ionic microgels, we derive a statistical mechanical theorem, which proves exact within the cell model, for the electrostatic contribution to the osmotic pressure inside a permeable colloidal macroion. Applying the theorem, we demonstrate how the distribution of counterions within an ionic microgel determines the internal osmotic pressure. By combining the electrostatic pressure, which we compute via both Poisson-Boltzmann theory and molecular dynamics simulation, with the elastic pressure, modeled via the Flory-Rehner theory of swollen polymer networks, we show how deswelling of ionic microgels with increasing concentration of particles can result from a redistribution of counterions that reduces electrostatic pressure. A linearized approximation for the electrostatic pressure, which proves remarkably accurate, provides physical insight and greatly eases numerical calculations for practical applications. Comparing with experiments, we explain why soft particles in deionized suspensions deswell upon increasing concentration and why this effect may be suppressed at higher ionic strength. The failure of the uniform ideal-gas approximation to adequately account for counterion-induced deswelling below close packing of microgels is attributed to neglect of spatial variation of the counterion density profile and the electrostatic pressure of incompletely neutralized macroions.

Simulation of electron-proton coupling with a Monte Carlo method: application to cytochrome c3 using continuum electrostatics.

PubMed Central

Baptista, A M; Martel, P J; Soares, C M

1999-01-01

A new method is presented for simulating the simultaneous binding equilibrium of electrons and protons on protein molecules, which makes it possible to study the full equilibrium thermodynamics of redox and protonation processes, including electron-proton coupling. The simulations using this method reflect directly the pH and electrostatic potential of the environment, thus providing a much closer and realistic connection with experimental parameters than do usual methods. By ignoring the full binding equilibrium, calculations usually overlook the twofold effect that binding fluctuations have on the behavior of redox proteins: first, they affect the energy of the system by creating partially occupied sites; second, they affect its entropy by introducing an additional empty/occupied site disorder (here named occupational entropy). The proposed method is applied to cytochrome c3 of Desulfovibrio vulgaris Hildenborough to study its redox properties and electron-proton coupling (redox-Bohr effect), using a continuum electrostatic method based on the linear Poisson-Boltzmann equation. Unlike previous studies using other methods, the full reduction order of the four hemes at physiological pH is successfully predicted. The sites more strongly involved in the redox-Bohr effect are identified by analysis of their titration curves/surfaces and the shifts of their midpoint redox potentials and pKa values. Site-site couplings are analyzed using statistical correlations, a method much more realistic than the usual analysis based on direct interactions. The site found to be more strongly involved in the redox-Bohr effect is propionate D of heme I, in agreement with previous studies; other likely candidates are His67, the N-terminus, and propionate D of heme IV. Even though the present study is limited to equilibrium conditions, the possible role of binding fluctuations in the concerted transfer of protons and electrons under nonequilibrium conditions is also discussed. The occupational entropy contributions to midpoint redox potentials and pKa values are computed and shown to be significant. PMID:10354425

Comparison of all atom, continuum, and linear fitting empirical models for charge screening effect of aqueous medium surrounding a protein molecule

NASA Astrophysics Data System (ADS)

Takahashi, Takuya; Sugiura, Junnnosuke; Nagayama, Kuniaki

2002-05-01

To investigate the role hydration plays in the electrostatic interactions of proteins, the time-averaged electrostatic potential of the B1 domain of protein G in an aqueous solution was calculated with full atomic molecular dynamics simulations that explicitly considers every atom (i.e., an all atom model). This all atom calculated potential was compared with the potential obtained from an electrostatic continuum model calculation. In both cases, the charge-screening effect was fairly well formulated with an effective relative dielectric constant which increased linearly with increasing charge-charge distance. This simulated linear dependence agrees with the experimentally determined linear relation proposed by Pickersgill. Cut-off approximations for Coulomb interactions failed to reproduce this linear relation. Correlation between the all atom model and the continuum models was found to be better than the respective correlation calculated for linear fitting to the two models. This confirms that the continuum model is better at treating the complicated shapes of protein conformations than the simple linear fitting empirical model. We have tried a sigmoid fitting empirical model in addition to the linear one. When weights of all data were treated equally, the sigmoid model, which requires two fitting parameters, fits results of both the all atom and the continuum models less accurately than the linear model which requires only one fitting parameter. When potential values are chosen as weighting factors, the fitting error of the sigmoid model became smaller, and the slope of both linear fitting curves became smaller. This suggests the screening effect of an aqueous medium within a short range, where potential values are relatively large, is smaller than that expected from the linear fitting curve whose slope is almost 4. To investigate the linear increase of the effective relative dielectric constant, the Poisson equation of a low-dielectric sphere in a high-dielectric medium was solved and charges distributed near the molecular surface were indicated as leading to the apparent linearity.

Quadrupole terms in the Maxwell equations: Debye-Hückel theory in quadrupolarizable solvent and self-salting-out of electrolytes.

PubMed

Slavchov, Radomir I

2014-04-28

If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Hückel theory. The quadrupolar version of the Debye-Hückel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Hückel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient γ± known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally γ±. Comparison with experimental data for γ± for various electrolytes allows for the estimation of the quadrupolar length of water: LQ ≈ 2 Å, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy.

Filling of a Poisson trap by a population of random intermittent searchers.

PubMed

Bressloff, Paul C; Newby, Jay M

2012-03-01

We extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→∞, in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f(n)(t). The latter is determined by the integrated Poisson rate μ(t)=∫(0)(t)λ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite N. We thus determine how the mean first passage time (MFPT) for filling the target depends on N and n.

Convergence of Spectral Discretizations of the Vlasov--Poisson System

DOE PAGES

Manzini, G.; Funaro, D.; Delzanno, G. L.

2017-09-26

Here we prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in detail for the 1D-1Vmore » case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence under suitable regularity assumptions on the exact solution.« less

Wigner surmises and the two-dimensional homogeneous Poisson point process.

PubMed

Sakhr, Jamal; Nieminen, John M

2006-04-01

We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre's ensemble of 2 x 2 complex non-Hermitian random matrices.

Twisted Quantum Lax Equations

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter

We show the construction of twisted quantum Lax equations associated with quantum groups, and solve these equations using factorization properties of the corresponding quantum groups. Our construction generalizes in many respects the AKS construction for Lie groups and the construction of M. A. Semenov-Tian-Shansky for the Lie-Poisson case.

Accelerating electrostatic surface potential calculation with multi-scale approximation on graphics processing units.

PubMed

Anandakrishnan, Ramu; Scogland, Tom R W; Fenley, Andrew T; Gordon, John C; Feng, Wu-chun; Onufriev, Alexey V

2010-06-01

Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed-up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson-Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multi-scale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone. Copyright (c) 2010 Elsevier Inc. All rights reserved.

Numerical generation of two-dimensional grids by the use of Poisson equations with grid control at boundaries

NASA Technical Reports Server (NTRS)

Sorenson, R. L.; Steger, J. L.

1980-01-01

A method for generating boundary-fitted, curvilinear, two dimensional grids by the use of the Poisson equations is presented. Grids of C-type and O-type were made about airfoils and other shapes, with circular, rectangular, cascade-type, and other outer boundary shapes. Both viscous and inviscid spacings were used. In all cases, two important types of grid control can be exercised at both inner and outer boundaries. First is arbitrary control of the distances between the boundaries and the adjacent lines of the same coordinate family, i.e., stand-off distances. Second is arbitrary control of the angles with which lines of the opposite coordinate family intersect the boundaries. Thus, both grid cell size (or aspect ratio) and grid cell skewness are controlled at boundaries. Reasonable cell size and shape are ensured even in cases wherein extreme boundary shapes would tend to cause skewness or poorly controlled grid spacing. An inherent feature of the Poisson equations is that lines in the interior of the grid smoothly connect the boundary points (the grid mapping functions are second order differentiable).

Intertime jump statistics of state-dependent Poisson processes.

PubMed

Daly, Edoardo; Porporato, Amilcare

2007-01-01

A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.

Analytical solutions for avalanche-breakdown voltages of single-diffused Gaussian junctions

NASA Astrophysics Data System (ADS)

Shenai, K.; Lin, H. C.

1983-03-01

Closed-form solutions of the potential difference between the two edges of the depletion layer of a single diffused Gaussian p-n junction are obtained by integrating Poisson's equation and equating the magnitudes of the positive and negative charges in the depletion layer. By using the closed form solution of the static Poisson's equation and Fulop's average ionization coefficient, the ionization integral in the depletion layer is computed, which yields the correct values of avalanche breakdown voltage, depletion layer thickness at breakdown, and the peak electric field as a function of junction depth. Newton's method is used for rapid convergence. A flowchart to perform the calculations with a programmable hand-held calculator, such as the TI-59, is shown.

Vectorized multigrid Poisson solver for the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Barkai, D.; Brandt, M. A.

1984-01-01

The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details.

Computation of solar perturbations with Poisson series

NASA Technical Reports Server (NTRS)

Broucke, R.

1974-01-01

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

Competitive adsorption and ordered packing of counterions near highly charged surfaces: From mean-field theory to Monte Carlo simulations.

PubMed

Wen, Jiayi; Zhou, Shenggao; Xu, Zhenli; Li, Bo

2012-04-01

Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling.

DIFFUSED SOLUTE-SOLVENT INTERFACE WITH POISSON-BOLTZMANN ELECTROSTATICS: FREE-ENERGY VARIATION AND SHARP-INTERFACE LIMIT.

PubMed

Li, B O; Liu, Yuan

A phase-field free-energy functional for the solvation of charged molecules (e.g., proteins) in aqueous solvent (i.e., water or salted water) is constructed. The functional consists of the solute volumetric and solute-solvent interfacial energies, the solute-solvent van der Waals interaction energy, and the continuum electrostatic free energy described by the Poisson-Boltzmann theory. All these are expressed in terms of phase fields that, for low free-energy conformations, are close to one value in the solute phase and another in the solvent phase. A key property of the model is that the phase-field interpolation of dielectric coefficient has the vanishing derivative at both solute and solvent phases. The first variation of such an effective free-energy functional is derived. Matched asymptotic analysis is carried out for the resulting relaxation dynamics of the diffused solute-solvent interface. It is shown that the sharp-interface limit is exactly the variational implicit-solvent model that has successfully captured capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states of underlying biomolecular systems as found in experiment and molecular dynamics simulations. Our phase-field approach and analysis can be used to possibly couple the description of interfacial fluctuations for efficient numerical computations of biomolecular interactions.

Scrutinizing human MHC polymorphism: Supertype analysis using Poisson-Boltzmann electrostatics and clustering.

PubMed

Mumtaz, Shahzad; Nabney, Ian T; Flower, Darren R

2017-10-01

Peptide-binding MHC proteins are thought the most variable across the human population; the extreme MHC polymorphism observed is functionally important and results from constrained divergent evolution. MHCs have vital functions in immunology and homeostasis: cell surface MHC class I molecules report cell status to CD8+ T cells, NKT cells and NK cells, thus playing key roles in pathogen defence, as well as mediating smell recognition, mate choice, Adverse Drug Reactions, and transplantation rejection. MHC peptide specificity falls into several supertypes exhibiting commonality of binding. It seems likely that other supertypes exist relevant to other functions. Since comprehensive experimental characterization is intractable, structure-based bioinformatics is the only viable solution. We modelled functional MHC proteins by homology and used calculated Poisson-Boltzmann electrostatics projected from the top surface of the MHC as multi-dimensional descriptors, analysing them using state-of-the-art dimensionality reduction techniques and clustering algorithms. We were able to recover the 3 MHC loci as separate clusters and identify clear sub-groups within them, vindicating unequivocally our choice of both data representation and clustering strategy. We expect this approach to make a profound contribution to the study of MHC polymorphism and its functional consequences, and, by extension, other burgeoning structural systems, such as GPCRs. Copyright © 2017 Elsevier Inc. All rights reserved.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

PubMed

Horno, J; González-Caballero, F; González-Fernández, C F

1990-01-01

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Efficiency optimization of a fast Poisson solver in beam dynamics simulation

NASA Astrophysics Data System (ADS)

Zheng, Dawei; Pöplau, Gisela; van Rienen, Ursula

2016-01-01

Calculating the solution of Poisson's equation relating to space charge force is still the major time consumption in beam dynamics simulations and calls for further improvement. In this paper, we summarize a classical fast Poisson solver in beam dynamics simulations: the integrated Green's function method. We introduce three optimization steps of the classical Poisson solver routine: using the reduced integrated Green's function instead of the integrated Green's function; using the discrete cosine transform instead of discrete Fourier transform for the Green's function; using a novel fast convolution routine instead of an explicitly zero-padded convolution. The new Poisson solver routine preserves the advantages of fast computation and high accuracy. This provides a fast routine for high performance calculation of the space charge effect in accelerators.

