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.

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.

Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus

NASA Astrophysics Data System (ADS)

Buring, Ricardo; Kiselev, Arthemy V.; Rutten, Nina

2018-02-01

Let \\mathscr{P} be a Poisson structure on a finite-dimensional affine real manifold. Can \\mathscr{P} be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach - with respect to all affine Poisson manifolds - to finding a class of solutions to this deformation problem. For that reasoning, several types of graphs are needed. In this paper we outline the algorithms to generate those graphs. The graphs that encode deformations are classified by the number of internal vertices k; for k ≤ 4 we present all solutions of the deformation problem. For k ≥ 5, first reproducing the pentagon-wheel picture suggested at k = 6 by Kontsevich and Willwacher, we construct the heptagon-wheel cocycle that yields a new unique solution without 2-loops and tadpoles at k = 8.

The solution of large multi-dimensional Poisson problems

NASA Technical Reports Server (NTRS)

Stone, H. S.

1974-01-01

The Buneman algorithm for solving Poisson problems can be adapted to solve large Poisson problems on computers with a rotating drum memory so that the computation is done with very little time lost due to rotational latency of the drum.

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

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

PubMed

Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

2016-01-07

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 applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

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

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S.; Genovese, L.

2016-01-07

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 applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and themore » linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.« less

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.

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.

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

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.

Kinetics of the electric double layer formation modelled by the finite difference method

NASA Astrophysics Data System (ADS)

Valent, Ivan

2017-11-01

Dynamics of the elctric double layer formation in 100 mM NaCl solution for sudden potentail steps of 10 and 20 mV was simulated using the Poisson-Nernst-Planck theory and VLUGR2 solver for partial differential equations. The used approach was verified by comparing the obtained steady-state solution with the available exact solution. The simulations allowed for detailed analysis of the relaxation processes of the individual ions and the electric potential. Some computational aspects of the problem were discussed.

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.

Combined analysis of magnetic and gravity anomalies using normalized source strength (NSS)

NASA Astrophysics Data System (ADS)

Li, L.; Wu, Y.

2017-12-01

Gravity field and magnetic field belong to potential fields which lead inherent multi-solution. Combined analysis of magnetic and gravity anomalies based on Poisson's relation is used to determinate homology gravity and magnetic anomalies and decrease the ambiguity. The traditional combined analysis uses the linear regression of the reduction to pole (RTP) magnetic anomaly to the first order vertical derivative of the gravity anomaly, and provides the quantitative or semi-quantitative interpretation by calculating the correlation coefficient, slope and intercept. In the calculation process, due to the effect of remanent magnetization, the RTP anomaly still contains the effect of oblique magnetization. In this case the homology gravity and magnetic anomalies display irrelevant results in the linear regression calculation. The normalized source strength (NSS) can be transformed from the magnetic tensor matrix, which is insensitive to the remanence. Here we present a new combined analysis using NSS. Based on the Poisson's relation, the gravity tensor matrix can be transformed into the pseudomagnetic tensor matrix of the direction of geomagnetic field magnetization under the homologous condition. The NSS of pseudomagnetic tensor matrix and original magnetic tensor matrix are calculated and linear regression analysis is carried out. The calculated correlation coefficient, slope and intercept indicate the homology level, Poisson's ratio and the distribution of remanent respectively. We test the approach using synthetic model under complex magnetization, the results show that it can still distinguish the same source under the condition of strong remanence, and establish the Poisson's ratio. Finally, this approach is applied in China. The results demonstrated that our approach is feasible.

Collisional effects on the numerical recurrence in Vlasov-Poisson simulations

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

Pezzi, Oreste; Valentini, Francesco; Camporeale, Enrico

The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456–1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used,more » an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.« less

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

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.

Poisson Approximation-Based Score Test for Detecting Association of Rare Variants.

PubMed

Fang, Hongyan; Zhang, Hong; Yang, Yaning

2016-07-01

Genome-wide association study (GWAS) has achieved great success in identifying genetic variants, but the nature of GWAS has determined its inherent limitations. Under the common disease rare variants (CDRV) hypothesis, the traditional association analysis methods commonly used in GWAS for common variants do not have enough power for detecting rare variants with a limited sample size. As a solution to this problem, pooling rare variants by their functions provides an efficient way for identifying susceptible genes. Rare variant typically have low frequencies of minor alleles, and the distribution of the total number of minor alleles of the rare variants can be approximated by a Poisson distribution. Based on this fact, we propose a new test method, the Poisson Approximation-based Score Test (PAST), for association analysis of rare variants. Two testing methods, namely, ePAST and mPAST, are proposed based on different strategies of pooling rare variants. Simulation results and application to the CRESCENDO cohort data show that our methods are more powerful than the existing methods. © 2016 John Wiley & Sons Ltd/University College London.

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

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.

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.

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.

Rapid computation of directional wellbore drawdown in a confined aquifer via Poisson resummation

NASA Astrophysics Data System (ADS)

Blumenthal, Benjamin J.; Zhan, Hongbin

2016-08-01

We have derived a rapidly computed analytical solution for drawdown caused by a partially or fully penetrating directional wellbore (vertical, horizontal, or slant) via Green's function method. The mathematical model assumes an anisotropic, homogeneous, confined, box-shaped aquifer. Any dimension of the box can have one of six possible boundary conditions: 1) both sides no-flux; 2) one side no-flux - one side constant-head; 3) both sides constant-head; 4) one side no-flux; 5) one side constant-head; 6) free boundary conditions. The solution has been optimized for rapid computation via Poisson Resummation, derivation of convergence rates, and numerical optimization of integration techniques. Upon application of the Poisson Resummation method, we were able to derive two sets of solutions with inverse convergence rates, namely an early-time rapidly convergent series (solution-A) and a late-time rapidly convergent series (solution-B). From this work we were able to link Green's function method (solution-B) back to image well theory (solution-A). We then derived an equation defining when the convergence rate between solution-A and solution-B is the same, which we termed the switch time. Utilizing the more rapidly convergent solution at the appropriate time, we obtained rapid convergence at all times. We have also shown that one may simplify each of the three infinite series for the three-dimensional solution to 11 terms and still maintain a maximum relative error of less than 10-14.

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

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.

Evaluation of Shiryaev-Roberts procedure for on-line environmental radiation monitoring.

PubMed

Watson, Mara M; Seliman, Ayman F; Bliznyuk, Valery N; DeVol, Timothy A

2018-04-30

Water can become contaminated as a result of a leak from a nuclear facility, such as a waste facility, or from clandestine nuclear activity. Low-level on-line radiation monitoring is needed to detect these events in real time. A Bayesian control chart method, Shiryaev-Roberts (SR) procedure, was compared with classical methods, 3-σ and cumulative sum (CUSUM), for quantifying an accumulating signal from an extractive scintillating resin flow-cell detection system. Solutions containing 0.10-5.0 Bq/L of 99 Tc, as T99cO 4 - were pumped through a flow cell packed with extractive scintillating resin used in conjunction with a Beta-RAM Model 5 HPLC detector. While T99cO 4 - accumulated on the resin, time series data were collected. Control chart methods were applied to the data using statistical algorithms developed in MATLAB. SR charts were constructed using Poisson (Poisson SR) and Gaussian (Gaussian SR) probability distributions of count data to estimate the likelihood ratio. Poisson and Gaussian SR charts required less volume of radioactive solution at a fixed concentration to exceed the control limit in most cases than 3-σ and CUSUM control charts, particularly solutions with lower activity. SR is thus the ideal control chart for low-level on-line radiation monitoring. Once the control limit was exceeded, activity concentrations were estimated from the SR control chart using the control chart slope on a semi-logarithmic plot. A linear regression fit was applied to averaged slope data for five activity concentration groupings for Poisson and Gaussian SR control charts. A correlation coefficient (R 2 ) of 0.77 for Poisson SR and 0.90 for Gaussian SR suggest this method will adequately estimate activity concentration for an unknown solution. Copyright © 2018 Elsevier Ltd. All rights reserved.

Nonlinear Poisson Equation for Heterogeneous Media

PubMed Central

Hu, Langhua; Wei, Guo-Wei

2012-01-01

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. PMID:22947937

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.

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.

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

Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

NASA Astrophysics Data System (ADS)

Huang, Feimin; Li, Tianhong; Yu, Huimin; Yuan, Difan

2018-06-01

We are concerned with the global existence and large time behavior of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile. Moreover, the novelty in this paper is about the unform bound with respect to time for the weak solutions of the isentropic Euler-Poisson system.

Nonlinear Poisson equation for heterogeneous media.

PubMed

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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.

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.

1987-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace-Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil-water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximate boundary generation.

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

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.

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.

Tenth NASTRAN User's Colloquium

NASA Technical Reports Server (NTRS)

1982-01-01

The development of the NASTRAN computer program, a general purpose finite element computer code for structural analysis, was discussed. The application and development of NASTRAN is presented in the following topics: improvements and enhancements; developments of pre and postprocessors; interactive review system; the use of harmonic expansions in magnetic field problems; improving a dynamic model with test data using Linwood; solution of axisymmetric fluid structure interaction problems; large displacements and stability analysis of nonlinear propeller structures; prediction of bead area contact load at the tire wheel interface; elastic plastic analysis of an overloaded breech ring; finite element solution of torsion and other 2-D Poisson equations; new capability for elastic aircraft airloads; usage of substructuring analysis in the get away special program; solving symmetric structures with nonsymmetric loads; evaluation and reduction of errors induced by Guyan transformation.

The scaling of relativistic double-year widths - Poisson-Vlasov solutions and particle-in-cell simulations

NASA Technical Reports Server (NTRS)

Sulkanen, Martin E.; Borovsky, Joseph E.

1992-01-01

The study of relativistic plasma double layers is described through the solution of the one-dimensional, unmagnetized, steady-state Poisson-Vlasov equations and by means of one-dimensional, unmagnetized, particle-in-cell simulations. The thickness vs potential-drop scaling law is extended to relativistic potential drops and relativistic plasma temperatures. The transition in the scaling law for 'strong' double layers suggested by analytical two-beam models by Carlqvist (1982) is confirmed, and causality problems of standard double-layer simulation techniques applied to relativistic plasma systems are discussed.

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.

Evaluation of Shiryaev-Roberts Procedure for On-line Environmental Radiation Monitoring

NASA Astrophysics Data System (ADS)

Watson, Mara Mae

An on-line radiation monitoring system that simultaneously concentrates and detects radioactivity is needed to detect an accidental leakage from a nuclear waste disposal facility or clandestine nuclear activity. Previous studies have shown that classical control chart methods can be applied to on-line radiation monitoring data to quickly detect these events as they occur; however, Bayesian control chart methods were not included in these studies. This work will evaluate the performance of a Bayesian control chart method, the Shiryaev-Roberts (SR) procedure, compared to classical control chart methods, Shewhart 3-sigma and cumulative sum (CUSUM), for use in on-line radiation monitoring of 99Tc in water using extractive scintillating resin. Measurements were collected by pumping solutions containing 0.1-5 Bq/L of 99Tc, as 99T cO4-, through a flow cell packed with extractive scintillating resin coupled to a Beta-RAM Model 5 HPLC detector. While 99T cO4- accumulated on the resin, simultaneous measurements were acquired in 10-s intervals and then re-binned to 100-s intervals. The Bayesian statistical method, Shiryaev-Roberts procedure, and classical control chart methods, Shewhart 3-sigma and cumulative sum (CUSUM), were applied to the data using statistical algorithms developed in MATLAB RTM. Two SR control charts were constructed using Poisson distributions and Gaussian distributions to estimate the likelihood ratio, and are referred to as Poisson SR and Gaussian SR to indicate the distribution used to calculate the statistic. The Poisson and Gaussian SR methods required as little as 28.9 mL less solution at 5 Bq/L and as much as 170 mL less solution at 0.5 Bq/L to exceed the control limit than the Shewhart 3-sigma method. The Poisson SR method needed as little as 6.20 mL less solution at 5 Bq/L and up to 125 mL less solution at 0.5 Bq/L to exceed the control limit than the CUSUM method. The Gaussian SR and CUSUM method required comparable solution volumes for test solutions containing at least 1.5 Bq/L of 99T c. For activity concentrations less than 1.5 Bq/L, the Gaussian SR method required as much as 40.8 mL less solution at 0.5 Bq/L to exceed the control limit than the CUSUM method. Both SR methods were able to consistently detect test solutions containing 0.1 Bq/L, unlike the Shewhart 3-sigma and CUSUM methods. Although the Poisson SR method required as much as 178 mL less solution to exceed the control limit than the Gaussian SR method, the Gaussian SR false positive of 0% was much lower than the Poisson SR false positive rate of 1.14%. A lower false positive rate made it easier to differentiate between a false positive and an increase in mean count rate caused by activity accumulating on the resin. The SR procedure is thus the ideal tool for low-level on-line radiation monitoring using extractive scintillating resin, because it needed less volume in most cases to detect an upward shift in the mean count rate than the Shewhart 3-sigma and CUSUM methods and consistently detected lower activity concentrations. The desired results for the monitoring scheme, however, need to be considered prior to choosing between the Poisson and Gaussian distribution to estimate the likelihood ratio, because each was advantageous under different circumstances. Once the control limit was exceeded, activity concentrations were estimated from the SR control chart using the slope of the control chart on a semi-logarithmic plot. Five of nine test solutions for the Poisson SR control chart produced concentration estimates within 30% of the actual value, but the worst case was 263.2% different than the actual value. The estimations for the Gaussian SR control chart were much more precise, with six of eight solutions producing estimates within 30%. Although the activity concentrations estimations were only mediocre for the Poisson SR control chart and satisfactory for the Gaussian SR control chart, these results demonstrate that a relationship exists between activity concentration and the SR control chart magnitude that can be exploited to determine the activity concentration from the SR control chart. More complex methods should be investigated to improve activity concentration estimations from the SR control charts.

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

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.

The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

Application of zero-inflated poisson mixed models in prognostic factors of hepatitis C.

PubMed

Akbarzadeh Baghban, Alireza; Pourhoseingholi, Asma; Zayeri, Farid; Jafari, Ali Akbar; Alavian, Seyed Moayed

2013-01-01

In recent years, hepatitis C virus (HCV) infection represents a major public health problem. Evaluation of risk factors is one of the solutions which help protect people from the infection. This study aims to employ zero-inflated Poisson mixed models to evaluate prognostic factors of hepatitis C. The data was collected from a longitudinal study during 2005-2010. First, mixed Poisson regression (PR) model was fitted to the data. Then, a mixed zero-inflated Poisson model was fitted with compound Poisson random effects. For evaluating the performance of the proposed mixed model, standard errors of estimators were compared. The results obtained from mixed PR showed that genotype 3 and treatment protocol were statistically significant. Results of zero-inflated Poisson mixed model showed that age, sex, genotypes 2 and 3, the treatment protocol, and having risk factors had significant effects on viral load of HCV patients. Of these two models, the estimators of zero-inflated Poisson mixed model had the minimum standard errors. The results showed that a mixed zero-inflated Poisson model was the almost best fit. The proposed model can capture serial dependence, additional overdispersion, and excess zeros in the longitudinal count data.

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.

Functionally-fitted energy-preserving integrators for Poisson systems

NASA Astrophysics Data System (ADS)

Wang, Bin; Wu, Xinyuan

2018-07-01

In this paper, a new class of energy-preserving integrators is proposed and analysed for Poisson systems by using functionally-fitted technology. The integrators exactly preserve energy and have arbitrarily high order. It is shown that the proposed approach allows us to obtain the energy-preserving methods derived in [12] by Cohen and Hairer (2011) and in [1] by Brugnano et al. (2012) for Poisson systems. Furthermore, we study the sufficient conditions that ensure the existence of a unique solution and discuss the order of the new energy-preserving integrators.

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.

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.

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

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,…

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.

A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems

NASA Astrophysics Data System (ADS)

Liu, Hailiang; Wang, Zhongming

2017-01-01

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.

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.

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.

Properties of the Bivariate Delayed Poisson Process

DTIC Science & Technology

1974-07-01

and Lewis (1972) in their Berkeley Symposium paper and here their analysis of the bivariate Poisson processes (without Poisson noise) is carried... Poisson processes . They cannot, however, be independent Poisson processes because their events are associated in pairs by the displace- ment centres...process because its marginal processes for events of each type are themselves (univariate) Poisson processes . Cox and Lewis (1972) assumed a

Analytical stress intensity solution for the Stable Poisson Loaded specimen

NASA Technical Reports Server (NTRS)

Ghosn, Louis J.; Calomino, Anthony M.; Brewer, David N.

1993-01-01

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-curve determination. The crack mouth opening displacements (CMODs) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMODs, and crack displacement profiles, are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials.

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.

Stability and Physical Accuracy Analysis of the Numerical Solutions to Wigner-Poisson Modeling of Resonant Tunneling Diodes

DTIC Science & Technology

2013-03-22

discrete Wigner function is periodic in momentum space. The periodicity follows from the Fourier transform of the density matrix. The inverse...resonant-tunneling diode . The Green function method has been one of alternatives. Another alternative was to utilize the Wigner function . The Wigner ... function approach to the simulation of a resonant-tunneling diode offers many advantages. In the limit of the classical physics the Wigner equation

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.

Derivation of the Navier-Stokes-Poisson System with Radiation for an Accretion Disk

NASA Astrophysics Data System (ADS)

Ducomet, Bernard; Nečasová, Šárka; Pokorný, Milan; Rodríguez-Bellido, M. Angeles

2018-01-01

We study the 3-D compressible barotropic radiation fluid dynamics system describing the motion of the compressible rotating viscous fluid with gravitation and radiation confined to a straight layer Ω _{ɛ } = ω × (0,ɛ ) , where ω is a 2-D domain. We show that weak solutions in the 3-D domain converge to the strong solution of—the rotating 2-D Navier-Stokes-Poisson system with radiation in ω as ɛ → 0 for all times less than the maximal life time of the strong solution of the 2-D system when the Froude number is small (Fr=O(√{ɛ })) ,—the rotating pure 2-D Navier-Stokes system with radiation in ω as ɛ → 0 when Fr=O(1).

Preconditioner and convergence study for the Quantum Computer Aided Design (QCAD) nonlinear poisson problem posed on the Ottawa Flat 270 design geometry.

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

Kalashnikova, Irina

2012-05-01

A numerical study aimed to evaluate different preconditioners within the Trilinos Ifpack and ML packages for the Quantum Computer Aided Design (QCAD) non-linear Poisson problem implemented within the Albany code base and posed on the Ottawa Flat 270 design geometry is performed. This study led to some new development of Albany that allows the user to select an ML preconditioner with Zoltan repartitioning based on nodal coordinates, which is summarized. Convergence of the numerical solutions computed within the QCAD computational suite with successive mesh refinement is examined in two metrics, the mean value of the solution (an L{sup 1} norm)more » and the field integral of the solution (L{sup 2} norm).« less

Derivation of the Navier-Stokes-Poisson System with Radiation for an Accretion Disk

NASA Astrophysics Data System (ADS)

Ducomet, Bernard; Nečasová, Šárka; Pokorný, Milan; Rodríguez-Bellido, M. Angeles

2018-06-01

We study the 3-D compressible barotropic radiation fluid dynamics system describing the motion of the compressible rotating viscous fluid with gravitation and radiation confined to a straight layer Ω _{ɛ } = ω × (0,ɛ ) , where ω is a 2-D domain. We show that weak solutions in the 3-D domain converge to the strong solution of—the rotating 2-D Navier-Stokes-Poisson system with radiation in ω as ɛ → 0 for all times less than the maximal life time of the strong solution of the 2-D system when the Froude number is small (Fr={O}(√{ɛ })),—the rotating pure 2-D Navier-Stokes system with radiation in ω as ɛ → 0 when Fr={O}(1).

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.

The existence and concentration of positive solutions for a nonlinear Schrödinger-Poisson system with critical growth

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

Zhang, Jianjun

2014-03-15

We consider the Schrödinger-Poisson system: −ε{sup 2}Δu + V(x)u + ϕ(x)u = f(u),−Δϕ = u{sup 2} in R{sup 3}, where the nonlinear term f is of critical growth. In this paper, we construct a solution (u{sub ε}, ϕ{sub ε}) of the above elliptic system, which concentrates at an isolated component of positive locally minimum points of V as ε → 0 under certain conditions on f. In particular, the monotonicity of (f(s))/(s{sup 3}) and the so-called Ambrosetti-Rabinowitz condition are not required.

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.

Quantification of integrated HIV DNA by repetitive-sampling Alu-HIV PCR on the basis of poisson statistics.

PubMed

De Spiegelaere, Ward; Malatinkova, Eva; Lynch, Lindsay; Van Nieuwerburgh, Filip; Messiaen, Peter; O'Doherty, Una; Vandekerckhove, Linos

2014-06-01

Quantification of integrated proviral HIV DNA by repetitive-sampling Alu-HIV PCR is a candidate virological tool to monitor the HIV reservoir in patients. However, the experimental procedures and data analysis of the assay are complex and hinder its widespread use. Here, we provide an improved and simplified data analysis method by adopting binomial and Poisson statistics. A modified analysis method on the basis of Poisson statistics was used to analyze the binomial data of positive and negative reactions from a 42-replicate Alu-HIV PCR by use of dilutions of an integration standard and on samples of 57 HIV-infected patients. Results were compared with the quantitative output of the previously described Alu-HIV PCR method. Poisson-based quantification of the Alu-HIV PCR was linearly correlated with the standard dilution series, indicating that absolute quantification with the Poisson method is a valid alternative for data analysis of repetitive-sampling Alu-HIV PCR data. Quantitative outputs of patient samples assessed by the Poisson method correlated with the previously described Alu-HIV PCR analysis, indicating that this method is a valid alternative for quantifying integrated HIV DNA. Poisson-based analysis of the Alu-HIV PCR data enables absolute quantification without the need of a standard dilution curve. Implementation of the CI estimation permits improved qualitative analysis of the data and provides a statistical basis for the required minimal number of technical replicates. © 2014 The American Association for Clinical Chemistry.

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

Large-Time Behavior of Solutions to Vlasov-Poisson-Fokker-Planck Equations: From Evanescent Collisions to Diffusive Limit

NASA Astrophysics Data System (ADS)

Herda, Maxime; Rodrigues, L. Miguel

2018-03-01

The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates that are uniform with respect to initial data taken in a bounded set of a weighted L^2 space, and where dependencies on the mean-free path τ and the Debye length δ are made explicit. In our analysis the mean free path covers the full range of possible values: from the regime of evanescent collisions τ → ∞ to the strongly collisional regime τ → 0. As a counterpart, the largeness of the Debye length, that enforces a weakly nonlinear regime, is used to close our nonlinear estimates. Accordingly we pay a special attention to relax as much as possible the τ -dependent constraint on δ ensuring exponential decay with explicit τ -dependent rates towards the stationary solution. In the strongly collisional limit τ → 0, we also examine all possible asymptotic regimes selected by a choice of observation time scale. Here also, our emphasis is on strong convergence, uniformity with respect to time and to initial data in bounded sets of a L^2 space. Our proofs rely on a detailed study of the nonlinear elliptic equation defining stationary solutions and a careful tracking and optimization of parameter dependencies of hypocoercive/hypoelliptic estimates.

Determination of Diffusion Coefficients in Cement-Based Materials: An Inverse Problem for the Nernst-Planck and Poisson Models

NASA Astrophysics Data System (ADS)

Szyszkiewicz-Warzecha, Krzysztof; Jasielec, Jerzy J.; Fausek, Janusz; Filipek, Robert

2016-08-01

Transport properties of ions have significant impact on the possibility of rebars corrosion thus the knowledge of a diffusion coefficient is important for reinforced concrete durability. Numerous tests for the determination of diffusion coefficients have been proposed but analysis of some of these tests show that they are too simplistic or even not valid. Hence, more rigorous models to calculate the coefficients should be employed. Here we propose the Nernst-Planck and Poisson equations, which take into account the concentration and electric potential field. Based on this model a special inverse method is presented for determination of a chloride diffusion coefficient. It requires the measurement of concentration profiles or flux on the boundary and solution of the NPP model to define the goal function. Finding the global minimum is equivalent to the determination of diffusion coefficients. Typical examples of the application of the presented method are given.

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)

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

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1983-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Poisson image reconstruction with Hessian Schatten-norm regularization.

PubMed

Lefkimmiatis, Stamatios; Unser, Michael

2013-11-01

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupted by Poisson noise. In this paper, we propose an efficient framework for Poisson image reconstruction, under a regularization approach, which depends on matrix-valued regularization operators. In particular, the employed regularizers involve the Hessian as the regularization operator and Schatten matrix norms as the potential functions. For the solution of the problem, we propose two optimization algorithms that are specifically tailored to the Poisson nature of the noise. These algorithms are based on an augmented-Lagrangian formulation of the problem and correspond to two variants of the alternating direction method of multipliers. Further, we derive a link that relates the proximal map of an l(p) norm with the proximal map of a Schatten matrix norm of order p. This link plays a key role in the development of one of the proposed algorithms. Finally, we provide experimental results on natural and biological images for the task of Poisson image deblurring and demonstrate the practical relevance and effectiveness of the proposed framework.

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

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Existence and uniqueness, attraction for stochastic age-structured population systems with diffusion and Poisson jump

NASA Astrophysics Data System (ADS)

Chen, Huabin

2013-08-01

In this paper, the problems about the existence and uniqueness, attraction for strong solution of stochastic age-structured population systems with diffusion and Poisson jump are considered. Under the non-Lipschitz condition with the Lipschitz condition being considered as a special case, the existence and uniqueness for such systems is firstly proved by using the Burkholder-Davis-Gundy inequality (B-D-G inequality) and Itô's formula. And then by using a novel inequality technique, some sufficient conditions ensuring the existence for the domain of attraction are established. As another by-product, the exponential stability in mean square moment of strong solution for such systems can be also discussed.

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.

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

On the delay analysis of a TDMA channel with finite buffer capacity

NASA Technical Reports Server (NTRS)

Yan, T.-Y.

1982-01-01

The throughput performance of a TDMA channel with finite buffer capacity for transmitting data messages is considered. Each station has limited message buffer capacity and has Poisson message arrivals. Message arrivals will be blocked if the buffers are congested. Using the embedded Markov chain model, the solution procedure for the limiting system-size probabilities is presented in a recursive fashion. Numerical examples are given to demonstrate the tradeoffs between the blocking probabilities and the buffer sizing strategy.

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

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

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.

Electrostatic forces in the Poisson-Boltzmann systems

NASA Astrophysics Data System (ADS)

Xiao, Li; Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2013-09-01

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

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.

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.

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.

Inhomogeneity of the density of Parascaris spp. eggs in faeces of individual foals and the use of hypothesis testing for treatment decision making.

PubMed

Wilkes, E J A; Cowling, A; Woodgate, R G; Hughes, K J

2016-10-15

Faecal egg counts (FEC) are used widely for monitoring of parasite infection in animals, treatment decision-making and estimation of anthelmintic efficacy. When a single count or sample mean is used as a point estimate of the expectation of the egg distribution over some time interval, the variability in the egg density is not accounted for. Although variability, including quantifying sources, of egg count data has been described, the spatiotemporal distribution of nematode eggs in faeces is not well understood. We believe that statistical inference about the mean egg count for treatment decision-making has not been used previously. The aim of this study was to examine the density of Parascaris eggs in solution and faeces and to describe the use of hypothesis testing for decision-making. Faeces from two foals with Parascaris burdens were mixed with magnesium sulphate solution and 30 McMaster chambers were examined to determine the egg distribution in a well-mixed solution. To examine the distribution of eggs in faeces from an individual animal, three faecal piles from a foal with a known Parascaris burden were obtained, from which 81 counts were performed. A single faecal sample was also collected daily from 20 foals on three consecutive days and a FEC was performed on three separate portions of each sample. As appropriate, Poisson or negative binomial confidence intervals for the distribution mean were calculated. Parascaris eggs in a well-mixed solution conformed to a homogeneous Poisson process, while the egg density in faeces was not homogeneous, but aggregated. This study provides an extension from homogeneous to inhomogeneous Poisson processes, leading to an understanding of why Poisson and negative binomial distributions correspondingly provide a good fit for egg count data. The application of one-sided hypothesis tests for decision-making is presented. Copyright © 2016 Elsevier B.V. All rights reserved.

Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution.

PubMed

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

2007-10-07

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface

NASA Astrophysics Data System (ADS)

Coons, Marc P.; Herbert, John M.

2018-06-01

Widely used continuum solvation models for electronic structure calculations, including popular polarizable continuum models (PCMs), usually assume that the continuum environment is isotropic and characterized by a scalar dielectric constant, ɛ. This assumption is invalid at a liquid/vapor interface or any other anisotropic solvation environment. To address such scenarios, we introduce a more general formalism based on solution of Poisson's equation for a spatially varying dielectric function, ɛ(r). Inspired by nonequilibrium versions of PCMs, we develop a similar formalism within the context of Poisson's equation that includes the out-of-equilibrium dielectric response that accompanies a sudden change in the electron density of the solute, such as that which occurs in a vertical ionization process. A multigrid solver for Poisson's equation is developed to accommodate the large spatial grids necessary to discretize the three-dimensional electron density. We apply this methodology to compute vertical ionization energies (VIEs) of various solutes at the air/water interface and compare them to VIEs computed in bulk water, finding only very small differences between the two environments. VIEs computed using approximately two solvation shells of explicit water molecules are in excellent agreement with experiment for F-(aq), Cl-(aq), neat liquid water, and the hydrated electron, although errors for Li+(aq) and Na+(aq) are somewhat larger. Nonequilibrium corrections modify VIEs by up to 1.2 eV, relative to models based only on the static dielectric constant, and are therefore essential to obtain agreement with experiment. Given that the experiments (liquid microjet photoelectron spectroscopy) may be more sensitive to solutes situated at the air/water interface as compared to those in bulk water, our calculations provide some confidence that these experiments can indeed be interpreted as measurements of VIEs in bulk water.

Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface.

PubMed

Coons, Marc P; Herbert, John M

2018-06-14

Widely used continuum solvation models for electronic structure calculations, including popular polarizable continuum models (PCMs), usually assume that the continuum environment is isotropic and characterized by a scalar dielectric constant, ε. This assumption is invalid at a liquid/vapor interface or any other anisotropic solvation environment. To address such scenarios, we introduce a more general formalism based on solution of Poisson's equation for a spatially varying dielectric function, ε(r). Inspired by nonequilibrium versions of PCMs, we develop a similar formalism within the context of Poisson's equation that includes the out-of-equilibrium dielectric response that accompanies a sudden change in the electron density of the solute, such as that which occurs in a vertical ionization process. A multigrid solver for Poisson's equation is developed to accommodate the large spatial grids necessary to discretize the three-dimensional electron density. We apply this methodology to compute vertical ionization energies (VIEs) of various solutes at the air/water interface and compare them to VIEs computed in bulk water, finding only very small differences between the two environments. VIEs computed using approximately two solvation shells of explicit water molecules are in excellent agreement with experiment for F - (aq), Cl - (aq), neat liquid water, and the hydrated electron, although errors for Li + (aq) and Na + (aq) are somewhat larger. Nonequilibrium corrections modify VIEs by up to 1.2 eV, relative to models based only on the static dielectric constant, and are therefore essential to obtain agreement with experiment. Given that the experiments (liquid microjet photoelectron spectroscopy) may be more sensitive to solutes situated at the air/water interface as compared to those in bulk water, our calculations provide some confidence that these experiments can indeed be interpreted as measurements of VIEs in bulk water.

