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.

ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation

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

Sousbie, Thierry, E-mail: tsousbie@gmail.com; Department of Physics, The University of Tokyo, Tokyo 113-0033; Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033

2016-09-15

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the bestmore » way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.« less

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.

Three dimensional cylindrical Kadomtsev-Petviashvili equation in a very dense electron-positron-ion plasma

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

Moslem, W. M.; Sabry, R.; Shukla, P. K.

2010-03-15

By using the hydrodynamic equations of ions, Thomas-Fermi electron/positron density distribution, and Poisson equation, a three-dimensional cylindrical Kadomtsev-Petviashvili (CKP) equation is derived for small but finite amplitude ion-acoustic waves. The generalized expansion method is used to analytically solve the CKP equation. New class of solutions admits a train of well-separated bell-shaped periodic pulses is obtained. At certain condition, the latter degenerates to solitary wave solution. The effects of physical parameters on the solitary pulse structures are examined. Furthermore, the energy integral equation is used to study the existence regions of the localized pulses. The present study might be helpful tomore » understand the excitation of nonlinear ion-acoustic waves in a very dense astrophysical objects such as white dwarfs.« less

Three-Dimensional Effects of Crack Closure in Laminated Composite Plates Subjected to Bending Loads

DTIC Science & Technology

1994-06-01

Approved by: •UW. Kwon, Thesis Advisor wathe D.K~elleher, Chairman Department of Mechanical Engineering ii ABSTRACT Fracture is one of the dominant...5 A. OVERVIEW .......................................... 5 B. CONSTITUTIVE EQUATION .............................. 9 1. Isotropic...the elemental nodes. B. CONSTITUTIVE EQUATION The material property matrix [D] is a symmetric matrix which includes elasticity moduli and Poisson’s

Three-dimensional zonal grids about arbitrary shapes by Poisson's equation

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.

1988-01-01

A method for generating 3-D finite difference grids about or within arbitrary shapes is presented. The 3-D Poisson equations are solved numerically, with values for the inhomogeneous terms found automatically by the algorithm. Those inhomogeneous terms have the effect near boundaries of reducing cell skewness and imposing arbitrary cell height. The method allows the region of interest to be divided into zones (blocks), allowing the method to be applicable to almost any physical domain. A FORTRAN program called 3DGRAPE has been written to implement the algorithm. Lastly, a method for redistributing grid points along lines normal to boundaries will be described.

Prediction of unsteady transonic flow around missile configurations

NASA Technical Reports Server (NTRS)

Nixon, D.; Reisenthel, P. H.; Torres, T. O.; Klopfer, G. H.

1990-01-01

This paper describes the preliminary development of a method for predicting the unsteady transonic flow around missiles at transonic and supersonic speeds, with the final goal of developing a computer code for use in aeroelastic calculations or during maneuvers. The basic equations derived for this method are an extension of those derived by Klopfer and Nixon (1989) for steady flow and are a subset of the Euler equations. In this approach, the five Euler equations are reduced to an equation similar to the three-dimensional unsteady potential equation, and a two-dimensional Poisson equation. In addition, one of the equations in this method is almost identical to the potential equation for which there are well tested computer codes, allowing the development of a prediction method based in part on proved technology.

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

LSI arrays for space stations

NASA Technical Reports Server (NTRS)

Gassaway, J. D.

1976-01-01

Two approaches have been taken to study CCD's and some of their fundamental limitations. First a numerical analysis approach has been developed to solve the coupled transport and Poisson's equation for a thorough analysis of charge transfer in a CCD structure. The approach is formulated by treating the minority carriers as a surface distribution at the Si-SiO2 interface and setting up coupled difference equations for the charge and the potential. The SOR method is proposed for solving the two dimensional Poisson's equation for the potential. Methods are suggested for handling the discontinuities to improve convergence. Second, CCD shift registers were fabricated with parameters which should allow complete charge transfer independent of the transfer electrode gap width. A test instrument was designed and constructed which can be used to test this, or any similar, three phase CCD shift register.

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

PubMed Central

Długosz, Maciej; Trylska, Joanna

2008-01-01

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

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

PubMed

Cohen, Yossi; Rothman, Daniel H

2017-04-01

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

A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensions

NASA Astrophysics Data System (ADS)

Exl, Lukas

2017-12-01

An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled, the overall computation error is driven by the convergence of the finite Fourier series of the density. For smooth and fast-decaying densities the proposed method will be spectrally accurate. The method scales with O(N log N) operations, where N is the total number of discretization points in the Cartesian grid. The majority of the computational costs come from fast Fourier transforms (FFT), which makes it ideal for GPU computation. Several numerical computations on CPU and GPU validate the method and show efficiency and convergence behavior. Tests are performed using the Vienna Scientific Cluster 3 (VSC3). A free MATLAB implementation for CPU and GPU is provided to the interested community.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Four-dimensional gravity as an almost-Poisson system

NASA Astrophysics Data System (ADS)

Ita, Eyo Eyo

2015-04-01

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

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

NASA Astrophysics Data System (ADS)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

SIERRA - A 3-D device simulator for reliability modeling

NASA Astrophysics Data System (ADS)

Chern, Jue-Hsien; Arledge, Lawrence A., Jr.; Yang, Ping; Maeda, John T.

1989-05-01

SIERRA is a three-dimensional general-purpose semiconductor-device simulation program which serves as a foundation for investigating integrated-circuit (IC) device and reliability issues. This program solves the Poisson and continuity equations in silicon under dc, transient, and small-signal conditions. Executing on a vector/parallel minisupercomputer, SIERRA utilizes a matrix solver which uses an incomplete LU (ILU) preconditioned conjugate gradient square (CGS, BCG) method. The ILU-CGS method provides a good compromise between memory size and convergence rate. The authors have observed a 5x to 7x speedup over standard direct methods in simulations of transient problems containing highly coupled Poisson and continuity equations such as those found in reliability-oriented simulations. The application of SIERRA to parasitic CMOS latchup and dynamic random-access memory single-event-upset studies is described.

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

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

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

2014-05-15

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

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

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

Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations

NASA Astrophysics Data System (ADS)

Qiang, Ji

2017-10-01

A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of O(Nu(logNmode)) , where Nu is the total number of unknowns and Nmode is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage of using an artificial boundary condition in a large extended computational domain. The new 3D Poisson solver is parallelized using a message passing interface (MPI) on multi-processor computers and shows a reasonable parallel performance up to hundreds of processor cores.

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1986-01-01

Various graduate research activities in the field of computer science are reported. Among the topics discussed are: (1) failure probabilities in multi-version software; (2) Gaussian Elimination on parallel computers; (3) three dimensional Poisson solvers on parallel/vector computers; (4) automated task decomposition for multiple robot arms; (5) multi-color incomplete cholesky conjugate gradient methods on the Cyber 205; and (6) parallel implementation of iterative methods for solving linear equations.

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.

From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

NASA Astrophysics Data System (ADS)

Yang, Xiao; Du, Dianlou

2010-08-01

The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

Grid generation in three dimensions by Poisson equations with control of cell size and skewness at boundary surfaces

NASA Technical Reports Server (NTRS)

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

1983-01-01

An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

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.

Elliptic surface grid generation in three-dimensional space

NASA Technical Reports Server (NTRS)

Kania, Lee

1992-01-01

A methodology for surface grid generation in three dimensional space is described. The method solves a Poisson equation for each coordinate on arbitrary surfaces using successive line over-relaxation. The complete surface curvature terms were discretized and retained within the nonhomogeneous term in order to preserve surface definition; there is no need for conventional surface splines. Control functions were formulated to permit control of grid orthogonality and spacing. A method for interpolation of control functions into the domain was devised which permits their specification not only at the surface boundaries but within the interior as well. An interactive surface generation code which makes use of this methodology is currently under development.

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

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

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

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Vectorized multigrid Poisson solver for the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Barkai, D.; Brandt, M. A.

1984-01-01

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

Further Improvement in 3DGRAPE

NASA Technical Reports Server (NTRS)

Alter, Stephen

2004-01-01

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1980-01-01

A method for generating two dimensional finite difference grids about airfoils and other shapes by the use of the Poisson differential equation is developed. The inhomogeneous terms are automatically chosen such that two important effects are imposed on the grid at both the inner and outer boundaries. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. A FORTRAN computer program has been written to use this method. A description of the program, a discussion of the control parameters, and a set of sample cases are included.

Two dimensional analytical model for a reconfigurable field effect transistor

NASA Astrophysics Data System (ADS)

Ranjith, R.; Jayachandran, Remya; Suja, K. J.; Komaragiri, Rama S.

2018-02-01

This paper presents two-dimensional potential and current models for a reconfigurable field effect transistor (RFET). Two potential models which describe subthreshold and above-threshold channel potentials are developed by solving two-dimensional (2D) Poisson's equation. In the first potential model, 2D Poisson's equation is solved by considering constant/zero charge density in the channel region of the device to get the subthreshold potential characteristics. In the second model, accumulation charge density is considered to get above-threshold potential characteristics of the device. The proposed models are applicable for the device having lightly doped or intrinsic channel. While obtaining the mathematical model, whole body area is divided into two regions: gated region and un-gated region. The analytical models are compared with technology computer-aided design (TCAD) simulation results and are in complete agreement for different lengths of the gated regions as well as at various supply voltage levels.

Asymptotic analysis of the narrow escape problem in dendritic spine shaped domain: three dimensions

NASA Astrophysics Data System (ADS)

Li, Xiaofei; Lee, Hyundae; Wang, Yuliang

2017-08-01

This paper deals with the three-dimensional narrow escape problem in a dendritic spine shaped domain, which is composed of a relatively big head and a thin neck. The narrow escape problem is to compute the mean first passage time of Brownian particles traveling from inside the head to the end of the neck. The original model is to solve a mixed Dirichlet-Neumann boundary value problem for the Poisson equation in the composite domain, and is computationally challenging. In this paper we seek to transfer the original problem to a mixed Robin-Neumann boundary value problem by dropping the thin neck part, and rigorously derive the asymptotic expansion of the mean first passage time with high order terms. This study is a nontrivial three-dimensional generalization of the work in Li (2014 J. Phys. A: Math. Theor. 47 505202), where a two-dimensional analogue domain is considered.

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.

Semi-Lagrangian particle methods for high-dimensional Vlasov-Poisson systems

NASA Astrophysics Data System (ADS)

Cottet, Georges-Henri

2018-07-01

This paper deals with the implementation of high order semi-Lagrangian particle methods to handle high dimensional Vlasov-Poisson systems. It is based on recent developments in the numerical analysis of particle methods and the paper focuses on specific algorithmic features to handle large dimensions. The methods are tested with uniform particle distributions in particular against a recent multi-resolution wavelet based method on a 4D plasma instability case and a 6D gravitational case. Conservation properties, accuracy and computational costs are monitored. The excellent accuracy/cost trade-off shown by the method opens new perspective for accurate simulations of high dimensional kinetic equations by particle methods.

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.

The scaling of oblique plasma double layers

NASA Technical Reports Server (NTRS)

Borovsky, J. E.

1983-01-01

Strong oblique plasma double layers are investigated using three methods, i.e., electrostatic particle-in-cell simulations, numerical solutions to the Poisson-Vlasov equations, and analytical approximations to the Poisson-Vlasov equations. The solutions to the Poisson-Vlasov equations and numerical simulations show that strong oblique double layers scale in terms of Debye lengths. For very large potential jumps, theory and numerical solutions indicate that all effects of the magnetic field vanish and the oblique double layers follow the same scaling relation as the field-aligned double layers.

Reference manual for the POISSON/SUPERFISH Group of Codes

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

Not Available

1987-01-01

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

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.

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.

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.

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.

Numerical solutions of incompressible Navier-Stokes equations using modified Bernoulli's law

NASA Astrophysics Data System (ADS)

Shatalov, A.; Hafez, M.

2003-11-01

Simulations of incompressible flows are important for many practical applications in aeronautics and beyond, particularly in the high Reynolds number regime. The present formulation is based on Helmholtz velocity decomposition where the velocity is presented as the gradient of a potential plus a rotational component. Substituting in the continuity equation yields a Poisson equation for the potential which is solved with a zero normal derivative at solid surfaces. The momentum equation is used to update the rotational component with no slip/no penetration surface boundary conditions. The pressure is related to the potential function through a special relation which is a generalization of Bernoulli's law, with a viscous term included. Results of calculations for two- and three-dimensional problems prove that the present formulation is a valid approach, with some possible benefits compared to existing methods.

Three-dimensional elliptic grid generation for an F-16

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.

1988-01-01

A case history depicting the effort to generate a computational grid for the simulation of transonic flow about an F-16 aircraft at realistic flight conditions is presented. The flow solver for which this grid is designed is a zonal one, using the Reynolds averaged Navier-Stokes equations near the surface of the aircraft, and the Euler equations in regions removed from the aircraft. A body conforming global grid, suitable for the Euler equation, is first generated using 3-D Poisson equations having inhomogeneous terms modeled after the 2-D GRAPE code. Regions of the global grid are then designated for zonal refinement as appropriate to accurately model the flow physics. Grid spacing suitable for solution of the Navier-Stokes equations is generated in the refinement zones by simple subdivision of the given coarse grid intervals. That grid generation project is described, with particular emphasis on the global coarse grid.

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.

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.

Thermophysical and Mechanical Properties of Granite and Its Effects on Borehole Stability in High Temperature and Three-Dimensional Stress

PubMed Central

Bao-lin, Liu; Hai-yan, Zhu; Chuan-liang, Yan; Zhi-jun, Li; Zhi-qiao, Wang

2014-01-01

When exploiting the deep resources, the surrounding rock readily undergoes the hole shrinkage, borehole collapse, and loss of circulation under high temperature and high pressure. A series of experiments were conducted to discuss the compressional wave velocity, triaxial strength, and permeability of granite cored from 3500 meters borehole under high temperature and three-dimensional stress. In light of the coupling of temperature, fluid, and stress, we get the thermo-fluid-solid model and governing equation. ANSYS-APDL was also used to stimulate the temperature influence on elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability. In light of the results, we establish a temperature-fluid-stress model to illustrate the granite's stability. The compressional wave velocity and elastic modulus, decrease as the temperature rises, while poisson ratio and permeability of granite increase. The threshold pressure and temperature are 15 MPa and 200°C, respectively. The temperature affects the fracture pressure more than the collapse pressure, but both parameters rise with the increase of temperature. The coupling of thermo-fluid-solid, greatly impacting the borehole stability, proves to be a good method to analyze similar problems of other formations. PMID:24778592

Thermophysical and mechanical properties of granite and its effects on borehole stability in high temperature and three-dimensional stress.

PubMed

Wang, Yu; Liu, Bao-lin; Zhu, Hai-yan; Yan, Chuan-liang; Li, Zhi-jun; Wang, Zhi-qiao

2014-01-01

When exploiting the deep resources, the surrounding rock readily undergoes the hole shrinkage, borehole collapse, and loss of circulation under high temperature and high pressure. A series of experiments were conducted to discuss the compressional wave velocity, triaxial strength, and permeability of granite cored from 3500 meters borehole under high temperature and three-dimensional stress. In light of the coupling of temperature, fluid, and stress, we get the thermo-fluid-solid model and governing equation. ANSYS-APDL was also used to stimulate the temperature influence on elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability. In light of the results, we establish a temperature-fluid-stress model to illustrate the granite's stability. The compressional wave velocity and elastic modulus, decrease as the temperature rises, while poisson ratio and permeability of granite increase. The threshold pressure and temperature are 15 MPa and 200 °C, respectively. The temperature affects the fracture pressure more than the collapse pressure, but both parameters rise with the increase of temperature. The coupling of thermo-fluid-solid, greatly impacting the borehole stability, proves to be a good method to analyze similar problems of other formations.

Fractal electrodynamics via non-integer dimensional space approach

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

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.

Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations

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

Jia, Jun; Liu, Jie

2011-01-01

In this paper, we present an accurate, efficient and stable numerical method for the incompressible Navier-Stokes equations (NSEs). The method is based on (1) an equivalent pressure Poisson equation formulation of the NSE with proper pressure boundary conditions, which facilitates the design of high-order and stable numerical methods, and (2) the Krylov deferred correction (KDC) accelerated method of lines transpose (mbox MoL{sup T}), which is very stable, efficient, and of arbitrary order in time. Numerical tests with known exact solutions in three dimensions show that the new method is spectrally accurate in time, and a numerical order of convergence 9more » was observed. Two-dimensional computational results of flow past a cylinder and flow in a bifurcated tube are also reported.« less

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

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

Hirotani, Kouichi

2015-01-10

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

Computations of Complex Three-Dimensional Turbulent Free Jets

NASA Technical Reports Server (NTRS)

Wilson, Robert V.; Demuren, Ayodeji O.

1997-01-01

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets.

Two-Dimensional Grids About Airfoils and Other Shapes

NASA Technical Reports Server (NTRS)

Sorenson, R.

1982-01-01

GRAPE computer program generates two-dimensional finite-difference grids about airfoils and other shapes by use of Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including limited number of sharp corners. Numerically stable and computationally fast, GRAPE provides aerodynamic analyst with efficient and consistant means of grid generation.

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.

Super-stable Poissonian structures

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

In this paper we characterize classes of Poisson processes whose statistical structures are super-stable. We consider a flow generated by a one-dimensional ordinary differential equation, and an ensemble of particles ‘surfing’ the flow. The particles start from random initial positions, and are propagated along the flow by stochastic ‘wave processes’ with general statistics and general cross correlations. Setting the initial positions to be Poisson processes, we characterize the classes of Poisson processes that render the particles’ positions—at all times, and invariantly with respect to the wave processes—statistically identical to their initial positions. These Poisson processes are termed ‘super-stable’ and facilitate the generalization of the notion of stationary distributions far beyond the realm of Markov dynamics.

Numerical simulation on hydromechanical coupling in porous media adopting three-dimensional pore-scale model.

PubMed

Liu, Jianjun; Song, Rui; Cui, Mengmeng

2014-01-01

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view.

Numerical Simulation on Hydromechanical Coupling in Porous Media Adopting Three-Dimensional Pore-Scale Model

PubMed Central

Liu, Jianjun; Song, Rui; Cui, Mengmeng

2014-01-01

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view. PMID:24955384

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

NASA Astrophysics Data System (ADS)

Basu, Anirban

2016-11-01

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

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.

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 study of trends and techniques for space base electronics

NASA Technical Reports Server (NTRS)

Trotter, J. D.; Wade, T. E.; Gassaway, J. D.

1979-01-01

The use of dry processing and alternate dielectrics for processing wafers is reported. A two dimensional modeling program was written for the simulation of short channel MOSFETs with nonuniform substrate doping. A key simplifying assumption used is that the majority carriers can be represented by a sheet charge at the silicon dioxide-silicon interface. In solving current continuity equation, the program does not converge. However, solving the two dimensional Poisson equation for the potential distribution was achieved. The status of other 2D MOSFET simulation programs are summarized.

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.

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

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

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.

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.

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.

Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows

NASA Astrophysics Data System (ADS)

Suzuki, Yukihito

2018-03-01

A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn-Hilliard and Allen-Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

Two-dimensional mesh embedding for Galerkin B-spline methods

NASA Technical Reports Server (NTRS)

Shariff, Karim; Moser, Robert D.

1995-01-01

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

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.

Investigation of the complex electroviscous effects on electrolyte (single and multiphase) flow in porous medi.

NASA Astrophysics Data System (ADS)

Bolet, A. J. S.; Linga, G.; Mathiesen, J.

2017-12-01

Surface charge is an important control parameter for wall-bounded flow of electrolyte solution. The electroviscous effect has been studied theoretically in model geometries such as infinite capillaries. However, in more complex geometries a quantification of the electroviscous effect is a non-trival task due to strong non-linarites of the underlying equations. In general, one has to rely on numerical methods. Here we present numerical studies of the full three-dimensional steady state Stokes-Poisson-Nernst-Planck problem in order to model electrolyte transport in artificial porous samples. The simulations are performed using the finite element method. From the simulation, we quantity how the electroviscous effect changes the general flow permeability in complex three-dimensional porous media. The porous media we consider are mostly generated artificially by connecting randomly dispersed cylindrical pores. Furthermore, we present results of electric driven two-phase immiscible flow in two dimensions. The simulations are performed by augmenting the above equations with a phase field model to handle and track the interaction between the two fluids (using parameters corresponding to oil-water interfaces, where oil non-polar). In particular, we consider the electro-osmotic effect on imbibition due to charged walls and electrolyte-solution.

On the Hamilton approach of the dissipative systems

NASA Astrophysics Data System (ADS)

Zimin, B. A.; Zorin, I. S.; Sventitskaya, V. E.