Modifying Poisson equation for near-solute dielectric polarization and solvation free energy

NASA Astrophysics Data System (ADS)

Yang, Pei-Kun

2016-06-01

The dielectric polarization P is important for calculating the stability of protein conformation and the binding affinity of protein-protein/ligand interactions and for exploring the nonthermal effect of an external electric field on biomolecules. P was decomposed into the product of the electric dipole moment per molecule p; bulk solvent density Nbulk; and relative solvent molecular density g. For a molecular solute, 4πr2p(r) oscillates with the distance r to the solute, and g(r) has a large peak in the near-solute region, as observed in molecular dynamics (MD) simulations. Herein, the Poisson equation was modified for computing p based on the modified Gauss's law of Maxwell's equations, and the potential of the mean force was used for computing g. For one or two charged atoms in a water cluster, the solvation free energies of the solutes obtained by these equations were similar to those obtained from MD simulations.

Filtering with Marked Point Process Observations via Poisson Chaos Expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun Wei, E-mail: wsun@mathstat.concordia.ca; Zeng Yong, E-mail: zengy@umkc.edu; Zhang Shu, E-mail: zhangshuisme@hotmail.com

2013-06-15

We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical schememore » based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.« less

Statistical shape analysis using 3D Poisson equation--A quantitatively validated approach.

PubMed

Gao, Yi; Bouix, Sylvain

2016-05-01

Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures. Copyright © 2016 Elsevier B.V. All rights reserved.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Chromatin ionic atmosphere analyzed by a mesoscale electrostatic approach.

PubMed

Gan, Hin Hark; Schlick, Tamar

2010-10-20

Characterizing the ionic distribution around chromatin is important for understanding the electrostatic forces governing chromatin structure and function. Here we develop an electrostatic model to handle multivalent ions and compute the ionic distribution around a mesoscale chromatin model as a function of conformation, number of nucleosome cores, and ionic strength and species using Poisson-Boltzmann theory. This approach enables us to visualize and measure the complex patterns of counterion condensation around chromatin by examining ionic densities, free energies, shielding charges, and correlations of shielding charges around the nucleosome core and various oligonucleosome conformations. We show that: counterions, especially divalent cations, predominantly condense around the nucleosomal and linker DNA, unburied regions of histone tails, and exposed chromatin surfaces; ionic screening is sensitively influenced by local and global conformations, with a wide ranging net nucleosome core screening charge (56-100e); and screening charge correlations reveal conformational flexibility and interactions among chromatin subunits, especially between the histone tails and parental nucleosome cores. These results provide complementary and detailed views of ionic effects on chromatin structure for modest computational resources. The electrostatic model developed here is applicable to other coarse-grained macromolecular complexes. Copyright © 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Electrostatics of aquaporin and aquaglyceroporin channels correlates with their transport selectivity

PubMed Central

Oliva, Romina; Calamita, Giuseppe; Thornton, Janet M.; Pellegrini-Calace, Marialuisa

2010-01-01

Aquaporins are homotetrameric channel proteins, which allow the diffusion of water and small solutes across biological membranes. According to their transport function, aquaporins can be divided into “orthodox aquaporins”, which allow the flux of water molecules only, and “aquaglyceroporins”, which facilitate the diffusion of glycerol and other small solutes in addition to water. The contribution of individual residues in the pore to the selectivity of orthodox aquaporins and aquaglyceroporins is not yet fully understood. To gain insights into aquaporin selectivity, we focused on the sequence variation and electrostatics of their channels. The continuum Poisson-Boltzmann electrostatic potential along the channel was calculated and compared for ten three-dimensional-structures which are representatives of different aquaporin subfamilies, and a panel of functionally characterized mutants, for which high-accuracy three-dimensional-models could be derived. Interestingly, specific electrostatic profiles associated with the main selectivity to water or glycerol could be identified. In particular: (i) orthodox aquaporins showed a distinctive electrostatic potential maximum at the periplasmic side of the channel around the aromatic/Arg (ar/R) constriction site; (ii) aquaporin-0 (AQP0), a mammalian aquaporin with considerably low water permeability, had an additional deep minimum at the cytoplasmic side; (iii) aquaglyceroporins showed a rather flat potential all along the channel; and (iv) the bifunctional protozoan PfAQP had an unusual all negative profile. Evaluation of electrostatics of the mutants, along with a thorough sequence analysis of the aquaporin pore-lining residues, illuminated the contribution of specific residues to the electrostatics of the channels and possibly to their selectivity. PMID:20147624

Stabilized finite element methods to simulate the conductances of ion channels

NASA Astrophysics Data System (ADS)

Tu, Bin; Xie, Yan; Zhang, Linbo; Lu, Benzhuo

2015-03-01

We have previously developed a finite element simulator, ichannel, to simulate ion transport through three-dimensional ion channel systems via solving the Poisson-Nernst-Planck equations (PNP) and Size-modified Poisson-Nernst-Planck equations (SMPNP), and succeeded in simulating some ion channel systems. However, the iterative solution between the coupled Poisson equation and the Nernst-Planck equations has difficulty converging for some large systems. One reason we found is that the NP equations are advection-dominated diffusion equations, which causes troubles in the usual FE solution. The stabilized schemes have been applied to compute fluids flow in various research fields. However, they have not been studied in the simulation of ion transport through three-dimensional models based on experimentally determined ion channel structures. In this paper, two stabilized techniques, the SUPG and the Pseudo Residual-Free Bubble function (PRFB) are introduced to enhance the numerical robustness and convergence performance of the finite element algorithm in ichannel. The conductances of the voltage dependent anion channel (VDAC) and the anthrax toxin protective antigen pore (PA) are simulated to validate the stabilization techniques. Those two stabilized schemes give reasonable results for the two proteins, with decent agreement with both experimental data and Brownian dynamics (BD) simulations. For a variety of numerical tests, it is found that the simulator effectively avoids previous numerical instability after introducing the stabilization methods. Comparison based on our test data set between the two stabilized schemes indicates both SUPG and PRFB have similar performance (the latter is slightly more accurate and stable), while SUPG is relatively more convenient to implement.

Condensation of monovalent and divalent metal ions on a Langmuir monolayer

NASA Astrophysics Data System (ADS)

Bloch, J. Mati; Yun, Wenbing

1990-01-01

A system that consists of a monolayer spread on a solution containing a monovalent and a divalent ion is investigated. The solution of the Poisson-Boltzmann-Stern equation for this system indicates that the metal ions segregating to the surface can be found in two distinct states. Divalent ions are chemically condensed on the monolayer, while monovalent ions are electrically attracted to it. We derive simple expressions for the charge left on the surfactant monolayer and the amount of metal ions condensed on the monolayer. These formulas reproduce very accurately (to within pro milles) the values obtained using the nonlinear Grahame equation and eliminate the need to solve that equation. That permits a simple identification of the state of the surfactant monolayer and we propose a universal condensation chart that characterizes the state of the surfactant. We further derive a chemical equilibrium equation for the surface components that has considerable range of validity. This equation requires a knowledge of the bulk concentrations only, and thus allows in many cases the identification of the state of the monolayer, avoiding the need to solve the full nonlinear Poisson-Boltzmann equation. All existing experimental results on Langmuir systems are in good agreement with the one-dimensional Poisson-Boltzmann-Stern model with no adjustable parameters. Several of these fits are presented in this work and are also mapped on the condensation chart. Our calculations point to some characteristic differences between the monovalent and the divalent ions that explain why it is possible to build Langmuir-Blodgett multilayers from divalent compensated surfactants but not from monovalent ones.

Computational simulations of supersonic magnetohydrodynamic flow control, power and propulsion systems

NASA Astrophysics Data System (ADS)

Wan, Tian

This work is motivated by the lack of fully coupled computational tool that solves successfully the turbulent chemically reacting Navier-Stokes equation, the electron energy conservation equation and the electric current Poisson equation. In the present work, the abovementioned equations are solved in a fully coupled manner using fully implicit parallel GMRES methods. The system of Navier-Stokes equations are solved using a GMRES method with combined Schwarz and ILU(0) preconditioners. The electron energy equation and the electric current Poisson equation are solved using a GMRES method with combined SOR and Jacobi preconditioners. The fully coupled method has also been implemented successfully in an unstructured solver, US3D, and convergence test results were presented. This new method is shown two to five times faster than the original DPLR method. The Poisson solver is validated with analytic test problems. Then, four problems are selected; two of them are computed to explore the possibility of onboard MHD control and power generation, and the other two are simulation of experiments. First, the possibility of onboard reentry shock control by a magnetic field is explored. As part of a previous project, MHD power generation onboard a re-entry vehicle is also simulated. Then, the MHD acceleration experiments conducted at NASA Ames research center are simulated. Lastly, the MHD power generation experiments known as the HVEPS project are simulated. For code validation, the scramjet experiments at University of Queensland are simulated first. The generator section of the HVEPS test facility is computed then. The main conclusion is that the computational tool is accurate for different types of problems and flow conditions, and its accuracy and efficiency are necessary when the flow complexity increases.

Super-stable Poissonian structures

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

In this paper we characterize classes of Poisson processes whose statistical structures are super-stable. We consider a flow generated by a one-dimensional ordinary differential equation, and an ensemble of particles ‘surfing’ the flow. The particles start from random initial positions, and are propagated along the flow by stochastic ‘wave processes’ with general statistics and general cross correlations. Setting the initial positions to be Poisson processes, we characterize the classes of Poisson processes that render the particles’ positions—at all times, and invariantly with respect to the wave processes—statistically identical to their initial positions. These Poisson processes are termed ‘super-stable’ and facilitate the generalization of the notion of stationary distributions far beyond the realm of Markov dynamics.

Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!

NASA Astrophysics Data System (ADS)

Nutku, Yavuz

2003-07-01

Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems.

Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows

NASA Technical Reports Server (NTRS)

Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark

1998-01-01

A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action

NASA Astrophysics Data System (ADS)

Chekhov, L. O.; Mazzocco, M.

2017-12-01

Let \\mathscr A be the space of bilinear forms on C^N with defining matrices A endowed with a quadratic Poisson structure of reflection equation type. The paper begins with a short description of previous studies of the structure, and then this structure is extended to systems of bilinear forms whose dynamics is governed by the natural action A\\mapsto B ABT} of the {GL}_N Poisson-Lie group on \\mathscr A. A classification is given of all possible quadratic brackets on (B, A)\\in {GL}_N× \\mathscr A preserving the Poisson property of the action, thus endowing \\mathscr A with the structure of a Poisson homogeneous space. Besides the product Poisson structure on {GL}_N× \\mathscr A, there are two other (mutually dual) structures, which (unlike the product Poisson structure) admit reductions by the Dirac procedure to a space of bilinear forms with block upper triangular defining matrices. Further generalisations of this construction are considered, to triples (B,C, A)\\in {GL}_N× {GL}_N× \\mathscr A with the Poisson action A\\mapsto B ACT}, and it is shown that \\mathscr A then acquires the structure of a Poisson symmetric space. Generalisations to chains of transformations and to the quantum and quantum affine algebras are investigated, as well as the relations between constructions of Poisson symmetric spaces and the Poisson groupoid. Bibliography: 30 titles.

A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brinkman, D., E-mail: Daniel.Brinkman@asu.edu; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287; Heitzinger, C., E-mail: Clemens.Heitzinger@asu.edu

2014-01-15

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.

Numerical solution of the Hele-Shaw equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitaker, N.

1987-04-01

An algorithm is presented for approximating the motion of the interface between two immiscible fluids in a Hele-Shaw cell. The interface is represented by a set of volume fractions. We use the Simple Line Interface Calculation method along with the method of fractional steps to transport the interface. The equation of continuity leads to a Poisson equation for the pressure. The Poisson equation is discretized. Near the interface where the velocity field is discontinuous, the discretization is based on a weak formulation of the continuity equation. Interpolation is used on each side of the interface to increase the accuracy ofmore » the algorithm. The weak formulation as well as the interpolation are based on the computed volume fractions. This treatment of the interface is new. The discretized equations are solved by a modified conjugate gradient method. Surface tension is included and the curvature is computed through the use of osculating circles. For perturbations of small amplitude, a surprisingly good agreement is found between the numerical results and linearized perturbation theory. Numerical results are presented for the finite amplitude growth of unstable fingers. 62 refs., 13 figs.« less

Extrusion of transmitter, water and ions generates forces to close fusion pore.