Rayleigh-Sommerfield Diffraction vs Fresnel-Kirchhoff, Fourier Propagation and Poisson's Spot

NASA Technical Reports Server (NTRS)

Lucke, Robert L.

2004-01-01

The boundary conditions imposed on the diffraction problem in order to obtain the Fresnel-Kirchhoff (FK) solution are well-known to be mathematically inconsistent and to be violated by the solution when the observation point is close to the diffracting screen 1-3. These problems are absent in the Rayleigh-Sommerfeld (RS) solution. The difference between RS and FK is in the inclination factor and is usually immaterial because the inclination factor is approximated by unity. But when this approximation is not valid, FK can lead to unacceptable answers. Calculating the on-axis intensity of Poisson s spot provides a critical test, a test passed by RS and failed by FK. FK fails because (a) convergence of the integral depends on how it is evaluated and (b) when the convergence problem is xed, the predicted amplitude at points near the obscuring disk is not consistent with the assumed boundary conditions.

Modeling laser velocimeter signals as triply stochastic Poisson processes

NASA Technical Reports Server (NTRS)

Mayo, W. T., Jr.

1976-01-01

Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

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

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

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.

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

PubMed

Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

2014-02-01

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

Double layers without current

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

Perkins, F.W.; Sun, Y.C.

1980-11-01

The steady-state solution of the nonlinear Vlasov-Poisson equations is reduced to a nonlinear eigenvalue problem for the case of double-layer (potential drop) boundary conditions. Solutions with no relative electron-ion drifts are found. The kinetic stability is discussed. Suggestions for creating these states in experiments and computer simulations are offered.

Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

ERIC Educational Resources Information Center

Fulcher, Lewis P.

1979-01-01

Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance.

PubMed

Poplová, Michaela; Sovka, Pavel; Cifra, Michal

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal.

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance

PubMed Central

Poplová, Michaela; Sovka, Pavel

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal. PMID:29216207

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.

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.

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.

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.

Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions

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

Lu Benzhuo; Holst, Michael J.; Center for Theoretical Biological Physics, University of California San Diego, La Jolla, CA 92093

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised formore » time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.« less

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions

PubMed Central

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

2010-01-01

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems. PMID:21709855

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

PubMed

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

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

Double Fourier Series Solution of Poisson’s Equation on a Sphere.

DTIC Science & Technology

1980-10-29

algebraic systems, the solution of these systems, and the inverse transform of the solution in Fourier space back to physi- cal space. 6. Yee, S. Y. K...Multiply each count in steps (2) through (5) by K] 7. Inverse transform um(0j j = 1, J - 1, to obtain u k; set u(P) = u 0 (P). [K(J - 1) log 2 K

An Elliptic PDE Approach for Shape Characterization

PubMed Central

Haidar, Haissam; Bouix, Sylvain; Levitt, James; McCarley, Robert W.; Shenton, Martha E.; Soul, Janet S.

2009-01-01

This paper presents a novel approach to analyze the shape of anatomical structures. Our methodology is rooted in classical physics and in particular Poisson's equation, a fundamental partial differential equation [1]. The solution to this equation and more specifically its equipotential surfaces display properties that are useful for shape analysis. We present a numerical algorithm to calculate the length of streamlines formed by the gradient field of the solution to this equation for 2D and 3D objects. The length of the streamlines along the equipotential surfaces was used to build a new function which can characterize the shape of objects. We illustrate our method on 2D synthetic and natural shapes as well as 3D medical data. PMID:17271986

Generic buckling curves for specially orthotropic rectangular plates

NASA Technical Reports Server (NTRS)

Brunnelle, E. J.; Oyibo, G. A.

1983-01-01

Using a double affine transformation, the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion. These dual representations are characterized by a single material constant, called the generalized rigidity ratio, whose range is predicted to be the closed interval from 0 to 1 (if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect); when natural boundary conditions are considered a generalized Poisson's ratio is introduced. Thus the buckling results are valid for any specially orthotropic material; hence the curves presented in the text are generic rather than specific. The solution trends are twofold; the buckling coefficients decrease with decreasing generalized rigidity ratio and, when applicable, they decrease with increasing generalized Poisson's ratio. Since the isotropic plate is one limiting case of the above analysis, it is also true that isotropic buckling coefficients decrease with increasing Poission's ratio.

[Application of negative binomial regression and modified Poisson regression in the research of risk factors for injury frequency].

PubMed

Cao, Qingqing; Wu, Zhenqiang; Sun, Ying; Wang, Tiezhu; Han, Tengwei; Gu, Chaomei; Sun, Yehuan

2011-11-01

To Eexplore the application of negative binomial regression and modified Poisson regression analysis in analyzing the influential factors for injury frequency and the risk factors leading to the increase of injury frequency. 2917 primary and secondary school students were selected from Hefei by cluster random sampling method and surveyed by questionnaire. The data on the count event-based injuries used to fitted modified Poisson regression and negative binomial regression model. The risk factors incurring the increase of unintentional injury frequency for juvenile students was explored, so as to probe the efficiency of these two models in studying the influential factors for injury frequency. The Poisson model existed over-dispersion (P < 0.0001) based on testing by the Lagrangemultiplier. Therefore, the over-dispersion dispersed data using a modified Poisson regression and negative binomial regression model, was fitted better. respectively. Both showed that male gender, younger age, father working outside of the hometown, the level of the guardian being above junior high school and smoking might be the results of higher injury frequencies. On a tendency of clustered frequency data on injury event, both the modified Poisson regression analysis and negative binomial regression analysis can be used. However, based on our data, the modified Poisson regression fitted better and this model could give a more accurate interpretation of relevant factors affecting the frequency of injury.

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.

Inverse Jacobi multiplier as a link between conservative systems and Poisson structures

NASA Astrophysics Data System (ADS)

García, Isaac A.; Hernández-Bermejo, Benito

2017-08-01

Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed. From the local point of view, due to the flow-box theorem we restrict ourselves to neighborhoods of singularities. In this sense, we characterize Poisson structures around the typical zero-Hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non-vanishing first jet by connecting with the classical Poincaré center problem. From the global point of view, we connect the property of being strictly conservative (the invariant measure must be positive) with the existence of a Poisson structure depending on the phase space dimension. Finally, weak conservativeness in dimension two is introduced by the extension of inverse Jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed. Examples including Lotka-Volterra systems, quadratic isochronous centers, and non-smooth oscillators are provided.

Elastic properties of rigid fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Chen, J.; Thorpe, M. F.; Davis, L. C.

1995-05-01

We study the elastic properties of rigid fiber-reinforced composites with perfect bonding between fibers and matrix, and also with sliding boundary conditions. In the dilute region, there exists an exact analytical solution. Around the rigidity threshold we find the elastic moduli and Poisson's ratio by decomposing the deformation into a compression mode and a rotation mode. For perfect bonding, both modes are important, whereas only the compression mode is operative for sliding boundary conditions. We employ the digital-image-based method and a finite element analysis to perform computer simulations which confirm our analytical predictions.

Saint-Venant end effects for materials with negative Poisson's ratios

NASA Technical Reports Server (NTRS)

Lakes, R. S.

1992-01-01

Results are presented from an analysis of Saint-Venant end effects for materials with negative Poisson's ratio. Examples are presented showing that slow decay of end stress occurs in circular cylinders of negative Poisson's ratio, whereas a sandwich panel containing rigid face sheets and a compliant core exhibits no anomalous effects for negative Poisson's ratio (but exhibits slow stress decay for core Poisson's ratios approaching 0.5). In sand panels with stiff but not perfectly rigid face sheets, a negative Poisson's ratio results in end stress decay, which is faster than it would be otherwise. It is suggested that the slow decay previously predicted for sandwich strips in plane deformation as a result of the geometry can be mitigated by the use of a negative Poisson's ratio material for the core.

On computations of the integrated space shuttle flowfield using overset grids

NASA Technical Reports Server (NTRS)

Chiu, I-T.; Pletcher, R. H.; Steger, J. L.

1990-01-01

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield.

Integrable particle systems vs solutions to the KP and 2D Toda equations

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

Ruijsenaars, S.N.

Starting from the relation between integrable relativistic N-particle systems with hyperbolic interactions and elementary N-soliton solutions to the KP and 2D Toda equations, we show how fusion properties of the soliton solutions are mirrored by fusion properties of the Poisson commuting particle dynamics. We also obtain previously known relations between elliptic solutions and integrable N-particle systems with elliptic interactions, without invoking finite-gap integration theory. {copyright} 1997 Academic Press, Inc.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Characterizing the performance of the Conway-Maxwell Poisson generalized linear model.

PubMed

Francis, Royce A; Geedipally, Srinivas Reddy; Guikema, Seth D; Dhavala, Soma Sekhar; Lord, Dominique; LaRocca, Sarah

2012-01-01

Count data are pervasive in many areas of risk analysis; deaths, adverse health outcomes, infrastructure system failures, and traffic accidents are all recorded as count events, for example. Risk analysts often wish to estimate the probability distribution for the number of discrete events as part of doing a risk assessment. Traditional count data regression models of the type often used in risk assessment for this problem suffer from limitations due to the assumed variance structure. A more flexible model based on the Conway-Maxwell Poisson (COM-Poisson) distribution was recently proposed, a model that has the potential to overcome the limitations of the traditional model. However, the statistical performance of this new model has not yet been fully characterized. This article assesses the performance of a maximum likelihood estimation method for fitting the COM-Poisson generalized linear model (GLM). The objectives of this article are to (1) characterize the parameter estimation accuracy of the MLE implementation of the COM-Poisson GLM, and (2) estimate the prediction accuracy of the COM-Poisson GLM using simulated data sets. The results of the study indicate that the COM-Poisson GLM is flexible enough to model under-, equi-, and overdispersed data sets with different sample mean values. The results also show that the COM-Poisson GLM yields accurate parameter estimates. The COM-Poisson GLM provides a promising and flexible approach for performing count data regression. © 2011 Society for Risk Analysis.

An investigation of stress wave propagation in a shear deformable nanobeam based on modified couple stress theory

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, Majid; Shariati, Mahmoud

2016-04-01

This paper presents a new investigation for propagation of stress wave in a nanobeam based on modified couple stress theory. Using Euler-Bernoulli beam theory, Timoshenko beam theory, and Reddy beam theory, the effect of shear deformation is investigated. This nonclassical model contains a material length scale parameter to capture the size effect and the Poisson effect is incorporated in the current model. Governing equations of motion are obtained by Hamilton's principle and solved explicitly. This solution leads to obtain two phase velocities for shear deformable beams in different directions. Effects of shear deformation, material length scale parameter, and Poisson's ratio on the behavior of these phase velocities are investigated and discussed. The results also show a dual behavior for phase velocities against Poisson's ratio.

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.; ,

1985-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximative boundary generation. This error evaluation can be used to develop highly accurate CVBEM models of the heat transport process, and the resulting model can be used as a test case for evaluating the precision of domain models based on finite elements or finite differences.

Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

NASA Astrophysics Data System (ADS)

Larmier, Coline; Zoia, Andrea; Malvagi, Fausto; Dumonteil, Eric; Mazzolo, Alain

2018-02-01

Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called 'Poisson Box Sampling', PBS) aimed at improving the accuracy of the CLS approach for transport in d-dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.

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

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.

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.

Understanding poisson regression.

PubMed

Hayat, Matthew J; Higgins, Melinda

2014-04-01

Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes. Copyright 2014, SLACK Incorporated.

An inelastic analysis of a welded aluminum joint

NASA Astrophysics Data System (ADS)

Vaughan, R. E.

1994-09-01

Butt-weld joints are most commonly designed into pressure vessels which then become as reliable as the weakest increment in the weld chain. In practice, weld material properties are determined from tensile test specimen and provided to the stress analyst in the form of a stress versus strain diagram. Variations in properties through the thickness of the weld and along the width of the weld have been suspect but not explored because of inaccessibility and cost. The purpose of this study is to investigate analytical and computational methods used for analysis of welds. The weld specimens are analyzed using classical elastic and plastic theory to provide a basis for modeling the inelastic properties in a finite-element solution. The results of the analysis are compared to experimental data to determine the weld behavior and the accuracy of prediction methods. The weld considered in this study is a multiple-pass aluminum 2219-T87 butt weld with thickness of 1.40 in. The weld specimen is modeled using the finite-element code ABAQUS. The finite-element model is used to produce the stress-strain behavior in the elastic and plastic regimes and to determine Poisson's ratio in the plastic region. The value of Poisson's ratio in the plastic regime is then compared to experimental data. The results of the comparisons are used to explain multipass weld behavior and to make recommendations concerning the analysis and testing of welds.

An inelastic analysis of a welded aluminum joint

NASA Technical Reports Server (NTRS)

Vaughan, R. E.

1994-01-01

Butt-weld joints are most commonly designed into pressure vessels which then become as reliable as the weakest increment in the weld chain. In practice, weld material properties are determined from tensile test specimen and provided to the stress analyst in the form of a stress versus strain diagram. Variations in properties through the thickness of the weld and along the width of the weld have been suspect but not explored because of inaccessibility and cost. The purpose of this study is to investigate analytical and computational methods used for analysis of welds. The weld specimens are analyzed using classical elastic and plastic theory to provide a basis for modeling the inelastic properties in a finite-element solution. The results of the analysis are compared to experimental data to determine the weld behavior and the accuracy of prediction methods. The weld considered in this study is a multiple-pass aluminum 2219-T87 butt weld with thickness of 1.40 in. The weld specimen is modeled using the finite-element code ABAQUS. The finite-element model is used to produce the stress-strain behavior in the elastic and plastic regimes and to determine Poisson's ratio in the plastic region. The value of Poisson's ratio in the plastic regime is then compared to experimental data. The results of the comparisons are used to explain multipass weld behavior and to make recommendations concerning the analysis and testing of welds.

Physically consistent data assimilation method based on feedback control for patient-specific blood flow analysis.

PubMed

Ii, Satoshi; Adib, Mohd Azrul Hisham Mohd; Watanabe, Yoshiyuki; Wada, Shigeo

2018-01-01

This paper presents a novel data assimilation method for patient-specific blood flow analysis based on feedback control theory called the physically consistent feedback control-based data assimilation (PFC-DA) method. In the PFC-DA method, the signal, which is the residual error term of the velocity when comparing the numerical and reference measurement data, is cast as a source term in a Poisson equation for the scalar potential field that induces flow in a closed system. The pressure values at the inlet and outlet boundaries are recursively calculated by this scalar potential field. Hence, the flow field is physically consistent because it is driven by the calculated inlet and outlet pressures, without any artificial body forces. As compared with existing variational approaches, although this PFC-DA method does not guarantee the optimal solution, only one additional Poisson equation for the scalar potential field is required, providing a remarkable improvement for such a small additional computational cost at every iteration. Through numerical examples for 2D and 3D exact flow fields, with both noise-free and noisy reference data as well as a blood flow analysis on a cerebral aneurysm using actual patient data, the robustness and accuracy of this approach is shown. Moreover, the feasibility of a patient-specific practical blood flow analysis is demonstrated. Copyright © 2017 John Wiley & Sons, Ltd.

Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis.

PubMed

Armstrong, Ben G; Gasparrini, Antonio; Tobias, Aurelio

2014-11-24

The time stratified case cross-over approach is a popular alternative to conventional time series regression for analysing associations between time series of environmental exposures (air pollution, weather) and counts of health outcomes. These are almost always analyzed using conditional logistic regression on data expanded to case-control (case crossover) format, but this has some limitations. In particular adjusting for overdispersion and auto-correlation in the counts is not possible. It has been established that a Poisson model for counts with stratum indicators gives identical estimates to those from conditional logistic regression and does not have these limitations, but it is little used, probably because of the overheads in estimating many stratum parameters. The conditional Poisson model avoids estimating stratum parameters by conditioning on the total event count in each stratum, thus simplifying the computing and increasing the number of strata for which fitting is feasible compared with the standard unconditional Poisson model. Unlike the conditional logistic model, the conditional Poisson model does not require expanding the data, and can adjust for overdispersion and auto-correlation. It is available in Stata, R, and other packages. By applying to some real data and using simulations, we demonstrate that conditional Poisson models were simpler to code and shorter to run than are conditional logistic analyses and can be fitted to larger data sets than possible with standard Poisson models. Allowing for overdispersion or autocorrelation was possible with the conditional Poisson model but when not required this model gave identical estimates to those from conditional logistic regression. Conditional Poisson regression models provide an alternative to case crossover analysis of stratified time series data with some advantages. The conditional Poisson model can also be used in other contexts in which primary control for confounding is by fine stratification.

A Generalized QMRA Beta-Poisson Dose-Response Model.

PubMed

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2016-10-01

Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single-hit dose-response models are the most commonly used dose-response models in QMRA. Denoting PI(d) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, PI(d|α,β,r*), is proposed in which the minimum number of organisms required for causing infection, K min , is not fixed, but a random variable following a geometric distribution with parameter 0

Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels

PubMed Central

SINGER, A.; GILLESPIE, D.; NORBURY, J.; EISENBERG, R. S.

2009-01-01

Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst–Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current–voltage (I–V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I–V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages). PMID:19809600

Poisson Regression Analysis of Illness and Injury Surveillance Data

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

Frome E.L., Watkins J.P., Ellis E.D.

2012-12-12

The Department of Energy (DOE) uses illness and injury surveillance to monitor morbidity and assess the overall health of the work force. Data collected from each participating site include health events and a roster file with demographic information. The source data files are maintained in a relational data base, and are used to obtain stratified tables of health event counts and person time at risk that serve as the starting point for Poisson regression analysis. The explanatory variables that define these tables are age, gender, occupational group, and time. Typical response variables of interest are the number of absences duemore » to illness or injury, i.e., the response variable is a count. Poisson regression methods are used to describe the effect of the explanatory variables on the health event rates using a log-linear main effects model. Results of fitting the main effects model are summarized in a tabular and graphical form and interpretation of model parameters is provided. An analysis of deviance table is used to evaluate the importance of each of the explanatory variables on the event rate of interest and to determine if interaction terms should be considered in the analysis. Although Poisson regression methods are widely used in the analysis of count data, there are situations in which over-dispersion occurs. This could be due to lack-of-fit of the regression model, extra-Poisson variation, or both. A score test statistic and regression diagnostics are used to identify over-dispersion. A quasi-likelihood method of moments procedure is used to evaluate and adjust for extra-Poisson variation when necessary. Two examples are presented using respiratory disease absence rates at two DOE sites to illustrate the methods and interpretation of the results. In the first example the Poisson main effects model is adequate. In the second example the score test indicates considerable over-dispersion and a more detailed analysis attributes the over-dispersion to extra-Poisson variation. The R open source software environment for statistical computing and graphics is used for analysis. Additional details about R and the data that were used in this report are provided in an Appendix. Information on how to obtain R and utility functions that can be used to duplicate results in this report are provided.« less

Poisson Mixture Regression Models for Heart Disease Prediction.

PubMed

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

Poisson Mixture Regression Models for Heart Disease Prediction

PubMed Central

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

NASA Astrophysics Data System (ADS)

Camporeale, E.; Delzanno, G. L.; Bergen, B. K.; Moulton, J. D.

2016-01-01

We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

Minimum risk wavelet shrinkage operator for Poisson image denoising.

PubMed

Cheng, Wu; Hirakawa, Keigo

2015-05-01

The pixel values of images taken by an image sensor are said to be corrupted by Poisson noise. To date, multiscale Poisson image denoising techniques have processed Haar frame and wavelet coefficients--the modeling of coefficients is enabled by the Skellam distribution analysis. We extend these results by solving for shrinkage operators for Skellam that minimizes the risk functional in the multiscale Poisson image denoising setting. The minimum risk shrinkage operator of this kind effectively produces denoised wavelet coefficients with minimum attainable L2 error.

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

Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

NASA Astrophysics Data System (ADS)

Costiner, Sorin; Ta'asan, Shlomo

1995-07-01

Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

Poincaré chaos and unpredictable functions

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2017-07-01

The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.

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.

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.

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.

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.

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

Electrolyte solutions at curved electrodes. I. Mesoscopic approach

NASA Astrophysics Data System (ADS)

Reindl, Andreas; Bier, Markus; Dietrich, S.

2017-04-01

Within the Poisson-Boltzmann approach, electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance C on the surface charge density σ and the ionic strength I are examined as a function of the wall curvature. The surface charge density has a strong effect on the capacitance for small curvatures, whereas for large curvatures the behavior becomes independent of σ. An expansion for small curvatures gives rise to capacitance coefficients which depend only on a single parameter, allowing for a convenient analysis. The universal behavior at large curvatures can be captured by an analytic expression.

Theory of the formation of the electric double layer at the ion exchange membrane-solution interface.

PubMed

Moya, A A

2015-02-21

This work aims to extend the study of the formation of the electric double layer at the interface defined by a solution and an ion-exchange membrane on the basis of the Nernst-Planck and Poisson equations, including different values of the counter-ion diffusion coefficient and the dielectric constant in the solution and membrane phases. The network simulation method is used to obtain the time evolution of the electric potential, the displacement electric vector, the electric charge density and the ionic concentrations at the interface between a binary electrolyte solution and a cation-exchange membrane with total co-ion exclusion. The numerical results for the temporal evolution of the interfacial electric potential and the surface electric charge are compared with analytical solutions derived in the limit of the shortest times by considering the Poisson equation for a simple cationic diffusion process. The steady-state results are justified from the Gouy-Chapman theory for the diffuse double layer in the limits of similar and high bathing ionic concentrations with respect to the fixed-charge concentration inside the membrane. Interesting new physical insights arise from the interpretation of the process of the formation of the electric double layer at the ion exchange membrane-solution interface on the basis of a membrane model with total co-ion exclusion.

Bayesian analysis of volcanic eruptions

NASA Astrophysics Data System (ADS)

Ho, Chih-Hsiang

1990-10-01

The simple Poisson model generally gives a good fit to many volcanoes for volcanic eruption forecasting. Nonetheless, empirical evidence suggests that volcanic activity in successive equal time-periods tends to be more variable than a simple Poisson with constant eruptive rate. An alternative model is therefore examined in which eruptive rate(λ) for a given volcano or cluster(s) of volcanoes is described by a gamma distribution (prior) rather than treated as a constant value as in the assumptions of a simple Poisson model. Bayesian analysis is performed to link two distributions together to give the aggregate behavior of the volcanic activity. When the Poisson process is expanded to accomodate a gamma mixing distribution on λ, a consequence of this mixed (or compound) Poisson model is that the frequency distribution of eruptions in any given time-period of equal length follows the negative binomial distribution (NBD). Applications of the proposed model and comparisons between the generalized model and simple Poisson model are discussed based on the historical eruptive count data of volcanoes Mauna Loa (Hawaii) and Etna (Italy). Several relevant facts lead to the conclusion that the generalized model is preferable for practical use both in space and time.

Elasticity of α-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio

NASA Astrophysics Data System (ADS)

Yeganeh-Haeri, Amir; Weidner, Donald J.; Parise, John B.

1992-07-01

Laser Brillouin spectroscopy was used to determine the adiabatic single-crystal elastic stiffness coefficients of silicon dioxide (SiO_2) in the α-cristobalite structure. This SiO_2 polymorph, unlike other silicas and silicates, exhibits a negative Poisson's ratio; α-cristobalite contracts laterally when compressed and expands laterally when stretched. Tensorial analysis of the elastic coefficients shows that Poisson's ratio reaches a maximum value of -0.5 in some directions, whereas averaged values for the single-phased aggregate yield a Poisson's ratio of -0.16.

Questionable Validity of Poisson Assumptions in a Combined Loglinear/MDS Mapping Model.

ERIC Educational Resources Information Center

Gleason, John M.

1993-01-01

This response to an earlier article on a combined log-linear/MDS model for mapping journals by citation analysis discusses the underlying assumptions of the Poisson model with respect to characteristics of the citation process. The importance of empirical data analysis is also addressed. (nine references) (LRW)

Background stratified Poisson regression analysis of cohort data.

PubMed

Richardson, David B; Langholz, Bryan

2012-03-01

Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models.

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.

Ion flux through membrane channels--an enhanced algorithm for the Poisson-Nernst-Planck model.

PubMed

Dyrka, Witold; Augousti, Andy T; Kotulska, Malgorzata

2008-09-01

A novel algorithmic scheme for numerical solution of the 3D Poisson-Nernst-Planck model is proposed. The algorithmic improvements are universal and independent of the detailed physical model. They include three major steps: an adjustable gradient-based step value, an adjustable relaxation coefficient, and an optimized segmentation of the modeled space. The enhanced algorithm significantly accelerates the speed of computation and reduces the computational demands. The theoretical model was tested on a regular artificial channel and validated on a real protein channel-alpha-hemolysin, proving its efficiency. (c) 2008 Wiley Periodicals, Inc.

Theory of multicolor lattice gas - A cellular automaton Poisson solver

NASA Technical Reports Server (NTRS)

Chen, H.; Matthaeus, W. H.; Klein, L. W.

1990-01-01

The present class of models for cellular automata involving a quiescent hydrodynamic lattice gas with multiple-valued passive labels termed 'colors', the lattice collisions change individual particle colors while preserving net color. The rigorous proofs of the multicolor lattice gases' essential features are rendered more tractable by an equivalent subparticle representation in which the color is represented by underlying two-state 'spins'. Schemes for the introduction of Dirichlet and Neumann boundary conditions are described, and two illustrative numerical test cases are used to verify the theory. The lattice gas model is equivalent to a Poisson equation solution.

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.

New method for blowup of the Euler-Poisson system

NASA Astrophysics Data System (ADS)

Kwong, Man Kam; Yuen, Manwai

2016-08-01

In this paper, we provide a new method for establishing the blowup of C2 solutions for the pressureless Euler-Poisson system with attractive forces for RN (N ≥ 2) with ρ(0, x0) > 0 and Ω 0 i j ( x 0 ) = /1 2 [" separators=" ∂ i u j ( 0 , x 0 ) - ∂ j u i ( 0 , x 0 ) ] = 0 at some point x0 ∈ RN. By applying the generalized Hubble transformation div u ( t , x 0 ( t ) ) = /N a ˙ ( t ) a ( t ) to a reduced Riccati differential inequality derived from the system, we simplify the inequality into the Emden equation a ̈ ( t ) = - /λ a ( t ) N - 1 , a ( 0 ) = 1 , a ˙ ( 0 ) = /div u ( 0 , x 0 ) N . Known results on its blowup set allow us to easily obtain the blowup conditions of the Euler-Poisson system.

Mixed Poisson distributions in exact solutions of stochastic autoregulation models.

PubMed

Iyer-Biswas, Srividya; Jayaprakash, C

2014-11-01

In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of autoactivation and autoinhibition. Using the Poisson representation, a technique whose particular usefulness in the context of nonlinear gene regulation models we elucidate, we find exact results for these feedback models in the steady state. Further, we exploit this representation to analyze the parameter spaces of each model, determine which dimensionless combinations of rates are the shape determinants for each distribution, and thus demarcate where in the parameter space qualitatively different behaviors arise. These behaviors include power-law-tailed distributions, bimodal distributions, and sub-Poisson distributions. We also show how these distribution shapes change when the strength of the feedback is tuned. Using our results, we reexamine how well the autoinhibition and autoactivation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation, respectively.

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

PB-AM: An open-source, fully analytical linear poisson-boltzmann solver.

PubMed

Felberg, Lisa E; Brookes, David H; Yap, Eng-Hui; Jurrus, Elizabeth; Baker, Nathan A; Head-Gordon, Teresa

2017-06-05

We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized PB equation, for molecules represented as non-overlapping spherical cavities. The PB-AM software package includes the generation of outputs files appropriate for visualization using visual molecular dynamics, 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-Boltzmann 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. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Leveraging the Cloud for Integrated Network Experimentation

DTIC Science & Technology

2014-03-01

kernel settings, or any of the low-level subcomponents. 3. Scalable Solutions: Businesses can build scalable solutions for their clients , ranging from...values. These values 13 can assume several distributions that include normal, Pareto , uniform, exponential and Poisson, among others [21]. Additionally, D...communication, the web client establishes a connection to the server before traffic begins to flow. Web servers do not initiate connections to clients in

Concentration Dependent Physical Properties of Ge1-xSnx Solid Solution

NASA Astrophysics Data System (ADS)

Jivani, A. R.; Jani, A. R.

2011-12-01

Our own proposed potential is used to investigate few physical properties like total energy, bulk modulus, pressure derivative of bulk modulus, elastic constants, pressure derivative of elastic constants, Poisson's ratio and Young's modulus of Ge1-xSnx solid solution with x is atomic concentration of α-Sn. The potential combines linear plus quadratic types of electron-ion interaction. First time screening function proposed by Sarkar et al is used to investigate the properties of the Ge-Sn solid solution system.

Bayesian Poisson hierarchical models for crash data analysis: Investigating the impact of model choice on site-specific predictions.

PubMed

Khazraee, S Hadi; Johnson, Valen; Lord, Dominique

2018-08-01

The Poisson-gamma (PG) and Poisson-lognormal (PLN) regression models are among the most popular means for motor vehicle crash data analysis. Both models belong to the Poisson-hierarchical family of models. While numerous studies have compared the overall performance of alternative Bayesian Poisson-hierarchical models, little research has addressed the impact of model choice on the expected crash frequency prediction at individual sites. This paper sought to examine whether there are any trends among candidate models predictions e.g., that an alternative model's prediction for sites with certain conditions tends to be higher (or lower) than that from another model. In addition to the PG and PLN models, this research formulated a new member of the Poisson-hierarchical family of models: the Poisson-inverse gamma (PIGam). Three field datasets (from Texas, Michigan and Indiana) covering a wide range of over-dispersion characteristics were selected for analysis. This study demonstrated that the model choice can be critical when the calibrated models are used for prediction at new sites, especially when the data are highly over-dispersed. For all three datasets, the PIGam model would predict higher expected crash frequencies than would the PLN and PG models, in order, indicating a clear link between the models predictions and the shape of their mixing distributions (i.e., gamma, lognormal, and inverse gamma, respectively). The thicker tail of the PIGam and PLN models (in order) may provide an advantage when the data are highly over-dispersed. The analysis results also illustrated a major deficiency of the Deviance Information Criterion (DIC) in comparing the goodness-of-fit of hierarchical models; models with drastically different set of coefficients (and thus predictions for new sites) may yield similar DIC values, because the DIC only accounts for the parameters in the lowest (observation) level of the hierarchy and ignores the higher levels (regression coefficients). Copyright © 2018. Published by Elsevier Ltd.