2018-05-01

In this paper we consider the problem of constructing equations describing the states of dissipative dynamical systems (media with absorption or damping). The approaches of Lagrange and Hamilton are discussed. A non-symplectic extension of the Poisson brackets is formulated. The application of the Hamiltonian formalism here makes it possible to obtain explicit equations for the dynamics of a nonlinear elastic system with damping and a one-dimensional continuous medium with internal friction.

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions

NASA Astrophysics Data System (ADS)

Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo

2016-04-01

The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.

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

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

Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu; Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex; Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr

2016-08-15

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 themore » 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.« less

Direct numerical simulation of human phonation

NASA Astrophysics Data System (ADS)

Bodony, Daniel; Saurabh, Shakti

2017-11-01

The generation and propagation of the human voice in three-dimensions is studied using direct numerical simulation. A full body domain is employed for the purpose of directly computing the sound in the region past the speaker's mouth. The air in the vocal tract is modeled as a compressible and viscous fluid interacting with the elastic vocal folds. The vocal fold tissue material properties are multi-layered, with varying stiffness, and a linear elastic transversely isotropic model is utilized and implemented in a quadratic finite element code. The fluid-solid domains are coupled through a boundary-fitted interface and utilize a Poisson equation-based mesh deformation method. A kinematic constraint based on a specified minimum gap between the vocal folds is applied to prevent collision during glottal closure. Both near VF flow dynamics and far-field acoustics have been studied. A comparison is drawn to current two-dimensional simulations as well as to data from the literature. Near field vocal fold dynamics and glottal flow results are studied and in good agreement with previous three-dimensional phonation studies. Far-field acoustic characteristics, when compared to their two-dimensional counterpart, are shown to be sensitive to the dimensionality. Supported by the National Science Foundation (CAREER Award Number 1150439).

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.

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.

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

GRAPE- TWO-DIMENSIONAL GRIDS ABOUT AIRFOILS AND OTHER SHAPES BY THE USE OF POISSON'S EQUATION

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1994-01-01

The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids, including those about airfoils. In a grid used for computing aerodynamic flow over an airfoil, or any other body shape, the surface of the body is usually treated as an inner boundary and often cannot be easily represented as an analytic function. The GRAPE computer program was developed to incorporate a method for generating two-dimensional finite-difference grids about airfoils and other shapes by the use of the Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including a limited number of sharp corners. The GRAPE program has been developed to be numerically stable and computationally fast. GRAPE can provide the aerodynamic analyst with an efficient and consistent means of grid generation. The GRAPE procedure generates a grid between an inner and an outer boundary by utilizing an iterative procedure to solve the Poisson differential equation subject to geometrical restraints. In this method, the inhomogeneous terms of the equation are automatically chosen such that two important effects are imposed on the grid. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. Along with the iterative solution to Poisson's equation, a technique of coarse-fine sequencing is employed to accelerate numerical convergence. GRAPE program control cards and input data are entered via the NAMELIST feature. Each variable has a default value such that user supplied data is kept to a minimum. Basic input data consists of the boundary specification, mesh point spacings on the boundaries, and mesh line angles at the boundaries. Output consists of a dataset containing the grid data and, if requested, a plot of the generated mesh. The GRAPE program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 135K (octal) of 60 bit words. For plotted output the commercially available DISSPLA graphics software package is required. The GRAPE program was developed in 1980.

Parallel Computing of Upwelling in a Rotating Stratified Flow

NASA Astrophysics Data System (ADS)

Cui, A.; Street, R. L.

1997-11-01

A code for the three-dimensional, unsteady, incompressible, and turbulent flow has been implemented on the IBM SP2, using message passing. The effects of rotation and variable density are included. A finite volume method is used to discretize the Navier-Stokes equations in general curvilinear coordinates on a non-staggered grid. All the spatial derivatives are approximated using second-order central differences with the exception of the convection terms, which are handled with special upwind-difference schemes. The semi-implicit, second-order accurate, time-advancement scheme employs the Adams-Bashforth method for the explicit terms and Crank-Nicolson for the implicit terms. A multigrid method, with the four-color ZEBRA as smoother, is used to solve the Poisson equation for pressure, while the momentum equations are solved with an approximate factorization technique. The code was successfully validated for a variety test cases. Simulations of a laboratory model of coastal upwelling in a rotating annulus are in progress and will be presented.

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

NASA Technical Reports Server (NTRS)

Tessler, A.; Annett, M. S.; Gendron, G.

2001-01-01

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

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.

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.

Introduction to quantized LIE groups and algebras

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

Tjin, T.

1992-10-10

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl[sub 2] is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxtermore » equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl[sub 2] algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.« less

Electrokinetic motion of a rectangular nanoparticle in a nanochannel

NASA Astrophysics Data System (ADS)

Movahed, Saeid; Li, Dongqing

2012-08-01

This article presents a theoretical study of electrokinetic motion of a negatively charged cubic nanoparticle in a three-dimensional nanochannel with a circular cross-section. Effects of the electrophoretic and the hydrodynamic forces on the nanoparticle motion are examined. Because of the large applied electric field over the nanochannel, the impact of the Brownian force is negligible in comparison with the electrophoretic and the hydrodynamic forces. The conventional theories of electrokinetics such as the Poisson-Boltzmann equation and the Helmholtz-Smoluchowski slip velocity approach are no longer applicable in the small nanochannels. In this study, and at each time step, first, a set of highly coupled partial differential equations including the Poisson-Nernst-Plank equation, the Navier-Stokes equations, and the continuity equation was solved to find the electric potential, ionic concentration field, and the flow field around the nanoparticle. Then, the electrophoretic and hydrodynamic forces acting on the negatively charged nanoparticle were determined. Following that, the Newton second law was utilized to find the velocity of the nanoparticle. Using this model, effects of surface electric charge of the nanochannel, bulk ionic concentration, the size of the nanoparticle, and the radius of the nanochannel on the nanoparticle motion were investigated. Increasing the bulk ionic concentration or the surface charge of the nanochannel will increase the electroosmotic flow, and hence affect the particle's motion. It was also shown that, unlike microchannels with thin EDL, the change in nanochannel size will change the EDL field and the ionic concentration field in the nanochannel, affecting the particle's motion. If the nanochannel size is fixed, a larger particle will move faster than a smaller particle under the same conditions.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

NASA Astrophysics Data System (ADS)

Kopp, Michael; Vattis, Kyriakos; Skordis, Constantinos

2017-12-01

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2 d -dimensional phase space density. The ScM also allows calculating the d -dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2 d -dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d =2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

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.

Three-dimensionally bonded spongy graphene material with super compressive elasticity and near-zero Poisson's ratio.

PubMed

Wu, Yingpeng; Yi, Ningbo; Huang, Lu; Zhang, Tengfei; Fang, Shaoli; Chang, Huicong; Li, Na; Oh, Jiyoung; Lee, Jae Ah; Kozlov, Mikhail; Chipara, Alin C; Terrones, Humberto; Xiao, Peishuang; Long, Guankui; Huang, Yi; Zhang, Fan; Zhang, Long; Lepró, Xavier; Haines, Carter; Lima, Márcio Dias; Lopez, Nestor Perea; Rajukumar, Lakshmy P; Elias, Ana L; Feng, Simin; Kim, Seon Jeong; Narayanan, N T; Ajayan, Pulickel M; Terrones, Mauricio; Aliev, Ali; Chu, Pengfei; Zhang, Zhong; Baughman, Ray H; Chen, Yongsheng

2015-01-20

It is a challenge to fabricate graphene bulk materials with properties arising from the nature of individual graphene sheets, and which assemble into monolithic three-dimensional structures. Here we report the scalable self-assembly of randomly oriented graphene sheets into additive-free, essentially homogenous graphene sponge materials that provide a combination of both cork-like and rubber-like properties. These graphene sponges, with densities similar to air, display Poisson's ratios in all directions that are near-zero and largely strain-independent during reversible compression to giant strains. And at the same time, they function as enthalpic rubbers, which can recover up to 98% compression in air and 90% in liquids, and operate between -196 and 900 °C. Furthermore, these sponges provide reversible liquid absorption for hundreds of cycles and then discharge it within seconds, while still providing an effective near-zero Poisson's ratio.

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.

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.

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

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

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

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.

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

NASA Astrophysics Data System (ADS)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

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.

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

NASA Astrophysics Data System (ADS)

Fuentealba, Oscar; Matulich, Javier; Pérez, Alfredo; Pino, Miguel; Rodríguez, Pablo; Tempo, David; Troncoso, Ricardo

2018-01-01

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis is performed in terms of two-dimensional gauge fields for isl(2,R) , being isomorphic to the Poincaré algebra in 3D. Although the algebra is not semisimple, the formulation can still be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer k, and defined through a suitable generalization of the Gelfand-Dikii polynomials. The symmetries of the hierarchy are explicitly found. For k ≥ 1, the corresponding conserved charges span an infinite-dimensional Abelian algebra without central extensions, so that they are in involution; while in the case of k = 0, they generate the BMS3 algebra. In the special case of k = 1, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to the ones of a specific type of the Hirota-Satsuma coupled KdV systems. For k ≥ 1, the hierarchy also includes the so-called perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of k. Remarkably, the dynamics can be fully geometrized so as to describe the evolution of spacelike surfaces embedded in locally flat spacetimes. Indeed, General Relativity in 3D can be endowed with a suitable set of boundary conditions, so that the Einstein equations precisely reduce to the ones of the hierarchy aforementioned. The symmetries of the integrable systems then arise as diffeomorphisms that preserve the asymptotic form of the spacetime metric, and therefore, they become Noetherian. The infinite set of conserved charges is then recovered from the corresponding surface integrals in the canonical approach.

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

NASA Astrophysics Data System (ADS)

Qiang, Ji

2016-06-01

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral solver scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

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

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

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

Recognizing human activities using appearance metric feature and kinematics feature

NASA Astrophysics Data System (ADS)

Qian, Huimin; Zhou, Jun; Lu, Xinbiao; Wu, Xinye

2017-05-01

The problem of automatically recognizing human activities from videos through the fusion of the two most important cues, appearance metric feature and kinematics feature, is considered. And a system of two-dimensional (2-D) Poisson equations is introduced to extract the more discriminative appearance metric feature. Specifically, the moving human blobs are first detected out from the video by background subtraction technique to form a binary image sequence, from which the appearance feature designated as the motion accumulation image and the kinematics feature termed as centroid instantaneous velocity are extracted. Second, 2-D discrete Poisson equations are employed to reinterpret the motion accumulation image to produce a more differentiated Poisson silhouette image, from which the appearance feature vector is created through the dimension reduction technique called bidirectional 2-D principal component analysis, considering the balance between classification accuracy and time consumption. Finally, a cascaded classifier based on the nearest neighbor classifier and two directed acyclic graph support vector machine classifiers, integrated with the fusion of the appearance feature vector and centroid instantaneous velocity vector, is applied to recognize the human activities. Experimental results on the open databases and a homemade one confirm the recognition performance of the proposed algorithm.

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

PubMed

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

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

Fractional Poisson Fields and Martingales

NASA Astrophysics Data System (ADS)

Aletti, Giacomo; Leonenko, Nikolai; Merzbach, Ely

2018-02-01

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

Constant fields and constant gradients in open ionic channels.

PubMed Central

Chen, D P; Barcilon, V; Eisenberg, R S

1992-01-01

Ions enter cells through pores in proteins that are holes in dielectrics. The energy of interaction between ion and charge induced on the dielectric is many kT, and so the dielectric properties of channel and pore are important. We describe ionic movement by (three-dimensional) Nemst-Planck equations (including flux and net charge). Potential is described by Poisson's equation in the pore and Laplace's equation in the channel wall, allowing induced but not permanent charge. Asymptotic expansions are constructed exploiting the long narrow shape of the pore and the relatively high dielectric constant of the pore's contents. The resulting one-dimensional equations can be integrated numerically; they can be analyzed when channels are short or long (compared with the Debye length). Traditional constant field equations are derived if the induced charge is small, e.g., if the channel is short or if the total concentration gradient is zero. A constant gradient of concentration is derived if the channel is long. Plots directly comparable to experiments are given of current vs voltage, reversal potential vs. concentration, and slope conductance vs. concentration. This dielectric theory can easily be tested: its parameters can be determined by traditional constant field measurements. The dielectric theory then predicts current-voltage relations quite different from constant field, usually more linear, when gradients of total concentration are imposed. Numerical analysis shows that the interaction of ion and channel can be described by a mean potential if, but only if, the induced charge is negligible, that is to say, the electric field is spatially constant. Images FIGURE 1 PMID:1376159

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution.

PubMed

Inouye, David; Yang, Eunho; Allen, Genevera; Ravikumar, Pradeep

2017-01-01

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.

Stress concentrations for straight-shank and countersunk holes in plates subjected to tension, bending, and pin loading

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Newman, J. C., Jr.

1992-01-01

A three dimensional stress concentration analysis was conducted on straight shank and countersunk (rivet) holes in a large plate subjected to various loading conditions. Three dimensional finite element analysis were performed with 20 node isoparametric elements. The plate material was assumed to be linear elastic and isotropic, with a Poisson ratio of 0.3. Stress concentration along the bore of the hole were computed for several ratios of hole radius to plate thickness (0.1 to 2.5) and ratios of countersink depth to plate thickness (0.25 to 1). The countersink angles were varied from 80 to 100 degrees in some typical cases, but the angle was held constant at 100 degrees for most cases. For straight shank holes, three types of loading were considered: remote tension, remote bending, and wedge loading in the hole. Results for remote tension and wedge loading were used to estimate stress concentration for simulated rivet in pin loading. For countersunk holes only remote tension and bending were considered. Based on the finite element results, stress concentration equations were developed. Whenever possible, the present results were compared with other numerical solutions and experimental results from the literature.

Darboux transformation and explicit solutions for some (2+1)-dimensional equations

NASA Astrophysics Data System (ADS)

Wang, Yan; Shen, Lijuan; Du, Dianlou

2007-06-01

Three systems of (2+1)-dimensional soliton equations and their decompositions into the (1+1)-dimensional soliton equations are proposed. These equations include KPI, CKP, MKPI. With the help of Darboux transformation of (1+1)-dimensional equations, we get the explicit solutions of the (2+1)-dimensional equations.

Necessary and sufficient conditions for the stability of a sleeping top described by three forms of dynamic equations

NASA Astrophysics Data System (ADS)

Ge, Zheng-Ming

2008-04-01

Necessary and sufficient conditions for the stability of a sleeping top described by dynamic equations of six state variables, Euler equations, and Poisson equations, by a two-degree-of-freedom system, Krylov equations, and by a one-degree-of-freedom system, nutation angle equation, is obtained by the Lyapunov direct method, Ge-Liu second instability theorem, an instability theorem, and a Ge-Yao-Chen partial region stability theorem without using the first approximation theory altogether.

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.

Intrinsic delay of permeable base transistor

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

Chen, Wenchao; Guo, Jing; So, Franky

2014-07-28

Permeable base transistors (PBTs) fabricated by vacuum deposition or solution process have the advantages of easy fabrication and low power operation and are a promising device structure for flexible electronics. Intrinsic delay of PBT, which characterizes the speed of the transistor, is investigated by solving the three-dimensional Poisson equation and drift-diffusion equation self-consistently using finite element method. Decreasing the emitter thickness lowers the intrinsic delay by improving on-current, and a thinner base is also preferred for low intrinsic delay because of fewer carriers in the base region at off-state. The intrinsic delay exponentially decreases as the emitter contact Schottky barriermore » height decreases, and it linearly depends on the carrier mobility. With an optimized emitter contact barrier height and device geometry, a sub-nano-second intrinsic delay can be achieved with a carrier mobility of ∼10 cm{sup 2}/V/s obtainable in solution processed indium gallium zinc oxide, which indicates the potential of solution processed PBTs for GHz operations.« less

The stochastic energy-Casimir method

NASA Astrophysics Data System (ADS)

Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.

2018-04-01

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"

Study on longitudinal dispersion relation in one-dimensional relativistic plasma: Linear theory and Vlasov simulation

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

Zhang, H.; Wu, S. Z.; Zhou, C. T.

2013-09-15

The dispersion relation of one-dimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the Vlasov-Poisson equations, the linear dispersion relation is derived for the proper one-dimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with establishedmore » linear theory.« less

Poisson equation for the Mercedes diagram in string theory at genus one

NASA Astrophysics Data System (ADS)

Basu, Anirban

2016-03-01

The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three-loop Feynman diagram contributes to the {D}12{{ R }}4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one- and two-loop Feynman diagrams. We calculate its contribution to the {D}12{{ R }}4 amplitude.

Three-dimensional fabric reinforced plastics for cryogenic use

NASA Astrophysics Data System (ADS)

Iwasaki, Y.; Yasuda, J.; Hirokawa, T.; Noma, K.; Nishijima, S.; Okada, T.

Three-dimensional fabric reinforced plastics (3DFRPs) have been developed as insulating and/or structural materials in superconducting magnets. Three-dimensional fabrics were designed with practical applications in fibre composites of 3DFRP. The mechanical properties such as Young's modulus, Poisson's ratio, tensile strength and the compressive strength down to liquid helium temperature were measured. Thermal contraction was also measured. The cryogenic characteristics of 3DFRPs were compared with those of conventional laminates. The newly developed 3DFRPs were found to show satisfactory characteristics not only at room temperature but also at low temperatures.

Modeling of monolayer charge-stabilized colloidal crystals with static hexagonal crystal lattice

NASA Astrophysics Data System (ADS)

Nagatkin, A. N.; Dyshlovenko, P. E.

2018-01-01

The mathematical model of monolayer colloidal crystals of charged hard spheres in liquid electrolyte is proposed. The particles in the monolayer are arranged into the two-dimensional hexagonal crystal lattice. The model enables finding elastic constants of the crystals from the stress-strain dependencies. The model is based on the nonlinear Poisson-Boltzmann differential equation. The Poisson-Boltzmann equation is solved numerically by the finite element method for any spatial configuration. The model has five geometrical and electrical parameters. The model is used to study the crystal with particles comparable in size with the Debye length of the electrolyte. The first- and second-order elastic constants are found for a broad range of densities. The model crystal turns out to be stable relative to small uniform stretching and shearing. It is also demonstrated that the Cauchy relation is not fulfilled in the crystal. This means that the pair effective interaction of any kind is not sufficient to proper model the elasticity of colloids within the one-component approach.

On the biophysics of cathodal galvanotaxis in rat prostate cancer cells: Poisson-Nernst-Planck equation approach.

PubMed

Borys, Przemysław

2012-06-01

Rat prostate cancer cells have been previously investigated using two cell lines: a highly metastatic one (Mat-Ly-Lu) and a nonmetastatic one (AT-2). It turns out that the highly metastatic Mat-Ly-Lu cells exhibit a phenomenon of cathodal galvanotaxis in an electric field which can be blocked by interrupting the voltage-gated sodium channel (VGSC) activity. The VGSC activity is postulated to be characteristic for metastatic cells and seems to be a reasonable driving force for motile behavior. However, the classical theory of cellular motion depends on calcium ions rather than sodium ions. The current research provides a theoretical connection between cellular sodium inflow and cathodal galvanotaxis of Mat-Ly-Lu cells. Electrical repulsion of intracellular calcium ions by entering sodium ions is proposed after depolarization starting from the cathodal side. The disturbance in the calcium distribution may then drive actin polymerization and myosin contraction. The presented modeling is done within a continuous one-dimensional Poisson-Nernst-Planck equation framework.

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov-Poisson Equation during Violent Relaxation

NASA Astrophysics Data System (ADS)

Beraldo e Silva, Leandro; de Siqueira Pedra, Walter; Sodré, Laerte; Perico, Eder L. D.; Lima, Marcos

2017-09-01

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10{--}12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

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.

Anisotropic fractal media by vector calculus in non-integer dimensional space

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

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.

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution

PubMed Central

Inouye, David; Yang, Eunho; Allen, Genevera; Ravikumar, Pradeep

2017-01-01

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section. PMID:28983398

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 3DGRAPE book: Theory, users' manual, examples

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.

1989-01-01

A users' manual for a new three-dimensional grid generator called 3DGRAPE is presented. The program, written in FORTRAN, is capable of making zonal (blocked) computational grids in or about almost any shape. Grids are generated by the solution of Poisson's differential equations in three dimensions. The program automatically finds its own values for inhomogeneous terms which give near-orthogonality and controlled grid cell height at boundaries. Grids generated by 3DGRAPE have been applied to both viscous and inviscid aerodynamic problems, and to problems in other fluid-dynamic areas. The smoothness for which elliptic methods are known is seen here, including smoothness across zonal boundaries. An introduction giving the history, motivation, capabilities, and philosophy of 3DGRAPE is presented first. Then follows a chapter on the program itself. The input is then described in detail. A chapter on reading the output and debugging follows. Three examples are then described, including sample input data and plots of output. Last is a chapter on the theoretical development of the method.