PubMed

Tajparast, M; Glavinović, M I

2009-05-01

During exocytosis the fusion pore opens rapidly, then dilates gradually, and may subsequently close completely, but what controls its dynamics is not well understood. In this study we focus our attention on forces acting on the pore wall, and which are generated solely by the passage of transmitter, ions and water through the open fusion pore. The transport through the charged cylindrical nano-size pore is simulated using a coupled system of Poisson-Nernst-Planck and Navier-Stokes equations and the forces that act radially on the wall of the fusion pore are then estimated. Four forces are considered: a) inertial force, b) pressure, c) viscotic force, and d) electrostatic force. The inertial and viscotic forces are small, but the electrostatic force and the pressure are typically significant. High vesicular pressure tends to open the fusion pore, but the pressure induced by the transport of charged particles (glutamate, ions), which is predominant when the pore wall charge density is high tends to close the pore. The electrostatic force, which also depends on the charge density on the pore wall, is weakly repulsive before the pore dilates, but becomes attractive and pronounced as the pore dilates. Given that the vesicular concentration of free transmitter can change rapidly due to the release, or owing to the dissociation from the gel matrix, we evaluated how much and how rapidly a change of the vesicular K(+)-glutamate(-) concentration affects the concentration of glutamate(-) and ions in the pore and how such changes alter the radial force on the wall of the fusion pore. A step-like rise of the vesicular K(+)-glutamate(-) concentration leads to a chain of events. Pore concentration (and efflux) of both K(+) and glutamate(-) rise reaching their new steady-state values in less than 100 ns. Interestingly within a similar time interval the pore concentration of Na(+) also rises, whereas that of Cl(-) diminishes, although their extra-cellular concentration does not change. Finally such changes affect also the water movement. Water efflux changes bi-phasically, first increasing before decreasing to a new, but lower steady-state value. Nevertheless, even under such conditions an overall approximate neutrality of the pore is maintained remarkably well, and the electrostatic, but also inertial, viscotic and pressure forces acting on the pore wall remain constant. In conclusion the extrusion of the vesicular content generates forces, primarily the force due to the electro-kinetically induced pressure and electrostatic force (both influenced by the pore radius and even more by the charge density on the pore wall), which tend to close the fusion pore.

Two dimensional nonplanar evolution of electrostatic shock waves in pair-ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Rizvi, H.

2012-01-15

Electrostatic waves in a two dimensional nonplanar geometry are studied in an unmagnetized, dissipative pair-ion plasma in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The nonplanar Kadomtsev-Petviashvili-Burgers (KPB) as well as the Burgers Kadomtsev-Petviashvili (Burgers KP) equations are derived using the small amplitude expansion method and the range of applicability of both the equations are discussed. The system under consideration is observed to admit compressive rarefactive shocks. The present study may have relevance to understand the formation of twomore » dimensional nonplanar electrostatic shocks in laboratory plasmas.« less

Analog Computer Solution of the Electrodiffusion Equation for a Simple Membrane

ERIC Educational Resources Information Center

Onega, Ronald J.

1972-01-01

An analog solution was obtained for the Nenst-Planck and Poisson equations which describe the ion concentration across a simple membrane held at a potential difference. The electric field variation within the membrane was also determined. (Author/TS)

Electrostatic interaction between dissimilar colloids at fluid interfaces

NASA Astrophysics Data System (ADS)

Majee, Arghya; Schmetzer, Timo; Bier, Markus

2018-04-01

The electrostatic interaction between two nonidentical, moderately charged colloids situated in close proximity of each other at a fluid interface is studied. By resorting to a well-justified model system, this problem is analytically solved within the framework of linearized Poisson-Boltzmann density functional theory. The resulting interaction comprises a surface and a line part, both of which, as functions of the interparticle separation, show a rich behavior including monotonic as well as nonmonotonic variations. In almost all cases, these variations cannot be captured correctly by using the superposition approximation. Moreover, expressions for the surface tensions, the line tensions and the fluid-fluid interfacial tension, which are all independent of the interparticle separation, are obtained. Our results are expected to be particularly useful for emulsions stabilized by oppositely charged particles.

Electrostatic attraction between overall neutral surfaces.

PubMed

Adar, Ram M; Andelman, David; Diamant, Haim

2016-08-01

Two overall neutral surfaces with positively and negatively charged domains ("patches") have been shown in recent experiments to exhibit long-range attraction when immersed in an ionic solution. Motivated by the experiments, we calculate analytically the osmotic pressure between such surfaces within the Poisson-Boltzmann framework, using a variational principle for the surface-averaged free energy. The electrostatic potential, calculated beyond the linear Debye-Hückel theory, yields an overall attraction at large intersurface separations, over a wide range of the system's controlled length scales. In particular, the attraction is stronger and occurs at smaller separations for surface patches of larger size and charge density. In this large patch limit, we find that the attraction-repulsion crossover separation is inversely proportional to the square of the patch-charge density and to the Debye screening length.

Poisson equation for the Mercedes diagram in string theory at genus one

NASA Astrophysics Data System (ADS)

Basu, Anirban

2016-03-01

The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three-loop Feynman diagram contributes to the {D}12{{ R }}4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one- and two-loop Feynman diagrams. We calculate its contribution to the {D}12{{ R }}4 amplitude.

Three-dimensional zonal grids about arbitrary shapes by Poisson's equation

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.

1988-01-01

A method for generating 3-D finite difference grids about or within arbitrary shapes is presented. The 3-D Poisson equations are solved numerically, with values for the inhomogeneous terms found automatically by the algorithm. Those inhomogeneous terms have the effect near boundaries of reducing cell skewness and imposing arbitrary cell height. The method allows the region of interest to be divided into zones (blocks), allowing the method to be applicable to almost any physical domain. A FORTRAN program called 3DGRAPE has been written to implement the algorithm. Lastly, a method for redistributing grid points along lines normal to boundaries will be described.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrett, C. Kristopher; Hauck, Cory D.

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE PAGES

Garrett, C. Kristopher; Hauck, Cory D.

2018-04-05

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

Diffuse sorption modeling.

PubMed

Pivovarov, Sergey

2009-04-01

This work presents a simple solution for the diffuse double layer model, applicable to calculation of surface speciation as well as to simulation of ionic adsorption within the diffuse layer of solution in arbitrary salt media. Based on Poisson-Boltzmann equation, the Gaines-Thomas selectivity coefficient for uni-bivalent exchange on clay, K(GT)(Me(2+)/M(+))=(Q(Me)(0.5)/Q(M)){M(+)}/{Me(2+)}(0.5), (Q is the equivalent fraction of cation in the exchange capacity, and {M(+)} and {Me(2+)} are the ionic activities in solution) may be calculated as [surface charge, mueq/m(2)]/0.61. The obtained solution of the Poisson-Boltzmann equation was applied to calculation of ionic exchange on clays and to simulation of the surface charge of ferrihydrite in 0.01-6 M NaCl solutions. In addition, a new model of acid-base properties was developed. This model is based on assumption that the net proton charge is not located on the mathematical surface plane but diffusely distributed within the subsurface layer of the lattice. It is shown that the obtained solution of the Poisson-Boltzmann equation makes such calculations possible, and that this approach is more efficient than the original diffuse double layer model.

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Electrophoresis of a charged soft particle in a charged cavity with arbitrary double-layer thickness.

PubMed

Chen, Wei J; Keh, Huan J

2013-08-22

An analysis for the quasi-steady electrophoretic motion of a soft particle composed of a charged spherical rigid core and an adsorbed porous layer positioned at the center of a charged spherical cavity filled with an arbitrary electrolyte solution is presented. Within the porous layer, frictional segments with fixed charges are assumed to distribute uniformly. Through the use of the linearized Poisson-Boltzmann equation and the Laplace equation, the equilibrium double-layer potential distribution and its perturbation caused by the applied electric field are separately determined. The modified Stokes and Brinkman equations governing the fluid flow fields outside and inside the porous layer, respectively, are solved subsequently. An explicit formula for the electrokinetic migration velocity of the soft particle in terms of the fixed charge densities on the rigid core surface, in the porous layer, and on the cavity wall is obtained from a balance between its electrostatic and hydrodynamic forces. This formula is valid for arbitrary values of κa, λa, r0/a, and a/b, where κ is the Debye screening parameter, λ is the reciprocal of the length characterizing the extent of flow penetration inside the porous layer, a is the radius of the soft particle, r0 is the radius of the rigid core of the particle, and b is the radius of the cavity. In the limiting cases of r0 = a and r0 = 0, the migration velocity for the charged soft sphere reduces to that for a charged impermeable sphere and that for a charged porous sphere, respectively, in the charged cavity. The effect of the surface charge at the cavity wall on the particle migration can be significant, and the particle may reverse the direction of its migration.

Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

ERIC Educational Resources Information Center

Aliev, Nihan; Jahanshahi, Mohammad

2002-01-01

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

Ionic Channels as Natural Nanodevices

DTIC Science & Technology

2006-05-01

introduce the numerical techniques required to simulate charge transport in ion channels. [1] Using Poisson- Nernst -Planck-type (PNP) equations ...Eisenberg. 2003. Ionic diffusion through protein channels: from molecular description to continuum equations . Nanotech 2003, 3: 439-442. 4...Nadler, B., Schuss, Z., Singer, A., and R. S. Eisenberg. 2004. Ionic diffusion through confined geometries: from Langevin equations to partial

A Boundary Value Problem for Introductory Physics?

ERIC Educational Resources Information Center

Grundberg, Johan

2008-01-01

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

LSI arrays for space stations

NASA Technical Reports Server (NTRS)

Gassaway, J. D.

1976-01-01

Two approaches have been taken to study CCD's and some of their fundamental limitations. First a numerical analysis approach has been developed to solve the coupled transport and Poisson's equation for a thorough analysis of charge transfer in a CCD structure. The approach is formulated by treating the minority carriers as a surface distribution at the Si-SiO2 interface and setting up coupled difference equations for the charge and the potential. The SOR method is proposed for solving the two dimensional Poisson's equation for the potential. Methods are suggested for handling the discontinuities to improve convergence. Second, CCD shift registers were fabricated with parameters which should allow complete charge transfer independent of the transfer electrode gap width. A test instrument was designed and constructed which can be used to test this, or any similar, three phase CCD shift register.

De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity

NASA Astrophysics Data System (ADS)

Berra-Montiel, Jasel; Molgado, Alberto; Serrano-Blanco, David

2017-12-01

We analyse the behaviour of the MacDowell-Mansouri action with internal symmetry group SO(4, 1) under the De Donder-Weyl Hamiltonian formulation. The field equations, known in this formalism as the De Donder-Weyl equations, are obtained by means of the graded Poisson-Gerstenhaber bracket structure present within the De Donder-Weyl formulation. The decomposition of the internal algebra so(4, 1)≃so(3, 1)\\oplus{R}3, 1 allows the symmetry breaking SO(4, 1)\\toSO(3, 1) , which reduces the original action to the Palatini action without the topological term. We demonstrate that, in contrast to the Lagrangian approach, this symmetry breaking can be performed indistinctly in the polysymplectic formalism either before or after the variation of the De Donder-Weyl Hamiltonian has been done, recovering Einstein’s equations via the Poisson-Gerstenhaber bracket.

Application of the sine-Poisson equation in solar magnetostatics

NASA Technical Reports Server (NTRS)

Webb, G. M.; Zank, G. P.

1990-01-01

Solutions of the sine-Poisson equations are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model (j) is directed along the x-axis, where x is the horizontal ignorable coordinate; (j) varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. Solutions for the magnetostatic potential A corresponding to the one-soliton, two-soliton, and breather solutions of the sine-Gordon equation are studied. Depending on the values of the free parameters in the soliton solutions, horizontally periodic magnetostatic structures are obtained possessing either a single X-type neutral point, multiple neural X-points, or solutions without X-points.

Research on ponderomotive driven Vlasov–Poisson system in electron acoustic wave parametric region

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xiao, C. Z.; Huang, T. W.; Liu, Z. J.

2014-03-15

Theoretical analysis and corresponding 1D Particle-in-Cell (PIC) simulations of ponderomotive driven Vlasov–Poisson system in electron acoustic wave (EAW) parametric region are demonstrated. Theoretical analysis identifies that under the resonant condition, a monochromatic EAW can be excited when the wave number of the drive ponderomotive force satisfies 0.26≲k{sub d}λ{sub D}≲0.53. If k{sub d}λ{sub D}≲0.26, nonlinear superposition of harmonic waves can be resonantly excited, called kinetic electrostatic electron nonlinear waves. Numerical simulations have demonstrated these wave excitation and evolution dynamics, in consistence with the theoretical predictions. The physical nature of these two waves is supposed to be interaction of harmonic waves, andmore » their similar phase space properties are also discussed.« less

Necessary and sufficient conditions for the stability of a sleeping top described by three forms of dynamic equations

NASA Astrophysics Data System (ADS)

Ge, Zheng-Ming

2008-04-01

Necessary and sufficient conditions for the stability of a sleeping top described by dynamic equations of six state variables, Euler equations, and Poisson equations, by a two-degree-of-freedom system, Krylov equations, and by a one-degree-of-freedom system, nutation angle equation, is obtained by the Lyapunov direct method, Ge-Liu second instability theorem, an instability theorem, and a Ge-Yao-Chen partial region stability theorem without using the first approximation theory altogether.