AQUEOUS PROTONATION PROPERTIES OF AMPHOTERIC NANOPARTICLES

EPA Science Inventory

A divergence is predicted between the acidity behavior of charged sites on micron sized colloidal particles and nanoparticles. Utilizing the approximate analytical solution to the Poisson-Boltzmann equation published by Ohshima et al. (1982), findings from the work included: 1):...

A meta-model analysis of a finite element simulation for defining poroelastic properties of intervertebral discs.

PubMed

Nikkhoo, Mohammad; Hsu, Yu-Chun; Haghpanahi, Mohammad; Parnianpour, Mohamad; Wang, Jaw-Lin

2013-06-01

Finite element analysis is an effective tool to evaluate the material properties of living tissue. For an interactive optimization procedure, the finite element analysis usually needs many simulations to reach a reasonable solution. The meta-model analysis of finite element simulation can be used to reduce the computation of a structure with complex geometry or a material with composite constitutive equations. The intervertebral disc is a complex, heterogeneous, and hydrated porous structure. A poroelastic finite element model can be used to observe the fluid transferring, pressure deviation, and other properties within the disc. Defining reasonable poroelastic material properties of the anulus fibrosus and nucleus pulposus is critical for the quality of the simulation. We developed a material property updating protocol, which is basically a fitting algorithm consisted of finite element simulations and a quadratic response surface regression. This protocol was used to find the material properties, such as the hydraulic permeability, elastic modulus, and Poisson's ratio, of intact and degenerated porcine discs. The results showed that the in vitro disc experimental deformations were well fitted with limited finite element simulations and a quadratic response surface regression. The comparison of material properties of intact and degenerated discs showed that the hydraulic permeability significantly decreased but Poisson's ratio significantly increased for the degenerated discs. This study shows that the developed protocol is efficient and effective in defining material properties of a complex structure such as the intervertebral disc.

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

NASA Technical Reports Server (NTRS)

Baker, A. J.

1982-01-01

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

LIMEPY: Lowered Isothermal Model Explorer in PYthon

NASA Astrophysics Data System (ADS)

Gieles, Mark; Zocchi, Alice

2017-10-01

LIMEPY solves distribution function (DF) based lowered isothermal models. It solves Poisson's equation used on input parameters and offers fast solutions for isotropic/anisotropic, single/multi-mass models, normalized DF values, density and velocity moments, projected properties, and generates discrete samples.

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.

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.

Improved Denoising via Poisson Mixture Modeling of Image Sensor Noise.

PubMed

Zhang, Jiachao; Hirakawa, Keigo

2017-04-01

This paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs. A quantile analysis in pixel, wavelet transform, and variance stabilization domains reveal that the tails of Poisson, signal-dependent Gaussian, and Poisson-Gaussian models are too short to capture real sensor noise behavior. A new Poisson mixture noise model is proposed to correct the mismatch of tail behavior. Based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data, we propose a mixture of Poisson denoising method to remove the denoising artifacts without affecting image details, such as edge and textures. Experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique.

Hierarchical Approach to 'Atomistic' 3-D MOSFET Simulation

NASA Technical Reports Server (NTRS)

Asenov, Asen; Brown, Andrew R.; Davies, John H.; Saini, Subhash

1999-01-01

We present a hierarchical approach to the 'atomistic' simulation of aggressively scaled sub-0.1 micron MOSFET's. These devices are so small that their characteristics depend on the precise location of dopant atoms within them, not just on their average density. A full-scale three-dimensional drift-diffusion atomistic simulation approach is first described and used to verify more economical, but restricted, options. To reduce processor time and memory requirements at high drain voltage, we have developed a self-consistent option based on a solution of the current continuity equation restricted to a thin slab of the channel. This is coupled to the solution of the Poisson equation in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison to the full self-consistent solution. At low drain voltage, a single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. In this case, the current is calculated by solving the current continuity equation in a drift approximation only, also in a thin slab containing the MOSFET channel. The regions of applicability for the different components of this hierarchical approach are illustrated in example simulations covering the random dopant-induced threshold voltage fluctuations, threshold voltage lowering, threshold voltage asymmetry, and drain current fluctuations.

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

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.

Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.

PubMed

Khazraee, S Hadi; Sáez-Castillo, Antonio Jose; Geedipally, Srinivas Reddy; Lord, Dominique

2015-05-01

The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model. © 2014 Society for Risk Analysis.

Reference analysis of the signal + background model in counting experiments

NASA Astrophysics Data System (ADS)

Casadei, D.

2012-01-01

The model representing two independent Poisson processes, labelled as ``signal'' and ``background'' and both contributing additively to the total number of counted events, is considered from a Bayesian point of view. This is a widely used model for the searches of rare or exotic events in presence of a background source, as for example in the searches performed by high-energy physics experiments. In the assumption of prior knowledge about the background yield, a reference prior is obtained for the signal alone and its properties are studied. Finally, the properties of the full solution, the marginal reference posterior, are illustrated with few examples.

Analysis of the Poisson-Nernst-Planck equation in a ball for modeling the Voltage-Current relation in neurobiological microdomains

NASA Astrophysics Data System (ADS)

Cartailler, J.; Schuss, Z.; Holcman, D.

2017-01-01

The electro-diffusion of ions is often described by the Poisson-Nernst-Planck (PNP) equations, which couple nonlinearly the charge concentration and the electric potential. This model is used, among others, to describe the motion of ions in neuronal micro-compartments. It remains at this time an open question how to determine the relaxation and the steady state distribution of voltage when an initial charge of ions is injected into a domain bounded by an impermeable dielectric membrane. The purpose of this paper is to construct an asymptotic approximation to the solution of the stationary PNP equations in a d-dimensional ball (d = 1 , 2 , 3) in the limit of large total charge. In this geometry the PNP system reduces to the Liouville-Gelfand-Bratú (LGB) equation, with the difference that the boundary condition is Neumann, not Dirichlet, and there is a minus sign in the exponent of the exponential term. The entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. These differences replace attraction by repulsion in the LGB equation, thus completely changing the solution. We find that the voltage is maximal in the center and decreases toward the boundary. We also find that the potential drop between the center and the surface increases logarithmically in the total number of charges and not linearly, as in classical capacitance theory. This logarithmic singularity is obtained for d = 3 from an asymptotic argument and cannot be derived from the analysis of the phase portrait. These results are used to derive the relation between the outward current and the voltage in a dendritic spine, which is idealized as a dielectric sphere connected smoothly to the nerve axon by a narrow neck. This is a fundamental microdomain involved in neuronal communication. We compute the escape rate of an ion from the steady density in a ball, which models a neuronal spine head, to a small absorbing window in the sphere. We predict that the current is defined by the narrow neck that is connected to the sphere by a small absorbing window, as suggested by the narrow escape theory, while voltage is controlled by the PNP equations independently of the neck.

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.

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.

Sparse Poisson noisy image deblurring.

PubMed

Carlavan, Mikael; Blanc-Féraud, Laure

2012-04-01

Deblurring noisy Poisson images has recently been a subject of an increasing amount of works in many areas such as astronomy and biological imaging. In this paper, we focus on confocal microscopy, which is a very popular technique for 3-D imaging of biological living specimens that gives images with a very good resolution (several hundreds of nanometers), although degraded by both blur and Poisson noise. Deconvolution methods have been proposed to reduce these degradations, and in this paper, we focus on techniques that promote the introduction of an explicit prior on the solution. One difficulty of these techniques is to set the value of the parameter, which weights the tradeoff between the data term and the regularizing term. Only few works have been devoted to the research of an automatic selection of this regularizing parameter when considering Poisson noise; therefore, it is often set manually such that it gives the best visual results. We present here two recent methods to estimate this regularizing parameter, and we first propose an improvement of these estimators, which takes advantage of confocal images. Following these estimators, we secondly propose to express the problem of the deconvolution of Poisson noisy images as the minimization of a new constrained problem. The proposed constrained formulation is well suited to this application domain since it is directly expressed using the antilog likelihood of the Poisson distribution and therefore does not require any approximation. We show how to solve the unconstrained and constrained problems using the recent alternating-direction technique, and we present results on synthetic and real data using well-known priors, such as total variation and wavelet transforms. Among these wavelet transforms, we specially focus on the dual-tree complex wavelet transform and on the dictionary composed of curvelets and an undecimated wavelet transform.

Topographical variation of the elastic properties of articular cartilage in the canine knee.

PubMed

Jurvelin, J S; Arokoski, J P; Hunziker, E B; Helminen, H J

2000-06-01

Equilibrium response of articular cartilage to indentation loading is controlled by the thickness (h) and elastic properties (shear modulus, mu, and Poisson's ratio, nu) of the tissue. In this study, we characterized topographical variation of Poisson's ratio of the articular cartilage in the canine knee joint (N=6). Poisson's ratio was measured using a microscopic technique. In this technique, the shape change of the cartilage disk was visualized while the cartilage was immersed in physiological solution and compressed in unconfined geometry. After a constant 5% axial strain, the lateral strain was measured during stress relaxation. At equilibrium, the lateral-to-axial strain ratio indicates the Poisson's ratio of the tissue. Indentation (equilibrium) data from our prior study (Arokoski et al., 1994. International Journal of Sports Medicine 15, 254-260) was re-analyzed using the Poisson's ratio results at the test site to derive values for shear and aggregate moduli. The lowest Poisson's ratio (0.070+/-0.016) located at the patellar surface of femur (FPI) and the highest (0.236+/-0.026) at the medial tibial plateau (TMI). The stiffest cartilage was found at the patellar groove of femur (micro=0.964+/-0.189MPa, H(a)=2.084+/-0. 409MPa) and the softest at the tibial plateaus (micro=0.385+/-0. 062MPa, H(a)=1.113+/-0.141MPa). Comparison of the mechanical results and the biochemical composition of the tissue (Jurvelin et al., 1988. Engineering in Medicine 17, 157-162) at the matched sites of the canine knee joint indicated a negative correlation between the Poisson's ratio and collagen-to-PG content ratio. This is in harmony with our previous findings which suggested that, in unconfined compression, the degree of lateral expansion in different tissue zones is related to collagen-to-PG ratio of the zone.

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.

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.

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.

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.

Explicitly Representing the Solvation Shell in Continuum Solvent Calculations

PubMed Central

Svendsen, Hallvard F.; Merz, Kenneth M.

2009-01-01

A method is presented to explicitly represent the first solvation shell in continuum solvation calculations. Initial solvation shell geometries were generated with classical molecular dynamics simulations. Clusters consisting of solute and 5 solvent molecules were fully relaxed in quantum mechanical calculations. The free energy of solvation of the solute was calculated from the free energy of formation of the cluster and the solvation free energy of the cluster calculated with continuum solvation models. The method has been implemented with two continuum solvation models, a Poisson-Boltzmann model and the IEF-PCM model. Calculations were carried out for a set of 60 ionic species. Implemented with the Poisson-Boltzmann model the method gave an unsigned average error of 2.1 kcal/mol and a RMSD of 2.6 kcal/mol for anions, for cations the unsigned average error was 2.8 kcal/mol and the RMSD 3.9 kcal/mol. Similar results were obtained with the IEF-PCM model. PMID:19425558

Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps

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

Di Nunno, Giulia, E-mail: giulian@math.uio.no; Khedher, Asma, E-mail: asma.khedher@tum.de; Vanmaele, Michèle, E-mail: michele.vanmaele@ugent.be

We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate-approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure withmore » infinite activity and models in which these small variations are modeled with a Brownian motion or are cut off. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the approximation of the market prices and we derive an estimation of the model risk.« less

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.

The electric double layer at a metal electrode in pure water

NASA Astrophysics Data System (ADS)

Brüesch, Peter; Christen, Thomas

2004-03-01

Pure water is a weak electrolyte that dissociates into hydronium ions and hydroxide ions. In contact with a charged electrode a double layer forms for which neither experimental nor theoretical studies exist, in contrast to electrolytes containing extrinsic ions like acids, bases, and solute salts. Starting from a self-consistent solution of the one-dimensional modified Poisson-Boltzmann equation, which takes into account activity coefficients of point-like ions, we explore the properties of the electric double layer by successive incorporation of various correction terms like finite ion size, polarization, image charge, and field dissociation. We also discuss the effect of the usual approximation of an average potential as required for the one-dimensional Poisson-Boltzmann equation, and conclude that the one-dimensional approximation underestimates the ion density. We calculate the electric potential, the ion distributions, the pH-values, the ion-size corrected activity coefficients, and the dissociation constants close to the electric double layer and compare the results for the various model corrections.

Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models.

PubMed

Li, Bo; Zhao, Yanxiang

2013-01-01

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.

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.

Testing a Poisson Counter Model for Visual Identification of Briefly Presented, Mutually Confusable Single Stimuli in Pure Accuracy Tasks

ERIC Educational Resources Information Center

Kyllingsbaek, Soren; Markussen, Bo; Bundesen, Claus

2012-01-01

The authors propose and test a simple model of the time course of visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks. The model implies that during stimulus analysis, tentative categorizations that stimulus i belongs to category j are made at a constant Poisson rate, v(i, j). The analysis is…

Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.

PubMed

Hougaard, P; Lee, M L; Whitmore, G A

1997-12-01

Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

Poisson structure on a space with linear SU(2) fuzziness

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Fatollahi, Amir H.; Shariati, Ahmad

2009-07-01

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum as well as the Euler parametrization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.

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

A Hands-on Activity for Teaching the Poisson Distribution Using the Stock Market

ERIC Educational Resources Information Center

Dunlap, Mickey; Studstill, Sharyn

2014-01-01

The number of increases a particular stock makes over a fixed period follows a Poisson distribution. This article discusses using this easily-found data as an opportunity to let students become involved in the data collection and analysis process.

Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo.

PubMed

Schmidt, Philip J; Pintar, Katarina D M; Fazil, Aamir M; Topp, Edward

2013-09-01

Dose-response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose-response model parameters are estimated using limited epidemiological data is rarely quantified. Second-order risk characterization approaches incorporating uncertainty in dose-response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta-Poisson dose-response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta-Poisson dose-response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta-Poisson dose-response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta-Poisson model are proposed, and simple algorithms to evaluate actual beta-Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta-Poisson dose-response model parameters is attributable to the absence of low-dose data. This region includes beta-Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility. © Her Majesty the Queen in Right of Canada 2013. Reproduced with the permission of the Minister of the Public Health Agency of Canada.

A geometric multigrid preconditioning strategy for DPG system matrices

DOE PAGES

Roberts, Nathan V.; Chan, Jesse

2017-08-23

Here, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan (2010, 2011) guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general – though there are some results for Poisson, e.g.– is how best to precondition the DPG system matrix, so that iterative solvers may be used to allow solution of large-scale problems.

Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution.

PubMed

Chang, Chien C; Kuo, Chih-Yu; Wang, Chang-Yi

2011-11-01

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.

PubMed

Ahmadi, S M; Campoli, G; Amin Yavari, S; Sajadi, B; Wauthle, R; Schrooten, J; Weinans, H; Zadpoor, A A

2014-06-01

Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations. Copyright © 2014 Elsevier Ltd. All rights reserved.

Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes.

PubMed

Lord, Dominique; Guikema, Seth D; Geedipally, Srinivas Reddy

2008-05-01

This paper documents the application of the Conway-Maxwell-Poisson (COM-Poisson) generalized linear model (GLM) for modeling motor vehicle crashes. The COM-Poisson distribution, originally developed in 1962, has recently been re-introduced by statisticians for analyzing count data subjected to over- and under-dispersion. This innovative distribution is an extension of the Poisson distribution. The objectives of this study were to evaluate the application of the COM-Poisson GLM for analyzing motor vehicle crashes and compare the results with the traditional negative binomial (NB) model. The comparison analysis was carried out using the most common functional forms employed by transportation safety analysts, which link crashes to the entering flows at intersections or on segments. To accomplish the objectives of the study, several NB and COM-Poisson GLMs were developed and compared using two datasets. The first dataset contained crash data collected at signalized four-legged intersections in Toronto, Ont. The second dataset included data collected for rural four-lane divided and undivided highways in Texas. Several methods were used to assess the statistical fit and predictive performance of the models. The results of this study show that COM-Poisson GLMs perform as well as NB models in terms of GOF statistics and predictive performance. Given the fact the COM-Poisson distribution can also handle under-dispersed data (while the NB distribution cannot or has difficulties converging), which have sometimes been observed in crash databases, the COM-Poisson GLM offers a better alternative over the NB model for modeling motor vehicle crashes, especially given the important limitations recently documented in the safety literature about the latter type of model.

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.

Ionization effects and linear stability in a coaxial plasma device

NASA Astrophysics Data System (ADS)

Kurt, Erol; Kurt, Hilal; Bayhan, Ulku

2009-03-01

A 2-D computer simulation of a coaxial plasma device depending on the conservation equations of electrons, ions and excited atoms together with the Poisson equation for a plasma gun is carried out. Some characteristics of the plasma focus device (PF) such as critical wave numbers a c and voltages U c in the cases of various pressures Pare estimated in order to satisfy the necessary conditions of traveling particle densities ( i.e. plasma patterns) via a linear analysis. Oscillatory solutions are characterized by a nonzero imaginary part of the growth rate Im ( σ) for all cases. The model also predicts the minimal voltage ranges of the system for certain pressure intervals.

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.

Anisotropic norm-oriented mesh adaptation for a Poisson problem

NASA Astrophysics Data System (ADS)

Brèthes, Gautier; Dervieux, Alain

2016-10-01

We present a novel formulation for the mesh adaptation of the approximation of a Partial Differential Equation (PDE). The discussion is restricted to a Poisson problem. The proposed norm-oriented formulation extends the goal-oriented formulation since it is equation-based and uses an adjoint. At the same time, the norm-oriented formulation somewhat supersedes the goal-oriented one since it is basically a solution-convergent method. Indeed, goal-oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that, as mesh size is increased (more degrees of freedom), only this output is proven to tend to its continuous analog while the solution field itself may not converge. A remarkable quality of goal-oriented metric-based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization, in the well-identified set of metrics, of a well-defined functional. In the new proposed formulation, we amplify this advantage. We search, in the same well-identified set of metrics, the minimum of a norm of the approximation error. The norm is prescribed by the user and the method allows addressing the case of multi-objective adaptation like, for example in aerodynamics, adaptating the mesh for drag, lift and moment in one shot. In this work, we consider the basic linear finite-element approximation and restrict our study to L2 norm in order to enjoy second-order convergence. Numerical examples for the Poisson problem are computed.

Marginalized zero-inflated Poisson models with missing covariates.

PubMed

Benecha, Habtamu K; Preisser, John S; Divaris, Kimon; Herring, Amy H; Das, Kalyan

2018-05-11

Unlike zero-inflated Poisson regression, marginalized zero-inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school-based fluoride mouthrinse program. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

PubMed Central

Neti, Prasad V.S.V.; Howell, Roger W.

2010-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log-normal (LN) distribution function (J Nucl Med. 2006;47:1049–1058) with the aid of autoradiography. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analysis of these earlier data. Methods The measured distributions of α-particle tracks per cell were subjected to statistical tests with Poisson, LN, and Poisson-lognormal (P-LN) models. Results The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL of 210Po-citrate. When cells were exposed to 67 kBq/mL, the P-LN distribution function gave a better fit; however, the underlying activity distribution remained log-normal. Conclusion The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution. PMID:18483086

Mechanical properties investigation on single-wall ZrO2 nanotubes: A finite element method with equivalent Poisson's ratio for chemical bonds

NASA Astrophysics Data System (ADS)

Yang, Xiao; Li, Huijian; Hu, Minzheng; Liu, Zeliang; Wärnå, John; Cao, Yuying; Ahuja, Rajeev; Luo, Wei

2018-04-01

A method to obtain the equivalent Poisson's ratio in chemical bonds as classical beams with finite element method was proposed from experimental data. The UFF (Universal Force Field) method was employed to calculate the elastic force constants of Zrsbnd O bonds. By applying the equivalent Poisson's ratio, the mechanical properties of single-wall ZrNTs (ZrO2 nanotubes) were investigated by finite element analysis. The nanotubes' Young's modulus (Y), Poisson's ratio (ν) of ZrNTs as function of diameters, length and chirality have been discussed, respectively. We found that the Young's modulus of single-wall ZrNTs is calculated to be between 350 and 420 GPa.

Generic Schemes for Single-Molecule Kinetics. 2: Information Content of the Poisson Indicator.

PubMed

Avila, Thomas R; Piephoff, D Evan; Cao, Jianshu

2017-08-24

Recently, we described a pathway analysis technique (paper 1) for analyzing generic schemes for single-molecule kinetics based upon the first-passage time distribution. Here, we employ this method to derive expressions for the Poisson indicator, a normalized measure of stochastic variation (essentially equivalent to the Fano factor and Mandel's Q parameter), for various renewal (i.e., memoryless) enzymatic reactions. We examine its dependence on substrate concentration, without assuming all steps follow Poissonian kinetics. Based upon fitting to the functional forms of the first two waiting time moments, we show that, to second order, the non-Poissonian kinetics are generally underdetermined but can be specified in certain scenarios. For an enzymatic reaction with an arbitrary intermediate topology, we identify a generic minimum of the Poisson indicator as a function of substrate concentration, which can be used to tune substrate concentration to the stochastic fluctuations and to estimate the largest number of underlying consecutive links in a turnover cycle. We identify a local maximum of the Poisson indicator (with respect to substrate concentration) for a renewal process as a signature of competitive binding, either between a substrate and an inhibitor or between multiple substrates. Our analysis explores the rich connections between Poisson indicator measurements and microscopic kinetic mechanisms.

Multi-Parameter Linear Least-Squares Fitting to Poisson Data One Count at a Time

NASA Technical Reports Server (NTRS)

Wheaton, W.; Dunklee, A.; Jacobson, A.; Ling, J.; Mahoney, W.; Radocinski, R.

1993-01-01

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multi-component linear model, with underlying physical count rates or fluxes which are to be estimated from the data.

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1972-01-01

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

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

Acoustic and elastic waves in metamaterials for underwater applications

NASA Astrophysics Data System (ADS)

Titovich, Alexey S.

Elastic effects in acoustic metamaterials are investigated. Water-based periodic arrays of elastic scatterers, sonic crystals, suffer from low transmission due to the impedance and index mismatch of typical engineering materials with water. A new type of acoustic metamaterial element is proposed that can be tuned to match the acoustic properties of water in the quasi-static regime. The element comprises a hollow elastic cylindrical shell fitted with an optimized internal substructure consisting of a central mass supported by an axisymmetric distribution of elastic stiffeners, which dictate the shell's effective bulk modulus and density. The derived closed form scattering solution for this system shows that the subsonic flexural waves excited in the shell by the attachment of stiffeners are suppressed by including a sufficiently large number of such stiffeners. As an example of refraction-based wave steering, a cylindrical-to-plane wave lens is designed by varying the bulk modulus in the array according to the conformal mapping of a unit circle to a square. Elastic shells provide rich scattering properties, mainly due to their ability to support highly dispersive flexural waves. Analysis of flexural-borne waves on a pair of shells yields an analytical expression for the width of a flexural resonance, which is then used with the theory of multiple scattering to accurately predict the splitting of the resonance frequency. This analysis leads to the discovery of the acoustic Poisson-like effect in a periodic wave medium. This effect redirects an incident acoustic wave by 90° in an otherwise acoustically transparent sonic crystal. An unresponsive "deaf" antisymmetric mode locked to band gap boundaries is unlocked by matching Bragg scattering with a quadrupole flexural resonance of the shell. The dynamic effect causes normal unidirectional wave motion to strongly couple to perpendicular motion, analogous to the quasi-static Poisson effect in solids. The Poisson-like effect is demonstrated using the first flexural resonance of an acrylic shell. This represent a new type of material which cannot be accurately described as an effective acoustic medium. The study concludes with an analysis of a non-zero shear modulus in a pentamode cloak via the two-scale method with the shear modulus as the perturbation parameter.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

NASA Astrophysics Data System (ADS)

Tschirhart, Hugo; Platini, Thierry

2018-05-01

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

The Poisson-Helmholtz-Boltzmann model.

PubMed

Bohinc, K; Shrestha, A; May, S

2011-10-01

We present a mean-field model of a one-component electrolyte solution where the mobile ions interact not only via Coulomb interactions but also through a repulsive non-electrostatic Yukawa potential. Our choice of the Yukawa potential represents a simple model for solvent-mediated interactions between ions. We employ a local formulation of the mean-field free energy through the use of two auxiliary potentials, an electrostatic and a non-electrostatic potential. Functional minimization of the mean-field free energy leads to two coupled local differential equations, the Poisson-Boltzmann equation and the Helmholtz-Boltzmann equation. Their boundary conditions account for the sources of both the electrostatic and non-electrostatic interactions on the surface of all macroions that reside in the solution. We analyze a specific example, two like-charged planar surfaces with their mobile counterions forming the electrolyte solution. For this system we calculate the pressure between the two surfaces, and we analyze its dependence on the strength of the Yukawa potential and on the non-electrostatic interactions of the mobile ions with the planar macroion surfaces. In addition, we demonstrate that our mean-field model is consistent with the contact theorem, and we outline its generalization to arbitrary interaction potentials through the use of a Laplace transformation. © EDP Sciences / Società Italiana di Fisica / Springer-Verlag 2011

Electroneutral models for dynamic Poisson-Nernst-Planck systems

NASA Astrophysics Data System (ADS)

Song, Zilong; Cao, Xiulei; Huang, Huaxiong

2018-01-01

The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modeling and computational challenges. In this paper, we derive simplified electroneutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First, it is much cheaper to solve them numerically. Second, EN models are easier to deal with compared to the original PNP system; therefore, it would also be easier to derive macroscopic models for cellular structures using EN models. Even though the approach used here is applicable to higher-dimensional cases, this paper mainly focuses on the one-dimensional system, including the general multi-ion case. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to the EN system for the bulk region. This EN system can be solved directly and efficiently without computing the solution in the boundary layer. The derivation is based on matched asymptotics, and the key idea is to bring back higher-order contributions into the effective boundary conditions. For Dirichlet boundary conditions, the higher-order terms can be neglected and the classical results (continuity of electrochemical potential) are recovered. For flux boundary conditions, higher-order terms account for the accumulation of ions in boundary layer and neglecting them leads to physically incorrect solutions. To validate the EN model, numerical computations are carried out for several examples. Our results show that solving the EN model is much more efficient than the original PNP system. Implemented with the Hodgkin-Huxley model, the computational time for solving the EN model is significantly reduced without sacrificing the accuracy of the solution due to the fact that it allows for relatively large mesh and time-step sizes.

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.

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.

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.

QMRA for Drinking Water: 2. The Effect of Pathogen Clustering in Single-Hit Dose-Response Models.

PubMed

Nilsen, Vegard; Wyller, John

2016-01-01

Spatial and/or temporal clustering of pathogens will invalidate the commonly used assumption of Poisson-distributed pathogen counts (doses) in quantitative microbial risk assessment. In this work, the theoretically predicted effect of spatial clustering in conventional "single-hit" dose-response models is investigated by employing the stuttering Poisson distribution, a very general family of count distributions that naturally models pathogen clustering and contains the Poisson and negative binomial distributions as special cases. The analysis is facilitated by formulating the dose-response models in terms of probability generating functions. It is shown formally that the theoretical single-hit risk obtained with a stuttering Poisson distribution is lower than that obtained with a Poisson distribution, assuming identical mean doses. A similar result holds for mixed Poisson distributions. Numerical examples indicate that the theoretical single-hit risk is fairly insensitive to moderate clustering, though the effect tends to be more pronounced for low mean doses. Furthermore, using Jensen's inequality, an upper bound on risk is derived that tends to better approximate the exact theoretical single-hit risk for highly overdispersed dose distributions. The bound holds with any dose distribution (characterized by its mean and zero inflation index) and any conditional dose-response model that is concave in the dose variable. Its application is exemplified with published data from Norovirus feeding trials, for which some of the administered doses were prepared from an inoculum of aggregated viruses. The potential implications of clustering for dose-response assessment as well as practical risk characterization are discussed. © 2016 Society for Risk Analysis.

Discrimination between native and intentionally misfolded conformations of proteins: ES/IS, a new method for calculating conformational free energy that uses both dynamics simulations with an explicit solvent and an implicit solvent continuum model.

PubMed

Vorobjev, Y N; Almagro, J C; Hermans, J

1998-09-01

A new method for calculating the total conformational free energy of proteins in water solvent is presented. The method consists of a relatively brief simulation by molecular dynamics with explicit solvent (ES) molecules to produce a set of microstates of the macroscopic conformation. Conformational energy and entropy are obtained from the simulation, the latter in the quasi-harmonic approximation by analysis of the covariance matrix. The implicit solvent (IS) dielectric continuum model is used to calculate the average solvation free energy as the sum of the free energies of creating the solute-size hydrophobic cavity, of the van der Waals solute-solvent interactions, and of the polarization of water solvent by the solute's charges. The reliability of the solvation free energy depends on a number of factors: the details of arrangement of the protein's charges, especially those near the surface; the definition of the molecular surface; and the method chosen for solving the Poisson equation. Molecular dynamics simulation in explicit solvent relaxes the protein's conformation and allows polar surface groups to assume conformations compatible with interaction with solvent, while averaging of internal energy and solvation free energy tend to enhance the precision. Two recently developed methods--SIMS, for calculation of a smooth invariant molecular surface, and FAMBE, for solution of the Poisson equation via a fast adaptive multigrid boundary element--have been employed. The SIMS and FAMBE programs scale linearly with the number of atoms. SIMS is superior to Connolly's MS (molecular surface) program: it is faster, more accurate, and more stable, and it smooths singularities of the molecular surface. Solvation free energies calculated with these two programs do not depend on molecular position or orientation and are stable along a molecular dynamics trajectory. We have applied this method to calculate the conformational free energy of native and intentionally misfolded globular conformations of proteins (the EMBL set of deliberately misfolded proteins) and have obtained good discrimination in favor of the native conformations in all instances.

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

Fractional poisson--a simple dose-response model for human norovirus.

PubMed

Messner, Michael J; Berger, Philip; Nappier, Sharon P

2014-10-01

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (<100), estimation error is small for the fractional Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.

Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.

PubMed

Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai

2011-01-01

Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs. Published by Elsevier Ltd.

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.

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.

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.

Algorithms for parallel and vector computations

NASA Technical Reports Server (NTRS)

Ortega, James M.