On the extraction of pressure fields from PIV velocity measurements in turbines

NASA Astrophysics Data System (ADS)

Villegas, Arturo; Diez, Fancisco J.

2012-11-01

In this study, the pressure field for a water turbine is derived from particle image velocimetry (PIV) measurements. Measurements are performed in a recirculating water channel facility. The PIV measurements include calculating the tangential and axial forces applied to the turbine by solving the integral momentum equation around the airfoil. The results are compared with the forces obtained from the Blade Element Momentum theory (BEMT). Forces are calculated by using three different methods. In the first method, the pressure fields are obtained from PIV velocity fields by solving the Poisson equation. The boundary conditions are obtained from the Navier-Stokes momentum equations. In the second method, the pressure at the boundaries is determined by spatial integration of the pressure gradients along the boundaries. In the third method, applicable only to incompressible, inviscid, irrotational, and steady flow, the pressure is calculated using the Bernoulli equation. This approximated pressure is known to be accurate far from the airfoil and outside of the wake for steady flows. Additionally, the pressure is used to solve for the force from the integral momentum equation on the blade. From the three methods proposed to solve for pressure and forces from PIV measurements, the first one, which is solved by using the Poisson equation, provides the best match to the BEM theory calculations.

Aerodynamic simulation on massively parallel systems

NASA Technical Reports Server (NTRS)

Haeuser, Jochem; Simon, Horst D.

1992-01-01

This paper briefly addresses the computational requirements for the analysis of complete configurations of aircraft and spacecraft currently under design to be used for advanced transportation in commercial applications as well as in space flight. The discussion clearly shows that massively parallel systems are the only alternative which is both cost effective and on the other hand can provide the necessary TeraFlops, needed to satisfy the narrow design margins of modern vehicles. It is assumed that the solution of the governing physical equations, i.e., the Navier-Stokes equations which may be complemented by chemistry and turbulence models, is done on multiblock grids. This technique is situated between the fully structured approach of classical boundary fitted grids and the fully unstructured tetrahedra grids. A fully structured grid best represents the flow physics, while the unstructured grid gives best geometrical flexibility. The multiblock grid employed is structured within a block, but completely unstructured on the block level. While a completely unstructured grid is not straightforward to parallelize, the above mentioned multiblock grid is inherently parallel, in particular for multiple instruction multiple datastream (MIMD) machines. In this paper guidelines are provided for setting up or modifying an existing sequential code so that a direct parallelization on a massively parallel system is possible. Results are presented for three parallel systems, namely the Intel hypercube, the Ncube hypercube, and the FPS 500 system. Some preliminary results for an 8K CM2 machine will also be mentioned. The code run is the two dimensional grid generation module of Grid, which is a general two dimensional and three dimensional grid generation code for complex geometries. A system of nonlinear Poisson equations is solved. This code is also a good testcase for complex fluid dynamics codes, since the same datastructures are used. All systems provided good speedups, but message passing MIMD systems seem to be best suited for large miltiblock applications.

Simulation Methods for Poisson Processes in Nonstationary Systems.

DTIC Science & Technology

1978-08-01

for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the...and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

SSME Turbopump Turbine Computations

NASA Technical Reports Server (NTRS)

Jorgenson, P. G. E.

1985-01-01

A two-dimensional viscous code was developed to be used in the prediction of the flow in the SSME high-pressure turbopump blade passages. The rotor viscous code (RVC) employs a four-step Runge-Kutta scheme to solve the two-dimensional, thin-layer Navier-Stokes equations. The Baldwin-Lomax eddy-viscosity model is used for these turbulent flow calculations. A viable method was developed to use the relative exit conditions from an upstream blade row as the inlet conditions to the next blade row. The blade loading diagrams are compared with the meridional values obtained from an in-house quasithree-dimensional inviscid code. Periodic boundary conditions are imposed on a body-fitted C-grid computed by using the GRAPE GRids about Airfoils using Poisson's Equation (GRAPE) code. Total pressure, total temperature, and flow angle are specified at the inlet. The upstream-running Riemann invariant is extrapolated from the interior. Static pressure is specified at the exit such that mass flow is conserved from blade row to blade row, and the conservative variables are extrapolated from the interior. For viscous flows the noslip condition is imposed at the wall. The normal momentum equation gives the pressure at the wall. The density at the wall is obtained from the wall total temperature.

Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

An implicit time-marching method for the three-dimensional Navier-Stokes equations of contravariant velocity components

NASA Astrophysics Data System (ADS)

Daiguji, Hisaaki; Yamamoto, Satoru

1988-12-01

The implicit time-marching finite-difference method for solving the three-dimensional compressible Euler equations developed by the authors is extended to the Navier-Stokes equations. The distinctive features of this method are to make use of momentum equations of contravariant velocities instead of physical boundaries, and to be able to treat the periodic boundary condition for the three-dimensional impeller flow easily. These equations can be solved by using the same techniques as the Euler equations, such as the delta-form approximate factorization, diagonalization and upstreaming. In addition to them, a simplified total variation diminishing scheme by the authors is applied to the present method in order to capture strong shock waves clearly. Finally, the computed results of the three-dimensional flow through a transonic compressor rotor with tip clearance are shown.

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.

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

NASA Astrophysics Data System (ADS)

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

2006-09-01

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

The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods

NASA Astrophysics Data System (ADS)

Ge, Z.; Kruse, H. P.; Marsden, J. E.

1996-01-01

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material and derive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame.

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

NASA Astrophysics Data System (ADS)

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

1991-11-01

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

Weak solutions of the three-dimensional vorticity equation with vortex singularities

NASA Technical Reports Server (NTRS)

Winckelmans, G.; Leonard, A.

1988-01-01

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

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

NASA Astrophysics Data System (ADS)

Geng, Weihua; Zhao, Shan

2017-12-01

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

Elliptic generation of composite three-dimensional grids about realistic aircraft

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1986-01-01

An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid generation method are presented along with results of the present application, a wing-body configuration based on the F-16 fighter aircraft.

On the three dimensional structure of stratospheric material transport associated with various types of waves

NASA Astrophysics Data System (ADS)

Kinoshita, T.; Sato, K.

2016-12-01

The Transformed Eulerian-Mean (TEM) equations were derived by Andrews and McIntyre (1976, 1978) and have been widely used to examine wave-mean flow interaction in the meridional cross section. According to previous studies, the Brewer-Dobson circulation in the stratosphere is driven by planetary waves, baroclinic waves, and inertia-gravity waves, and that the meridional circulation from the summer hemisphere to the winter hemisphere in the mesosphere is mainly driven by gravity waves (e.g., Garcia and Boville 1994; Plumb and Semeniuk 2003; Watanabe et al. 2008; Okamoto et al. 2011). However, the TEM equations do not provide the three-dimensional view of the transport, so that the three dimensional TEM equations have been formulated (Hoskins et al. 1983, Trenberth 1986, Plumb 1985, 1986, Takaya and Nakamura 1997, 2001, Miyahara 2006, Kinoshita et al. 2010, Noda 2010, Kinoshita and Sato 2013a, b, and Noda 2014). On the other hand, the TEM equations cannot properly treat the lower boundary and unstable waves. The Mass-weighted Isentropic Mean (MIM) equations derived by Iwasaki (1989, 1990) are the equations that overcome those problems and the formulation of three-dimensional MIM equations have been studied. The present study applies the three-dimensional TEM and MIM equations to the ERA-Interim reanalysis data and examines the climatological character of three-dimensional structure of Stratospheric Brewer-Dobson circulation. Next, we will discuss how to treat the flow associated with spatial structure of stationary waves.

Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems

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

Ng, C.; Bhattacharjee, A.; Skiff, F.

2006-05-15

Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show thatmore » the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered as true eigenmodes (which they are not in the collisionless theory). For BGK modes, our interest is motivated by recent discoveries of electrostatic solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is quite mature, there appear to be no exact three-dimensional solutions in the literature (except for the limiting case when the magnetic field is sufficiently strong so that one can apply the guiding-center approximation). We show, in fact, that two- and three-dimensional solutions that depend only on energy do not exist. However, if solutions depend on both energy and angular momentum, we can construct exact three-dimensional solutions for the unmagnetized case, and two-dimensional solutions for the case with a finite magnetic field. The latter are shown to be exact, fully electromagnetic solutions of the steady-state Vlasov-Poisson-Ampere system.« less

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

On a modified form of navier-stokes equations for three-dimensional flows.

PubMed

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

PubMed Central

Venetis, J.

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

DOE PAGES

Shao, Xuan-Min

2016-04-12

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider,more » rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.« less

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

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.

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

PubMed

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

2018-03-13

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

Dynamical behavior for the three-dimensional generalized Hasegawa-Mima equations

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

Zhang Ruifeng; Guo Boling; Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088

2007-01-15

The long time behavior of solution of the three-dimensional generalized Hasegawa-Mima [Phys. Fluids 21, 87 (1978)] equations with dissipation term is considered. The global attractor problem of the three-dimensional generalized Hasegawa-Mima equations with periodic boundary condition was studied. Applying the method of uniform a priori estimates, the existence of global attractor of this problem was proven, and also the dimensions of the global attractor are estimated.

Three-dimensional finite element analysis for high velocity impact. [of projectiles from space debris

NASA Technical Reports Server (NTRS)

Chan, S. T. K.; Lee, C. H.; Brashears, M. R.

1975-01-01

A finite element algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the Eulerian hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent finite element analysis utilizing three-dimensional isoparametric elements, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

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

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

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

2013-02-15

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

Poisson structure of dynamical systems with three degrees of freedom

NASA Astrophysics Data System (ADS)

Gümral, Hasan; Nutku, Yavuz

1993-12-01

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure.

Electroosmotic flow and mixing in microchannels with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Tang, G. H.; Li, Zhuo; Wang, J. K.; He, Y. L.; Tao, W. Q.

2006-11-01

Understanding the electroosmotic flow in microchannels is of both fundamental and practical significance for the design and optimization of various microfluidic devices to control fluid motion. In this paper, a lattice Boltzmann equation, which recovers the nonlinear Poisson-Boltzmann equation, is used to solve the electric potential distribution in the electrolytes, and another lattice Boltzmann equation, which recovers the Navier-Stokes equation including the external force term, is used to solve the velocity fields. The method is validated by the electric potential distribution in the electrolytes and the pressure driven pulsating flow. Steady-state and pulsating electroosmotic flows in two-dimensional parallel uniform and nonuniform charged microchannels are studied with this lattice Boltzmann method. The simulation results show that the heterogeneous surface potential distribution and the electroosmotic pulsating flow can induce chaotic advection and thus enhance the mixing in microfluidic systems efficiently.

2-D modeling and analysis of short-channel behavior of a front high- K gate stack triple-material gate SB SON MOSFET

NASA Astrophysics Data System (ADS)

Banerjee, Pritha; Kumari, Tripty; Sarkar, Subir Kumar

2018-02-01

This paper presents the 2-D analytical modeling of a front high- K gate stack triple-material gate Schottky Barrier Silicon-On-Nothing MOSFET. Using the two-dimensional Poisson's equation and considering the popular parabolic potential approximation, expression for surface potential as well as the electric field has been considered. In addition, the response of the proposed device towards aggressive downscaling, that is, its extent of immunity towards the different short-channel effects, has also been considered in this work. The analytical results obtained have been validated using the simulated results obtained using ATLAS, a two-dimensional device simulator from SILVACO.

A numerical code for a three-dimensional magnetospheric MHD equilibrium model

NASA Technical Reports Server (NTRS)

Voigt, G.-H.

1992-01-01

Two dimensional and three dimensional MHD equilibrium models were begun for Earth's magnetosphere. The original proposal was motivated by realizing that global, purely data based models of Earth's magnetosphere are inadequate for studying the underlying plasma physical principles according to which the magnetosphere evolves on the quasi-static convection time scale. Complex numerical grid generation schemes were established for a 3-D Poisson solver, and a robust Grad-Shafranov solver was coded for high beta MHD equilibria. Thus, the effects were calculated of both the magnetopause geometry and boundary conditions on the magnetotail current distribution.

Multigrid calculation of three-dimensional turbomachinery flows

NASA Technical Reports Server (NTRS)

Caughey, David A.

1989-01-01

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

A Few Integrable Dynamical Systems, Recurrence Operators, Expanding Integrable Models and Hamiltonian Structures by the r-Matrix Method

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Muhammad, Iqbal; Yue, Chao

2017-10-01

We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov-Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the (2+1)-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of (2+1)-dimensional expanding dynamical model of the (2+1)-dimensional dynamical system is generated as well. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

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

NASA Astrophysics Data System (ADS)

Sugioka, Hideyuki

2016-12-01

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

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis

2016-11-01

A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. In all the cases, the results are found to be in very good agreement with published data and savings in computational resources are achieved.

Electrodiffusion Models of Neurons and Extracellular Space Using the Poisson-Nernst-Planck Equations—Numerical Simulation of the Intra- and Extracellular Potential for an Axon Model

PubMed Central

Pods, Jurgis; Schönke, Johannes; Bastian, Peter

2013-01-01

In neurophysiology, extracellular signals—as measured by local field potentials (LFP) or electroencephalography—are of great significance. Their exact biophysical basis is, however, still not fully understood. We present a three-dimensional model exploiting the cylinder symmetry of a single axon in extracellular fluid based on the Poisson-Nernst-Planck equations of electrodiffusion. The propagation of an action potential along the axonal membrane is investigated by means of numerical simulations. Special attention is paid to the Debye layer, the region with strong concentration gradients close to the membrane, which is explicitly resolved by the computational mesh. We focus on the evolution of the extracellular electric potential. A characteristic up-down-up LFP waveform in the far-field is found. Close to the membrane, the potential shows a more intricate shape. A comparison with the widely used line source approximation reveals similarities and demonstrates the strong influence of membrane currents. However, the electrodiffusion model shows another signal component stemming directly from the intracellular electric field, called the action potential echo. Depending on the neuronal configuration, this might have a significant effect on the LFP. In these situations, electrodiffusion models should be used for quantitative comparisons with experimental data. PMID:23823244

TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE

NASA Technical Reports Server (NTRS)

Vu, B. T.

1994-01-01

TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.

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.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Theoretical predictions for the phase stability of dense binary mixtures

NASA Astrophysics Data System (ADS)

Macfarlane, J. J.

1983-08-01

A new approach is developed for evaluating the mixing properties of binary solutions at high pressure. This involves solving Poisson's equation throughout three-dimensional cubic lattices, consistent with Thomas-Fermi-Dirac (TFD) theory. Zero temperature calculations are carried out for a variety of compositions and crystal structures in 3 pressure groups relevant to Jovian planetary interiors. Pseudopotentials based on the two-component-plasma model (with a uniform electron background) are fitted to the solid-state results, and are then used in liquid-state calculations using hard-sphere perturbation theory. TFD results if H-He solutions find critical temperatures (above which all compositions are soluble) to be approx. 0.500, and 1500 K at pressures of 10, 100, and 1000 Mbar, respectively. These temperatures are much lower than those obtained using free electron perturbation theory, where Tcrit approx. 10,000 K at 10 Mbar.

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.

Macroscopic Modeling of a One-Dimensional Electrochemical Cell using the Poisson-Nernst-Planck Equations

NASA Astrophysics Data System (ADS)

Yan, David

This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and the scheme's stability and convergence properties are discussed. While evaluating different methods for discretizing the coupled flux boundary condition, we discover a thresholding behaviour in the adaptive time stepper, and perform additional tests to investigate it. Finally, a method based on ghost points is chosen for its favorable numerical properties compared to the alternatives. With this method, we are able to run simulations with a large range of parameters, including any value of the nondimensionalized Debye length epsilon. The numerical code is first used to run simulations to explore the effects of polarization, surface coverage, and temperature. The code is also used to perform frequency sweeps of input signals in order to mimic impedance spectroscopy experiments. Finally, in Chapter 5, we use our model to apply ramped voltages to electrochemical systems, and show theoretical and simulated current-voltage curves for liquid and solid thin films, cells with blocking (polarized) electrodes, and electrolytes with background charge. Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. No general theory of linear-sweep voltammetry is available, however, for unsupported electrolytes and for other situations where diffuse charge effects play a role. We show theoretical and simulated current-voltage curves for liquid and solid thin films, cells with blocking electrodes, and membranes with fixed background charge. The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, but capacitive charging of the double layers is also studied, for early time transients at reactive electrodes and for non-reactive blocking electrodes. The final chapter highlights the role of diffuse charge in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

PubMed Central

Li, Zhilin; Lai, Ming-Chih

2012-01-01

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

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

NASA Astrophysics Data System (ADS)

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

2013-11-01

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

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

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

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

Biomolecular surface construction by PDE transform.

PubMed

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

2012-03-01

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

Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

NASA Astrophysics Data System (ADS)

Bienaymé, Olivier

2018-04-01

We have studied the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carried out the analysis by developing a numerical resolution of the 2D2V (two-dimensional in the physical space, 2D, and two-dimensional in the velocity motion, 2V) collisionless Boltzmann equation and modelling the stellar motions within the plane of the Galaxy within the solar neighbourhood. We recover similar results to those obtained by other authors using N-body simulations, but we are also able to numerically identify faint structures thanks to the cancelling of the Poisson noise. We find that the ratio of the bar pattern speed to the local circular frequency is in the range ΩB/Ω = 1.77 to 1.91. If the Galactic bar angle orientation is within the range from 24 to 45 degrees, the bar pattern speed is between 46 and 49 km s-1 kpc-1.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

PubMed

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (ψ,θ,γ,μ) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Construction of Three Dimensional Solutions for the Maxwell Equations

NASA Technical Reports Server (NTRS)

Yefet, A.; Turkel, E.

1998-01-01

We consider numerical solutions for the three dimensional time dependent Maxwell equations. We construct a fourth order accurate compact implicit scheme and compare it to the Yee scheme for free space in a box.

Drag Minimization for Wings and Bodies in Supersonic Flow

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Fuller, Franklyn B

1958-01-01

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

Solution of the surface Euler equations for accurate three-dimensional boundary-layer analysis of aerodynamic configurations

NASA Technical Reports Server (NTRS)

Iyer, V.; Harris, J. E.

1987-01-01

The three-dimensional boundary-layer equations in the limit as the normal coordinate tends to infinity are called the surface Euler equations. The present paper describes an accurate method for generating edge conditions for three-dimensional boundary-layer codes using these equations. The inviscid pressure distribution is first interpolated to the boundary-layer grid. The surface Euler equations are then solved with this pressure field and a prescribed set of initial and boundary conditions to yield the velocities along the two surface coordinate directions. Results for typical wing and fuselage geometries are presented. The smoothness and accuracy of the edge conditions obtained are found to be superior to the conventional interpolation procedures.

Trends and Techniques for Space Base Electronics

NASA Technical Reports Server (NTRS)

Trotter, J. D.; Wade, T. E.; Gassaway, J. D.

1979-01-01

Simulations of various phosphorus and boron diffusions in SOS were completed and a sputtering system, furnaces, and photolithography related equipment were set up. Double layer metal experiments initially utilized wet chemistry techniques. By incorporating ultrasonic etching of the vias, premetal cleaning a modified buffered HF, phosphorus doped vapox, and extended sintering, yields of 98% were obtained using the standard test pattern. A two dimensional modeling program was written for simulating short channel MOSFETs with nonuniform substrate doping. A key simplifying assumption used is that the majority carriers can be represented by a sheet charge at the silicon dioxide silicon interface. Although the program is incomplete, the two dimensional Poisson equation for the potential distribution was achieved. The status of other Z-D MOSFET simulation programs is summarized.

Symplectic discretization for spectral element solution of Maxwell's equations

NASA Astrophysics Data System (ADS)

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

2009-08-01

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

Massively Parallel Solution of Poisson Equation on Coarse Grain MIMD Architectures

NASA Technical Reports Server (NTRS)

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

1998-01-01

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

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.

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.

Modeling self-consistent multi-class dynamic traffic flow

NASA Astrophysics Data System (ADS)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

Some problems of the calculation of three-dimensional boundary layer flows on general configurations

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Mosinskis, G. J.; Rehn, J. A.

1973-01-01

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.

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.

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.

A semi-implicit finite difference model for three-dimensional tidal circulation,

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1992-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

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 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.

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Three-dimensional marginal separation

NASA Technical Reports Server (NTRS)

Duck, Peter W.