A systematic Monte Carlo simulation study of the primitive model planar electrical double layer over an extended range of concentrations, electrode charges, cation diameters and valences

NASA Astrophysics Data System (ADS)

Valiskó, Mónika; Kristóf, Tamás; Gillespie, Dirk; Boda, Dezső

2018-02-01

The purpose of this study is to provide data for the primitive model of the planar electrical double layer, where ions are modeled as charged hard spheres, the solvent as an implicit dielectric background (with dielectric constant ɛ = 78.5), and the electrode as a smooth, uniformly charged, hard wall. We use canonical and grand canonical Monte Carlo simulations to compute the concentration profiles, from which the electric field and electrostatic potential profiles are obtained by solving Poisson's equation. We report data for an extended range of parameters including 1:1, 2:1, and 3:1 electrolytes at concentrations c = 0.0001 - 1 M near electrodes carrying surface charges up to σ = ±0.5 Cm-2. The anions are monovalent with a fixed diameter d- = 3 Å, while the charge and diameter of cations are varied in the range z+ = 1, 2, 3 and d+ = 1.5, 3, 6, and 9 Å (the temperature is 298.15 K). We provide all the raw data in the supplementary material (ftp://ftp.aip.org/epaps/aip_advances/E-AAIDBI-8-084802">supplementary material).

Structure and osmotic pressure of ionic microgel dispersions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hedrick, Mary M.; Department of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58108-6050; Chung, Jun Kyung

We investigate structural and thermodynamic properties of aqueous dispersions of ionic microgels—soft colloidal gel particles that exhibit unusual phase behavior. Starting from a coarse-grained model of microgel macroions as charged spheres that are permeable to microions, we perform simulations and theoretical calculations using two complementary implementations of Poisson-Boltzmann (PB) theory. Within a one-component model, based on a linear-screening approximation for effective electrostatic pair interactions, we perform molecular dynamics simulations to compute macroion-macroion radial distribution functions, static structure factors, and macroion contributions to the osmotic pressure. For the same model, using a variational approximation for the free energy, we compute bothmore » macroion and microion contributions to the osmotic pressure. Within a spherical cell model, which neglects macroion correlations, we solve the nonlinear PB equation to compute microion distributions and osmotic pressures. By comparing the one-component and cell model implementations of PB theory, we demonstrate that the linear-screening approximation is valid for moderately charged microgels. By further comparing cell model predictions with simulation data for osmotic pressure, we chart the cell model’s limits in predicting osmotic pressures of salty dispersions.« less

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov-Poisson Equation during Violent Relaxation

NASA Astrophysics Data System (ADS)

Beraldo e Silva, Leandro; de Siqueira Pedra, Walter; Sodré, Laerte; Perico, Eder L. D.; Lima, Marcos

2017-09-01

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10{--}12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

A MATHEMATICAL MODEL FOR CALCULATING ELECTRICAL CONDITIONS IN WIRE-DUCT ELECTROSTATIC PRECIPITATION DEVICES

EPA Science Inventory

The article reports the development of a new method of calculating electrical conditions in wire-duct electrostatic precipitation devices. The method, based on a numerical solution to the governing differential equations under a suitable choice of boundary conditions, accounts fo...

Composite laminates with negative through-the-thickness Poisson's ratios

NASA Technical Reports Server (NTRS)

Herakovich, C. T.

1984-01-01

A simple analysis using two dimensional lamination theory combined with the appropriate three dimensional anisotropic constitutive equation is presented to show some rather surprising results for the range of values of the through-the-thickness effective Poisson's ratio nu sub xz for angle ply laminates. Results for graphite-epoxy show that the through-the-thickness effective Poisson's ratio can range from a high of 0.49 for a 90 laminate to a low of -0.21 for a + or - 25s laminate. It is shown that negative values of nu sub xz are also possible for other laminates.

Composite laminates with negative through-the-thickness Poisson's ratios

NASA Technical Reports Server (NTRS)

Herakovich, C. T.

1984-01-01

A simple analysis using two-dimensional lamination theory combined with the appropriate three-dimensional anisotropic constitutive equation is presented to show some rather surprising results for the range of values of the through-the-thickness effective Poisson's ratio nu sub xz for angle ply laminates. Results for graphite-epoxy show that the through-the-thickness effective Poisson's ratio can range from a high of 0.49 for a 90 laminate to a low of -0.21 for a + or - 25s laminate. It is shown that negative values of nu sub xz are also possible for other laminates.

Gridless particle technique for the Vlasov-Poisson system in problems with high degree of symmetry

NASA Astrophysics Data System (ADS)

Boella, E.; Coppa, G.; D'Angola, A.; Peiretti Paradisi, B.

2018-03-01

In the paper, gridless particle techniques are presented in order to solve problems involving electrostatic, collisionless plasmas. The method makes use of computational particles having the shape of spherical shells or of rings, and can be used to study cases in which the plasma has spherical or axial symmetry, respectively. As a computational grid is absent, the technique is particularly suitable when the plasma occupies a rapidly changing space region.

Two dimensional electrostatic shock waves in relativistic electron positron ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Rizvi, H.

2010-05-15

Ion-acoustic shock waves (IASWs) are studied in an unmagnetized plasma consisting of electrons, positrons and hot ions. In this regard, Kadomtsev-Petviashvili-Burgers (KPB) equation is derived using the small amplitude perturbation expansion method. The dependence of the IASWs on various plasma parameters is numerically investigated. It is observed that ratio of ion to electron temperature, kinematic viscosity, positron concentration, and the relativistic ion streaming velocity affect the structure of the IASW. Limiting case of the KPB equation is also discussed. Stability of KPB equation is also presented. The present investigation may have relevance in the study of electrostatic shock waves inmore » relativistic electron-positron-ion plasmas.« less

The Poisson-Boltzmann theory for the two-plates problem: some exact results.

PubMed

Xing, Xiang-Jun

2011-12-01

The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

Electromagnetic gyrokinetic simulation in GTS

NASA Astrophysics Data System (ADS)

Ma, Chenhao; Wang, Weixing; Startsev, Edward; Lee, W. W.; Ethier, Stephane

2017-10-01

We report the recent development in the electromagnetic simulations for general toroidal geometry based on the particle-in-cell gyrokinetic code GTS. Because of the cancellation problem, the EM gyrokinetic simulation has numerical difficulties in the MHD limit where k⊥ρi -> 0 and/or β >me /mi . Recently several approaches has been developed to circumvent this problem: (1) p∥ formulation with analytical skin term iteratively approximated by simulation particles (Yang Chen), (2) A modified p∥ formulation with ∫ dtE∥ used in place of A∥ (Mishichenko); (3) A conservative theme where the electron density perturbation for the Poisson equation is calculated from an electron continuity equation (Bao) ; (4) double-split-weight scheme with two weights, one for Poisson equation and one for time derivative of Ampere's law, each with different splits designed to remove large terms from Vlasov equation (Startsev). These algorithms are being implemented into GTS framework for general toroidal geometry. The performance of these different algorithms will be compared for various EM modes.

The Euler-Poisson-Darboux equation for relativists

NASA Astrophysics Data System (ADS)

Stewart, John M.

2009-09-01

The Euler-Poisson-Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space-time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space-times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm.

Drift dust acoustic soliton in the presence of field-aligned sheared flow and nonextensivity effects

NASA Astrophysics Data System (ADS)

Shah, AttaUllah; Mushtaq, A.; Farooq, M.; Khan, Aurangzeb; Aman-ur-Rehman

2018-05-01

Low frequency electrostatic dust drift acoustic (DDA) waves are studied in an inhomogeneous dust magnetoplasma comprised of dust components of opposite polarity, Boltzmannian ions, and nonextensive distributed electrons. The magnetic-field-aligned dust sheared flow drives the electrostatic drift waves in the presence of ions and electrons. The sheared flow decreases or increases the frequency of the DDA wave, mostly depending on its polarity. The conditions of instability for this mode, with nonextensivity and dust streaming effects, are discussed. The nonlinear dynamics is then investigated for the DDA wave by deriving the Koeteweg-deVries (KdV) nonlinear equation. The KdV equation yields an electrostatic structure in the form of a DDA soliton. The relevancy of the work to laboratory four component dusty plasmas is illustrated.

Electrostatic shocks and solitons in pair-ion plasmas in a two-dimensional geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Mahmood, S.; Imtiaz, N.

2009-12-15

Nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion plasmas in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The Kadomtsev-Petviashvili-Burger equation is derived using the small amplitude expansion method. The Kadomtsev-Petviashvili equation for pair-ion plasmas is also presented by ignoring the dissipative effects. Both compressive and rarefactive shocks and solitary waves are found to exist in pair-ion plasmas. The dependence of compression and rarefaction on the temperature ratios between the ion species is numerically shown. The present study maymore » have relevance to the understanding of the formation of electrostatic shocks and solitons in laboratory produced pair-ion plasmas.« less

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers.

PubMed

Cooper, Christopher D; Bardhan, Jaydeep P; Barba, L A

2014-03-01

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one gpu card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

An electrostatic Particle-In-Cell code on multi-block structured meshes

NASA Astrophysics Data System (ADS)

Meierbachtol, Collin S.; Svyatskiy, Daniil; Delzanno, Gian Luca; Vernon, Louis J.; Moulton, J. David

2017-12-01

We present an electrostatic Particle-In-Cell (PIC) code on multi-block, locally structured, curvilinear meshes called Curvilinear PIC (CPIC). Multi-block meshes are essential to capture complex geometries accurately and with good mesh quality, something that would not be possible with single-block structured meshes that are often used in PIC and for which CPIC was initially developed. Despite the structured nature of the individual blocks, multi-block meshes resemble unstructured meshes in a global sense and introduce several new challenges, such as the presence of discontinuities in the mesh properties and coordinate orientation changes across adjacent blocks, and polyjunction points where an arbitrary number of blocks meet. In CPIC, these challenges have been met by an approach that features: (1) a curvilinear formulation of the PIC method: each mesh block is mapped from the physical space, where the mesh is curvilinear and arbitrarily distorted, to the logical space, where the mesh is uniform and Cartesian on the unit cube; (2) a mimetic discretization of Poisson's equation suitable for multi-block meshes; and (3) a hybrid (logical-space position/physical-space velocity), asynchronous particle mover that mitigates the performance degradation created by the necessity to track particles as they move across blocks. The numerical accuracy of CPIC was verified using two standard plasma-material interaction tests, which demonstrate good agreement with the corresponding analytic solutions. Compared to PIC codes on unstructured meshes, which have also been used for their flexibility in handling complex geometries but whose performance suffers from issues associated with data locality and indirect data access patterns, PIC codes on multi-block structured meshes may offer the best compromise for capturing complex geometries while also maintaining solution accuracy and computational efficiency.

An electrostatic Particle-In-Cell code on multi-block structured meshes

DOE PAGES

Meierbachtol, Collin S.; Svyatskiy, Daniil; Delzanno, Gian Luca; ...

2017-09-14

We present an electrostatic Particle-In-Cell (PIC) code on multi-block, locally structured, curvilinear meshes called Curvilinear PIC (CPIC). Multi-block meshes are essential to capture complex geometries accurately and with good mesh quality, something that would not be possible with single-block structured meshes that are often used in PIC and for which CPIC was initially developed. In spite of the structured nature of the individual blocks, multi-block meshes resemble unstructured meshes in a global sense and introduce several new challenges, such as the presence of discontinuities in the mesh properties and coordinate orientation changes across adjacent blocks, and polyjunction points where anmore » arbitrary number of blocks meet. In CPIC, these challenges have been met by an approach that features: (1) a curvilinear formulation of the PIC method: each mesh block is mapped from the physical space, where the mesh is curvilinear and arbitrarily distorted, to the logical space, where the mesh is uniform and Cartesian on the unit cube; (2) a mimetic discretization of Poisson's equation suitable for multi-block meshes; and (3) a hybrid (logical-space position/physical-space velocity), asynchronous particle mover that mitigates the performance degradation created by the necessity to track particles as they move across blocks. The numerical accuracy of CPIC was verified using two standard plasma–material interaction tests, which demonstrate good agreement with the corresponding analytic solutions. And compared to PIC codes on unstructured meshes, which have also been used for their flexibility in handling complex geometries but whose performance suffers from issues associated with data locality and indirect data access patterns, PIC codes on multi-block structured meshes may offer the best compromise for capturing complex geometries while also maintaining solution accuracy and computational efficiency.« less

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

NASA Astrophysics Data System (ADS)

Cooper, Christopher D.; Bardhan, Jaydeep P.; Barba, L. A.

2014-03-01

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the APBS solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is on the order of 1-2% error, when running on one GPU card (NVIDIA Tesla C2075), compared with APBS running on six Intel Xeon CPU cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using GPUs via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

Geometries in Soft Matter From Geometric Frustration, Liquid Droplets to Electrostatics in Solution

NASA Astrophysics Data System (ADS)

Yao, Zhenwei

This thesis explores geometric aspects of soft matter systems. The topics covered fall into three categories: (i) geometric frustrations, including the interplay of geometry and topological defects in two dimensional systems, and the frustration of a planar sheet attached to a curved surface; (ii) geometries of liquid droplets, including the curvature driven instabilities of toroidal liquid droplets and the self-propulsion of droplets on a spatially varying surface topography; (iii) the study of the electric double layer structure around charged spherical interfaces by a geometric method. In (i), we study the crystalline order on capillary bridges with varying Gaussian curvature. Energy requires the appearance of topological defects on the surface, which are natural spots for biological activity and chemical functionalization. We further study how liquid crystalline order deforms flexible structured vesicles. In particular we find faceted tetrahedral vesicle as the ground state, which may lead to the design of supra-molecular structures with tetrahedral symmetry and new classes of nano-carriers. Furthermore, by a simple paper model we explore the geometric frustration on a planar sheet when brought to a negative curvature surface in a designed elasto-capillary system. In (ii), motivated by the idea of realizing crystalline order on a stable toroidal droplet and a beautiful experiment on toroidal droplets, we study the Rayleigh instability and the shrinking instability of thin and fat toroidal droplets, where the toroidal geometry plays an essential role. In (iii), by a geometric mapping we construct an approximate analytic spherical solution to the nonlinear Poisson-Boltzmann equation, and identify the applicability regime of the solution. The derived geometric solution enables further analytical study of spherical electrostatic systems such as colloidal suspensions.

