Blow-up conditions for two dimensional modified Euler-Poisson equations
Lee, Yongki
2016-09-01
The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow-up for some initial configurations. This article strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional modified Euler-Poisson system with a modified Riesz transform where the singularity at the origin is removed. We identify upper-thresholds for finite time blow-up of solutions for the modified Euler-Poisson equations with attractive/repulsive forcing.
An adaptive, high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations
Wang, Bei; Colella, Phil
2012-01-01
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.
Settle, Sean O.
2013-01-01
The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.
Messaris, G. T.; Papastavrou, C. A.; Loukopoulos, V. C.; Karahalios, G. T.
2009-08-01
A new finite-difference method is presented for the numerical solution of the Navier-Stokes equations of motion of a viscous incompressible fluid in two (or three) dimensions and in the primitive-variable formulation. Introducing two auxiliary functions of the coordinate system and considering the form of the initial equation on lines passing through the nodal point (x0, y0) and parallel to the coordinate axes, we can separate it into two parts that are finally reduced to ordinary differential equations, one for each dimension. The final system of linear equations in n-unknowns is solved by an iterative technique and the method converges rapidly giving satisfactory results. For the pressure variable we consider a pressure Poisson equation with suitable Neumann boundary conditions. Numerical results, confirming the accuracy of the proposed method, are presented for configurations of interest, like Poiseuille flow and the flow between two parallel plates with step under the presence of a pressure gradient.
Crouseilles, Nicolas; Lemou, Mohammed; Méhats, Florian; Zhao, Xiaofei
2017-10-01
In this work, we focus on the numerical resolution of the four dimensional phase space Vlasov-Poisson system subject to a uniform strong external magnetic field. To do so, we consider a Particle-in-Cell based method, for which the characteristics are reformulated by means of the two-scale formalism, which is well-adapted to handle highly-oscillatory equations. Then, a numerical scheme is derived for the two-scale equations. The so-obtained scheme enjoys a uniform accuracy property, meaning that its accuracy does not depend on the small parameter. Several numerical results illustrate the capabilities of the method.
Two-dimensional Green`s function Poisson solution appropriate for cylindrical-symmetry simulations
Energy Technology Data Exchange (ETDEWEB)
Riley, M.E.
1998-04-01
This report describes the numerical procedure used to implement the Green`s function method for solving the Poisson equation in two-dimensional (r,z) cylindrical coordinates. The procedure can determine the solution to a problem with any or all of the applied voltage boundary conditions, dielectric media, floating (insulated) conducting media, dielectric surface charging, and volumetric space charge. The numerical solution is reasonably fast, and the dimension of the linear problem to be solved is that of the number of elements needed to represent the surfaces, not the whole computational volume. The method of solution is useful in the simulation of plasma particle motion in the vicinity of complex surface structures as found in microelectronics plasma processing applications. This report is a stand-alone supplement to the previous Sandia Technical Report SAND98-0537 presenting the two-dimensional Cartesian Poisson solver.
Beatification: Flattening the Poisson Bracket for Two-Dimensional Fluid and Plasma Theories
Viscondi, Thiago F; Morrison, Philip J
2016-01-01
A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables.
Energy Technology Data Exchange (ETDEWEB)
Riley, M.E.
1998-03-01
This report describes the numerical procedure used to implement the Green`s function method for solving the Poisson equation in two-dimensional Cartesian coordinates. The procedure can determine the solution to a problem with any or all of applied voltage boundary conditions, dielectric media, floating (insulated) conducting media, dielectric surface charging, periodic (reflective) boundary conditions, and volumetric space charge. The numerical solution is reasonably fast, and the dimension of the linear problem to be solved is that of the number of elements needed to represent the surfaces, not the whole computational volume. The method of solution is useful in the simulation of plasma particle motion in the vicinity of complex surface structures as found in microelectronics plasma processing applications. A FORTRAN implementation of this procedure is available from the author.
UPWIND DISCONTINUOUS GALERKIN METHODS FOR TWO DIMENSIONAL NEUTRON TRANSPORT EQUATIONS
Institute of Scientific and Technical Information of China (English)
袁光伟; 沈智军; 闫伟
2003-01-01
In this paper the upwind discontinuous Galerkin methods with triangle meshes for two dimensional neutron transport equations will be studied.The stability for both of the semi-discrete and full-discrete method will be proved.
Operator splitting for two-dimensional incompressible fluid equations
Holden, Helge; Karper, Trygve K
2011-01-01
We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier-Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data are sufficiently regular.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Control Operator for the Two-Dimensional Energized Wave Equation
Directory of Open Access Journals (Sweden)
Sunday Augustus REJU
2006-07-01
Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.
Numerical blowup in two-dimensional Boussinesq equations
Yin, Zhaohua
2009-01-01
In this paper, we perform a three-stage numerical relay to investigate the finite time singularity in the two-dimensional Boussinesq approximation equations. The initial asymmetric condition is the middle-stage output of a $2048^2$ run, the highest resolution in our study is $40960^2$, and some signals of numerical blowup are observed.
δ-Phosphorene: a two dimensional material with a highly negative Poisson's ratio.
Wang, Haidi; Li, Xingxing; Li, Pai; Yang, Jinlong
2017-01-05
As a basic mechanical parameter, Poisson's ratio (ν) measures the mechanical responses of solids against external loads. In rare cases, materials have a negative Poisson's ratio (NPR), and present an interesting auxetic effect. That is, when a material is stretched in one direction, it will expand in the perpendicular direction. To design modern nanoscale electromechanical devices with special functions, two dimensional (2D) auxetic materials are highly desirable. In this work, based on first principles calculations, we rediscover the previously proposed δ-phosphorene (δ-P) nanosheets [Jie Guan, et al., Phys. Rev. Lett., 2014, 113, 046804] which are good auxetic materials with a high NPR. The results show that the Young's modulus and Poisson's ratio of δ-P are all anisotropic. The NPR value along the grooved direction is up to -0.267, which is much higher than the recently reported 2D auxetic materials. The auxetic effect of δ-P originating from its puckered structure is robust and insensitive to the number of layers due to weak interlayer interactions. Moreover, δ-P possesses good flexibility because of its relatively small Young's modulus and high critical crack strain. If δ-P can be synthesized, these extraordinary properties would endow it with great potential in designing low dimensional electromechanical devices.
Lyapunov Computational Method for Two-Dimensional Boussinesq Equation
Mabrouk, Anouar Ben
2010-01-01
A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable and analyzed for local truncation error for consistency. The stability is checked by using Lyapunov criterion and the convergence is studied. Some numerical implementations are provided at the end of the paper to validate the theoretical results.
Chavanis, Pierre-Henri
2013-01-01
We complete the literature on the statistical mechanics of point vortices in two-dimensional hydrodynamics. Using a maximum entropy principle, we determine the multi-species Boltzmann-Poisson equation and establish a form of virial theorem. Using a maximum entropy production principle (MEPP), we derive a set of relaxation equations towards statistical equilibrium. These relaxation equations can be used as a numerical algorithm to compute the maximum entropy state. We mention the analogies with the Fokker-Planck equations derived by Debye and H\\"uckel for electrolytes. We then consider the limit of strong mixing (or low energy). To leading order, the relationship between the vorticity and the stream function at equilibrium is linear and the maximization of the entropy becomes equivalent to the minimization of the enstrophy. This expansion is similar to the Debye-H\\"uckel approximation for electrolytes, except that the temperature is negative instead of positive so that the effective interaction between like-si...
Equation of State of the Two-Dimensional Hubbard Model
Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-01
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.
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Taha Aziz
2013-01-01
Full Text Available The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.
Institute of Scientific and Technical Information of China (English)
XIONG Lei; LI haijiao; ZHANG Lewen
2008-01-01
The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions, 4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.
The Chandrasekhar's Equation for Two-Dimensional Hypothetical White Dwarfs
De, Sanchari
2014-01-01
In this article we have extended the original work of Chandrasekhar on the structure of white dwarfs to the two-dimensional case. Although such two-dimensional stellar objects are hypothetical in nature, we strongly believe that the work presented in this article may be prescribed as Master of Science level class problem for the students in physics.
Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations
Directory of Open Access Journals (Sweden)
Chunrong Zhu
2016-11-01
Full Text Available In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.
Stabilities for nonisentropic Euler-Poisson equations.
Cheung, Ka Luen; Wong, Sen
2015-01-01
We establish the stabilities and blowup results for the nonisentropic Euler-Poisson equations by the energy method. By analysing the second inertia, we show that the classical solutions of the system with attractive forces blow up in finite time in some special dimensions when the energy is negative. Moreover, we obtain the stabilities results for the system in the cases of attractive and repulsive forces.
Directory of Open Access Journals (Sweden)
Yan Li
2012-01-01
Full Text Available We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.
Auxetic two-dimensional lattice with Poisson's Ratio arbitrarily close to -1
Cabras, L
2014-01-01
In this paper we propose a new lattice structure having macroscopic Poisson's ratio arbitrarily close to the stability limit -1. We tested experimentally the effective Poisson's ratio of the micro-structured medium; the uniaxial test has been performed on a thermoplastic lattice produced with a 3d printing technology. A theoretical analysis of the effective properties has been performed and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis has been performed on three micro-geometry leading to an isotropic behaviour for the cases of three-fold and six-fold symmetry and to a cubic behaviour for the case of four-fold symmetry.
NONLINEAR GALERKIN METHODS FOR SOLVING TWO DIMENSIONAL NEWTON-BOUSSINESQ EQUATIONS
Institute of Scientific and Technical Information of China (English)
GUOBOLING
1995-01-01
The nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations are proposed. The existence and uniqueness of global generalized solution of these equations,and the convergence of approximate solutions are also obtained.
Directory of Open Access Journals (Sweden)
A. Aghili
2011-12-01
Full Text Available In this work,we present new theorems on two-dimensional Laplace transformation. We also develop some applications based on these results. The two-dimensional Laplace transformation is useful in the solution of non-homogeneous partial differential equations. In the last section a boundary value problem is solved by using the double Laplace-Carson transform.
Solution of two-dimensional Fredholm integral equation via RBF-triangular method
Directory of Open Access Journals (Sweden)
Amir Fallahzadeh
2012-04-01
Full Text Available In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed method increases.
Yehorchenko, Irina
2010-01-01
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional and hidden symmetries of the original equations.
Asymptotic Behavior of the Newton-Boussinesq Equation in a Two-Dimensional Channel
Fucci, Guglielmo; Singh, Preeti
2007-01-01
We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also establish the regularity of the global attractor.
TWO-DIMENSIONAL RIEMANN PROBLEMS:FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Li Jiequan; Sheng Wancheng; Zhang Tong; Zheng Yuxi
2009-01-01
In this paper we survey the authors' and related work on two-dimensional Rie-mann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections: 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
赵才地
2004-01-01
This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.
Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time
Institute of Scientific and Technical Information of China (English)
YAN Jun
2005-01-01
The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.
REGULARITY OF POISSON EQUATION IN SOME LOGARITHMIC SPACE
Institute of Scientific and Technical Information of China (English)
Jia Huilian; Li Dongsheng; Wang Lihe
2007-01-01
In this note, the regularity of Poisson equation -△u = f with f lying in logarithmic function space Lp(LogL)a(Ω)(1＜p ＜∞, a ∈ R) is studied. The result of the note generalizes the W2,p estimate of Poisson equation in Lp(Ω).
Loop equations and Virasoro constraints in non-perturbative two-dimensional quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R.; Verlinde, H. (Princeton Univ., NJ (USA). Joseph Henry Labs.); Verlinde, E. (Institute for Advanced Study, Princeton, NJ (USA). School of Natural Sciences)
1991-01-21
We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one-matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. We give an interpretation of these equations in topological gravity and discuss their extension to multi-matrix models. For the multi-critical models the loop equation naturally singles out the operators corresponding to the primary fields of the minimal models. (orig.).
Loop Equations and Virasoro Constraints in Non-Perturbative Two-Dimensional Quantum Gravity
Dijkgraaf, Robbert; Verlinde, Herman; Verlinde, Erik
We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one-matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. We give an interpretation of these equations in topological gravity and discuss their extension to multi-matrix models. For the multi-critical models the loop equation naturally singles out the operators corresponding to the primary fields of the minimal models.
Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations
Abdulwahhab, Muhammad Alim
2016-10-01
Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.
Solution of the two- dimensional heat equation for a rectangular plate
Directory of Open Access Journals (Sweden)
Nurcan BAYKUŞ SAVAŞANERİL
2015-11-01
Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.
Analytic Solution for Two-Dimensional Heat Equation for an Ellipse Region
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Nurcan Baykus Savasaneril
2016-01-01
Full Text Available In this study, an altenative method is presented for the solution of two-dimensional heat equation in an ellipse region. In this method, the solution function of the problem is based on the Green, and therefore on elliptic functions. To do this, it is made use of the basic consepts associated with elliptic integrals, conformal mappings and Green functions.
de Snoo, H; Winkler, Henrik
2005-01-01
The class of two-dimensional trace-normed canonical systems of differential equations on R is considered with selfadjoint interface conditions at 0. If one or both of the intervals around 0 are H-indivisible the interface conditions which give rise to selfadjoint relations (multi-valued operators) a
The transfer function analysis of various schemes for the two-dimensional shallow-water equations
Neta, B.; DeVito, C.L.
1988-01-01
In this paper various finite difference and finite element approximations to the linearized two-dimensional shallow-water equations are analyzed. This analysis complements previous results for the one-dimensional case. The first author would like to thank the NPS Foundation Research program for its support of this research.
T, M P Ramirez
2012-01-01
Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the two-dimensional Electrical Impedance Equation, when the conductivity function arises from geometrical figures, located within bounded domains.
Bound states of two-dimensional Schr\\"{o}dinger-Newton equations
Stubbe, Joachim
2008-01-01
We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schr\\"{o}dinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.
Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM
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Reza Abazari
2013-01-01
Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.
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Musa Danjuma SHEHU
2008-06-01
Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.
Group classification of steady two-dimensional boundary-layer stagnation-point flow equations
Nadjafikhah, Mehdi; Hejazi, Seyed Reza
2010-01-01
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
Directory of Open Access Journals (Sweden)
Sohrab Bazm
2016-02-01
Full Text Available In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficiency and accuracy of the method.
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
Energy Technology Data Exchange (ETDEWEB)
Molabahrami, A. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of)], E-mail: a_m_bahrami@yahoo.com; Khani, F. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of); Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)], E-mail: farzad_khani59@yahoo.com; Hamedi-Nezhad, S. [Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)
2007-10-29
In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple.
Derivation of relativistic wave equation from the Poisson process
Indian Academy of Sciences (India)
Tomoshige Kudo; Ichiro Ohba
2002-08-01
A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum.
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S. M. Sadatrasoul
2014-01-01
Full Text Available We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2, and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.
The Analysis of the Two-dimensional Diffusion Equation With a Source
Directory of Open Access Journals (Sweden)
Sunday Augustus REJU
2006-07-01
Full Text Available This study presents a new variant analysis and simulations of the two-dimensional energized wave equation remarkably different from the diffusion equations studied earlier studied. The objective functional and the dynamical energized wave are penalized to form a function called the Hamiltonian function. From this function, we obtained the necessary conditions for the optimal solutions using the maximum principle. By applying the Fourier solution to the first order differential equation, the analytical solutions for the state and control are obtained. The solutions are simulated to give visual physical interpretation of the waves and the numerical values.
Parker, E. N.
1985-01-01
The dynamics of magnetic fibrils in the convective zone of a star is investigated analytically, deriving mean-field equations for the two-dimensional transverse motion of an incompressible fluid containing numerous small widely spaced circular cylinders. The equations of Parker (1982) are extended to account for the inertial effects of local flow around the cylinders. The linear field equation for the stream function at the onset of convection is then rewritten, neglecting large-scale heat transport, and used to construct a model of convective counterflow. The Kelvin impulse and fluid momentum, convective motion initiated by a horizontal impulse, and the effects of a viscous boundary layer are considered in appendices.
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Vineet K., E-mail: vineetsriiitm@gmail.com [ISRO Telemetry, Tracking and Command Network (ISTRAC), Bangalore-560058 (India); Awasthi, Mukesh K. [Department of Mathematics, University of Petroleum and Energy Studies, Dehradun-248007 (India); Singh, Sarita [Department of Mathematics, WIT- Uttarakhand Technical University, Dehradun-248007 (India)
2013-12-15
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
Directory of Open Access Journals (Sweden)
Vineet K. Srivastava
2013-12-01
Full Text Available This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM, for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
Difference equations and cluster algebras I: Poisson bracket for integrable difference equations
Inoue, Rei
2010-01-01
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Liouville equation, from the view point of the general T-system and Y-system. We also study the Poisson structure for the cluster algebra, and give the associated Poisson bracket for the two difference equations.
Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schriidinger Equation
Institute of Scientific and Technical Information of China (English)
陈亚铭; 朱华君; 宋松和
2011-01-01
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
Regularity of Stagnation Point-form Solutions of the Two-dimensional Euler Equations
Sarria, Alejandro
2013-01-01
A class of semi-bounded solutions of the two-dimensional incompressible Euler equations, satisfying either periodic or Dirichlet boundary conditions, is examined. For smooth initial data, new blowup criteria in terms of the initial concavity profile is presented and the effects that the boundary conditions have on the global regularity of solutions is discussed. In particular, by deriving a formula for a general solution along Lagrangian trajectories, we describe how p...
Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2003-01-01
The subject of the paper is the derivation and analysis of third order finite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the first order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation from the piecewise constants, to feed into the calculation of the fluxes. We estimate the truncation error and give numerical examples to demonstrate the higher order...
Measurement of the Equation of State of the Two-Dimensional Hubbard Model
Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael
2016-05-01
The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 constitute benchmarks for state-of-the-art theoretical approaches.
Quadrature-free spline method for two-dimensional Navier-Stokes equation
Institute of Scientific and Technical Information of China (English)
HU Xian-liang; HAN Dan-fu
2008-01-01
In this paper,a quadrature-free scheme of spline method for two-dimensional Navier-Stokes equation is derived,which can dramatically improve the efficiency of spline method for fluid problems proposed by Lai and Wenston(2004). Additionally,the explicit formulation for boundary condition with up to second order derivatives is presented. The numerical simulations on several benchmark problems show that the scheme is very efficient.
Eventual Regularity of the Two-Dimensional Boussinesq Equations with Supercritical Dissipation
Jiu, Quansen; Wu, Jiahong; Yang, Wanrong
2015-02-01
This paper studies solutions of the two-dimensional incompressible Boussinesq equations with fractional dissipation. The spatial domain is a periodic box. The Boussinesq equations concerned here govern the coupled evolution of the fluid velocity and the temperature and have applications in fluid mechanics and geophysics. When the dissipation is in the supercritical regime (the sum of the fractional powers of the Laplacians in the velocity and the temperature equations is less than 1), the classical solutions of the Boussinesq equations are not known to be global in time. Leray-Hopf type weak solutions do exist. This paper proves that such weak solutions become eventually regular (smooth after some time ) when the fractional Laplacian powers are in a suitable supercritical range. This eventual regularity is established by exploiting the regularity of a combined quantity of the vorticity and the temperature as well as the eventual regularity of a generalized supercritical surface quasi-geostrophic equation.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
2016-10-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
Anti-periodic traveling wave solution to a forced two-dimensional generalized KdV-Burgers equation
Institute of Scientific and Technical Information of China (English)
TAN Junyu
2003-01-01
The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied.Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.
Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection
Anglin, J. R.; Schulz, A.
2017-01-01
Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for noninteracting fermions on a two-dimensional lattice [Qiao, Jung, and MacDonald, Nano Lett. 11, 3453 (2011), 10.1021/nl201941f; Qiao et al., Phys. Rev. Lett. 112, 206601 (2014), 10.1103/PhysRevLett.112.206601]. Here we confirm this result analytically in the corresponding continuum k .p model, by solving the associated two-dimensional Dirac equation, in the presence of a "checkerboard" potential that provides a right-angled intersection between two zero-line modes. The method by which we obtain our analytical solutions is systematic and potentially generalizable to similar problems involving intersections of one-dimensional systems.
Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation
Institute of Scientific and Technical Information of China (English)
Ying-xi Wang; Shuang-mu Linguang; Nan-rong Zhao; Yi-jing Yan
2011-01-01
A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change,compatible to the electron transfer process governed by atomic packing density model.We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively,and introduce the coupling effect coming from both fluctuations and equilibrium variances.The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived,based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique.We explicitly elaborate the short time and long time approximations.The relationship between the two-dimensional description and the one-dimensional theory is also discussed.
A high order multi-resolution solver for the Poisson equation with application to vortex methods
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Spietz, Henrik Juul; Walther, Jens Honore
A high order method is presented for solving the Poisson equation subject to mixed free-space and periodic boundary conditions by using fast Fourier transforms (FFT). The high order convergence is achieved by deriving mollified Green’s functions from a high order regularization function which...... provides a correspondingly smooth solution to the Poisson equation.The high order regularization function may be obtained analogous to the approximate deconvolution method used in turbulence models and strongly relates to deblurring algorithms used in image processing. At first we show that the regularized...... by super-positioning an inter-mesh correction. For sufficiently smooth vector fields this multi-resolution correction can be achieved without the loss of convergence rate. An implementation of the multi-resolution solver in a two-dimensional re-meshed particle-mesh based vortex method is presented...
Small global solutions to the damped two-dimensional Boussinesq equations
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong; Xu, Xiaojing
The two-dimensional (2D) incompressible Euler equations have been thoroughly investigated and the resolution of the global (in time) existence and uniqueness issue is currently in a satisfactory status. In contrast, the global regularity problem concerning the 2D inviscid Boussinesq equations remains widely open. In an attempt to understand this problem, we examine the damped 2D Boussinesq equations and study how damping affects the regularity of solutions. Since the damping effect is insufficient in overcoming the difficulty due to the “vortex stretching”, we seek unique global small solutions and the efforts have been mainly devoted to minimizing the smallness assumption. By positioning the solutions in a suitable functional setting (more precisely, the homogeneous Besov space B˚∞,11), we are able to obtain a unique global solution under a minimal smallness assumption.
A high order solver for the unbounded Poisson equation
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight......In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order...
Robust iterative observer for source localization for Poisson equation
Majeed, Muhammad Usman
2017-01-05
Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.
Kuiper, Logan K
2016-01-01
An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.
On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅰ)
Institute of Scientific and Technical Information of China (English)
HUANG Dai-wen; GUO Bo-ling
2007-01-01
The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered.It is assumed that the depth of the ocean is a positive constant.Firstly,if the initial data are square integrable,then by Fadeo-Galerkin method,the existence of the global weak solutions for the problem is obtained.Secondly, if the initial data and their vertical derivatives axe all square integrable,then by Faedo-Galerkin method and anisotropic inequalities,the existerce and uniqueness of the giobal weakly strong solution for the above initial boundary problem axe obtained.
On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅱ)
Institute of Scientific and Technical Information of China (English)
HUANG Dai-wen; GUO Bo-ling
2007-01-01
The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially.Here the depth of the ocean is positive but not always a constant.By Faedo-Galerkin method and anisotropic inequalities,the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained.Moreover,by studying the asymptotic behavior of solutions for the above problem,the energy is exponential decay with time is proved.
Cellular neural network analysis for two-dimensional bioheat transfer equation.
Niu, J H; Wang, H Z; Zhang, H X; Yan, J Y; Zhu, Y S
2001-09-01
The cellular neural network (CNN) method is applied to solve the Pennes bioheat transfer equation, and its feasibility is demonstrated. Numerical solutions were obtained for a cellular neural network for a two-dimensional steady-state temperature field obtained from focused and unfocused ultrasound heat sources. Transient-state temperature fields were also studied and compared with experimental results obtained elsewhere. The cellular neural networks' key features of asynchronous parallel processing, continuous-time dynamics and local interaction enable real-time temperature field estimation for clinical hyperthermia.
Ultrashort light bullets described by the two-dimensional sine-Gordon equation
Leblond, Hervé; 10.1103/PHYSREVA.81.063815
2011-01-01
By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...
Exact Solutions of Two-dimensional and Tri-dimensional Consolidation Equations
Di Francesco, Romolo
2011-01-01
The exact solution of Terzaghi's consolidation equation has further highlighted the limits of this theory in the one-dimensional field as, like Taylor's approximate solution, it overestimates the decay times of the phenomenon; on the other hand, one only needs to think about the accumulation pattern of sedimentary-basin soils to understand how their internal structure fits in more with the model of transversely isotropic medium, so as to result in the development of two- and three-dimensional consolidation models. This is the reason why, using Terzaghi's theory and his exact solution as starting point, two-dimensional and three-dimensional consolidation equations have been proposed, in an attempt to find their corresponding exact solutions which constitute more reliable forecasting models. Lastly, results show how this phenomenon is predominantly influenced by the dimensions of the horizontal plane affected by soil consolidation and permeabilities that behave according to three coordinate axes.
Generalized scale-invariant solutions to the two-dimensional stationary Navier-Stokes equations
Guillod, Julien
2014-01-01
New explicit solutions to the incompressible Navier-Stokes equations in $\\mathbb{R}^{2}\\setminus\\left\\{ \\boldsymbol{0}\\right\\}$ are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant under a particular combination of the scaling and rotational symmetries. They are the only solutions invariant under this new symmetry in the same way as the Hamel solutions are the only scale-invariant solutions. While the Hamel solutions are parameterized by a discrete parameter $n$, the flux $\\Phi$ and an angle $\\theta_{0}$, the new solutions generalize the Hamel solutions by introducing an additional parameter $a$ which produces a rotation. The new solutions decay like $\\left|\\boldsymbol{x}\\right|^{-1}$ as the Hamel solutions, and exhibit spiral behavior. The new variety of asymptotes induced by the existence of these solutions further emphasizes the difficulties faced when trying to establish the asymptotic behavior of the Navier-Stokes equations in a two-dimensional ...
Stability of Schr(o)dinger-Poisson type equations
Institute of Scientific and Technical Information of China (English)
Juan HUANG; Jian ZHANG; Guang-gan CHEN
2009-01-01
Variational methods are used to study the nonlinear Schr(o)dinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Halniltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.