1988-01-01

The three dimensional marginal separation of a boundary layer along a line of symmetry is considered. The key equation governing the displacement function is derived, and found to be a nonlinear integral equation in two space variables. This is solved iteratively using a pseudo-spectral approach, based partly in double Fourier space, and partly in physical space. Qualitatively, the results are similar to previously reported two dimensional results (which are also computed to test the accuracy of the numerical scheme); however quantitatively the three dimensional results are much different.

Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

PubMed

Yan, Zhenya; Konotop, V V

2009-09-01

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

Triggering Excimer Lasers by Photoionization from Corona Discharges

NASA Astrophysics Data System (ADS)

Xiong, Zhongmin; Duffey, Thomas; Brown, Daniel; Kushner, Mark

2009-10-01

High repetition rate ArF (192 nm) excimer lasers are used for photolithography sources in microelectronics fabrication. In highly attaching gas mixtures, preionization is critical to obtaining stable, reproducible glow discharges. Photoionization from a separate corona discharge is one technique for preionization which triggers the subsequent electron avalanche between the main electrodes. Photoionization triggering of an ArF excimer laser sustained in multi-atmosphere Ne/Ar/F2/Xe gas mixtures has been investigated using a 2-dimensional plasma hydrodynamics model including radiation transport. Continuity equations for charged and neutral species, and Poisson's equation are solved coincident with the electron temperature with transport coefficients obtained from solutions of Boltzmann's equation. Photoionizing radiation is produced by a surface discharge which propagates along a corona-bar located adjacent to the discharge electrodes. The consequences of pulse power waveform, corona bar location, capacitance and gas mixture on uniformity, symmetry and gain of the avalanche discharge will be discussed.

The equilibrium and stability of the gaseous component of the galaxy, 2

NASA Technical Reports Server (NTRS)

Kellman, S. A.

1971-01-01

A time-independent, linear, plane and axially-symmetric stability analysis was performed on a self-gravitating, plane-parallel, isothermal layer of nonmagnetic, nonrotating gas. The gas layer was immersed in a plane-stratified field isothermal layer of stars which supply a self-consistent gravitational field. Only the gaseous component was perturbed. Expressions were derived for the perturbed gas potential and perturbed gas density that satisfied both the Poisson and hydrostatic equilibrium equations. The equation governing the size of the perturbations in the mid-plane was found to be analogous to the one-dimensional time-independent Schrodinger equation for a particle bound by a potential well, and with similar boundary conditions. The radius of the neutral state was computed numerically and compared with the Jeans' and Ledoux radius. The inclusion of a rigid stellar component increased the Ledoux radius, though only slightly. Isodensity contours of the neutrual or marginally unstable state were constructed.

A Galerkin formulation of the MIB method for three dimensional elliptic interface problems

PubMed Central

Xia, Kelin; Wei, Guo-Wei

2014-01-01

We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the first known near second order accurate method for C1 continuous or H2 continuous solutions associated with a Lipschitz continuous interface in a 3D setting. PMID:25309038

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Equation of state of the one- and three-dimensional Bose-Bose gases

NASA Astrophysics Data System (ADS)

Chiquillo, Emerson

2018-06-01

We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schrödinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation supports self-trapped brightlike solitonic droplets and self-trapped darklike solitons. At low temperature, we also find that the pressure and the number of particles of symmetric quantum droplets have a nontrivial dependence on the chemical potential and the difference between the intra- and the interspecies coupling constants.

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.

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

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

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

Topological BF Theories

NASA Astrophysics Data System (ADS)

Sǎraru, Silviu-Constantin

Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.

Decoupling of the nernst-planck and poisson equations. Application to a membrane system at overlimiting currents.

PubMed

Urtenov, Mahamet A-Kh; Kirillova, Evgeniya V; Seidova, Natalia M; Nikonenko, Victor V

2007-12-27

This paper deals with one-dimensional stationary Nernst-Planck and Poisson (NPP) equations describing ion electrodiffusion in multicomponent solution/electrode or ion-conductive membrane systems. A general method for resolving ordinary and singularly perturbed problems with these equations is developed. This method is based on the decoupling of NPP equations that results in deduction of an equation containing only the terms with different powers of the electrical field and its derivatives. Then, the solution of this equation, analytical in several cases or numerical, is substituted into the Nernst-Planck equations for calculating the concentration profile for each ion present in the system. Different ionic species are grouped in valency classes that allows one to reduce the dimension of the original set of equations and leads to a relatively easy treatment of multi-ion systems. When applying the method developed, the main attention is paid to ion transfer at limiting and overlimiting currents, where a significant deviation from local electroneutrality occurs. The boundary conditions and different approximations are examined: the local electroneutrality (LEN) assumption and the original assumption of quasi-uniform distribution of the space charge density (QCD). The relations between the ion fluxes at limiting and overlimiting currents are discussed. In particular, attention is paid to the "exaltation" of counterion transfer toward an ion-exchange membrane by co-ion flux leaking through the membrane or generated at the membrane/solution interface. The structure of the multi-ion concentration field in a depleted diffusion boundary layer (DBL) near an ion-exchange membrane at overlimiting currents is analyzed. The presence of salt ions and hydrogen and hydroxyl ions generated in the course of the water "splitting" reaction is considered. The thickness of the DBL and its different zones, as functions of applied current density, are found by fitting experimental current-voltage curves.

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

PubMed

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

2016-08-01

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

Three ways to solve critical ϕ4 theory on 4 ‑ 𝜖 dimensional real projective space: Perturbation, bootstrap, and Schwinger-Dyson equation

NASA Astrophysics Data System (ADS)

Hasegawa, Chika; Nakayama, Yu

2018-03-01

In this paper, we solve the two-point function of the lowest dimensional scalar operator in the critical ϕ4 theory on 4 ‑ 𝜖 dimensional real projective space in three different methods. The first is to use the conventional perturbation theory, and the second is to impose the cross-cap bootstrap equation, and the third is to solve the Schwinger-Dyson equation under the assumption of conformal invariance. We find that the three methods lead to mutually consistent results but each has its own advantage.

Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

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

Kraloua, B.; Hennad, A.

The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

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.

Calculation of the electron wave function in a graded-channel double-heterojunction modulation-doped field-effect transistor

NASA Technical Reports Server (NTRS)

Mui, D. S. L.; Patil, M. B.; Morkoc, H.

1989-01-01

Three double-heterojunction modulation-doped field-effect transistor structures with different channel composition are investigated theoretically. All of these transistors have an In(x)Ga(1-x)As channel sandwiched between two doped Al(0.3)Ga(0.7)As barriers with undoped spacer layers. In one of the structures, x varies from 0 from either heterojunction to 0.15 at the center of the channel quadratically; in the other two, constant values of x of 0 and 0.15 are used. The Poisson and Schroedinger equations are solved self-consistently for the electron wave function in all three cases. The results showed that the two-dimensional electron gas (2DEG) concentration in the channel of the quadratically graded structure is higher than the x = 0 one and slightly lower than the x = 0.15 one, and the mean distance of the 2DEG is closer to the center of the channel for this transistor than the other two. These two effects have important implications on the electron mobility in the channel.

Generalized Lie symmetry approach for fractional order systems of differential equations. III

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.

Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo

NASA Astrophysics Data System (ADS)

Matejczyk, Bartłomiej; Valiskó, Mónika; Wolfram, Marie-Therese; Pietschmann, Jan-Frederik; Boda, Dezső

2017-03-01

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolyte model. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge, electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.

Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo.

PubMed

Matejczyk, Bartłomiej; Valiskó, Mónika; Wolfram, Marie-Therese; Pietschmann, Jan-Frederik; Boda, Dezső

2017-03-28

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolytemodel. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge,electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.

PubMed

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards

NASA Astrophysics Data System (ADS)

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

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.

Multi-Dimensional Quantum Effect Simulation Using a Density-Gradient Model and Script-Level Programming Techniques

NASA Technical Reports Server (NTRS)

Rafferty, Connor S.; Biegel, Bryan A.; Yu, Zhi-Ping; Ancona, Mario G.; Bude, J.; Dutton, Robert W.; Saini, Subhash (Technical Monitor)

1998-01-01

A density-gradient (DG) model is used to calculate quantum-mechanical corrections to classical carrier transport in MOS (Metal Oxide Semiconductor) inversion/accumulation layers. The model is compared to measured data and to a fully self-consistent coupled Schrodinger and Poisson equation (SCSP) solver. Good agreement is demonstrated for MOS capacitors with gate oxide as thin as 21 A. It is then applied to study carrier distribution in ultra short MOSFETs (Metal Oxide Semiconductor Field Effect Transistor) with surface roughness. This work represents the first implementation of the DG formulation on multidimensional unstructured meshes. It was enabled by a powerful scripting approach which provides an easy-to-use and flexible framework for solving the fourth-order PDEs (Partial Differential Equation) of the DG model.

Phase-resolved fluid dynamic forces of a flapping foil energy harvester based on PIV measurements

NASA Astrophysics Data System (ADS)

Liburdy, James

2017-11-01

Two-dimensional particle image velocimetry measurements are performed in a wind tunnel to evaluate the spatial and temporal fluid dynamic forces acting on a flapping foil operating in the energy harvesting regime. Experiments are conducted at reduced frequencies (k = fc/U) of 0.05 - 0.2, pitching angle of, and heaving amplitude of A / c = 0.6. The phase-averaged pressure field is obtained by integrating the pressure Poisson equation. Fluid dynamic forces are then obtained through the integral momentum equation. Results are compared with a simple force model based on the concept of flow impulse. These results help to show the detailed force distributions, their transient nature and aide in understanding the impact of the fluid flow structures that contribute to the power production.

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

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of thismore » object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.« less

Three dimensional fluid-kinetic model of a magnetically guided plasma jet

NASA Astrophysics Data System (ADS)

Ramos, Jesús J.; Merino, Mario; Ahedo, Eduardo

2018-06-01

A fluid-kinetic model of the collisionless plasma flow in a convergent-divergent magnetic nozzle is presented. The model combines the leading-order Vlasov equation and the fluid continuity and perpendicular momentum equation for magnetized electrons, and the fluid equations for cold ions, which must be solved iteratively to determine the self-consistent plasma response in a three-dimensional magnetic field. The kinetic electron solution identifies three electron populations and provides the plasma density and pressure tensor. The far downstream asymptotic behavior shows the anisotropic cooling of the electron populations. The fluid equations determine the electric potential and the fluid velocities. In the small ion-sound gyroradius case, the solution is constructed one magnetic line at a time. In the large ion-sound gyroradius case, ion detachment from magnetic lines makes the problem fully three-dimensional.

Visualising elastic anisotropy: theoretical background and computational implementation

NASA Astrophysics Data System (ADS)

Nordmann, J.; Aßmus, M.; Altenbach, H.

2018-02-01

In this article, we present the technical realisation for visualisations of characteristic parameters of the fourth-order elasticity tensor, which is classified by three-dimensional symmetry groups. Hereby, expressions for spatial representations of uc(Young)'s modulus and bulk modulus as well as plane representations of shear modulus and uc(Poisson)'s ratio are derived and transferred into a comprehensible form to computer algebra systems. Additionally, we present approaches for spatial representations of both latter parameters. These three- and two-dimensional representations are implemented into the software MATrix LABoratory. Exemplary representations of characteristic materials complete the present treatise.

Three-dimensional compact explicit-finite difference time domain scheme with density variation

NASA Astrophysics Data System (ADS)

Tsuchiya, Takao; Maruta, Naoki

2018-07-01

In this paper, the density variation is implemented in the three-dimensional compact-explicit finite-difference time-domain (CE-FDTD) method. The formulation is first developed based on the continuity equation and the equation of motion, which include the density. Some numerical demonstrations are performed for the three-dimensional sound wave propagation in a two density layered medium. The numerical results are compared with the theoretical results to verify the proposed formulation.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

On local strong solutions to the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum

NASA Astrophysics Data System (ADS)

Song, Sisi

2018-04-01

This paper concerns the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum on Ω \\subset R^3. The domain Ω \\subset R^3 is a general connected smooth one, either bounded or unbounded. In particular, the initial density can have compact support when Ω is unbounded. First, we obtain the local existence and uniqueness of strong solution to the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations without any compatibility condition assumed on the initial data. Then, we also prove the continuous dependence of strong solution on the initial data under an additional compatibility condition.

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

PubMed

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

1992-01-05

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

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.

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

PubMed

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

2011-10-15

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

A three-dimensional kinematic model for the dissolution of crystals

NASA Astrophysics Data System (ADS)

Tellier, C. R.

1989-06-01

The two-dimensional kinematic theory developed by Frank is extended into three dimensions. It is shown that the theoretical equations for the propagation vector associated with the displacement of a moving surface element can be directly derived from the polar equation of the slowness surface.

Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2007-08-01

We demonstrate that partner symmetries provide a lift of noninvariant solutions of the three-dimensional Boyer-Finley equation to noninvariant solutions of the four-dimensional hyperbolic complex Monge-Ampère equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Monge-Ampère equation. Using these solutions we construct new Ricci-flat ultra-hyperbolic metrics with non-zero curvature tensor that have no Killing vectors.

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

NASA Astrophysics Data System (ADS)

Palit, S.; Chowdhury, A. Roy

1995-08-01

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

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.

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.

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

PubMed

Koehl, Patrice; Delarue, Marc

2010-02-14

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

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

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

Evans, Gregory Herbert; Chen, Ken Shuang

2004-06-01

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using themore » finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.« less

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

A panning DLT procedure for three-dimensional videography.

PubMed

Yu, B; Koh, T J; Hay, J G

1993-06-01

The direct linear transformation (DLT) method [Abdel-Aziz and Karara, APS Symposium on Photogrammetry. American Society of Photogrammetry, Falls Church, VA (1971)] is widely used in biomechanics to obtain three-dimensional space coordinates from film and video records. This method has some major shortcomings when used to analyze events which take place over large areas. To overcome these shortcomings, a three-dimensional data collection method based on the DLT method, and making use of panning cameras, was developed. Several small single control volumes were combined to construct a large total control volume. For each single control volume, a regression equation (calibration equation) is developed to express each of the 11 DLT parameters as a function of camera orientation, so that the DLT parameters can then be estimated from arbitrary camera orientations. Once the DLT parameters are known for at least two cameras, and the associated two-dimensional film or video coordinates of the event are obtained, the desired three-dimensional space coordinates can be computed. In a laboratory test, five single control volumes (in a total control volume of 24.40 x 2.44 x 2.44 m3) were used to test the effect of the position of the single control volume on the accuracy of the computed three dimensional space coordinates. Linear and quadratic calibration equations were used to test the effect of the order of the equation on the accuracy of the computed three dimensional space coordinates. For four of the five single control volumes tested, the mean resultant errors associated with the use of the linear calibration equation were significantly larger than those associated with the use of the quadratic calibration equation. The position of the single control volume had no significant effect on the mean resultant errors in computed three dimensional coordinates when the quadratic calibration equation was used. Under the same data collection conditions, the mean resultant errors in the computed three dimensional coordinates associated with the panning and stationary DLT methods were 17 and 22 mm, respectively. The major advantages of the panning DLT method lie in the large image sizes obtained and in the ease with which the data can be collected. The method also has potential for use in a wide variety of contexts. The major shortcoming of the method is the large amount of digitizing necessary to calibrate the total control volume. Adaptations of the method to reduce the amount of digitizing required are being explored.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

A dual potential formulation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Gegg, S. G.; Pletcher, R. H.; Steger, J. L.

1989-01-01

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

A computer program for fitting smooth surfaces to an aircraft configuration and other three dimensional geometries

NASA Technical Reports Server (NTRS)

Craidon, C. B.

1975-01-01

A computer program that uses a three-dimensional geometric technique for fitting a smooth surface to the component parts of an aircraft configuration is presented. The resulting surface equations are useful in performing various kinds of calculations in which a three-dimensional mathematical description is necessary. Programs options may be used to compute information for three-view and orthographic projections of the configuration as well as cross-section plots at any orientation through the configuration. The aircraft geometry input section of the program may be easily replaced with a surface point description in a different form so that the program could be of use for any three-dimensional surface equations.

Global existence of the three-dimensional viscous quantum magnetohydrodynamic model

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

Yang, Jianwei, E-mail: yangjianwei@ncwu.edu.cn; Ju, Qiangchang, E-mail: qiangchang-ju@yahoo.com

2014-08-15

The global-in-time existence of weak solutions to the viscous quantum Magnetohydrodynamic equations in a three-dimensional torus with large data is proved. The global existence of weak solutions to the viscous quantum Magnetohydrodynamic equations is shown by using the Faedo-Galerkin method and weak compactness techniques.

A PDF projection method: A pressure algorithm for stand-alone transported PDFs

NASA Astrophysics Data System (ADS)

Ghorbani, Asghar; Steinhilber, Gerd; Markus, Detlev; Maas, Ulrich

2015-03-01

In this paper, a new formulation of the projection approach is introduced for stand-alone probability density function (PDF) methods. The method is suitable for applications in low-Mach number transient turbulent reacting flows. The method is based on a fractional step method in which first the advection-diffusion-reaction equations are modelled and solved within a particle-based PDF method to predict an intermediate velocity field. Then the mean velocity field is projected onto a space where the continuity for the mean velocity is satisfied. In this approach, a Poisson equation is solved on the Eulerian grid to obtain the mean pressure field. Then the mean pressure is interpolated at the location of each stochastic Lagrangian particle. The formulation of the Poisson equation avoids the time derivatives of the density (due to convection) as well as second-order spatial derivatives. This in turn eliminates the major sources of instability in the presence of stochastic noise that are inherent in particle-based PDF methods. The convergence of the algorithm (in the non-turbulent case) is investigated first by the method of manufactured solutions. Then the algorithm is applied to a one-dimensional turbulent premixed flame in order to assess the accuracy and convergence of the method in the case of turbulent combustion. As a part of this work, we also apply the algorithm to a more realistic flow, namely a transient turbulent reacting jet, in order to assess the performance of the method.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

NASA Technical Reports Server (NTRS)

Robertson, D. K.

1985-01-01

Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

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.

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

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2013-12-01

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

A generalized Poisson solver for first-principles device simulations

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

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

2016-01-28

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

Computations of Wall Distances Based on Differential Equations

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

Fully three-dimensional direct numerical simulation of a plunging breaker

NASA Astrophysics Data System (ADS)

Lubin, Pierre; Vincent, Stéphane; Caltagirone, Jean-Paul; Abadie, Stéphane

2003-07-01

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier-Stokes equations in air and water. The interface tracking is achieved by a Lax-Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne

2011-11-01

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

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

PubMed

Guo, Qing; Wan, Fangyi

2017-01-01

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

A molecular level prototype for mechanoelectrical transducer in mammalian hair cells

PubMed Central

Park, Jinkyoung

2013-01-01

The mechanoelectrical transducer (MET) is a crucial component of mammalian auditory system. The gating mechanism of the MET channel remains a puzzling issue, though there are many speculations, due to the lack of essential molecular building blocks. To understand the working principle of mammalian MET, we propose a molecular level prototype which constitutes a charged blocker, a realistic ion channel and its surrounding membrane. To validate the proposed prototype, we make use of a well-established ion channel theory, the Poisson-Nernst-Planck equations, for three-dimensional (3D) numerical simulations. A wide variety of model parameters, including bulk ion concentration, applied external voltage, blocker charge and blocker displacement, are explored to understand the basic function of the proposed MET prototype. We show that our prototype prediction of channel open probability in response to blocker relative displacement is in a remarkable accordance with experimental observation of rat cochlea outer hair cells. Our results appear to suggest that tip links which connect hair bundles gate MET channels. PMID:23625048

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

NASA Astrophysics Data System (ADS)

Murakami, Masakatsu; Honrubia, Javier

2017-10-01

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

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

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

NASA Astrophysics Data System (ADS)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

Some integrable maps and their Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Hone, A. N. W.; Kouloukas, T. E.; Quispel, G. R. W.

2018-01-01

We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the Laurent property, and the tropical (or ultradiscrete) analogue of this homogeneous recurrence confirms the quadratic degree growth found empirically by Demskoi et al. We prove that the tau function also satisfies two different bilinear equations, each of which is a reduction of the Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence). Furthermore, these bilinear equations are related to reductions of particular two-dimensional integrable lattice equations, of discrete KdV or discrete Toda type. These connections, as well as the cluster algebra structure of the bilinear equations, allow a direct construction of Poisson brackets, Lax pairs and first integrals for the birational maps. As a consequence of the latter results, we show how each member of the family can be lifted to a system that is integrable in the Liouville sense, clarifying observations made previously in the original DTKQ case.

Equilibrium structures of carbon diamond-like clusters and their elastic properties

NASA Astrophysics Data System (ADS)

Lisovenko, D. S.; Baimova, Yu. A.; Rysaeva, L. Kh.; Gorodtsov, V. A.; Dmitriev, S. V.