1995-01-01

This is a final report on work performed under NASA grant NAG-1-1112-FOP during the period March, 1990 through February 1995. Four major topics are covered: (1) solution of nonlinear poisson-type equations; (2) parallel reduced system conjugate gradient method; (3) orderings for conjugate gradient preconditioners, and (4) SOR as a preconditioner.

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

Stiffness of frictional contact of dissimilar elastic solids

DOE PAGES

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; ...

2017-12-22

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

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

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

NASA Astrophysics Data System (ADS)

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; Xu, Haitao; Pharr, George M.

2018-03-01

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This paper gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the friction coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations - adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. The correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.

Copy number variants calling for single cell sequencing data by multi-constrained optimization.

PubMed

Xu, Bo; Cai, Hongmin; Zhang, Changsheng; Yang, Xi; Han, Guoqiang

2016-08-01

Variations in DNA copy number carry important information on genome evolution and regulation of DNA replication in cancer cells. The rapid development of single-cell sequencing technology allows one to explore gene expression heterogeneity among single-cells, thus providing important cancer cell evolution information. Single-cell DNA/RNA sequencing data usually have low genome coverage, which requires an extra step of amplification to accumulate enough samples. However, such amplification will introduce large bias and makes bioinformatics analysis challenging. Accurately modeling the distribution of sequencing data and effectively suppressing the bias influence is the key to success variations analysis. Recent advances demonstrate the technical noises by amplification are more likely to follow negative binomial distribution, a special case of Poisson distribution. Thus, we tackle the problem CNV detection by formulating it into a quadratic optimization problem involving two constraints, in which the underling signals are corrupted by Poisson distributed noises. By imposing the constraints of sparsity and smoothness, the reconstructed read depth signals from single-cell sequencing data are anticipated to fit the CNVs patterns more accurately. An efficient numerical solution based on the classical alternating direction minimization method (ADMM) is tailored to solve the proposed model. We demonstrate the advantages of the proposed method using both synthetic and empirical single-cell sequencing data. Our experimental results demonstrate that the proposed method achieves excellent performance and high promise of success with single-cell sequencing data. Crown Copyright © 2016. Published by Elsevier Ltd. All rights reserved.

Doubly stochastic Poisson process models for precipitation at fine time-scales

NASA Astrophysics Data System (ADS)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

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.

Structural, thermodynamic, and electrical properties of polar fluids and ionic solutions on a hypersphere: Results of simulations

NASA Astrophysics Data System (ADS)

Caillol, J. M.; Levesque, D.

1992-01-01

The reliability and the efficiency of a new method suitable for the simulations of dielectric fluids and ionic solutions is established by numerical computations. The efficiency depends on the use of a simulation cell which is the surface of a four-dimensional sphere. The reliability originates from a charge-charge potential solution of the Poisson equation in this confining volume. The computation time, for systems of a few hundred molecules, is reduced by a factor of 2 or 3 compared to this of a simulation performed in a cubic volume with periodic boundary conditions and the Ewald charge-charge potential.

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.

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.

Simultaneous reconstruction and segmentation for dynamic SPECT imaging

NASA Astrophysics Data System (ADS)

Burger, Martin; Rossmanith, Carolin; Zhang, Xiaoqun

2016-10-01

This work deals with the reconstruction of dynamic images that incorporate characteristic dynamics in certain subregions, as arising for the kinetics of many tracers in emission tomography (SPECT, PET). We make use of a basis function approach for the unknown tracer concentration by assuming that the region of interest can be divided into subregions with spatially constant concentration curves. Applying a regularised variational framework reminiscent of the Chan-Vese model for image segmentation we simultaneously reconstruct both the labelling functions of the subregions as well as the subconcentrations within each region. Our particular focus is on applications in SPECT with the Poisson noise model, resulting in a Kullback-Leibler data fidelity in the variational approach. We present a detailed analysis of the proposed variational model and prove existence of minimisers as well as error estimates. The latter apply to a more general class of problems and generalise existing results in literature since we deal with a nonlinear forward operator and a nonquadratic data fidelity. A computational algorithm based on alternating minimisation and splitting techniques is developed for the solution of the problem and tested on appropriately designed synthetic data sets. For those we compare the results to those of standard EM reconstructions and investigate the effects of Poisson noise in the data.

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.

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

NASA Technical Reports Server (NTRS)

Helenbrook, B. T.; Atkins, H. L.

2006-01-01

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Spotlight SAR interferometry for terrain elevation mapping and interferometric change detection

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

Eichel, P.H.; Ghiglia, D.C.; Jakowatz, C.V. Jr.

1996-02-01

In this report, we employ an approach quite different from any previous work; we show that a new methodology leads to a simpler and clearer understanding of the fundamental principles of SAR interferometry. This methodology also allows implementation of an important collection mode that has not been demonstrated to date. Specifically, we introduce the following six new concepts for the processing of interferometric SAR (INSAR) data: (1) processing using spotlight mode SAR imaging (allowing ultra-high resolution), as opposed to conventional strip-mapping techniques; (2) derivation of the collection geometry constraints required to avoid decorrelation effects in two-pass INSAR; (3) derivation ofmore » maximum likelihood estimators for phase difference and the change parameter employed in interferometric change detection (ICD); (4) processing for the two-pass case wherein the platform ground tracks make a large crossing angle; (5) a robust least-squares method for two-dimensional phase unwrapping formulated as a solution to Poisson`s equation, instead of using traditional path-following techniques; and (6) the existence of a simple linear scale factor that relates phase differences between two SAR images to terrain height. We show both theoretical analysis, as well as numerous examples that employ real SAR collections to demonstrate the innovations listed above.« less

Probabilistic reasoning in data analysis.

PubMed

Sirovich, Lawrence

2011-09-20

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on probabilistic reasoning in the analysis of biological data. General probabilistic frameworks are introduced, and a number of standard probability distributions are described using simple intuitive ideas. Particular attention is focused on random arrivals that are independent of prior history (Markovian events), with an emphasis on waiting times, Poisson processes, and Poisson probability distributions. The use of these various probability distributions is applied to biomedical problems, including several classic experimental studies.

Photon counting statistics analysis of biophotons from hands.

PubMed

Jung, Hyun-Hee; Woo, Won-Myung; Yang, Joon-Mo; Choi, Chunho; Lee, Jonghan; Yoon, Gilwon; Yang, Jong S; Soh, Kwang-Sup

2003-05-01

The photon counting statistics of biophotons emitted from hands is studied with a view to test its agreement with the Poisson distribution. The moments of observed probability up to seventh order have been evaluated. The moments of biophoton emission from hands are in good agreement while those of dark counts of photomultiplier tube show large deviations from the theoretical values of Poisson distribution. The present results are consistent with the conventional delta-value analysis of the second moment of probability.

Flow study in the cross sectional planes of a turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Abdallah, S.; Tabakoff, W.

1977-01-01

A numerical study of the nonviscous flow characteristics in the cross-sectional planes of a radial inflow turbine scroll is presented. The velocity potential is used in the formulation to determine the flow velocity in these planes resulting from the continuous mass discharge. The effect of the through flow velocity is simulated by a continuous distribution of source/sink in the cross-section. A special iterative procedure is devised to handle the solution of the resulting Poisson's differential equation with Neumann boundary conditions in a domain with generally curved boundaries. The analysis is used to determine the effects of the radius of curvature, the location of the scroll section and its geometry on the flow characteristics in the turbine scroll.

A Unified Framework for Complex Networks with Degree Trichotomy Based on Markov Chains.

PubMed

Hui, David Shui Wing; Chen, Yi-Chao; Zhang, Gong; Wu, Weijie; Chen, Guanrong; Lui, John C S; Li, Yingtao

2017-06-16

This paper establishes a Markov chain model as a unified framework for describing the evolution processes in complex networks. The unique feature of the proposed model is its capability in addressing the formation mechanism that can reflect the "trichotomy" observed in degree distributions, based on which closed-form solutions can be derived. Important special cases of the proposed unified framework are those classical models, including Poisson, Exponential, Power-law distributed networks. Both simulation and experimental results demonstrate a good match of the proposed model with real datasets, showing its superiority over the classical models. Implications of the model to various applications including citation analysis, online social networks, and vehicular networks design, are also discussed in the paper.

Analytical study of mixed electroosmotic-pressure-driven flow in rectangular micro-channels

NASA Astrophysics Data System (ADS)

Movahed, Saeid; Kamali, Reza; Eghtesad, Mohammad; Khosravifard, Amir

2013-09-01

Operational state of many miniaturized devices deals with flow field in microchannels. Pressure-driven flow (PDF) and electroosmotic flow (EOF) can be recognized as the two most important types of the flow field in such channels. EOF has many advantages in comparison with PDF, such as being vibration free and not requiring any external mechanical pumps or moving parts. However, the disadvantages of this type of flow such as Joule heating, electrophoresis demixing, and not being suitable for mobile devices must be taken into consideration carefully. By using mixed electroosmotic/pressure-driven flow, the role of EOF in producing desired velocity profile will be reduced. In this way, the advantages of EOF can be exploited, and its disadvantages can be prevented. Induced pressure gradient can be utilized in order to control the separation in the system. Furthermore, in many complicated geometries such as T-shape microchannels, turns may induce pressure gradient to the electroosmotic velocity. While analytical formulas are completely essential for analysis and control of any industrial and laboratory microdevices, lack of such formulas in the literature for solving Poisson-Boltzmann equation and predicting electroosmotic velocity field in rectangular domains is evident. In the present study, first a novel method is proposed to solve Poisson-Boltzmann equation (PBE). Subsequently, this solution is utilized to find the electroosmotic and the mixed electroosmotic/pressure-driven velocity profile in a rectangular domain of the microchannels. To demonstrate the accuracy of the presented analytical method in solving PBE and finding electroosmotic velocity, a general nondimensional example is analyzed, and the results are compared with the solution of boundary element method. Additionally, the effects of different nondimensional parameters and also aspect ratio of channels on the electroosmotic part of the flow field will be investigated.

Association of Biocompatible Peritoneal Dialysis Solutions with Peritonitis Risk, Treatment, and Outcomes

PubMed Central

Cho, Yeoungjee; Badve, Sunil V.; Hawley, Carmel M.; McDonald, Stephen P.; Brown, Fiona G.; Boudville, Neil; Bannister, Kym M.; Clayton, Philip A.

2013-01-01

Summary Background and objectives The effect of biocompatible peritoneal dialysis (PD) solutions on PD-related peritonitis is unclear. This study sought to evaluate the relationship between use of biocompatible solutions and the probability of occurrence or clinical outcomes of peritonitis. Design, setting, participants, & measurements The study included all incident Australian patients receiving PD between January 1, 2007, and December 31, 2010, using Australia and New Zealand Dialysis and Transplant Registry data. All multicompartment PD solutions of neutral pH were categorized as biocompatible solutions. The independent predictors of peritonitis and the use of biocompatible solutions were determined by multivariable, multilevel mixed-effects Poisson and logistic regression analysis, respectively. Sensitivity analyses, including propensity score matching, were performed. Results Use of biocompatible solutions gradually declined (from 7.5% in 2007 to 4.2% in 2010), with preferential use among smaller units and among younger patients without diabetes mellitus. Treatment with biocompatible solution was associated with significantly greater overall rate of peritonitis (0.67 versus 0.47 episode per patient-year; incidence rate ratio, 1.49; 95% confidence interval [CI], 1.19 to 1.89) and with shorter time to first peritonitis (hazard ratio [HR], 1.48; 95% CI, 1.17 to 1.87), a finding replicated in propensity score–matched cohorts (HR, 1.36; 95% CI, 1.09 to 1.71). Conclusions In an observational registry study, use of biocompatible PD solutions was associated with higher overall peritonitis rates and shorter time to first peritonitis. Further randomized studies adequately powered for a primary peritonitis outcome are warranted. PMID:23949232

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…

Temperature dependences of the time of electron-electron interactions in two-dimensional heterojunction

NASA Astrophysics Data System (ADS)

Bukhenskyy, K. V.; Dubois, A. B.; Kucheryavyy, S. I.; Mashnina, S. N.; Safoshkin, A. S.; Baukov, A. A.; Shchigorev, E. Yu

2017-12-01

The article discusses the joint solution of the Schrödinger and Poisson equations for two-dimensional semiconductor heterojunction. The application of a triangular potential of well approximation for the calculation of the electron-electron interaction is offered in the paper. The influence of the parameters of the selected approximation was analyzed.

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…

Invariant Poisson-Nijenhuis structures on Lie groups and classification

NASA Astrophysics Data System (ADS)

Ravanpak, Zohreh; Rezaei-Aghdam, Adel; Haghighatdoost, Ghorbanali

We study right-invariant (respectively, left-invariant) Poisson-Nijenhuis structures (P-N) on a Lie group G and introduce their infinitesimal counterpart, the so-called r-n structures on the corresponding Lie algebra 𝔤. We show that r-n structures can be used to find compatible solutions of the classical Yang-Baxter equation (CYBE). Conversely, two compatible r-matrices from which one is invertible determine an r-n structure. We classify, up to a natural equivalence, all r-matrices and all r-n structures with invertible r on four-dimensional symplectic real Lie algebras. The result is applied to show that a number of dynamical systems which can be constructed by r-matrices on a phase space whose symmetry group is Lie group a G, can be specifically determined.

Simulation of diffuse-charge capacitance in electric double layer capacitors

NASA Astrophysics Data System (ADS)

Sun, Ning; Gersappe, Dilip

2017-01-01

We use a Lattice Boltzmann Model (LBM) in order to simulate diffuse-charge dynamics in Electric Double Layer Capacitors (EDLCs). Simulations are carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). The steric effect of concentrated solutions is considered by using a Modified Poisson-Nernst-Planck (MPNP) equations and compared with regular Poisson-Nernst-Planck (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. Our studies show how electrode morphology can be used to tailor the properties of supercapacitors.

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

Possible Statistics of Two Coupled Random Fields: Application to Passive Scalar

NASA Technical Reports Server (NTRS)

Dubrulle, B.; He, Guo-Wei; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

We use the relativity postulate of scale invariance to derive the similarity transformations between two coupled scale-invariant random elds at different scales. We nd the equations leading to the scaling exponents. This formulation is applied to the case of passive scalars advected i) by a random Gaussian velocity field; and ii) by a turbulent velocity field. In the Gaussian case, we show that the passive scalar increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a log-normal distribution. In the turbulent case, we show that when the velocity increments follow a log-Poisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains the experimental observations of Ruiz et al. about the temperature increments.

A novel method for the accurate evaluation of Poisson's ratio of soft polymer materials.

PubMed

Lee, Jae-Hoon; Lee, Sang-Soo; Chang, Jun-Dong; Thompson, Mark S; Kang, Dong-Joong; Park, Sungchan; Park, Seonghun

2013-01-01

A new method with a simple algorithm was developed to accurately measure Poisson's ratio of soft materials such as polyvinyl alcohol hydrogel (PVA-H) with a custom experimental apparatus consisting of a tension device, a micro X-Y stage, an optical microscope, and a charge-coupled device camera. In the proposed method, the initial positions of the four vertices of an arbitrarily selected quadrilateral from the sample surface were first measured to generate a 2D 1st-order 4-node quadrilateral element for finite element numerical analysis. Next, minimum and maximum principal strains were calculated from differences between the initial and deformed shapes of the quadrilateral under tension. Finally, Poisson's ratio of PVA-H was determined by the ratio of minimum principal strain to maximum principal strain. This novel method has an advantage in the accurate evaluation of Poisson's ratio despite misalignment between specimens and experimental devices. In this study, Poisson's ratio of PVA-H was 0.44 ± 0.025 (n = 6) for 2.6-47.0% elongations with a tendency to decrease with increasing elongation. The current evaluation method of Poisson's ratio with a simple measurement system can be employed to a real-time automated vision-tracking system which is used to accurately evaluate the material properties of various soft materials.

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach.

PubMed

Mohammadi, Tayeb; Kheiri, Soleiman; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach

PubMed Central

Mohammadi, Tayeb; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables “number of blood donation” and “number of blood deferral”: as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models. PMID:27703493

Analysis of overdispersed count data: application to the Human Papillomavirus Infection in Men (HIM) Study.

PubMed

Lee, J-H; Han, G; Fulp, W J; Giuliano, A R

2012-06-01

The Poisson model can be applied to the count of events occurring within a specific time period. The main feature of the Poisson model is the assumption that the mean and variance of the count data are equal. However, this equal mean-variance relationship rarely occurs in observational data. In most cases, the observed variance is larger than the assumed variance, which is called overdispersion. Further, when the observed data involve excessive zero counts, the problem of overdispersion results in underestimating the variance of the estimated parameter, and thus produces a misleading conclusion. We illustrated the use of four models for overdispersed count data that may be attributed to excessive zeros. These are Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial models. The example data in this article deal with the number of incidents involving human papillomavirus infection. The four models resulted in differing statistical inferences. The Poisson model, which is widely used in epidemiology research, underestimated the standard errors and overstated the significance of some covariates.

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

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.

Log Normal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of Alpha Particle Track Autoradiography

PubMed Central

Neti, Prasad V.S.V.; Howell, Roger W.

2008-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log normal distribution function (J Nucl Med 47, 6 (2006) 1049-1058) with the aid of an autoradiographic approach. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analyses of these data. Methods The measured distributions of alpha particle tracks per cell were subjected to statistical tests with Poisson (P), log normal (LN), and Poisson – log normal (P – LN) models. Results The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL 210Po-citrate. When cells were exposed to 67 kBq/mL, the P – LN distribution function gave a better fit, however, the underlying activity distribution remained log normal. Conclusions The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution. PMID:16741316

Pattern analysis of community health center location in Surabaya using spatial Poisson point process

NASA Astrophysics Data System (ADS)

Kusumaningrum, Choriah Margareta; Iriawan, Nur; Winahju, Wiwiek Setya

2017-11-01

Community health center (puskesmas) is one of the closest health service facilities for the community, which provide healthcare for population on sub-district level as one of the government-mandated community health clinics located across Indonesia. The increasing number of this puskesmas does not directly comply the fulfillment of basic health services needed in such region. Ideally, a puskesmas has to cover up to maximum 30,000 people. The number of puskesmas in Surabaya indicates an unbalance spread in all of the area. This research aims to analyze the spread of puskesmas in Surabaya using spatial Poisson point process model in order to get the effective location of Surabaya's puskesmas which based on their location. The results of the analysis showed that the distribution pattern of puskesmas in Surabaya is non-homogeneous Poisson process and is approched by mixture Poisson model. Based on the estimated model obtained by using Bayesian mixture model couple with MCMC process, some characteristics of each puskesmas have no significant influence as factors to decide the addition of health center in such location. Some factors related to the areas of sub-districts have to be considered as covariate to make a decision adding the puskesmas in Surabaya.

Poisson-Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain.

PubMed

Lee, Sangyoon; Lee, Min Seok; Kang, Moon Gi

2018-03-29

The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson-Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson-Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods.

The lunar libration: comparisons between various models - a model fitted to LLR observations

NASA Astrophysics Data System (ADS)

Chapront, J.; Francou, G.

2005-09-01

We consider 4 libration models: 3 numerical models built by JPL (ephemerides for the libration in DE245, DE403 and DE405) and an analytical model improved with numerical complements fitted to recent LLR observations. The analytical solution uses 3 angular variables (ρ1, ρ2, τ) which represent the deviations with respect to Cassini's laws. After having referred the models to a unique reference frame, we study the differences between the models which depend on gravitational and tidal parameters of the Moon, as well as amplitudes and frequencies of the free librations. It appears that the differences vary widely depending of the above quantities. They correspond to a few meters displacement on the lunar surface, reminding that LLR distances are precise to the centimeter level. Taking advantage of the lunar libration theory built by Moons (1984) and improved by Chapront et al. (1999) we are able to establish 4 solutions and to represent their differences by Fourier series after a numerical substitution of the gravitational constants and free libration parameters. The results are confirmed by frequency analyses performed separately. Using DE245 as a basic reference ephemeris, we approximate the differences between the analytical and numerical models with Poisson series. The analytical solution - improved with numerical complements under the form of Poisson series - is valid over several centuries with an internal precision better than 5 centimeters.

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

Electroosmosis over charge-modulated surfaces with finite electrical double layer thicknesses: Asymptotic and numerical investigations

NASA Astrophysics Data System (ADS)

Ghosh, Uddipta; Mandal, Shubhadeep; Chakraborty, Suman

2017-06-01

Here we attempt to solve the fully coupled Poisson-Nernst-Planck-Navier-Stokes equations, to ascertain the influence of finite electric double layer (EDL) thickness on coupled charge and fluid dynamics over patterned charged surfaces. We go beyond the well-studied "weak-field" limit and obtain numerical solutions for a wide range of EDL thicknesses, applied electric field strengths, and the surface potentials. Asymptotic solutions to the coupled system are also derived using a combination of singular and regular perturbation, for thin EDLs and low surface potential, and good agreement between the two solutions is observed. Counterintuitively to common arguments, our analysis reveals that finite EDL thickness may either increase or decrease the "free-stream velocity" (equivalent to net throughput), depending on the strength of the applied electric field. We also unveil a critical EDL thickness for which the effect of finite EDL thickness on the free-stream velocity is the most prominent. Finally, we demonstrate that increasing the surface potential and the applied field tends to influence the overall flow patterns in the contrasting manners. These results may be of profound importance in developing a comprehensive theoretical basis for designing electro-osmotically actuated microfluidic mixtures.

Improved central confidence intervals for the ratio of Poisson means

NASA Astrophysics Data System (ADS)

Cousins, R. D.

The problem of confidence intervals for the ratio of two unknown Poisson means was "solved" decades ago, but a closer examination reveals that the standard solution is far from optimal from the frequentist point of view. We construct a more powerful set of central confidence intervals, each of which is a (typically proper) subinterval of the corresponding standard interval. They also provide upper and lower confidence limits which are more restrictive than the standard limits. The construction follows Neyman's original prescription, though discreteness of the Poisson distribution and the presence of a nuisance parameter (one of the unknown means) lead to slightly conservative intervals. Philosophically, the issue of the appropriateness of the construction method is similar to the issue of conditioning on the margins in 2×2 contingency tables. From a frequentist point of view, the new set maintains (over) coverage of the unknown true value of the ratio of means at each stated confidence level, even though the new intervals are shorter than the old intervals by any measure (except for two cases where they are identical). As an example, when the number 2 is drawn from each Poisson population, the 90% CL central confidence interval on the ratio of means is (0.169, 5.196), rather than (0.108, 9.245). In the cited literature, such confidence intervals have applications in numerous branches of pure and applied science, including agriculture, wildlife studies, manufacturing, medicine, reliability theory, and elementary particle physics.

Extended Poisson process modelling and analysis of grouped binary data.

PubMed

Faddy, Malcolm J; Smith, David M

2012-05-01

A simple extension of the Poisson process results in binomially distributed counts of events in a time interval. A further extension generalises this to probability distributions under- or over-dispersed relative to the binomial distribution. Substantial levels of under-dispersion are possible with this modelling, but only modest levels of over-dispersion - up to Poisson-like variation. Although simple analytical expressions for the moments of these probability distributions are not available, approximate expressions for the mean and variance are derived, and used to re-parameterise the models. The modelling is applied in the analysis of two published data sets, one showing under-dispersion and the other over-dispersion. More appropriate assessment of the precision of estimated parameters and reliable model checking diagnostics follow from this more general modelling of these data sets. © 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Crystalline nucleation in undercooled liquids: a Bayesian data-analysis approach for a nonhomogeneous Poisson process.

PubMed

Filipponi, A; Di Cicco, A; Principi, E

2012-12-01

A Bayesian data-analysis approach to data sets of maximum undercooling temperatures recorded in repeated melting-cooling cycles of high-purity samples is proposed. The crystallization phenomenon is described in terms of a nonhomogeneous Poisson process driven by a temperature-dependent sample nucleation rate J(T). The method was extensively tested by computer simulations and applied to real data for undercooled liquid Ge. It proved to be particularly useful in the case of scarce data sets where the usage of binned data would degrade the available experimental information.

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

Numerical Solution of the Extended Nernst-Planck Model.

PubMed

Samson; Marchand

1999-07-01

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed. Copyright 1999 Academic Press.

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

Influence of nonelectrostatic ion-ion interactions on double-layer capacitance

NASA Astrophysics Data System (ADS)

Zhao, Hui

2012-11-01

Recently a Poisson-Helmholtz-Boltzmann (PHB) model [Bohinc , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.031130 85, 031130 (2012)] was developed by accounting for solvent-mediated nonelectrostatic ion-ion interactions. Nonelectrostatic interactions are described by a Yukawa-like pair potential. In the present work, we modify the PHB model by adding steric effects (finite ion size) into the free energy to derive governing equations. The modified PHB model is capable of capturing both ion specificity and ion crowding. This modified model is then employed to study the capacitance of the double layer. More specifically, we focus on the influence of nonelectrostatic ion-ion interactions on charging a double layer near a flat surface in the presence of steric effects. We numerically compute the differential capacitance as a function of the voltage under various conditions. At small voltages and low salt concentrations (dilute solution), we find out that the predictions from the modified PHB model are the same as those from the classical Poisson-Boltzmann theory, indicating that nonelectrostatic ion-ion interactions and steric effects are negligible. At moderate voltages, nonelectrostatic ion-ion interactions play an important role in determining the differential capacitance. Generally speaking, nonelectrostatic interactions decrease the capacitance because of additional nonelectrostatic repulsion among excess counterions inside the double layer. However, increasing the voltage gradually favors steric effects, which induce a condensed layer with crowding of counterions near the electrode. Accordingly, the predictions from the modified PHB model collapse onto those computed by the modified Poisson-Boltzmann theory considering steric effects alone. Finally, theoretical predictions are compared and favorably agree with experimental data, in particular, in concentrated solutions, leading one to conclude that the modified PHB model adequately predicts the diffuse-charge dynamics of the double layer with ion specificity and steric effects.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

The impact of short term synaptic depression and stochastic vesicle dynamics on neuronal variability

PubMed Central

Reich, Steven

2014-01-01

Neuronal variability plays a central role in neural coding and impacts the dynamics of neuronal networks. Unreliability of synaptic transmission is a major source of neural variability: synaptic neurotransmitter vesicles are released probabilistically in response to presynaptic action potentials and are recovered stochastically in time. The dynamics of this process of vesicle release and recovery interacts with variability in the arrival times of presynaptic spikes to shape the variability of the postsynaptic response. We use continuous time Markov chain methods to analyze a model of short term synaptic depression with stochastic vesicle dynamics coupled with three different models of presynaptic spiking: one model in which the timing of presynaptic action potentials are modeled as a Poisson process, one in which action potentials occur more regularly than a Poisson process (sub-Poisson) and one in which action potentials occur more irregularly (super-Poisson). We use this analysis to investigate how variability in a presynaptic spike train is transformed by short term depression and stochastic vesicle dynamics to determine the variability of the postsynaptic response. We find that sub-Poisson presynaptic spiking increases the average rate at which vesicles are released, that the number of vesicles released over a time window is more variable for smaller time windows than larger time windows and that fast presynaptic spiking gives rise to Poisson-like variability of the postsynaptic response even when presynaptic spike times are non-Poisson. Our results complement and extend previously reported theoretical results and provide possible explanations for some trends observed in recorded data. PMID:23354693

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Aksu, H.; Spehert, T.

1975-01-01

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Geometrical Effects on Nonlinear Electrodiffusion in Cell Physiology

NASA Astrophysics Data System (ADS)

Cartailler, J.; Schuss, Z.; Holcman, D.

2017-12-01

We report here new electrical laws, derived from nonlinear electrodiffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck equations for charge concentration and electric potential as a model of electrodiffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. As the number of charge increases, they concentrate at the end of cusp-shaped funnel. These results can be used in the design of nanopipettes and help to understand the local voltage changes inside dendrites and axons with heterogeneous local geometry.

Six-component semi-discrete integrable nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

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.

The two ∇6 R 4 type invariants and their higher order generalisation

NASA Astrophysics Data System (ADS)

Bossard, Guillaume; Verschinin, Valentin

2015-07-01

We show that there are two distinct classes of ∇6 R 4 type supersymmetry invariants in maximal supergravity. The second class includes a coupling in F 2∇4 R 4 that generalises to 1/8 BPS protected F 2 k ∇4 R 4 couplings. We work out the supersymmetry constraints on the corresponding threshold functions, and argue that the functions in the second class satisfy to homogeneous differential equations for arbitrary k ≥ 1, such that the corresponding exact threshold functions in type II string theory should be proportional to Eisenstein series, which we identify. This analysis explains in particular that the exact ∇6 R 4 threshold function is the sum of an Eisenstein function and a solution to an inhomogeneous Poisson equation in string theory.

Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1986-01-01

A large class of two- and three-dimensional, nonseparable elliptic partial differential equations (PDEs) is presently solved by means of novel one-step (D'Yakanov-Gunn) and two-step (accelerated one-step) iterative procedures, using a local, discrete Fourier analysis. In addition to being easily implemented and applicable to a variety of boundary conditions, these procedures are found to be computationally efficient on the basis of the results of numerical comparison with other established methods, which lack the present one's: (1) insensitivity to grid cell size and aspect ratio, and (2) ease of convergence rate estimation by means of the coefficient of the PDE being solved. The two-step procedure is numerically demonstrated to outperform the one-step procedure in the case of PDEs with variable coefficients.

Electronic health record analysis via deep poisson factor models

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

Henao, Ricardo; Lu, James T.; Lucas, Joseph E.

Electronic Health Record (EHR) phenotyping utilizes patient data captured through normal medical practice, to identify features that may represent computational medical phenotypes. These features may be used to identify at-risk patients and improve prediction of patient morbidity and mortality. We present a novel deep multi-modality architecture for EHR analysis (applicable to joint analysis of multiple forms of EHR data), based on Poisson Factor Analysis (PFA) modules. Each modality, composed of observed counts, is represented as a Poisson distribution, parameterized in terms of hidden binary units. In-formation from different modalities is shared via a deep hierarchy of common hidden units. Activationmore » of these binary units occurs with probability characterized as Bernoulli-Poisson link functions, instead of more traditional logistic link functions. In addition, we demon-strate that PFA modules can be adapted to discriminative modalities. To compute model parameters, we derive efficient Markov Chain Monte Carlo (MCMC) inference that scales efficiently, with significant computational gains when compared to related models based on logistic link functions. To explore the utility of these models, we apply them to a subset of patients from the Duke-Durham patient cohort. We identified a cohort of over 12,000 patients with Type 2 Diabetes Mellitus (T2DM) based on diagnosis codes and laboratory tests out of our patient population of over 240,000. Examining the common hidden units uniting the PFA modules, we identify patient features that represent medical concepts. Experiments indicate that our learned features are better able to predict mortality and morbidity than clinical features identified previously in a large-scale clinical trial.« less

Electronic health record analysis via deep poisson factor models

DOE PAGES

Henao, Ricardo; Lu, James T.; Lucas, Joseph E.; ...