Application of the method of images on electrostatic phenomena in aqueous Al2O3 and ZrO2 suspensions.

PubMed

Cordelair, Jens; Greil, Peter

2003-09-15

A new solution for the Poisson equation for the diffuse part of the double layer around spherical particles will be presented. The numerical results are compared with the solution of the well-known DLVO theory. The range of the diffuse layer differs considerably in the two theories. Also, the inconsistent representation of the surface and diffuse layer charge in the DLVO theory do not occur in the new theory. Experimental zeta potential measurements were used to determine the charge of colloidal Al2O3 and ZrO2 particles. It is shown that the calculated charge can be interpreted as a superposition of independent H+ and OH- adsorption isotherms. The corresponding Langmuir adsorption isotherms are taken to model the zeta potential dependence on pH. In the vicinity of the isoelectric point the model fits well with the experimental data, but at higher ion concentrations considerable deviations occur. The deviations are discussed. Furthermore, the numerical results for the run of the potential in the diffuse part of the double layer were used to determine the electrostatic interaction potential between the particles in correlation with the zeta potential measurements. The corresponding total interaction potentials, including the van der Waals attraction, were taken to calculate the coagulation half-life for a suspension with a particle loading of 2 vol%. It is shown that stability against coagulation is maintained for Al2O3 particles in the pH region between 3.3 and 7 and for ZrO2 only around pH 5. Stability against flocculation can be achieved in the pH regime between 4.5 and 7 for Al2O3, while the examined ZrO2 particles are not stable against flocculation in aqueous suspensions.

An electrostatic Particle-In-Cell code on multi-block structured meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meierbachtol, Collin S.; Svyatskiy, Daniil; Delzanno, Gian Luca

We present an electrostatic Particle-In-Cell (PIC) code on multi-block, locally structured, curvilinear meshes called Curvilinear PIC (CPIC). Multi-block meshes are essential to capture complex geometries accurately and with good mesh quality, something that would not be possible with single-block structured meshes that are often used in PIC and for which CPIC was initially developed. In spite of the structured nature of the individual blocks, multi-block meshes resemble unstructured meshes in a global sense and introduce several new challenges, such as the presence of discontinuities in the mesh properties and coordinate orientation changes across adjacent blocks, and polyjunction points where anmore » arbitrary number of blocks meet. In CPIC, these challenges have been met by an approach that features: (1) a curvilinear formulation of the PIC method: each mesh block is mapped from the physical space, where the mesh is curvilinear and arbitrarily distorted, to the logical space, where the mesh is uniform and Cartesian on the unit cube; (2) a mimetic discretization of Poisson's equation suitable for multi-block meshes; and (3) a hybrid (logical-space position/physical-space velocity), asynchronous particle mover that mitigates the performance degradation created by the necessity to track particles as they move across blocks. The numerical accuracy of CPIC was verified using two standard plasma–material interaction tests, which demonstrate good agreement with the corresponding analytic solutions. And compared to PIC codes on unstructured meshes, which have also been used for their flexibility in handling complex geometries but whose performance suffers from issues associated with data locality and indirect data access patterns, PIC codes on multi-block structured meshes may offer the best compromise for capturing complex geometries while also maintaining solution accuracy and computational efficiency.« less

From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

NASA Astrophysics Data System (ADS)

Yang, Xiao; Du, Dianlou

2010-08-01

The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kovchavtsev, A. P., E-mail: kap@isp.nsc.ru; Tsarenko, A. V.; Guzev, A. A.

The influence of electron energy quantization in a space-charge region on the accumulation capacitance of the InAs-based metal-oxide-semiconductor capacitors (MOSCAPs) has been investigated by modeling and comparison with the experimental data from Au/anodic layer(4-20 nm)/n-InAs(111)A MOSCAPs. The accumulation capacitance for MOSCAPs has been calculated by the solution of Poisson equation with different assumptions and the self-consistent solution of Schrödinger and Poisson equations with quantization taken into account. It was shown that the quantization during the MOSCAPs accumulation capacitance calculations should be taken into consideration for the correct interface states density determination by Terman method and the evaluation of gate dielectric thicknessmore » from capacitance-voltage measurements.« less

Solution of Poisson equations for 3-dimensional grid generations. [computations of a flow field over a thin delta wing

NASA Technical Reports Server (NTRS)

Fujii, K.

1983-01-01

A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.

Electrostatic correlations at the Stern layer: Physics or chemistry?

NASA Astrophysics Data System (ADS)

Travesset, A.; Vangaveti, S.

2009-11-01

We introduce a minimal free energy describing the interaction of charged groups and counterions including both classical electrostatic and specific interactions. The predictions of the model are compared against the standard model for describing ions next to charged interfaces, consisting of Poisson-Boltzmann theory with additional constants describing ion binding, which are specific to the counterion and the interfacial charge ("chemical binding"). It is shown that the "chemical" model can be appropriately described by an underlying "physical" model over several decades in concentration, but the extracted binding constants are not uniquely defined, as they differ depending on the particular observable quantity being studied. It is also shown that electrostatic correlations for divalent (or higher valence) ions enhance the surface charge by increasing deprotonation, an effect not properly accounted within chemical models. The charged phospholipid phosphatidylserine is analyzed as a concrete example with good agreement with experimental results. We conclude with a detailed discussion on the limitations of chemical or physical models for describing the rich phenomenology of charged interfaces in aqueous media and its relevance to different systems with a particular emphasis on phospholipids.

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

NASA Technical Reports Server (NTRS)

Hoots, F. R.; Fitzpatrick, P. M.

1979-01-01

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

A genuinely discontinuous approach for multiphase EHD problems

NASA Astrophysics Data System (ADS)

Natarajan, Mahesh; Desjardins, Olivier

2017-11-01

Electrohydrodynamics (EHD) involves solving the Poisson equation for the electric field potential. For multiphase flows, although the electric field potential is a continuous quantity, due to the discontinuity in the electric permittivity between the phases, additional jump conditions at the interface, for the normal and tangential components of the electric field need to be satisfied. All approaches till date either ignore the jump conditions, or involve simplifying assumptions, and hence yield unconvincing results even for simple test problems. In the present work, we develop a genuinely discontinuous approach for the Poisson equation for multiphase flows using a Finite Volume Unsplit Volume of Fluid method. The governing equation and the jump conditions without assumptions are used to develop the method, and its efficiency is demonstrated by comparison of the numerical results with canonical test problems having exact solutions. Postdoctoral Associate, Department of Mechanical and Aerospace Engineering.

Simulation of Devices with Molecular Potentials

DTIC Science & Technology

2013-12-22

10] W. R. Frensley, Wigner - function model of a resonant-tunneling semiconductor de- vice, Phys. Rev. B, 36 (1987), pp. 1570–1580. 6 [11] M. J...develop the principal investigator’s Wigner -Poisson code and extend that code to deal with longer devices and more complex barrier profiles. Over...Research Triangle Park, NC 27709-2211 Molecular Confirmation, Sparse Interpolation, Wigner -Poisson Equation, Parallel Algorithms REPORT DOCUMENTATION PAGE 11

Full multi grid method for electric field computation in point-to-plane streamer discharge in air at atmospheric pressure

NASA Astrophysics Data System (ADS)

Kacem, S.; Eichwald, O.; Ducasse, O.; Renon, N.; Yousfi, M.; Charrada, K.

2012-01-01

Streamers dynamics are characterized by the fast propagation of ionized shock waves at the nanosecond scale under very sharp space charge variations. The streamer dynamics modelling needs the solution of charged particle transport equations coupled to the elliptic Poisson's equation. The latter has to be solved at each time step of the streamers evolution in order to follow the propagation of the resulting space charge electric field. In the present paper, a full multi grid (FMG) and a multi grid (MG) methods have been adapted to solve Poisson's equation for streamer discharge simulations between asymmetric electrodes. The validity of the FMG method for the computation of the potential field is first shown by performing direct comparisons with analytic solution of the Laplacian potential in the case of a point-to-plane geometry. The efficiency of the method is also compared with the classical successive over relaxation method (SOR) and MUltifrontal massively parallel solver (MUMPS). MG method is then applied in the case of the simulation of positive streamer propagation and its efficiency is evaluated from comparisons to SOR and MUMPS methods in the chosen point-to-plane configuration. Very good agreements are obtained between the three methods for all electro-hydrodynamics characteristics of the streamer during its propagation in the inter-electrode gap. However in the case of MG method, the computational time to solve the Poisson's equation is at least 2 times faster in our simulation conditions.

Nonlinear dissipative and dispersive electrostatic structures in unmagnetized relativistic electron-ion plasma with warm ions and trapped electrons

NASA Astrophysics Data System (ADS)

Masood, W.; Hamid, Naira; Ilyas, Iffat; Siddiq, M.

2017-06-01

In this paper, we have investigated electrostatic solitary and shock waves in an unmagnetized relativistic electron-ion (ei) plasma in the presence of warm ions and trapped electrons. In this regard, we have derived the trapped Korteweg-de Vries Burgers (TKdVB) equation using the small amplitude approximation method, which to the best of our knowledge has not been investigated in plasmas. Since the TKdVB equation involves fractional nonlinearity on account of trapped electrons, we have employed a smartly crafted extension of the tangent hyperbolic method and presented the solution of the TKdVB equation in this paper. The limiting cases of the TKdVB equation yield trapped Burgers (TB) and trapped Korteweg-de Vries (TKdV) equations. We have also presented the solutions of TB and TKdV equations. We have also explored how the plasma parameters affect the propagation characteristics of the nonlinear structures obtained for these modified nonlinear partial differential equations. We hope that the present work will open new vistas of research in the nonlinear plasma theory both in classical and quantum plasmas.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model

NASA Astrophysics Data System (ADS)

Wan, Li; Xu, Shixin; Liao, Maijia; Liu, Chun; Sheng, Ping

2014-01-01

In this work, we treat the Poisson-Nernst-Planck (PNP) equations as the basis for a consistent framework of the electrokinetic effects. The static limit of the PNP equations is shown to be the charge-conserving Poisson-Boltzmann (CCPB) equation, with guaranteed charge neutrality within the computational domain. We propose a surface potential trap model that attributes an energy cost to the interfacial charge dissociation. In conjunction with the CCPB, the surface potential trap can cause a surface-specific adsorbed charge layer σ. By defining a chemical potential μ that arises from the charge neutrality constraint, a reformulated CCPB can be reduced to the form of the Poisson-Boltzmann equation, whose prediction of the Debye screening layer profile is in excellent agreement with that of the Poisson-Boltzmann equation when the channel width is much larger than the Debye length. However, important differences emerge when the channel width is small, so the Debye screening layers from the opposite sides of the channel overlap with each other. In particular, the theory automatically yields a variation of σ that is generally known as the "charge regulation" behavior, attendant with predictions of force variation as a function of nanoscale separation between two charged surfaces that are in good agreement with the experiments, with no adjustable or additional parameters. We give a generalized definition of the ζ potential that reflects the strength of the electrokinetic effect; its variations with the concentration of surface-specific and surface-nonspecific salt ions are shown to be in good agreement with the experiments. To delineate the behavior of the electro-osmotic (EO) effect, the coupled PNP and Navier-Stokes equations are solved numerically under an applied electric field tangential to the fluid-solid interface. The EO effect is shown to exhibit an intrinsic time dependence that is noninertial in its origin. Under a step-function applied electric field, a pulse of fluid flow is followed by relaxation to a new ion distribution, owing to the diffusive counter current. We have numerically evaluated the Onsager coefficients associated with the EO effect, L21, and its reverse streaming potential effect, L12, and show that L12=L21 in accordance with the Onsager relation. We conclude by noting some of the challenges ahead.

Study of the extra-ionic electron distributions in semi-metallic structures by nuclear quadrupole resonance techniques

NASA Technical Reports Server (NTRS)

Murty, A. N.

1976-01-01

A straightforward self-consistent method was developed to estimate solid state electrostatic potentials, fields and field gradients in ionic solids. The method is a direct practical application of basic electrostatics to solid state and also helps in the understanding of the principles of crystal structure. The necessary mathematical equations, derived from first principles, were presented and the systematic computational procedure developed to arrive at the solid state electrostatic field gradients values was given.