2017-04-01

Three-dimensional carbon diamond-like phases consisting of sp 3-hybridized atoms, obtained by linking of carcasses of fullerene-like molecules, are studied by methods of molecular dynamics modeling. For eight cubic and one hexagonal diamond-like phases on the basis of four types of fullerene-like molecules, equilibrium configurations are found and the elastic constants are calculated. The results obtained by the method of molecular dynamics are used for analytical calculations of the elastic characteristics of the diamond- like phases with the cubic and hexagonal anisotropy. It is found that, for a certain choice of the dilatation axis, three of these phases have negative Poisson's ratio, i.e., are partial auxetics. The variability of the engineering elasticity coefficients (Young's modulus, Poisson's ratio, shear modulus, and bulk modulus) is analyzed.

Three-dimensional modeling of the plasma arc in arc welding

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

Xu, G.; Tsai, H. L.; Hu, J.

2008-11-15

Most previous three-dimensional modeling on gas tungsten arc welding (GTAW) and gas metal arc welding (GMAW) focuses on the weld pool dynamics and assumes the two-dimensional axisymmetric Gaussian distributions for plasma arc pressure and heat flux. In this article, a three-dimensional plasma arc model is developed, and the distributions of velocity, pressure, temperature, current density, and magnetic field of the plasma arc are calculated by solving the conservation equations of mass, momentum, and energy, as well as part of the Maxwell's equations. This three-dimensional model can be used to study the nonaxisymmetric plasma arc caused by external perturbations such asmore » an external magnetic field. It also provides more accurate boundary conditions when modeling the weld pool dynamics. The present work lays a foundation for true three-dimensional comprehensive modeling of GTAW and GMAW including the plasma arc, weld pool, and/or electrode.« less

Closedness of orbits in a space with SU(2) Poisson structure

NASA Astrophysics Data System (ADS)

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

2014-06-01

The closedness of orbits of central forces is addressed in a three-dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically symmetric potential energies, it is only the Kepler problem for which all bounded orbits are closed. In analogy with the case of the ordinary space, a conserved vector (apart from the angular momentum) is explicitly constructed, which is responsible for the orbits being closed. This is the analog of the Laplace-Runge-Lenz vector. The algebra of the constants of the motion is also worked out.

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

PubMed

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

2007-01-01

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

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

PubMed

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

2001-09-01

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

Shell-crossing in quasi-one-dimensional flow

NASA Astrophysics Data System (ADS)

Rampf, Cornelius; Frisch, Uriel

2017-10-01

Blow-up of solutions for the cosmological fluid equations, often dubbed shell-crossing or orbit crossing, denotes the breakdown of the single-stream regime of the cold-dark-matter fluid. At this instant, the velocity becomes multi-valued and the density singular. Shell-crossing is well understood in one dimension (1D), but not in higher dimensions. This paper is about quasi-one-dimensional (Q1D) flow that depends on all three coordinates but differs only slightly from a strictly 1D flow, thereby allowing a perturbative treatment of shell-crossing using the Euler-Poisson equations written in Lagrangian coordinates. The signature of shell-crossing is then just the vanishing of the Jacobian of the Lagrangian map, a regular perturbation problem. In essence, the problem of the first shell-crossing, which is highly singular in Eulerian coordinates, has been desingularized by switching to Lagrangian coordinates, and can then be handled by perturbation theory. Here, all-order recursion relations are obtained for the time-Taylor coefficients of the displacement field, and it is shown that the Taylor series has an infinite radius of convergence. This allows the determination of the time and location of the first shell-crossing, which is generically shown to be taking place earlier than for the unperturbed 1D flow. The time variable used for these statements is not the cosmic time t but the linear growth time τ ˜ t2/3. For simplicity, calculations are restricted to an Einstein-de Sitter universe in the Newtonian approximation, and tailored initial data are used. However it is straightforward to relax these limitations, if needed.

Stress-intensity factor equations for cracks in three-dimensional finite bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Raju, I. S.

1981-01-01

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

A two dimensional analytical modeling of surface potential in triple metal gate (TMG) fully-depleted Recessed-Source/Drain (Re-S/D) SOI MOSFET

NASA Astrophysics Data System (ADS)

Priya, Anjali; Mishra, Ram Awadh

2016-04-01

In this paper, analytical modeling of surface potential is proposed for new Triple Metal Gate (TMG) fully depleted Recessed-Source/Dain Silicon On Insulator (SOI) Metal Oxide Semiconductor Field Effect Transistor (MOSFET). The metal with the highest work function is arranged near the source region and the lowest one near the drain. Since Recessed-Source/Drain SOI MOSFET has higher drain current as compared to conventional SOI MOSFET due to large source and drain region. The surface potential model developed by 2D Poisson's equation is verified by comparison to the simulation result of 2-dimensional ATLAS simulator. The model is compared with DMG and SMG devices and analysed for different device parameters. The ratio of metal gate length is varied to optimize the result.

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

PubMed

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

2007-02-01

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

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

NASA Astrophysics Data System (ADS)

Gavish, Nir

2018-04-01

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

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.

A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

DOE PAGES

Devendran, Dharshi; Graves, Daniel; Johansen, Hans; ...

2017-05-08

In this paper, we present a fourth-order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

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

Devendran, Dharshi; Graves, Daniel; Johansen, Hans

In this paper, we present a fourth-order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

IMFIT: A FAST, FLEXIBLE NEW PROGRAM FOR ASTRONOMICAL IMAGE FITTING

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

Erwin, Peter; Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München

2015-02-01

I describe a new, open-source astronomical image-fitting program called IMFIT, specialized for galaxies but potentially useful for other sources, which is fast, flexible, and highly extensible. A key characteristic of the program is an object-oriented design that allows new types of image components (two-dimensional surface-brightness functions) to be easily written and added to the program. Image functions provided with IMFIT include the usual suspects for galaxy decompositions (Sérsic, exponential, Gaussian), along with Core-Sérsic and broken-exponential profiles, elliptical rings, and three components that perform line-of-sight integration through three-dimensional luminosity-density models of disks and rings seen at arbitrary inclinations. Available minimization algorithmsmore » include Levenberg-Marquardt, Nelder-Mead simplex, and Differential Evolution, allowing trade-offs between speed and decreased sensitivity to local minima in the fit landscape. Minimization can be done using the standard χ{sup 2} statistic (using either data or model values to estimate per-pixel Gaussian errors, or else user-supplied error images) or Poisson-based maximum-likelihood statistics; the latter approach is particularly appropriate for cases of Poisson data in the low-count regime. I show that fitting low-signal-to-noise ratio galaxy images using χ{sup 2} minimization and individual-pixel Gaussian uncertainties can lead to significant biases in fitted parameter values, which are avoided if a Poisson-based statistic is used; this is true even when Gaussian read noise is present.« less

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

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.

Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System

NASA Technical Reports Server (NTRS)

Mager, Arthur

1952-01-01

The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

A finite element approach for solution of the 3D Euler equations

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.; Dechaumphai, P.

1986-01-01

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

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

DTIC Science & Technology

2004-07-07

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

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

NASA Astrophysics Data System (ADS)

Liska, Sebastian; Colonius, Tim

2017-02-01

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

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

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Fairén, Víctor

1998-11-01

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

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

NASA Technical Reports Server (NTRS)

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

1975-01-01

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

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

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

Gonis, Antonios; Zhang, Xiaoguang

2012-01-01

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

Tensorial Basis Spline Collocation Method for Poisson's Equation

NASA Astrophysics Data System (ADS)

Plagne, Laurent; Berthou, Jean-Yves

2000-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-09-01

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

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.

Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations. Ph.D. Thesis - Old Dominion Univ.

NASA Technical Reports Server (NTRS)

Smith, R. E.

1981-01-01

A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

Generalized master equations for non-Poisson dynamics on networks.

PubMed

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

2012-10-01

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

Generalized master equations for non-Poisson dynamics on networks

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

Clinical characterization of 2D pressure field in human left ventricles

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

Biomolecular surface construction by PDE transform

PubMed Central

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

2011-01-01

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

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

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2015-04-05

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

Object-oriented code SUR for plasma kinetic simulation

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

Levchenko, V.D.; Sigov, Y.S.

1995-12-31

We have developed a self-consistent simulation code based on object-oriented model of plasma (OOMP) for solving the Vlasov/Poisson (V/P), Vlasov/Maxwell (V/M), Bhatnagar-Gross-Krook (BGK) as well as Fokker-Planck (FP) kinetic equations. The application of an object-oriented approach (OOA) to simulation of plasmas and plasma-like media by means of splitting methods permits to uniformly describe and solve the wide circle of plasma kinetics problems, including those being very complicated: many-dimensional, relativistic, with regard for collisions, specific boundary conditions etc. This paper gives the brief description of possibilities of the SUR code, as a concrete realization of OOMP.

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.

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.

Intermittency and Alignment in Strong RMHD Turbulence

NASA Astrophysics Data System (ADS)

Chandran, B. D. G.; Schekochihin, A. A.; Mallet, A.

2015-12-01

Intermittency is one of the critical unsolved problems in solar-wind turbulence. Intermittency is important not just because it affects the observable properties of turbulence in the inertial range, but also because it modifies the nature of turbulent dissipation at small scales. In this talk, I will present recent work by colleagues A. Schekochihin, A. Mallet, and myself that focuses on the development of intermittency within the inertial range of solar-wind turbulence. We restrict our analysis to the transverse, non-compressive component of the turbulence. Previous work has shown that this component of the turbulence is anisotropic, varying most rapidly in directions perpendicular to the magnetic field. We argue that, deep within the inertial range, this component of the turbulence is well modeled by the equations of reduced magnetohydrodynamics (RMHD). We then develop an analytic model of intermittent, three-dimensional, strong, reduced magnetohydrodynamic turbulence with zero cross helicity. We take the fluctuation amplitudes to have a log-Poisson distribution and incorporate into the model a new phenomenology of scale-dependent dynamic alignment. The log-Poisson distribution in our model is characterized by two parameters. To calculate these parameters, we make use of two assumptions: that the energy cascade rate is independent of scale within the inertial range and that the most intense coherent structures at scale lambda are sheet-like with a volume filling factor proportional to lambda. We then compute the scalings of the power spectrum, the kurtosis, higher-order structure functions, and three different average alignment angles. We also carry out a direct numerical simulation of RMHD turbulence. The scalings in our model are similar to the scalings in this simulation as well as the structure-function scalings observed in the slow solar wind.

Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.

PubMed

Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew

2014-12-26

Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

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

Barnich, Glenn; Troessaert, Cedric

2009-04-15

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

Alternative Derivations for the Poisson Integral Formula

ERIC Educational Resources Information Center

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

2006-01-01

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

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

Macroscopic response in active nonlinear photonic crystals.

PubMed

Alagappan, Gandhi; John, Sajeev; Li, Er Ping

2013-09-15

We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.

KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

NASA Astrophysics Data System (ADS)

El-Shorbagy, Kh. H.; Mahassen, Hania; El-Bendary, Atef Ahmed

2017-12-01

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev-Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.

Numerical study of He/CF{sub 3}I pulsed discharge used to produce iodine atom in chemical oxygen-iodine laser

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

Zhang Jiao; Wang Yanhui; Wang Dezhen

2013-04-15

The pulsed discharge for producing iodine atoms from the alkyl and perfluoroalky iodides (CH{sub 3}I, CF{sub 3}I, etc.) is the most efficient method for achieving the pulse operating mode of a chemical oxygen-iodine laser. In this paper, a one-dimensional fluid model is developed to study the characteristics of pulsed discharge in CF{sub 3}I-He mixture. By solving continuity equation, momentum equation, Poisson equation, Boltzmann equation, and an electric circuit equation, the temporal evolution of discharge current density and various discharge products, especially the atomic iodine, are investigated. The dependence of iodine atom density on discharge parameters is also studied. The resultsmore » show that iodine atom density increases with the pulsed width and pulsed voltage amplitude. The mixture ratio of CF{sub 3}I and helium plays a more significant role in iodine atom production. For a constant voltage amplitude, there exists an optimal mixture ratio under which the maximum iodine atom concentration is achieved. The bigger the applied voltage amplitude is, the higher partial pressure of CF{sub 3}I is needed to obtain the maximum iodine atom concentration.« less

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

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

Lue Xing; Sun Kun; Wang Pan

In the framework of Bell-polynomial manipulations, under investigation hereby are three single-field bilinearizable equations: the (1+1)-dimensional shallow water wave model, Boiti-Leon-Manna-Pempinelli model, and (2+1)-dimensional Sawada-Kotera model. Based on the concept of scale invariance, a direct and unifying Bell-polynomial scheme is employed to achieve the Baecklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Baecklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Baecklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Baecklund transformations can be linearized into the correspondingmore » Lax pairs.« less

Multi-material Additive Manufacturing of Metamaterials with Giant, Tailorable Negative Poisson's Ratios.

PubMed

Chen, Da; Zheng, Xiaoyu

2018-06-14

Nature has evolved with a recurring strategy to achieve unusual mechanical properties through coupling variable elastic moduli from a few GPa to below KPa within a single tissue. The ability to produce multi-material, three-dimensional (3D) micro-architectures with high fidelity incorporating dissimilar components has been a major challenge in man-made materials. Here we show multi-modulus metamaterials whose architectural element is comprised of encoded elasticity ranging from rigid to soft. We found that, in contrast to ordinary architected materials whose negative Poisson's ratio is dictated by their geometry, these type of metamaterials are capable of displaying Poisson's ratios from extreme negative to zero, independent of their 3D micro-architecture. The resulting low density metamaterials is capable of achieving functionally graded, distributed strain amplification capabilities within the metamaterial with uniform micro-architectures. Simultaneous tuning of Poisson's ratio and moduli within the 3D multi-materials could open up a broad array of material by design applications ranging from flexible armor, artificial muscles, to actuators and bio-mimetic materials.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.

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.

Graphic Simulations of the Poisson Process.

DTIC Science & Technology

1982-10-01

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

3DGRAPE/AL User's Manual

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.; Alter, Stephen J.

1995-01-01

This document is a users' manual for a new three-dimensional structured multiple-block volume g generator called 3DGRAPE/AL. It is a significantly improved version of the previously-released a widely-distributed programs 3DGRAPE and 3DMAGGS. It generates volume grids by iteratively solving the Poisson Equations in three-dimensions. The right-hand-side terms are designed so that user-specific; grid cell heights and user-specified grid cell skewness near boundary surfaces result automatically, with little user intervention. The code is written in Fortran-77, and can be installed with or without a simple graphical user interface which allows the user to watch as the grid is generated. An introduction describing the improvements over the antecedent 3DGRAPE code is presented first. Then follows a chapter on the basic grid generator program itself, and comments on installing it. The input is then described in detail. After that is a description of the Graphical User Interface. Five example cases are shown next, with plots of the results. Following that is a chapter on two input filters which allow use of input data generated elsewhere. Last is a treatment of the theory embodied in the code.

Operator induced multigrid algorithms using semirefinement

NASA Technical Reports Server (NTRS)

Decker, Naomi; Vanrosendale, John

1989-01-01

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two and three dimensional model problems are presented, together with a two level analysis explaining these results.

Numerical study of active control of mixing in electro-osmotic flows by temperature difference using lattice Boltzmann methods.

PubMed

Alizadeh, A; Wang, J K; Pooyan, S; Mirbozorgi, S A; Wang, M

2013-10-01

In this paper, the effect of temperature difference between inlet flow and walls on the electro-osmotic flow through a two-dimensional microchannel is investigated. The main objective is to study the effect of temperature variations on the distribution of ions and consequently internal electric potential field, electric body force, and velocity fields in an electro-osmotic flow. We assume constant temperature and zeta potential on walls and use the mean temperature of each cross section to characterize the Boltzmann ion distribution across the channel. Based on these assumptions, the multiphysical transports are still able to be described by the classical Poisson-Boltzmann model. In this work, the Navier-Stokes equation for fluid flow, the Poisson-Boltzmann equation for ion distribution, and the energy equation for heat transfer are solved by a couple lattice Boltzmann method. The modeling results indicate that the temperature difference between walls and the inlet solution may lead to two symmetrical vortices at the entrance region of the microchannel which is appropriate for mixing enhancements. The advantage of this phenomenon for active control of mixing in electro-osmotic flow is the manageability of the vortex scale without extra efforts. For instance, the effective domain of this pattern could broaden by the following modulations: decreasing the external electric potential field, decreasing the electric double layer thickness, or increasing the temperature difference between inlet flow and walls. This work may provide a novel strategy for design or optimization of microsystems. Copyright © 2013 Elsevier Inc. All rights reserved.

Complex wet-environments in electronic-structure calculations

NASA Astrophysics Data System (ADS)

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

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

Body and Surface Wave Modeling of Observed Seismic Events. Part 2.

DTIC Science & Technology

1987-05-12

is based on expand - ing the complete three dimensional solution of the wave equation expressed in cylindrical S coordinates in an asymptotic form which...using line source (2-D) theory. It is based on expand - ing the complete three dimensional solution of the wave equation expressed in cylindrical...generating synthetic point-source seismograms for shear dislocation sources using line source (2-D) theory. It is based on expanding the complete three

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

A 3D, fully Eulerian, VOF-based solver to study the interaction between two fluids and moving rigid bodies using the fictitious domain method

NASA Astrophysics Data System (ADS)

Pathak, Ashish; Raessi, Mehdi

2016-04-01

We present a three-dimensional (3D) and fully Eulerian approach to capturing the interaction between two fluids and moving rigid structures by using the fictitious domain and volume-of-fluid (VOF) methods. The solid bodies can have arbitrarily complex geometry and can pierce the fluid-fluid interface, forming contact lines. The three-phase interfaces are resolved and reconstructed by using a VOF-based methodology. Then, a consistent scheme is employed for transporting mass and momentum, allowing for simulations of three-phase flows of large density ratios. The Eulerian approach significantly simplifies numerical resolution of the kinematics of rigid bodies of complex geometry and with six degrees of freedom. The fluid-structure interaction (FSI) is computed using the fictitious domain method. The methodology was developed in a message passing interface (MPI) parallel framework accelerated with graphics processing units (GPUs). The computationally intensive solution of the pressure Poisson equation is ported to GPUs, while the remaining calculations are performed on CPUs. The performance and accuracy of the methodology are assessed using an array of test cases, focusing individually on the flow solver and the FSI in surface-piercing configurations. Finally, an application of the proposed methodology in simulations of the ocean wave energy converters is presented.

A Hamiltonian approach to Thermodynamics

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

Baldiotti, M.C., E-mail: baldiotti@uel.br; Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br; Molina, C., E-mail: cmolina@usp.br

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensivelymore » used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.« less

Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages

NASA Astrophysics Data System (ADS)

Kim, Jeonglae; Davidson, Scott; Mani, Ali

2017-11-01

Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.

A simple quantum mechanical treatment of scattering in nanoscale transistors

NASA Astrophysics Data System (ADS)

Venugopal, R.; Paulsson, M.; Goasguen, S.; Datta, S.; Lundstrom, M. S.

2003-05-01

We present a computationally efficient, two-dimensional quantum mechanical simulation scheme for modeling dissipative electron transport in thin body, fully depleted, n-channel, silicon-on-insulator transistors. The simulation scheme, which solves the nonequilibrium Green's function equations self consistently with Poisson's equation, treats the effect of scattering using a simple approximation inspired by the "Büttiker probes," often used in mesoscopic physics. It is based on an expansion of the active device Hamiltonian in decoupled mode space. Simulation results are used to highlight quantum effects, discuss the physics of scattering and to relate the quantum mechanical quantities used in our model to experimentally measured low field mobilities. Additionally, quantum boundary conditions are rigorously derived and the effects of strong off-equilibrium transport are examined. This paper shows that our approximate treatment of scattering, is an efficient and useful simulation method for modeling electron transport in nanoscale, silicon-on-insulator transistors.

The Semigeostrophic Equations Discretized in Reference and Dual Variables

NASA Astrophysics Data System (ADS)

Cullen, Mike; Gangbo, Wilfrid; Pisante, Giovanni

2007-08-01

We study the evolution of a system of n particles {\\{(x_i, v_i)\\}_{i=1}n} in {mathbb{R}^{2d}} . That system is a conservative system with a Hamiltonian of the form {H[μ]=W22(μ, νn)} , where W 2 is the Wasserstein distance and μ is a discrete measure concentrated on the set {\\{(x_i, v_i)\\}_{i=1}n} . Typically, μ(0) is a discrete measure approximating an initial L ∞ density and can be chosen randomly. When d = 1, our results prove convergence of the discrete system to a variant of the semigeostrophic equations. We obtain that the limiting densities are absolutely continuous with respect to the Lebesgue measure. When {\\{ν^n\\}_{n=1}^infty} converges to a measure concentrated on a special d-dimensional set, we obtain the Vlasov-Monge-Ampère (VMA) system. When, d = 1 the VMA system coincides with the standard Vlasov-Poisson system.