2016-01-01

Electronic Health Record (EHR) phenotyping utilizes patient data captured through normal medical practice, to identify features that may represent computational medical phenotypes. These features may be used to identify at-risk patients and improve prediction of patient morbidity and mortality. We present a novel deep multi-modality architecture for EHR analysis (applicable to joint analysis of multiple forms of EHR data), based on Poisson Factor Analysis (PFA) modules. Each modality, composed of observed counts, is represented as a Poisson distribution, parameterized in terms of hidden binary units. In-formation from different modalities is shared via a deep hierarchy of common hidden units. Activationmore » of these binary units occurs with probability characterized as Bernoulli-Poisson link functions, instead of more traditional logistic link functions. In addition, we demon-strate that PFA modules can be adapted to discriminative modalities. To compute model parameters, we derive efficient Markov Chain Monte Carlo (MCMC) inference that scales efficiently, with significant computational gains when compared to related models based on logistic link functions. To explore the utility of these models, we apply them to a subset of patients from the Duke-Durham patient cohort. We identified a cohort of over 12,000 patients with Type 2 Diabetes Mellitus (T2DM) based on diagnosis codes and laboratory tests out of our patient population of over 240,000. Examining the common hidden units uniting the PFA modules, we identify patient features that represent medical concepts. Experiments indicate that our learned features are better able to predict mortality and morbidity than clinical features identified previously in a large-scale clinical trial.« less

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson-Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

NASA Astrophysics Data System (ADS)

Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra

2014-11-01

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson-Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals

NASA Astrophysics Data System (ADS)

Frejlich, Pedro; Mărcuț, Ioan

2018-03-01

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

PubMed

Frejlich, Pedro; Mărcuț, Ioan

2018-01-01

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

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

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro

2017-04-01

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Assessment of Poisson, probit and linear models for genetic analysis of presence and number of black spots in Corriedale sheep.

PubMed

Peñagaricano, F; Urioste, J I; Naya, H; de los Campos, G; Gianola, D

2011-04-01

Black skin spots are associated with pigmented fibres in wool, an important quality fault. Our objective was to assess alternative models for genetic analysis of presence (BINBS) and number (NUMBS) of black spots in Corriedale sheep. During 2002-08, 5624 records from 2839 animals in two flocks, aged 1 through 6 years, were taken at shearing. Four models were considered: linear and probit for BINBS and linear and Poisson for NUMBS. All models included flock-year and age as fixed effects and animal and permanent environmental as random effects. Models were fitted to the whole data set and were also compared based on their predictive ability in cross-validation. Estimates of heritability ranged from 0.154 to 0.230 for BINBS and 0.269 to 0.474 for NUMBS. For BINBS, the probit model fitted slightly better to the data than the linear model. Predictions of random effects from these models were highly correlated, and both models exhibited similar predictive ability. For NUMBS, the Poisson model, with a residual term to account for overdispersion, performed better than the linear model in goodness of fit and predictive ability. Predictions of random effects from the Poisson model were more strongly correlated with those from BINBS models than those from the linear model. Overall, the use of probit or linear models for BINBS and of a Poisson model with a residual for NUMBS seems a reasonable choice for genetic selection purposes in Corriedale sheep. © 2010 Blackwell Verlag GmbH.

Waiting-time distributions of magnetic discontinuities: clustering or Poisson process?

PubMed

Greco, A; Matthaeus, W H; Servidio, S; Dmitruk, P

2009-10-01

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Waiting-time distributions of magnetic discontinuities: Clustering or Poisson process?

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

Greco, A.; Matthaeus, W. H.; Servidio, S.

2009-10-15

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Spatial variation of natural radiation and childhood leukaemia incidence in Great Britain.

PubMed

Richardson, S; Monfort, C; Green, M; Draper, G; Muirhead, C

This paper describes an analysis of the geographical variation of childhood leukaemia incidence in Great Britain over a 15 year period in relation to natural radiation (gamma and radon). Data at the level of the 459 district level local authorities in England, Wales and regional districts in Scotland are analysed in two complementary ways: first, by Poisson regressions with the inclusion of environmental covariates and a smooth spatial structure; secondly, by a hierarchical Bayesian model in which extra-Poisson variability is modelled explicitly in terms of spatial and non-spatial components. From this analysis, we deduce a strong indication that a main part of the variability is accounted for by a local neighbourhood 'clustering' structure. This structure is furthermore relatively stable over the 15 year period for the lymphocytic leukaemias which make up the majority of observed cases. We found no evidence of a positive association of childhood leukaemia incidence with outdoor or indoor gamma radiation levels. There is no consistent evidence of any association with radon levels. Indeed, in the Poisson regressions, a significant positive association was only observed for one 5-year period, a result which is not compatible with a stable environmental effect. Moreover, this positive association became clearly non-significant when over-dispersion relative to the Poisson distribution was taken into account.

Differential expression analysis for RNAseq using Poisson mixed models

PubMed Central

Sun, Shiquan; Hood, Michelle; Scott, Laura; Peng, Qinke; Mukherjee, Sayan; Tung, Jenny

2017-01-01

Abstract Identifying differentially expressed (DE) genes from RNA sequencing (RNAseq) studies is among the most common analyses in genomics. However, RNAseq DE analysis presents several statistical and computational challenges, including over-dispersed read counts and, in some settings, sample non-independence. Previous count-based methods rely on simple hierarchical Poisson models (e.g. negative binomial) to model independent over-dispersion, but do not account for sample non-independence due to relatedness, population structure and/or hidden confounders. Here, we present a Poisson mixed model with two random effects terms that account for both independent over-dispersion and sample non-independence. We also develop a scalable sampling-based inference algorithm using a latent variable representation of the Poisson distribution. With simulations, we show that our method properly controls for type I error and is generally more powerful than other widely used approaches, except in small samples (n <15) with other unfavorable properties (e.g. small effect sizes). We also apply our method to three real datasets that contain related individuals, population stratification or hidden confounders. Our results show that our method increases power in all three data compared to other approaches, though the power gain is smallest in the smallest sample (n = 6). Our method is implemented in MACAU, freely available at www.xzlab.org/software.html. PMID:28369632

First-principles prediction of Si-doped Fe carbide as one of the possible constituents of Earth's inner core

NASA Astrophysics Data System (ADS)

Das, Tilak; Chatterjee, Swastika; Ghosh, Sujoy; Saha-Dasgupta, Tanusri

2017-09-01

We perform a computational study based on first-principles calculations to investigate the relative stability and elastic properties of the doped and undoped Fe carbide compounds at 200-364 GPa. We find that upon doping a few weight percent of Si impurities at the carbon sites in Fe7C3 carbide phases, the values of Poisson's ratio and density increase while VP, and VS decrease compared to their undoped counterparts. This leads to marked improvement in the agreement of seismic parameters such as P wave and S wave velocity, Poisson's ratio, and density with the Preliminary Reference Earth Model (PREM) data. The agreement with PREM data is found to be better for the orthorhombic phase of iron carbide (o-Fe7C3) compared to hexagonal phase (h-Fe7C3). Our theoretical analysis indicates that Fe carbide containing Si impurities can be a possible constituent of the Earth's inner core. Since the density of undoped Fe7C3 is low compared to that of inner core, as discussed in a recent theoretical study, our proposal of Si-doped Fe7C3 can provide an alternative solution as an important component of the Earth's inner core.

Using perinatal morbidity scoring tools as a primary study outcome.

PubMed

Hutcheon, Jennifer A; Bodnar, Lisa M; Platt, Robert W

2017-11-01

Perinatal morbidity scores are tools that score or weight different adverse events according to their relative severity. Perinatal morbidity scores are appealing for maternal-infant health researchers because they provide a way to capture a broad range of adverse events to mother and newborn while recognising that some events are considered more serious than others. However, they have proved difficult to implement as a primary outcome in applied research studies because of challenges in testing if the scores are significantly different between two or more study groups. We outline these challenges and describe a solution, based on Poisson regression, that allows differences in perinatal morbidity scores to be formally evaluated. The approach is illustrated using an existing maternal-neonatal scoring tool, the Adverse Outcome Index, to evaluate the safety of labour and delivery before and after the closure of obstetrical services in small rural communities. Applying the proposed Poisson regression to the case study showed a protective risk ratio for adverse outcome following closures as compared with the original analysis, where no difference was found. This approach opens the door for considerably broader use of perinatal morbidity scoring tools as a primary outcome in applied population and clinical maternal-infant health research studies. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Development of a finite element based delamination analysis for laminates subject to extension, bending, and torsion

NASA Technical Reports Server (NTRS)

Hooper, Steven J.

1989-01-01

Delamination is a common failure mode of laminated composite materials. This type of failure frequently occurs at the free edges of laminates where singular interlaminar stresses are developed due to the difference in Poisson's ratios between adjacent plies. Typically the delaminations develop between 90 degree plies and adjacent angle plies. Edge delamination has been studied by several investigators using a variety of techniques. Recently, Chan and Ochoa applied the quasi-three-dimensional finite element model to the analysis of a laminate subject to bending, extension, and torsion. This problem is of particular significance relative to the structural integrity of composite helicopter rotors. The task undertaken was to incorporate Chan and Ochoa's formulation into a Raju Q3DG program. The resulting program is capable of modeling extension, bending, and torsional mechanical loadings as well as thermal and hygroscopic loadings. The addition of the torsional and bending loading capability will provide the capability to perform a delamination analysis of a general unsymmetric laminate containing four cracks, each of a different length. The solutions obtained using this program are evaluated by comparing them with solutions from a full three-dimensional finite element solution. This comparison facilitates the assessment of three dimensional affects such as the warping constraint imposed by the load frame grips. It wlso facilitates the evaluation of the external load representation employed in the Q3D formulation. Finally, strain energy release rates computed from the three-dimensional results are compared with those predicted using the quasi-three-dimensional formulation.

Cracked rocks with positive and negative Poisson's ratio: real-crack properties extracted from pressure dependence of elastic-wave velocities

NASA Astrophysics Data System (ADS)

Zaitsev, Vladimir Y.; Radostin, Andrey V.; Dyskin, Arcady V.; Pasternak, Elena

2017-04-01

We report results of analysis of literature data on P- and S-wave velocities of rocks subjected to variable hydrostatic pressure. Out of about 90 examined samples, in more than 40% of the samples the reconstructed Poisson's ratios are negative for lowest confining pressure with gradual transition to the conventional positive values at higher pressure. The portion of rocks exhibiting negative Poisson's ratio appeared to be unexpectedly high. To understand the mechanism of negative Poisson's ratio, pressure dependences of P- and S-wave velocities were analyzed using the effective medium model in which the reduction in the elastic moduli due to cracks is described in terms of compliances with respect to shear and normal loading that are imparted to the rock by the presence of cracks. This is in contrast to widely used descriptions of effective cracked medium based on a specific crack model (e.g., penny-shape crack) in which the ratio between normal and shear compliances of such a crack is strictly predetermined. The analysis of pressure-dependences of the elastic wave velocities makes it possible to reveal the ratio between pure normal and shear compliances (called q-ratio below) for real defects and quantify their integral content in the rock. The examination performed demonstrates that a significant portion (over 50%) of cracks exhibit q-ratio several times higher than that assumed for the conventional penny-shape cracks. This leads to faster reduction of the Poisson's ratio with increasing the crack concentration. Samples with negative Poisson's ratio are characterized by elevated q-ratio and simultaneously crack concentration. Our results clearly indicate that the traditional crack model is not adequate for a significant portion of rocks and that the interaction between the opposite crack faces leading to domination of the normal compliance and reduced shear displacement discontinuity can play an important role in the mechanical behavior of rocks.

Quantifying biological samples using Linear Poisson Independent Component Analysis for MALDI-ToF mass spectra

PubMed Central

Deepaisarn, S; Tar, P D; Thacker, N A; Seepujak, A; McMahon, A W

2018-01-01

Abstract Motivation Matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI) facilitates the analysis of large organic molecules. However, the complexity of biological samples and MALDI data acquisition leads to high levels of variation, making reliable quantification of samples difficult. We present a new analysis approach that we believe is well-suited to the properties of MALDI mass spectra, based upon an Independent Component Analysis derived for Poisson sampled data. Simple analyses have been limited to studying small numbers of mass peaks, via peak ratios, which is known to be inefficient. Conventional PCA and ICA methods have also been applied, which extract correlations between any number of peaks, but we argue makes inappropriate assumptions regarding data noise, i.e. uniform and Gaussian. Results We provide evidence that the Gaussian assumption is incorrect, motivating the need for our Poisson approach. The method is demonstrated by making proportion measurements from lipid-rich binary mixtures of lamb brain and liver, and also goat and cow milk. These allow our measurements and error predictions to be compared to ground truth. Availability and implementation Software is available via the open source image analysis system TINA Vision, www.tina-vision.net. Contact paul.tar@manchester.ac.uk Supplementary information Supplementary data are available at Bioinformatics online. PMID:29091994

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law

NASA Astrophysics Data System (ADS)

Torres-Cordoba, Rafael; Martinez-Garcia, Edgar

2017-10-01

This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r )=φ(r (τ)) ) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle-beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian; Punjabi, Naresh M.

2013-01-01

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis. PMID:22241689

Analyte concentration at the tip of a nanopipette.

PubMed

Calander, Nils

2009-10-15

Concentration of molecules within the tips of nanopipettes when applying a DC voltage is herein investigated using finite-element simulations. The ion concentrations and fluxes due to diffusion, electro-migration, and electro-osmotic flow, and the electric potential are determined by the simultaneous solution of the Nernst-Planck, Poisson, and Navier-Stokes equations within the water solution containing sodium and chloride ions and negatively charged molecules. The electric potential within the pipette glass wall is at the same time determined by the Poisson equation together with appropriate boundary conditions and accounts for a field effect through the wall. Fixed negative surface charge on both the internal and external glass surfaces of the nanopipette is included together with the field effect through the glass wall to account for the electric double layer and the electro-osmosis. The inclusion of the field effect through the pipette wall is new compared to previous modeling of similar structures and is shown to be crucial for the behavior at the tip. It is demonstrated that the concentration of molecules is a consequence of ionic charge accumulation at the tip screening the electric field, thereby slowing down the electrophoretic motion of the molecules, which is further slowed down or stopped by the oppositely directed electro-osmosis. It is also shown that the trapping is very sensitive to the properties of the molecule, that is, its electrophoretic mobility and diffusion coefficient, the properties of the pipette, the ionic strength of the solution, and the applied electric field.

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

NASA Astrophysics Data System (ADS)

Martínez-Torres, David; Miranda, Eva

2018-01-01

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

Weather variability and the incidence of cryptosporidiosis: comparison of time series poisson regression and SARIMA models.

PubMed

Hu, Wenbiao; Tong, Shilu; Mengersen, Kerrie; Connell, Des

2007-09-01

Few studies have examined the relationship between weather variables and cryptosporidiosis in Australia. This paper examines the potential impact of weather variability on the transmission of cryptosporidiosis and explores the possibility of developing an empirical forecast system. Data on weather variables, notified cryptosporidiosis cases, and population size in Brisbane were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics for the period of January 1, 1996-December 31, 2004, respectively. Time series Poisson regression and seasonal auto-regression integrated moving average (SARIMA) models were performed to examine the potential impact of weather variability on the transmission of cryptosporidiosis. Both the time series Poisson regression and SARIMA models show that seasonal and monthly maximum temperature at a prior moving average of 1 and 3 months were significantly associated with cryptosporidiosis disease. It suggests that there may be 50 more cases a year for an increase of 1 degrees C maximum temperature on average in Brisbane. Model assessments indicated that the SARIMA model had better predictive ability than the Poisson regression model (SARIMA: root mean square error (RMSE): 0.40, Akaike information criterion (AIC): -12.53; Poisson regression: RMSE: 0.54, AIC: -2.84). Furthermore, the analysis of residuals shows that the time series Poisson regression appeared to violate a modeling assumption, in that residual autocorrelation persisted. The results of this study suggest that weather variability (particularly maximum temperature) may have played a significant role in the transmission of cryptosporidiosis. A SARIMA model may be a better predictive model than a Poisson regression model in the assessment of the relationship between weather variability and the incidence of cryptosporidiosis.

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data.

PubMed

Sepúlveda, Nuno; Campino, Susana G; Assefa, Samuel A; Sutherland, Colin J; Pain, Arnab; Clark, Taane G

2013-02-26

The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model. Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates. In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data.

A Conway-Maxwell-Poisson (CMP) model to address data dispersion on positron emission tomography.

PubMed

Santarelli, Maria Filomena; Della Latta, Daniele; Scipioni, Michele; Positano, Vincenzo; Landini, Luigi

2016-10-01

Positron emission tomography (PET) in medicine exploits the properties of positron-emitting unstable nuclei. The pairs of γ- rays emitted after annihilation are revealed by coincidence detectors and stored as projections in a sinogram. It is well known that radioactive decay follows a Poisson distribution; however, deviation from Poisson statistics occurs on PET projection data prior to reconstruction due to physical effects, measurement errors, correction of deadtime, scatter, and random coincidences. A model that describes the statistical behavior of measured and corrected PET data can aid in understanding the statistical nature of the data: it is a prerequisite to develop efficient reconstruction and processing methods and to reduce noise. The deviation from Poisson statistics in PET data could be described by the Conway-Maxwell-Poisson (CMP) distribution model, which is characterized by the centring parameter λ and the dispersion parameter ν, the latter quantifying the deviation from a Poisson distribution model. In particular, the parameter ν allows quantifying over-dispersion (ν<1) or under-dispersion (ν>1) of data. A simple and efficient method for λ and ν parameters estimation is introduced and assessed using Monte Carlo simulation for a wide range of activity values. The application of the method to simulated and experimental PET phantom data demonstrated that the CMP distribution parameters could detect deviation from the Poisson distribution both in raw and corrected PET data. It may be usefully implemented in image reconstruction algorithms and quantitative PET data analysis, especially in low counting emission data, as in dynamic PET data, where the method demonstrated the best accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

Internal electric fields of electrolytic solutions induced by space-charge polarization

NASA Astrophysics Data System (ADS)

Sawada, Atsushi

2006-10-01

The dielectric dispersion of electrolytic solutions prepared using chlorobenzene as a solvent and tetrabutylammonium tetraphenylborate as a solute is analyzed in terms of space-charge polarization in order to derive the ionic constants, and the Stokes radius obtained is discussed in comparison with the values that have been measured by conductometry. A homogeneous internal electric field is assumed for simplicity in the analysis of the space-charge polarization. The justification of the approximation by the homogeneous field is discussed from two points of view: one is the accuracy of the Stokes radius value observed and the other is the effect of bound charges on electrodes in which they level the highly inhomogeneous field, which has been believed in the past. In order to investigate the actual electric field, numerical calculations based on the Poisson equation are carried out by considering the influence of the bound charges. The variation of the number of bound charges with time is clarified by determining the relaxation function of the dielectric constant attributed to the space-charge polarization. Finally, a technique based on a two-field approximation, where homogeneous and hyperbolic fields are independently applied in relevant frequency ranges, is introduced to analyze the space-charge polarization of the electrolytic solutions, and further improvement of the accuracy in the determination of the Stokes radius is achieved.

Mechanical Properties of Additively Manufactured Thick Honeycombs.

PubMed

Hedayati, Reza; Sadighi, Mojtaba; Mohammadi Aghdam, Mohammad; Zadpoor, Amir Abbas

2016-07-23

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson's ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions.

Multiple co-clustering based on nonparametric mixture models with heterogeneous marginal distributions

PubMed Central

Yoshimoto, Junichiro; Shimizu, Yu; Okada, Go; Takamura, Masahiro; Okamoto, Yasumasa; Yamawaki, Shigeto; Doya, Kenji

2017-01-01

We propose a novel method for multiple clustering, which is useful for analysis of high-dimensional data containing heterogeneous types of features. Our method is based on nonparametric Bayesian mixture models in which features are automatically partitioned (into views) for each clustering solution. This feature partition works as feature selection for a particular clustering solution, which screens out irrelevant features. To make our method applicable to high-dimensional data, a co-clustering structure is newly introduced for each view. Further, the outstanding novelty of our method is that we simultaneously model different distribution families, such as Gaussian, Poisson, and multinomial distributions in each cluster block, which widens areas of application to real data. We apply the proposed method to synthetic and real data, and show that our method outperforms other multiple clustering methods both in recovering true cluster structures and in computation time. Finally, we apply our method to a depression dataset with no true cluster structure available, from which useful inferences are drawn about possible clustering structures of the data. PMID:29049392

Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces

NASA Astrophysics Data System (ADS)

Zhao, Jihong; Liu, Qiao

2017-07-01

In Guo and Wang (2012) [10], Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a strongly coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. We show that some weighted negative Besov norms of solutions are preserved along time evolution, and obtain the optimal time decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

Formulation of the Multi-Hit Model With a Non-Poisson Distribution of Hits

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

Vassiliev, Oleg N., E-mail: Oleg.Vassiliev@albertahealthservices.ca

2012-07-15

Purpose: We proposed a formulation of the multi-hit single-target model in which the Poisson distribution of hits was replaced by a combination of two distributions: one for the number of particles entering the target and one for the number of hits a particle entering the target produces. Such an approach reflects the fact that radiation damage is a result of two different random processes: particle emission by a radiation source and interaction of particles with matter inside the target. Methods and Materials: Poisson distribution is well justified for the first of the two processes. The second distribution depends on howmore » a hit is defined. To test our approach, we assumed that the second distribution was also a Poisson distribution. The two distributions combined resulted in a non-Poisson distribution. We tested the proposed model by comparing it with previously reported data for DNA single- and double-strand breaks induced by protons and electrons, for survival of a range of cell lines, and variation of the initial slopes of survival curves with radiation quality for heavy-ion beams. Results: Analysis of cell survival equations for this new model showed that they had realistic properties overall, such as the initial and high-dose slopes of survival curves, the shoulder, and relative biological effectiveness (RBE) In most cases tested, a better fit of survival curves was achieved with the new model than with the linear-quadratic model. The results also suggested that the proposed approach may extend the multi-hit model beyond its traditional role in analysis of survival curves to predicting effects of radiation quality and analysis of DNA strand breaks. Conclusions: Our model, although conceptually simple, performed well in all tests. The model was able to consistently fit data for both cell survival and DNA single- and double-strand breaks. It correctly predicted the dependence of radiation effects on parameters of radiation quality.« less

Dynamic Response of Layered TiB/Ti Functionally Graded Material Specimens

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

Byrd, Larry; Beberniss, Tim; Chapman, Ben

2008-02-15

This paper covers the dynamic response of rectangular (25.4x101.6x3.175 mm) specimens manufactured from layers of TiB/Ti. The layers contained volume fractions of TiB that varied from 0 to 85% and thus formed a functionally graded material. Witness samples of the 85% TiB material were also tested to provide a baseline for the statistical variability of the test techniques. Static and dynamic tests were performed to determine the in situ material properties and fundamental frequencies. Damping in the material/ fixture was also found from the dynamic response. These tests were simulated using composite beam theory which gave an analytical solution, andmore » using finite element analysis. The response of the 85% TiB specimens was found to be much more uniform than the functionally graded material and the dynamic response more uniform than the static response. A least squares analysis of the data using the analytical solutions were used to determine the elastic modulus and Poisson's ratio of each layer. These results were used to model the response in the finite element analysis. The results indicate that current analytical and numerical methods for modeling the material give similar and adequate predictions for natural frequencies if the measured property values were used. The models did not agree as well if the properties from the manufacturer or those of Hill and Linn were used.« less

Analytic solution of magnetic induction distribution of ideal hollow spherical field sources

NASA Astrophysics Data System (ADS)

Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

2017-12-01

The Halbach type hollow spherical permanent magnet arrays (HSPMA) are volume compacted, energy efficient field sources, and capable of producing multi-Tesla field in the cavity of the array, which have attracted intense interests in many practical applications. Here, we present analytical solutions of magnetic induction to the ideal HSPMA in entire space, outside of array, within the cavity of array, and in the interior of the magnet. We obtain solutions using concept of magnetic charge to solve the Poisson's and Laplace's equations for the HSPMA. Using these analytical field expressions inside the material, a scalar demagnetization function is defined to approximately indicate the regions of magnetization reversal, partial demagnetization, and inverse magnetic saturation. The analytical field solution provides deeper insight into the nature of HSPMA and offer guidance in designing optimized one.

Vibrational Power Flow Analysis of Rods and Beams

NASA Technical Reports Server (NTRS)

Wohlever, James Christopher; Bernhard, R. J.

1988-01-01

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

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.

Three-dimensional elasticity solution of an infinite plate with a circular hole

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.

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.

Electroosmotic flow of Phan-Thien-Tanner fluids at high zeta potentials: An exact analytical solution

NASA Astrophysics Data System (ADS)

Sarma, Rajkumar; Deka, Nabajit; Sarma, Kuldeep; Mondal, Pranab Kumar

2018-06-01

We present a mathematical model to study the electroosmotic flow of a viscoelastic fluid in a parallel plate microchannel with a high zeta potential, taking hydrodynamic slippage at the walls into account in the underlying analysis. We use the simplified Phan-Thien-Tanner (s-PTT) constitutive relationships to describe the rheological behavior of the viscoelastic fluid, while Navier's slip law is employed to model the interfacial hydrodynamic slip. Here, we derive analytical solutions for the potential distribution, flow velocity, and volumetric flow rate based on the complete Poisson-Boltzmann equation (without considering the frequently used Debye-Hückel linear approximation). For the underlying electrokinetic transport, this investigation primarily reveals the influence of fluid rheology, wall zeta potential as modulated by the interfacial electrochemistry and interfacial slip on the velocity distribution, volumetric flow rate, and fluid stress, as well as the apparent viscosity. We show that combined with the viscoelasticity of the fluid, a higher wall zeta potential and slip coefficient lead to a phenomenal enhancement in the volumetric flow rate. We believe that this analysis, besides providing a deep theoretical insight to interpret the transport process, will also serve as a fundamental design tool for microfluidic devices/systems under electrokinetic influence.

Poisson-event-based analysis of cell proliferation.

PubMed

Summers, Huw D; Wills, John W; Brown, M Rowan; Rees, Paul

2015-05-01

A protocol for the assessment of cell proliferation dynamics is presented. This is based on the measurement of cell division events and their subsequent analysis using Poisson probability statistics. Detailed analysis of proliferation dynamics in heterogeneous populations requires single cell resolution within a time series analysis and so is technically demanding to implement. Here, we show that by focusing on the events during which cells undergo division rather than directly on the cells themselves a simplified image acquisition and analysis protocol can be followed, which maintains single cell resolution and reports on the key metrics of cell proliferation. The technique is demonstrated using a microscope with 1.3 μm spatial resolution to track mitotic events within A549 and BEAS-2B cell lines, over a period of up to 48 h. Automated image processing of the bright field images using standard algorithms within the ImageJ software toolkit yielded 87% accurate recording of the manually identified, temporal, and spatial positions of the mitotic event series. Analysis of the statistics of the interevent times (i.e., times between observed mitoses in a field of view) showed that cell division conformed to a nonhomogeneous Poisson process in which the rate of occurrence of mitotic events, λ exponentially increased over time and provided values of the mean inter mitotic time of 21.1 ± 1.2 hours for the A549 cells and 25.0 ± 1.1 h for the BEAS-2B cells. Comparison of the mitotic event series for the BEAS-2B cell line to that predicted by random Poisson statistics indicated that temporal synchronisation of the cell division process was occurring within 70% of the population and that this could be increased to 85% through serum starvation of the cell culture. © 2015 International Society for Advancement of Cytometry.

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.

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.

Optimal Matched Filter in the Low-number Count Poisson Noise Regime and Implications for X-Ray Source Detection

NASA Astrophysics Data System (ADS)

Ofek, Eran O.; Zackay, Barak

2018-04-01

Detection of templates (e.g., sources) embedded in low-number count Poisson noise is a common problem in astrophysics. Examples include source detection in X-ray images, γ-rays, UV, neutrinos, and search for clusters of galaxies and stellar streams. However, the solutions in the X-ray-related literature are sub-optimal in some cases by considerable factors. Using the lemma of Neyman–Pearson, we derive the optimal statistics for template detection in the presence of Poisson noise. We demonstrate that, for known template shape (e.g., point sources), this method provides higher completeness, for a fixed false-alarm probability value, compared with filtering the image with the point-spread function (PSF). In turn, we find that filtering by the PSF is better than filtering the image using the Mexican-hat wavelet (used by wavdetect). For some background levels, our method improves the sensitivity of source detection by more than a factor of two over the popular Mexican-hat wavelet filtering. This filtering technique can also be used for fast PSF photometry and flare detection; it is efficient and straightforward to implement. We provide an implementation in MATLAB. The development of a complete code that works on real data, including the complexities of background subtraction and PSF variations, is deferred for future publication.

Zero-inflated Poisson regression models for QTL mapping applied to tick-resistance in a Gyr × Holstein F2 population

PubMed Central

Silva, Fabyano Fonseca; Tunin, Karen P.; Rosa, Guilherme J.M.; da Silva, Marcos V.B.; Azevedo, Ana Luisa Souza; da Silva Verneque, Rui; Machado, Marco Antonio; Packer, Irineu Umberto

2011-01-01

Now a days, an important and interesting alternative in the control of tick-infestation in cattle is to select resistant animals, and identify the respective quantitative trait loci (QTLs) and DNA markers, for posterior use in breeding programs. The number of ticks/animal is characterized as a discrete-counting trait, which could potentially follow Poisson distribution. However, in the case of an excess of zeros, due to the occurrence of several noninfected animals, zero-inflated Poisson and generalized zero-inflated distribution (GZIP) may provide a better description of the data. Thus, the objective here was to compare through simulation, Poisson and ZIP models (simple and generalized) with classical approaches, for QTL mapping with counting phenotypes under different scenarios, and to apply these approaches to a QTL study of tick resistance in an F2 cattle (Gyr × Holstein) population. It was concluded that, when working with zero-inflated data, it is recommendable to use the generalized and simple ZIP model for analysis. On the other hand, when working with data with zeros, but not zero-inflated, the Poisson model or a data-transformation-approach, such as square-root or Box-Cox transformation, are applicable. PMID:22215960

Holonomy, quantum mechanics and the signal-tuned Gabor approach to the striate cortex

NASA Astrophysics Data System (ADS)

Torreão, José R. A.

2016-02-01

It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantum systems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantum system whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantum mechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.

Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.

PubMed

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2017-07-01

For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<β and β>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve. © 2016 Society for Risk Analysis.