Kinetic theory for electrostatic waves due to transverse velocity shears

NASA Technical Reports Server (NTRS)

Ganguli, G.; Lee, Y. C.; Palmadesso, P. J.

1988-01-01

A kinetic theory in the form of an integral equation is provided to study the electrostatic oscillations in a collisionless plasma immersed in a uniform magnetic field and a nonuniform transverse electric field. In the low temperature limit the dispersion differential equation is recovered for the transverse Kelvin-Helmholtz modes for arbitrary values of K parallel, where K parallel is the component of the wave vector in the direction of the external magnetic field assumed in the z direction. For higher temperatures the ion-cyclotron-like modes described earlier in the literature by Ganguli, Lee and Plamadesso are recovered. In this article, the integral equation is reduced to a second-order differential equation and a study is made of the kinetic Kelvin-Helmholtz and ion-cyclotron-like modes that constitute the two branches of oscillation in a magnetized plasma including a transverse inhomogeneous dc electric field.

40 CFR 60.453 - Performance test and compliance provisions.

Code of Federal Regulations, 2010 CFR

2010-07-01

....45 Manual electrostatic spray 0.60 Flow coat 0.85 Dip coat 0.85 Nonrotational automatic electrostatic... applied (G) during the calendar month for each affected facility by the following equation: EC16NO91.038... affected facility that uses a capture system and a control device that destroys VOC's (e.g., incinerator...

Bimodal pair f-KdV dynamics in star-forming clouds

NASA Astrophysics Data System (ADS)

Karmakar, Pralay Kumar; Haloi, Archana; Roy, Supriya

2018-04-01

A theoretical formalism for investigating the bimodal conjugational mode dynamics of hybrid source, dictated by a unique pair of forced Korteweg-de Vries (f-KdV) equations in a complex turbo-magnetized star-forming cloud, is reported. It uses a standard multi-scale analysis executed over the cloud-governing equations in a closure form to derive the conjugated pair f-KdV system. We numerically see the structural features of two distinctive classes of eigenmode patterns stemming from the conjoint gravito-electrostatic interplay. The electrostatic compressive monotonic aperiodic shock-like patterns and gravitational compressive non-monotonic oscillatory shock-like structures are excitable. It is specifically revealed that the constitutive grain-charge (grain-mass) acts as electrostatic stabilizer (gravitational destabilizer) against the global cloud collapse dynamics. The basic features of the nonlinear coherent structures are confirmed in systematic phase-plane landscapes, indicating electrostatic irregular non-homoclinic open trajectories and gravitational atypical non-chaotic homoclinic fixed-point attractors. The relevance in the real astro-cosmic scenarios of the early phases of structure formation via wave-driven fluid-accretive transport processes is summarily emphasized.

Fast, adaptive summation of point forces in the two-dimensional Poisson equation

NASA Technical Reports Server (NTRS)

Van Dommelen, Leon; Rundensteiner, Elke A.

1989-01-01

A comparatively simple procedure is presented for the direct summation of the velocity field introduced by point vortices which significantly reduces the required number of operations by replacing selected partial sums by asymptotic series. Tables are presented which demonstrate the speed of this algorithm in terms of the mere doubling of computational time in dealing with a doubling of the number of vortices; current methods involve a computational time extension by a factor of 4. This procedure need not be restricted to the solution of the Poisson equation, and may be applied to other problems involving groups of points in which the interaction between elements of different groups can be simplified when the distance between groups is sufficiently great.

A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1980-01-01

A method for generating two dimensional finite difference grids about airfoils and other shapes by the use of the Poisson differential equation is developed. The inhomogeneous terms are automatically chosen such that two important effects are imposed on the grid at both the inner and outer boundaries. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. A FORTRAN computer program has been written to use this method. A description of the program, a discussion of the control parameters, and a set of sample cases are included.

STIR: Improved Electrolyte Surface Exchange via Atomically Strained Surfaces

DTIC Science & Technology

2015-09-03

at the University of Delaware. Concomitant with the experimental work, we also conducted numerical simulations of the experiments. A Poisson- Nernst ...oxygen ion lattice site results in a reaction volume and an associated Vex·ΔP term in the Arrhenius rate equation . In addition, tensile strain (i.e...simulations of the experiments. In recent work at the University of Delaware [9-13], we used finite element solution of generalized Poisson- Nernst -Planck

Evaluation of Tensile Young's Modulus and Poisson's Ratio of a Bi-modular Rock from the Displacement Measurements in a Brazilian Test

NASA Astrophysics Data System (ADS)

Patel, Shantanu; Martin, C. Derek

2018-02-01

Unlike metals, rocks show bi-modularity (different Young's moduli and Poisson's ratios in compression and tension). Displacements monitored during the Brazilian test are used in this study to obtain the Young's modulus and Poisson's ratio in tension. New equations for the displacements in a Brazilian test are derived considering the bi-modularity in the stress-strain relations. The digital image correlation technique was used to monitor the displacements of the Brazilian disk flat surface. To validate the Young's modulus and Poisson's ratio obtained from the Brazilian test, the results were compared with the values from the direct tension tests. The results obtained from the Brazilian test were repetitive and within 3.5% of the value obtained from the direct tension test for the rock tested.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

PB-AM: An open-source, fully analytical linear poisson-boltzmann solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Felberg, Lisa E.; Brookes, David H.; Yap, Eng-Hui

2016-11-02

We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized Poisson Boltzmann equation. The PB-AM software package includes the generation of outputs files appropriate for visualization using VMD, a Brownian dynamics scheme that uses periodic boundary conditions to simulate dynamics, the ability to specify docking criteria, and offers two different kinetics schemes to evaluate biomolecular association rate constants. Given that PB-AM defines mutual polarization completely and accurately, it can be refactored as a many-body expansion to explore 2- and 3-body polarization. Additionally, the software has been integrated into the Adaptive Poisson-Boltzmannmore » Solver (APBS) software package to make it more accessible to a larger group of scientists, educators and students that are more familiar with the APBS framework.« less

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Coupled electrostatic and material surface stresses yield anomalous particle interactions and deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kemp, B. A., E-mail: bkemp@astate.edu; Nikolayev, I.; Sheppard, C. J.

2016-04-14

Like-charges repel, and opposite charges attract. This fundamental tenet is a result of Coulomb's law. However, the electrostatic interactions between dielectric particles remain topical due to observations of like-charged particle attraction and the self-assembly of colloidal systems. Here, we show, using both an approximate description and an exact solution of Maxwell's equations, that nonlinear charged particle forces result even for linear material systems and can be responsible for anomalous electrostatic interactions such as like-charged particle attraction and oppositely charged particle repulsion. Furthermore, these electrostatic interactions and the deformation of such particles have fundamental implications for our understanding of macroscopic electrodynamics.

Convergence of the flow of a chemically reacting gaseous mixture to incompressible Euler equations in a unbounded domain

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam

2017-12-01

The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. We study the combined quasineutral and inviscid limit from the flow of chemically reacting gaseous mixture governed by Poisson equation to incompressible Euler equations with the ill-prepared initial data in the unbounded domain R^2× T. Furthermore, the convergence rates are obtained.

On the extraction of pressure fields from PIV velocity measurements in turbines

NASA Astrophysics Data System (ADS)

Villegas, Arturo; Diez, Fancisco J.

2012-11-01

In this study, the pressure field for a water turbine is derived from particle image velocimetry (PIV) measurements. Measurements are performed in a recirculating water channel facility. The PIV measurements include calculating the tangential and axial forces applied to the turbine by solving the integral momentum equation around the airfoil. The results are compared with the forces obtained from the Blade Element Momentum theory (BEMT). Forces are calculated by using three different methods. In the first method, the pressure fields are obtained from PIV velocity fields by solving the Poisson equation. The boundary conditions are obtained from the Navier-Stokes momentum equations. In the second method, the pressure at the boundaries is determined by spatial integration of the pressure gradients along the boundaries. In the third method, applicable only to incompressible, inviscid, irrotational, and steady flow, the pressure is calculated using the Bernoulli equation. This approximated pressure is known to be accurate far from the airfoil and outside of the wake for steady flows. Additionally, the pressure is used to solve for the force from the integral momentum equation on the blade. From the three methods proposed to solve for pressure and forces from PIV measurements, the first one, which is solved by using the Poisson equation, provides the best match to the BEM theory calculations.

C1 finite elements on non-tensor-product 2d and 3d manifolds.

PubMed

Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg

2016-01-01

Geometrically continuous ( G k ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are C k also for non-tensor-product layout. This paper describes and analyzes one such concrete C 1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G 1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson's equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O ( h 3 ) convergence in the L ∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis.

Treatment of charge singularities in implicit solvent models.

PubMed

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-21

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 A for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Treatment of charge singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-01

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2Å for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Etude de la physico-chime d'un magnetoplasma de chlore pour la gravure sous-micrometrique

NASA Astrophysics Data System (ADS)

Pauna, Olivier Daniel

The aim of this thesis is to achieve a better understanding of physical and chemical phenomena occurring in a high-density plasma designed for sub-micron etching of thin films. The plasma is produced in chlorine by means of an electromagnetic surface wave and it can be confined by a uniform static magnetic field. The flexibility offered by the reactor in terms of operating conditions makes possible a parametric study of the influence of the magnetic confinement on the plasma characteristics. Thus, we have examined the plasma properties by means of several diagnostics techniques, including electrostatic probes, laser photodetachment of negative ions, ion acoustic wave propagation and optical emission spectroscopy. First, we investigated the influence of the operating conditions on the spatial properties of the plasma; this includes electric characteristics (electrons, positive and negative ions) as well as chemical characteristics (reactive neutrals). Second, we studied the impact of the reactor aspect ratio (i.e. reactor length/radius ratio) on both electrical and chemical characteristics. Together with these experimental studies, we have developed a bidimensional fluid model, by solving self-consistently the first two moments of Bolzmann equation and Poisson's equation. Using a semi-implicit scheme, it was possible to maintain a short computation time and to use this model to investigate a diffusion plasma in an electropositive gas. We were thus able to estimate the value of the diffusion coefficient in the direction perpendicular to the magnetic field. The results thus obtained are in good qualitative agreement with the diffusion coefficient proposed by Liebermann and Lichtenberg.

Analyte preconcentration in nanofluidic channels with nonuniform zeta potential

NASA Astrophysics Data System (ADS)

Eden, A.; McCallum, C.; Storey, B. D.; Pennathur, S.; Meinhart, C. D.

2017-12-01

It is well known that charged analytes in the presence of nonuniform electric fields concentrate at locations where the relevant driving forces balance, and a wide range of ionic stacking and focusing methods are commonly employed to leverage these physical mechanisms in order to improve signal levels in biosensing applications. In particular, nanofluidic channels with spatially varying conductivity distributions have been shown to provide increased preconcentration of charged analytes due to the existence of a finite electric double layer (EDL), in which electrostatic attraction and repulsion from charged surfaces produce nonuniform transverse ion distributions. In this work, we use numerical simulations to show that one can achieve greater levels of sample accumulation by using field-effect control via wall-embedded electrodes to tailor the surface potential heterogeneity in a nanochannel with overlapped EDLs. In addition to previously demonstrated stacking and focusing mechanisms, we find that the coupling between two-dimensional ion distributions and the axial electric field under overlapped EDL conditions can generate an ion concentration polarization interface in the middle of the channel. Under an applied electric field, this interface can be used to concentrate sample ions between two stationary regions of different surface potential and charge density. Our numerical model uses the Poisson-Nernst-Planck system of equations coupled with the Stokes equation to demonstrate the phenomenon, and we discuss in detail the driving forces behind the predicted sample enhancement. The numerical velocity and salt concentration profiles exhibit good agreement with analytical results from a simplified one-dimensional area-averaged model for several limiting cases, and we show predicted amplification ratios of up to 105.

Electrostatic twisted modes in multi-component dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayub, M. K.; National Centre for Physics, Shahdra Valley Road, Quaid-i-Azam University Campus, Islamabad 44000; Pohang University of Sciences and Technology, Pohang, Gyeongbuk 790-784

Various electrostatic twisted modes are re-investigated with finite orbital angular momentum in an unmagnetized collisionless multi-component dusty plasma, consisting of positive/negative charged dust particles, ions, and electrons. For this purpose, hydrodynamical equations are employed to obtain paraxial equations in terms of density perturbations, while assuming the Gaussian and Laguerre-Gaussian (LG) beam solutions. Specifically, approximated solutions for potential problem are studied by using the paraxial approximation and expressed the electric field components in terms of LG functions. The energy fluxes associated with these modes are computed and corresponding expressions for orbital angular momenta are derived. Numerical analyses reveal that radial/angular modemore » numbers as well as dust number density and dust charging states strongly modify the LG potential profiles attributed to different electrostatic modes. Our results are important for understanding particle transport and energy transfer due to wave excitations in multi-component dusty plasmas.« less

Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries

NASA Astrophysics Data System (ADS)

Gillis, T.; Winckelmans, G.; Chatelain, P.