Method of model reduction and multifidelity models for solute transport in random layered porous media

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

Xu, Zhijie; Tartakovsky, Alexandre M.

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersionmore » initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.« less

5D Tempest simulations of kinetic edge turbulence

NASA Astrophysics Data System (ADS)

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

2006-10-01

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

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

NASA Astrophysics Data System (ADS)

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

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

Cosmological applications of singular hypersurfaces in general relativity

NASA Astrophysics Data System (ADS)

Laguna-Castillo, Pablo

Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.

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

PubMed Central

Chen, Duan; Wei, Guo-Wei

2010-01-01

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

Theoretical study of the two-dimensional electron mobility in strained III-nitride heterostructures

NASA Astrophysics Data System (ADS)

Yu, Tsung-Hsing; Brennan, Kevin F.

2001-04-01

We present calculations of the two-dimensional (2D) electron mobility in III-nitride heterojunction structures in the presence of spontaneous and piezoelectrically induced polarization effects. The calculations are made using a self-consistent solution of the Schrödinger, Poisson, charge and potential balance equations. It is found that the polarization fields act to significantly increase the 2D sheet charge concentration while reducing the mobility. The mobility reduction results from the enhanced band bending and subsequent attraction of the electrons to the heterointerface where they experience increased surface roughness scattering. Good agreement is obtained between the theoretical calculations and experimental measurements over the full temperature range examined. Comparison of the mobility in InGaN/GaN to AlGaN/GaN heterostructures is made. It is found that the mobility is significantly higher in the InGaN/GaN structure than in the AlGaN/GaN structure.

Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach.

PubMed

Camargo, Manuel; Téllez, Gabriel

2008-04-07

The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlation functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions.

Transport characteristics of a ZnMgO/ZnO hetero junction and the effect of temperature and Mg content

NASA Astrophysics Data System (ADS)

Uslu, Salih; Yarar, Zeki

2017-02-01

The Ensemble Monte Carlo method is used to calculate the transport characteristics of two dimensional electron gas (2DEG) at a ZnMgO/ZnO hetero structure. The spontaneous and piezoelectric polarizations are considered and there is no intentional doping in either material. Numerical Schrödinger and Poisson equations are solved self consistently to obtain the scattering rates of various scattering mechanisms. The density of carriers, each energy sub bands, potential profile and corresponding wave functions are obtained from the self consistent calculations. The self consistent sub band wave functions of acoustic and optic phonon scattering and interface roughness scattering are used in Monte Carlo method to obtain transport characteristics at ZnMgO/ZnO junction. Two dimensional electron gas confined to ZnMgO/ZnO hetero structure is studied and the effect of temperature and Mg content are investigated.

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.

Deterministic multidimensional nonuniform gap sampling.

PubMed

Worley, Bradley; Powers, Robert

2015-12-01

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

Killing vector fields in three dimensions: a method to solve massive gravity field equations

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

Three-dimensional finite elements for the analysis of soil contamination using a multiple-porosity approach

NASA Astrophysics Data System (ADS)

El-Zein, Abbas; Carter, John P.; Airey, David W.

2006-06-01

A three-dimensional finite-element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non-equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro-pores of aggregated topsoils, as well as non-equilibrium sorption. A Galerkin weighted-residual statement for the three-dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer.

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

NASA Astrophysics Data System (ADS)

Braun, Stefan; Kluwick, Alfred

2004-09-01

Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall shear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter Gamma characterizing, for example, the angle of attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value Gamma_c of Gamma only. Here we investigate three-dimensional unsteady perturbations of an incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near Gamma_c. Specifically, it is shown that the integro differential equation which governs these disturbances if Gamma_c {-} Gamma {=} O(1) reduces to a nonlinear partial differential equation known as the Fisher equation as Gamma approaches the critical value Gamma_c. This in turn leads to a significant simplification of the problem allowing, among other things, a systematic study of devices used in boundary-layer control and an analytical investigation of the conditions leading to the formation of finite-time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also, it is found that it is possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite-time blow-up may be extended beyond the blow-up time, thereby generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.

The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction

PubMed Central

Williamson, Ross S.; Sahani, Maneesh; Pillow, Jonathan W.

2015-01-01

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron’s probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as “single-spike information” to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex. PMID:25831448

Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Effect of solid distribution on elastic properties of open-cell cellular solids using numerical and experimental methods.

PubMed

Zargarian, A; Esfahanian, M; Kadkhodapour, J; Ziaei-Rad, S

2014-09-01

Effect of solid distribution between edges and vertices of three-dimensional cellular solid with an open-cell structure was investigated both numerically and experimentally. Finite element analysis (FEA) with continuum elements and appropriate periodic boundary condition was employed to calculate the elastic properties of cellular solids using tetrakaidecahedral (Kelvin) unit cell. Relative densities between 0.01 and 0.1 and various values of solid fractions were considered. In order to validate the numerical model, three scaffolds with the relative density of 0.08, but different amounts of solid in vertices, were fabricated via 3-D printing technique. Good agreement was observed between numerical simulation and experimental results. Results of numerical simulation showed that, at low relative densities (<0.03), Young׳s modulus increased by shifting materials away from edges to vertices at first and then decreased after reaching a critical point. However, for the high values of relative density, Young׳s modulus increased monotonically. Mechanisms of such a behavior were discussed in detail. Results also indicated that Poisson׳s ratio decreased by increasing relative density and solid fraction in vertices. By fitting a curve to the data obtained from the numerical simulation and considering the relative density and solid fraction in vertices, empirical relations were derived for Young׳s modulus and Poisson׳s ratio. Copyright © 2014 Elsevier Ltd. All rights reserved.

One-dimensional transport equation models for sound energy propagation in long spaces: theory.

PubMed

Jing, Yun; Larsen, Edward W; Xiang, Ning

2010-04-01

In this paper, a three-dimensional transport equation model is developed to describe the sound energy propagation in a long space. Then this model is reduced to a one-dimensional model by approximating the solution using the method of weighted residuals. The one-dimensional transport equation model directly describes the sound energy propagation in the "long" dimension and deals with the sound energy in the "short" dimensions by prescribed functions. Also, the one-dimensional model consists of a coupled set of N transport equations. Only N=1 and N=2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to significantly increase, which diminishes the advantage of the model in terms of its computational efficiency.

Determination of aerodynamic sensitivity coefficients based on the three-dimensional full potential equation

NASA Technical Reports Server (NTRS)

Elbanna, Hesham M.; Carlson, Leland A.

1992-01-01

The quasi-analytical approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used to reduce the effort associated with obtaining the sensitivity equations, and the large sensitivity system is solved using 'state of the art' routines. Results are compared to those obtained by the direct finite difference approach and both methods are evaluated to determine their computational accuracy and efficiency. The quasi-analytical approach is shown to be accurate and efficient for large aerodynamic systems.

The method of lines in three dimensional fracture mechanics

NASA Technical Reports Server (NTRS)

Gyekenyesi, J.; Berke, L.

1980-01-01

A review of recent developments in the calculation of design parameters for fracture mechanics by the method of lines (MOL) is presented. Three dimensional elastic and elasto-plastic formulations are examined and results from previous and current research activities are reported. The application of MOL to the appropriate partial differential equations of equilibrium leads to coupled sets of simultaneous ordinary differential equations. Solutions of these equations are obtained by the Peano-Baker and by the recurrance relations methods. The advantages and limitations of both solution methods from the computational standpoint are summarized.

A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Padé approximants.

PubMed

Lin, Ying-Tsong; Collis, Jon M; Duda, Timothy F

2012-11-01

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

NASA Technical Reports Server (NTRS)

Stein, M.; Stein, P. A.

1978-01-01

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Quantum statistics of Raman scattering model with Stokes mode generation

NASA Technical Reports Server (NTRS)

Tanatar, Bilal; Shumovsky, Alexander S.

1994-01-01

The model describing three coupled quantum oscillators with decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. Due to the Manley-Rowe relations the problem of exact eigenvalues and eigenstates is reduced to the calculation of new orthogonal polynomials defined both by the difference and differential equations. The quantum statistical properties are examined in the case when initially: the Stokes mode is in the vacuum state; the Rayleigh mode is in the number state; and the vibration mode is in the number of or squeezed states. The collapses and revivals are obtained for different initial conditions as well as the change in time the sub-Poisson distribution by the super-Poisson distribution and vice versa.

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

SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson-Boltzmann equation.

PubMed

Xie, Yang; Ying, Jinyong; Xie, Dexuan

2017-03-30

SMPBS (Size Modified Poisson-Boltzmann Solvers) is a web server for computing biomolecular electrostatics using finite element solvers of the size modified Poisson-Boltzmann equation (SMPBE). SMPBE not only reflects ionic size effects but also includes the classic Poisson-Boltzmann equation (PBE) as a special case. Thus, its web server is expected to have a broader range of applications than a PBE web server. SMPBS is designed with a dynamic, mobile-friendly user interface, and features easily accessible help text, asynchronous data submission, and an interactive, hardware-accelerated molecular visualization viewer based on the 3Dmol.js library. In particular, the viewer allows computed electrostatics to be directly mapped onto an irregular triangular mesh of a molecular surface. Due to this functionality and the fast SMPBE finite element solvers, the web server is very efficient in the calculation and visualization of electrostatics. In addition, SMPBE is reconstructed using a new objective electrostatic free energy, clearly showing that the electrostatics and ionic concentrations predicted by SMPBE are optimal in the sense of minimizing the objective electrostatic free energy. SMPBS is available at the URL: smpbs.math.uwm.edu © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Progress Report on SAM Reduced-Order Model Development for Thermal Stratification and Mixing during Reactor Transients

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

Hu, R.

This report documents the initial progress on the reduced-order flow model developments in SAM for thermal stratification and mixing modeling. Two different modeling approaches are pursued. The first one is based on one-dimensional fluid equations with additional terms accounting for the thermal mixing from both flow circulations and turbulent mixing. The second approach is based on three-dimensional coarse-grid CFD approach, in which the full three-dimensional fluid conservation equations are modeled with closure models to account for the effects of turbulence.

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.

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

Three-dimensional multigrid algorithms for the flux-split Euler equations

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Thomas, James L.; Whitfield, David L.

1988-01-01

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

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.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Efficient implementation of a 3-dimensional ADI method on the iPSC/860

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

Van der Wijngaart, R.F.

1993-12-31

A comparison is made between several domain decomposition strategies for the solution of three-dimensional partial differential equations on a MIMD distributed memory parallel computer. The grids used are structured, and the numerical algorithm is ADI. Important implementation issues regarding load balancing, storage requirements, network latency, and overlap of computations and communications are discussed. Results of the solution of the three-dimensional heat equation on the Intel iPSC/860 are presented for the three most viable methods. It is found that the Bruno-Cappello decomposition delivers optimal computational speed through an almost complete elimination of processor idle time, while providing good memory efficiency.

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

NASA Technical Reports Server (NTRS)

Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.

1995-01-01

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

The efficient simulation of separated three-dimensional viscous flows using the boundary-layer equations

NASA Technical Reports Server (NTRS)

Van Dalsem, W. R.; Steger, J. L.

1985-01-01

A simple and computationally efficient algorithm for solving the unsteady three-dimensional boundary-layer equations in the time-accurate or relaxation mode is presented. Results of the new algorithm are shown to be in quantitative agreement with detailed experimental data for flow over a swept infinite wing. The separated flow over a 6:1 ellipsoid at angle of attack, and the transonic flow over a finite-wing with shock-induced 'mushroom' separation are also computed and compared with available experimental data. It is concluded that complex, separated, three-dimensional viscous layers can be economically and routinely computed using a time-relaxation boundary-layer algorithm.

Three-dimensional boundary layers approaching separation

NASA Technical Reports Server (NTRS)

Williams, J. C., III

1976-01-01

The theory of semi-similar solutions of the laminar boundary layer equations is applied to several flows in which the boundary layer approaches a three-dimensional separation line. The solutions obtained are used to deduce the nature of three-dimensional separation. It is shown that in these cases separation is of the "ordinary" type. A solution is also presented for a case in which a vortex is embedded within the three-dimensional boundary layer.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

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.

Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations

NASA Astrophysics Data System (ADS)

Guo, Xiu-Rong

2016-06-01

We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Shandong Provincial Natural Science Foundation of China under Grant Nos. ZR2012AQ011, ZR2013AL016, ZR2015EM042, National Social Science Foundation of China under Grant No. 13BJY026, the Development of Science and Technology Project under Grant No. 2015NS1048 and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58

Numerical aerodynamic simulation facility. [for flows about three-dimensional configurations

NASA Technical Reports Server (NTRS)

Bailey, F. R.; Hathaway, A. W.

1978-01-01

Critical to the advancement of computational aerodynamics capability is the ability to simulate flows about three-dimensional configurations that contain both compressible and viscous effects, including turbulence and flow separation at high Reynolds numbers. Analyses were conducted of two solution techniques for solving the Reynolds averaged Navier-Stokes equations describing the mean motion of a turbulent flow with certain terms involving the transport of turbulent momentum and energy modeled by auxiliary equations. The first solution technique is an implicit approximate factorization finite-difference scheme applied to three-dimensional flows that avoids the restrictive stability conditions when small grid spacing is used. The approximate factorization reduces the solution process to a sequence of three one-dimensional problems with easily inverted matrices. The second technique is a hybrid explicit/implicit finite-difference scheme which is also factored and applied to three-dimensional flows. Both methods are applicable to problems with highly distorted grids and a variety of boundary conditions and turbulence models.

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

NASA Technical Reports Server (NTRS)

Buell, Jeffrey C.

1988-01-01

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

A reconstruction algorithm for three-dimensional object-space data using spatial-spectral multiplexing

NASA Astrophysics Data System (ADS)

Wu, Zhejun; Kudenov, Michael W.

2017-05-01

This paper presents a reconstruction algorithm for the Spatial-Spectral Multiplexing (SSM) optical system. The goal of this algorithm is to recover the three-dimensional spatial and spectral information of a scene, given that a one-dimensional spectrometer array is used to sample the pupil of the spatial-spectral modulator. The challenge of the reconstruction is that the non-parametric representation of the three-dimensional spatial and spectral object requires a large number of variables, thus leading to an underdetermined linear system that is hard to uniquely recover. We propose to reparameterize the spectrum using B-spline functions to reduce the number of unknown variables. Our reconstruction algorithm then solves the improved linear system via a least- square optimization of such B-spline coefficients with additional spatial smoothness regularization. The ground truth object and the optical model for the measurement matrix are simulated with both spatial and spectral assumptions according to a realistic field of view. In order to test the robustness of the algorithm, we add Poisson noise to the measurement and test on both two-dimensional and three-dimensional spatial and spectral scenes. Our analysis shows that the root mean square error of the recovered results can be achieved within 5.15%.

A three-dimensional, finite element model for coastal and estuarine circulation

USGS Publications Warehouse

Walters, R.A.

1992-01-01

This paper describes the development and application of a three-dimensional model for coastal and estuarine circulation. The model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for salt so that density gradient forcing is included in the momentum equations. The model is applied to a study of Delaware Bay, U.S.A., where salinity intrusion is the primary focus. ?? 1991.

Computation of Three-Dimensional Boundary Layers Including Separation

DTIC Science & Technology

1987-02-01

As demonstrated by the 1968 and 1980 -1981 STANFORD Conferences, integral methods remain a valuable engineering tool to calculate the effects of...has been given by WHITFIELD, 1980 , which is valid over the whole thickness of the boundary layer. Another method to generate a velocity profiles...boundary layer equations and inviscid equations. A very clear presentation of the problem is given for example by VELOMAN, 1980 . 6.3. Three-dimensional

A multiblock/multizone code (PAB 3D-v2) for the three-dimensional Navier-Stokes equations: Preliminary applications

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.

1990-01-01

The development and applications of multiblock/multizone and adaptive grid methodologies for solving the three-dimensional simplified Navier-Stokes equations are described. Adaptive grid and multiblock/multizone approaches are introduced and applied to external and internal flow problems. These new implementations increase the capabilities and flexibility of the PAB3D code in solving flow problems associated with complex geometry.

The three dimensional motion and stability of a rotating space station: Cable-counterweight configuration

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Evans, K. S.

1974-01-01

The three dimensional equations of motion for a cable connected space station--counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the inplane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria.

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.

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.

Electrostatics of electron-hole interactions in van der Waals heterostructures

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Localization of intense electromagnetic waves in a relativistically hot plasma.

PubMed

Shukla, P K; Eliasson, B

2005-02-18

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

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

Conservative regularization of compressible dissipationless two-fluid plasmas

NASA Astrophysics Data System (ADS)

Krishnaswami, Govind S.; Sachdev, Sonakshi; Thyagaraja, A.

2018-02-01

This paper extends our earlier approach [cf. A. Thyaharaja, Phys. Plasmas 17, 032503 (2010) and Krishnaswami et al., Phys. Plasmas 23, 022308 (2016)] to obtaining à priori bounds on enstrophy in neutral fluids and ideal magnetohydrodynamics. This results in a far-reaching local, three-dimensional, non-linear, dispersive generalization of a KdV-type regularization to compressible/incompressible dissipationless 2-fluid plasmas and models derived therefrom (quasi-neutral, Hall, and ideal MHD). It involves the introduction of vortical and magnetic "twirl" terms λl 2 ( w l + ( q l / m l ) B ) × ( ∇ × w l ) in the ion/electron velocity equations ( l = i , e ) where w l are vorticities. The cut-off lengths λl and number densities nl must satisfy λl 2 n l = C l , where Cl are constants. A novel feature is that the "flow" current ∑ l q l n l v l in Ampère's law is augmented by a solenoidal "twirl" current ∑ l ∇ × ∇ × λl 2 j flow , l . The resulting equations imply conserved linear and angular momenta and a positive definite swirl energy density E * which includes an enstrophic contribution ∑ l ( 1 / 2 ) λl 2 ρ l wl 2 . It is shown that the equations admit a Hamiltonian-Poisson bracket formulation. Furthermore, singularities in ∇ × B are conservatively regularized by adding ( λB 2 / 2 μ 0 ) ( ∇ × B ) 2 to E * . Finally, it is proved that among regularizations that admit a Hamiltonian formulation and preserve the continuity equations along with the symmetries of the ideal model, the twirl term is unique and minimal in non-linearity and space derivatives of velocities.

Low-pressure hydrogen discharge maintenance in a large-size plasma source with localized high radio-frequency power deposition

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

Todorov, D.; Shivarova, A., E-mail: ashiva@phys.uni-sofia.bg; Paunska, Ts.

2015-03-15

The development of the two-dimensional fluid-plasma model of a low-pressure hydrogen discharge, presented in the study, is regarding description of the plasma maintenance in a discharge vessel with the configuration of the SPIDER source. The SPIDER source, planned for the neutral-beam-injection plasma-heating system of ITER, is with localized high RF power deposition to its eight drivers (cylindrical-coil inductive discharges) and a large-area second chamber, common for all the drivers. The continuity equations for the charged particles (electrons and the three types of positive ions) and for the neutral species (atoms and molecules), their momentum equations, the energy balance equations formore » electrons, atoms and molecules and the Poisson equations are involved in the discharge description. In addition to the local processes in the plasma volume, the surface processes of particle reflection and conversion on the walls as well as for a heat exchange with the walls are included in the model. The analysis of the results stresses on the role of the fluxes (particle and energy fluxes) in the formation of the discharge structure. The conclusion is that the discharge behavior is completely obeyed to non-locality. The latter is displayed by: (i) maximum values of plasma parameters (charged particle densities and temperatures of the neutral species) outside the region of the RF power deposition, (ii) shifted maxima of the electron density and temperature, of the plasma potential and of the electron production, (iii) an electron flux, with a vortex structure, strongly exceeding the total ion flux which gives evidence of a discharge regime of non-ambipolarity and (iv) a spatial distribution of the densities of the neutral species resulting from their fluxes.« less

The NonConforming Virtual Element Method for the Stokes Equations

DOE PAGES

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

2016-01-01

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

4D pressure MRI: validation through in-vitro experiments and simulations

NASA Astrophysics Data System (ADS)

Schiavazzi, Daniele; Amili, Omid; Coletti, Filippo

2017-11-01

Advances in MRI scan technology and recently developed acquisition sequences have led to the development of 4D flow MRI, a protocol capable of characterizing in-vivo hemodynamics in patients. Thus, the availability of phase-averaged time-resolved three-dimensional blood velocities has opened new opportunities for computing a wide spectrum of totally non-invasive hemodynamic indicators. In this regard, relative pressures play a particularly important role, as they are routinely employed in the clinic to detect cardiovascular abnormalities (e.g., in peripheral artery disease, valve stenosis, hypertension, etc.). In the first part of the talk, we discuss how the relative pressures can be robustly computed through the solution of a pressure Poisson equation and how noise in the velocities affects their estimate. Routine application of these techniques in the clinic, require however a thorough validation on multiple patients/anatomies and systematic comparisons with in-vitro and simulated representations. Thus, the second part of the talk illustrates the use of numerical simulation and in-vitro experimental protocols to validate these indicators with reference to aortic and cerebral vascular anatomies.