Parallel Cartesian grid refinement for 3D complex flow simulations

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2013-11-01

A second order accurate method for discretizing the Navier-Stokes equations on 3D unstructured Cartesian grids is presented. Although the grid generator is based on the oct-tree hierarchical method, fully unstructured data-structure is adopted enabling robust calculations for incompressible flows, avoiding both the need of synchronization of the solution between different levels of refinement and usage of prolongation/restriction operators. The current solver implements a hybrid staggered/non-staggered grid layout, employing the implicit fractional step method to satisfy the continuity equation. The pressure-Poisson equation is discretized by using a novel second order fully implicit scheme for unstructured Cartesian grids and solved using an efficient Krylov subspace solver. The momentum equation is also discretized with second order accuracy and the high performance Newton-Krylov method is used for integrating them in time. Neumann and Dirichlet conditions are used to validate the Poisson solver against analytical functions and grid refinement results to a significant reduction of the solution error. The effectiveness of the fractional step method results in the stability of the overall algorithm and enables the performance of accurate multi-resolution real life simulations. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482.

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.

Analysis of energy states in modulation doped multiquantum well heterostructures

NASA Technical Reports Server (NTRS)

Ji, G.; Henderson, T.; Peng, C. K.; Huang, D.; Morkoc, H.

1990-01-01

A precise and effective numerical procedure to model the band diagram of modulation doped multiquantum well heterostructures is presented. This method is based on a self-consistent iterative solution of the Schroedinger equation and the Poisson equation. It can be used rather easily in any arbitrary modulation-doped structure. In addition to confined energy subbands, the unconfined states can be calculated as well. Examples on realistic device structures are given to demonstrate capabilities of this procedure. The numerical results are in good agreement with experiments. With the aid of this method the transitions involving both the confined and unconfined conduction subbands in a modulation doped AlGaAs/GaAs superlattice, and in a strained layer InGaAs/GaAs superlattice are identified. These results represent the first observation of unconfined transitions in modulation doped multiquantum well structures.

Differential expression analysis for RNAseq using Poisson mixed models.

PubMed

Sun, Shiquan; Hood, Michelle; Scott, Laura; Peng, Qinke; Mukherjee, Sayan; Tung, Jenny; Zhou, Xiang

2017-06-20

Identifying differentially expressed (DE) genes from RNA sequencing (RNAseq) studies is among the most common analyses in genomics. However, RNAseq DE analysis presents several statistical and computational challenges, including over-dispersed read counts and, in some settings, sample non-independence. Previous count-based methods rely on simple hierarchical Poisson models (e.g. negative binomial) to model independent over-dispersion, but do not account for sample non-independence due to relatedness, population structure and/or hidden confounders. Here, we present a Poisson mixed model with two random effects terms that account for both independent over-dispersion and sample non-independence. We also develop a scalable sampling-based inference algorithm using a latent variable representation of the Poisson distribution. With simulations, we show that our method properly controls for type I error and is generally more powerful than other widely used approaches, except in small samples (n <15) with other unfavorable properties (e.g. small effect sizes). We also apply our method to three real datasets that contain related individuals, population stratification or hidden confounders. Our results show that our method increases power in all three data compared to other approaches, though the power gain is smallest in the smallest sample (n = 6). Our method is implemented in MACAU, freely available at www.xzlab.org/software.html. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

DISCRETE COMPOUND POISSON PROCESSES AND TABLES OF THE GEOMETRIC POISSON DISTRIBUTION.

DTIC Science & Technology

A concise summary of the salient properties of discrete Poisson processes , with emphasis on comparing the geometric and logarithmic Poisson processes . The...the geometric Poisson process are given for 176 sets of parameter values. New discrete compound Poisson processes are also introduced. These...processes have properties that are particularly relevant when the summation of several different Poisson processes is to be analyzed. This study provides the

A Poisson process approximation for generalized K-5 confidence regions

NASA Technical Reports Server (NTRS)

Arsham, H.; Miller, D. R.

1982-01-01

One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.

Analysis of single-molecule fluorescence spectroscopic data with a Markov-modulated Poisson process.

PubMed

Jäger, Mark; Kiel, Alexander; Herten, Dirk-Peter; Hamprecht, Fred A

2009-10-05

We present a photon-by-photon analysis framework for the evaluation of data from single-molecule fluorescence spectroscopy (SMFS) experiments using a Markov-modulated Poisson process (MMPP). A MMPP combines a discrete (and hidden) Markov process with an additional Poisson process reflecting the observation of individual photons. The algorithmic framework is used to automatically analyze the dynamics of the complex formation and dissociation of Cu2+ ions with the bidentate ligand 2,2'-bipyridine-4,4'dicarboxylic acid in aqueous media. The process of association and dissociation of Cu2+ ions is monitored with SMFS. The dcbpy-DNA conjugate can exist in two or more distinct states which influence the photon emission rates. The advantage of a photon-by-photon analysis is that no information is lost in preprocessing steps. Different model complexities are investigated in order to best describe the recorded data and to determine transition rates on a photon-by-photon basis. The main strength of the method is that it allows to detect intermittent phenomena which are masked by binning and that are difficult to find using correlation techniques when they are short-lived.

Flood return level analysis of Peaks over Threshold series under changing climate

NASA Astrophysics Data System (ADS)

Li, L.; Xiong, L.; Hu, T.; Xu, C. Y.; Guo, S.

2016-12-01

Obtaining insights into future flood estimation is of great significance for water planning and management. Traditional flood return level analysis with the stationarity assumption has been challenged by changing environments. A method that takes into consideration the nonstationarity context has been extended to derive flood return levels for Peaks over Threshold (POT) series. With application to POT series, a Poisson distribution is normally assumed to describe the arrival rate of exceedance events, but this distribution assumption has at times been reported as invalid. The Negative Binomial (NB) distribution is therefore proposed as an alternative to the Poisson distribution assumption. Flood return levels were extrapolated in nonstationarity context for the POT series of the Weihe basin, China under future climate scenarios. The results show that the flood return levels estimated under nonstationarity can be different with an assumption of Poisson and NB distribution, respectively. The difference is found to be related to the threshold value of POT series. The study indicates the importance of distribution selection in flood return level analysis under nonstationarity and provides a reference on the impact of climate change on flood estimation in the Weihe basin for the future.

Survival analysis of clinical mastitis data using a nested frailty Cox model fit as a mixed-effects Poisson model.

PubMed

Elghafghuf, Adel; Dufour, Simon; Reyher, Kristen; Dohoo, Ian; Stryhn, Henrik

2014-12-01

Mastitis is a complex disease affecting dairy cows and is considered to be the most costly disease of dairy herds. The hazard of mastitis is a function of many factors, both managerial and environmental, making its control a difficult issue to milk producers. Observational studies of clinical mastitis (CM) often generate datasets with a number of characteristics which influence the analysis of those data: the outcome of interest may be the time to occurrence of a case of mastitis, predictors may change over time (time-dependent predictors), the effects of factors may change over time (time-dependent effects), there are usually multiple hierarchical levels, and datasets may be very large. Analysis of such data often requires expansion of the data into the counting-process format - leading to larger datasets - thus complicating the analysis and requiring excessive computing time. In this study, a nested frailty Cox model with time-dependent predictors and effects was applied to Canadian Bovine Mastitis Research Network data in which 10,831 lactations of 8035 cows from 69 herds were followed through lactation until the first occurrence of CM. The model was fit to the data as a Poisson model with nested normally distributed random effects at the cow and herd levels. Risk factors associated with the hazard of CM during the lactation were identified, such as parity, calving season, herd somatic cell score, pasture access, fore-stripping, and proportion of treated cases of CM in a herd. The analysis showed that most of the predictors had a strong effect early in lactation and also demonstrated substantial variation in the baseline hazard among cows and between herds. A small simulation study for a setting similar to the real data was conducted to evaluate the Poisson maximum likelihood estimation approach with both Gaussian quadrature method and Laplace approximation. Further, the performance of the two methods was compared with the performance of a widely used estimation approach for frailty Cox models based on the penalized partial likelihood. The simulation study showed good performance for the Poisson maximum likelihood approach with Gaussian quadrature and biased variance component estimates for both the Poisson maximum likelihood with Laplace approximation and penalized partial likelihood approaches. Copyright © 2014. Published by Elsevier B.V.

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

Exact Closed-form Solutions for Lamb's Problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-04-01

In this article, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem, for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's (1974) integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson (1974), which strongly confirms the correctness of our explicit formulas. It is hoped that in due time, these formulas may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Exact closed-form solutions for Lamb's problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-07-01

In this paper, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson, which strongly confirms the correctness of our explicit formulae. It is hoped that in due time, these formulae may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Characteristics of 0.8- and 0.2-microns gate length In(x)Ga(1-x) As/In(0.52)Al(0.48)As/InP (0.53 less than or equal to x less than or equal to 0.70) modulation-doped field-effect transistors at cryogenic temperatures

NASA Technical Reports Server (NTRS)

Lai, Richard; Bhattacharya, Pallab K.; Yang, David; Brock, Timothy L.; Alterovitz, Samuel A.; Downey, Alan N.

1993-01-01

The performance characteristics of InP-based In(x)Ga(1-x)As/In(0.52)Al(0.48)As (0.53 is less than or equal to x is less than or equal to 0.70) pseudomorphic modulation-doped field-effect transistors (MODFET's) as a function of strain in the channel, gate, length, and temperature were investigated analytically and experimentally. The strain in the channel was varied by varying the In composition x. The temperature was varied in the range of 40-300 K and the devices have gate lengths L(sub g) of 0.8 and 0.2 microns. Analysis of the device was done using a one-dimensional self consistent solution of the Poisson and Schroedinger equations in the channel, a two-dimensional Poisson solver to obtain the channel electric field, and a Monte Carlo simulation to estimate the carrier transit times in the channel. An increase in the value of the cutoff frequency is predicted for an increase in In composition, a decrease in temperature, and a decrease in gate length. The improvements seen with decreasing temperature, decreasing gate length, and increased In composition were smaller than those predicted by analysis. The experimental results on pseudomorphic InGaAs/InAlAs MODFET's showed that there is a 15-30 percent improvement in cutoff frequency in both the 0.8- and 0.2-micron gate length devices when the temperature is lowered from 300 to 40 K.

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

NASA Astrophysics Data System (ADS)

Frahm, Klaus M.; Shepelyansky, Dima L.

2014-04-01

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.

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.

Selecting the right statistical model for analysis of insect count data by using information theoretic measures.

PubMed

Sileshi, G

2006-10-01

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

Method for resonant measurement

DOEpatents

Rhodes, G.W.; Migliori, A.; Dixon, R.D.

1996-03-05

A method of measurement of objects to determine object flaws, Poisson`s ratio ({sigma}) and shear modulus ({mu}) is shown and described. First, the frequency for expected degenerate responses is determined for one or more input frequencies and then splitting of degenerate resonant modes are observed to identify the presence of flaws in the object. Poisson`s ratio and the shear modulus can be determined by identification of resonances dependent only on the shear modulus, and then using that shear modulus to find Poisson`s ratio using other modes dependent on both the shear modulus and Poisson`s ratio. 1 fig.

A comparison of different statistical methods analyzing hypoglycemia data using bootstrap simulations.

PubMed

Jiang, Honghua; Ni, Xiao; Huster, William; Heilmann, Cory

2015-01-01

Hypoglycemia has long been recognized as a major barrier to achieving normoglycemia with intensive diabetic therapies. It is a common safety concern for the diabetes patients. Therefore, it is important to apply appropriate statistical methods when analyzing hypoglycemia data. Here, we carried out bootstrap simulations to investigate the performance of the four commonly used statistical models (Poisson, negative binomial, analysis of covariance [ANCOVA], and rank ANCOVA) based on the data from a diabetes clinical trial. Zero-inflated Poisson (ZIP) model and zero-inflated negative binomial (ZINB) model were also evaluated. Simulation results showed that Poisson model inflated type I error, while negative binomial model was overly conservative. However, after adjusting for dispersion, both Poisson and negative binomial models yielded slightly inflated type I errors, which were close to the nominal level and reasonable power. Reasonable control of type I error was associated with ANCOVA model. Rank ANCOVA model was associated with the greatest power and with reasonable control of type I error. Inflated type I error was observed with ZIP and ZINB models.

Determination of oral mucosal Poisson's ratio and coefficient of friction from in-vivo contact pressure measurements.

PubMed

Chen, Junning; Suenaga, Hanako; Hogg, Michael; Li, Wei; Swain, Michael; Li, Qing

2016-01-01

Despite their considerable importance to biomechanics, there are no existing methods available to directly measure apparent Poisson's ratio and friction coefficient of oral mucosa. This study aimed to develop an inverse procedure to determine these two biomechanical parameters by utilizing in vivo experiment of contact pressure between partial denture and beneath mucosa through nonlinear finite element (FE) analysis and surrogate response surface (RS) modelling technique. First, the in vivo denture-mucosa contact pressure was measured by a tactile electronic sensing sheet. Second, a 3D FE model was constructed based on the patient CT images. Third, a range of apparent Poisson's ratios and the coefficients of friction from literature was considered as the design variables in a series of FE runs for constructing a RS surrogate model. Finally, the discrepancy between computed in silico and measured in vivo results was minimized to identify the best matching Poisson's ratio and coefficient of friction. The established non-invasive methodology was demonstrated effective to identify such biomechanical parameters of oral mucosa and can be potentially used for determining the biomaterial properties of other soft biological tissues.

Stationary spiral flow in polytropic stellar models

PubMed Central

Pekeris, C. L.

1980-01-01

It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models. PMID:16592825

The transverse Poisson's ratio of composites.

NASA Technical Reports Server (NTRS)

Foye, R. L.

1972-01-01

An expression is developed that makes possible the prediction of Poisson's ratio for unidirectional composites with reference to any pair of orthogonal axes that are normal to the direction of the reinforcing fibers. This prediction appears to be a reasonable one in that it follows the trends of the finite element analysis and the bounding estimates, and has the correct limiting value for zero fiber content. It can only be expected to apply to composites containing stiff, circular, isotropic fibers bonded to a soft matrix material.

The Spot of Arago and Its Role in Aberration Analysis.

DTIC Science & Technology

1983-12-01

Finally, my family and in- laws were always there with patience, love and support. This thesis would have been impossible were it not for my wife...five was chosen to judge the entries. The panel members were Laplace, Biot, Arago, Sime6n Denis Poisson and Joseph - Louis Gay- Lussac . Laplace, Biot and...Poisson were staunch adherents of P the particle theory of light while Arago advocated Fresnel’s view. P - *..*. ..-. 9 Gay- Lussac , a chemist, was

Limits, discovery and cut optimization for a Poisson process with uncertainty in background and signal efficiency: TRolke 2.0

NASA Astrophysics Data System (ADS)

Lundberg, J.; Conrad, J.; Rolke, W.; Lopez, A.

2010-03-01

A C++ class was written for the calculation of frequentist confidence intervals using the profile likelihood method. Seven combinations of Binomial, Gaussian, Poissonian and Binomial uncertainties are implemented. The package provides routines for the calculation of upper and lower limits, sensitivity and related properties. It also supports hypothesis tests which take uncertainties into account. It can be used in compiled C++ code, in Python or interactively via the ROOT analysis framework. Program summaryProgram title: TRolke version 2.0 Catalogue identifier: AEFT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license No. of lines in distributed program, including test data, etc.: 3431 No. of bytes in distributed program, including test data, etc.: 21 789 Distribution format: tar.gz Programming language: ISO C++. Computer: Unix, GNU/Linux, Mac. Operating system: Linux 2.6 (Scientific Linux 4 and 5, Ubuntu 8.10), Darwin 9.0 (Mac-OS X 10.5.8). RAM:˜20 MB Classification: 14.13. External routines: ROOT ( http://root.cern.ch/drupal/) Nature of problem: The problem is to calculate a frequentist confidence interval on the parameter of a Poisson process with statistical or systematic uncertainties in signal efficiency or background. Solution method: Profile likelihood method, Analytical Running time:<10 seconds per extracted limit.

Information transmission in hippocampal CA1 neuron models in the presence of poisson shot noise: the case of periodic sub-threshold spike trains.

PubMed

Kawaguchi, Minato; Mino, Hiroyuki; Durand, Dominique M

2006-01-01

This article presents an analysis of the information transmission of periodic sub-threshold spike trains in a hippocampal CA1 neuron model in the presence of a homogeneous Poisson shot noise. In the computer simulation, periodic sub-threshold spike trains were presented repeatedly to the midpoint of the main apical branch, while the homogeneous Poisson shot noise was applied to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the inter spike intervals were generated and then the probability, p(T), of the inter-spike interval histogram corresponding to the spike interval, r, of the periodic input spike trains was estimated to obtain an index of information transmission. In the present article, it is shown that at a specific amplitude of the homogeneous Poisson shot noise, p(T) was found to be maximized, as well as the possibility to encode the periodic sub-threshold spike trains became greater. It was implied that setting the amplitude of the homogeneous Poisson shot noise to the specific values which maximize the information transmission might contribute to efficiently encoding the periodic sub-threshold spike trains by utilizing the stochastic resonance.

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data

PubMed Central

2013-01-01

Background The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model. Results Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates. Conclusions In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data. PMID:23442253

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Coulette, David

2016-08-01

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.

Does the U.S. exercise contagion on Italy? A theoretical model and empirical evidence

NASA Astrophysics Data System (ADS)

Cerqueti, Roy; Fenga, Livio; Ventura, Marco

2018-06-01

This paper deals with the theme of contagion in financial markets. At this aim, we develop a model based on Mixed Poisson Processes to describe the abnormal returns of financial markets of two considered countries. In so doing, the article defines the theoretical conditions to be satisfied in order to state that one of them - the so-called leader - exercises contagion on the others - the followers. Specifically, we employ an invariant probabilistic result stating that a suitable transformation of a Mixed Poisson Process is still a Mixed Poisson Process. The theoretical claim is validated by implementing an extensive simulation analysis grounded on empirical data. The countries considered are the U.S. (as the leader) and Italy (as the follower) and the period under scrutiny is very large, ranging from 1970 to 2014.

Brain, music, and non-Poisson renewal processes

NASA Astrophysics Data System (ADS)

Bianco, Simone; Ignaccolo, Massimiliano; Rider, Mark S.; Ross, Mary J.; Winsor, Phil; Grigolini, Paolo

2007-06-01

In this paper we show that both music composition and brain function, as revealed by the electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a technique of statistical analysis recently developed by our group, the aging experiment (AE). First, we find that in both cases the distances between two consecutive events are described by nonexponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities Ψ(t) are well fitted by stretched exponentials [ Ψ(t)∝exp (-(γt)α) , with 0.5<α<1 .] The second step rests on the adoption of AE, which shows that these are renewal processes. We show that the stretched exponential, due to its renewal character, is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index μ=1+α . Adopting the AE procedure we find that both EEG and music composition yield μ<2 . On the basis of the recently discovered complexity matching effect, according to which a complex system S with μS<2 responds only to a complex driving signal P with μP⩽μS , we conclude that the results of our analysis may explain the influence of music on the human brain.

Numerical Analysis of 2-D and 3-D MHD Flows Relevant to Fusion Applications

DOE PAGES

Khodak, Andrei

2017-08-21

Here, the analysis of many fusion applications such as liquid-metal blankets requires application of computational fluid dynamics (CFD) methods for electrically conductive liquids in geometrically complex regions and in the presence of a strong magnetic field. A current state of the art general purpose CFD code allows modeling of the flow in complex geometric regions, with simultaneous conjugated heat transfer analysis in liquid and surrounding solid parts. Together with a magnetohydrodynamics (MHD) capability, the general purpose CFD code will be a valuable tool for the design and optimization of fusion devices. This paper describes an introduction of MHD capability intomore » the general purpose CFD code CFX, part of the ANSYS Workbench. The code was adapted for MHD problems using a magnetic induction approach. CFX allows introduction of user-defined variables using transport or Poisson equations. For MHD adaptation of the code three additional transport equations were introduced for the components of the magnetic field, in addition to the Poisson equation for electric potential. The Lorentz force is included in the momentum transport equation as a source term. Fusion applications usually involve very strong magnetic fields, with values of the Hartmann number of up to tens of thousands. In this situation a system of MHD equations become very rigid with very large source terms and very strong variable gradients. To increase system robustness, special measures were introduced during the iterative convergence process, such as linearization using source coefficient for momentum equations. The MHD implementation in general purpose CFD code was tested against benchmarks, specifically selected for liquid-metal blanket applications. Results of numerical simulations using present implementation closely match analytical solutions for a Hartmann number of up to 1500 for a 2-D laminar flow in the duct of square cross section, with conducting and nonconducting walls. Results for a 3-D test case are also included.« less

Numerical Analysis of 2-D and 3-D MHD Flows Relevant to Fusion Applications

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

Khodak, Andrei

Here, the analysis of many fusion applications such as liquid-metal blankets requires application of computational fluid dynamics (CFD) methods for electrically conductive liquids in geometrically complex regions and in the presence of a strong magnetic field. A current state of the art general purpose CFD code allows modeling of the flow in complex geometric regions, with simultaneous conjugated heat transfer analysis in liquid and surrounding solid parts. Together with a magnetohydrodynamics (MHD) capability, the general purpose CFD code will be a valuable tool for the design and optimization of fusion devices. This paper describes an introduction of MHD capability intomore » the general purpose CFD code CFX, part of the ANSYS Workbench. The code was adapted for MHD problems using a magnetic induction approach. CFX allows introduction of user-defined variables using transport or Poisson equations. For MHD adaptation of the code three additional transport equations were introduced for the components of the magnetic field, in addition to the Poisson equation for electric potential. The Lorentz force is included in the momentum transport equation as a source term. Fusion applications usually involve very strong magnetic fields, with values of the Hartmann number of up to tens of thousands. In this situation a system of MHD equations become very rigid with very large source terms and very strong variable gradients. To increase system robustness, special measures were introduced during the iterative convergence process, such as linearization using source coefficient for momentum equations. The MHD implementation in general purpose CFD code was tested against benchmarks, specifically selected for liquid-metal blanket applications. Results of numerical simulations using present implementation closely match analytical solutions for a Hartmann number of up to 1500 for a 2-D laminar flow in the duct of square cross section, with conducting and nonconducting walls. Results for a 3-D test case are also included.« less

Large Occurrence Patterns of New Zealand Deep Earthquakes: Characterization by Use of a Switching Poisson Model

NASA Astrophysics Data System (ADS)

Shaochuan, Lu; Vere-Jones, David

2011-10-01

The paper studies the statistical properties of deep earthquakes around North Island, New Zealand. We first evaluate the catalogue coverage and completeness of deep events according to cusum (cumulative sum) statistics and earlier literature. The epicentral, depth, and magnitude distributions of deep earthquakes are then discussed. It is worth noting that strong grouping effects are observed in the epicentral distribution of these deep earthquakes. Also, although the spatial distribution of deep earthquakes does not change, their occurrence frequencies vary from time to time, active in one period, relatively quiescent in another. The depth distribution of deep earthquakes also hardly changes except for events with focal depth less than 100 km. On the basis of spatial concentration we partition deep earthquakes into several groups—the Taupo-Bay of Plenty group, the Taranaki group, and the Cook Strait group. Second-order moment analysis via the two-point correlation function reveals only very small-scale clustering of deep earthquakes, presumably limited to some hot spots only. We also suggest that some models usually used for shallow earthquakes fit deep earthquakes unsatisfactorily. Instead, we propose a switching Poisson model for the occurrence patterns of deep earthquakes. The goodness-of-fit test suggests that the time-varying activity is well characterized by a switching Poisson model. Furthermore, detailed analysis carried out on each deep group by use of switching Poisson models reveals similar time-varying behavior in occurrence frequencies in each group.

Impact of traffic congestion on road accidents: a spatial analysis of the M25 motorway in England.

PubMed

Wang, Chao; Quddus, Mohammed A; Ison, Stephen G

2009-07-01

Traffic congestion and road accidents are two external costs of transport and the reduction of their impacts is often one of the primary objectives for transport policy makers. The relationship between traffic congestion and road accidents however is not apparent and less studied. It is speculated that there may be an inverse relationship between traffic congestion and road accidents, and as such this poses a potential dilemma for transport policy makers. This study aims to explore the impact of traffic congestion on the frequency of road accidents using a spatial analysis approach, while controlling for other relevant factors that may affect road accidents. The M25 London orbital motorway, divided into 70 segments, was chosen to conduct this study and relevant data on road accidents, traffic and road characteristics were collected. A robust technique has been developed to map M25 accidents onto its segments. Since existing studies have often used a proxy to measure the level of congestion, this study has employed a precise congestion measurement. A series of Poisson based non-spatial (such as Poisson-lognormal and Poisson-gamma) and spatial (Poisson-lognormal with conditional autoregressive priors) models have been used to account for the effects of both heterogeneity and spatial correlation. The results suggest that traffic congestion has little or no impact on the frequency of road accidents on the M25 motorway. All other relevant factors have provided results consistent with existing studies.

Orientational analysis of planar fibre systems observed as a Poisson shot-noise process.

PubMed

Kärkkäinen, Salme; Lantuéjoul, Christian

2007-10-01

We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Kärkkäinen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampling lines is constant. This assumption is proved to be valid asymptotically for Boolean models and dead leaves models, under some regularity conditions. In this work, we derive the scaled variogram and its approximations for a planar Poisson shot-noise process using the modified Bessel function. In the case of reasonable high resolution of the observed image, the scaled variogram has an approximate functional relation to the point intensity, and in the case of high resolution the relation is proportional. As the obtained relations are approximative, they are tested on simulations. The existing orientation analysis method based on the proportional relation is further experimented on images with different resolutions. The new result, the asymptotic proportionality between the scaled variograms and the point intensities for a Poisson shot-noise process, completes the earlier results for the Boolean models and for the dead leaves models.

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

Assessing model uncertainty using hexavalent chromium and ...

EPA Pesticide Factsheets

Introduction: The National Research Council recommended quantitative evaluation of uncertainty in effect estimates for risk assessment. This analysis considers uncertainty across model forms and model parameterizations with hexavalent chromium [Cr(VI)] and lung cancer mortality as an example. The objective of this analysis is to characterize model uncertainty by evaluating the variance in estimates across several epidemiologic analyses.Methods: This analysis compared 7 publications analyzing two different chromate production sites in Ohio and Maryland. The Ohio cohort consisted of 482 workers employed from 1940-72, while the Maryland site employed 2,357 workers from 1950-74. Cox and Poisson models were the only model forms considered by study authors to assess the effect of Cr(VI) on lung cancer mortality. All models adjusted for smoking and included a 5-year exposure lag, however other latency periods and model covariates such as age and race were considered. Published effect estimates were standardized to the same units and normalized by their variances to produce a standardized metric to compare variability in estimates across and within model forms. A total of 7 similarly parameterized analyses were considered across model forms, and 23 analyses with alternative parameterizations were considered within model form (14 Cox; 9 Poisson). Results: Across Cox and Poisson model forms, adjusted cumulative exposure coefficients for 7 similar analyses ranged from 2.47

Developing descriptors to predict mechanical properties of nanotubes.

PubMed

Borders, Tammie L; Fonseca, Alexandre F; Zhang, Hengji; Cho, Kyeongjae; Rusinko, Andrew

2013-04-22

Descriptors and quantitative structure property relationships (QSPR) were investigated for mechanical property prediction of carbon nanotubes (CNTs). 78 molecular dynamics (MD) simulations were carried out, and 20 descriptors were calculated to build quantitative structure property relationships (QSPRs) for Young's modulus and Poisson's ratio in two separate analyses: vacancy only and vacancy plus methyl functionalization. In the first analysis, C(N2)/C(T) (number of non-sp2 hybridized carbons per the total carbons) and chiral angle were identified as critical descriptors for both Young's modulus and Poisson's ratio. Further analysis and literature findings indicate the effect of chiral angle is negligible at larger CNT radii for both properties. Raman spectroscopy can be used to measure C(N2)/C(T), providing a direct link between experimental and computational results. Poisson's ratio approaches two different limiting values as CNT radii increases: 0.23-0.25 for chiral and armchair CNTs and 0.10 for zigzag CNTs (surface defects <3%). In the second analysis, the critical descriptors were C(N2)/C(T), chiral angle, and M(N)/C(T) (number of methyl groups per total carbons). These results imply new types of defects can be represented as a new descriptor in QSPR models. Finally, results are qualified and quantified against experimental data.

Characterization and modeling of tensile behavior of ceramic woven fabric composites

NASA Technical Reports Server (NTRS)

Kuo, Wen-Shyong; Chen, Wennei Y.; Parvizi-Majidi, Azar; Chou, Tsu-Wei

1991-01-01

This paper examines the tensile behavior of SiC/SiC fabric composites. In the characterization effort, the stress-strain relation and damage evolution are studied with a series of loading and unloading tensile test experiments. The stress-strain relation is linear in response to the initial loading and becomes nonlinear when loading exceeds the proportional limit. Transverse cracking has been observed to be a dominant damage mode governing the nonlinear deformation. The damage is initiated at the inter-tow pores where fiber yarns cross over each other. In the modeling work, the analysis is based upon a fiber bundle model, in which fiber undulation in the warp and fill directions and gaps among fiber yarns have been taken into account. Two limiting cases of fabric stacking arrangements are studied. Closed form solutions are obtained for the composite stiffness and Poisson's ratio. Transverse cracking in the composite is discussed by applying a constant failure strain criterion.

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.

Topics in elementary particle physics

NASA Astrophysics Data System (ADS)

Jin, Xiang

The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

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.

Effective implementation of wavelet Galerkin method

NASA Astrophysics Data System (ADS)

Finěk, Václav; Šimunková, Martina

2012-11-01

It was proved by W. Dahmen et al. that an adaptive wavelet scheme is asymptotically optimal for a wide class of elliptic equations. This scheme approximates the solution u by a linear combination of N wavelets and a benchmark for its performance is the best N-term approximation, which is obtained by retaining the N largest wavelet coefficients of the unknown solution. Moreover, the number of arithmetic operations needed to compute the approximate solution is proportional to N. The most time consuming part of this scheme is the approximate matrix-vector multiplication. In this contribution, we will introduce our implementation of wavelet Galerkin method for Poisson equation -Δu = f on hypercube with homogeneous Dirichlet boundary conditions. In our implementation, we identified nonzero elements of stiffness matrix corresponding to the above problem and we perform matrix-vector multiplication only with these nonzero elements.

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

Random Dopant Induced Threshold Voltage Lowering and Fluctuations in Sub-0.1 (micron)meter MOSFET's: A 3-D 'Atomistic' Simulation Study

NASA Technical Reports Server (NTRS)

Asenov, Asen

1998-01-01

A three-dimensional (3-D) "atomistic" simulation study of random dopant induced threshold voltage lowering and fluctuations in sub-0.1 microns MOSFET's is presented. For the first time a systematic analysis of random dopant effects down to an individual dopant level was carried out in 3-D on a scale sufficient to provide quantitative statistical predictions. Efficient algorithms based on a single multigrid solution of the Poisson equation followed by the solution of a simplified current continuity equation are used in the simulations. The effects of various MOSFET design parameters, including the channel length and width, oxide thickness and channel doping, on the threshold voltage lowering and fluctuations are studied using typical samples of 200 atomistically different MOSFET's. The atomistic results for the threshold voltage fluctuations were compared with two analytical models based on dopant number fluctuations. Although the analytical models predict the general trends in the threshold voltage fluctuations, they fail to describe quantitatively the magnitude of the fluctuations. The distribution of the atomistically calculated threshold voltage and its correlation with the number of dopants in the channel of the MOSFET's was analyzed based on a sample of 2500 microscopically different devices. The detailed analysis shows that the threshold voltage fluctuations are determined not only by the fluctuation in the dopant number, but also in the dopant position.