2018-02-01

We present a fast and efficient Fourier-based solver for the Poisson problem around an arbitrary geometry in an unbounded 3D domain. This solver merges two rewarding approaches, the lattice Green's function method and the immersed interface method, using the Sherman-Morrison-Woodbury decomposition formula. The method is intended to be second order up to the boundary. This is verified on two potential flow benchmarks. We also further analyse the iterative process and the convergence behavior of the proposed algorithm. The method is applicable to a wide range of problems involving a Poisson equation around inner bodies, which goes well beyond the present validation on potential flows.

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

DOE PAGES

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; ...

2013-01-01

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less

The establishment and application of direct coupled electrostatic-structural field model in electrostatically controlled deployable membrane antenna

NASA Astrophysics Data System (ADS)

Gu, Yongzhen; Duan, Baoyan; Du, Jingli

2018-05-01

The electrostatically controlled deployable membrane antenna (ECDMA) is a promising space structure due to its low weight, large aperture and high precision characteristics. However, it is an extreme challenge to describe the coupled field between electrostatic and membrane structure accurately. A direct coupled method is applied to solve the coupled problem in this paper. Firstly, the membrane structure and electrostatic field are uniformly described by energy, considering the coupled problem is an energy conservation phenomenon. Then the direct coupled electrostatic-structural field governing equilibrium equations are obtained by energy variation approach. Numerical results show that the direct coupled method improves the computing efficiency by 36% compared with the traditional indirect coupled method with the same level accuracy. Finally, the prototype has been manufactured and tested and the ECDMA finite element simulations show good agreement with the experiment results as the maximum surface error difference is 6%.

A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations

NASA Astrophysics Data System (ADS)

Qiang, Ji

2017-10-01

A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of O(Nu(logNmode)) , where Nu is the total number of unknowns and Nmode is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage of using an artificial boundary condition in a large extended computational domain. The new 3D Poisson solver is parallelized using a message passing interface (MPI) on multi-processor computers and shows a reasonable parallel performance up to hundreds of processor cores.

Electrokinetics Models for Micro and Nano Fluidic Impedance Sensors

DTIC Science & Technology

2010-11-01

primitive Differential-Algebraic Equations (DAEs), used to process and interpret the experimentally measured electrical impedance data (Sun and Morgan...field, and species respectively. A second-order scheme was used to calculate the ionic species distribution. The linearized algebraic equations were...is governed by the Poisson equation 2 0 0 r i i i F z cε ε φ∇ + =∑ where ε0 and εr are, respectively, the electrical permittivity in the vacuum

Stochastic analysis of three-dimensional flow in a bounded domain

USGS Publications Warehouse

Naff, R.L.; Vecchia, A.V.

1986-01-01

A commonly accepted first-order approximation of the equation for steady state flow in a fully saturated spatially random medium has the form of Poisson's equation. This form allows for the advantageous use of Green's functions to solve for the random output (hydraulic heads) in terms of a convolution over the random input (the logarithm of hydraulic conductivity). A solution for steady state three- dimensional flow in an aquifer bounded above and below is presented; consideration of these boundaries is made possible by use of Green's functions to solve Poisson's equation. Within the bounded domain the medium hydraulic conductivity is assumed to be a second-order stationary random process as represented by a simple three-dimensional covariance function. Upper and lower boundaries are taken to be no-flow boundaries; the mean flow vector lies entirely in the horizontal dimensions. The resulting hydraulic head covariance function exhibits nonstationary effects resulting from the imposition of boundary conditions. Comparisons are made with existing infinite domain solutions.

Introduction to quantized LIE groups and algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tjin, T.

1992-10-10

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl[sub 2] is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxtermore » equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl[sub 2] algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.« less

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

PubMed

Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten

2016-08-09

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

A regularized vortex-particle mesh method for large eddy simulation

NASA Astrophysics Data System (ADS)

Spietz, H. J.; Walther, J. H.; Hejlesen, M. M.

2017-11-01

We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green's function solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy Simulation by including a dynamic subfilter-scale model based on test-filters compatible with the aforementioned regularization functions. Further the subfilter-scale model uses Lagrangian averaging, which is a natural candidate in light of the Lagrangian nature of vortex particle methods. A multiresolution variation of the method is applied to simulate the benchmark problem of the flow past a square cylinder at Re = 22000 and the obtained results are compared to results from the literature.

SIERRA - A 3-D device simulator for reliability modeling

NASA Astrophysics Data System (ADS)

Chern, Jue-Hsien; Arledge, Lawrence A., Jr.; Yang, Ping; Maeda, John T.

1989-05-01

SIERRA is a three-dimensional general-purpose semiconductor-device simulation program which serves as a foundation for investigating integrated-circuit (IC) device and reliability issues. This program solves the Poisson and continuity equations in silicon under dc, transient, and small-signal conditions. Executing on a vector/parallel minisupercomputer, SIERRA utilizes a matrix solver which uses an incomplete LU (ILU) preconditioned conjugate gradient square (CGS, BCG) method. The ILU-CGS method provides a good compromise between memory size and convergence rate. The authors have observed a 5x to 7x speedup over standard direct methods in simulations of transient problems containing highly coupled Poisson and continuity equations such as those found in reliability-oriented simulations. The application of SIERRA to parasitic CMOS latchup and dynamic random-access memory single-event-upset studies is described.

Effect of collisions on photoelectron sheath in a gas

NASA Astrophysics Data System (ADS)

Sodha, Mahendra Singh; Mishra, S. K.

2016-02-01

This paper presents a study of the effect of the collision of electrons with atoms/molecules on the structure of a photoelectron sheath. Considering the half Fermi-Dirac distribution of photo-emitted electrons, an expression for the electron density in the sheath has been derived in terms of the electric potential and the structure of the sheath has been investigated by incorporating Poisson's equation in the analysis. The method of successive approximations has been used to solve Poisson's equation with the solution for the electric potential in the case of vacuum, obtained earlier [Sodha and Mishra, Phys. Plasmas 21, 093704 (2014)], being used as the zeroth order solution for the present analysis. The inclusion of collisions influences the photoelectron sheath structure significantly; a reduction in the sheath width with increasing collisions is obtained.

Methodology for extraction of space charge density profiles at nanoscale from Kelvin probe force microscopy measurements.

PubMed

Villeneuve-Faure, C; Boudou, L; Makasheva, K; Teyssedre, G

2017-12-15

To understand the physical phenomena occurring at metal/dielectric interfaces, determination of the charge density profile at nanoscale is crucial. To deal with this issue, charges were injected applying a DC voltage on lateral Al-electrodes embedded in a SiN x thin dielectric layer. The surface potential induced by the injected charges was probed by Kelvin probe force microscopy (KPFM). It was found that the KPFM frequency mode is a better adapted method to probe accurately the charge profile. To extract the charge density profile from the surface potential two numerical approaches based on the solution to Poisson's equation for electrostatics were investigated: the second derivative model method, already reported in the literature, and a new 2D method based on the finite element method (FEM). Results highlight that the FEM is more robust to noise or artifacts in the case of a non-flat initial surface potential. Moreover, according to theoretical study the FEM appears to be a good candidate for determining charge density in dielectric films with thicknesses in the range from 10 nm to 10 μm. By applying this method, the charge density profile was determined at nanoscale, highlighting that the charge cloud remains close to the interface.

Density functional theory study of defect energies and space charge distribution at a solid-oxide electrolyte surface

NASA Astrophysics Data System (ADS)

Han, Chu; Bongiorno, Angelo

2014-03-01

Yttrium-doped barium zirconate (BZY) is a proton conducting electrolyte forming a class of novel materials for new generation of solid oxide fuel cells, for hydrogen separation and purification, and for electrolysis of water. Here we use density functional theory calculations to compute the energy of protons and oxygen vacancies at the surface and in the bulk of lightly Y-doped BZY materials. We found that protons are energetically more stable at the surface termination than in the bulk of BZY by about 1 eV. In contrast, doubly-positively charged oxygen vacancies are found to form iso-energetic defects at both the terminal surface layer and in the bulk of BZY, while in the sub-surface region the defect energy raises by about 1 eV with respect to the value in the bulk. The energetic behavior of protons and oxygen vacancies in the near surface region of BZY is attributed to the competition of strain and electrostatic effects. Lattice model representations of BZY surfaces are then used in combination with Monte Carlo simulations to solve the Poisson-Boltzmann equation and investigate the implication of the results above on the structure of the space charge region at the surface of BZY materials.

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

2014-03-01

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

Effect of double-layer polarization on the forces that act on a nanosized cylindrical particle in an ac electrical field.

PubMed

Zhao, Hui; Bau, Haim H

2008-06-17

The polarization of, the forces acting on, and the electroosmotic flow field around a cylindrical particle of radius a* and uniform zeta potential zeta* submerged in an electrolyte solution and subjected to alternating electric fields are computed by solving the Poisson-Nernst-Planck (PNP) equations (the standard model). The dipole coefficient and the electrostatic and hydrodynamic forces are calculated as functions of the electric field's frequency, the solute concentration, and the particle's surface charge. The calculations are not restricted to small Debye screening lengths (lambdaD*). At relatively low frequencies, the polarization coefficient is nearly frequency-independent. As the frequency increases above D*/a*(2), where D* is the effective diffusion coefficient, the polarization coefficient initially increases, attains a maximum, and then decreases to an asymptotic value (when the frequency exceeds (1+Du)D*/lambdaD(*2), where Du is the Dukhin number). At low frequencies, when (lambdaD*/a*)(2)e(|zeta*F*/(2R*T*)|) < 1, the PNP calculations are in excellent agreement with the predictions of the Dukhin-Shilov (DS) low-frequency theory. At high frequencies, when lambda D*/a* < 1, the PNP calculations are in excellent agreement with the Maxwell-Wagner-O'Konski (MWO) theory.

Dissipative particle dynamics: Effects of thermostating schemes on nano-colloid electrophoresis

NASA Astrophysics Data System (ADS)

Hassanzadeh Afrouzi, Hamid; Moshfegh, Abouzar; Farhadi, Mousa; Sedighi, Kurosh

2018-05-01

A novel fully explicit approach using dissipative particle dynamics (DPD) method is introduced in the present study to model the electrophoretic transport of nano-colloids in an electrolyte solution. Slater type charge smearing function included in 3D Ewald summation method is employed to treat electrostatic interaction. Performance of various thermostats are challenged to control the system temperature and study the dynamic response of colloidal electrophoretic mobility under practical ranges of external electric field (0 . 072 < E < 0 . 361 v/nm) covering linear to non-linear response regime, and ionic salt concentration (0.049 < SC < 0 . 69 [M]) covering weak to strong Debye screening of the colloid. System temperature and electrophoretic mobility both show a direct and inverse relationships respectively with electric field and colloidal repulsion; although they each respectively behave direct and inverse trends with salt concentration under various thermostats. Nosé-Hoover-Lowe-Andersen and Lowe-Andersen thermostats are found to function more effectively under high electric fields (E > 0 . 145[v/nm ]) while thermal equilibrium is maintained. Reasonable agreements are achieved by benchmarking the system radial distribution function with available EW3D modellings, as well as comparing reduced mobility against conventional Smoluchowski and Hückel theories, and numerical solution of Poisson-Boltzmann equation.

Calculating pH-dependent free energy of proteins by using Monte Carlo protonation probabilities of ionizable residues.

PubMed

Huang, Qiang; Herrmann, Andreas

2012-03-01

Protein folding, stability, and function are usually influenced by pH. And free energy plays a fundamental role in analysis of such pH-dependent properties. Electrostatics-based theoretical framework using dielectric solvent continuum model and solving Poisson-Boltzmann equation numerically has been shown to be very successful in understanding the pH-dependent properties. However, in this approach the exact computation of pH-dependent free energy becomes impractical for proteins possessing more than several tens of ionizable sites (e.g. > 30), because exact evaluation of the partition function requires a summation over a vast number of possible protonation microstates. Here we present a method which computes the free energy using the average energy and the protonation probabilities of ionizable sites obtained by the well-established Monte Carlo sampling procedure. The key feature is to calculate the entropy by using the protonation probabilities. We used this method to examine a well-studied protein (lysozyme) and produced results which agree very well with the exact calculations. Applications to the optimum pH of maximal stability of proteins and protein-DNA interactions have also resulted in good agreement with experimental data. These examples recommend our method for application to the elucidation of the pH-dependent properties of proteins.

Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

NASA Astrophysics Data System (ADS)

Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi; El Achouby, Hicham; Feddi, El Mustapha; Dujardin, Francis

2015-02-01

Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image-charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

2D Mesh Manipulation

DTIC Science & Technology

2011-11-01

the Poisson form of the equations can also be generated by manipulating the computational space , so forcing functions become superfluous . The...ABSTRACT Unstructured methods for region discretization have become common in computational fluid dynamics (CFD) analysis because of certain benefits...application of Winslow elliptic smoothing equations to unstructured meshes. It has been shown that it is not necessary for the computational space of

Plasma Modes

NASA Astrophysics Data System (ADS)

Dubin, D. H. E.