Solving the Poisson partial differential equation using vector space projection methods
Marendic, Boris
This research presents a new approach at solving the Poisson partial differential equation using Vector Space Projection (VSP) methods. The work attacks the Poisson equation as encountered in two-dimensional phase unwrapping problems, and in two-dimensional electrostatic problems. Algorithms are developed by first considering simple one-dimensional cases, and then extending them to two-dimensional problems. In the context of phase unwrapping of two-dimensional phase functions, we explore an approach to the unwrapping using a robust extrapolation-projection algorithm. The unwrapping is done iteratively by modification of the Gerchberg-Papoulis (GP) extrapolation algorithm, and the solution is refined by projecting onto the available global data. An important contribution to the extrapolation algorithm is the formulation of the algorithm with the relaxed bandwidth constraint, and the proof that such modified GP extrapolation algorithm still converges. It is also shown that the unwrapping problem is ill-posed in the VSP setting, and that the modified GP algorithm is the missing link to pushing the iterative algorithm out of the trap solution under certain conditions. Robustness of the algorithm is demonstrated through its performance in a noisy environment. Performance is demonstrated by applying it to phantom phase functions, as well as to the real phase functions. Results are compared to well known algorithms in literature. Unlike many existing unwrapping methods which perform unwrapping locally, this work approaches the unwrapping problem from a globally, and eliminates the need for guiding instruments, like quality maps. VSP algorithm also very effectively battles problems of shadowing and holes, where data is not available or is heavily corrupted. In solving the classical Poisson problems in electrostatics, we demonstrate the effectiveness and ease of implementation of the VSP methodology to solving the equation, as well as imposing of the boundary conditions
National Research Council Canada - National Science Library
S Pamuk; N Pamuk
2014-01-01
In this paper, we obtain the particular exact solutions of the two-dimensional heat and mass transfer equation with power-law temperature-dependent thermal con- ductivity using the Adomian's decomposition method...
Non-Lie Symmetry Group and New Exact Solutions for the Two-Dimensional KdV-Burgers Equation
Institute of Scientific and Technical Information of China (English)
WANG Hong; TIAN Ying-Hui; CHEN Han-Lin
2011-01-01
@@ By using the modified Clarkson-Kruskal (CK) direct method, we obtain the non-Lie symmetry group of the two-dimensional KdV-Burgers equation.Under some constraint conditions, Lie point symmetry is also obtained.Through the symmetry group, some new exact solutions of the two-dimensional KdV-Burgers equation are found.%By using the modified Clarkson-Kruskal (CK) direct method, we obtain the non-Lie symmetry group of the two-dimensional KdV-Burgers equation. Under some constraint conditions, Lie point symmetry is also obtained.Through the symmetry group, some new exact solutions of the two-dimensional KdV-Burgers equation are found.
Arikan, Orhan
1994-05-01
Well bore measurements of conductivity, gravity, and surface measurements of magnetotelluric fields can be modeled as a two-dimensional integral equation with additive measurement noise. The governing integral equation has the form of convolution in the first dimension and projection in the second dimension. However, these two operations are not in separable form. In these applications, given a set of measurements, efficient and robust estimation of the underlying physical property is required. For this purpose, a regularized inversion algorithm for the governing integral equation is presented in this paper. Singular value decomposition of the measurement kernels is used to exploit convolution-projection structure of the integral equation, leading to a form where measurements are related to the physical property by a two-stage operation: projection followed by convolution. On the other hand, estimation of the physical property can be carried out by a two-stage inversion algorithm: deconvolution followed by back projection. A regularization method for the required multichannel deconvolution is given. Some important details of the algorithm are addressed in an application to wellbore induction measurements of conductivity.
Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations
Guoqiang, Han; Jiong, Wang
2001-09-01
In this paper, we analyze the existence of asymptotic error expansion of the Nystrom solution for two-dimensional nonlinear Fredholm integral equations of the second kind. We show that the Nystrom solution admits an error expansion in powers of the step-size h and the step-size k. For a special choice of the numerical quadrature, the leading terms in the error expansion for the Nystrom solution contain only even powers of h and k, beginning with terms h2p and k2q. These expansions are useful for the application of Richardson extrapolation and for obtaining sharper error bounds. Numerical examples show that how Richardson extrapolation gives a remarkable increase of precision, in addition to faster convergence.
The solution of the two-dimensional sine-Gordon equation using the method of lines
Bratsos, A. G.
2007-09-01
The method of lines is used to transform the initial/boundary-value problem associated with the two-dimensional sine-Gordon equation in two space variables into a second-order initial-value problem. The finite-difference methods are developed by replacing the matrix-exponential term in a recurrence relation with rational approximants. The resulting finite-difference methods are analyzed for local truncation error, stability and convergence. To avoid solving the nonlinear system a predictor-corrector scheme using the explicit method as predictor and the implicit as corrector is applied. Numerical solutions for cases involving the most known from the bibliography line and ring solitons are given.
Malkov, Ewgenij A.; Poleshkin, Sergey O.; Kudryavtsev, Alexey N.; Shershnev, Anton A.
2016-10-01
The paper presents the software implementation of the Boltzmann equation solver based on the deterministic finite-difference method. The solver allows one to carry out parallel computations of rarefied flows on a hybrid computational cluster with arbitrary number of central processor units (CPU) and graphical processor units (GPU). Employment of GPUs leads to a significant acceleration of the computations, which enables us to simulate two-dimensional flows with high resolution in a reasonable time. The developed numerical code was validated by comparing the obtained solutions with the Direct Simulation Monte Carlo (DSMC) data. For this purpose the supersonic flow past a flat plate at zero angle of attack is used as a test case.
Directory of Open Access Journals (Sweden)
Boričić Zoran
2009-01-01
Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation
Lannes, David
2007-01-01
A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \\cite{matsuno3} and Choi \\cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equati...
Institute of Scientific and Technical Information of China (English)
GONG Lun-Xun; CAO Jian-Li; PAN Jun-Ting; ZHANG Hua; JIAO Wan-Tang
2008-01-01
Based on the second integrable case of known two-dimensional Hamiltonian system with a quartic potential, we propose a 4×4 matrix spectral problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differential equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable case of the two-dimensional Hamiltonian system.
Indian Academy of Sciences (India)
ALY R SEADAWY
2017-09-01
Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the twodimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraicmethods. We found the electrostatic field potential and electric field in the form travellingwave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of $\\it{Mathematica}$ program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
Directory of Open Access Journals (Sweden)
Chunye Gong
2014-01-01
Full Text Available It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE with iterative implicit finite difference method is O(MxMyN2. In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
Wang, Zhiheng
2014-12-10
A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.
Gauge Poisson representations for birth/death master equations
Drummond, P D
2002-01-01
Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes - found in many fields of physics, chemistry and biology - into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a stochastic gauge technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results...
Stochastic poisson equations associated to lie algebroids and some refinements of a principal bundle
Ivan, Gheorghe
2010-01-01
The aim of this paper is to present the stochastic Poisson equations associated to Lie algebroids. The stochastic Poisson equations associated to a refinement of a concrete principal bundle are determined.
Directory of Open Access Journals (Sweden)
S.I. Denisov
2013-10-01
Full Text Available Using the modified stochastic Landau-Lifshitz equation driven by Poisson white noise, we derive the generalized Fokker-Planck equation for the probability density function of the nanoparticle magnetic moment. In our calculations we employ the Ito interpretation of stochastic equations and take into account the fact that the magnetic moment direction can be changed by this noise instantaneously. The analysis of the stationary solution of the generalized Fokker-Planck equation shows that the distribution of the free magnetic moment in Poisson white noise is not uniform. This feature of the stationary distribution arises from using the Ito interpretation of the stochastic Landau-Lifshitz equation.
Tone, Florentina
2011-01-01
Pursuing our work in [18], [17], [20], [5], we consider in this article the two-dimensional thermohydraulics equations. We discretize these equations in time using the implicit Euler scheme and we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.
Quenched dynamics of two-dimensional solitons and vortices in the Gross-Pitaevskii equation
Chen, Qian-Yong; Malomed, Boris A
2012-01-01
We consider a two-dimensional (2D) counterpart of the experiment that led to the creation of quasi-1D bright solitons in Bose-Einstein condensates (BECs) [Nature 417, 150--153 (2002)]. We start by identifying the ground state of the 2D Gross-Pitaevskii equation for repulsive interactions, with a harmonic-oscillator (HO) trap, and with or without an optical lattice (OL). Subsequently, we switch the sign of the interaction to induce interatomic attraction and monitor the ensuing dynamics. Regions of the stable self-trapping and catastrophic collapse of 2D fundamental solitons are identified in the parameter plane of the OL strength and BEC norm. The increase of the OL strength expands the persistence domain for the solitons to larger norms. For single-charged solitary vortices, in addition to the survival and collapse regimes, an intermediate one is identified, where the vortex resists the collapse but loses its structure, transforming into a fundamental soliton. The same setting may also be implemented in the ...
Numerical investigations on the finite time singularity in two-dimensional Boussinesq equations
Yin, Z
2006-01-01
To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system describes a cap-like hot zone of fluid rising from the bottom, while the edges of the cap lag behind, forming eye-like vortices. The hot liquid is driven by the buoyancy and meanwhile attracted by the vortices, which leads to the singularity-forming mechanism in our simulation. In the previous 2D Boussinesq simulations, the symmetricial initial data is used. However, it is observed that the adoption of symmetry leads to coordinate singularity. Moreover, as demonstrated in this work that the locations of peak values for the vorticity and the temperature gradient becomes far apart as $t$ approaches the predicted blow-up time. This suggests that the symmetry assumption may be unreasonable for searching solution blow-ups. One of the main contributions of this work is to propose a...
General solution of the Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2016-06-15
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.
Hamiltonian structure for two-dimensional extended Green-Naghdi equations
Matsuno, Yoshimasa
2016-06-01
The two-dimensional Green-Naghdi (GN) shallow-water model for surface gravity waves is extended to incorporate the arbitrary higher-order dispersive effects. This can be achieved by developing a novel asymptotic analysis applied to the basic nonlinear water wave problem. The linear dispersion relation for the extended GN system is then explored in detail. In particular, we use its characteristics to discuss the well-posedness of the linearized problem. As illustrative examples of approximate model equations, we derive a higher-order model that is accurate to the fourth power of the dispersion parameter in the case of a flat bottom topography, and address the related issues such as the linear dispersion relation, conservation laws and the pressure distribution at the fluid bottom on the basis of this model. The original Green-Naghdi (GN) model is then briefly described in the case of an uneven bottom topography. Subsequently, the extended GN system presented here is shown to have the same Hamiltonian structure as that of the original GN system. Last, we demonstrate that Zakharov's Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.
Time integration algorithms for the two-dimensional Euler equations on unstructured meshes
Slack, David C.; Whitaker, D. L.; Walters, Robert W.
1994-06-01
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
Positioning in a flat two-dimensional space-time: the delay master equation
Coll, Bartolomé; Morales-Lladosa, Juan Antonio
2010-01-01
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\\bf 73}, 084017 (2006); {\\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. We illustrate these result...
Poisson-Nernst-Planck equations in a ball
Cartailler, Z Schuss J
2015-01-01
The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratu-type equation with the difference that the boundary condition is Neumann, not Dirichlet and there a minus sign in the exponent of the exponential term. The entire boundary is impermeable to the ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct a steady radial solution and find that the potential is maximal in the center and decreases toward the boundary. We study the limit of large charge in dimension 1,2 and 3. For the case of a small absorbing window in the sphere, we find the escape rate of an ion from the steady density.
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2014-06-01
Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.
Generalized master equations for non-Poisson dynamics on networks
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.
Localization of Point Sources for Poisson Equation using State Observers
Majeed, M. U.
2016-08-09
A method based On iterative observer design is presented to solve point source localization problem for Poisson equation with riven boundary data. The procedure involves solution of multiple boundary estimation sub problems using the available Dirichlet and Neumann data from different parts of the boundary. A weighted sum of these solution profiles of sub-problems localizes point sources inside the domain. Method to compute these weights is also provided. Numerical results are presented using finite differences in a rectangular domain. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
H. S. Shukla
2014-11-01
Full Text Available In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
Institute of Scientific and Technical Information of China (English)
XING Yong-Zhong
2009-01-01
The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.
Asymptotic Preserving schemes for highly oscillatory Vlasov–Poisson equations
Energy Technology Data Exchange (ETDEWEB)
Crouseilles, Nicolas [INRIA-Rennes Bretagne Atlantique, IPSO Project (France); Lemou, Mohammed [CNRS and IRMAR, Université de Rennes 1 and INRIA-Rennes Bretagne Atlantique, IPSO Project (France); Méhats, Florian, E-mail: florian.mehats@univ-rennes1.fr [IRMAR, Université de Rennes 1 and INRIA-Rennes Bretagne Atlantique, IPSO Project (France)
2013-09-01
This work is devoted to the numerical simulation of a Vlasov–Poisson model describing a charged particle beam under the action of a rapidly oscillating external field. We construct an Asymptotic Preserving numerical scheme for this kinetic equation in the highly oscillatory limit. This scheme enables to simulate the problem without using any time step refinement technique. Moreover, since our numerical method is not based on the derivation of the simulation of asymptotic models, it works in the regime where the solution does not oscillate rapidly, and in the highly oscillatory regime as well. Our method is based on a “two scale” reformulation of the initial equation, with the introduction of an additional periodic variable.
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe
2015-06-01
In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e......We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show...
Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/43/37/375209
2010-01-01
We show that the two-dimensional, nonlinear Schr\\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.
High-order Hamiltonian splitting for Vlasov-Poisson equations
Casas, Fernando; Faou, Erwan; Mehrenberger, Michel
2015-01-01
We consider the Vlasov-Poisson equation in a Hamiltonian framework and derive new time splitting methods based on the decomposition of the Hamiltonian functional between the kinetic and electric energy. Assuming smoothness of the solutions, we study the order conditions of such methods. It appears that these conditions are of Runge-Kutta-Nystr{\\"o}m type. In the one dimensional case, the order conditions can be further simplified, and efficient methods of order 6 with a reduced number of stages can be constructed. In the general case, high-order methods can also be constructed using explicit computations of commutators. Numerical results are performed and show the benefit of using high-order splitting schemes in that context. Complete and self-contained proofs of convergence results and rigorous error estimates are also given.
Institute of Scientific and Technical Information of China (English)
Bai Jing-Song; Zhang Zhan-Ji; Li Ping; Zhong Min
2006-01-01
Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional (2D) multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.
Fang, Li; Guo, Zhenhua
2016-04-01
The aim of this paper is to establish the global well-posedness and large-time asymptotic behavior of the strong solution to the Cauchy problem of the two-dimensional compressible Navier-Stokes equations with vacuum. It is proved that if the shear viscosity {μ} is a positive constant and the bulk viscosity {λ} is the power function of the density, that is, {λ=ρ^{β}} with {β in [0,1],} then the Cauchy problem of the two-dimensional compressible Navier-Stokes equations admits a unique global strong solution provided that the initial data are of small total energy. This result can be regarded as the extension of the well-posedness theory of classical compressible Navier-Stokes equations [such as Huang et al. (Commun Pure Appl Math 65:549-585, 2012) and Li and Xin (http://arxiv.org/abs/1310.1673) respectively]. Furthermore, the large-time behavior of the strong solution to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations had been also obtained.
Marco Pedro Ramirez-Tachiquin; Cesar Marco Antonio Robles Gonzalez; Rogelio Adrian Hernandez-Becerril; Ariana Guadalupe Bucio Ramirez
2013-01-01
Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichlet boundary value problem corresponding to the two-dimensional electrical impedance equation. The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unit circle. To warrant the effectiveness of the posed method, we consider several examples of conductivity functions, whose boundary condi...
Directory of Open Access Journals (Sweden)
shadan sadigh behzadi
2012-03-01
Full Text Available In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i Modified Adomian decomposition method (MADM, (ii Variational iteration method (VIM, (iii Homotopy analysis method (HAM and (iv Modified homotopy perturbation method (MHPM. The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.
Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon
2017-09-01
Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.
Poisson brackets of mappings obtained as ( q,- p) reductions of lattice equations
Tran, Dinh T.; van der Kamp, Peter H.; Quispel, G. R. W.
2016-11-01
In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived from a Lagrangian, using the so-called Ostrogradsky transformation. The ( q,- p) reductions are ( p + q)-dimensional maps and explicit Poisson brackets for such reductions of the discrete KdV equation, the discrete Lotka-Volterra equation, and the discrete Liouville equation are included. Lax representations of these equations can be used to construct sufficiently many integrals for the reductions. As examples we show that the (3,-2) reductions of the integrable partial difference equations are Liouville integrable in their own right.
Directory of Open Access Journals (Sweden)
Mohammad Siddique
2010-08-01
Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
Multilevel Methods for the Poisson-Boltzmann Equation
Holst, Michael Jay
We consider the numerical solution of the Poisson -Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial differential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coefficients representing material interfaces, rapid nonlinearities, and three spatial dimensions. Similar equations occur in various applications, including nuclear physics, semiconductor physics, population genetics, astrophysics, and combustion. In this thesis, we study the PBE, discretizations, and develop multilevel-based methods for approximating the solutions of these types of equations. We first outline the physical model and derive the PBE, which describes the electrostatic potential of a large complex biomolecule lying in a solvent. We next study the theoretical properties of the linearized and nonlinear PBE using standard function space methods; since this equation has not been previously studied theoretically, we provide existence and uniqueness proofs in both the linearized and nonlinear cases. We also analyze box-method discretizations of the PBE, establishing several properties of the discrete equations which are produced. In particular, we show that the discrete nonlinear problem is well-posed. We study and develop linear multilevel methods for interface problems, based on algebraic enforcement of Galerkin or variational conditions, and on coefficient averaging procedures. Using a stencil calculus, we show that in certain simplified cases the two approaches are equivalent, with different averaging procedures corresponding to different prolongation operators. We also develop methods for nonlinear problems based on a nonlinear multilevel method, and on linear multilevel methods combined with a globally convergent damped-inexact-Newton method. We derive a necessary and sufficient descent condition for the inexact-Newton direction, enabling the development of extremely
Tomé, M. F.; Bertoco, J.; Oishi, C. M.; Araujo, M. S. B.; Cruz, D.; Pinho, F. T.; Vynnycky, M.
2016-04-01
This work is concerned with the numerical solution of the K-BKZ integral constitutive equation for two-dimensional time-dependent free surface flows. The numerical method proposed herein is a finite difference technique for simulating flows possessing moving surfaces that can interact with solid walls. The main characteristics of the methodology employed are: the momentum and mass conservation equations are solved by an implicit method; the pressure boundary condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times t‧ is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by a second-order Runge-Kutta method. This new technique is verified by solving shear and uniaxial elongational flows. Furthermore, an analytic solution for fully developed channel flow is obtained that is employed in the verification and assessment of convergence with mesh refinement of the numerical solution. For free surface flows, the assessment of convergence with mesh refinement relies on a jet impinging on a rigid surface and a comparison of the simulation of a extrudate swell problem studied by Mitsoulis (2010) [44] was performed. Finally, the new code is used to investigate in detail the jet buckling phenomenon of K-BKZ fluids.
A Finite-Element Solution of the Navier-Stokes Equations for Two-Dimensional and Axis-Symmetric Flow
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Sven Ø. Wille
1980-04-01
Full Text Available The finite element formulation of the Navier-Stokes equations is derived for two-dimensional and axis-symmetric flow. The simple triangular, T6, isoparametric element is used. The velocities are interpolated by quadratic polynomials and the pressure is interpolated by linear polynomials. The non-linear simultaneous equations are solved iteratively by the Newton-Raphson method and the element matrix is given in the Newton-Raphson form. The finite element domain is organized in substructures and an equation solver which works on each substructure is specially designed. This equation solver needs less storage in the computer and is faster than the traditional banded equation solver. To reduce the amount of input data an automatic mesh generator is designed. The input consists of the coordinates of eight points defining each substructure with the corresponding boundary conditions. In order to interpret the results they are plotted on a calcomp plotter. Examples of plots of the velocities, the streamlines and the pressure inside a two-dimensional flow divider and an axis-symmetric expansion of a tube are shown for various Reynolds numbers.
A correction on two dimensional KdV equation with topography
Institute of Scientific and Technical Information of China (English)
XU Zhaoting; Efim PELINOVSKY; SHEN Guojin; Tapiana TALIPOVA
2004-01-01
The correction on the 2D KdV equation derived by Djordjevic and Redekopp is presented. A lapsus calami in the 2D KdV equation is removed by means of the conservation principle of the energy flux in a wave ray tube. The results show that the coefficient of the third term in the inhomogeneous term of 2D KdV equation in the paper of Djordjevic and Redekopp is 2, instead of 3.
Initial and Boundary Value Problems for Two-Dimensional Non-hydrostatic Boussinesq Equations
Institute of Scientific and Technical Information of China (English)
沈春; 孙梅娜
2005-01-01
Based on the theory of stratification, the weU-posedness of the initial and boundary value problems for the system of twodimensional non-hydrostatic Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for some representative initial and boundary value problems. Several special cases were discussed.
Construction of Green's Functions for the Two-Dimensional Static Klein-Gordon Equation
Institute of Scientific and Technical Information of China (English)
MELNIKOV Yu. A.
2011-01-01
In contrast to the cognate Laplace equation, for which a vast number of Green's functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion.This study is based on our experience recently gained on the construction of Green's functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computerfriendly representations of their Green's functions are obtained, most of which have never been published before.
Szmelter, J.; Marchant, M. J.; Evans, A.; Weatherill, N. P.
A cell vertex finite volume Jameson scheme is used to solve the 2D compressible, laminar, viscous fluid flow equations on locally embedded multiblock meshes. The proposed algorithm is applicable to both the Euler and Navier-Stokes equations. It is concluded that the adaptivity method is very successful in efficiently improving the accuracy of the solution. Both the mesh generator and the flow equation solver which are based on a quadtree data structure offer good flexibility in the treatment of interfaces. It is concluded that methods under consideration lead to accurate flow solutions.
Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.
1997-01-01
Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.
CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION
Institute of Scientific and Technical Information of China (English)
Benyu Guo; Songnian He; Heping Ma
2002-01-01
A mixed Chebyshev spectral-finite element method is proposed for solving two-dimensionalunsteady Navier-Stokes equation. The generalized stability and convergence are proved.The numerical results show the advantages of this method.
Two-Dimensional Saddle Point Equation of Ginzburg-Landau Hamiltonian for the Diluted Ising Model
Institute of Scientific and Technical Information of China (English)
WU Xin-Tian
2006-01-01
@@ The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
From Discreteness to Continuity: Dislocation Equation for Two-Dimensional Triangular Lattice
Institute of Scientific and Technical Information of China (English)
WANG Shao-Feng
2007-01-01
@@ A systematic method from the discreteness to the continuity is presented for the dislocation equation of the triangular lattice. A modification of the Peierls equation has been derived strictly. The modified equation includes the higher order corrections of the discrete effect which are important for the core structure of dislocation. It is observed that the modified equation possesses a universal form which is model-independent except the factors.The factors, which depend on the detail of the model, are related to the derivatives of the kernel at its zero point in the wave-vector space. The results open a way to deal with the complicated models because what one needs to do is to investigate the behaviour near the zero point of the kernel in the wave-vector space instead of calculating the kernel completely.
Institute of Scientific and Technical Information of China (English)
HUANG RUI; YIN JING-XUE; WANG LIANG-WEI
2011-01-01
In this paper we consider the initial boundary value problem of CahnHilliard equation with concentration dependent mobility and gradient dependent potential. By the Lp type estimates and the theory of Morrey spaces, we prove the H(o)der continuity of the solutions. Then we obtain the existence of global classical solutions. The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.
An equation for pressure of a two-dimensional Yukawa liquid
Feng, Yan; Li, Wei; Wang, Qiaoling; Lin, Wei; Goree, John; Liu, Bin
2016-10-01
Thermodynamic behavior of two-dimensional (2D) dusty plasmas has been studied experimentally and theoretically recently. As a crucial parameter in thermodynamics, the pressure of dusty plasmas arises from frequent collisions of individual dust particles. Here, equilibrium molecular dynamical simulations were performed to study the pressure of 2D Yukawa liquids. A simple analytical expression for the pressure of a 2D Yukawa liquid is found by fitting the obtained pressure data over a wide range of temperatures, from the coldest close to the melting point, to the hottest about 70 times higher than the melting points. The obtained expression verifies that the pressure can be written as the sum of a potential term which is a simple multiple of the Coulomb potential energy at a distance of Wigner-Seitz radius, and a kinetic term which is a multiple of the one for an ideal gas. Dimensionless coefficients for each of these terms are found empirically, by fitting. The resulting analytical expression, with its empirically determined coefficients, is plotted as isochors, or curves of constant area. These results should be applicable to 2D dusty plasmas. Work in China supported by by the National Natural Science Foundation of China under Grant No. 11505124, the 1000 Youth Talents Plan, and startup funds from Soochow University. Work in the US supported by DOE & NSF.
Two-Dimensional Riemann Solver for Euler Equations of Gas Dynamics
Brio, M.; Zakharian, A. R.; Webb, G. M.
2001-02-01
We construct a Riemann solver based on two-dimensional linear wave contributions to the numerical flux that generalizes the one-dimensional method due to Roe (1981, J. Comput. Phys.43, 157). The solver is based on a multistate Riemann problem and is suitable for arbitrary triangular grids or any other finite volume tessellations of the plane. We present numerical examples illustrating the performance of the method using both first- and second-order-accurate numerical solutions. The numerical flux contributions are due to one-dimensional waves and multidimensional waves originating from the corners of the computational cell. Under appropriate CFL restrictions, the contributions of one-dimensional waves dominate the flux, which explains good performance of dimensionally split solvers in practice. The multidimensional flux corrections increase the accuracy and stability, allowing a larger time step. The improvements are more pronounced on a coarse mesh and for large CFL numbers. For the second-order method, the improvements can be comparable to the improvements resulting from a less diffusive limiter.
Zhang, Jiwei; Xu, Zhenli; Wu, Xiaonan
2009-04-01
This paper aims to design local absorbing boundary conditions (LABCs) for the two-dimensional nonlinear Schrödinger equations on a rectangle by extending the unified approach. Based on the time-splitting idea, the main process of the unified approach is to approximate the kinetic energy part by a one-way equation, unite it with the potential energy equation, and then obtain the well-posed and accurate LABCs on the artificial boundaries. In the corners, we use the (1,1)-Padé approximation to the kinetic term and also unite it with the nonlinear term to give some local corner boundary conditions. Numerical tests are given to verify the stable and tractable advantages of the method.