Influence of chromatic aberrations on space charge ion optics.

PubMed

Whealton, J H; Tsai, C C

1978-04-01

By solution to the Poisson-Vlasov equation the influence of fluctuations (chromatic aberrations) on ion optics is shown for various accelerator designs : (1) cylindrical bore triode with various aspect ratios, (2) pseudo-Pierce shaped electrode triode at various aspect ratios, (3) insulated coating emission electrode triode for various preacceleration potentials, and (4) cylindrical bore tetrodes for various field distributions. Fluctuation levels of 20% can be very important in limiting the ion optics in certain cases.

Proceedings of the DARPA/AFML Review of Progress in Quantitative Nondestructive Evaluation, 8-13 July, La Jolla, California.

DTIC Science & Technology

1980-07-01

Solution of the Nonlinear Eddy Current and Loss Problems in Quasilinear Poisson Equation in a Nonuniform the Solid Rotors of Large Turbogenerators...stable probe support and aiid possibly also for the effect of a nonuniform Scanning mechanisms, especially for test pieces of magnetic field...without specimen): defects such as inclusions, voids, delaminations, 55 db and nonuniform particle distribution. Due to im- Dynamic range: 50 to 70

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.

Development of a Fuel Spill/Vapor Migration Modeling System.

DTIC Science & Technology

1985-12-01

transforms resulting in a direct solution of the differential equation. A second order finite * difference approximation to the Poisson equation A2*j is...7 O-A64 043 DEVELOPMENT OF A FUEL SPILL/VPOR MIGRATION MODELING 1/2 SYSTEM(U) TRACER TECHNOLOGIES ESCONDIDO Cflo IL 0 ENGLAND ET AL. DEC 85 RFURL...AFWAL-TR-85-2089 DEVELOPMENT OF A FUEL SPILL/VAPOR MIGRATION MODELING SYSTEM W.G. England * L.H. Teuscher TRACER TECHNOLOGIES DTIC *2120 WEST MISSION

Lateral tunneling through voltage-controlled barriers

NASA Technical Reports Server (NTRS)

Manion, S. J.; Bell, L. D.; Kaiser, W. J.; Maker, P. D.; Muller, R. E.

1991-01-01

The paper reports on a detailed experimental investigation of lateral tunneling between electrodes of a two-dimensional electron gas separated by the voltage-controlled barrier of a nanometer Schottky gate. The experimental data are modeled using the WKB method to calculate the tunneling probability of electrons through a barrier whose shape is determined from a solution of the two-dimensional Poisson equation. This model is in excellent agreement with the experimental data over a two order of magnitude range of current.

Higher spin Chern-Simons theory and the super Boussinesq hierarchy

NASA Astrophysics Data System (ADS)

Gutperle, Michael; Li, Yi

2018-05-01

In this paper, we construct a map between a solution of supersymmetric Chern-Simons higher spin gravity based on the superalgebra sl(3|2) with Lifshitz scaling and the N = 2 super Boussinesq hierarchy. We show that under this map the time evolution equations of both theories coincide. In addition, we identify the Poisson structure of the Chern-Simons theory induced by gauge transformation with the second Hamiltonian structure of the super Boussinesq hierarchy.

Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

NASA Astrophysics Data System (ADS)

Jo, Hang-Hyun; Perotti, Juan I.; Kaski, Kimmo; Kertész, János

2014-01-01

Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

PubMed Central

Gongadze, E.; van Rienen, U.; Kralj-Iglič, V.; Iglič, A.

2012-01-01

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin-Poisson-Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin-Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson-Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field. PMID:22263808

Improved confidence intervals when the sample is counted an integer times longer than the blank.

PubMed

Potter, William Edward; Strzelczyk, Jadwiga Jodi

2011-05-01

Past computer solutions for confidence intervals in paired counting are extended to the case where the ratio of the sample count time to the blank count time is taken to be an integer, IRR. Previously, confidence intervals have been named Neyman-Pearson confidence intervals; more correctly they should have been named Neyman confidence intervals or simply confidence intervals. The technique utilized mimics a technique used by Pearson and Hartley to tabulate confidence intervals for the expected value of the discrete Poisson and Binomial distributions. The blank count and the contribution of the sample to the gross count are assumed to be Poisson distributed. The expected value of the blank count, in the sample count time, is assumed known. The net count, OC, is taken to be the gross count minus the product of IRR with the blank count. The probability density function (PDF) for the net count can be determined in a straightforward manner.

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.

FAST TRACK COMMUNICATION: Shear coordinate description of the quantized versal unfolding of a D4 singularity

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2010-11-01

In this communication, by using Teichmüller theory of a sphere with four holes/orbifold points, we obtain a system of flat coordinates on the general affine cubic surface having a D4 singularity at the origin. We show that the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere coincides with the Etingof-Ginzburg Poisson bracket on the affine D4 cubic. We prove that this bracket is the image under the Riemann-Hilbert map of the Poisson-Lie bracket on \\oplus _{1}^3\\mathfrak {sl}^\\ast (2,{{\\bb C}}) . We realize the action of the mapping class group by the action of the braid group on the geodesic functions. This action coincides with the procedure of analytic continuation of solutions of the sixth Painlevé equation. Finally, we produce the explicit quantization of the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere and of the braid group action.

Massively parallel algorithms for real-time wavefront control of a dense adaptive optics system

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

Fijany, A.; Milman, M.; Redding, D.

1994-12-31

In this paper massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. The authors have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although, this represents an optimal computation, due the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. They develop a novel algorithm,more » designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. Due to these features, this algorithm is significantly more efficient than other Fast Poisson Solvers for implementation on massively parallel architectures. The authors also discuss two massively parallel, algorithmically specialized, architectures for low-cost and optimal implementation of the Fast Invariant Imbedding algorithm.« less

Data-Driven Significance Estimation for Precise Spike Correlation

PubMed Central

Grün, Sonja

2009-01-01

The mechanisms underlying neuronal coding and, in particular, the role of temporal spike coordination are hotly debated. However, this debate is often confounded by an implicit discussion about the use of appropriate analysis methods. To avoid incorrect interpretation of data, the analysis of simultaneous spike trains for precise spike correlation needs to be properly adjusted to the features of the experimental spike trains. In particular, nonstationarity of the firing of individual neurons in time or across trials, a spike train structure deviating from Poisson, or a co-occurrence of such features in parallel spike trains are potent generators of false positives. Problems can be avoided by including these features in the null hypothesis of the significance test. In this context, the use of surrogate data becomes increasingly important, because the complexity of the data typically prevents analytical solutions. This review provides an overview of the potential obstacles in the correlation analysis of parallel spike data and possible routes to overcome them. The discussion is illustrated at every stage of the argument by referring to a specific analysis tool (the Unitary Events method). The conclusions, however, are of a general nature and hold for other analysis techniques. Thorough testing and calibration of analysis tools and the impact of potentially erroneous preprocessing stages are emphasized. PMID:19129298

On the Singularity of the Vlasov-Poisson System

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

and Hong Qin, Jian Zheng

2013-04-26

The Vlasov-Poisson system can be viewed as the collisionless limit of the corresponding Fokker- Planck-Poisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the Fokker-Planck-Poisson system when the collision frequency v approaches zero. However, we show that the colllisionless Vlasov-Poisson system is a singular limit of the collisional Fokker-Planck-Poisson system, and Landau's result can be recovered only as the approaching zero from the positive side.

On the singularity of the Vlasov-Poisson system

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

Zheng, Jian; Qin, Hong; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08550

2013-09-15

The Vlasov-Poisson system can be viewed as the collisionless limit of the corresponding Fokker-Planck-Poisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the Fokker-Planck-Poisson system when the collision frequency ν approaches zero. However, we show that the collisionless Vlasov-Poisson system is a singular limit of the collisional Fokker-Planck-Poisson system, and Landau's result can be recovered only as the ν approaches zero from the positive side.

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

NASA Astrophysics Data System (ADS)

Radev, Dimitar; Lokshina, Izabella

2010-11-01

The paper examines self-similar (or fractal) properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced fractal models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behavior of IP network traffic data are developed and applied. Numerical examples are provided; and simulation results are obtained and analyzed.

Effect of non-Poisson samples on turbulence spectra from laser velocimetry

NASA Technical Reports Server (NTRS)

Sree, Dave; Kjelgaard, Scott O.; Sellers, William L., III

1994-01-01

Spectral analysis of laser velocimetry (LV) data plays an important role in characterizing a turbulent flow and in estimating the associated turbulence scales, which can be helpful in validating theoretical and numerical turbulence models. The determination of turbulence scales is critically dependent on the accuracy of the spectral estimates. Spectral estimations from 'individual realization' laser velocimetry data are typically based on the assumption of a Poisson sampling process. What this Note has demonstrated is that the sampling distribution must be considered before spectral estimates are used to infer turbulence scales.

Effect of ion concentration, solution and membrane permittivity on electric energy storage and capacitance.

PubMed

Tajparast, Mohammad; Glavinović, Mladen I

2018-06-06

Bio-membranes as capacitors store electric energy, but their permittivity is low whereas the permittivity of surrounding solution is high. To evaluate the effective capacitance of the membrane/solution system and determine the electric energy stored within the membrane and in the solution, we estimated their electric variables using Poisson-Nernst-Planck simulations. We calculated membrane and solution capacitances from stored electric energy. The effective capacitance was calculated by fitting a six-capacitance model to charges (fixed and ion) and associated potentials, because it cannot be considered as a result of membrane and solution capacitance in series. The electric energy stored within the membrane (typically much smaller than that in the solution), depends on the membrane permittivity, but also on the external electric field, surface charge density, water permittivity and ion concentration. The effect on capacitances is more specific. Solution capacitance rises with greater solution permittivity or ion concentration, but the membrane capacitance (much smaller than solution capacitance) is only influenced by its permittivity. Interestingly, the effective capacitance is independent of membrane or solution permittivity, but rises as the ion concentration increases and surface charge becomes positive. Experimental estimates of membrane capacitance are thus not necessarily a reliable index of its surface area. Copyright © 2018. Published by Elsevier B.V.

Relative age effect in elite soccer: More early-born players, but no better valued, and no paragon clubs or countries

PubMed Central

Doyle, John R.

2018-01-01

The paper analyses two datasets of elite soccer players (top 1000 professionals and UEFA Under-19 Youth League). In both, we find a Relative Age Effect (RAE) for frequency, but not for value. That is, while there are more players born at the start of the competition year, their transfer values are no higher, nor are they given more game time. We use Poisson regression to derive a transparent index of the discrimination present in RAE. Also, because Poisson is valid for small frequency counts, it supports analysis at the disaggregated levels of country and club. From this, we conclude there are no paragon clubs or countries immune to RAE; that is clubs and countries do not differ systematically in the RAE they experience; also, that Poisson regression is a powerful and flexible method of analysing RAE data. PMID:29420576

Study of photon correlation techniques for processing of laser velocimeter signals

NASA Technical Reports Server (NTRS)

Mayo, W. T., Jr.

1977-01-01

The objective was to provide the theory and a system design for a new type of photon counting processor for low level dual scatter laser velocimeter (LV) signals which would be capable of both the first order measurements of mean flow and turbulence intensity and also the second order time statistics: cross correlation auto correlation, and related spectra. A general Poisson process model for low level LV signals and noise which is valid from the photon-resolved regime all the way to the limiting case of nonstationary Gaussian noise was used. Computer simulation algorithms and higher order statistical moment analysis of Poisson processes were derived and applied to the analysis of photon correlation techniques. A system design using a unique dual correlate and subtract frequency discriminator technique is postulated and analyzed. Expectation analysis indicates that the objective measurements are feasible.

On the fractal characterization of Paretian Poisson processes

NASA Astrophysics Data System (ADS)

Eliazar, Iddo I.; Sokolov, Igor M.

2012-06-01

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.

Nambu-Poisson gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-06-01

We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action, give its first order expansion in the Nambu-Poisson tensor and relate it to a Nambu-Poisson matrix model.

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.

Mechanical properties of regular porous biomaterials made from truncated cube repeating unit cells: Analytical solutions and computational models.

PubMed

Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A

2016-03-01

Additive manufacturing (AM) has enabled fabrication of open-cell porous biomaterials based on repeating unit cells. The micro-architecture of the porous biomaterials and, thus, their physical properties could then be precisely controlled. Due to their many favorable properties, porous biomaterials manufactured using AM are considered as promising candidates for bone substitution as well as for several other applications in orthopedic surgery. The mechanical properties of such porous structures including static and fatigue properties are shown to be strongly dependent on the type of the repeating unit cell based on which the porous biomaterial is built. In this paper, we study the mechanical properties of porous biomaterials made from a relatively new unit cell, namely truncated cube. We present analytical solutions that relate the dimensions of the repeating unit cell to the elastic modulus, Poisson's ratio, yield stress, and buckling load of those porous structures. We also performed finite element modeling to predict the mechanical properties of the porous structures. The analytical solution and computational results were found to be in agreement with each other. The mechanical properties estimated using both the analytical and computational techniques were somewhat higher than the experimental data reported in one of our recent studies on selective laser melted Ti-6Al-4V porous biomaterials. In addition to porosity, the elastic modulus and Poisson's ratio of the porous structures were found to be strongly dependent on the ratio of the length of the inclined struts to that of the uninclined (i.e. vertical or horizontal) struts, α, in the truncated cube unit cell. The geometry of the truncated cube unit cell approaches the octahedral and cube unit cells when α respectively approaches zero and infinity. Consistent with those geometrical observations, the analytical solutions presented in this study approached those of the octahedral and cube unit cells when α approached respectively 0 and infinity. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

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.

Mechanical properties of additively manufactured octagonal honeycombs.

PubMed

Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A

2016-12-01

Honeycomb structures have found numerous applications as structural and biomedical materials due to their favourable properties such as low weight, high stiffness, and porosity. Application of additive manufacturing and 3D printing techniques allows for manufacturing of honeycombs with arbitrary shape and wall thickness, opening the way for optimizing the mechanical and physical properties for specific applications. In this study, the mechanical properties of honeycomb structures with a new geometry, called octagonal honeycomb, were investigated using analytical, numerical, and experimental approaches. An additive manufacturing technique, namely fused deposition modelling, was used to fabricate the honeycomb from polylactic acid (PLA). The honeycombs structures were then mechanically tested under compression and the mechanical properties of the structures were determined. In addition, the Euler-Bernoulli and Timoshenko beam theories were used for deriving analytical relationships for elastic modulus, yield stress, Poisson's ratio, and buckling stress of this new design of honeycomb structures. Finite element models were also created to analyse the mechanical behaviour of the honeycombs computationally. The analytical solutions obtained using Timoshenko beam theory were close to computational results in terms of elastic modulus, Poisson's ratio and yield stress, especially for relative densities smaller than 25%. The analytical solutions based on the Timoshenko analytical solution and the computational results were in good agreement with experimental observations. Finally, the elastic properties of the proposed honeycomb structure were compared to those of other honeycomb structures such as square, triangular, hexagonal, mixed, diamond, and Kagome. The octagonal honeycomb showed yield stress and elastic modulus values very close to those of regular hexagonal honeycombs and lower than the other considered honeycombs. Copyright © 2016 Elsevier B.V. All rights reserved.

Truly self-consistent solution of Kohn-Sham equations for extended systems with inhomogeneous electron gas

NASA Astrophysics Data System (ADS)

Shul'man, A. Ya; Posvyanskii, D. V.

2014-05-01

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistent solution method for infinite systems involves iterations with alternate solutions of the Poisson and Schrödinger equations. One of problems with such an approach is that the charge distribution, updated by solving the Schrodinger equation, may be incompatible with the boundary conditions of the Poisson equation for Coulomb potential. The resulting instability or divergence manifests itself most appreciably in the case of infinitely extended systems because the corresponding boundary-value problem becomes singular. In this work the stable iterative scheme for solving the Kohn-Sham equations for infinite systems with inhomogeneous electron gas is described based on eliminating the long-range character of the Coulomb interaction, which causes the tight coupling of the charge distribution with the boundary conditions. This algorithm has been previously successfully implemented in the calculation of work function and surface energy of simple metals in the jellium model. Here it is used to calculate the energy spectrum of quasi-two-dimensional electron gas in the accumulation layer at the semiconductor surface n-InAs. The electrons in such a structure occupy states that belong to both discrete and continuous parts of the energy spectrum. This causes the problems of convergence in the usually used approaches, which do not exist in our case. Because of the narrow bandgap of InAs, it is necessary to take the nonparabolicity of the conduction band into account; this is done by means of a new effective mass method. The calculated quasi-two-dimensional energy bands correspond well to experimental data measured by the angle resolved photoelectron spectroscopy technique.

Model-independent constraints on modified gravity from current data and from the Euclid and SKA future surveys

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

Taddei, Laura; Martinelli, Matteo; Amendola, Luca, E-mail: taddei@thphys.uni-heidelberg.de, E-mail: martinelli@lorentz.leidenuniv.nl, E-mail: amendola@thphys.uni-heidelberg.de

2016-12-01

The aim of this paper is to constrain modified gravity with redshift space distortion observations and supernovae measurements. Compared with a standard ΛCDM analysis, we include three additional free parameters, namely the initial conditions of the matter perturbations, the overall perturbation normalization, and a scale-dependent modified gravity parameter modifying the Poisson equation, in an attempt to perform a more model-independent analysis. First, we constrain the Poisson parameter Y (also called G {sub eff}) by using currently available f σ{sub 8} data and the recent SN catalog JLA. We find that the inclusion of the additional free parameters makes the constraintsmore » significantly weaker than when fixing them to the standard cosmological value. Second, we forecast future constraints on Y by using the predicted growth-rate data for Euclid and SKA missions. Here again we point out the weakening of the constraints when the additional parameters are included. Finally, we adopt as modified gravity Poisson parameter the specific Horndeski form, and use scale-dependent forecasts to build an exclusion plot for the Yukawa potential akin to the ones realized in laboratory experiments, both for the Euclid and the SKA surveys.« less

Probabilistic structural analysis methods for improving Space Shuttle engine reliability

NASA Technical Reports Server (NTRS)

Boyce, L.

1989-01-01

Probabilistic structural analysis methods are particularly useful in the design and analysis of critical structural components and systems that operate in very severe and uncertain environments. These methods have recently found application in space propulsion systems to improve the structural reliability of Space Shuttle Main Engine (SSME) components. A computer program, NESSUS, based on a deterministic finite-element program and a method of probabilistic analysis (fast probability integration) provides probabilistic structural analysis for selected SSME components. While computationally efficient, it considers both correlated and nonnormal random variables as well as an implicit functional relationship between independent and dependent variables. The program is used to determine the response of a nickel-based superalloy SSME turbopump blade. Results include blade tip displacement statistics due to the variability in blade thickness, modulus of elasticity, Poisson's ratio or density. Modulus of elasticity significantly contributed to blade tip variability while Poisson's ratio did not. Thus, a rational method for choosing parameters to be modeled as random is provided.

A Three-dimensional Polymer Scaffolding Material Exhibiting a Zero Poisson's Ratio.

PubMed

Soman, Pranav; Fozdar, David Y; Lee, Jin Woo; Phadke, Ameya; Varghese, Shyni; Chen, Shaochen

2012-05-14

Poisson's ratio describes the degree to which a material contracts (expands) transversally when axially strained. A material with a zero Poisson's ratio does not transversally deform in response to an axial strain (stretching). In tissue engineering applications, scaffolding having a zero Poisson's ratio (ZPR) may be more suitable for emulating the behavior of native tissues and accommodating and transmitting forces to the host tissue site during wound healing (or tissue regrowth). For example, scaffolding with a zero Poisson's ratio may be beneficial in the engineering of cartilage, ligament, corneal, and brain tissues, which are known to possess Poisson's ratios of nearly zero. Here, we report a 3D biomaterial constructed from polyethylene glycol (PEG) exhibiting in-plane Poisson's ratios of zero for large values of axial strain. We use digital micro-mirror device projection printing (DMD-PP) to create single- and double-layer scaffolds composed of semi re-entrant pores whose arrangement and deformation mechanisms contribute the zero Poisson's ratio. Strain experiments prove the zero Poisson's behavior of the scaffolds and that the addition of layers does not change the Poisson's ratio. Human mesenchymal stem cells (hMSCs) cultured on biomaterials with zero Poisson's ratio demonstrate the feasibility of utilizing these novel materials for biological applications which require little to no transverse deformations resulting from axial strains. Techniques used in this work allow Poisson's ratio to be both scale-independent and independent of the choice of strut material for strains in the elastic regime, and therefore ZPR behavior can be imparted to a variety of photocurable biomaterial.

From Loss of Memory to Poisson.

ERIC Educational Resources Information Center

Johnson, Bruce R.

1983-01-01

A way of presenting the Poisson process and deriving the Poisson distribution for upper-division courses in probability or mathematical statistics is presented. The main feature of the approach lies in the formulation of Poisson postulates with immediate intuitive appeal. (MNS)

An alternative to reduction of surface pressure to sea level

NASA Technical Reports Server (NTRS)

Deardorff, J. W.

1982-01-01

The pitfalls of the present method of reducing surface pressure to sea level are reviewed, and an alternative, adjusted pressure, P, is proposed. P is obtained from solution of a Poisson equation over a continental region, using the simplest boundary condition along the perimeter or coastline where P equals the sea level pressure. The use of P would avoid the empiricisms and disadvantages of pressure reduction to sea level, and would produce surface pressure charts which depict the true geostrophic wind at the surface.

Spectral multigrid methods for the solution of homogeneous turbulence problems

NASA Technical Reports Server (NTRS)

Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.

1987-01-01

New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

Towards classical spectrum generating algebras for f-deformations

NASA Astrophysics Data System (ADS)

Kullock, Ricardo; Latini, Danilo

2016-01-01

In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.

Theory of ion-matrix-sheath dynamics

NASA Astrophysics Data System (ADS)

Kos, L.; Tskhakaya, D. D.

2018-01-01

The time evolution of a one-dimensional, uni-polar ion sheath (an "ion matrix sheath") is investigated. The analytical solutions for the ion-fluid and Poisson's equations are found for an arbitrary time dependence of the wall-applied negative potential. In the case that the wall potential is large and remains constant after its ramp-up application, the explicit time dependencies of the sheath's parameters during the initial stage of the process are given. The characteristic rate of approaching the stationary state, satisfying the Child-Langmuir law, is determined.

Lateral trapping of DNA inside a voltage gated nanopore

NASA Astrophysics Data System (ADS)

Töws, Thomas; Reimann, Peter

2017-06-01

The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic, fully three-dimensional setup as well as analytical approximations for a simplified model are worked out. By applying a suitable voltage to the membrane electrode, the DNA can be forced to preferably traverse the pore either along the pore axis or at a small but finite distance from the pore wall.

Acoustic Inverse Scattering for Breast Cancer Microcalcification Detection. Addendum

DTIC Science & Technology

2011-12-01

the center. To conserve space, few are shown here. A graph comparing the spatial location and the error in reconstruction will follow...following graphs show the error in reconstruction as a function of position of the object along the x-axis, y-axis and the diagonal in the fourth quadrant of...the well-known Kirchhoff – Poisson formulas (see, e.g., Refs. [33,34]) allow one to rep- resent the solution p(x,t) in terms of the spherical means

Biocompatible Zr-Al-Fe bulk metallic glasses with large plasticity

NASA Astrophysics Data System (ADS)

Hua, NengBin; Li, Ran; Wang, JianFeng; Zhang, Tao

2012-09-01

In the present study, high-zirconium ternary Zr-Al-Fe bulk metallic glasses (BMGs) with low Young's modulus and good plasticity were developed. Zr75Al7.5Fe17.5 BMG exhibits a low Young's modulus of 70 GPa and high Poisson's ratio of 0.403. Pronounced plasticity was demonstrated under both compression and bending conditions for the BMGs. Furthermore, the alloys show high corrosion resistance in phosphate buffered solution. The combination of desirable mechanical and chemical properties implies potential for biomedical applications.

Compact scheme for systems of equations applied to fundamental problems of mechanics of continua

NASA Technical Reports Server (NTRS)

Klimkowski, Jerzy Z.

1990-01-01

Compact scheme formulation was used in the treatment of boundary conditions for a system of coupled diffusion and Poisson equations. Models and practical solutions of specific engineering problems arising in solid mechanics, chemical engineering, heat transfer and fuid mechanics are described and analyzed for efficiency and accuracy. Only 2-D cases are discussed and a new method of numerical treatment of boundary conditions common in the fundamental problems of mechanics of continua is presented.

Predictive model for convective flows induced by surface reactivity contrast

NASA Astrophysics Data System (ADS)

Davidson, Scott M.; Lammertink, Rob G. H.; Mani, Ali

2018-05-01

Concentration gradients in a fluid adjacent to a reactive surface due to contrast in surface reactivity generate convective flows. These flows result from contributions by electro- and diffusio-osmotic phenomena. In this study, we have analyzed reactive patterns that release and consume protons, analogous to bimetallic catalytic conversion of peroxide. Similar systems have typically been studied using either scaling analysis to predict trends or costly numerical simulation. Here, we present a simple analytical model, bridging the gap in quantitative understanding between scaling relations and simulations, to predict the induced potentials and consequent velocities in such systems without the use of any fitting parameters. Our model is tested against direct numerical solutions to the coupled Poisson, Nernst-Planck, and Stokes equations. Predicted slip velocities from the model and simulations agree to within a factor of ≈2 over a multiple order-of-magnitude change in the input parameters. Our analysis can be used to predict enhancement of mass transport and the resulting impact on overall catalytic conversion, and is also applicable to predicting the speed of catalytic nanomotors.

An analytical method for the inverse Cauchy problem of Lame equation in a rectangle

NASA Astrophysics Data System (ADS)

Grigor’ev, Yu

2018-04-01

In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Theory of space-charge polarization for determining ionic constants of electrolytic solutions

NASA Astrophysics Data System (ADS)

Sawada, Atsushi

2007-06-01

A theoretical expression of the complex dielectric constant attributed to space-charge polarization has been derived under an electric field calculated using Poisson's equation considering the effects of bound charges on ions. The frequency dependence of the complex dielectric constant of chlorobenzene solutions doped with tetrabutylammonium tetraphenylborate (TBATPB) has been analyzed using the theoretical expression, and the impact of the bound charges on the complex dielectric constant has been clarified quantitatively in comparison with a theory that does not consider the effect of the bound charges. The Stokes radius of TBA +(=TPB-) determined by the present theory shows a good agreement with that determined by conductometry in the past; hence, the present theory should be applicable to the direct determination of the mobility of ion species in an electrolytic solution without the need to measure ionic limiting equivalent conductance and transport number.

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

GRAPEVINE: Grids about anything by Poisson's equation in a visually interactive networking environment

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.; Mccann, Karen

1992-01-01

A proven 3-D multiple-block elliptic grid generator, designed to run in 'batch mode' on a supercomputer, is improved by the creation of a modern graphical user interface (GUI) running on a workstation. The two parts are connected in real time by a network. The resultant system offers a significant speedup in the process of preparing and formatting input data and the ability to watch the grid solution converge by replotting the grid at each iteration step. The result is a reduction in user time and CPU time required to generate the grid and an enhanced understanding of the elliptic solution process. This software system, called GRAPEVINE, is described, and certain observations are made concerning the creation of such software.

Relaxation dynamics in the presence of pulse multiplicative noise sources with different correlation properties

NASA Astrophysics Data System (ADS)

Kargovsky, A. V.; Chichigina, O. A.; Anashkina, E. I.; Valenti, D.; Spagnolo, B.

2015-10-01

The relaxation dynamics of a system described by a Langevin equation with pulse multiplicative noise sources with different correlation properties is considered. The solution of the corresponding Fokker-Planck equation is derived for Gaussian white noise. Moreover, two pulse processes with regulated periodicity are considered as a noise source: the dead-time-distorted Poisson process and the process with fixed time intervals, which is characterized by an infinite correlation time. We find that the steady state of the system is dependent on the correlation properties of the pulse noise. An increase of the noise correlation causes the decrease of the mean value of the solution at the steady state. The analytical results are in good agreement with the numerical ones.

Relaxation dynamics in the presence of pulse multiplicative noise sources with different correlation properties.

PubMed

Kargovsky, A V; Chichigina, O A; Anashkina, E I; Valenti, D; Spagnolo, B

2015-10-01

The relaxation dynamics of a system described by a Langevin equation with pulse multiplicative noise sources with different correlation properties is considered. The solution of the corresponding Fokker-Planck equation is derived for Gaussian white noise. Moreover, two pulse processes with regulated periodicity are considered as a noise source: the dead-time-distorted Poisson process and the process with fixed time intervals, which is characterized by an infinite correlation time. We find that the steady state of the system is dependent on the correlation properties of the pulse noise. An increase of the noise correlation causes the decrease of the mean value of the solution at the steady state. The analytical results are in good agreement with the numerical ones.

77 FR 13691 - Qualification of Drivers; Exemption Applications; Vision

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-07

..., ocular hypertension, retinal detachment, cataracts and corneal scaring. In most cases, their eye... Application of Multiple Regression Analysis of a Poisson Process,'' Journal of American Statistical...

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.

Statistical analysis of excitation energies in actinide and rare-earth nuclei

NASA Astrophysics Data System (ADS)

Levon, A. I.; Magner, A. G.; Radionov, S. V.

2018-04-01

Statistical analysis of distributions of the collective states in actinide and rare-earth nuclei is performed in terms of the nearest-neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level repulsion density and that suggested by Brody to the NNSDs were applied for the analysis. We found an intermediate character of the experimental spectra between the order and the chaos for a number of rare-earth and actinide nuclei. The spectra are closer to the Wigner distribution for energies limited by 3 MeV, and to the Poisson distribution for data including higher excitation energies and higher spins. The latter result is in agreement with the theoretical calculations. These features are confirmed by the cumulative distributions, where the Wigner contribution dominates at smaller spacings while the Poisson one is more important at larger spacings, and our linear approach improves the comparison with experimental data at all desired spacings.

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

PubMed Central

Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui

2016-01-01

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions. PMID:27087704

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

NASA Astrophysics Data System (ADS)

Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui

2016-05-01

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures.