This chapter explores several aspects of the linear electrostatic normal modes of oscillation for a single-species non-neutral plasma in a Penning trap. Linearized fluid equations of motion are developed, assuming the plasma is cold but collisionless, which allow derivation of the cold plasma dielectric tensor and the electrostatic wave equation. Upper hybrid and magnetized plasma waves in an infinite uniform plasma are described. The effect of the plasma surface in a bounded plasma system is considered, and the properties of surface plasma waves are characterized. The normal modes of a cylindrical plasma column are discussed, and finally, modes of spheroidal plasmas, and finite temperature effects on the modes, are briefly described.

GRAPE- TWO-DIMENSIONAL GRIDS ABOUT AIRFOILS AND OTHER SHAPES BY THE USE OF POISSON'S EQUATION

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1994-01-01

The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids, including those about airfoils. In a grid used for computing aerodynamic flow over an airfoil, or any other body shape, the surface of the body is usually treated as an inner boundary and often cannot be easily represented as an analytic function. The GRAPE computer program was developed to incorporate a method for generating two-dimensional finite-difference grids about airfoils and other shapes by the use of the Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including a limited number of sharp corners. The GRAPE program has been developed to be numerically stable and computationally fast. GRAPE can provide the aerodynamic analyst with an efficient and consistent means of grid generation. The GRAPE procedure generates a grid between an inner and an outer boundary by utilizing an iterative procedure to solve the Poisson differential equation subject to geometrical restraints. In this method, the inhomogeneous terms of the equation are automatically chosen such that two important effects are imposed on the grid. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. Along with the iterative solution to Poisson's equation, a technique of coarse-fine sequencing is employed to accelerate numerical convergence. GRAPE program control cards and input data are entered via the NAMELIST feature. Each variable has a default value such that user supplied data is kept to a minimum. Basic input data consists of the boundary specification, mesh point spacings on the boundaries, and mesh line angles at the boundaries. Output consists of a dataset containing the grid data and, if requested, a plot of the generated mesh. The GRAPE program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 135K (octal) of 60 bit words. For plotted output the commercially available DISSPLA graphics software package is required. The GRAPE program was developed in 1980.

Multifluid Theory of Solitons

NASA Astrophysics Data System (ADS)

Verheest, Frank

2008-03-01

After introducing the basic multifluid model equations, this review discusses three different methods to describe nonlinear plasma waves, by giving a rather general overview of the relevant methodology, followed by a specific and recent application. First, reductive perturbation analysis is applicable to waves that are not too strongly nonlinear, if their linear counterparts have an acoustic-like dispersion at low frequencies. It is discussed for electrostatic modes, with a brief application to dusty plasma waves. The typical paradigm for such problems is the well known KdV equation and its siblings. Stationary waves with larger amplitudes can be treated, i.a., via the fluid-dynamic approach pioneered by McKenzie, which focuses on essential insights into the limitations that restrict the range of available solitary electrostatic solutions. As an illustration, novel electrostatic solutions have been found in plasmas with two-temperature electron species that are relevant in understanding certain magnetospheric plasma observations. The older cousin of the large-amplitude technique is the Sagdeev pseudopotential description, to which the newer fluid-dynamic approach is essentially equivalent. Because the Sagdeev analysis has mostly been applied to electrostatic waves, some recent results are given for electromagnetic modes in pair plasmas, to show its versatility.

GroPBS: Fast Solver for Implicit Electrostatics of Biomolecules

PubMed Central

Bertelshofer, Franziska; Sun, Liping; Greiner, Günther; Böckmann, Rainer A.

2015-01-01

Knowledge about the electrostatic potential on the surface of biomolecules or biomembranes under physiological conditions is an important step in the attempt to characterize the physico-chemical properties of these molecules and, in particular, also their interactions with each other. Additionally, knowledge about solution electrostatics may also guide the design of molecules with specified properties. However, explicit water models come at a high computational cost, rendering them unsuitable for large design studies or for docking purposes. Implicit models with the water phase treated as a continuum require the numerical solution of the Poisson–Boltzmann equation (PBE). Here, we present a new flexible program for the numerical solution of the PBE, allowing for different geometries, and the explicit and implicit inclusion of membranes. It involves a discretization of space and the computation of the molecular surface. The PBE is solved using finite differences, the resulting set of equations is solved using a Gauss–Seidel method. It is shown for the example of the sucrose transporter ScrY that the implicit inclusion of a surrounding membrane has a strong effect also on the electrostatics within the pore region and, thus, needs to be carefully considered, e.g., in design studies on membrane proteins. PMID:26636074

BMS3 invariant fluid dynamics at null infinity

NASA Astrophysics Data System (ADS)

Penna, Robert F.

2018-02-01

We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Gyrofluid turbulence models with kinetic effects

NASA Astrophysics Data System (ADS)

Dorland, W.; Hammett, G. W.

1993-03-01

Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u∥, T∥, and T⊥ along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived that may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau damping model [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)], which is equivalent to a multipole approximation to the plasma dispersion function, extended to include finite Larmor radius effects (FLR). In particular, new dissipative, nonlinear terms are found that model the perpendicular phase mixing of the distribution function along contours of constant electrostatic potential. These ``FLR phase-mixing'' terms introduce a hyperviscositylike damping ∝k⊥2‖Φkk×k'‖, which should provide a physics-based damping mechanism at high k⊥ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three-dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

Ionic channels: natural nanotubes described by the drift diffusion equations

NASA Astrophysics Data System (ADS)

Eisenberg, Bob

2000-05-01

Ionic channels are a large class of proteins with holes down their middle that control a wide range of cellular functions important in health and disease. Ionic channels can be analysed using a combination of the Poisson and drift diffusion equations familiar from computational electronics because their behavior is dominated by the electrical properties of their simple structure.

Three-Dimensional Effects of Crack Closure in Laminated Composite Plates Subjected to Bending Loads

DTIC Science & Technology

1994-06-01

Approved by: •UW. Kwon, Thesis Advisor wathe D.K~elleher, Chairman Department of Mechanical Engineering ii ABSTRACT Fracture is one of the dominant...5 A. OVERVIEW .......................................... 5 B. CONSTITUTIVE EQUATION .............................. 9 1. Isotropic...the elemental nodes. B. CONSTITUTIVE EQUATION The material property matrix [D] is a symmetric matrix which includes elasticity moduli and Poisson’s

Numerical prediction of three-dimensional juncture region flow using the parabolic Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.; Orzechowski, J. A.

1979-01-01

A numerical solution algorithm is established for prediction of subsonic turbulent three-dimensional flows in aerodynamic configuration juncture regions. A turbulence closure model is established using the complete Reynolds stress. Pressure coupling is accomplished using the concepts of complementary and particular solutions to a Poisson equation. Specifications for data input juncture geometry modification are presented.

High order solution of Poisson problems with piecewise constant coefficients and interface jumps

NASA Astrophysics Data System (ADS)

Marques, Alexandre Noll; Nave, Jean-Christophe; Rosales, Rodolfo Ruben

2017-04-01

We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson problems in rectangular domains-which requires the BIM solution at interfaces/boundaries only. These Poisson problems involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples of the algorithm applied to Poisson problems involving complex geometries, including cases in which the solution is discontinuous. We show that the algorithm produces solutions that converge with either 3rd or 4th order of accuracy, depending on the type of boundary condition and solution discontinuity.

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pabst, M., E-mail: M.Pabst@fz-juelich.de

2014-06-14

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10{sup −4} so the Fourier-Bessel series can be approximatedmore » by elementary functions. The time development of the system is characterized by two time constants, τ{sub c} and τ{sub g}. The constant τ{sub c} describes the approach to the stationary state of the total charge and the potential. τ{sub c} is several orders of magnitude smaller than the geometry-dependent constant τ{sub g}, which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.« less

Probing protein orientation near charged nanosurfaces for simulation-assisted biosensor design.

PubMed

Cooper, Christopher D; Clementi, Natalia C; Barba, Lorena A

2015-09-28

Protein-surface interactions are ubiquitous in biological processes and bioengineering, yet are not fully understood. In biosensors, a key factor determining the sensitivity and thus the performance of the device is the orientation of the ligand molecules on the bioactive device surface. Adsorption studies thus seek to determine how orientation can be influenced by surface preparation, varying surface charge, and ambient salt concentration. In this work, protein orientation near charged nanosurfaces is obtained under electrostatic effects using the Poisson-Boltzmann equation, in an implicit-solvent model. Sampling the free energy for protein G B1 D4' at a range of tilt and rotation angles with respect to the charged surface, we calculated the probability of the protein orientations and observed a dipolar behavior. This result is consistent with published experimental studies and combined Monte Carlo and molecular dynamics simulations using this small protein, validating our method. More relevant to biosensor technology, antibodies such as immunoglobulin G are still a formidable challenge to molecular simulation, due to their large size. With the Poisson-Boltzmann model, we obtained the probability distribution of orientations for the iso-type IgG2a at varying surface charge and salt concentration. This iso-type was not found to have a preferred orientation in previous studies, unlike the iso-type IgG1 whose larger dipole moment was assumed to make it easier to control. Our results show that the preferred orientation of IgG2a can be favorable for biosensing with positive charge on the surface of 0.05 C/m(2) or higher and 37 mM salt concentration. The results also show that local interactions dominate over dipole moment for this protein. Improving immunoassay sensitivity may thus be assisted by numerical studies using our method (and open-source code), guiding changes to fabrication protocols or protein engineering of ligand molecules to obtain more favorable orientations.

Probing protein orientation near charged nanosurfaces for simulation-assisted biosensor design

NASA Astrophysics Data System (ADS)

Cooper, Christopher D.; Clementi, Natalia C.; Barba, Lorena A.

2015-09-01

Protein-surface interactions are ubiquitous in biological processes and bioengineering, yet are not fully understood. In biosensors, a key factor determining the sensitivity and thus the performance of the device is the orientation of the ligand molecules on the bioactive device surface. Adsorption studies thus seek to determine how orientation can be influenced by surface preparation, varying surface charge, and ambient salt concentration. In this work, protein orientation near charged nanosurfaces is obtained under electrostatic effects using the Poisson-Boltzmann equation, in an implicit-solvent model. Sampling the free energy for protein G B1 D4' at a range of tilt and rotation angles with respect to the charged surface, we calculated the probability of the protein orientations and observed a dipolar behavior. This result is consistent with published experimental studies and combined Monte Carlo and molecular dynamics simulations using this small protein, validating our method. More relevant to biosensor technology, antibodies such as immunoglobulin G are still a formidable challenge to molecular simulation, due to their large size. With the Poisson-Boltzmann model, we obtained the probability distribution of orientations for the iso-type IgG2a at varying surface charge and salt concentration. This iso-type was not found to have a preferred orientation in previous studies, unlike the iso-type IgG1 whose larger dipole moment was assumed to make it easier to control. Our results show that the preferred orientation of IgG2a can be favorable for biosensing with positive charge on the surface of 0.05 C/m2 or higher and 37 mM salt concentration. The results also show that local interactions dominate over dipole moment for this protein. Improving immunoassay sensitivity may thus be assisted by numerical studies using our method (and open-source code), guiding changes to fabrication protocols or protein engineering of ligand molecules to obtain more favorable orientations.

Dielectric boundary force and its crucial role in gramicidin

NASA Astrophysics Data System (ADS)

Nadler, Boaz; Hollerbach, Uwe; Eisenberg, R. S.

2003-08-01

In an electrostatic problem with nonuniform geometry, a charge Q in one region induces surface charges [called dielectric boundary charges (DBC)] at boundaries between different dielectrics. These induced surface charges, in return, exert a force [called dielectric boundary force (DBF)] on the charge Q that induced them. The DBF is often overlooked. It is not present in standard continuum theories of (point) ions in or near membranes and proteins, such as Gouy-Chapman, Debye-Huckel, Poisson-Boltzmann or Poisson-Nernst- Planck. The DBF is important when a charge Q is near dielectric interfaces, for example, when ions permeate through protein channels embedded in biological membranes. In this paper, we define the DBF and calculate it explicitly for a planar dielectric wall and for a tunnel geometry resembling the ionic channel gramicidin. In general, we formulate the DBF in a form useful for continuum theories, namely, as a solution of a partial differential equation with boundary conditions. The DBF plays a crucial role in the permeation of ions through the gramicidin channel. A positive ion in the channel produces a DBF of opposite sign to that of the fixed charge force (FCF) produced by the permanent charge of the gramicidin polypeptide, and so the net force on the positive ion is reduced. A negative ion creates a DBF of the same sign as the FCF and so the net (repulsive) force on the negative ion is increased. Thus, a positive ion can permeate the channel, while a negative ion is excluded from it. In gramicidin, it is this balance between the FCF and DBF that allows only singly charged positive ions to move into and through the channel. The DBF is not directly responsible, however, for selectivity between the alkali metal ions (e.g., Li+, Na+, K+): we prove that the DBF on a mobile spherical ion is independent of the ion’s radius.