Note on a differentiation formula, with application to the two-dimensional Schrödinger equation
2017-01-01
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue problem for the two-dimensional Schrödinger equation, where standard methods converge very slowly while the approach proposed here gives accurate results. The presented approach has the merit of being conceptually simple and might prove useful in other instances. PMID:28178300
Zabihi, F.; Saffarian, M.
2016-07-01
The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.
Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the convergence of time-dependent Euler-Maxwell equations to compressible Euler-Poisson equations in a torus via the non-relativistic limit is studied.The local existence of smooth solutions to both systems is proved by using energy estimates for first order symmetrizable hyperbolic systems. For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order. The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2015-10-15
Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.
A Genuinely Two-Dimensional Scheme for the Compressible Euler Equations
Sidilkover, David
1996-01-01
We present a new genuinely multidimensional discretization for the compressible Euler equations. It is the only high-resolution scheme known to us where Gauss-Seidel relaxation is stable when applied as a smoother directly to the resulting high-resolution scheme. This allows us to construct a very simple and highly efficient multigrid steady-state solver. The scheme is formulated on triangular (possibly unstructured) meshes.
Numerical computation of the critical energy constant for two-dimensional Boussinesq equations
Kolkovska, N.; Angelow, K.
2015-10-01
The critical energy constant is of significant interest for the theoretical and numerical analysis of Boussinesq type equations. In the one-dimensional case this constant is evaluated exactly. In this paper we propose a method for numerical evaluation of this constant in the multi-dimensional cases by computing the ground state. Aspects of the numerical implementation are discussed and many numerical results are demonstrated.
The Difference Format of Landau-Lifshitz Equation in Two-dimensional Case
Directory of Open Access Journals (Sweden)
Zhong Taiyong
2015-01-01
Full Text Available In this paper, the author considers a difference scheme of Laudau-Lifshitz equation (LL for short and modulus of unj which are constantly remaining equal to 1. Using this iteration format error which is ordered to t/2h2 , the author comes to a conclusion based on several initial simulations. According to some conditions, the author gives the numerical solution, the examples of exact solution and the error comparisons of the solutions.
MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1997-10-01
A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)
Energy Technology Data Exchange (ETDEWEB)
Chen, Yong [Ningbo Univ., Ningbo (China). Department of Mathematics; Shanghai Jiao-Tong Univ., Shangai (China). Department of Physics; Chinese Academy of sciences, Beijing (China). Key Laboratory of Mathematics Mechanization
2005-03-01
A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion.
T., M P Ramirez; Hernandez-Becerril, R A
2012-01-01
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation. The analysis is performed by interpolating piecewise separable-variables conductivity functions, that are eventually used in the numerical calculations in order to obtain finite sets of orthonormal functions, whose linear combinations succeed to approach the imposed boundary conditions. To warrant the effectiveness of the numerical method, we study six different examples of conductivity. The boundary condition for every case is selected considering one exact solution of the Electrical Impedance Equation. The work intends to discuss the contributions of these results into the field of the Electrical Impedance Tomography.
Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
B. A. Jacobs
2014-01-01
Full Text Available A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.
Ying, Michael; Yung, Dennis M C; Ho, Karen K L
2008-01-01
This study aimed to develop a new two-dimensional (2-D) ultrasound thyroid volume estimation equation using three-dimensional (3-D) ultrasound as the standard of reference, and to compare the thyroid volume estimation accuracy of the new equation with three previously reported equations. 2-D and 3-D ultrasound examinations of the thyroid gland were performed in 150 subjects with normal serum thyrotropin (TSH, thyroid-stimulating hormone) and free thyroxine (fT4) levels (63 men and 87 women, age range: 17 to 71 y). In each subject, the volume of both thyroid lobes was measured by 3-D ultrasound. On 2-D ultrasound, the craniocaudal (CC), lateromedial (LM) and anteroposterior (AP) dimensions of the thyroid lobes were measured. The equation was derived by correlating the volume of the thyroid lobes measured with 3-D ultrasound and the product of the three dimensions measured with 2-D ultrasound using linear regression analysis, in 75 subjects without thyroid nodule. The accuracy of thyroid volume estimation of the new equation and the three previously reported equations was evaluated and compared in another 75 subjects (without thyroid nodule, n = 30; with thyroid nodule, n = 45). It is suggested that volume of thyroid lobe may be estimated as: volume of thyroid lobe = 0.38.(CC.LM.AP) + 1.76. Result showed that the new equation (16.9% to 36.1%) had a significantly smaller thyroid volume estimation error than the previously reported equations (20.8% to 54.9%) (p thyroid volume estimation error when thyroid glands with nodules were examined (p thyroid volume equation, 2-D ultrasound can be a useful alternative in thyroid volume measurement when 3-D ultrasound is not available.
Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type
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Kulenović MRS
2011-01-01
Full Text Available Abstract We investigate global dynamics of the following systems of difference equations x n + 1 = α 1 + β 1 x n A 1 + y n y n + 1 = γ 2 y n A 2 + B 2 x n + y n , n = 0 , 1 , 2 , … where the parameters α 1, β 1, A 1, γ 2, A 2, B 2 are positive numbers, and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. We show that this system has rich dynamics which depends on the region of parametric space. We show that the basins of attractions of different locally asymptotically stable equilibrium points or non-hyperbolic equilibrium points are separated by the global stable manifolds of either saddle points or non-hyperbolic equilibrium points. We give examples of a globally attractive non-hyperbolic equilibrium point and a semi-stable non-hyperbolic equilibrium point. We also give an example of two local attractors with precisely determined basins of attraction. Finally, in some regions of parameters, we give an explicit formula for the global stable manifold. Mathematics Subject Classification (2000 Primary: 39A10, 39A11 Secondary: 37E99, 37D10
Aizawa, N.; Kuznetsova, Z.; Toppan, F.
2016-04-01
Conformal Galilei algebras (CGAs) labeled by d, ℓ (where d is the number of space dimensions and ℓ denotes a spin-ℓ representation w.r.t. the 𝔰𝔩(2) subalgebra) admit two types of central extensions, the ordinary one (for any d and half-integer ℓ) and the exotic central extension which only exists for d = 2 and ℓ ∈ ℕ. For both types of central extensions, invariant second-order partial differential equations (PDEs) with continuous spectrum were constructed by Aizawa et al. [J. Phys. A 46, 405204 (2013)]. It was later proved by Aizawa et al. [J. Math. Phys. 3, 031701 (2015)] that the ordinary central extensions also lead to oscillator-like PDEs with discrete spectrum. We close in this paper the existing gap, constructing a new class of second-order invariant PDEs for the exotic centrally extended CGAs; they admit a discrete and bounded spectrum when applied to a lowest weight representation. These PDEs are markedly different with respect to their ordinary counterparts. The ℓ = 1 case (which is the prototype of this class of extensions, just like the ℓ = /1 2 Schrödinger algebra is the prototype of the ordinary centrally extended CGAs) is analyzed in detail.
Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations
Lacave, Christophe; Masmoudi, Nader
2016-09-01
We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size {\\varepsilon} separated by distances {d_{\\varepsilon}} and the fluid fills the exterior. If the inclusions are distributed on the unit square, the asymptotic behavior depends on the limit of {d_{\\varepsilon}}\\varepsilon} when {\\varepsilon} goes to zero. If {frac{d_{\\varepsilon}}\\varepsilon to infty}, then the limit motion is not perturbed by the porous medium, namely, we recover the Euler solution in the whole space. If, on the contrary, {frac{d_{\\varepsilon}}\\varepsilon to 0}, then the fluid cannot penetrate the porous region, namely, the limit velocity verifies the Euler equations in the exterior of an impermeable square. If the inclusions are distributed on the unit segment then the behavior depends on the geometry of the inclusion: it is determined by the limit of {frac{d_{\\varepsilon}/\\varepsilon^{2+frac1γ}} where {γ in (0,infty]} is related to the geometry of the lateral boundaries of the obstacles. If {d_{\\varepsilon}/\\varepsilon^{2+frac1γ} to infty}, then the presence of holes is not felt at the limit, whereas an impermeable wall appears if this limit is zero. Therefore, for a distribution in one direction, the critical distance depends on the shape of the inclusions; in particular, it is equal to {\\varepsilon3} for balls.
Instability theory of the Navier-Stokes-Poisson equations
Jang, Juhi
2011-01-01
The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with adiabatic exponent $6/5 < \\gamma < 4/3$.
Institute of Scientific and Technical Information of China (English)
SONG; Yuquan(宋玉泉); LIU; Shumei(刘术梅)
2002-01-01
Superplastic forming has been extensively applied to manufacture parts and components with complex shapes or high-precisions. However, superplastic formation is in multi-stress state. In a long time, uniaxial tensile constitutive equation has been directly generalized to deal with multi-stress state. Whether so doing is feasible or not needs to be proved in theory. This paper first summarizes the establishing processes of superplastic tensile and bulging constitutive equation with variable m, and, using the analytical expressions of equivalent stress ? and equivalent strain rateof free bulge based on the fundamentals of continuum medium plastic mechanics, derives the analytical expressions of optimum loading rules for superplastic free bulge. By comparing the quantitative results on typical superplastic alloy ZnAl22, it is shown that one-dimensional tensile constitutive equations cannot be directly generalized to deal with two-dimensional bulging quantitative mechanical problems; only superplastic bulging constitutive equation based on bulging stress state can be used to treat the quantitative mechanical problems of bulge.
AN ACCURATE SOLUTION OF THE POISSON EQUATION BY THE FINITE DIFFERENCE-CHEBYSHEV-TAU METHOD
Institute of Scientific and Technical Information of China (English)
Hani I. Siyyam
2001-01-01
A new finite difference-Chebyshev-Tau method for the solution of the twodimensional Poisson equation is presented. Some of the numerical results are also presented which indicate that the method is satisfactory and compatible to other methods.
Energy Technology Data Exchange (ETDEWEB)
Yao Yuqin [College of Sciences, Shanghai University, Shanghai 200436 (China)] e-mail: yyqinw@126.com
2005-11-01
In this paper, based on the well-known Sine-Poisson equation, a new Sine-Poisson equation expansion method with constant coefficients or variable coefficients is presented, which can be used to construct more new exact solutions of nonlinear evolution equations in mathematical physics. The KdV-mKdV equation and the typical breaking soliton equation are chosen to illustrate our method such that many types of new exact solutions are obtained, which include exponential solutions, kink-shaped solutions, singular solutions and soliton-like solutions.
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang [Department of Physics, Ho Chi Minh City University of Pedagogy, 280 An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-05-15
The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.
Directory of Open Access Journals (Sweden)
M. G. Hafez
2016-01-01
Full Text Available Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons.
Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations.
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)]PRLTAO0031-900710.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.
Convergence of the Vlasov-Poisson-Fokker- Planck system to the incompressible Euler equations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We establish the convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations in this paper. The convergence is rigorously proved on the time interval where the smooth solution to the incompressible Euler equations exists. The proof relies on the compactness argument and the so-called relative-entropy method.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Because of the strong structural sensitivity of superplasticity, the deformation rule must be affected by stress-state. It is necessary to prove whether one-dimensional tensile constitutive equation can be directly generalized to deal with the two-dimensional mechanical problems or not. In this paper, theoretical results of fill-forming bulge have been derived from both one-dimensional tensile and two-dimensional bulging constitutive equation with variable m value. By comparing theoretical analysis and experimental results made on typical superplastic alloy Zn-wt22%Al, it is shown that one-dimensional tensile constitutive equation cannot be directly generalized to deal with two-dimensional mechanical questions. A method to correct deviation between theoretical and experimental results is also proposed.
A multiresolution method for solving the Poisson equation using high order regularization
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Walther, Jens Honore
2016-01-01
We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches and regulari......We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches...... and regularized Green's functions corresponding to the difference in the spatial resolution between the patches. The full solution is obtained utilizing the linearity of the Poisson equation enabling super-position of solutions. We show that the multiresolution Poisson solver produces convergence rates...... that correspond to the regularization order of the derived Green's functions....
High-order finite-difference methods for Poisson's equation
van Linde, Hendrik Jan
1971-01-01
In this thesis finite-difference approximations to the three boundary value problems for Poisson’s equation are given, with discretization errors of O(H^3) for the mixed boundary value problem, O(H^3 |ln(h)| for the Neumann problem and O(H^4)for the Dirichlet problem respectively . First an operator
Directory of Open Access Journals (Sweden)
N. N. Nefedov
2016-01-01
Full Text Available Parabolic singularly perturbed problems have been actively studied in recent years in connection with a large number of practical applications: chemical kinetics, synergetics, astrophysics, biology, and so on. In this work a singularly perturbed periodic problem for a parabolic reaction-diﬀusion equation is studied in the two-dimensional case. The case when there is an internal transition layer under unbalanced nonlinearity is considered. The internal layer is localised near the so called transitional curve. An asymptotic expansion of the solution is constructed and an asymptotics for the transitional curve is determined. The asymptotical expansion consists of a regular part, an interior layer part and a boundary part. In this work we focus on the interior layer part. In order to describe it in the neighborhood of the transition curve the local coordinate system is introduced and the stretched variables are used. To substantiate the asymptotics thus constructed, the asymptotic method of diﬀerential inequalities is used. The upper and lower solutions are constructed by suﬃciently complicated modiﬁcation of the asymptotic expansion of the solution. The Lyapunov asymptotical stability of the solution was proved by using the method of contracting barriers. This method is based on the asymptotic comparison principle and uses the upper and lower solutions which are exponentially tending to the solution to the problem. As a result, the solution is locally unique.The article is published in the authors’ wording.
Fast and accurate solution of the Poisson equation in an immersed setting
Marques, Alexandre Noll; Rosales, Rodolfo Ruben
2014-01-01
We present a fast and accurate algorithm for the Poisson equation in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson equations with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson equations in rectangular domains --- which requires the BIM solution at interfaces/boundaries only. These Poisson equations involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high ord...
Bruning, J.; Dobrokhotov, S.Y.; Katsnelson, M.I.; Minenkov, D.S.
2016-01-01
We consider the two-dimensional stationary Schrodinger and Dirac equations in the case of radial symmetry. A radially symmetric potential simulates the tip of a scanning tunneling microscope. We construct semiclassical asymptotic forms for generalized eigenfunctions and study the local density of st
Retinex Poisson Equation: a Model for Color Perception
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Nicola Limare
2011-04-01
Full Text Available In 1964 Edwin H. Land formulated the Retinex theory, the first attempt to simulate and explain how the human visual system perceives color. Unfortunately, the Retinex Land-McCann original algorithm is both complex and not fully specified. Indeed, this algorithm computes at each pixel an average of a very large set of paths on the image. For this reason, Retinex has received several interpretations and implementations which, among other aims, attempt to tune down its excessive complexity. But, Morel et al. have shown that the original Retinex algorithm can be formalized as a (discrete partial differential equation. This article describes the PDE-Retinex, a fast implementation of the Land-McCann original theory using only two DFT’s.
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
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,…
Global Well-posedness of Compressible Bipolar Navier-Stokes-Poisson Equations
Institute of Scientific and Technical Information of China (English)
Yi Quan LIN; Cheng Chun HAO; Hai Liang LI
2012-01-01
We consider the initial value problem for multi-dimensional bipolar compressible NavierStokes-Poisson equations,and show the global existence and uniqueness of the strong solution in hybrid Besov spaces with the initial data close to an equilibrium state.
Institute of Scientific and Technical Information of China (English)
宋丽娜; 王维国
2012-01-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Song, Li-Na; Wang, Wei-Guo
2012-08-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Cannata, F; Nishnianidze, D N
2002-01-01
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations of Higher order SUSY Quantum Mechanics (HSUSY QM) with supercharges allowing for separation of variables. 2)The second one is a generalization of shape invariance. While in one dimension shape invariance allows to solve algebraically a class of (exactly solvable) quantum problems, its generalization to higher dimensions has not been yet explored. Here we provide a formal framework in HSUSY QM for two-dimensional quantum mechanical systems for which shape invariance holds. Given the knowledge of one eigenvalue and eigenfunction, shape invariance allows to construct a chain of new eigenfunctions and eigenvalues. These methods are applied to a two-dimensional quantum system, and partial explicit solvability is achieved in the sense that only part of the spectrum is found analyt...
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Mazarei
2012-01-01
Full Text Available This paper presents numerical solution of elliptic partial differential equations (Poisson's equation using a combination of logarithmic and multiquadric radial basis function networks. This method uses a special combination between logarithmic and multiquadric radial basis functions with a parameter r. Further, the condition number which arises in the process is discussed, and a comparison is made between them with our earlier studies and previously known ones. It is shown that the system is stable.
Krylov, N. V.; Priola, E.
2017-09-01
We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.
Application of the Poisson-Nernst-Planck equations to the migration test
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Krabbenhøft, Jørgen
2008-01-01
The Poisson-Nernst-Planck (PNP) equations are applied to model the migration test. A detailed analysis of the equations is presented and the effects of a number of common, simplifying assumptions are quantified. In addition, closed-form solutions for the effective chloride diffusivity based...... on the full PNP equations are derived, a number of experiments are analyzed in detail, and a new, truly accelerated migration test is proposed. Finally, we present a finite element procedure for numerical solution of the PNP equations....
On a Hamilton-Poisson Approach of the Maxwell-Bloch Equations with a Control
Lăzureanu, Cristian
2017-09-01
In this paper we consider the 3D real-valued Maxwell-Bloch equations with a parametric control given by \\dot {x}=y+az+byz,\\dot {y}=xz,\\dot {z}=-xy (a,b\\in \\mathbb {R}). We give two Lie-Poisson structures of this system that are related with well-known Lie algebras. Moreover, we construct infinitely many Hamilton-Poisson realizations of this system. We also analyze the stability of the equilibrium points, as well as the existence of periodic orbits. In addition, we emphasize some connections between the energy-Casimir mapping of the considered system and the above-mentioned dynamical elements.
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Pham, Dang-Lan [Institute for Computational Science and Technology, Quang Trung Software Town, District 12, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: hoanglv@hcmup.edu.vn [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-08-15
Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.
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Abdollah BORHANIFAR
2013-01-01
Full Text Available In this study fractional Poisson equation is scrutinized through finite difference using shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of solution for the fractional Poisson equation are proved. Exact and numerical solution are constructed and compared. Then numerical result shows the efficiency of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Zhang Guangjun [School of Aerospace, Xi' an Jiao Tong University, Xi' an (China) and School of Life and Science and Technology, Xi' an Jiao Tong University, Xi' an (China) and School of Science, Air Force Engineering University, Xi' an (China)], E-mail: Zhanggj3@126.com; Xu Jianxue [School of Aerospace, Xi' an Jiao Tong University, Xi' an (China)], E-mail: jxxu@mail.xjtu.edu.cn; Wang Jue [School of Life and Science and Technology, Xi' an Jiao Tong University, Xi' an (China); Yue Zhifeng; Zou Hailin [School of Aerospace, Xi' an Jiao Tong University, Xi' an (China)
2009-11-30
In this paper stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator is analyzed by moment method. This kind of novel transition refers to the one among three potential well on two sides of bifurcation point of original system at the presence of internal noise. Several conclusions are drawn. First, the semi-analytical result of stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator can be obtained, and the semi-analytical result is qualitatively compatible with the one of Monte Carlo simulation. Second, a bifurcation of double-branch fixed point curves occurs in the moment equations with noise intensity as their bifurcation parameter. Third, the bifurcation of moment equations corresponds to stochastic resonance of original system. Finally, the mechanism of stochastic resonance is presented from another viewpoint through analyzing the energy transfer induced by the bifurcation of moment equation.
Exact solutions of a two-dimensional cubic–quintic discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Khare, Avinash; Rasmussen, Kim Ø; Samuelsen, Mogens Rugholm
2011-01-01
We show that a two-dimensional generalized cubic–quintic Ablowitz–Ladik lattice admits periodic solutions that can be expressed in analytical form. The framework for the stability analysis of these solutions is developed and applied to reveal the intricate stability behavior of this nonlinear sys...
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm
A regularisation method for solving the Poisson equation using Green’s functions is presented.The method is shown to obtain a convergence rate which corresponds to the design of the regularised Green’s function and a spectral-like convergence rate is obtained using a spectrally ideal regularisation...... the appropriate regularised Green’s functions. Using an analogy to the particle-particle particle-mesh method, a framework for calculating multi-resolution solutions using local refinement patches is presented. The regularised Poisson solver is shown to maintain a high order converging solution for different...... configurations of the refinement patches.The regularised Poisson solver has been implemented in a high order particle-mesh based vortex method for simulating incompressible fluid flow. A re-meshing of the vortex particlesis used to ensure the convergence of the method and a re-projection of the vorticity field...
Application of wavelets to a Poisson equation solver and its parallel processing
Energy Technology Data Exchange (ETDEWEB)
Tanaka, Nobuatsu [Toshiba Corp., Kawasaki, Kanagawa (Japan)
1998-03-01
This paper describes a powerful and simple new wavelet-based preconditioning method for the CG solvers of Poisson equation. The equation can be solved with an iterative matrix solver, however, in the absence of our method, the computing time will increase exponentially with respect to an increase in grid points. Use of our technique leads to a matrix with a bounded condition number so that computing time is reduced significantly. Results from our numerical experiments confirm the power and accuracy of our wavelet-based preconditioning method. Unlike many preconditioning methods which are not suitable for vector and parallel processing, our algorithm can take advantage of the extra processing capabilities and enhance computing performance. For example, a speed up of over 100 fold can be achieved when solving Poisson equations on a Cray T3D using 128 processors in parallel. (author)
Self-energy modified Poisson-Nernst-Planck equations: WKB and finite-difference approaches
Xu, Zhenli; Liu, Pei
2014-01-01
We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in ionic fluids of inhomogeneous dielectric environment. The model includes the induced-charge effect due to the dielectric inhomogeneity and the ionic correlation effect by coupling the self-Green's function through solving a generalized Debye-Huckel (DH) equation. We develop numerical methods for the system composed of the Nernst-Planck, Poisson, and DH equations. Particularly, towards the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the sparse inversion of symmetric and positive definite matrix. 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 with the prediction by the classical PNP results. We find that, at the length scale of the interface separation ~10nm, the results of...
A novel protocol for linearization of the Poisson-Boltzmann equation
Tsekov, R
2014-01-01
A new protocol for linearization of the Poisson-Boltzmann equation is proposed and the resultant electrostatic equation coincides formally with the Debye-Huckel equation, the solution of which is well known for many electrostatic problems. The protocol is examined on the example of electrostatically stabilized nano-bubbles and it is shown that stable nano-bubbles could be present in aqueous solutions of anionic surfactants near the critical temperature, if the surface potential is constant. At constant surface charge non nano-bubbles could exist.
Xie, Dexuan; Jiang, Yi
2016-10-01
The nonlocal dielectric approach has been studied for more than forty years but only limited to water solvent until the recent work of Xie et al. (2013) [20]. As the development of this recent work, in this paper, a nonlocal modified Poisson-Boltzmann equation (NMPBE) is proposed to incorporate nonlocal dielectric effects into the classic Poisson-Boltzmann equation (PBE) for protein in ionic solvent. The focus of this paper is to present an efficient finite element algorithm and a related software package for solving NMPBE. Numerical results are reported to validate this new software package and demonstrate its high performance for protein molecules. They also show the potential of NMPBE as a better predictor of electrostatic solvation and binding free energies than PBE.
Poisson equation for the three loop ladder diagram in string theory at genus one
Basu, Anirban
2016-01-01
The three loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D^{12} R^4 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.
Poisson equation for the three-loop ladder diagram in string theory at genus one
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.
Large Deviations for Stochastic Partial Differential Equations Driven by a Poisson Random Measure
Budhiraja, Amarjit; Dupuis, Paul
2012-01-01
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential equations (PDE). A systematic framework for the study of probabilities of deviations of the stochastic PDE from the deterministic PDE is through the theory of large deviations. The goal of this work is to develop the large deviation theory for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. Although the analogous questions for finite dimensional systems have been well studied, there are currently no general results in the infinite dimensional setting. This is in part due to the fact that in this setting solutions may have little spatial regularity, and thus classical approximation methods for large deviation analysis become intractable. The approach taken here, which is based on a variational representation for nonnegative func...
Numerical solution of stochastic differential equations with Poisson and Lévy white noise
Grigoriu, M.
2009-08-01
A fixed time step method is developed for integrating stochastic differential equations (SDE’s) with Poisson white noise (PWN) and Lévy white noise (LWN). The method for integrating SDE’s with PWN has the same structure as that proposed by Kim [Phys. Rev. E 76, 011109 (2007)], but is established by using different arguments. The integration of SDE’s with LWN is based on a representation of Lévy processes by sums of scaled Brownian motions and compound Poisson processes. It is shown that the numerical solutions of SDE’s with PWN and LWN converge weakly to the exact solutions of these equations, so that they can be used to estimate not only marginal properties but also distributions of functionals of the exact solutions. Numerical examples are used to demonstrate the applications and the accuracy of the proposed integration algorithms.
Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
Holst, Michael; Yu, Zeyun; Zhou, Yongcheng; Zhu, Yunrong
2010-01-01
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a priori pointwise estimates and the first complete solution and approximation theory for the Poisson-Boltzmann equation. It also made possible the first provably convergent discretization of the PBE, and allowed for the development of a provably convergent AFEM for the PBE. However, in practice the regularization turns out to be numerically ill-conditioned. In this article, we examine a second regularization, and establish a number of basic results to ensure that the new approach produces the same mathematical advantages of the original regularization, without the ill-conditioning property. We then design an AFEM scheme based on the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This res...
On Wiener-Poisson Type Multivalued Stochastic Differential Equations with Non-Lipschitz Coefficients
Institute of Scientific and Technical Information of China (English)
Jing WU
2013-01-01
In this paper,we prove local uniqueness for multivalued stochastic differential equations with Poisson jumps.Then existence and uniqueness of global solutions is obtained under the conditions that the coefficients satisfy locally Lipschitz continuity and one-sided linear growth of b.Moreover,we also prove the Markov property of the solution and the existence of invariant measures for the corresponding transition semigroup.
An inverse source problem of the Poisson equation with Cauchy data
Directory of Open Access Journals (Sweden)
Ji-Chuan Liu
2017-05-01
Full Text Available In this article, we study an inverse source problem of the Poisson equation with Cauchy data. We want to find iterative algorithms to detect the hidden source within a body from measurements on the boundary. Our goal is to reconstruct the location, the size and the shape of the hidden source. This problem is ill-posed, regularization techniques should be employed to obtain the regularized solution. Numerical examples show that our proposed algorithms are valid and effective.