PubMed

Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A; Huang, Yonggang; Zhang, Yihui

2016-05-01

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2017-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

Nonlinear Finite Element Analysis of Metals and Metal Matrix Composites: A Local-Global Investigation

DTIC Science & Technology

1992-10-01

and SiC/Al [47] possess good chemical bonding and experience mechanical clamping due to the differences in thermal expansion coefficients between...Coefficient of Thermal 2.70 x 10.6 *F-1 4.09 x 10-6 *C-1 Expansion (ca) Poisson’s Ratio (v) 0.25 0.25 Fiber Diameter (d) 0.0056 in 0.014224 cm...Properties of the matrix (as fabricated) Coefficient of Thermal 5.4 x 10-6 "F1 9.72 x 10-6 "C-1 Expansion (a) Poisson’s Ratio (v) 0.351 0.351 Longitudinal

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2018-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2}. An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

Characterization of Nonhomogeneous Poisson Processes Via Moment Conditions.

DTIC Science & Technology

1986-08-01

Poisson processes play an important role in many fields. The Poisson process is one of the simplest counting processes and is a building block for...place of independent increments. This provides a somewhat different viewpoint for examining Poisson processes . In addition, new characterizations for

Constructions and classifications of projective Poisson varieties.

PubMed

Pym, Brent

2018-01-01

This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

Constructions and classifications of projective Poisson varieties

NASA Astrophysics Data System (ADS)

Pym, Brent

2018-03-01

This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

Log-normal frailty models fitted as Poisson generalized linear mixed models.

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Time distributions of solar energetic particle events: Are SEPEs really random?

NASA Astrophysics Data System (ADS)

Jiggens, P. T. A.; Gabriel, S. B.

2009-10-01

Solar energetic particle events (SEPEs) can exhibit flux increases of several orders of magnitude over background levels and have always been considered to be random in nature in statistical models with no dependence of any one event on the occurrence of previous events. We examine whether this assumption of randomness in time is correct. Engineering modeling of SEPEs is important to enable reliable and efficient design of both Earth-orbiting and interplanetary spacecraft and future manned missions to Mars and the Moon. All existing engineering models assume that the frequency of SEPEs follows a Poisson process. We present analysis of the event waiting times using alternative distributions described by Lévy and time-dependent Poisson processes and compared these with the usual Poisson distribution. The results show significant deviation from a Poisson process and indicate that the underlying physical processes might be more closely related to a Lévy-type process, suggesting that there is some inherent “memory” in the system. Inherent Poisson assumptions of stationarity and event independence are investigated, and it appears that they do not hold and can be dependent upon the event definition used. SEPEs appear to have some memory indicating that events are not completely random with activity levels varying even during solar active periods and are characterized by clusters of events. This could have significant ramifications for engineering models of the SEP environment, and it is recommended that current statistical engineering models of the SEP environment should be modified to incorporate long-term event dependency and short-term system memory.

Hurdle models for multilevel zero-inflated data via h-likelihood.

PubMed

Molas, Marek; Lesaffre, Emmanuel

2010-12-30

Count data often exhibit overdispersion. One type of overdispersion arises when there is an excess of zeros in comparison with the standard Poisson distribution. Zero-inflated Poisson and hurdle models have been proposed to perform a valid likelihood-based analysis to account for the surplus of zeros. Further, data often arise in clustered, longitudinal or multiple-membership settings. The proper analysis needs to reflect the design of a study. Typically random effects are used to account for dependencies in the data. We examine the h-likelihood estimation and inference framework for hurdle models with random effects for complex designs. We extend the h-likelihood procedures to fit hurdle models, thereby extending h-likelihood to truncated distributions. Two applications of the methodology are presented. Copyright © 2010 John Wiley & Sons, Ltd.

Monitoring Poisson observations using combined applications of Shewhart and EWMA charts

NASA Astrophysics Data System (ADS)

Abujiya, Mu'azu Ramat

2017-11-01

The Shewhart and exponentially weighted moving average (EWMA) charts for nonconformities are the most widely used procedures of choice for monitoring Poisson observations in modern industries. Individually, the Shewhart EWMA charts are only sensitive to large and small shifts, respectively. To enhance the detection abilities of the two schemes in monitoring all kinds of shifts in Poisson count data, this study examines the performance of combined applications of the Shewhart, and EWMA Poisson control charts. Furthermore, the study proposes modifications based on well-structured statistical data collection technique, ranked set sampling (RSS), to detect shifts in the mean of a Poisson process more quickly. The relative performance of the proposed Shewhart-EWMA Poisson location charts is evaluated in terms of the average run length (ARL), standard deviation of the run length (SDRL), median run length (MRL), average ratio ARL (ARARL), average extra quadratic loss (AEQL) and performance comparison index (PCI). Consequently, all the new Poisson control charts based on RSS method are generally more superior than most of the existing schemes for monitoring Poisson processes. The use of these combined Shewhart-EWMA Poisson charts is illustrated with an example to demonstrate the practical implementation of the design procedure.

Comment on: 'A Poisson resampling method for simulating reduced counts in nuclear medicine images'.

PubMed

de Nijs, Robin

2015-07-21

In order to be able to calculate half-count images from already acquired data, White and Lawson published their method based on Poisson resampling. They verified their method experimentally by measurements with a Co-57 flood source. In this comment their results are reproduced and confirmed by a direct numerical simulation in Matlab. Not only Poisson resampling, but also two direct redrawing methods were investigated. Redrawing methods were based on a Poisson and a Gaussian distribution. Mean, standard deviation, skewness and excess kurtosis half-count/full-count ratios were determined for all methods, and compared to the theoretical values for a Poisson distribution. Statistical parameters showed the same behavior as in the original note and showed the superiority of the Poisson resampling method. Rounding off before saving of the half count image had a severe impact on counting statistics for counts below 100. Only Poisson resampling was not affected by this, while Gaussian redrawing was less affected by it than Poisson redrawing. Poisson resampling is the method of choice, when simulating half-count (or less) images from full-count images. It simulates correctly the statistical properties, also in the case of rounding off of the images.

[Statistical (Poisson) motor unit number estimation. Methodological aspects and normal results in the extensor digitorum brevis muscle of healthy subjects].

PubMed

Murga Oporto, L; Menéndez-de León, C; Bauzano Poley, E; Núñez-Castaín, M J

Among the differents techniques for motor unit number estimation (MUNE) there is the statistical one (Poisson), in which the activation of motor units is carried out by electrical stimulation and the estimation performed by means of a statistical analysis based on the Poisson s distribution. The study was undertaken in order to realize an approximation to the MUNE Poisson technique showing a coprehensible view of its methodology and also to obtain normal results in the extensor digitorum brevis muscle (EDB) from a healthy population. One hundred fourteen normal volunteers with age ranging from 10 to 88 years were studied using the MUNE software contained in a Viking IV system. The normal subjects were divided into two age groups (10 59 and 60 88 years). The EDB MUNE from all them was 184 49. Both, the MUNE and the amplitude of the compound muscle action potential (CMAP) were significantly lower in the older age group (p< 0.0001), showing the MUNE a better correlation with age than CMAP amplitude ( 0.5002 and 0.4142, respectively p< 0.0001). Statistical MUNE method is an important way for the assessment to the phisiology of the motor unit. The value of MUNE correlates better with the neuromuscular aging process than CMAP amplitude does.

Bayesian semi-parametric analysis of Poisson change-point regression models: application to policy making in Cali, Colombia.

PubMed

Park, Taeyoung; Krafty, Robert T; Sánchez, Alvaro I

2012-07-27

A Poisson regression model with an offset assumes a constant baseline rate after accounting for measured covariates, which may lead to biased estimates of coefficients in an inhomogeneous Poisson process. To correctly estimate the effect of time-dependent covariates, we propose a Poisson change-point regression model with an offset that allows a time-varying baseline rate. When the nonconstant pattern of a log baseline rate is modeled with a nonparametric step function, the resulting semi-parametric model involves a model component of varying dimension and thus requires a sophisticated varying-dimensional inference to obtain correct estimates of model parameters of fixed dimension. To fit the proposed varying-dimensional model, we devise a state-of-the-art MCMC-type algorithm based on partial collapse. The proposed model and methods are used to investigate an association between daily homicide rates in Cali, Colombia and policies that restrict the hours during which the legal sale of alcoholic beverages is permitted. While simultaneously identifying the latent changes in the baseline homicide rate which correspond to the incidence of sociopolitical events, we explore the effect of policies governing the sale of alcohol on homicide rates and seek a policy that balances the economic and cultural dependencies on alcohol sales to the health of the public.

Negative Binomial Process Count and Mixture Modeling.

PubMed

Zhou, Mingyuan; Carin, Lawrence

2015-02-01

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural, and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

PubMed

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

2018-01-01

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Accident prediction model for public highway-rail grade crossings.

PubMed

Lu, Pan; Tolliver, Denver

2016-05-01

Considerable research has focused on roadway accident frequency analysis, but relatively little research has examined safety evaluation at highway-rail grade crossings. Highway-rail grade crossings are critical spatial locations of utmost importance for transportation safety because traffic crashes at highway-rail grade crossings are often catastrophic with serious consequences. The Poisson regression model has been employed to analyze vehicle accident frequency as a good starting point for many years. The most commonly applied variations of Poisson including negative binomial, and zero-inflated Poisson. These models are used to deal with common crash data issues such as over-dispersion (sample variance is larger than the sample mean) and preponderance of zeros (low sample mean and small sample size). On rare occasions traffic crash data have been shown to be under-dispersed (sample variance is smaller than the sample mean) and traditional distributions such as Poisson or negative binomial cannot handle under-dispersion well. The objective of this study is to investigate and compare various alternate highway-rail grade crossing accident frequency models that can handle the under-dispersion issue. The contributions of the paper are two-fold: (1) application of probability models to deal with under-dispersion issues and (2) obtain insights regarding to vehicle crashes at public highway-rail grade crossings. Copyright © 2016 Elsevier Ltd. All rights reserved.

A poisson process model for hip fracture risk.

PubMed

Schechner, Zvi; Luo, Gangming; Kaufman, Jonathan J; Siffert, Robert S

2010-08-01

The primary method for assessing fracture risk in osteoporosis relies primarily on measurement of bone mass. Estimation of fracture risk is most often evaluated using logistic or proportional hazards models. Notwithstanding the success of these models, there is still much uncertainty as to who will or will not suffer a fracture. This has led to a search for other components besides mass that affect bone strength. The purpose of this paper is to introduce a new mechanistic stochastic model that characterizes the risk of hip fracture in an individual. A Poisson process is used to model the occurrence of falls, which are assumed to occur at a rate, lambda. The load induced by a fall is assumed to be a random variable that has a Weibull probability distribution. The combination of falls together with loads leads to a compound Poisson process. By retaining only those occurrences of the compound Poisson process that result in a hip fracture, a thinned Poisson process is defined that itself is a Poisson process. The fall rate is modeled as an affine function of age, and hip strength is modeled as a power law function of bone mineral density (BMD). The risk of hip fracture can then be computed as a function of age and BMD. By extending the analysis to a Bayesian framework, the conditional densities of BMD given a prior fracture and no prior fracture can be computed and shown to be consistent with clinical observations. In addition, the conditional probabilities of fracture given a prior fracture and no prior fracture can also be computed, and also demonstrate results similar to clinical data. The model elucidates the fact that the hip fracture process is inherently random and improvements in hip strength estimation over and above that provided by BMD operate in a highly "noisy" environment and may therefore have little ability to impact clinical practice.

Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains

NASA Astrophysics Data System (ADS)

Wang, Fengwen

2018-05-01

This paper presents a systematic approach for designing 3D auxetic lattice materials, which exhibit constant negative Poisson's ratios over large strain intervals. A unit cell model mimicking tensile tests is established and based on the proposed model, the secant Poisson's ratio is defined as the negative ratio between the lateral and the longitudinal engineering strains. The optimization problem for designing a material unit cell with a target Poisson's ratio is formulated to minimize the average lateral engineering stresses under the prescribed deformations. Numerical results demonstrate that 3D auxetic lattice materials with constant Poisson's ratios can be achieved by the proposed optimization formulation and that two sets of material architectures are obtained by imposing different symmetry on the unit cell. Moreover, inspired by the topology-optimized material architecture, a subsequent shape optimization is proposed by parametrizing material architectures using super-ellipsoids. By designing two geometrical parameters, simple optimized material microstructures with different target Poisson's ratios are obtained. By interpolating these two parameters as polynomial functions of Poisson's ratios, material architectures for any Poisson's ratio in the interval of ν ∈ [ - 0.78 , 0.00 ] are explicitly presented. Numerical evaluations show that interpolated auxetic lattice materials exhibit constant Poisson's ratios in the target strain interval of [0.00, 0.20] and that 3D auxetic lattice material architectures with programmable Poisson's ratio are achievable.

Classifying next-generation sequencing data using a zero-inflated Poisson model.

PubMed

Zhou, Yan; Wan, Xiang; Zhang, Baoxue; Tong, Tiejun

2018-04-15

With the development of high-throughput techniques, RNA-sequencing (RNA-seq) is becoming increasingly popular as an alternative for gene expression analysis, such as RNAs profiling and classification. Identifying which type of diseases a new patient belongs to with RNA-seq data has been recognized as a vital problem in medical research. As RNA-seq data are discrete, statistical methods developed for classifying microarray data cannot be readily applied for RNA-seq data classification. Witten proposed a Poisson linear discriminant analysis (PLDA) to classify the RNA-seq data in 2011. Note, however, that the count datasets are frequently characterized by excess zeros in real RNA-seq or microRNA sequence data (i.e. when the sequence depth is not enough or small RNAs with the length of 18-30 nucleotides). Therefore, it is desired to develop a new model to analyze RNA-seq data with an excess of zeros. In this paper, we propose a Zero-Inflated Poisson Logistic Discriminant Analysis (ZIPLDA) for RNA-seq data with an excess of zeros. The new method assumes that the data are from a mixture of two distributions: one is a point mass at zero, and the other follows a Poisson distribution. We then consider a logistic relation between the probability of observing zeros and the mean of the genes and the sequencing depth in the model. Simulation studies show that the proposed method performs better than, or at least as well as, the existing methods in a wide range of settings. Two real datasets including a breast cancer RNA-seq dataset and a microRNA-seq dataset are also analyzed, and they coincide with the simulation results that our proposed method outperforms the existing competitors. The software is available at http://www.math.hkbu.edu.hk/∼tongt. xwan@comp.hkbu.edu.hk or tongt@hkbu.edu.hk. Supplementary data are available at Bioinformatics online.

Effects of overlapping electric double layer on mass transport of a macro-solute across porous wall of a micro/nanochannel for power law fluid.

PubMed

Bhattacharjee, Saikat; Mondal, Mrinmoy; De, Sirshendu

2017-05-01

Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye-Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential -73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Unimodularity criteria for Poisson structures on foliated manifolds

NASA Astrophysics Data System (ADS)

Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury

2018-03-01

We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data.

PubMed

Rodrigues, Josemar; Cancho, Vicente G; de Castro, Mário; Balakrishnan, N

2012-12-01

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis--latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de São Carlos, São Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de São Carlos, São Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

Eruption patterns of the chilean volcanoes Villarrica, Llaima, and Tupungatito

NASA Astrophysics Data System (ADS)

Muñoz, Miguel

1983-09-01

The historical eruption records of three Chilean volcanoes have been subjected to many statistical tests, and none have been found to differ significantly from random, or Poissonian, behaviour. The statistical analysis shows rough conformity with the descriptions determined from the eruption rate functions. It is possible that a constant eruption rate describes the activity of Villarrica; Llaima and Tupungatito present complex eruption rate patterns that appear, however, to have no statistical significance. Questions related to loading and extinction processes and to the existence of shallow secondary magma chambers to which magma is supplied from a deeper system are also addressed. The analysis and the computation of the serial correlation coefficients indicate that the three series may be regarded as stationary renewal processes. None of the test statistics indicates rejection of the Poisson hypothesis at a level less than 5%, but the coefficient of variation for the eruption series at Llaima is significantly different from the value expected for a Poisson process. Also, the estimates of the normalized spectrum of the counting process for the three series suggest a departure from the random model, but the deviations are not found to be significant at the 5% level. Kolmogorov-Smirnov and chi-squared test statistics, applied directly to ascertaining to which probability P the random Poisson model fits the data, indicate that there is significant agreement in the case of Villarrica ( P=0.59) and Tupungatito ( P=0.3). Even though the P-value for Llaima is a marginally significant 0.1 (which is equivalent to rejecting the Poisson model at the 90% confidence level), the series suggests that nonrandom features are possibly present in the eruptive activity of this volcano.

Stationary and non-stationary occurrences of miniature end plate potentials are well described as stationary and non-stationary Poisson processes in the mollusc Navanax inermis.

PubMed

Cappell, M S; Spray, D C; Bennett, M V

1988-06-28

Protractor muscles in the gastropod mollusc Navanax inermis exhibit typical spontaneous miniature end plate potentials with mean amplitude 1.71 +/- 1.19 (standard deviation) mV. The evoked end plate potential is quantized, with a quantum equal to the miniature end plate potential amplitude. When their rate is stationary, occurrence of miniature end plate potentials is a random, Poisson process. When non-stationary, spontaneous miniature end plate potential occurrence is a non-stationary Poisson process, a Poisson process with the mean frequency changing with time. This extends the random Poisson model for miniature end plate potentials to the frequently observed non-stationary occurrence. Reported deviations from a Poisson process can sometimes be accounted for by the non-stationary Poisson process and more complex models, such as clustered release, are not always needed.

A test of inflated zeros for Poisson regression models.

PubMed

He, Hua; Zhang, Hui; Ye, Peng; Tang, Wan

2017-01-01

Excessive zeros are common in practice and may cause overdispersion and invalidate inference when fitting Poisson regression models. There is a large body of literature on zero-inflated Poisson models. However, methods for testing whether there are excessive zeros are less well developed. The Vuong test comparing a Poisson and a zero-inflated Poisson model is commonly applied in practice. However, the type I error of the test often deviates seriously from the nominal level, rendering serious doubts on the validity of the test in such applications. In this paper, we develop a new approach for testing inflated zeros under the Poisson model. Unlike the Vuong test for inflated zeros, our method does not require a zero-inflated Poisson model to perform the test. Simulation studies show that when compared with the Vuong test our approach not only better at controlling type I error rate, but also yield more power.

Spacelab system analysis: The modified free access protocol: An access protocol for communication systems with periodic and Poisson traffic

NASA Technical Reports Server (NTRS)

Ingels, Frank; Owens, John; Daniel, Steven

1989-01-01

The protocol definition and terminal hardware for the modified free access protocol, a communications protocol similar to Ethernet, are developed. A MFA protocol simulator and a CSMA/CD math model are also developed. The protocol is tailored to communication systems where the total traffic may be divided into scheduled traffic and Poisson traffic. The scheduled traffic should occur on a periodic basis but may occur after a given event such as a request for data from a large number of stations. The Poisson traffic will include alarms and other random traffic. The purpose of the protocol is to guarantee that scheduled packets will be delivered without collision. This is required in many control and data collection systems. The protocol uses standard Ethernet hardware and software requiring minimum modifications to an existing system. The modification to the protocol only affects the Ethernet transmission privileges and does not effect the Ethernet receiver.

Weber's law implies neural discharge more regular than a Poisson process.

PubMed

Kang, Jing; Wu, Jianhua; Smerieri, Anteo; Feng, Jianfeng

2010-03-01

Weber's law is one of the basic laws in psychophysics, but the link between this psychophysical behavior and the neuronal response has not yet been established. In this paper, we carried out an analysis on the spike train statistics when Weber's law holds, and found that the efferent spike train of a single neuron is less variable than a Poisson process. For population neurons, Weber's law is satisfied only when the population size is small (< 10 neurons). However, if the population neurons share a weak correlation in their discharges and individual neuronal spike train is more regular than a Poisson process, Weber's law is true without any restriction on the population size. Biased competition attractor network also demonstrates that the coefficient of variation of interspike interval in the winning pool should be less than one for the validity of Weber's law. Our work links Weber's law with neural firing property quantitatively, shedding light on the relation between psychophysical behavior and neuronal responses.

Calculation of the Poisson cumulative distribution function

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Nolty, Robert G.; Scheuer, Ernest M.

1990-01-01

A method for calculating the Poisson cdf (cumulative distribution function) is presented. The method avoids computer underflow and overflow during the process. The computer program uses this technique to calculate the Poisson cdf for arbitrary inputs. An algorithm that determines the Poisson parameter required to yield a specified value of the cdf is presented.

Poisson's Ratio of a Hyperelastic Foam Under Quasi-static and Dynamic Loading

DOE PAGES

Sanborn, Brett; Song, Bo

2018-06-03

Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratiomore » of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. Here, the Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.« less

Poisson's Ratio of a Hyperelastic Foam Under Quasi-static and Dynamic Loading

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

Sanborn, Brett; Song, Bo

Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratiomore » of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. Here, the Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.« less

Theoretical aspects of fracture mechanics

NASA Astrophysics Data System (ADS)

Atkinson, C.; Craster, R. V.

1995-03-01

In this review we try to cover various topics in fracture mechanics in which mathematical analysis can be used both to aid numerical methods and cast light on key features of the stress field. The dominant singular near crack tip stress field can often be parametrized in terms of three parameters K(sub I), K(sub II) and K(sub III) designating three fracture modes each having an angular variation entirely specified for the stress tensor and displacement vector. These results and contact zone models for removing the interpenetration anomaly are described. Generalizations of the above results to viscoelastic media are described. For homogeneous media with constant Poisson's ratio the angular variation of singular crack tip stresses and displacements are shown to be the same for all time and the same inverse square root singularity as occurs in the elastic medium case is found (this being true for a time varying Poisson ratio too). Only the stress intensity factor varies through time dependence of loads and relaxation properties of the medium. For cracks against bimaterial interfaces both the stress singularity and angular form evolve with time as a function of the time dependent properties of the bimaterial. Similar behavior is identified for sharp notches in viscoelastic plates. The near crack tip behavior in material with non-linear stress strain laws is also identified and stress singularities classified in terms of the hardening exponent for power law hardening materials. Again for interface cracks the near crack tip behavior requires careful analysis and it is shown that more than one singular term may be present in the near crack tip stress field. A variety of theory and applications is presented for inhomogeneous elastic media, coupled thermoelasticity etc. Methods based on reciprocal theorems and dual functions which can also aid in getting awkward singular stress behavior from numerical solutions are also reviewed. Finally theoretical calculations of fiber reinforced and particulate composite toughening mechanisms are briefly reviewed.

Crustal structure in Ethiopia and Kenya from receiver function analysis: Implications for rift development in eastern Africa

NASA Astrophysics Data System (ADS)

Dugda, Mulugeta T.; Nyblade, Andrew A.; Julia, Jordi; Langston, Charles A.; Ammon, Charles J.; Simiyu, Silas

2005-01-01

Crustal structure in Kenya and Ethiopia has been investigated using receiver function analysis of broadband seismic data to determine the extent to which the Cenozoic rifting and magmatism has modified the thickness and composition of the Proterozoic crust in which the East African rift system developed. Data for this study come from broadband seismic experiments conducted in Ethiopia between 2000 and 2002 and in Kenya between 2001 and 2002. Two methods have been used to analyze the receiver functions, the H-κ method, and direct stacks of the waveforms, yielding consistent results. Crustal thickness to the east of the Kenya rift varies between 39 and 42 km, and Poisson's ratios for the crust vary between 0.24 and 0.27. To the west of the Kenya rift, Moho depths vary between 37 and 38 km, and Poisson's ratios vary between 0.24 and 0.27. These findings support previous studies showing that crust away from the Kenya rift has not been modified extensively by Cenozoic rifting and magmatism. Beneath the Ethiopian Plateau on either side of the Main Ethiopian Rift, crustal thickness ranges from 33 to 44 km, and Poisson's ratios vary from 0.23 to 0.28. Within the Main Ethiopian Rift, Moho depths vary from 27 to 38 km, and Poisson's ratios range from 0.27 to 0.35. A crustal thickness of 25 km and a Poisson's ratio of 0.36 were obtained for a single station in the Afar Depression. These results indicate that the crust beneath the Ethiopian Plateau has not been modified significantly by the Cenozoic rifting and magmatism, even though up to a few kilometers of flood basalts have been added, and that the crust beneath the rifted regions in Ethiopia has been thinned in many places and extensively modified by the addition of mafic rock. The latter finding is consistent with models for rift evolution, suggesting that magmatic segments with the Main Ethiopian Rift, characterized by dike intrusion and Quaternary volcanism, act now as the locus of extension rather than the rift border faults.

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.

The analysis of incontinence episodes and other count data in patients with overactive bladder by Poisson and negative binomial regression.

PubMed

Martina, R; Kay, R; van Maanen, R; Ridder, A

2015-01-01

Clinical studies in overactive bladder have traditionally used analysis of covariance or nonparametric methods to analyse the number of incontinence episodes and other count data. It is known that if the underlying distributional assumptions of a particular parametric method do not hold, an alternative parametric method may be more efficient than a nonparametric one, which makes no assumptions regarding the underlying distribution of the data. Therefore, there are advantages in using methods based on the Poisson distribution or extensions of that method, which incorporate specific features that provide a modelling framework for count data. One challenge with count data is overdispersion, but methods are available that can account for this through the introduction of random effect terms in the modelling, and it is this modelling framework that leads to the negative binomial distribution. These models can also provide clinicians with a clearer and more appropriate interpretation of treatment effects in terms of rate ratios. In this paper, the previously used parametric and non-parametric approaches are contrasted with those based on Poisson regression and various extensions in trials evaluating solifenacin and mirabegron in patients with overactive bladder. In these applications, negative binomial models are seen to fit the data well. Copyright © 2014 John Wiley & Sons, Ltd.

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

NASA Astrophysics Data System (ADS)

Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.

2016-05-01

This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

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.

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

Accurate analytical modeling of junctionless DG-MOSFET by green's function approach

NASA Astrophysics Data System (ADS)

Nandi, Ashutosh; Pandey, Nilesh

2017-11-01

An accurate analytical model of Junctionless double gate MOSFET (JL-DG-MOSFET) in the subthreshold regime of operation is developed in this work using green's function approach. The approach considers 2-D mixed boundary conditions and multi-zone techniques to provide an exact analytical solution to 2-D Poisson's equation. The Fourier coefficients are calculated correctly to derive the potential equations that are further used to model the channel current and subthreshold slope of the device. The threshold voltage roll-off is computed from parallel shifts of Ids-Vgs curves between the long channel and short-channel devices. It is observed that the green's function approach of solving 2-D Poisson's equation in both oxide and silicon region can accurately predict channel potential, subthreshold current (Isub), threshold voltage (Vt) roll-off and subthreshold slope (SS) of both long & short channel devices designed with different doping concentrations and higher as well as lower tsi/tox ratio. All the analytical model results are verified through comparisons with TCAD Sentaurus simulation results. It is observed that the model matches quite well with TCAD device simulations.

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.

SELF-GRAVITATIONAL FORCE CALCULATION OF SECOND-ORDER ACCURACY FOR INFINITESIMALLY THIN GASEOUS DISKS IN POLAR COORDINATES

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

Wang, Hsiang-Hsu; Taam, Ronald E.; Yen, David C. C., E-mail: yen@math.fju.edu.tw

Investigating the evolution of disk galaxies and the dynamics of proto-stellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using two-dimensional Cartesian or polar coordinates. In Cartesian coordinates, the calculations of the hydrodynamics and self-gravitational forces are relatively straightforward for attaining second-order accuracy. However, in polar coordinates, a second-order calculation of self-gravitational forces is required for matching the second-order accuracy of hydrodynamical schemes. We present a direct algorithm for calculating self-gravitational forces with second-order accuracy without artificial boundary conditions. The Poisson integral in polar coordinates ismore » expressed in a convolution form and the corresponding numerical complexity is nearly linear using a fast Fourier transform. Examples with analytic solutions are used to verify that the truncated error of this algorithm is of second order. The kernel integral around the singularity is applied to modify the particle method. The use of a softening length is avoided and the accuracy of the particle method is significantly improved.« less

Planar screening by charge polydisperse counterions

NASA Astrophysics Data System (ADS)

Trulsson, M.; Trizac, E.; Šamaj, L.

2018-01-01

We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), n(q) . We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions n(q) , for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous n(q) behaviour are already featured by discrete mixtures with a relatively small number of constituents.

A stochastical event-based continuous time step rainfall generator based on Poisson rectangular pulse and microcanonical random cascade models

NASA Astrophysics Data System (ADS)

Pohle, Ina; Niebisch, Michael; Zha, Tingting; Schümberg, Sabine; Müller, Hannes; Maurer, Thomas; Hinz, Christoph

2017-04-01

Rainfall variability within a storm is of major importance for fast hydrological processes, e.g. surface runoff, erosion and solute dissipation from surface soils. To investigate and simulate the impacts of within-storm variabilities on these processes, long time series of rainfall with high resolution are required. Yet, observed precipitation records of hourly or higher resolution are in most cases available only for a small number of stations and only for a few years. To obtain long time series of alternating rainfall events and interstorm periods while conserving the statistics of observed rainfall events, the Poisson model can be used. Multiplicative microcanonical random cascades have been widely applied to disaggregate rainfall time series from coarse to fine temporal resolution. We present a new coupling approach of the Poisson rectangular pulse model and the multiplicative microcanonical random cascade model that preserves the characteristics of rainfall events as well as inter-storm periods. In the first step, a Poisson rectangular pulse model is applied to generate discrete rainfall events (duration and mean intensity) and inter-storm periods (duration). The rainfall events are subsequently disaggregated to high-resolution time series (user-specified, e.g. 10 min resolution) by a multiplicative microcanonical random cascade model. One of the challenges of coupling these models is to parameterize the cascade model for the event durations generated by the Poisson model. In fact, the cascade model is best suited to downscale rainfall data with constant time step such as daily precipitation data. Without starting from a fixed time step duration (e.g. daily), the disaggregation of events requires some modifications of the multiplicative microcanonical random cascade model proposed by Olsson (1998): Firstly, the parameterization of the cascade model for events of different durations requires continuous functions for the probabilities of the multiplicative weights, which we implemented through sigmoid functions. Secondly, the branching of the first and last box is constrained to preserve the rainfall event durations generated by the Poisson rectangular pulse model. The event-based continuous time step rainfall generator has been developed and tested using 10 min and hourly rainfall data of four stations in North-Eastern Germany. The model performs well in comparison to observed rainfall in terms of event durations and mean event intensities as well as wet spell and dry spell durations. It is currently being tested using data from other stations across Germany and in different climate zones. Furthermore, the rainfall event generator is being applied in modelling approaches aimed at understanding the impact of rainfall variability on hydrological processes. Reference Olsson, J.: Evaluation of a scaling cascade model for temporal rainfall disaggregation, Hydrology and Earth System Sciences, 2, 19.30