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.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

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.

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

NASA Astrophysics Data System (ADS)

Gao, Shan; Liu, Zaiming

2010-03-01

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

Beyond single-stream with the Schrödinger method

NASA Astrophysics Data System (ADS)

Uhlemann, Cora; Kopp, Michael

2016-10-01

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

Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of state

NASA Astrophysics Data System (ADS)

Babajanova, Gulmira; Matrasulov, Jasur; Nakamura, Katsuhiro

2018-04-01

With use of the scheme of fast forward which realizes quasistatic or adiabatic dynamics in shortened timescale, we investigate a thermally isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size L =L (t ) . In the fast-forward variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity (L ˙) and acceleration (L ̈) of L besides rapidly changing state variables like effective temperature (T ) and L itself. The force is now a sum of nonadiabatic (NAD) and adiabatic contributions with the former caused by particles moving synchronously with kinetics of L and the latter by ideal bulk particles insensitive to such a kinetics. The ratio of NAD and adiabatic contributions does not depend on the particle number (N ) in the case of the soft-wall confinement, whereas such a ratio is controllable in the case of hard-wall confinement. We also reveal the condition when the NAD contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.

A novel multiphysic model for simulation of swelling equilibrium of ionized thermal-stimulus responsive hydrogels

NASA Astrophysics Data System (ADS)

Li, Hua; Wang, Xiaogui; Yan, Guoping; Lam, K. Y.; Cheng, Sixue; Zou, Tao; Zhuo, Renxi

2005-03-01

In this paper, a novel multiphysic mathematical model is developed for simulation of swelling equilibrium of ionized temperature sensitive hydrogels with the volume phase transition, and it is termed the multi-effect-coupling thermal-stimulus (MECtherm) model. This model consists of the steady-state Nernst-Planck equation, Poisson equation and swelling equilibrium governing equation based on the Flory's mean field theory, in which two types of polymer-solvent interaction parameters, as the functions of temperature and polymer-network volume fraction, are specified with or without consideration of the hydrogen bond interaction. In order to examine the MECtherm model consisting of nonlinear partial differential equations, a meshless Hermite-Cloud method is used for numerical solution of one-dimensional swelling equilibrium of thermal-stimulus responsive hydrogels immersed in a bathing solution. The computed results are in very good agreements with experimental data for the variation of volume swelling ratio with temperature. The influences of the salt concentration and initial fixed-charge density are discussed in detail on the variations of volume swelling ratio of hydrogels, mobile ion concentrations and electric potential of both interior hydrogels and exterior bathing solution.

Nonlinear ion acoustic waves scattered by vortexes

NASA Astrophysics Data System (ADS)

Ohno, Yuji; Yoshida, Zensho

2016-09-01

The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.

Multi-Subband Ensemble Monte Carlo simulations of scaled GAA MOSFETs

NASA Astrophysics Data System (ADS)

Donetti, L.; Sampedro, C.; Ruiz, F. G.; Godoy, A.; Gamiz, F.

2018-05-01

We developed a Multi-Subband Ensemble Monte Carlo simulator for non-planar devices, taking into account two-dimensional quantum confinement. It couples self-consistently the solution of the 3D Poisson equation, the 2D Schrödinger equation, and the 1D Boltzmann transport equation with the Ensemble Monte Carlo method. This simulator was employed to study MOS devices based on ultra-scaled Gate-All-Around Si nanowires with diameters in the range from 4 nm to 8 nm with gate length from 8 nm to 14 nm. We studied the output and transfer characteristics, interpreting the behavior in the sub-threshold region and in the ON state in terms of the spatial charge distribution and the mobility computed with the same simulator. We analyzed the results, highlighting the contribution of different valleys and subbands and the effect of the gate bias on the energy and velocity profiles. Finally the scaling behavior was studied, showing that only the devices with D = 4nm maintain a good control of the short channel effects down to the gate length of 8nm .

Toward negative Poisson's ratio composites: Investigation of the auxetic behavior of fibrous networks

NASA Astrophysics Data System (ADS)

Tatlier, Mehmet Seha

Random fibrous can be found among natural and synthetic materials. Some of these random fibrous networks possess negative Poisson's ratio and they are extensively called auxetic materials. The governing mechanisms behind this counter intuitive property in random networks are yet to be understood and this kind of auxetic material remains widely under-explored. However, most of synthetic auxetic materials suffer from their low strength. This shortcoming can be rectified by developing high strength auxetic composites. The process of embedding auxetic random fibrous networks in a polymer matrix is an attractive alternate route to the manufacture of auxetic composites, however before such an approach can be developed, a methodology for designing fibrous networks with the desired negative Poisson's ratios must first be established. This requires an understanding of the factors which bring about negative Poisson's ratios in these materials. In this study, a numerical model is presented in order to investigate the auxetic behavior in compressed random fiber networks. Finite element analyses of three-dimensional stochastic fiber networks were performed to gain insight into the effects of parameters such as network anisotropy, network density, and degree of network compression on the out-of-plane Poisson's ratio and Young's modulus. The simulation results suggest that the compression is the critical parameter that gives rise to negative Poisson's ratio while anisotropy significantly promotes the auxetic behavior. This model can be utilized to design fibrous auxetic materials and to evaluate feasibility of developing auxetic composites by using auxetic fibrous networks as the reinforcing layer.

SCORE-EVET: a computer code for the multidimensional transient thermal-hydraulic analysis of nuclear fuel rod arrays. [BWR; PWR

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

Benedetti, R. L.; Lords, L. V.; Kiser, D. M.

1978-02-01

The SCORE-EVET code was developed to study multidimensional transient fluid flow in nuclear reactor fuel rod arrays. The conservation equations used were derived by volume averaging the transient compressible three-dimensional local continuum equations in Cartesian coordinates. No assumptions associated with subchannel flow have been incorporated into the derivation of the conservation equations. In addition to the three-dimensional fluid flow equations, the SCORE-EVET code ocntains: (a) a one-dimensional steady state solution scheme to initialize the flow field, (b) steady state and transient fuel rod conduction models, and (c) comprehensive correlation packages to describe fluid-to-fuel rod interfacial energy and momentum exchange. Velocitymore » and pressure boundary conditions can be specified as a function of time and space to model reactor transient conditions such as a hypothesized loss-of-coolant accident (LOCA) or flow blockage.« less

An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design

NASA Technical Reports Server (NTRS)

Provenza, Andrew J.; Kenny, Andrew; Palazzolo, Alan B.

2003-01-01

A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.

Study of three-dimensional effects on vortex breakdown

NASA Technical Reports Server (NTRS)

Salas, M. D.; Kuruvila, G.

1988-01-01

The incompressible axisymmetric steady Navier-Stokes equations in primitive variables are used to simulate vortex breakdown. The equations, discretized using a second-order, central-difference scheme, are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers, based on vortex-core radius, as high as 1500. An attempt to study the stability of the axisymmetric solutions against three-dimensional perturbations is discussed.

Lax pair, conservation laws and solitons for a (2 + 1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong

2015-11-01

Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.

Nodal-line pairing with 1D-3D coupled Fermi surfaces: A model motivated by Cr-based superconductors

NASA Astrophysics Data System (ADS)

Wachtel, Gideon; Kim, Yong Baek

2016-09-01

Motivated by the recent discovery of a new family of chromium-based superconductors, we consider a two-band model, where a band of electrons dispersing only in one direction interacts with a band of electrons dispersing in all three directions. Strong 2 kf density fluctuations in the one-dimensional band induces attractive interactions between the three-dimensional electrons, which, in turn, makes the system superconducting. Solving the associated Eliashberg equations, we obtain a gap function which is peaked at the "poles" of the three-dimensional Fermi sphere, and decreases towards the "equator." When strong enough local repulsion is included, the gap actually changes sign around the equator and nodal rings are formed. These nodal rings manifest themselves in several experimentally observable quantities, some of which resemble unconventional observations in the newly discovered superconductors which motivated this work.

Research on Orbital Plasma-Electrodynamics (ROPE)

NASA Technical Reports Server (NTRS)

Wu, S. T.; Wright, K.

1994-01-01

Since the development of probe theory by Langmuir and Blodgett, the problem of current collection by a charged spherically or cylindrically symmetric body has been investigated by a number of authors. This paper overviews the development of a fully three-dimensional particle simulation code which can be used to understand the physics of current collection in three dimensions and can be used to analyze data resulting from the future tethered satellite system (TSS). According to the TSS configurations, two types of particle simulation models were constructed: a simple particle simulation (SIPS) and a super particle simulation (SUPS). The models study the electron transient response and its asymptotic behavior around a three dimensional, highly biased satellite. The potential distribution surrounding the satellite is determined by solving Laplace's equation in the SIPS model and by solving Poisson's equation in the SUPS model. Thus, the potential distribution in space is independent of the density distribution of the particles in the SUPS model but it does depend on the density distribution of the particles in the SUPS model. The evolution of the potential distribution in the SUPS model is described. When the spherical satellite is charged to a highly positive potential and immersed in a plasma with a uniform magnetic field, the formation of an electron torus in the equatorial plane (the plane in perpendicular to the magnetic field) and elongation of the torus along the magnetic field are found in both the SIPS and the SUPS models but the shape of the torus is different. The areas of high potential that exist in the polar regions in the SUPS model exaggerate the elongation of the electron torus along the magnetic field. The current collected by the satellite for different magentic field strengths is investigated in both models. Due to the nonlinear effects present in SUPS, the oscillating phenomenon of the current collection curve during the first 10 plasma periods can be seen (this does not appear in SIPS). From the parametric studies, it appears that the oscillating phenomenon of the current collection curve occurs only when the magnetic field strength is less than 0.2 gauss for the present model.

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.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Three-dimensional ionic conduction in the strained electrolytes of solid oxide fuel cells

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

Han, Yupei; Zou, Minda; Lv, Weiqiang

2016-05-07

Flexible power sources including fuel cells and batteries are the key to realizing flexible electronic devices with pronounced foldability. To understand the bending effects in these devices, theoretical analysis on three-dimensional (3-D) lattice bending is necessary. In this report, we derive a 3-D analytical model to analyze the effects of electrolyte crystal bending on ionic conductivity in flexible solid-state batteries/fuel cells. By employing solid oxide fuel cells as a materials' platform, the intrinsic parameters of bent electrolyte materials, including lattice constant, Young's modulus, and Poisson ratio, are evaluated. Our work facilitates the rational design of highly efficient flexible electrolytes formore » high-performance flexible device applications.« less

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.

Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates

NASA Astrophysics Data System (ADS)

Wilson, F.; Neukirch, T.

2018-01-01

We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the "pseudo-potential" (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a "fractional multipole" nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.

Dark soliton pair of ultracold Fermi gases for a generalized Gross-Pitaevskii equation model.

PubMed

Wang, Ying; Zhou, Yu; Zhou, Shuyu; Zhang, Yongsheng

2016-07-01

We present the theoretical investigation of dark soliton pair solutions for one-dimensional as well as three-dimensional generalized Gross-Pitaevskii equation (GGPE) which models the ultracold Fermi gas during Bardeen-Cooper-Schrieffer-Bose-Einstein condensates crossover. Without introducing any integrability constraint and via the self-similar approach, the three-dimensional solution of GGPE is derived based on the one-dimensional dark soliton pair solution, which is obtained through a modified F-expansion method combined with a coupled modulus-phase transformation technique. We discovered the oscillatory behavior of the dark soliton pair from the theoretical results obtained for the three-dimensional case. The calculated period agrees very well with the corresponding reported experimental result [Weller et al., Phys. Rev. Lett. 101, 130401 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.130401], demonstrating the applicability of the theoretical treatment presented in this work.

Lump Solitons in Surface Tension Dominated Flows

NASA Astrophysics Data System (ADS)

Milewski, Paul; Berger, Kurt

1999-11-01

The Kadomtsev-Petviashvilli I equation (KPI) which models small-amplitude, weakly three-dimensional surface-tension dominated long waves is integrable and allows for algebraically decaying lump solitary waves. It is not known (theoretically or numerically) whether the full free-surface Euler equations support such solutions. We consider an intermediate model, the generalised Benney-Luke equation (gBL) which is isotropic (not weakly three-dimensional) and contains KPI as a limit. We show numerically that: 1. gBL supports lump solitary waves; 2. These waves collide elastically and are stable; 3. They are generated by resonant flow over an obstacle.

Evaluation of out-of-core computer programs for the solution of symmetric banded linear equations. [simultaneous equations

NASA Technical Reports Server (NTRS)

Dunham, R. S.

1976-01-01

FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann

1993-01-01

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann; Usab, William J., Jr.

1993-01-01

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Modeling techniques for quantum cascade lasers

NASA Astrophysics Data System (ADS)

Jirauschek, Christian; Kubis, Tillmann

2014-03-01

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Modeling techniques for quantum cascade lasers

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

Jirauschek, Christian; Kubis, Tillmann

2014-03-15

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation ofmore » quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.« less

Deep circulations under simple classes of stratification

NASA Technical Reports Server (NTRS)

Salby, Murry L.

1989-01-01

Deep circulations where the motion field is vertically aligned over one or more scale heights are studied under barotropic and equivalent barotropic stratifications. The study uses two-dimensional equations reduced from the three-dimensional primitive equations in spherical geometry. A mapping is established between the full primitive equations and general shallow water behavior and the correspondence between variables describing deep atmospheric motion and those of shallow water behavior is established.

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Global well-posedness of three-dimensional Navier-Stokes equations with partial viscosity under helical symmetry

NASA Astrophysics Data System (ADS)

Liu, Jitao; Niu, Dongjuan

2017-06-01

In this paper, we investigate the global well-posedness of three-dimensional Navier-Stokes equations with horizontal viscosity under a special symmetric structure: helical symmetry. More precisely, by a revised Ladyzhenskaya-type inequality and utilizing the behavior of helical flows, we prove the global existence and uniqueness of weak and strong solutions to the three-dimensional helical flows. Our result reveals that for the issue of global well-posedness of the viscous helical flows, the horizontal viscosity plays the important role. To some extent, our work can be seen as a generalization of the result by Mahalov et al. (Arch Ration Mech Anal 112(3):193-222, 1990).

Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code

NASA Technical Reports Server (NTRS)

Manro, M. E.

1983-01-01

Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.

Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code

NASA Technical Reports Server (NTRS)

Weinberg, B. C.; Mcdonald, H.

1980-01-01

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils.

Fully decoupled monolithic projection method for natural convection problems

NASA Astrophysics Data System (ADS)

Pan, Xiaomin; Kim, Kyoungyoun; Lee, Changhoon; Choi, Jung-Il

2017-04-01

To solve time-dependent natural convection problems, we propose a fully decoupled monolithic projection method. The proposed method applies the Crank-Nicolson scheme in time and the second-order central finite difference in space. To obtain a non-iterative monolithic method from the fully discretized nonlinear system, we first adopt linearizations of the nonlinear convection terms and the general buoyancy term with incurring second-order errors in time. Approximate block lower-upper decompositions, along with an approximate factorization technique, are additionally employed to a global linearly coupled system, which leads to several decoupled subsystems, i.e., a fully decoupled monolithic procedure. We establish global error estimates to verify the second-order temporal accuracy of the proposed method for velocity, pressure, and temperature in terms of a discrete l2-norm. Moreover, according to the energy evolution, the proposed method is proved to be stable if the time step is less than or equal to a constant. In addition, we provide numerical simulations of two-dimensional Rayleigh-Bénard convection and periodic forced flow. The results demonstrate that the proposed method significantly mitigates the time step limitation, reduces the computational cost because only one Poisson equation is required to be solved, and preserves the second-order temporal accuracy for velocity, pressure, and temperature. Finally, the proposed method reasonably predicts a three-dimensional Rayleigh-Bénard convection for different Rayleigh numbers.

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.

Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

NASA Astrophysics Data System (ADS)

Lollchund, M. R.; Dookhitram, K.; Sunhaloo, M. S.; Boojhawon, R.

2013-04-01

In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

On non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2015-04-01

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

Matrix decomposition graphics processing unit solver for Poisson image editing

NASA Astrophysics Data System (ADS)

Lei, Zhao; Wei, Li

2012-10-01

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

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

PubMed

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

2018-01-20

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

The stress analysis method for three-dimensional composite materials

NASA Astrophysics Data System (ADS)

Nagai, Kanehiro; Yokoyama, Atsushi; Maekawa, Zen'ichiro; Hamada, Hiroyuki

1994-05-01

This study proposes a stress analysis method for three-dimensionally fiber reinforced composite materials. In this method, the rule-of mixture for composites is successfully applied to 3-D space in which material properties would change 3-dimensionally. The fundamental formulas for Young's modulus, shear modulus, and Poisson's ratio are derived. Also, we discuss a strength estimation and an optimum material design technique for 3-D composite materials. The analysis is executed for a triaxial orthogonally woven fabric, and their results are compared to the experimental data in order to verify the accuracy of this method. The present methodology can be easily understood with basic material mechanics and elementary mathematics, so it enables us to write a computer program of this theory without difficulty. Furthermore, this method can be applied to various types of 3-D composites because of its general-purpose characteristics.

Direct numerical simulation of the laminar-turbulent transition at hypersonic flow speeds on a supercomputer

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.; Fedorov, A. V.

2017-08-01

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar-turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier-Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton-Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar-turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar-turbulent transition.

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

PubMed

Vyalov, Ivan; Rocchia, Walter

2018-03-21

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

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

NASA Astrophysics Data System (ADS)

Vyalov, Ivan; Rocchia, Walter

2018-03-01

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

Calculation of laminar heating rates on three-dimensional configurations using the axisymmetric analogue

NASA Technical Reports Server (NTRS)

Hamilton, H. H., II

1980-01-01

A theoretical method was developed for computing approximate laminar heating rates on three dimensional configurations at angle of attack. The method is based on the axisymmetric analogue which is used to reduce the three dimensional boundary layer equations along surface streamlines to an equivalent axisymmetric form by using the metric coefficient which describes streamline divergence (or convergence). The method was coupled with a three dimensional inviscid flow field program for computing surface streamline paths, metric coefficients, and boundary layer edge conditions.

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

On the dimensionally correct kinetic theory of turbulence for parallel propagation

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

Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Ziebell, L. F., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Yoon, P. H., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br

2015-03-15

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectivelymore » emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms.« less

Advantages of multigrid methods for certifying the accuracy of PDE modeling

NASA Technical Reports Server (NTRS)

Forester, C. K.

1981-01-01

Numerical techniques for assessing and certifying the accuracy of the modeling of partial differential equations (PDE) to the user's specifications are analyzed. Examples of the certification process with conventional techniques are summarized for the three dimensional steady state full potential and the two dimensional steady Navier-Stokes equations using fixed grid methods (FG). The advantages of the Full Approximation Storage (FAS) scheme of the multigrid technique of A. Brandt compared with the conventional certification process of modeling PDE are illustrated in one dimension with the transformed potential equation. Inferences are drawn for how MG will improve the certification process of the numerical modeling of two and three dimensional PDE systems. Elements of the error assessment process that are common to FG and MG are analyzed.

Three-variable solution in the (2+1)-dimensional null-surface formulation

NASA Astrophysics Data System (ADS)

Harriott, Tina A.; Williams, J. G.

2018-04-01

The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact (2+1)-dimensional solution that depends nontrivially upon all three of the NSF's intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of (2+1)-dimensional general relativistic spacetimes discovered by Cavaglià.

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

Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

Quantum Theory of Three-Dimensional Superresolution Using Rotating-PSF Imagery

NASA Astrophysics Data System (ADS)

Prasad, S.; Yu, Z.

The inverse of the quantum Fisher information (QFI) matrix (and extensions thereof) provides the ultimate lower bound on the variance of any unbiased estimation of a parameter from statistical data, whether of intrinsically quantum mechanical or classical character. We calculate the QFI for Poisson-shot-noise-limited imagery using the rotating PSF that can localize and resolve point sources fully in all three dimensions. We also propose an experimental approach based on the use of computer generated hologram and projective measurements to realize the QFI-limited variance for the problem of super-resolving a closely spaced pair of point sources at a highly reduced photon cost. The paper presents a preliminary analysis of quantum-limited three-dimensional (3D) pair optical super-resolution (OSR) problem with potential applications to astronomical imaging and 3D space-debris localization.