Solution of Poisson's equation for finite systems using plane wave methods
Castro, A; Stott, M J; Castro, Alberto; Rubio, Angel
2003-01-01
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional theory code. Two basic methodologies are followed: calculation of correction terms, and imposition of a cut-off to the Coulomb potential. We conclude that these methods can be safely applied to finite or aperiodic systems with a reasonable control of speed and accuracy.
Solution of the Dirichlet Problem for the Poisson's Equation in a Multidimensional Infinite Layer
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O. D. Algazin
2015-01-01
Full Text Available The paper considers the multidimensional Poisson equation in the domain bounded by two parallel hyperplanes (in the multidimensional infinite layer. For an n-dimensional half-space method of solving boundary value problems for linear partial differential equations with constant coefficients is a Fourier transform to the variables in the boundary hyperplane. The same method can be used for an infinite layer, as is done in this paper in the case of the Dirichlet problem for the Poisson equation. For strip and infinite layer in three-dimensional space the solutions of this problem are known. And in the three-dimensional case Green's function is written as an infinite series. In this paper, the solution is obtained in the integral form and kernels of integrals are expressed in a finite form in terms of elementary functions and Bessel functions. A recurrence relation between the kernels of integrals for n-dimensional and (n + 2 -dimensional layers was obtained. In particular, is built the Green's function of the Laplace operator for the Dirichlet problem, through which the solution of the problem is recorded. Even in three-dimensional case we obtained new formula compared to the known. It is shown that the kernel of the integral representation of the solution of the Dirichlet problem for a homogeneous Poisson equation (Laplace equation is an approximate identity (δ-shaped system of functions. Therefore, if the boundary values are generalized functions of slow growth, the solution of the Dirichlet problem for the homogeneous equation (Laplace is written as a convolution of kernels with these functions.
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Bishnu P. Lamichhane
2013-01-01
Full Text Available We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagrange multiplier space forming biorthogonal and quasi-biorthogonal systems, respectively. We also establish an optimal a priori error estimate for both finite element approximations.
Solution Poisson-Boltzmann equation: Application in the Human Neuron Membrane
Soares, M A G; Cortez, C M
2008-01-01
With already demonstrated in previous work the equations that describe the space dependence of the electric potential are determined by the solution of the equation of Poisson-Boltzmann. In this work we consider these solutions for the membrane of the human neuron, using a model simplified for this structure considering the distribution of electrolytes in each side of the membrane, as well as the effect of glycocalyx and the lipidic bilayer. It was assumed that on both sides of the membrane the charges are homogeneously distributed and that the potential depends only on coordinate z.
Generalized Poisson-Boltzmann Equation Taking into Account Ionic Interaction and Steric Effects
Institute of Scientific and Technical Information of China (English)
刘新敏; 李航; 李睿; 田锐; 许晨阳
2012-01-01
Generalized Poisson l3oltzmann equation which takes into account both ionic interaction in bulk solution and steric effects of adsorbed ions has been suggested. We found that, for inorganic cations adsorption on negatively charged surface, the steric effect is not significant for surface charge density 〈 0.0032 C/dm2, while the ionic interaction is an important effect for electrolyte concentration 〉 0.15 tool/1 in bulk solution. We conclude that for most actual cases the original PB equation can give reliable result in describing inorganic cation adsorption.
Directory of Open Access Journals (Sweden)
Diem Dang Huan
2015-12-01
Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.
General form of the Euler-Poisson-Darboux equation and application of the transmutation method
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Elina L. Shishkina
2017-07-01
Full Text Available In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations.
Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media
Schmuck, Markus
2012-01-01
Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media. Homogenization analysis is performed for a two-component pe- riodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a given surface charge. Three new features arise in the upscaled equations: (i) the effective ionic diffusivities and mobilities become tensors, related to the microstructure; (ii) the effective permittivity is also a tensor, depending on the electrolyte/matrix permittivity ratio and the ratio of the Debye screening length to mean pore size; and (iii) the surface charge per volume appears as a continuous "background charge density". The coeffcient tensors in the macroscopic PNP equations can be calculated from periodic reference cell problem, and several examples are considered. For an insulating solid matrix, all gradients are corrected by a single tortuosit...
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...
Directory of Open Access Journals (Sweden)
Qingxue Huang
2017-01-01
Full Text Available In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent.
Leclerc, M
2012-01-01
We introduce a symmetric Poisson bracket that allows us to describe anticommuting fields on a classical level in the same way as commuting fields, without the use of Grassmann variables. By means of a simple example, we show how the Dirac bracket for the elimination of the second class constraints can be introduced, how the classical Hamiltonian equations can be derived and how quantization can be achieved through a direct correspondence principle. Finally, we show that the semiclassical limit of the corresponding Schroedinger equation leads back to the Hamilton-Jacobi equation of the classical theory. Summarizing, it is shown that the relations between classical and quantum theory are valid for fermionic fields in exactly the same way as in the bosonic case, and that there is no need to introduce anticommuting variables on a classical level.
Analytical solution of the Boltzmann-Poisson equation and its application to MIS tunneling junctions
Institute of Scientific and Technical Information of China (English)
Zhang Li-Zhi; Wang Zheng-Chuan
2009-01-01
In order to consider quantum transport under the influence of an electron-electron (e-e) interaction in a mesoscopic conductor, the Boltzmann equation and Poisson equation are investigated jointly. The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential concerned with e-e interaction are obtained, and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas-Fermi approximation. Then we apply these results to the tunneling junctions of a metal-insulatorsemiconductor (MIS) in which the electrons are accumulated near the interface of the semiconductor, and we find that the e-e interaction plays an important role in the transport procedure of this system. The electronic density, electric current as well as screening Coulombic potential in this case are studied, and we reveal the time and position dependence of these physical quantities explicitly affected by the e-e interaction.
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Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
On Higher-order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit
Energy Technology Data Exchange (ETDEWEB)
W.W. Lee and R.A. Kolesnikov
2009-02-17
In this paper, we present a simple iterative procedure for obtaining the higher order E x B and dE/dt (polarization) drifts associated with the gyrokinetic Vlasov-Poisson equations in the long wavelength limit of k⊥ρi ~ o(ε) and k⊥L ~ o(1), where ρi is the ion gyroradius, L is the scale length of the background inhomogeneity and ε is a smallness parameter. It can be shown that these new higher order k⊥ρi terms, which are also related to the higher order perturbations of the electrostatic potential Φ, should have negligible effects on turbulent and neoclassical transport in tokamaks, regardless of the form of the background distribution and the amplitude of the perturbation. To address further the issue of a non-Maxwellian plasma, higher order finite Larmor radius terms in the gyrokinetic Poisson's equation have been studied and shown to be unimportant as well. On the other hand, the terms of o(k2⊥ρi2) ~ o(ε) and k⊥L ~ o(1) can indeed have impact on microturbulence, especially in the linear stage, such as those arising from the difference between the guiding center and the gyrocenter densities due to the presence of the background gradients. These results will be compared with a recent study questioning the validity of the commonly used gyrokinetic equations for long time simulations.
Biswas, Debabrata; Kumar, Raghwendra
2015-01-01
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 (HPM) 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 condition (ABC) is best suited for large aspect ratios while a proposed non-local matching method, based on the solution of the Laplace equation, 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.
Institute of Scientific and Technical Information of China (English)
莫则尧; 符尚武
2003-01-01
Two dimensional three temperatures energy equation is a kind of very impor-tant partial differential equation. In general, we discrete such equation with full implicit nine points stencil on Lagrange structured grid and generate a non-linear sparse algebraic equation including nine diagonal lines. This paper will discuss the iterative solver for such non-linear equations. We linearize the equations by fixing the coefficient matrix, and iteratively solve the linearized algebraic equation with Krylov subspace iterative method. We have applied the iterative method presented in this paper to the code Lared-Ⅰ for numerical simulation of two dimensional threetemperatures radial fluid dynamics, and have obtained efficient results.
Free boundary value problem to 3D spherically symmetric compressible Navier-Stokes-Poisson equations
Kong, Huihui; Li, Hai-Liang
2017-02-01
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with γ -law pressure density function for 6/5 <γ ≤ 4/3. For stress-free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.
Error analysis of finite element method for Poisson-Nernst-Planck equations
Energy Technology Data Exchange (ETDEWEB)
Sun, Yuzhou; Sun, Pengtao; Zheng, Bin; Lin, Guang
2016-08-01
A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.
Poisson equation for the Mercedes diagram in string theory at genus one
Basu, Anirban
2015-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Kravchenko, Vladislav V [Seccion de Posgrado e Investigacion, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, C.P.07738 Mexico DF (Mexico)
2005-05-06
We consider the real stationary two-dimensional Schroedinger equation. With the aid of any of its particular solutions, we construct a Vekua equation possessing the following special property. The real parts of its solutions are solutions of the original Schroedinger equation and the imaginary parts are solutions of an associated Schroedinger equation with a potential having the form of a potential obtained after the Darboux transformation. Using Bers' theory of Taylor series for pseudoanalytic functions, we obtain a locally complete system of solutions of the original Schroedinger equation which can be constructed explicitly for an ample class of Schroedinger equations. For example it is possible when the potential is a function of one Cartesian, spherical, parabolic or elliptic variable. We give some examples of application of the proposed procedure for obtaining a locally complete system of solutions of the Schroedinger equation. The procedure is algorithmically simple and can be implemented with the aid of a computer system of symbolic or numerical calculation.
DEFF Research Database (Denmark)
Gaididei, Yu. B.; Christiansen, Peter Leth
2008-01-01
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered...... and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under...
Jansen, TL; Hayashi, T; Zhuang, W; Mukamel, S
2005-01-01
The effects of hydrogen-bond forming and breaking kinetics on the linear and coherent third-order infrared spectra of the OH stretch of HOD in D2O are described by Markovian, not necessarily Gaussian, fluctuations and simulated using the stochastic Liouville equations. Slow (0.5 ps) fluctuations are
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation
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Jiang Wei
2016-01-01
Full Text Available The novelty and innovativeness of this paper are the combination of reproducing kernel theory and spline, this leads to a new simple but effective numerical method for solving variable-order anomalous sub-diffusion equation successfully. This combination overcomes the weaknesses of piecewise polynomials that can not be used to solve differential equations directly because of lack of the smoothness. Moreover, new bases of reproducing kernel spaces are constructed. On the other hand, the existence of any ε-approximate solution is proved and an effective method for obtaining the ε-approximate solution is established. A numerical example is given to show the accuracy and effectiveness of theoretical results.
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Puskar Raj SHARMA
2012-01-01
Full Text Available Aim of the paper is to investigate solution of twodimensional linear parabolic partial differential equation with non-local boundary conditions using Homotopy Perturbation Method (HPM. This method is not only reliable in obtaining solution of such problems in series form with high accuracy but it also guarantees considerable saving of the calculation volume and time as compared to other methods. The application of the method has been illustrated through an example
Harris, Robert C; Boschitsch, Alexander H; Fenley, Marcia O
2017-08-08
Many researchers compute surface maps of the electrostatic potential (φ) with the Poisson-Boltzmann (PB) equation to relate the structural information obtained from X-ray and NMR experiments to biomolecular functions. Here we demonstrate that the usual method of obtaining these surface maps of φ, by interpolating from neighboring grid points on the solution grid generated by a PB solver, generates large errors because of the large discontinuity in the dielectric constant (and thus in the normal derivative of φ) at the surface. The Cartesian Poisson-Boltzmann solver contains several features that reduce the numerical noise in surface maps of φ: First, CPB introduces additional mesh points at the Cartesian grid/surface intersections where the PB equation is solved. This procedure ensures that the solution for interior mesh points only references nodes on the interior or on the surfaces; similarly for exterior points. Second, for added points on the surface, a second order least-squares reconstruction (LSR) is implemented that analytically incorporates the discontinuities at the surface. LSR is used both during the solution phase to compute φ at the surface and during postprocessing to obtain φ, induced charges, and ionic pressures. Third, it uses an adaptive grid where the finest grid cells are located near the molecular surface.
Sensitivities to parameterization in the size-modified Poisson-Boltzmann equation.
Harris, Robert C; Boschitsch, Alexander H; Fenley, Marcia O
2014-02-21
Experimental results have demonstrated that the numbers of counterions surrounding nucleic acids differ from those predicted by the nonlinear Poisson-Boltzmann equation, NLPBE. Some studies have fit these data against the ion size in the size-modified Poisson-Boltzmann equation, SMPBE, but the present study demonstrates that other parameters, such as the Stern layer thickness and the molecular surface definition, can change the number of bound ions by amounts comparable to varying the ion size. These parameters will therefore have to be fit simultaneously against experimental data. In addition, the data presented here demonstrate that the derivative, SK, of the electrostatic binding free energy, ΔGel, with respect to the logarithm of the salt concentration is sensitive to these parameters, and experimental measurements of SK could be used to parameterize the model. However, although better values for the Stern layer thickness and ion size and better molecular surface definitions could improve the model's predictions of the numbers of ions around biomolecules and SK, ΔGel itself is more sensitive to parameters, such as the interior dielectric constant, which in turn do not significantly affect the distributions of ions around biomolecules. Therefore, improved estimates of the ion size and Stern layer thickness to use in the SMPBE will not necessarily improve the model's predictions of ΔGel.
Duarte, Max; Massot, Marc; Bourdon, Anne
2013-01-01
In this paper we investigate the numerical solution of Poisson equations on adapted structured grids generated by multiresolution analysis. Such an approach not only involves important savings in computational costs, but also allows us to conduct a mathematical description of the numerical approximations in the context of biorthogonal wavelet decomposition. In contrast to most adaptive meshing techniques in the literature that solve the corresponding system of discrete equations level-wise throughout the set of adapted grids, we introduce a new numerical procedure, mainly based on inter-level operations, to represent in a consistent way the elliptic operators discretized on the adapted grid. In this way the discrete problem can be solved at once over the entire computational domain strongly coupling inter-grid relations as a completely separate process, independent of the mesh generation or any other grid-related data structure or geometric consideration, while the multiresolution framework guarantees numeric...
Mathematical stencil and its application in finite difference approximation to the Poisson equation
Institute of Scientific and Technical Information of China (English)
FENG Hui; ZHANG Baolin; LIU Yang
2005-01-01
The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.
Institute of Scientific and Technical Information of China (English)
Ying-hui ZHANG; Zhong TAN
2011-01-01
In this paper,we are concerned with the asymptotic behaviour of a weak solution to the NavierStokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p(ρ) =a(ρ)logd(ρ) for large (ρ).Here d ＞ 2,a ＞ 0.We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity.Using properties of this function,we can prove the strong convergence of the density to its limit state.The behaviour of the velocity field and kinetic energy is also briefly discussed.
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
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
Energy Technology Data Exchange (ETDEWEB)
Djouder, M., E-mail: djouder-madjid@ummto.dz; Kermoun, F.; Mitiche, M. D.; Lamrous, O. [Laboratoire de Physique et Chimie Quantique, Université Mouloud Mammeri Tizi-Ouzou, BP 17 RP, 15000 Tizi-Ouzou (Algeria)
2016-01-15
Dust particles observed in universe as well as in laboratory and technological plasma devices are still under investigation. At low temperature, these particles are strongly negatively charged and are able to form a 2D or 3D coulomb crystal. In this work, our aim was to check the ideal gas law validity for a 2D single-layer dust crystal recently reported in the literature. For this purpose, we have simulated, using the molecular dynamics method, its thermodynamic properties for different values of dust particles number and confinement parameters. The obtained results have allowed us to invalidate the ideal gas behaviour and to propose an effective equation of state which assumes a near zero dust temperature. Furthermore, the value of the calculated sound velocity was found to be in a good agreement with experimental data published elsewhere.
Hsieh, Y. H.; Yu, Y. T.; Tuan, P. H.; Tung, J. C.; Huang, K. F.; Chen, Y. F.
2017-02-01
The trajectory equations for classical periodic orbits in the equilateral-triangular and circular billiards are systematically extracted from quantum stationary coherent states. The relationship between the phase factors of quantum stationary coherent states and the initial positions of classical periodic orbits is analytically derived. In addition, the stationary coherent states with noncoprime parametric numbers are shown to correspond to the multiple periodic orbits, which cannot be explicable in the one-particle picture. The stationary coherent states are further verified to be linked to the resonant modes that are generally observed in the experimental wave system excited by a localized and unidirectional source. The excellent agreement between the resonant modes and the stationary coherent states not only manifests the importance of classical features in experimental systems but also paves the way to manipulate the mesoscopic wave functions localized on the periodic orbits for applications.
Halliday, I; Lishchuk, S V; Spencer, T J; Pontrelli, G; Evans, P C
2016-08-01
We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)10.1140/epjst/e2013-01834-y] and underscore the importance of a correct vesicle membrane condition.
A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation
Colmenares, José; Galizia, Antonella; Ortiz, Jesús; Clematis, Andrea; Rocchia, Walter
2014-01-01
The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs. PMID:25013789
Botello-Smith, Wesley M.; Luo, Ray
2016-01-01
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966
A combined MPI-CUDA parallel solution of linear and nonlinear Poisson-Boltzmann equation.
Colmenares, José; Galizia, Antonella; Ortiz, Jesús; Clematis, Andrea; Rocchia, Walter
2014-01-01
The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.
A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation
Directory of Open Access Journals (Sweden)
José Colmenares
2014-01-01
Full Text Available The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.
JavanNezhad, R.; Meshkatee, A. H.; Ghader, S.; Ahmadi-Givi, F.
2016-09-01
This study is devoted to application of the fourth-order compact MacCormack scheme to spatial differencing of the conservative form of two-dimensional and non-hydrostatic equation of a dry atmosphere. To advance the solution in time a four-stage Runge-Kutta method is used. To perform the simulations, two test cases including evolution of a warm bubble and a cold bubble in a neutral atmosphere with open and rigid boundaries are employed. In addition, the second-order MacCormack and the standard fourth-order compact MacCormack schemes are used to perform the simulations. Qualitative and quantitative assessment of the numerical results for different test cases exhibit the superiority of the fourth-order compact MacCormack scheme on the second-order method.
Golbabai, Ahmad; Nikpour, Ahmad
2016-10-01
In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.
Desbuquois, Rémi; Yefsah, Tarik; Chomaz, Lauriane; Weitenberg, Christof; Corman, Laura; Nascimbène, Sylvain; Dalibard, Jean
2014-07-11
We present a general "fit-free" method for measuring the equation of state (EoS) of a scale-invariant gas. This method, which is inspired from the procedure introduced by Ku et al. [Science 335, 563 (2012)] for the unitary three-dimensional Fermi gas, provides a general formalism which can be readily applied to any quantum gas in a known trapping potential, in the frame of the local density approximation. We implement this method on a weakly interacting two-dimensional Bose gas across the Berezinskii-Kosterlitz-Thouless transition and determine its EoS with unprecedented accuracy in the critical region. Our measurements provide an important experimental benchmark for classical-field approaches which are believed to accurately describe quantum systems in the weakly interacting but nonperturbative regime.
Mirzadeh, Mohammad; Squires, Todd; Gibou, Frederic
2010-11-01
We present a finite difference discretization of the non-linear Poisson-Boltzmann (PB) equation over complex geometries that has second order accurracy. The level-set method is adopted to represent the interface and Octree (in three dimensions) or Quadtree (in two dimensions) data stuructures are used to generate adaptive grids. Such an approach garanties that the finest grid resolution is located near the interface where EDL forms and creates very large electric field. Several numerical experiments are carried which indicate the second order accuracy both in the case of Dirichlet and Neumann boundary conditions in L2 and L∞ norms. Finally, we use our method to study the electrostatic interaction of double layers between charged particles in an unbounded bulk electrolyte as well as in a channel where the channel width is of the order of Debye length.
Solution of Poisson's equation in electrostatic Particle-In-Cell simulations
Kahnfeld, Daniel; Schneider, Ralf; Matyash, Konstantin; Lüskow, Karl; Bandelow, Gunnar; Kalentev, Oleksandr; Duras, Julia; Kemnitz, Stefan
2016-10-01
For spacecrafts the concept of ion thrusters presents a very efficient method of propulsion. Optimization of thrusters is imperative, but experimental access is difficult. Plasma simulations offer means to understand the plasma physics within an ion thruster and can aid the design of new thruster concepts. In order to achieve best simulation performances, code optimizations and parallelization strategies need to be investigated. In this work the role of different solution strategies for Poisson's equation in electrostatic Particle-in-Cell simulations of the HEMP-DM3a ion thruster was studied. The direct solution method of LU decomposition is compared to a stationary iterative method, the successive over-relaxation solver. Results and runtime of solvers were compared, and an outlook on further improvements and developments is presented. This work was supported by the German Space Agency DLR through Project 50RS1510..
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
Wong, Sen; Yuen, Manwai
2014-01-01
We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in R (N) . For time t ≥ 0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P = Kρ (γ) , where ρ is the density function, K is a constant, and γ > 1, we can show that the nontrivial C (1) solutions with nonslip boundary condition will blow up in finite time if H(0) satisfies some initial functional conditions defined by the integrals of f. Examples of the testing functions include r (N-1)ln(r + 1), r (N-1) e (r) , r (N-1)(r (3) - 3r (2) + 3r + ε), r (N-1)sin((π/2)(r/R)), and r (N-1)sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given.
Pabst, M
2014-06-14
Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10(-4) so the Fourier-Bessel series can be approximated by elementary functions. The time development of the system is characterized by two time constants, τ(c) and τ(g). The constant τ(c) describes the approach to the stationary state of the total charge and the potential. τ(c) is several orders of magnitude smaller than the geometry-dependent constant τ(g), which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.
Ion strength limit of computed excess functions based on the linearized Poisson-Boltzmann equation.
Fraenkel, Dan
2015-12-05
The linearized Poisson-Boltzmann (L-PB) equation is examined for its κ-range of validity (κ, Debye reciprocal length). This is done for the Debye-Hückel (DH) theory, i.e., using a single ion size, and for the SiS treatment (D. Fraenkel, Mol. Phys. 2010, 108, 1435), which extends the DH theory to the case of ion-size dissimilarity (therefore dubbed DH-SiS). The linearization of the PB equation has been claimed responsible for the DH theory's failure to fit with experiment at > 0.1 m; but DH-SiS fits with data of the mean ionic activity coefficient, γ± (molal), against m, even at m > 1 (κ > 0.33 Å(-1) ). The SiS expressions combine the overall extra-electrostatic potential energy of the smaller ion, as central ion-Ψa>b (κ), with that of the larger ion, as central ion-Ψb>a (κ); a and b are, respectively, the counterion and co-ion distances of closest approach. Ψa>b and Ψb>a are derived from the L-PB equation, which appears to conflict with their being effective up to moderate electrolyte concentrations (≈1 m). However, the L-PB equation can be valid up to κ ≥ 1.3 Å(-1) if one abandons the 1/κ criterion for its effectiveness and, instead, use, as criterion, the mean-field electrostatic interaction potential of the central ion with its ion cloud, at a radial distance dividing the cloud charge into two equal parts. The DH theory's failure is, thus, not because of using the L-PB equation; the lethal approximation is assigning a single size to the positive and negative ions. © 2015 Wiley Periodicals, Inc.
Two-dimensional analytical models for asymmetric fully depleted double-gate strained silicon MOSFETs
Institute of Scientific and Technical Information of China (English)
Liu Hong-Xia; Li Jin; Li Bin; Cao Lei; Yuan Bo
2011-01-01
This paper develops the simple and accurate two-dimensional analytical models for new asymmetric double-gate fully depleted strained-Si MOSFET. The models mainly include the analytical equations of the surface potential, surface electric field and threshold voltage, which are derived by solving two dimensional Poisson equation in strained-Si layer.The models are verified by numerical simulation. Besides offering the physical insight into device physics in the model,the new structure also provides the basic designing guidance for further immunity of short channel effect and drain-induced barrier-lowering of CMOS-based devices in nanometre scale.
Improving long time behavior of Poisson bracket mapping equation: a non-Hamiltonian approach.
Kim, Hyun Woo; Rhee, Young Min
2014-05-14
Understanding nonadiabatic dynamics in complex systems is a challenging subject. A series of semiclassical approaches have been proposed to tackle the problem in various settings. The Poisson bracket mapping equation (PBME) utilizes a partial Wigner transform and a mapping representation for its formulation, and has been developed to describe nonadiabatic processes in an efficient manner. Operationally, it is expressed as a set of Hamilton's equations of motion, similar to more conventional classical molecular dynamics. However, this original Hamiltonian PBME sometimes suffers from a large deviation in accuracy especially in the long time limit. Here, we propose a non-Hamiltonian variant of PBME to improve its behavior especially in that limit. As a benchmark, we simulate spin-boson and photosynthetic model systems and find that it consistently outperforms the original PBME and its Ehrenfest style variant. We explain the source of this improvement by decomposing the components of the mapping Hamiltonian and by assessing the energy flow between the system and the bath. We discuss strengths and weaknesses of our scheme with a viewpoint of offering future prospects.
DEFF Research Database (Denmark)
Paz-Garcia, Juan Manuel; Johannesson, Björn; Ottosen, Lisbeth M.
2011-01-01
, the electromigration and the electroosmotic transport contributors are taken into account. The Poisson's equation of electrostatics is used for the calculation of the electrical potential distribution based on the global charge balance. The effect of the electrode half-reactions is included. In addition to this, water...
Institute of Scientific and Technical Information of China (English)
沈春; 孙梅娜
2005-01-01
Based on the theory of stratification, the well-posedness of the initial and boundary value problems for the system of two-dimensional non-hydrostatic Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for some representative initial and boundary value problems. Several special cases were discussed.
ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION
HOLST, MICHAEL; MCCAMMON, JAMES ANDREW; YU, ZEYUN; ZHOU, YOUNGCHENG; ZHU, YUNRONG
2011-01-01
We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme
Juknevičius, Vaidas; Ruseckas, Julius; Armaitis, Jogundas
2017-09-01
This paper presents new findings concerning the dynamics of the slow height variations in surfaces produced by the two-dimensional isotropic Kuramoto-Sivashinsky equation with an additional nonlinear term. In addition to the disordered cellular patterns of specific size evident at small scales, slow height variations of scale-free character become increasingly evident when the system size is increased. This paper focuses on the parameter range in which the kinetic roughening with eventual saturation in surface roughness and coarseness is obtained, and the statistical and dynamical properties of surfaces in the long-time stationary regime are investigated. The resulting long-range scaling properties of the saturated surface roughness consistent with the power-law shape of the surface spectrum at small wave numbers are obtained in a wider parameter range than previously reported. The temporal properties of these long-range height variations are investigated by analysing the time series of surface roughness fluctuations. The resulting power-spectral densities can be expressed as a generalized Lorentzian whose cut-off frequency varies with system size. The dependence of this lower cut-off frequency on the smallest wave number connects spatial and temporal properties and gives new insight into the surface evolution on large scales.
Asllanaj, Fatmir; Fumeron, Sebastien
2012-07-01
Optical tomography is a medical imaging technique based on light propagation in the near infrared (NIR) part of the spectrum. We present a new way of predicting the short-pulsed NIR light propagation using a time-dependent two-dimensional-global radiative transfer equation in an absorbing and strongly anisotropically scattering medium. A cell-vertex finite-volume method is proposed for the discretization of the spatial domain. The closure relation based on the exponential scheme and linear interpolations was applied for the first time in the context of time-dependent radiative heat transfer problems. Details are given about the application of the original method on unstructured triangular meshes. The angular space (4πSr) is uniformly subdivided into discrete directions and a finite-differences discretization of the time domain is used. Numerical simulations for media with physical properties analogous to healthy and metastatic human liver subjected to a collimated short-pulsed NIR light are presented and discussed. As expected, discrepancies between the two kinds of tissues were found. In particular, the level of light flux was found to be weaker (inside the medium and at boundaries) in the healthy medium than in the metastatic one.
Chakavorty, Arghya; Li, Lin; Alexov, Emil
2016-10-30
Macromolecular interactions are essential for understanding numerous biological processes and are typically characterized by the binding free energy. Important component of the binding free energy is the electrostatics, which is frequently modeled via the solutions of the Poisson-Boltzmann Equations (PBE). However, numerous works have shown that the electrostatic component (ΔΔGelec ) of binding free energy is very sensitive to the parameters used and modeling protocol. This prompted some researchers to question the robustness of PBE in predicting ΔΔGelec . We argue that the sensitivity of the absolute ΔΔGelec calculated with PBE using different input parameters and definitions does not indicate PBE deficiency, rather this is what should be expected. We show how the apparent sensitivity should be interpreted in terms of the underlying changes in several numerous and physical parameters. We demonstrate that PBE approach is robust within each considered force field (CHARMM-27, AMBER-94, and OPLS-AA) once the corresponding structures are energy minimized. This observation holds despite of using two different molecular surface definitions, pointing again that PBE delivers consistent results within particular force field. The fact that PBE delivered ΔΔGelec values may differ if calculated with different modeling protocols is not a deficiency of PBE, but natural results of the differences of the force field parameters and potential functions for energy minimization. In addition, while the absolute ΔΔGelec values calculated with different force field differ, their ordering remains practically the same allowing for consistent ranking despite of the force field used. © 2016 Wiley Periodicals, Inc.
Hadamard States and Two-dimensional Gravity
Salehi, H
2001-01-01
We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.
Areias, P.; Rabczuk, T.; de Sá, J. César
2016-12-01
We propose an alternative crack propagation algorithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algorithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equations is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algorithm, we use five quasi-brittle benchmarks, all successfully solved.
DEFF Research Database (Denmark)
Johannesson, Björn
2010-01-01
A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson-Nernst-Planck ......A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson......, however, coupled in both directions. The governed set of equations is derived from a simplified version of the so-called hybrid mixture theory (HMT). This theory is a special version of the more ‘classical’ continuum mixture theories in the sense that it works with averaged equations at macro...
Institute of Scientific and Technical Information of China (English)
Junping YIN; Zhong TAN
2008-01-01
The authors prove two global existence results of strong solutions of the isen- tropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.
Energy Technology Data Exchange (ETDEWEB)
Konopelchenko, B [Dipartimento di Fisica, Universita di Lecce and Sezione INFN, 73100 Lecce (Italy); Alonso, L MartInez [Departamento de Fisica Teorica II, Universidad Complutense, E28040 Madrid (Spain); Medina, E [Departamento de Matematicas, Universidad de Cadiz, E11510 Puerto Real, Cadiz (Spain)
2010-10-29
It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation. Singular sectors of each dcKdV hierarchy are found to be described by solutions of higher genus dcKdV hierarchies. Concrete solutions exhibiting shock-type singularities are presented.
A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov-Poisson Equation
Myers, Andrew; Van Straalen, Brian
2016-01-01
Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new Particle-in-Cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update - charge deposition, force interpolation, the field solve, and the particle push - with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve comparable accuracy to the 2nd-order method with many fewer resolution elements.
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.
Directory of Open Access Journals (Sweden)
Yongsheng Jiang
2013-01-01
Full Text Available We study the following Schrödinger-Poisson system: , , , where are positive radial functions, , , and is allowed to take two different forms including and with . Two theorems for nonexistence of nontrivial solutions are established, giving two regions on the plane where the system has no nontrivial solutions.
Institute of Scientific and Technical Information of China (English)
韩厚德; 郑春雄
2002-01-01
The mixed finite element method is used to solve the exterior Poisson equations with higher-order local artificial boundary conditions in 3-D space. New unknowns are introduced to reduce the order of the derivatives of the unknown to two. The result is an equivalent mixed variational problem which was solved using bilinear finite elements. The primary advantage is that special finite elements are not needed on the adjacent layer of the artificial boundary for the higher-order derivatives. Error estimates are obtained for some local artificial boundary conditions with prescibed orders. A numerical example demonstrates the effectiveness of this method.
Institute of Scientific and Technical Information of China (English)
黄健; 戴正德
2004-01-01
在本文中,我们在Banach空间考虑二维广义Ginzburg-Landau方程的指数吸引子,且得到其分形维度估计.%In this paper, we consider the exponential attractor for the derivative two - dimensional Ginzburg - Landau equation in Banach space Xαp and also obtain the estimation of the fractal dimension.
Ying, Jinyong
2016-01-01
The size-modified Poisson-Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson-Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an ionic solvent. In this paper, a new SMPBE hybrid solver is developed using a solution decomposition, the Schwartz's overlapped domain decomposition, finite element, and finite difference. It is then programmed as a software package in C, Fortran, and Python based on the state-of-the-art finite element library DOLFIN from the FEniCS project. This software package is well validated on a Born ball model with analytical solution and a dipole model with a known physical properties. Numerical results on six proteins with different net charges demonstrate its high performance. Finally, this new SMPBE hybrid solver is shown to be numerically stable and convergent in the calculation of electrostatic solvation free energy for 216 biomolecules and binding free energy for a DNA-drug com...
Khodarahmi, Iman; Shakeri, Mostafa; Sharp, M; Amini, Amir A
2010-01-01
Pressure gradient across a Gaussian-shaped 87% area stenosis phantom was estimated by solving the pressure Poisson equation (PPE) for a steady flow mimicking the blood flow through the human iliac artery. The velocity field needed to solve the pressure equation was obtained using particle image velocimetry (PIV). A steady flow rate of 46.9 ml/s was used, which corresponds to a Reynolds number of 188 and 595 at the inlet and stenosis throat, respectively (in the range of mean Reynolds number encountered in-vivo). In addition, computational fluid dynamics (CFD) simulation of the same flow was performed. Pressure drops across the stenosis predicted by PPE/PIV and CFD were compared with those measured by a pressure catheter transducer. RMS errors relative to the measurements were 17% and 10% for PPE/PIV and CFD, respectively.
Lahiri, T.; Pal Majumder, T.; Ghosh, N. K.
2014-07-01
Commercialization of ferroelectric liquid crystal displays (FLCDs) suffers from mechanical and electro-convective instabilities. Impurity ions play a pivotal role in the latter case, and therefore we developed a mean-field type model to understand the complex role of space charges, particularly ions in a ferroelectric liquid crystal. Considering an effective ion-chirality relation, we obtained a modified Poisson-Boltzmann equation for ions dissolved into a chiral solvent like the ferroelectric smectic phase. A nonuniform director profile induced by the mean electrostatic potential of the ions is then calculated by solving an Euler-Lagrange equation for a helically twisted smectic state. A combination of effects resulting from molecular chirality and an electrostatically driven twist created by the ions seems to produce this nonuniform fluctuation in the director orientation. Finally, both theoretical and experimental points of view are presented on the prediction of this mean-field model.
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
Juday, Richard D. (Inventor)
1992-01-01
A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.
A two-dimensional threshold voltage analytical model for metal-gate/high-k/SiO2/Si stacked MOSFETs
Institute of Scientific and Technical Information of China (English)
Ma Fei; Liu Hong-Xia; Fan Ji-Bin; Wang Shu-Long
2012-01-01
In this paper the influences of the metal-gate and high-k/SiO2/Si stacked structure on the metal-oxidesemiconductor field-effect transistor (MOSFET) axe investigated.The flat-band voltage is revised by considering the influences of stacked structure and metal-semiconductor work function fluctuation. The two-dimensional Poisson's equation of potential distribution is presented.A threshold voltage analytical model for metal-gate/high-k/SiO2/Si stacked MOSFETs is developed by solving these Poisson's equations using the boundary conditions.The model is verified by a two-dimensional device simulator,which provides the basic design guidance for metal-gate/high-k/SiO2/Si stacked MOSFETs.
Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface.
Gongadze, Ekaterina; van Rienen, Ursula; Kralj-Iglič, Veronika; Iglič, Aleš
2011-06-01
Water ordering near a charged membrane surface is important for many biological processes such as binding of ligands to a membrane or transport of ions across it. In this work, the mean-field Poisson-Boltzmann theory for point-like ions, describing an electrolyte solution in contact with a planar charged surface, is modified by including the orientational ordering of water. Water molecules are considered as Langevin dipoles, while the number density of water is assumed to be constant everywhere in the electrolyte solution. It is shown that the dielectric permittivity of an electrolyte close to a charged surface is decreased due to the increased orientational ordering of water dipoles. The dielectric permittivity close to the charged surface is additionally decreased due to the finite size of ions and dipoles.
Two-dimensional capillary origami
Energy Technology Data Exchange (ETDEWEB)
Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu
2016-01-08
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Energy Technology Data Exchange (ETDEWEB)
W. W. Lee, and R. A. Kolesnikov
2009-11-20
We show in this Response that the nonlinear Poisson's equation in our original paper derived from the drift kinetic approach can be verified by using the nonlinear gyrokinetic Poisson's equation of Dubin et al. [Phys. Fluids 26, 3524 (1983)]. This nonlinear contribution in φ2 is indeed of the order of k4⊥ in the long wavelength limit and remains finite for zero ion temperature, in contrast to the nonlinear term by Parra and Catto [Plasma Phys. Control. Fusion 50, 065014 (2008)], which is of the order of k2⊥ and diverges for Ti → 0. For comparison, the leading term for the gyrokinetic Poisson's equation in this limit is of the order of k2⊥φ,
Frydel, Derek
2011-06-21
We incorporate ion polarizabilities into the Poisson-Boltzmann equation by modifying the effective dielectric constant and the Boltzmann distribution of ions. The extent of the polarizability effects is controlled by two parameters, γ(1) and γ(2); γ(1) determines the polarization effects in a dilute system and γ(2) regulates the dependence of the polarizability effects on the concentration of ions. For a polarizable ion in an aqueous solution γ(1) ≈ 0.01 and the polarizability effects are negligible. The conditions where γ(1) and/or γ(2) are large and the polarizability is relevant involve the low dielectric constant media, high surface charge, and/or large ionic concentrations. © 2011 American Institute of Physics
Carling; Williams; Bowtell
1998-12-01
Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; it follows a path determined by the forces acting upon it, as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature's body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creature's body and in the growth and dissolution of the vortex structures has been illustrated.
Two-dimensional optical spectroscopy
Cho, Minhaeng
2009-01-01
Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.
Institute of Scientific and Technical Information of China (English)
舒英; 章顺; 吴文青; 黄自萍
2002-01-01
本文对分子生物物理学中产生的线性Poisson-Boltzmann方程(PBE),给出了Mortar有限元方法的计算过程,数值计算例子表明,与一般的协调有限元方法相比,用Mortar元方法求解此类有间断系数的问题是非常有效的.
leMesurier, Brenton John; Christiansen, Peter Leth; Gaididei, Yuri B; Rasmussen, Jens Juul
2004-10-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.
Priimak, Dmitri
2014-01-01
We present finite differences numerical algorithm for solving 2D spatially homogeneous Boltzmann transport equation for semiconductor superlattices (SL) subject to time dependant electric field along SL axis and constant perpendicular magnetic field. Algorithm is implemented in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPUs. We compare performance and merits of one implementation versus another and discuss various methods of optimization.
Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten
2016-08-01
The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.
Two-Dimensional Toda-Heisenberg Lattice
Directory of Open Access Journals (Sweden)
Vadim E. Vekslerchik
2013-06-01
Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.
Mobility anisotropy of two-dimensional semiconductors
Lang, Haifeng; Zhang, Shuqing; Liu, Zhirong
2016-12-01
The carrier mobility of anisotropic two-dimensional semiconductors under longitudinal acoustic phonon scattering was theoretically studied using deformation potential theory. Based on the Boltzmann equation with the relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was derived, showing that the influence of effective mass on mobility anisotropy is larger than those of deformation potential constant or elastic modulus. Parameters were collected for various anisotropic two-dimensional materials (black phosphorus, Hittorf's phosphorus, BC2N , MXene, TiS3, and GeCH3) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio is overestimated by the previously described method.
Energy Technology Data Exchange (ETDEWEB)
Ryne, Robert D.
2011-11-07
A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs)to perform mixed convolutions and correlations of the charge density with the Green function. Descriptions are provided for algorithms based on theordinary Green function and for an integrated Green function (IGF). Due to its similarity to the widely used Hockney algorithm for solving Poisson'sequation in free space, this capability can be easily implemented in many existing particle-in-cell beam dynamics codes.
AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov-Poisson equation
Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin; Yu, Kwangmin
2016-07-01
We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov-Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes of computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.
Institute of Scientific and Technical Information of China (English)
A.S.J.AL-SAIF; 朱正佑
2003-01-01
The traditional differential quadrature method was improved by using the upwind difference scheme for the convectiveterms to solve the coupled two-dimensional incompressible Navier-stokes equations and heat equation. The new method was comparedwith the conventional differential quadrature method in the aspects of convergence and accuracy. The results show that the newmethod is more accurate, and has better convergence than the conventional differential quadrature method for numerically computingthe steady-state solution.
Poisson Equation in Static Field Problems Based on CUDA%静场Poisson方程的CUDA并行计算
Institute of Scientific and Technical Information of China (English)
周振华; 赖生建
2011-01-01
In this paper, electrostatic field problems are parallel numerical computed by Compute Unified Device Architecture (CUDA) programming. That is, Jacobi iterative calculation for algebra equation which is derived from Poisson equation by finite difference numerical method is migrated to CUDA programming architecture and calculated by Graphics Processing Unit (GPU). Highly parallel implementation of the new parallel architecture in Jacobi iterative computation is propose and discuss in detail. At last, by the numerical experiment, the computation efficiency and accuracy of the CPU and GPU computing system are compared by the different dimension problems, and Jacobi iterative computation in GPU has highly acceleration ration.%本文研究了静场问题中采用CUDA编程进行并行数值计算，即静场Poisson方程中用有限差分法形成的代数方程组，将求解方程组的Jacobi迭代计算移植到基于CUDA编程框架，在GPU中进行计算。提出了一种在Jacobi迭代计算中高效并行计算方式，最后通过数值实验，比较基于传统CPU和GPU两种不同计算体系下不同大小计算问题的计算效率和精度，得到CUDA编程的Jacobi迭代算法在GPU中运行具有非常高加速比。
基于双层位势的Poisson方程无奇异方法%A Nonsingular Method Based on Double Layer Potential for Poisson Equation
Institute of Scientific and Technical Information of China (English)
林鑫; 高发玲
2014-01-01
针对求解Poisson方程的边值问题，利用虚边界上分布的矩密度，得出基于双层位势的虚边界元方程。该方法有效地避免了奇异和强奇异积分的计算。数值算例证明了算法的有效性和精确性。%Towards the boundary problem of Poisson equation,different from the virtual boundary element equation based on the single layer potential,another virtual boundary collocation method (VBCM)is conducted based on double layer potential for Poisson problem,with the moment density distributed on the virtual boundary. The VBCM can avoid the singular,hyper-singular integral ,the numerical example presents the efficiency and accuracy of the method.
Topological aspect of disclinations in two-dimensional crystals
Institute of Scientific and Technical Information of China (English)
Qi Wei-Kai; Zhu Tao; Chen Yong; Ren Ji-Rong
2009-01-01
By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given.
Institute of Scientific and Technical Information of China (English)
酒全森
2000-01-01
Some estimates on 2-D Euler equations are given when initial vorticity ω belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dimensional Euler equations when ω0(2,1)∈L.
Colombo, Maria
2017-01-01
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
Dynamics of film. [two dimensional continua theory
Zak, M.
1979-01-01
The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets. The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles. The theory is illustrated by examples.
The characters of nonlinear vibration in the two-dimensional discrete monoatomic lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2005-01-01
The two-dimensional discrete monoatomic lattice is analyzed. Taking nearest-neighbor interaction into account, the characters of the nonlinear vibration in two-dimensional discrete monoatomic lattice are described by the two-dimensional cubic nonlinear Schrodinger equation. Considering the quartic nonlinear potential, the two-dimensional discrete-soliton trains and the solutions perturbed by the neck mode are presented.
Li, Jun-Jie; Yan, Jia-Bin; Huang, Xiang-Yu
2015-12-01
Meshfree method offers high accuracy and computational capability and constructs the shape function without relying on predefined elements. We comparatively analyze the global weak form meshfree methods, such as element-free Galerkin method (EFGM), the point interpolation method (PIM), and the radial point interpolation method (RPIM). Taking two dimensional Poisson equation as an example, we discuss the support-domain dimensionless size, the field nodes, and background element settings with respect to their effect on calculation accuracy of the meshfree method. RPIM and EFGM are applied to controlled-source two-dimensional electromagnetic modeling with fixed shape parameters. The accuracy of boundary conditions imposed directly and by a penalty function are discussed in the case of forward modeling of two-dimensional magnetotellurics in a homogeneous medium model. The coupling algorithm of EFG-PIM and EFG-RPIM are generated by integrating the PIM or RPIM and EFGM. The results of the numerical modeling suggest the following. First, the proposed meshfree method and corresponding coupled methods are well-suited for electromagnetic numerical modeling. The accuracy of the algorithm is the highest when the support-domain dimensionless size is 1.0 and the distribution of field nodes is consistent with the nodes of background elements. Second, the accuracy of PIM and RPIM are lower than that of EFGM for the Poisson equation but higher than EFGM for the homogeneous medium MT response. Third, RPIM overcomes the matrix inversion problem of PIM and has a wider selection of support-domain dimensionless sizes as compared to RPIM.
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.
Bound states of two-dimensional relativistic harmonic oscillators
Institute of Scientific and Technical Information of China (English)
Qiang Wen-Chao
2004-01-01
We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.
Long-range ordering of topological excitations in a two-dimensional superfluid far from equilibrium
Salman, Hayder; Maestrini, Davide
2016-10-01
We study the relaxation of a two-dimensional (2D) ultracold Bose gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable square and rectangular traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a nonzero coarse-grained vorticity field. The stream function of this emergent quasiclassical 2D flow is governed by a Poisson-Boltzmann equation. This equation reveals that maximum entropy states of a neutral vortex gas that describe the spectral condensation of energy can be classified into types of flow depending on whether or not the flow spontaneously acquires angular momentum. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square reveal that a large-scale monopole flow field with net angular momentum emerges that is consistent with predictions of the Poisson-Boltzmann equation. The results allow us to characterize the spectral energy condensate in a 2D quantum fluid that bears striking similarity to similar flows observed in experiments of 2D classical turbulence. By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum.
Tewary, V. K.; Quardokus, Rebecca C.; DelRio, Frank W.
2016-04-01
A Green's function (GF) method is developed for interpreting scanning probe microscopy (SPM) measurements on new two-dimensional (2D) materials. GFs for the Laplace/Poisson equations are calculated by using a virtual source method for two separate cases of a finite material containing a rectangular defect and a hexagonal defect. The prescribed boundary values are reproduced almost exactly by the calculated GFs. It is suggested that the GF is not just a mathematical artefact but a basic physical characteristic of material systems, which can be measured directly by SPM for 2D solids. This should make SPM an even more powerful technique for characterization of 2D materials.
Reference manual for the POISSON/SUPERFISH Group of Codes
Energy Technology Data Exchange (ETDEWEB)
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 finite number of points on a mesh in the plane.
Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; QIANG Tian
2009-01-01
We study the existence and stability of two-dimensional discrete breathers in a two-dimensional discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling.Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential (soft or hard), the interaction potential (attractive or repulsive)and the center of the two-dimensional gap breather (on a light or a heavy atom).
Two-dimensional liquid chromatography
DEFF Research Database (Denmark)
Græsbøll, Rune
of this thesis is on online comprehensive two-dimensional liquid chromatography (online LC×LC) with reverse phase in both dimensions (online RP×RP). Since online RP×RP has not been attempted before within this research group, a significant part of this thesis consists of knowledge and experience gained...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...
SYMPLECTIC STRUCTURE OF POISSON SYSTEM
Institute of Scientific and Technical Information of China (English)
SUN Jian-qiang; MA Zhong-qi; TIAN Yi-min; QIN Meng-zhao
2005-01-01
When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform.Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.
Turchetti, G.; Rambaldi, S.; Bazzani, A.; Comunian, M.; Pisent, A.
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribition obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G.; Rambaldi, S.; Bazzani, A. [Dipartimento di Fisica and INFN, Via Irnerio 46, 40126, Bologna (Italy); Comunian, M.; Pisent, A. [INFN Laboratori Nazionali di Legnaro (Italy)
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribution obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Birzvalk, Yu.A.
1977-10-01
The peculiarities of averaging of a function with respect to one of its coordinates are studied, resulting in the formulation of two-dimensional MHD problems in the zero-induction approximation. The transition to the two-dimensional approximation is achieved by averaging all of the functions analyzed with respect to one of the coordinates. It is shown that when there is symmetry in the Poisson equation for the potential, components of the scalar product v.rot B appear, as a result of the fact that rot B = O. However, their appearance can also be explained by a clearer, though less strict, method. The importance of consideration of these components must be estimated in each specific problem. An elementary modeling problem is solved allowing the relative significance of the current density component in the direction with respect to which averaging is performed to be estimated. 2 references, 4 figures.
Weakly disordered two-dimensional Frenkel excitons
Boukahil, A.; Zettili, Nouredine
2004-03-01
We report the results of studies of the optical properties of weakly disordered two- dimensional Frenkel excitons in the Coherent Potential Approximation (CPA). An approximate complex Green's function for a square lattice with nearest neighbor interactions is used in the self-consistent equation to determine the coherent potential. It is shown that the Density of States is very much affected by the logarithmic singularities in the Green's function. Our CPA results are in excellent agreement with previous investigations by Schreiber and Toyozawa using the Monte Carlo simulation.
Mobility anisotropy of two-dimensional semiconductors
Lang, Haifeng; Liu, Zhirong
2016-01-01
The carrier mobility of anisotropic two-dimensional (2D) semiconductors under longitudinal acoustic (LA) phonon scattering was theoretically studied with the deformation potential theory. Based on Boltzmann equation with relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was deduced, which shows that the influence of effective mass to the mobility anisotropy is larger than that of deformation potential constant and elastic modulus. Parameters were collected for various anisotropic 2D materials (black phosphorus, Hittorf's phosphorus, BC$_2$N, MXene, TiS$_3$, GeCH$_3$) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio was overestimated in the past.
Institute of Scientific and Technical Information of China (English)
陈亚文; 邹学文
2012-01-01
为了克服观测数据有限以及数据存在一定误差对参数反演结果的影响,提出了一种参数反演的有效算法.根据已知参数的先验分布和已经获得的有误差的监测数据,以贝叶斯推理作为理论基础,获得参数的联合后验概率密度函数,再利用马尔科夫链蒙特卡罗模拟对后验分布进行采样,获得参数的后验边缘概率密度,由此得到了参数的数学期望等有效的统计量.数值模拟结果表明,此算法能够有效地解决二维非线性抛物型方程的参数识别反问题,且具有较高的精度.%In order to overcome the limited observation data with noise, an inversion of the effective parameters algorithm is presented. First, according to the parameters,a priori distribution and the limited observation data with noise, Bayesian inference as a theoretical foundation,parameters of the joint posterior probability density function are obtained. Markov chain Monte Carlo simulation was taken to sample the posterior distribution to get the marginal posterior probability function of the parameters, and the statistical quantities such as the mathematic expectation were calculated. Experimental results show that this algorithm can successfully solve the problem of two-dimensional nonlinear parabolic equation parameter inversion and inversion results have higher accuracy.
Two dimensional unstable scar statistics.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)
2006-12-01
This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.
Juday, Richard D.
1992-01-01
Modified vernier scale gives accurate two-dimensional coordinates from maps, drawings, or cathode-ray-tube displays. Movable circular overlay rests on fixed rectangular-grid overlay. Pitch of circles nine-tenths that of grid and, for greatest accuracy, radii of circles large compared with pitch of grid. Scale enables user to interpolate between finest divisions of regularly spaced rule simply by observing which mark on auxiliary vernier rule aligns with mark on primary rule.
Beralso 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.
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...... series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of the asymptotic covariance, which is used in the simulations and the analysis of some...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
2009-01-01
In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model...... for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric ergodicity...
Li, Xian-Ying; Hu, Shi-Min
2013-02-01
Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.
Two-dimensional liquid chromatography
DEFF Research Database (Denmark)
Græsbøll, Rune
Two-dimensional liquid chromatography has received increasing interest due to the rise in demand for analysis of complex chemical mixtures. Separation of complex mixtures is hard to achieve as a simple consequence of the sheer number of analytes, as these samples might contain hundreds or even...... dimensions. As a consequence of the conclusions made within this thesis, the research group has, for the time being, decided against further development of online LC×LC systems, since it was not deemed ideal for the intended application, the analysis of the polar fraction of oil. Trap-and...