On the symmetries of integrability

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

Bellon, M.; Maillard, J.M.; Viallet, C.

1992-06-01

In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiatemore » the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.« less

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

NASA-Ames three-dimensional potential flow analysis system (POTFAN) equation solver code (SOLN) version 1

NASA Technical Reports Server (NTRS)

Davis, J. E.; Bonnett, W. S.; Medan, R. T.

1976-01-01

A computer program known as SOLN was developed as an independent segment of the NASA-Ames three-dimensional potential flow analysis systems of linear algebraic equations. Methods used include: LU decomposition, Householder's method, a partitioning scheme, and a block successive relaxation method. Due to the independent modular nature of the program, it may be used by itself and not necessarily in conjunction with other segments of the POTFAN system.

Stratified Shear Flows In Pipe Geometries

NASA Astrophysics Data System (ADS)

Harabin, George; Camassa, Roberto; McLaughlin, Richard; UNC Joint Fluids Lab Team Team

2015-11-01

Exact and series solutions to the full Navier-Stokes equations coupled to the advection diffusion equation are investigated in tilted three-dimensional pipe geometries. Analytic techniques for studying the three-dimensional problem provide a means for tackling interesting questions such as the optimal domain for mass transport, and provide new avenues for experimental investigation of diffusion driven flows. Both static and time dependent solutions will be discussed. NSF RTG DMS-0943851, NSF RTG ARC-1025523, NSF DMS-1009750.

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Liou, May-Fun

1989-01-01

An implicit procedure for solving parabolized Navier-Stokes equations under the assumption of a general equation of state for a gas in chemical equilibrium is given. A general and consistent approach for the evaluation of Jacobian matrices in the implicit operator avoids the use of unnecessary auxiliary quantities and approximations, and leads to a simple expression. Applications to two- and three-dimensional flow problems show efficiency in computer time and economy in storage.

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

NASA Astrophysics Data System (ADS)

Suárez, Abril; Chavanis, Pierre-Henri

2015-07-01

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

Center of Excellence in Theoretical Geoplasma Research

DTIC Science & Technology

1993-08-31

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

Vertically Integrated Models for Carbon Storage Modeling in Heterogeneous Domains

NASA Astrophysics Data System (ADS)

Bandilla, K.; Celia, M. A.

2017-12-01

Numerical modeling is an essential tool for studying the impacts of geologic carbon storage (GCS). Injection of carbon dioxide (CO2) into deep saline aquifers leads to multi-phase flow (injected CO2 and resident brine), which can be described by a set of three-dimensional governing equations, including mass-balance equation, volumetric flux equations (modified Darcy), and constitutive equations. This is the modeling approach on which commonly used reservoir simulators such as TOUGH2 are based. Due to the large density difference between CO2 and brine, GCS models can often be simplified by assuming buoyant segregation and integrating the three-dimensional governing equations in the vertical direction. The integration leads to a set of two-dimensional equations coupled with reconstruction operators for vertical profiles of saturation and pressure. Vertically-integrated approaches have been shown to give results of comparable quality as three-dimensional reservoir simulators when applied to realistic CO2 injection sites such as the upper sand wedge at the Sleipner site. However, vertically-integrated approaches usually rely on homogeneous properties over the thickness of a geologic layer. Here, we investigate the impact of general (vertical and horizontal) heterogeneity in intrinsic permeability, relative permeability functions, and capillary pressure functions. We consider formations involving complex fluvial deposition environments and compare the performance of vertically-integrated models to full three-dimensional models for a set of hypothetical test cases consisting of high permeability channels (streams) embedded in a low permeability background (floodplains). The domains are randomly generated assuming that stream channels can be represented by sinusoidal waves in the plan-view and by parabolas for the streams' cross-sections. Stream parameters such as width, thickness and wavelength are based on values found at the Ketzin site in Germany. Results from the vertically-integrated approach are compared to results using TOUGH2, both in terms of depth-averaged saturation and vertical saturation profiles.

Prescription-induced jump distributions in multiplicative Poisson processes.

PubMed

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

2011-06-01

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

Prescription-induced jump distributions in multiplicative Poisson processes

NASA Astrophysics Data System (ADS)

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

2011-06-01

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

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

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

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

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

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

DOE PAGES

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

2016-04-22

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

Three-Dimensional Lissajous Figures.

ERIC Educational Resources Information Center

D'Mura, John M.

1989-01-01

Described is a mechanically driven device for generating three-dimensional harmonic space figures with different frequencies and phase angles on the X, Y, and Z axes. Discussed are apparatus, viewing stereo pairs, equations of motion, and using space figures in classroom. (YP)

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

NASA Technical Reports Server (NTRS)

Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

1995-01-01

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

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.

Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Spaulding, M. L.

1977-01-01

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.

Siegert-state expansion for nonstationary systems. IV. Three-dimensional case

NASA Astrophysics Data System (ADS)

Tolstikhin, Oleg I.

2008-03-01

The Siegert-state expansion approach [O. I. Tolstikhin, Phys. Rev. A 73, 062705 (2006)] is extended to the three-dimensional case. Coupled equations defining the time evolution of coefficients in the expansion of the solution to the time-dependent Schrödinger equation in terms of partial-wave Siegert states are derived, and physical observables (probabilities of transitions to discrete states and the momentum distribution of ejected particles) are expressed in terms of these coefficients. The approach is implemented in terms of Siegert pseudostates and illustrated by calculations of the photodetachment of H- by strong high-frequency laser pulses. The present calculations demonstrate that the interference effect in the laser-atom interaction dynamics found recently in the one-dimensional case [K. Toyota , Phys. Rev. A 76, 043418 (2007)] reveals itself in the three-dimensional case as well.

Rota-Baxter operators on sl (2,C) and solutions of the classical Yang-Baxter equation

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

Pei, Jun, E-mail: peitsun@163.com; Bai, Chengming, E-mail: baicm@nankai.edu.cn; Guo, Li, E-mail: liguo@rutgers.edu

2014-02-15

We explicitly determine all Rota-Baxter operators (of weight zero) on sl (2,C) under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in sl (2,C), confirming the related study by Semenov-Tian-Shansky. In general, these Rota-Baxter operators give a family of solutions of the classical Yang-Baxter equation in the six-dimensional Lie algebra sl (2,C)⋉{sub ad{sup *}} sl (2,C){sup *}. They also give rise to three-dimensional pre-Lie algebras which in turn yield solutions of the classical Yang-Baxter equation in other six-dimensional Lie algebras.

Random transitions described by the stochastic Smoluchowski-Poisson system and by the stochastic Keller-Segel model.

PubMed

Chavanis, P H; Delfini, L

2014-03-01

We study random transitions between two metastable states that appear below a critical temperature in a one-dimensional self-gravitating Brownian gas with a modified Poisson equation experiencing a second order phase transition from a homogeneous phase to an inhomogeneous phase [P. H. Chavanis and L. Delfini, Phys. Rev. E 81, 051103 (2010)]. We numerically solve the N-body Langevin equations and the stochastic Smoluchowski-Poisson system, which takes fluctuations (finite N effects) into account. The system switches back and forth between the two metastable states (bistability) and the particles accumulate successively at the center or at the boundary of the domain. We explicitly show that these random transitions exhibit the phenomenology of the ordinary Kramers problem for a Brownian particle in a double-well potential. The distribution of the residence time is Poissonian and the average lifetime of a metastable state is given by the Arrhenius law; i.e., it is proportional to the exponential of the barrier of free energy ΔF divided by the energy of thermal excitation kBT. Since the free energy is proportional to the number of particles N for a system with long-range interactions, the lifetime of metastable states scales as eN and is considerable for N≫1. As a result, in many applications, metastable states of systems with long-range interactions can be considered as stable states. However, for moderate values of N, or close to a critical point, the lifetime of the metastable states is reduced since the barrier of free energy decreases. In that case, the fluctuations become important and the mean field approximation is no more valid. This is the situation considered in this paper. By an appropriate change of notations, our results also apply to bacterial populations experiencing chemotaxis in biology. Their dynamics can be described by a stochastic Keller-Segel model that takes fluctuations into account and goes beyond the usual mean field approximation.

Exact periodic cross-kink wave solutions for the new (2+1)-dimensional KdV equation in fluid flows and plasma physics.

PubMed

Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping

2016-10-01

The Korteweg-de Vries (KdV)-type models have been shown to describe many important physical situations such as fluid flows, plasma physics, and solid state physics. In this paper, a new (2 + 1)-dimensional KdV equation is discussed. Based on the Hirota's bilinear form and a generalized three-wave approach, we obtain new exact solutions for the new (2 + 1)-dimensional KdV equation. With the help of symbolic computation, the properties for some new solutions are presented with some figures.

Intermediate boundary conditions for LOD, ADI and approximate factorization methods

NASA Technical Reports Server (NTRS)

Leveque, R. J.

1985-01-01

A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

Adaptive and iterative methods for simulations of nanopores with the PNP-Stokes equations

NASA Astrophysics Data System (ADS)

Mitscha-Baude, Gregor; Buttinger-Kreuzhuber, Andreas; Tulzer, Gerhard; Heitzinger, Clemens

2017-06-01

We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule dynamics inside nanopore sensors. The source code is released online at http://github.com/mitschabaude/nanopores. We add to existing numerical approaches by deploying goal-oriented adaptive mesh refinement. To reduce the computation overhead of mesh adaptivity, our error estimator uses the much cheaper Poisson-Boltzmann equation as a simplified model, which is justified on heuristic grounds but shown to work well in practice. To address the nonlinearity in the full PNP-Stokes system, three different linearization schemes are proposed and investigated, with two segregated iterative approaches both outperforming a naive application of Newton's method. Numerical experiments are reported on a real-world nanopore sensor geometry. We also investigate two different models for the interaction of target molecules with the nanopore sensor through the PNP-Stokes equations. In one model, the molecule is of finite size and is explicitly built into the geometry; while in the other, the molecule is located at a single point and only modeled implicitly - after solution of the system - which is computationally favorable. We compare the resulting force profiles of the electric and velocity fields acting on the molecule, and conclude that the point-size model fails to capture important physical effects such as the dependence of charge selectivity of the sensor on the molecule radius.

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

PubMed

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

2013-11-20

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

Three-dimensional implicit lambda methods

NASA Technical Reports Server (NTRS)

Napolitano, M.; Dadone, A.

1983-01-01

This paper derives the three dimensional lambda-formulation equations for a general orthogonal curvilinear coordinate system and provides various block-explicit and block-implicit methods for solving them, numerically. Three model problems, characterized by subsonic, supersonic and transonic flow conditions, are used to assess the reliability and compare the efficiency of the proposed methods.

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

NASA Technical Reports Server (NTRS)

Saatchi, Sasan S.

1993-01-01

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

Comparison of two- and three-dimensional Navier-Stokes solutions with NASA experimental data for CAST-10 airfoil

NASA Technical Reports Server (NTRS)

Swanson, R. Charles; Radespiel, Rolf; Mccormick, V. Edward

1989-01-01

The two-dimensional (2-D) and three-dimensional Navier-Stokes equations are solved for flow over a NAE CAST-10 airfoil model. Recently developed finite-volume codes that apply a multistage time stepping scheme in conjunction with steady state acceleration techniques are used to solve the equations. Two-dimensional results are shown for flow conditions uncorrected and corrected for wind tunnel wall interference effects. Predicted surface pressures from 3-D simulations are compared with those from 2-D calculations. The focus of the 3-D computations is the influence of the sidewall boundary layers. Topological features of the 3-D flow fields are indicated. Lift and drag results are compared with experimental measurements.

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

Three-dimensional computer simulation of non-reacting jet-gas flow mixing in an MHD second stage combustor

NASA Astrophysics Data System (ADS)

Chang, S. L.; Lottes, S. A.; Berry, G. F.

Argonne National Laboratory is investigating the non-reacting jet-gas mixing patterns in a magnetohydrodynamics (MHD) second stage combustor by using a three-dimensional single-phase hydrodynamics computer program. The computer simulation is intended to enhance the understanding of flow and mixing patterns in the combustor, which in turn may improve downstream MHD channel performance. The code is used to examine the three-dimensional effects of the side walls and the distributed jet flows on the non-reacting jet-gas mixing patterns. The code solves the conservation equations of mass, momentum, and energy, and a transport equation of a turbulence parameter and allows permeable surfaces to be specified for any computational cell.

An efficient closed-form solution for acoustic emission source location in three-dimensional structures

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

Li, Xibing; Dong, Longjun, E-mail: csudlj@163.com; Australian Centre for Geomechanics, The University of Western Australia, Crawley, 6009

This paper presents an efficient closed-form solution (ECS) for acoustic emission(AE) source location in three-dimensional structures using time difference of arrival (TDOA) measurements from N receivers, N ≥ 6. The nonlinear location equations of TDOA are simplified to linear equations. The unique analytical solution of AE sources for unknown velocity system is obtained by solving the linear equations. The proposed ECS method successfully solved the problems of location errors resulting from measured deviations of velocity as well as the existence and multiplicity of solutions induced by calculations of square roots in existed close-form methods.

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Development of a three-dimensional supersonic inlet flow analysis

NASA Technical Reports Server (NTRS)

Buggeln, R. C.; Mcdonald, H.; Levy, R.; Kreskovsky, J. P.

1980-01-01

A method for computing three dimensional flow in supersonic inlets is described. An approximate set of governing equations is given for viscous flows which have a primary flow direction. The governing equations are written in general orthogonal coordinates. These equations are modified in the subsonic region of the flow to prevent the phenomenon of branching. Results are presented for the two sample cases: a Mach number equals 2.5 flow in a square duct, and a Mach number equals 3.0 flow in a research jet engine inlet. In the latter case the computed results are compared with the experimental data. A users' manual is included.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

Quantum field between moving mirrors: A three dimensional example

NASA Technical Reports Server (NTRS)

Hacyan, S.; Jauregui, Roco; Villarreal, Carlos

1995-01-01

The scalar quantum field uniformly moving plates in three dimensional space is studied. Field equations for Dirichlet boundary conditions are solved exactly. Comparison of the resulting wavefunctions with their instantaneous static counterpart is performed via Bogolubov coefficients. Unlike the one dimensional problem, 'particle' creation as well as squeezing may occur. The time dependent Casimir energy is also evaluated.

Solving the MHD equations by the space time conservation element and solution element method

NASA Astrophysics Data System (ADS)

Zhang, Moujin; John Yu, S.-T.; Henry Lin, S.-C.; Chang, Sin-Chung; Blankson, Isaiah

2006-05-01

We apply the space-time conservation element and solution element (CESE) method to solve the ideal MHD equations with special emphasis on satisfying the divergence free constraint of magnetic field, i.e., ∇ · B = 0. In the setting of the CESE method, four approaches are employed: (i) the original CESE method without any additional treatment, (ii) a simple corrector procedure to update the spatial derivatives of magnetic field B after each time marching step to enforce ∇ · B = 0 at all mesh nodes, (iii) a constraint-transport method by using a special staggered mesh to calculate magnetic field B, and (iv) the projection method by solving a Poisson solver after each time marching step. To demonstrate the capabilities of these methods, two benchmark MHD flows are calculated: (i) a rotated one-dimensional MHD shock tube problem and (ii) a MHD vortex problem. The results show no differences between different approaches and all results compare favorably with previously reported data.

A High Order Discontinuous Galerkin Method for 2D Incompressible Flows

NASA Technical Reports Server (NTRS)

Liu, Jia-Guo; Shu, Chi-Wang

1999-01-01

In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

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.

Numerical Modeling of Three-Dimensional Confined Flows

NASA Technical Reports Server (NTRS)

Greywall, M. S.

1981-01-01

A three dimensional confined flow model is presented. The flow field is computed by calculating velocity and enthalpy along a set of streamlines. The finite difference equations are obtained by applying conservation principles to streamtubes constructed around the chosen streamlines. With appropriate substitutions for the body force terms, the approach computes three dimensional magnetohydrodynamic channel flows. A listing of a computer code, based on this approach is presented in FORTRAN IV language. The code computes three dimensional compressible viscous flow through a rectangular duct, with the duct cross section specified along the axis.

Asymptotic symmetries of colored gravity in three dimensions

NASA Astrophysics Data System (ADS)

Joung, Euihun; Kim, Jaewon; Kim, Jihun; Rey, Soo-Jong

2018-03-01

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the SU( N)-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with SU( N, N) × SU( N, N) gauge group, the theory contains graviton, SU( N) Chern-Simons gauge fields and massless spin-two multiplets in the SU( N) adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of \\widehat{su(N)} Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.

Accurate Thermal Stresses for Beams: Normal Stress

NASA Technical Reports Server (NTRS)

Johnson, Theodore F.; Pilkey, Walter D.

2002-01-01

Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in this theory by employing an Airy stress function. The Airy stress function enables the reduction of the three-dimensional thermal stress problem to a two-dimensional one. Numerical results from the general theory of thermoelasticity are compared to those obtained from strength of materials. It is concluded that the theory of thermoelasticity for prismatic beams proposed in this paper can be used instead of strength of materials when precise stress results are desired.

Accurate Thermal Stresses for Beams: Normal Stress

NASA Technical Reports Server (NTRS)

Johnson, Theodore F.; Pilkey, Walter D.

2003-01-01

Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in this theory by employing an Airy stress function. The Airy stress function enables the reduction of the three-dimensional thermal stress problem to a two-dimensional one. Numerical results from the general theory of thermoelasticity are compared to those obtained from strength of materials. It is concluded that the theory of thermoelasticity for prismatic beams proposed in this paper can be used instead of strength of materials when precise stress results are desired.

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-local gravitational angular momentum and centre of mass from generalised Witten equations

NASA Astrophysics Data System (ADS)

Wieland, Wolfgang

2017-03-01

Witten's proof for the positivity of the ADM mass gives a definition of energy in terms of three-surface spinors. In this paper, we give a generalisation for the remaining six Poincaré charges at spacelike infinity, which are the angular momentum and centre of mass. The construction improves on certain three-surface spinor equations introduced by Shaw. We solve these equations asymptotically obtaining the ten Poincaré charges as integrals over the Nester-Witten two-form. We point out that the defining differential equations can be extended to three-surfaces of arbitrary signature and we study them on the entire boundary of a compact four-dimensional region of spacetime. The resulting quasi-local expressions for energy and angular momentum are integrals over a two-dimensional cross-section of the boundary. For any two consecutive such cross-sections, conservation laws are derived that determine the influx (outflow) of matter and gravitational radiation.

A Comparative Study of AlGaN and InGaN Back-Barriers in Ultrathin-Barrier AlN/GaN Heterostructures

NASA Astrophysics Data System (ADS)

All Abbas, J. M.; Atmaca, G.; Narin, P.; Kutlu, E.; Sarikavak-Lisesivdin, B.; Lisesivdin, S. B.

2017-08-01

Investigations of the effects of back-barrier introduction on the two-dimensional electron gas (2DEG) of ultrathin-barrier AlN/GaN heterostructures with AlGaN and InGaN back-barriers are carried out using self-consistent solutions of 1-dimensional Schrödinger-Poisson equations. Inserted AlGaN and InGaN back-barriers are used to provide a good 2DEG confinement thanks to raising the conduction band edge of GaN buffer with respect to GaN channel layer. Therefore, in this paper the influence of these back-barrier layers on sheet carrier density, 2DEG confinement, and mobility are systematically and comparatively investigated. As a result of calculations, although sheet carrier density is found to decrease with InGaN back-barrier layer, it is not changed with AlGaN back-barrier layer for suggested optimise heterostructures. Obtained results can give some insights for further experimental studies.

Wedge-Shaped GaN Nanowalls: A Potential Candidate for Two-Dimensional Electronics and Spintronics

NASA Astrophysics Data System (ADS)

Deb, Swarup; Dhar, Subhabrata

Schrödingerand Poisson equations are solved self-consistently in order to obtain the potential and charge density distribution in n-type GaN nanowalls tapered along c-axis by different angles. The study shows two-dimensional (2D) quantum confinement of electrons in the central vertical plane of the wall for the entire range of tapering. Calculation of room temperature electron mobility in the 2D channel shows a steady decrease with the increase of the inclination angle of the side facets with respect to the base. However, it is interesting to note that the mobility remains to be much larger than that of bulk GaN even for the inclination angle of 65∘. The properties of high mobility and the vertical orientation of the 2DEG plane in this system can be exploited in fabricating highly conducting transparent interconnects and field effect transistors, which can lead to large scale integration of 2D devices in future.