A two-dimensional analytical model for short channel junctionless double-gate MOSFETs
Jiang, Chunsheng; Liang, Renrong; Wang, Jing; Xu, Jun
2015-05-01
A physics-based analytical model of electrostatic potential for short-channel junctionless double-gate MOSFETs (JLDGMTs) operated in the subthreshold regime is proposed, in which the full two-dimensional (2-D) Poisson's equation is solved in channel region by a method of series expansion similar to Green's function. The expression of the proposed electrostatic potential is completely rigorous and explicit. Based on this expression, analytical models of threshold voltage, subthreshold swing, and subthreshold drain current for JLDGMTs were derived. Subthreshold behavior was studied in detail by changing different device parameters and bias conditions, including doping concentration, channel thickness, gate length, gate oxide thickness, drain voltage, and gate voltage. Results predicted by all the analytical models agree well with numerical solutions from the 2-D simulator. These analytical models can be used to investigate the operating mechanisms of nanoscale JLDGMTs and to optimize their device performance.
Nonlinear excitations in two-dimensional molecular structures with impurities
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth
1995-01-01
We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the imp......We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....
Matsuo, Kuniaki; Saleh, Bahaa E. A.; Teich, Malvin Carl
1982-12-01
We investigate the counting statistics for stationary and nonstationary cascaded Poisson processes. A simple equation is obtained for the variance-to-mean ratio in the limit of long counting times. Explicit expressions for the forward-recurrence and inter-event-time probability density functions are also obtained. The results are expected to be of use in a number of areas of physics.
On the continua in two-dimensional nonadiabatic magnetohydrodynamic spectra
De Ploey, A.; Van der Linden, R. A. M.; Belien, A. J. C.
2000-01-01
The equations for the continuous subspectra of the linear magnetohydrodynamic (MHD) normal modes spectrum of two-dimensional (2D) plasmas are derived in general curvilinear coordinates, taking nonadiabatic effects in the energy equation into account. Previously published derivations of continuous sp
2D sigma models and differential Poisson algebras
Arias, Cesar; Boulanger, Nicolas; Sundell, Per; Torres-Gomez, Alexander
2015-08-01
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
2D sigma models and differential Poisson algebras
Arias, Cesar; Sundell, Per; Torres-Gomez, Alexander
2015-01-01
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to any worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
2D sigma models and differential Poisson algebras
Energy Technology Data Exchange (ETDEWEB)
Arias, Cesar [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Boulanger, Nicolas [Service de Mécanique et Gravitation, Université de Mons - UMONS,20 Place du Parc, 7000 Mons (Belgium); Laboratoire de Mathématiques et Physique Théorique,Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson,Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)
2015-08-18
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
An adaptive fast multipole accelerated Poisson solver for complex geometries
Askham, T.; Cerfon, A. J.
2017-09-01
We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient ;black box; fast solver.
Two-dimensional quantum repeaters
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Two-dimensional capillary origami
Brubaker, N. D.; Lega, J.
2016-01-01
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid.
Two-dimensional cubic convolution.
Reichenbach, Stephen E; Geng, Frank
2003-01-01
The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.
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
Two-dimensional gauge theoretic supergravities
Cangemi, D.; Leblanc, M.
1994-05-01
We investigate two-dimensional supergravity theories, which can be built from a topological and gauge invariant action defined on an ordinary surface. One is the N = 1 supersymmetric extension of the Jackiw-Teitelboim model presented by Chamseddine in a superspace formalism. We complement the proof of Montano, Aoaki and Sonnenschein that this extension is topological and gauge invariant, based on the graded de Sitter algebra. Not only do the equations of motion correspond to the supergravity ones and do gauge transformations encompass local supersymmetries, but we also identify the ∫-theory with the superfield formalism action written by Chamseddine. Next, we show that the N = 1 supersymmetric extension of string-inspired two-dimensional dilaton gravity put forward by Park and Strominger cannot be written as a ∫-theory. As an alternative, we propose two topological and gauge theories that are based on a graded extension of the extended Poincaré algebra and satisfy a vanishing-curvature condition. Both models are supersymmetric extensions of the string-inspired dilaton gravity.
Navarrete, Alvaro; Paredes, Angel; Salgueiro, José R.; Michinel, Humberto
2017-01-01
We analyze theoretically the Schrödinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermo-optical media and can be regarded as an analog system for a self-gravitating self-interacting wave. We compute numerically the family of radially symmetric ground-state bright stationary solutions for focusing and defocusing local nonlinearity, keeping in both cases a focusing nonlocal nonlinearity. We also analyze excited states and oscillations induced by fixing the temperature at the borders of the material. We provide simulations of soliton interactions, drawing analogies with the dynamics of galactic cores in the scalar field dark-matter scenario.
Poisson hierarchy of discrete strings
Energy Technology Data Exchange (ETDEWEB)
Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)
2016-01-28
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
A UNIVERSAL VARIATIONAL FORMULATION FOR TWO DIMENSIONAL FLUID MECHANICS
Institute of Scientific and Technical Information of China (English)
何吉欢
2001-01-01
A universal variational formulation for two dimensional fluid mechanics is obtained, which is subject to the so-called parameter-constrained equations (the relationship between parameters in two governing equations). By eliminating the constraints, the generalized variational principle (GVPs) can be readily derived from the formulation. The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms. Some illustrative examples are given to testify the effectiveness and simplicity of the method.
Quasinormal frequencies of asymptotically flat two-dimensional black holes
Lopez-Ortega, A
2011-01-01
We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.
Phonon hydrodynamics in two-dimensional materials.
Cepellotti, Andrea; Fugallo, Giorgia; Paulatto, Lorenzo; Lazzeri, Michele; Mauri, Francesco; Marzari, Nicola
2015-03-06
The conduction of heat in two dimensions displays a wealth of fascinating phenomena of key relevance to the scientific understanding and technological applications of graphene and related materials. Here, we use density-functional perturbation theory and an exact, variational solution of the Boltzmann transport equation to study fully from first-principles phonon transport and heat conductivity in graphene, boron nitride, molybdenum disulphide and the functionalized derivatives graphane and fluorographene. In all these materials, and at variance with typical three-dimensional solids, normal processes keep dominating over Umklapp scattering well-above cryogenic conditions, extending to room temperature and more. As a result, novel regimes emerge, with Poiseuille and Ziman hydrodynamics, hitherto typically confined to ultra-low temperatures, characterizing transport at ordinary conditions. Most remarkably, several of these two-dimensional materials admit wave-like heat diffusion, with second sound present at room temperature and above in graphene, boron nitride and graphane.
Classifying Two-dimensional Hyporeductive Triple Algebras
Issa, A Nourou
2010-01-01
Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple systems) and two-dimensional real Bol algebras is given.
Two dimensional heat transfer problem in flow boiling in a rectangular minichannel
Directory of Open Access Journals (Sweden)
Hożejowska Sylwia
2015-01-01
Full Text Available The paper presents mathematical modelling of flow boiling heat transfer in a rectangular minichannel asymmetrically heated by a thin and one-sided enhanced foil. Both surfaces are available for observations due to the openings covered with glass sheets. Thus, changes in the colour of the plain foil surface can be registered and then processed. Plain side of the heating foil is covered with a base coat and liquid crystal paint. Observation of the opposite, enhanced surface of the minichannel allows for identification of the gas-liquid two-phase flow patterns and vapour quality. A two-dimensional mathematical model of heat transfer in three subsequent layers (sheet glass, heating foil, liquid was proposed. Heat transfer in all these layers was described with the respective equations: Laplace equation, Poisson equation and energy equation, subject to boundary conditions corresponding to the observed physical process. The solutions (temperature distributions in all three layers were obtained by Trefftz method. Additionally, the temperature of the boiling liquid was obtained by homotopy perturbation method (HPM combined with Trefftz method. The heat transfer coefficient, derived from Robin boundary condition, was estimated in both approaches. In comparison, the results by both methods show very good agreement especially when restricted to the thermal sublayer.
Two-dimensional function photonic crystals
Wu, Xiang-Yao; Liu, Xiao-Jing; Liang, Yu
2016-01-01
In this paper, we have firstly proposed two-dimensional function photonic crystals, which the dielectric constants of medium columns are the functions of space coordinates $\\vec{r}$, it is different from the two-dimensional conventional photonic crystals constituting by the medium columns of dielectric constants are constants. We find the band gaps of two-dimensional function photonic crystals are different from the two-dimensional conventional photonic crystals, and when the functions form of dielectric constants are different, the band gaps structure should be changed, which can be designed into the appropriate band gaps structures by the two-dimensional function photonic crystals.
Qiao, Yu; Chen, Minxin
2015-01-01
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 has a very similar form to one term of the LHS model, but LHS...
Two-dimensional nonlinear nonequilibrium kinetic theory under steady heat conduction.
Hyeon-Deuk, Kim
2005-04-01
The two-dimensional steady-state Boltzmann equation for hard-disk molecules in the presence of a temperature gradient has been solved explicitly to second order in density and the temperature gradient. The two-dimensional equation of state and some physical quantities are calculated from it and compared with those for the two-dimensional steady-state Bhatnagar-Gross-Krook equation and information theory. We have found that the same kind of qualitative differences as the three-dimensional case among these theories still appear in the two-dimensional case.
Two-dimensional effects in nonlinear Kronig-Penney models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
Zhang, Zhi-Yong; Tan, Han-Dong; Wang, Kun-Peng; Lin, Chang-Hong; Zhang, Bin; Xie, Mao-Bi
2016-03-01
Traditional two-dimensional (2D) complex resistivity forward modeling is based on Poisson's equation but spectral induced polarization (SIP) data are the coproducts of the induced polarization (IP) and the electromagnetic induction (EMI) effects. This is especially true under high frequencies, where the EMI effect can exceed the IP effect. 2D inversion that only considers the IP effect reduces the reliability of the inversion data. In this paper, we derive differential equations using Maxwell's equations. With the introduction of the Cole-Cole model, we use the finite-element method to conduct 2D SIP forward modeling that considers the EMI and IP effects simultaneously. The data-space Occam method, in which different constraints to the model smoothness and parametric boundaries are introduced, is then used to simultaneously obtain the four parameters of the Cole—Cole model using multi-array electric field data. This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity. To improve the computational efficiency, message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion. Synthetic datasets were tested using both serial and parallel algorithms, and the tests suggest that the proposed parallel algorithm is robust and efficient.
Statistical study of approximations to two dimensional inviscid turbulence
Energy Technology Data Exchange (ETDEWEB)
Glaz, H.M.
1977-09-01
A numerical technique is developed for studying the ergodic and mixing hypotheses for the dynamical systems arising from the truncated Fourier transformed two-dimensional inviscid Navier-Stokes equations. This method has the advantage of exactly conserving energy and entropy (i.e., total vorticity) in the inviscid case except for numerical error in solving the ordinary differential equations. The development of the mathematical model as an approximation to a real physical (turbulent) flow and the numerical results obtained are discussed.
Lou, James; Shih, Chun-Yu; Lee, Eric
2010-01-05
Diffusiophoresis in concentrated suspensions of spherical colloids with charge-regulated surface is investigated theoretically. The charge-regulated surface considered here is the generalization of conventional constant surface potential and constant surface charge density situations. Kuwabara's unit cell model is adopted to describe the system and a pseudospectral method based on Chebyshev polynomial is employed to solve the governing general electrokinetic equations. Excellent agreements with experimental data available in literature were obtained for the limiting case of constant surface potential and very dilute suspension. It is found, among other things, that in general the larger the number of dissociated functional groups on particle surface is, the higher the particle surface potential, hence the larger the magnitude of the particle mobility. The electric potential on particle surface depends on both the concentration of dissociated hydrogen ions and the concentration of electrolyte in the solution. The electric potential on particle surface turns out to be the dominant factor in the determination of the eventual particle diffusiophoretic mobility. Local maximum of diffusiophoretic mobility as a function of double layer thickness is observed. Its reason and influence is discussed. Corresponding behavior for the constant potential situation, however, may yield a monotonously increasing profile.
Topological defects in two-dimensional crystals
Chen, Yong; Qi, Wei-Kai
2008-01-01
By using topological current theory, we study the inner topological structure of the topological defects in two-dimensional (2D) crystal. We find that there are two elementary point defects topological current in two-dimensional crystal, one for dislocations and the other for disclinations. The topological quantization and evolution of topological defects in two-dimensional crystals are discussed. Finally, We compare our theory with Brownian-dynamics simulations in 2D Yukawa systems.
Singular analysis of two-dimensional bifurcation system
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Bifurcation properties of two-dimensional bifurcation system are studied in this paper.Universal unfolding and transition sets of the bifurcation equations are obtained.The whole parametric plane is divided into several different persistent regions according to the type of motion,and the different qualitative bifurcation diagrams in different persistent regions are given.The bifurcation properties of the two-dimensional bifurcation system are compared with its reduced one-dimensional system.It is found that the system which is reduced to one dimension has lost many bifurcation properties.
Dynamics of vortex interactions in two-dimensional flows
DEFF Research Database (Denmark)
Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.
2002-01-01
a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 a(c) ...The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...
On two-dimensional magnetic reconnection with nonuniform resistivity
Malyshkin, Leonid M.; Kulsrud, Russell M.
2010-12-01
In this paper, two theoretical approaches for the calculation of the rate of quasi-stationary, two-dimensional magnetic reconnection with nonuniform anomalous resistivity are considered in the framework of incompressible magnetohydrodynamics (MHD). In the first, 'global' equations approach, the MHD equations are approximately solved for a whole reconnection layer, including the upstream and downstream regions and the layer center. In the second, 'local' equations approach, the equations are solved across the reconnection layer, including only the upstream region and the layer center. Both approaches give the same approximate answer for the reconnection rate. Our theoretical model is in agreement with the results of recent simulations of reconnection with spatially nonuniform resistivity.
Institute of Scientific and Technical Information of China (English)
A. BOUCHIKHI
2012-01-01
This paper presents an investigation of a DC glow discharge at low pressure in the normal mode and with Einstein's relation of electron diffusivity. Two-dimensional distributions in Cartesian geometry are presented in the stationary state, including electric potential, electron and ion densities, longitudinal and transverse electrics fields as well as electron temperature. Our results are compared with those obtained in existing literature. The model used in this work is based on the first three moments of Boltzmann's equation. They serve as the continuity equation, the momentum transfer and the energy equations. The set of equations for charged particles presented in monatomic argon gas are coupled in a self-consistent way with Poisson's equation. A parametric study varying the cathode voltage, gas pressure, and secondary electron emission coefficient predicts many of the well-known features of DC discharges.
Two-dimensional metric and tetrad gravities as constrained second order systems
Kiriushcheva, N; Ghalati, R N
2006-01-01
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method for analyzing singular systems, we consider the Hamiltonian formulation of metric and tetrad gravities in two-dimensional Riemannian spacetime treating them as constrained higher-derivative theories. The algebraic structure of the Poisson brackets of the constraints and the corresponding gauge transformations are investigated in both cases.
Reinisch, Gilbert C.; Gazeau, Maxime
2016-07-01
In this paper we consider a basic two-level nonlinear quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant α is provided within 99.95% accuracy by the present first-order non-relativistic and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).
Energy Technology Data Exchange (ETDEWEB)
Celestin, Sebastien; Bonaventura, Zdenek; Zeghondy, Barbar; Bourdon, Anne [Ecole Centrale Paris, EM2C, UPR CNRS 288, Grande voie des vignes, 92295 Chatenay-Malabry Cedex (France); Segur, Pierre, E-mail: sebastien.celestin@em2c.ecp.f, E-mail: anne.bourdon@em2c.ecp.f [Universite de Toulouse, LAPLACE, UMR CNRS 5213, INPT, UPS, 118 route de Narbonne, 31062 Toulouse Cedex 9 (France)
2009-03-21
This paper presents the application of the ghost fluid method (GFM) to solve Poisson's equation for streamer discharge simulations between electrodes of complex geometries. This approach allows one to use a simple rectilinear grid and nevertheless take into account the influence of the exact shape of the electrode on the calculation of the potential and the electric field. First, the validity of the GFM approach concerning the computation of the electric field is demonstrated by performing direct comparisons in a point-to-plane geometry of the Laplacian potential and electric field calculated with this method and given by the analytical solution. Second, the GFM is applied to the simulation of a positive streamer propagation in a hyperboloid-to-plane configuration studied by Kulikovsky (1998 Phys. Rev. E 57 7066-74). Very good agreement is obtained with the results of Kulikovsky (1998) on all positive streamer characteristics during its propagation in the interelectrode gap. Then the GFM is applied to simulate the discharge in preheated air at atmospheric pressure in point-to-point geometry. The propagation of positive and negative streamers from both point electrodes is observed. After the interaction of both discharges, the very rapid propagation of the positive streamer towards the cathode in the volume pre-ionized by the negative streamer is presented. This structure of the discharge is in qualitative agreement with the experiment.
Strongly interacting two-dimensional Dirac fermions
Lim, L.K.; Lazarides, A.; Hemmerich, Andreas; de Morais Smith, C.
2009-01-01
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature
Topology optimization of two-dimensional waveguides
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting
Chen, Leiming; Lee, Chiu Fan; Toner, John
2016-07-01
Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χx,y that characterize these correlations.
Smoothed Particle Hydrodynamics Method for Two-dimensional Stefan Problem
Tarwidi, Dede
2016-01-01
Smoothed particle hydrodynamics (SPH) is developed for modelling of melting and solidification. Enthalpy method is used to solve heat conduction equations which involved moving interface between phases. At first, we study the melting of floating ice in the water for two-dimensional system. The ice objects are assumed as solid particles floating in fluid particles. The fluid and solid motion are governed by Navier-Stokes equation and basic rigid dynamics equation, respectively. We also propose a strategy to separate solid particles due to melting and solidification. Numerical results are obtained and plotted for several initial conditions.
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
Energy Technology Data Exchange (ETDEWEB)
Chatterjee, Kausik, E-mail: kausik.chatterjee@aggiemail.usu.edu [Strategic and Military Space Division, Space Dynamics Laboratory, North Logan, UT 84341 (United States); Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322 (United States); Roadcap, John R., E-mail: john.roadcap@us.af.mil [Air Force Research Laboratory, Kirtland AFB, NM 87117 (United States); Singh, Surendra, E-mail: surendra-singh@utulsa.edu [Department of Electrical Engineering, The University of Tulsa, Tulsa, OK 74104 (United States)
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.
Two-dimensional imaginary lobachevsky space. Separation of variables and contractions
Energy Technology Data Exchange (ETDEWEB)
Pogosyan, G. S., E-mail: pogosyan@theor.jinr.ru; Yakhno, A. [Universidad de Guadalajara, Departamento de Matematicas, CUCEI (Mexico)
2011-07-15
The Inoenue-Wigner contraction from the SO(2, 1) group to the E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the corresponding two-dimensional homogeneous spaces: two-dimensional one sheeted hyperboloid and two-dimensional pseudo-Euclidean space. Here we consider the contraction limits of some basis functions for the subgroup coordinates only.
Gauging the Poisson sigma model
Zucchini, Roberto
2008-01-01
We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to the a generalization of the Weil model worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field theory, Poisson--Weil sigma model. We study the BV cohomology of the model and show its relation to Hamiltonian basic and equivariant Poisson cohomology. As an application, we carry out the gauge fixing of the pure Weil model and of the Poisson--Weil model. In the first case, we obtain the 2--dimensional version of Donaldson--Witten topological gauge theory, describing the moduli space of flat connections on a closed surface. In the second case, we recover the gauged A topological sigma model worked out by Baptista describing the moduli space of solutions of the so--called vortex equations.
Two Dimensional Plasmonic Cavities on Moire Surfaces
Balci, Sinan; Kocabas, Askin; Karabiyik, Mustafa; Kocabas, Coskun; Aydinli, Atilla
2010-03-01
We investigate surface plasmon polariton (SPP) cavitiy modes on two dimensional Moire surfaces in the visible spectrum. Two dimensional hexagonal Moire surface can be recorded on a photoresist layer using Interference lithography (IL). Two sequential exposures at slightly different angles in IL generate one dimensional Moire surfaces. Further sequential exposure for the same sample at slightly different angles after turning the sample 60 degrees around its own axis generates two dimensional hexagonal Moire cavity. Spectroscopic reflection measurements have shown plasmonic band gaps and cavity states at all the azimuthal angles (omnidirectional cavity and band gap formation) investigated. The plasmonic band gap edge and the cavity states energies show six fold symmetry on the two dimensional Moire surface as measured in reflection measurements.
Two-dimensional function photonic crystals
Liu, Xiao-Jing; Liang, Yu; Ma, Ji; Zhang, Si-Qi; Li, Hong; Wu, Xiang-Yao; Wu, Yi-Heng
2017-01-01
In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.
Two-Dimensional Planetary Surface Lander
Hemmati, H.; Sengupta, A.; Castillo, J.; McElrath, T.; Roberts, T.; Willis, P.
2014-06-01
A systems engineering study was conducted to leverage a new two-dimensional (2D) lander concept with a low per unit cost to enable scientific study at multiple locations with a single entry system as the delivery vehicle.
Conductivity of a two-dimensional guiding center plasma.
Montgomery, D.; Tappert, F.
1972-01-01
The Kubo method is used to calculate the electrical conductivity of a two-dimensional, strongly magnetized plasma. The particles interact through (logarithmic) electrostatic potentials and move with their guiding center drift velocities (Taylor-McNamara model). The thermal equilibrium dc conductivity can be evaluated analytically, but the ac conductivity involves numerical solution of a differential equation. Both conductivities fall off as the inverse first power of the magnetic field strength.
Interior design of a two-dimensional semiclassic black hole
Levanony, Dana; 10.1103/PhysRevD.80.084008
2009-01-01
We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. The field equations admit two types of singularities, and their local asymptotic structure is investigated. One of these singularities is found to develop, as a spacelike singularity, inside the black hole. We then study the internal structure of the evaporating black hole from the horizon to the singularity.
Towards a two dimensional model of surface piezoelectricity
Monge Víllora, Oscar
2016-01-01
We want to understand the behaviour of flexoelectricity and surface piezoelectricity and distinguish them in order to go deep into the controversies of the filed. This motivate the construction of a model of continuum flexoelectric theory. The model proposed is a two-dimensional model that integrates the electromechanical equations that include the elastic, dielectric, piezoelectric and flexoelectric effect on a rectangular sample. As the flexoelectric and the surface piezoelectric effects ap...
Multiscale Analysis for Field-Effect Penetration through Two-Dimensional Materials.
Tian, Tian; Rice, Peter; Santos, Elton J G; Shih, Chih-Jen
2016-08-10
Gate-tunable two-dimensional (2D) materials-based quantum capacitors (QCs) and van der Waals heterostructures involve tuning transport or optoelectronic characteristics by the field effect. Recent studies have attributed the observed gate-tunable characteristics to the change of the Fermi level in the first 2D layer adjacent to the dielectrics, whereas the penetration of the field effect through the one-molecule-thick material is often ignored or oversimplified. Here, we present a multiscale theoretical approach that combines first-principles electronic structure calculations and the Poisson-Boltzmann equation methods to model penetration of the field effect through graphene in a metal-oxide-graphene-semiconductor (MOGS) QC, including quantifying the degree of "transparency" for graphene two-dimensional electron gas (2DEG) to an electric displacement field. We find that the space charge density in the semiconductor layer can be modulated by gating in a nonlinear manner, forming an accumulation or inversion layer at the semiconductor/graphene interface. The degree of transparency is determined by the combined effect of graphene quantum capacitance and the semiconductor capacitance, which allows us to predict the ranking for a variety of monolayer 2D materials according to their transparency to an electric displacement field as follows: graphene > silicene > germanene > WS2 > WTe2 > WSe2 > MoS2 > phosphorene > MoSe2 > MoTe2, when the majority carrier is electron. Our findings reveal a general picture of operation modes and design rules for the 2D-materials-based QCs.
Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems
Naeem, Imran; Naz, Rehana; Khan, Muhammad Danish
2015-12-01
This article analyses the nonclassical symmetries and group invariant solution of boundary layer equations for two-dimensional heated flows. First, we derive the nonclassical symmetry determining equations with the aid of the computer package SADE. We solve these equations directly to obtain nonclassical symmetries. We follow standard procedure of computing nonclassical symmetries and consider two different scenarios, ξ1≠0 and ξ1=0, ξ2≠0. Several nonclassical symmetries are reported for both scenarios. Furthermore, numerous group invariant solutions for nonclassical symmetries are derived. The similarity variables associated with each nonclassical symmetry are computed. The similarity variables reduce the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) in terms of similarity variables. The reduced system of ODEs are solved to obtain group invariant solution for governing boundary layer equations for two-dimensional heated flow problems. We successfully formulate a physical problem of heat transfer analysis for fluid flow over a linearly stretching porous plat and, with suitable boundary conditions, we solve this problem.
Energy Technology Data Exchange (ETDEWEB)
Perez Guerrero, Jesus Salvador
1995-12-31
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.
Time-Changed Poisson Processes
Kumar, A; Vellaisamy, P
2011-01-01
We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDE's. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDE's corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index $0<\\beta<1,$ when $\\beta $ is a rational number. We then use this result to obtain the governing DDE for the mass function of Poisson process time-changed by tempered stable subordinator. Our results extend and complement the results in Baeumer et al. \\cite{B-M-N} and Beghin et al. \\cite{BO-1} in several directions.
Interpolation by two-dimensional cubic convolution
Shi, Jiazheng; Reichenbach, Stephen E.
2003-08-01
This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.
TWO-DIMENSIONAL TOPOLOGY OF COSMOLOGICAL REIONIZATION
Energy Technology Data Exchange (ETDEWEB)
Wang, Yougang; Xu, Yidong; Chen, Xuelei [Key Laboratory of Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 China (China); Park, Changbom [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); Kim, Juhan, E-mail: wangyg@bao.ac.cn, E-mail: cbp@kias.re.kr [Center for Advanced Computation, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)
2015-11-20
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two-dimensional genus curve for the early, middle, and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometre Array.
Two dimensional topology of cosmological reionization
Wang, Yougang; Xu, Yidong; Chen, Xuelei; Kim, Juhan
2015-01-01
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two dimensional genus curve for the early, middle and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometer Array.
Pfeiffer, F.; Meyer-Koenig, W.
1949-01-01
By means of characteristics theory, formulas for the numerical treatment of stationary compressible supersonic flows for the two-dimensional and rotationally symmetrical cases have been obtained from their differential equations.
A novel schedule for solving the two-dimensional diffusion problem in fractal heat transfer
Directory of Open Access Journals (Sweden)
Xu Shu
2015-01-01
Full Text Available In this work, the local fractional variational iteration method is employed to obtain approximate analytical solution of the two-dimensional diffusion equation in fractal heat transfer with help of local fractional derivative and integral operators.
Two-dimensional x-ray diffraction
He, Bob B
2009-01-01
Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea
Matching Two-dimensional Gel Electrophoresis' Spots
DEFF Research Database (Denmark)
Dos Anjos, António; AL-Tam, Faroq; Shahbazkia, Hamid Reza
2012-01-01
This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches. This ar......This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches...
Towards two-dimensional search engines
Ermann, Leonardo; Chepelianskii, Alexei D.; Shepelyansky, Dima L.
2011-01-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Statistical properties of inf...
Institute of Scientific and Technical Information of China (English)
包敏; 邢孟道; 李亚超; 保铮
2011-01-01
Because of the long integration time of Medium Earth Orbit SAR (MEO SAR), the hyperbolic range equation based on linear trajectory module is not suit for MEO SAR. Considering this issue, a high-order modified hyperbolic range equation is proposed. Incorporating with an additional linear component and quartic component, quartic Taylor series expansion of it has exactly the same value as which of the actual range history of MEO SAR. Then, the two-dimensional spectrum based on high-order modified hyperbolic range is analytically derived by using an approximate azimuth stationary point, based on method of series reversion the accuracy of the two-dimensional spectrum is analyzed which is exactly equal to quartic phase term. Simulation results show that the proposed range equation and the two-dimensional spectrum are accurate which can give fine resolution imagery with the entire aperture.%中轨道合成孔径雷达(MEO SAR)轨道高度高,合成孔径时间长,直线运动轨迹模型下的双曲线距离方程不再适用.针对这一问题,该文提出了一种适用于MEO SAR的高阶修正双曲线距离方程,该距离方程通过引入一线性项和一四次项对双曲线距离方程进行修正,使得其能对MEO SAR真实斜距历程进行四阶精确逼近.在此基础上,采用驻相点近似的方法推导该距离方程下2维频谱的闭合解析解,并结合级数反演法对频谱精度进行分析,发现采用驻相点近似方法得到的频谱精度严格精确到四次相位项,能满足MEO SAR精确成像的要求,为了便于成像算法的设计,该文对2维频谱各部分的空变性进行了分析.最后,仿真结果表明:该文距离方程和频谱精度较高,能实现MEO SAR全孔径精确成像.
The Persistence Problem in Two-Dimensional Fluid Turbulence
Perlekar, Prasad; Mitra, Dhrubaditya; Pandit, Rahul
2010-01-01
We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter {\\Lambda} to distinguish between vortical and extensional regions. We then use a direct numerical simulation (DNS) of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with a universal exponent {\\theta} = 3.1 \\pm 0.2.
Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation
Directory of Open Access Journals (Sweden)
Panjit MUSIK
2004-01-01
Full Text Available This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular Automata (LGA, which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM, known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A specific two-dimensional nine-velocity square Lattice model (D2Q9 Model is used in the simulation with the velocity at the top of the cavity kept fixed. LBM is an efficient method for reproducing the dynamics of cavity flow and the results which are comparable to those of previous work.
Two-dimensional localized structures in harmonically forced oscillatory systems
Ma, Y.-P.; Knobloch, E.
2016-12-01
Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous presence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcation on one of them. The bifurcation structures of steady circular fronts and localized target patterns are computed in the Turing-stable and Turing-unstable regimes. In particular, localized target patterns grow along the solution branch via ring insertion at the core in a process reminiscent of defect-mediated snaking in one spatial dimension. Stability of axisymmetric solutions on these branches with respect to axisymmetric and nonaxisymmetric perturbations is determined, and parameter regimes with stable axisymmetric oscillons are identified. Direct numerical simulations reveal novel depinning dynamics of localized target patterns in the radial direction, and of circular and planar localized hexagonal patterns in the fully two-dimensional system.
Enstrophy inertial range dynamics in generalized two-dimensional turbulence
Iwayama, Takahiro; Watanabe, Takeshi
2016-07-01
We show that the transition to a k-1 spectrum in the enstrophy inertial range of generalized two-dimensional turbulence can be derived analytically using the eddy damped quasinormal Markovianized (EDQNM) closure. The governing equation for the generalized two-dimensional fluid system includes a nonlinear term with a real parameter α . This parameter controls the relationship between the stream function and generalized vorticity and the nonlocality of the dynamics. An asymptotic analysis accounting for the overwhelming dominance of nonlocal triads allows the k-1 spectrum to be derived based upon a scaling analysis. We thereby provide a detailed analytical explanation for the scaling transition that occurs in the enstrophy inertial range at α =2 in terms of the spectral dynamics of the EDQNM closure, which extends and enhances the usual phenomenological explanations.
Piezoelectricity in Two-Dimensional Materials
Wu, Tao
2015-02-25
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.
Kronecker Product of Two-dimensional Arrays
Institute of Scientific and Technical Information of China (English)
Lei Hu
2006-01-01
Kronecker sequences constructed from short sequences are good sequences for spread spectrum communication systems. In this paper we study a similar problem for two-dimensional arrays, and we determine the linear complexity of the Kronecker product of two arrays. Our result shows that similar good property on linear complexity holds for Kronecker product of arrays.
A novel two dimensional particle velocity sensor
Pjetri, Olti; Wiegerink, Remco J.; Lammerink, Theo S.; Krijnen, Gijs J.
2013-01-01
In this paper we present a two wire, two-dimensional particle velocity sensor. The miniature sensor of size 1.0x2.5x0.525 mm, consisting of only two crossed wires, shows excellent directional sensitivity in both directions, thus requiring no directivity calibration, and is relatively easy to fabrica
Two-dimensional microstrip detector for neutrons
Energy Technology Data Exchange (ETDEWEB)
Oed, A. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs.
Two-dimensional magma-repository interactions
Bokhove, O.
2001-01-01
Two-dimensional simulations of magma-repository interactions reveal that the three phases --a shock tube, shock reflection and amplification, and shock attenuation and decay phase-- in a one-dimensional flow tube model have a precursor. This newly identified phase ``zero'' consists of the impact of
Two-dimensional subwavelength plasmonic lattice solitons
Ye, F; Hu, B; Panoiu, N C
2010-01-01
We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai
A two-dimensional Dirac fermion microscope
DEFF Research Database (Denmark)
Bøggild, Peter; Caridad, Jose; Stampfer, Christoph
2017-01-01
in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2...
Nonlinear acoustic propagation in two-dimensional ducts
Nayfeh, A. H.; Tsai, M.-S.
1974-01-01
The method of multiple scales is used to obtain a second-order uniformly valid expansion for the nonlinear acoustic wave propagation in a two-dimensional duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear effects tend to flatten and broaden the absorption versus frequency curve, in qualitative agreement with the experimental observations. Moreover, the effect of the gas nonlinearity increases with increasing sound frequency, whereas the effect of the material nonlinearity decreases with increasing sound frequency.
AN APPROACH IN MODELING TWO-DIMENSIONAL PARTIALLY CAVITATING FLOW
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
An approach of modeling viscosity, unsteady partially cavitating flows around lifting bodies is presented. By employing an one-fluid Navier-Stokers solver, the algorithm is proved to be able to handle two-dimensional laminar cavitating flows at moderate Reynolds number. Based on the state equation of water-vapor mixture, the constructive relations of densities and pressures are established. To numerically simulate the cavity wall, different pseudo transition of density models are presumed. The finite-volume method is adopted and the algorithm can be extended to three-dimensional cavitating flows.
Electronics based on two-dimensional materials.
Fiori, Gianluca; Bonaccorso, Francesco; Iannaccone, Giuseppe; Palacios, Tomás; Neumaier, Daniel; Seabaugh, Alan; Banerjee, Sanjay K; Colombo, Luigi
2014-10-01
The compelling demand for higher performance and lower power consumption in electronic systems is the main driving force of the electronics industry's quest for devices and/or architectures based on new materials. Here, we provide a review of electronic devices based on two-dimensional materials, outlining their potential as a technological option beyond scaled complementary metal-oxide-semiconductor switches. We focus on the performance limits and advantages of these materials and associated technologies, when exploited for both digital and analog applications, focusing on the main figures of merit needed to meet industry requirements. We also discuss the use of two-dimensional materials as an enabling factor for flexible electronics and provide our perspectives on future developments.
Two-dimensional ranking of Wikipedia articles
Zhirov, A. O.; Zhirov, O. V.; Shepelyansky, D. L.
2010-10-01
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.
Two-Dimensional NMR Lineshape Analysis
Waudby, Christopher A.; Ramos, Andres; Cabrita, Lisa D.; Christodoulou, John
2016-04-01
NMR titration experiments are a rich source of structural, mechanistic, thermodynamic and kinetic information on biomolecular interactions, which can be extracted through the quantitative analysis of resonance lineshapes. However, applications of such analyses are frequently limited by peak overlap inherent to complex biomolecular systems. Moreover, systematic errors may arise due to the analysis of two-dimensional data using theoretical frameworks developed for one-dimensional experiments. Here we introduce a more accurate and convenient method for the analysis of such data, based on the direct quantum mechanical simulation and fitting of entire two-dimensional experiments, which we implement in a new software tool, TITAN (TITration ANalysis). We expect the approach, which we demonstrate for a variety of protein-protein and protein-ligand interactions, to be particularly useful in providing information on multi-step or multi-component interactions.
Towards two-dimensional search engines
Ermann, Leonardo; Shepelyansky, Dima L
2011-01-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Information flow properties on PageRank-CheiRank plane are analyzed for networks of British, French and Italian Universities, Wikipedia, Linux Kernel, gene regulation and other networks. Methods of spam links control are also analyzed.
Toward two-dimensional search engines
Ermann, L.; Chepelianskii, A. D.; Shepelyansky, D. L.
2012-07-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank-CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed.
A two-dimensional Dirac fermion microscope
Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-01
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
A two-dimensional Dirac fermion microscope.
Bøggild, Peter; Caridad, José M; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-09
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
Central simple Poisson algebras
Institute of Scientific and Technical Information of China (English)
SU Yucai; XU Xiaoping
2004-01-01
Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
Two-Dimensional Scheduling: A Review
Directory of Open Access Journals (Sweden)
Zhuolei Xiao
2013-07-01
Full Text Available In this study, we present a literature review, classification schemes and analysis of methodology for scheduling problems on Batch Processing machine (BP with both processing time and job size constraints which is also regarded as Two-Dimensional (TD scheduling. Special attention is given to scheduling problems with non-identical job sizes and processing times, with details of the basic algorithms and other significant results.
Two dimensional fermions in four dimensional YM
Narayanan, R
2009-01-01
Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in $R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the size of the torus in units of $\\frac{1}{\\Lambda_{SU(N)}}$ is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit.
Two-dimensional Kagome photonic bandgap waveguide
DEFF Research Database (Denmark)
Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou;
2000-01-01
The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out....
String breaking in two-dimensional QCD
Hornbostel, K J
1999-01-01
I present results of a numerical calculation of the effects of light quark-antiquark pairs on the linear heavy-quark potential in light-cone quantized two-dimensional QCD. I extract the potential from the Q-Qbar component of the ground-state wavefunction, and observe string breaking at the heavy-light meson pair threshold. I briefly comment on the states responsible for the breaking.
Two-dimensional supramolecular electron spin arrays.
Wäckerlin, Christian; Nowakowski, Jan; Liu, Shi-Xia; Jaggi, Michael; Siewert, Dorota; Girovsky, Jan; Shchyrba, Aneliia; Hählen, Tatjana; Kleibert, Armin; Oppeneer, Peter M; Nolting, Frithjof; Decurtins, Silvio; Jung, Thomas A; Ballav, Nirmalya
2013-05-07
A bottom-up approach is introduced to fabricate two-dimensional self-assembled layers of molecular spin-systems containing Mn and Fe ions arranged in a chessboard lattice. We demonstrate that the Mn and Fe spin states can be reversibly operated by their selective response to coordination/decoordination of volatile ligands like ammonia (NH3). Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Two dimensional echocardiographic detection of intraatrial masses.
DePace, N L; Soulen, R L; Kotler, M N; Mintz, G S
1981-11-01
With two dimensional echocardiography, a left atrial mass was detected in 19 patients. Of these, 10 patients with rheumatic mitral stenosis had a left atrial thrombus. The distinctive two dimensional echocardiographic features of left atrial thrombus included a mass of irregular nonmobile laminated echos within an enlarged atrial cavity, usually with a broad base of attachment to the posterior left atrial wall. Seven patients had a left atrial myxoma. Usually, the myxoma appeared as a mottled ovoid, sharply demarcated mobile mass attached to the interatrial septum. One patient had a right atrial angiosarcoma that appeared as a nonmobile mass extending from the inferior vena caval-right atrial junction into the right atrial cavity. One patient had a left atrial leiomyosarcoma producing a highly mobile mass attached to the lateral wall of the left atrium. M mode echocardiography detected six of the seven myxomas, one thrombus and neither of the other tumors. Thus, two dimensional echocardiography appears to be the technique of choice in the detection, localization and differentiation of intraatrial masses.
2D Poisson sigma models with gauged vectorial supersymmetry
Bonezzi, Roberto; Sundell, Per; Torres-Gomez, Alexander
2015-08-01
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
2D Poisson sigma models with gauged vectorial supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Bonezzi, Roberto [Dipartimento di Fisica ed Astronomia, Università di Bologna and INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)
2015-08-12
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
2D Poisson sigma models with gauged vectorial supersymmetry
2015-01-01
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
2D Poisson Sigma Models with Gauged Vectorial Supersymmetry
Bonezzi, Roberto; Torres-Gomez, Alexander
2015-01-01
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
Poisson Morphisms and Reduced Affine Poisson Group Actions
Institute of Scientific and Technical Information of China (English)
YANG Qi Lin
2002-01-01
We establish the concept of a quotient affine Poisson group, and study the reduced Poisson action of the quotient of an affine Poisson group G on the quotient of an affine Poisson G-variety V. The Poisson morphisms (including equivariant cases) between Poisson affine varieties are also discussed.
DEFF Research Database (Denmark)
Reck, Kasper; Thomsen, Erik Vilain; Hansen, Ole
2011-01-01
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...
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.
Two-dimensional gas of massless Dirac fermions in graphene.
Novoselov, K S; Geim, A K; Morozov, S V; Jiang, D; Katsnelson, M I; Grigorieva, I V; Dubonos, S V; Firsov, A A
2005-11-10
Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.
Two-Dimensional turbulence in the inverse cascade range
Yakhot, V
1999-01-01
A theory of two-dimensional turbulence in the inverse energy cascade range is presented. Strong time-dependence of the large-scale features of the flow ($\\bar{u^{2}}\\propto t$) results in decoupling of the large-scale dynamics from statistically steady-state small-scale random processes. This time-dependence is also a reason for the localness of the pressure-gradient terms in the equations governing the small-scale velocity difference PDF's. The derived expressions for the pressure gradient contributions lead to a gaussian statistics of transverse velocity differences. The solution for the PDF of longitudinal velocity differences is based on a smallness of the energy flux in two-dimensional turbulence. The theory makes a few quantitative predictions which can be tested experimentally. One of the most surprising results, derived in this paper, is that the small-scale transverse velocity differences are governed by a linear Langevin-like equation, strirred by a non-local universal gaussian random force. This ex...
Analytical two-dimensional model of solar cell current-voltage characteristics
Energy Technology Data Exchange (ETDEWEB)
Caldararu, F.; Caldararu, M.; Nan, S.; Nicolaescu, D.; Vasile, S. (ICCE, Bucharest (RO). R and D Center for Electron Devices)
1991-06-01
This paper describes an analytical two-dimensional model for pn junction solar cell I-V characteristic. In order to solve the two-dimensional equations for the minority carrier concentration the Laplace transformation method is used. The model eliminates Hovel's assumptions concerning a one-dimensional model and provides an I-V characteristic that is simpler than those derived from the one-dimensional model. The method can be extended to any other device with two-dimensional symmetry. (author).
Two-dimensional photonic crystal surfactant detection.
Zhang, Jian-Tao; Smith, Natasha; Asher, Sanford A
2012-08-07
We developed a novel two-dimensional (2-D) crystalline colloidal array photonic crystal sensing material for the visual detection of amphiphilic molecules in water. A close-packed polystyrene 2-D array monolayer was embedded in a poly(N-isopropylacrylamide) (PNIPAAm)-based hydrogel film. These 2-D photonic crystals placed on a mirror show intense diffraction that enables them to be used for visual determination of analytes. Binding of surfactant molecules attaches ions to the sensor that swells the PNIPAAm-based hydrogel. The resulting increase in particle spacing red shifts the 2-D diffracted light. Incorporation of more hydrophobic monomers increases the sensitivity to surfactants.
Theory of two-dimensional transformations
Kanayama, Yutaka J.; Krahn, Gary W.
1998-01-01
The article of record may be found at http://dx.doi.org/10.1109/70.720359 Robotics and Automation, IEEE Transactions on This paper proposes a new "heterogeneous" two-dimensional (2D) transformation group ___ to solve motion analysis/planning problems in robotics. In this theory, we use a 3×1 matrix to represent a transformation as opposed to a 3×3 matrix in the homogeneous formulation. First, this theory is as capable as the homogeneous theory, Because of the minimal size, its implement...
Two-dimensional ranking of Wikipedia articles
Zhirov, A O; Shepelyansky, D L
2010-01-01
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. We analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.
Sums of two-dimensional spectral triples
DEFF Research Database (Denmark)
Christensen, Erik; Ivan, Cristina
2007-01-01
construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly......, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval....
Binding energy of two-dimensional biexcitons
DEFF Research Database (Denmark)
Singh, Jai; Birkedal, Dan; Vadim, Lyssenko;
1996-01-01
Using a model structure for a two-dimensional (2D) biexciton confined in a quantum well, it is shown that the form of the Hamiltonian of the 2D biexciton reduces into that of an exciton. The binding energies and Bohr radii of a 2D biexciton in its various internal energy states are derived...... analytically using the fractional dimension approach. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be 0.228, which agrees very well with the recent experimental value. The results of our approach are compared with those of earlier theories....
Institute of Scientific and Technical Information of China (English)
HAN Xiu-Xun; WU Jie-Jun; LI Jie-Min; CONG Guang-Wei; LIU Xiang-Lin; ZHU Qin-Sheng; WANG Zhan-Guo
2005-01-01
@@ Low-temperature photoluminescence measurement is performed on an undoped Alx Ga1-xN/GaN heterostructure. Temperature-dependent Hall mobility confirms the formation of two-dimensional electron gas (2DEG) near the heterointerface. A weak photoluminescence (PL) peak with the energy of ～79meV lower than the free exciton (FE) emission of bulk GaN is related to the radiative recombination between electrons confined in the triangular well and the holes near the flat-band region of GaN. Its identification is supported by the solution of coupled one-dimensional Poisson and Schrodinger equations. When the temperature increases, the red shift of the 2DEG related emission peak is slower than that of the FE peak. The enhanced screening effect coming from the increasing 2DEG concentration and the varying electron distribution at two lowest subbands as a function of temperature account for such behaviour.
Two-dimensional wave propagation in layered periodic media
Quezada de Luna, Manuel
2014-09-16
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using highorder homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coeffi cient equations.
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D; Abdelhamid, H M; Morrison, P J
2016-01-01
A comprehensive study of a reduced version of Lust's equations, the extended magnetohydrodynamic (XMHD) model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality, is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way energy conservation along with four families of Casimir invariants are naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
Transport of Bose-Einstein condensates through two dimensional cavities
Energy Technology Data Exchange (ETDEWEB)
Hartmann, Timo
2015-06-01
The recent experimental advances in manipulating ultra-cold atoms make it feasible to study coherent transport of Bose-Einstein condensates (BEC) through various mesoscopic structures. In this work the quasi-stationary propagation of BEC matter waves through two dimensional cavities is investigated using numerical simulations within the mean-field approach of the Gross-Pitaevskii equation. The focus is on the interplay between interference effects and the interaction term in the non-linear wave equation. One sees that the transport properties show a complicated behaviour with multi-stability, hysteresis and dynamical instabilities for non-vanishing interaction. Furthermore, the prominent weak localization effect, which is a robust interference effect emerging after taking a configuration average, is reduced and partially inverted for non-vanishing interaction.
Hörmander multipliers on two-dimensional dyadic Hardy spaces
Daly, J.; Fridli, S.
2008-12-01
In this paper we are interested in conditions on the coefficients of a two-dimensional Walsh multiplier operator that imply the operator is bounded on certain of the Hardy type spaces Hp, 0Dokl. Akad. Nauk SSSR 109 (1956) 701-703; S.G. Mihlin, Multidimensional Singular Integrals and Integral Equations, Pergamon Press, 1965]. In this paper we extend these results to the two-dimensional dyadic Hardy spaces.
Two-Dimensional Theory of Scientific Representation
Directory of Open Access Journals (Sweden)
A Yaghmaie
2013-03-01
Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional.
Two-dimensional shape memory graphene oxide
Chang, Zhenyue; Deng, Junkai; Chandrakumara, Ganaka G.; Yan, Wenyi; Liu, Jefferson Zhe
2016-06-01
Driven by the increasing demand for micro-/nano-technologies, stimuli-responsive shape memory materials at nanoscale have recently attracted great research interests. However, by reducing the size of conventional shape memory materials down to approximately nanometre range, the shape memory effect diminishes. Here, using density functional theory calculations, we report the discovery of a shape memory effect in a two-dimensional atomically thin graphene oxide crystal with ordered epoxy groups, namely C8O. A maximum recoverable strain of 14.5% is achieved as a result of reversible phase transition between two intrinsically stable phases. Our calculations conclude co-existence of the two stable phases in a coherent crystal lattice, giving rise to the possibility of constructing multiple temporary shapes in a single material, thus, enabling highly desirable programmability. With an atomic thickness, excellent shape memory mechanical properties and electric field stimulus, the discovery of a two-dimensional shape memory graphene oxide opens a path for the development of exceptional micro-/nano-electromechanical devices.
Continuous magnetohydrodynamic spectra of two-dimensional coronal magnetostatic flux tubes
Belien, A. J. C.; Poedts, S.; Goedbloed, J. P.
1997-01-01
In this paper we derive the equations for the continuous ideal magnetohydrodynamic (MHD) spectrum of two-dimensional coronal loops, including gravity and expansion, in general curvilinear coordinates. The equations clearly show the coupling between Alfven and slow magnetosonic continuum waves when b
Two new integrable cases of two-dimensional quantum mechanics with a magnetic field
Marikhin, V. G.
2016-04-01
Two integrable cases of two-dimensional Schrödinger equation with a magnetic field are proposed. Using the polar coordinates and the symmetrical gauge, we will obtain solutions of these equations through biconfluent and confluent Heun functions. The quantization rules will be derived for both systems under consideration.
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2007-01-01
Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generafized discrete two-dimensional monatomic model.It is proven that the twodimensional compact-like discrete breathers exist not only in two-dimensional soft Ф4 potentials but also in hard two-dimensional Ф4 potentials and pure two-dimensional K4 lattices.The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Ф4 potential are determined by coupling parameter K4,while those in pure two-dimensional K4 lattices have no coupling with parameter K4.The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.
Hamiltonian and action formalisms for two-dimensional gyroviscous MHD
Morrison, P J; Acevedo, R
2014-01-01
A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD) model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.
Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics
Morrison, P. J.; Lingam, M.; Acevedo, R.
2014-08-01
A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.
Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Morrison, P. J., E-mail: morrison@physics.utexas.edu; Lingam, M., E-mail: manasvi@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States); Acevedo, R., E-mail: raul-ace60@yahoo.com [3311 Black Locust Dr., Sugar Land, Texas 77479 (United States)
2014-08-15
A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.
The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
Matsyuk, Roman Ya.
2008-02-01
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.
The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
Matsyuk, Roman Ya
2008-01-01
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.
The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
Directory of Open Access Journals (Sweden)
Roman Ya. Matsyuk
2008-02-01
Full Text Available The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo-Euclidean geometry.
Optimal excitation of two dimensional Holmboe instabilities
Constantinou, Navid C
2010-01-01
Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However these instabilities occur in tongues for a limited range of parameters. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that obtains for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges for parameter values ...
Probabilistic Universality in two-dimensional Dynamics
Lyubich, Mikhail
2011-01-01
In this paper we continue to explore infinitely renormalizable H\\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with the one-dimensional Cantor attractor is at most 1/2-H\\"older. Another formulation of this phenomenon is that the scaling structure of the H\\'enon Cantor attractor differs from its one-dimensional counterpart. However, in this paper we prove that the weight assigned by the canonical invariant measure to these bad spots tends to zero on microscopic scales. This phenomenon is called {\\it Probabilistic Universality}. It implies, in particular, that the Hausdorff dimension of the canonical measure is universal. In this way, universality and rigidity phenomena of one-dimensional dynamics assume a probabilistic nature in the two-dimensional world.
Two-dimensional position sensitive neutron detector
Indian Academy of Sciences (India)
A M Shaikh; S S Desai; A K Patra
2004-08-01
A two-dimensional position sensitive neutron detector has been developed. The detector is a 3He + Kr filled multiwire proportional counter with charge division position readout and has a sensitive area of 345 mm × 345 mm, pixel size 5 mm × 5 mm, active depth 25 mm and is designed for efficiency of 70% for 4 Å neutrons. The detector is tested with 0.5 bar 3He + 1.5 bar krypton gas mixture in active chamber and 2 bar 4He in compensating chamber. The pulse height spectrum recorded at an anode potential of 2000 V shows energy resolution of ∼ 25% for the 764 keV peak. A spatial resolution of 8 mm × 6 mm is achieved. The detector is suitable for SANS studies in the range of 0.02–0.25 Å-1.
Two-dimensional heterostructures for energy storage
Pomerantseva, Ekaterina; Gogotsi, Yury
2017-07-01
Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. We also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies.
Rationally synthesized two-dimensional polymers.
Colson, John W; Dichtel, William R
2013-06-01
Synthetic polymers exhibit diverse and useful properties and influence most aspects of modern life. Many polymerization methods provide linear or branched macromolecules, frequently with outstanding functional-group tolerance and molecular weight control. In contrast, extending polymerization strategies to two-dimensional periodic structures is in its infancy, and successful examples have emerged only recently through molecular framework, surface science and crystal engineering approaches. In this Review, we describe successful 2D polymerization strategies, as well as seminal research that inspired their development. These methods include the synthesis of 2D covalent organic frameworks as layered crystals and thin films, surface-mediated polymerization of polyfunctional monomers, and solid-state topochemical polymerizations. Early application targets of 2D polymers include gas separation and storage, optoelectronic devices and membranes, each of which might benefit from predictable long-range molecular organization inherent to this macromolecular architecture.
Janus Spectra in Two-Dimensional Flows
Liu, Chien-Chia; Cerbus, Rory T.; Chakraborty, Pinaki
2016-09-01
In large-scale atmospheric flows, soap-film flows, and other two-dimensional flows, the exponent of the turbulent energy spectra, α , may theoretically take either of two distinct values, 3 or 5 /3 , but measurements downstream of obstacles have invariably revealed α =3 . Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which α transitions from 3 to 5 /3 for the streamwise fluctuations but remains equal to 3 for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows.
Local doping of two-dimensional materials
Wong, Dillon; Velasco, Jr, Jairo; Ju, Long; Kahn, Salman; Lee, Juwon; Germany, Chad E.; Zettl, Alexander K.; Wang, Feng; Crommie, Michael F.
2016-09-20
This disclosure provides systems, methods, and apparatus related to locally doping two-dimensional (2D) materials. In one aspect, an assembly including a substrate, a first insulator disposed on the substrate, a second insulator disposed on the first insulator, and a 2D material disposed on the second insulator is formed. A first voltage is applied between the 2D material and the substrate. With the first voltage applied between the 2D material and the substrate, a second voltage is applied between the 2D material and a probe positioned proximate the 2D material. The second voltage between the 2D material and the probe is removed. The first voltage between the 2D material and the substrate is removed. A portion of the 2D material proximate the probe when the second voltage was applied has a different electron density compared to a remainder of the 2D material.
Two-dimensional fourier transform spectrometer
Energy Technology Data Exchange (ETDEWEB)
DeFlores, Lauren; Tokmakoff, Andrei
2016-10-25
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
FACE RECOGNITION USING TWO DIMENSIONAL LAPLACIAN EIGENMAP
Institute of Scientific and Technical Information of China (English)
Chen Jiangfeng; Yuan Baozong; Pei Bingnan
2008-01-01
Recently,some research efforts have shown that face images possibly reside on a nonlinear sub-manifold. Though Laplacianfaces method considered the manifold structures of the face images,it has limits to solve face recognition problem. This paper proposes a new feature extraction method,Two Dimensional Laplacian EigenMap (2DLEM),which especially considers the manifold structures of the face images,and extracts the proper features from face image matrix directly by using a linear transformation. As opposed to Laplacianfaces,2DLEM extracts features directly from 2D images without a vectorization preprocessing. To test 2DLEM and evaluate its performance,a series of ex-periments are performed on the ORL database and the Yale database. Moreover,several experiments are performed to compare the performance of three 2D methods. The experiments show that 2DLEM achieves the best performance.
Equivalency of two-dimensional algebras
Energy Technology Data Exchange (ETDEWEB)
Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S. [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica
2011-07-01
Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)
Confinement and dynamical regulation in two-dimensional convective turbulence
DEFF Research Database (Denmark)
Bian, N.H.; Garcia, O.E.
2003-01-01
In this work the nature of confinement improvement implied by the self-consistent generation of mean flows in two-dimensional convective turbulence is studied. The confinement variations are linked to two distinct regulation mechanisms which are also shown to be at the origin of low-frequency bur......In this work the nature of confinement improvement implied by the self-consistent generation of mean flows in two-dimensional convective turbulence is studied. The confinement variations are linked to two distinct regulation mechanisms which are also shown to be at the origin of low......-frequency bursting in the fluctuation level and the convective heat flux integral, both resulting in a state of large-scale intermittency. The first one involves the control of convective transport by sheared mean flows. This regulation relies on the conservative transfer of kinetic energy from tilted fluctuations...... to the mean component of the flow. Bursting can also result from the quasi-linear modification of the linear instability drive which is the mean pressure gradient. For each bursting process the relevant zero-dimensional model equations are given. These are finally coupled in a minimal model of convection...
Two Dimensional Connectivity for Vehicular Ad-Hoc Networks
Farivar, Masoud; Ashtiani, Farid
2008-01-01
In this paper, we focus on two-dimensional connectivity in sparse vehicular ad hoc networks (VANETs). In this respect, we find thresholds for the arrival rates of vehicles at entrances of a block of streets such that the connectivity is guaranteed for any desired probability. To this end, we exploit a mobility model recently proposed for sparse VANETs, based on BCMP open queuing networks and solve the related traffic equations to find the traffic characteristics of each street and use the results to compute the exact probability of connectivity along these streets. Then, we use the results from percolation theory and the proposed fast algorithms for evaluation of bond percolation problem in a random graph corresponding to the block of the streets. We then find sufficiently accurate two dimensional connectivity-related parameters, such as the average number of intersections connected to each other and the size of the largest set of inter-connected intersections. We have also proposed lower bounds for the case ...
Two-dimensional investigation of forced bubble oscillation under microgravity
Institute of Scientific and Technical Information of China (English)
HONG Ruoyu; Masahiro KAWAJI
2003-01-01
Recent referential studies of fluid interfaces subjected to small vibration under microgravity conditions are reviewed. An experimental investigation was carried out aboard the American Space Shuttle Discovery. Two-dimensional (2-D) modeling and simulation were conducted to further understand the experimental results. The oscillation of a bubble in fluid under surface tension is governed by the incompressible Navier-Stokes equations. The SIMPLEC algorithm was used to solve the partial differential equations on an Eulerian mesh in a 2-D coordinate. Free surfaces were represented with the volume of fluid (VOF) obtained by solving a kinematic equation. Surface tension was modeled via a continuous surface force (CSF) algorithm that ensures robustness and accuracy. A new surface reconstruction scheme, alternative phase integration (API) scheme, was adopted to solve the kinematic equation, and was compared with referential schemes. Numerical computations were conducted to simulate the transient behavior of an oscillating gas bubble in mineral oil under different conditions. The bubble positions and shapes under different external vibrations were obtained numerically. The computed bubble oscillation amplitudes were compared with experimental data.
All or nothing: On the small fluctuations of two-dimensional string theoretic black holes
Energy Technology Data Exchange (ETDEWEB)
Gilbert, Gerald [Univ. of Maryland, College Park, MD (United States); Raiten, Eric [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
1992-10-01
A comprehensive analysis of small fluctuations about two-dimensional string-theoretic and string-inspired black holes is presented. It is shown with specific examples that two-dimensional black holes behave in a radically different way from all known black holes in four dimensions. For both the SL(2,R)/U(1) black hole and the two-dimensional black hole coupled to a massive dilaton with constant field strength, it is shown that there are a {\\it continuous infinity} of solutions to the linearized equations of motion, which are such that it is impossible to ascertain the classical linear response. It is further shown that the two-dimensional black hole coupled to a massive, linear dilaton admits {\\it no small fluctuations at all}. We discuss possible implications of our results for the Callan-Giddings-Harvey-Strominger black hole.
Institute of Scientific and Technical Information of China (English)
屈哲; 陶可勤
2015-01-01
欧拉-泊松方程的椭圆函数周期解渐近性收敛模型是实现浮点数据模糊加密核心基础，广泛应用在通信编码和数据加密等领域。对浮点数据的模糊加密能有效保证网络中实时数据交互通信的安全，通过对浮点数据模糊加密稀疏集准确构造建模，提高加密性能。提出采用欧拉-泊松方程的椭圆函数周期解渐近性收敛数学建模的方法实现对浮点数据进行模糊加密，利用压缩映射原理来完成特征解分区处理，给出在控制单元的作用下对浮点数据进行密钥重整，求得欧拉-泊松方程椭圆函数在不定搜索下的三孤波解。通过数学推导证明了欧拉-泊松方程椭圆函数的周期解式渐进收敛性，实现对大数据库的数据加密，实验得出该加密数学模型的收敛性能较好，性能优越。%The elliptic function periodic solutions of the Euler Poisson equations asymptotic convergence of the model is the realization of floating-point data encryption based fuzzy core, widely used in the communication code and data encryption and other fields. The fuzzy of floating-point data encryption can effectively guarantee the real-time data communication net⁃work security, based on fuzzy set accurate floating-point data encryption sparse structure modeling, improve the encryption performance. Proposed elliptic function periodic using Euler Poisson equation method for the solution of asymptotic conver⁃gence of mathematical modeling to achieve floating-point fuzzy data encryption, by using the contraction mapping principle to complete the characteristic solution separately are given in the control unit under the action of the floating point data are key reforming, obtained the Euler Poisson equations of elliptic function in indefinite search the three solitary wave solu⁃tions. Through mathematical derivation of gradual convergence of the cycle solution of Euler Poisson equations of elliptic function is
On numerical evaluation of two-dimensional phase integrals
DEFF Research Database (Denmark)
Lessow, H.; Rusch, W.; Schjær-Jacobsen, Hans
1975-01-01
The relative advantages of several common numerical integration algorithms used in computing two-dimensional phase integrals are evaluated.......The relative advantages of several common numerical integration algorithms used in computing two-dimensional phase integrals are evaluated....
Institute of Scientific and Technical Information of China (English)
HOU Jing-Min
2009-01-01
We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagome optical lattice under an effective magnetic field,which can be realized with laser beams.We derive the generalized Harper's equations from the Schr(o)dinger equation.The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations.We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
Effects of finite laser pulse width on two-dimensional electronic spectroscopy
Leng, Xuan; Yue, Shuai; Weng, Yu-Xiang; Song, Kai; Shi, Qiang
2017-01-01
We combine the hierarchical equations of motion method and the equation-of-motion phase-matching approach to calculate two-dimensional electronic spectra of model systems. When the laser pulse is short enough, the current method reproduces the results based on third-order response function calculations in the impulsive limit. Finite laser pulse width is found to affect both the peak positions and shapes, as well as the time evolution of diagonal and cross peaks. Simulations of the two-color two-dimensional electronic spectra also show that, to observe quantum beats in the diagonal and cross peaks, it is necessary to excite the related excitonic states simultaneously.
Natale, Andrea
2016-01-01
We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretisation introduced in Natale and Cotter (2016a) and the SUPG discretisation of the vorticity advection equation. Such discretisations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non-local energy backscatter that characterises two-dimensional turbulent flows.
Stationary states of the two-dimensional nonlinear Schrödinger model with disorder
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth
1998-01-01
Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder. In the discr......Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder...
Cooperation in two-dimensional mixed-games
Amaral, Marco A; Wardil, Lucas
2015-01-01
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two individuals is uniformly drawn from a sample of two different games. Using the master equation approach we show that the random mixture of two games is equivalent to play the average game when (i) the strategies are statistically independent of the game distribution and (ii) the transition rates are linear functions of the payoffs. We also use Monte-Carlo simulations in a two dimensional lattice and mean-field techniques to investigate the scenario when the two above conditions do not hold. We find that even outside of such conditions, several quantities characterizing the mixed-games are still the same as the ones obtained in the average game when the two games are not very different.
Symmetry breaking of solitons in two-dimensional complex potentials
Yang, Jianke
2014-01-01
Symmetry breaking is reported for continuous families of solitons in the nonlinear Schr\\"odinger equation with a two-dimensional complex potential. This symmetry-breaking bifurcation is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, such symmetry breaking is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel stability properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenval...
Two dimensional fractional projectile motion in a resisting medium
Rosales, Juan; Guía, Manuel; Gómez, Francisco; Aguilar, Flor; Martínez, Juan
2014-07-01
In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)-1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.
Soliton nanoantennas in two-dimensional arrays of quantum dots
Gligorić, G; Hadžievski, Lj; Slepyan, G Ya; Malomed, B A
2015-01-01
We consider two-dimensional (2D) arrays of self-organized semiconductor quantum dots (QDs) strongly interacting with electromagnetic field in the regime of Rabi oscillations. The QD array built of two-level states is modelled by two coupled systems of discrete nonlinear Schr\\"{o}dinger equations. Localized modes in the form of single-peaked fundamental and vortical stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and radiative properties of the Rabi modes suggest a concept of a self-assembled 2D \\textit{% soliton-based nano-antenna}, which should be stable against imperfections In particular, we discuss the implementation of such a nano-antenna in the form of surface plasmon solitons in graphene, and illustrate possibilities to control their operation by means of optical tools.
Surface Ship Shock Modeling and Simulation: Two-Dimensional Analysis
Directory of Open Access Journals (Sweden)
Young S. Shin
1998-01-01
Full Text Available The modeling and simulation of the response of a surface ship system to underwater explosion requires an understanding of many different subject areas. These include the process of underwater explosion events, shock wave propagation, explosion gas bubble behavior and bubble-pulse loading, bulk and local cavitation, free surface effect, fluid-structure interaction, and structural dynamics. This paper investigates the effects of fluid-structure interaction and cavitation on the response of a surface ship using USA-NASTRAN-CFA code. First, the one-dimensional Bleich-Sandler model is used to validate the approach, and second, the underwater shock response of a two-dimensional mid-section model of a surface ship is predicted with a surrounding fluid model using a constitutive equation of a bilinear fluid which does not allow transmission of negative pressures.
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D.; Tassi, E.; Abdelhamid, H. M.; Morrison, P. J.
2017-01-01
A comprehensive study of the extended magnetohydrodynamic model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way, the energy conservation along with four families of Casimir invariants is naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular, normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
Anomaly matching condition in two-dimensional systems
Dubinkin, O; Gubankova, E
2016-01-01
Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in ${\\rm QCD}_4$, we derive its analog in two-dimensional system. It connects the transverse part of mixed vector-axial current two-point function with diagonal vector and axial current two-point functions. Being fully non-perturbative, this relation may be regarded as anomaly matching for conductivities or certain transport coefficients depending on the system. We consider the holographic RG flows in holographic Yang-Mills-Chern-Simons theory via the Hamilton-Jacobi equation with respect to the radial coordinate. Within this holographic model it is found that the RG flows for the following relations are diagonal: Son-Yamamoto relation and the left-right polarization operator. Thus the Son-Yamamoto relation holds at wide range of energy scales.
The modified cumulant expansion for two-dimensional isotropic turbulence
Tatsumi, T.; Yanase, S.
1981-09-01
The two-dimensional isotropic turbulence in an incompressible fluid is investigated using the modified zero fourth-order cumulant approximation. The dynamical equation for the energy spectrum obtained under this approximation is solved numerically and the similarity laws governing the solution in the energy-containing and enstrophy-dissipation ranges are derived analytically. At large Reynolds numbers the numerical solutions yield the k to the -3rd power inertial subrange spectrum which was predicted by Kraichnan (1967), Leith (1968) and Batchelor (1969), assuming a finite enstrophy dissipation in the inviscid limit. The energy-containing range is found to satisfy an inviscid similarity while the enstrophy-dissipation range is governed by the quasi-equilibrium similarity with respect to the enstrophy dissipation as proposed by Batchelor (1969). There exists a critical time which separates the initial period and the similarity period in which the enstrophy dissipation vanishes and remains non-zero respectively in the inviscid limit.
Two dimensional velocity distribution in open channels using Renyi entropy
Kumbhakar, Manotosh; Ghoshal, Koeli
2016-05-01
In this study, the entropy concept is employed for describing the two-dimensional velocity distribution in an open channel. Using the principle of maximum entropy, the velocity distribution is derived by maximizing the Renyi entropy by assuming dimensionless velocity as a random variable. The derived velocity equation is capable of describing the variation of velocity along both the vertical and transverse directions with maximum velocity occurring on or below the water surface. The developed model of velocity distribution is tested with field and laboratory observations and is also compared with existing entropy-based velocity distributions. The present model has shown good agreement with the observed data and its prediction accuracy is comparable with the other existing models.
Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls
Šamaj, Ladislav; Trizac, Emmanuel
2016-01-01
We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system).
De Finetti's dividend problem and impulse control for a two-dimensional insurance risk process
Czarna, Irmina
2009-01-01
Consider two insurance companies (or two branches of the same company) that have the same claims and they divide premia in some specified proportions. We model the occurrence of claims according to a Poisson process. The ruin is achieved if the corresponding two-dimensional risk process first leave the positive quadrant. We consider different kinds of linear barriers. We will consider two scenarios of controlled process. In first one when two-dimensional risk process hits the barrier the minimal amount of dividends is payed out to keep the risk process within the region bounded by the barrier. In the second scenario whenever process hits horizontal line, the risk process is reduced by paying dividend to some fixed point in the positive quadrant and waits there for the first claim to arrive. In both models we calculate discounted cumulative dividend payments until the ruin time.
Perspective: Two-dimensional resonance Raman spectroscopy
Molesky, Brian P.; Guo, Zhenkun; Cheshire, Thomas P.; Moran, Andrew M.
2016-11-01
Two-dimensional resonance Raman (2DRR) spectroscopy has been developed for studies of photochemical reaction mechanisms and structural heterogeneity in complex systems. The 2DRR method can leverage electronic resonance enhancement to selectively probe chromophores embedded in complex environments (e.g., a cofactor in a protein). In addition, correlations between the two dimensions of the 2DRR spectrum reveal information that is not available in traditional Raman techniques. For example, distributions of reactant and product geometries can be correlated in systems that undergo chemical reactions on the femtosecond time scale. Structural heterogeneity in an ensemble may also be reflected in the 2D spectroscopic line shapes of both reactive and non-reactive systems. In this perspective article, these capabilities of 2DRR spectroscopy are discussed in the context of recent applications to the photodissociation reactions of triiodide and myoglobin. We also address key differences between the signal generation mechanisms for 2DRR and off-resonant 2D Raman spectroscopies. Most notably, it has been shown that these two techniques are subject to a tradeoff between sensitivity to anharmonicity and susceptibility to artifacts. Overall, recent experimental developments and applications of the 2DRR method suggest great potential for the future of the technique.
Janus spectra in two-dimensional flows
Liu, Chien-Chia; Chakraborty, Pinaki
2016-01-01
In theory, large-scale atmospheric flows, soap-film flows and other two-dimensional flows may host two distinct types of turbulent energy spectra---in one, $\\alpha$, the spectral exponent of velocity fluctuations, equals $3$ and the fluctuations are dissipated at the small scales, and in the other, $\\alpha=5/3$ and the fluctuations are dissipated at the large scales---but measurements downstream of obstacles have invariably revealed $\\alpha = 3$. Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which $\\alpha$ has transitioned from $3$ to $5/3$ for the streamwise fluctuations but remains equal to $3$ for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows...
Comparative Two-Dimensional Fluorescence Gel Electrophoresis.
Ackermann, Doreen; König, Simone
2018-01-01
Two-dimensional comparative fluorescence gel electrophoresis (CoFGE) uses an internal standard to increase the reproducibility of coordinate assignment for protein spots visualized on 2D polyacrylamide gels. This is particularly important for samples, which need to be compared without the availability of replicates and thus cannot be studied using differential gel electrophoresis (DIGE). CoFGE corrects for gel-to-gel variability by co-running with the sample proteome a standardized marker grid of 80-100 nodes, which is formed by a set of purified proteins. Differentiation of reference and analyte is possible by the use of two fluorescent dyes. Variations in the y-dimension (molecular weight) are corrected by the marker grid. For the optional control of the x-dimension (pI), azo dyes can be used. Experiments are possible in both vertical and horizontal (h) electrophoresis devices, but hCoFGE is much easier to perform. For data analysis, commercial software capable of warping can be adapted.
Two-dimensional hexagonal semiconductors beyond graphene
Nguyen, Bich Ha; Hieu Nguyen, Van
2016-12-01
The rapid and successful development of the research on graphene and graphene-based nanostructures has been substantially enlarged to include many other two-dimensional hexagonal semiconductors (THS): phosphorene, silicene, germanene, hexagonal boron nitride (h-BN) and transition metal dichalcogenides (TMDCs) such as MoS2, MoSe2, WS2, WSe2 as well as the van der Waals heterostructures of various THSs (including graphene). The present article is a review of recent works on THSs beyond graphene and van der Waals heterostructures composed of different pairs of all THSs. One among the priorities of new THSs compared to graphene is the presence of a non-vanishing energy bandgap which opened up the ability to fabricate a large number of electronic, optoelectronic and photonic devices on the basis of these new materials and their van der Waals heterostructures. Moreover, a significant progress in the research on TMDCs was the discovery of valley degree of freedom. The results of research on valley degree of freedom and the development of a new technology based on valley degree of freedom-valleytronics are also presented. Thus the scientific contents of the basic research and practical applications os THSs are very rich and extremely promising.
Two-Dimensional Phononic Crystals: Disorder Matters.
Wagner, Markus R; Graczykowski, Bartlomiej; Reparaz, Juan Sebastian; El Sachat, Alexandros; Sledzinska, Marianna; Alzina, Francesc; Sotomayor Torres, Clivia M
2016-09-14
The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order/disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of two-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) and Raman thermometry based on a novel two-laser approach are used to study the phononic properties in the gigahertz (GHz) and terahertz (THz) regime, respectively. Finite element method simulations of the phonon dispersion relation and three-dimensional displacement fields furthermore enable the unique identification of the different hypersonic vibrations. The increase of surface roughness and the introduction of short-range disorder are shown to modify the phonon dispersion and phonon coherence in the hypersonic (GHz) range without affecting the room-temperature thermal conductivity. On the basis of these findings, we suggest a criteria for predicting phonon coherence as a function of roughness and disorder.
Two-dimensional topological photonic systems
Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng
2017-09-01
The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.
Radiation effects on two-dimensional materials
Energy Technology Data Exchange (ETDEWEB)
Walker, R.C. II; Robinson, J.A. [Department of Materials Science, Penn State, University Park, PA (United States); Center for Two-Dimensional Layered Materials, Penn State, University Park, PA (United States); Shi, T. [Department of Mechanical and Nuclear Engineering, Penn State, University Park, PA (United States); Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States); Silva, E.C. [GlobalFoundries, Malta, NY (United States); Jovanovic, I. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States)
2016-12-15
The effects of electromagnetic and particle irradiation on two-dimensional materials (2DMs) are discussed in this review. Radiation creates defects that impact the structure and electronic performance of materials. Determining the impact of these defects is important for developing 2DM-based devices for use in high-radiation environments, such as space or nuclear reactors. As such, most experimental studies have been focused on determining total ionizing dose damage to 2DMs and devices. Total dose experiments using X-rays, gamma rays, electrons, protons, and heavy ions are summarized in this review. We briefly discuss the possibility of investigating single event effects in 2DMs based on initial ion beam irradiation experiments and the development of 2DM-based integrated circuits. Additionally, beneficial uses of irradiation such as ion implantation to dope materials or electron-beam and helium-beam etching to shape materials have begun to be used on 2DMs and are reviewed as well. For non-ionizing radiation, such as low-energy photons, we review the literature on 2DM-based photo-detection from terahertz to UV. The majority of photo-detecting devices operate in the visible and UV range, and for this reason they are the focus of this review. However, we review the progress in developing 2DMs for detecting infrared and terahertz radiation. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Photodetectors based on two dimensional materials
Zheng, Lou; Zhongzhu, Liang; Guozhen, Shen
2016-09-01
Two-dimensional (2D) materials with unique properties have received a great deal of attention in recent years. This family of materials has rapidly established themselves as intriguing building blocks for versatile nanoelectronic devices that offer promising potential for use in next generation optoelectronics, such as photodetectors. Furthermore, their optoelectronic performance can be adjusted by varying the number of layers. They have demonstrated excellent light absorption, enabling ultrafast and ultrasensitive detection of light in photodetectors, especially in their single-layer structure. Moreover, due to their atomic thickness, outstanding mechanical flexibility, and large breaking strength, these materials have been of great interest for use in flexible devices and strain engineering. Toward that end, several kinds of photodetectors based on 2D materials have been reported. Here, we present a review of the state-of-the-art in photodetectors based on graphene and other 2D materials, such as the graphene, transition metal dichalcogenides, and so on. Project supported by the National Natural Science Foundation of China (Nos. 61377033, 61574132, 61504136) and the State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences.
Asymptotics for Two-dimensional Atoms
DEFF Research Database (Denmark)
Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip
2012-01-01
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....
Predicting Two-Dimensional Silicon Carbide Monolayers.
Shi, Zhiming; Zhang, Zhuhua; Kutana, Alex; Yakobson, Boris I
2015-10-27
Intrinsic semimetallicity of graphene and silicene largely limits their applications in functional devices. Mixing carbon and silicon atoms to form two-dimensional (2D) silicon carbide (SixC1-x) sheets is promising to overcome this issue. Using first-principles calculations combined with the cluster expansion method, we perform a comprehensive study on the thermodynamic stability and electronic properties of 2D SixC1-x monolayers with 0 ≤ x ≤ 1. Upon varying the silicon concentration, the 2D SixC1-x presents two distinct structural phases, a homogeneous phase with well dispersed Si (or C) atoms and an in-plane hybrid phase rich in SiC domains. While the in-plane hybrid structure shows uniform semiconducting properties with widely tunable band gap from 0 to 2.87 eV due to quantum confinement effect imposed by the SiC domains, the homogeneous structures can be semiconducting or remain semimetallic depending on a superlattice vector which dictates whether the sublattice symmetry is topologically broken. Moreover, we reveal a universal rule for describing the electronic properties of the homogeneous SixC1-x structures. These findings suggest that the 2D SixC1-x monolayers may present a new "family" of 2D materials, with a rich variety of properties for applications in electronics and optoelectronics.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We have analyzed the operating mechanism of the novel deep submicrometer SOI drive-in gate controlled hybrid transistor (DGCHT), which can effectively alleviate the contradiction between speed enhancement and power reduction in conventional MOS devices and can improve the output resistance. On the basis of this, the subthreshold current model of DGCHTs is proposed. The model takes into account the impact of lateral non-uniform doping profile on body effect, short-channel effect and carrier mobility. Considering the mobile charge, two-dimensional Poisson equation is solved with quasi-two-dimensional analysis and parabolic approximation of surface potential. With the surface potential obtained, the subthreshold current is figured out, including both the diffusion and drift component. The calculated results are in good agreement with the MEDICI numerical simulation results, indicating the correct description of the current characteristics of SOI DGCHT by the presented model. The model can also be considered as an important reference to the current simulation of deep submicrometer MOSFET with pocket implantation.
Xu, Hui-Fang; Dai, Yue-Hua; Xu, Jian-Bin; Li, Ning; Yang, Jin; Zheng, Chang-Yong
2015-05-01
A semi-analytical subthreshold surface potential model for double-doping polysilicon gate (DDPG) MOSFETs is presented. By introducing two rectangular sources located in the gate insulator and the channel-depleted region, the two-dimensional (2D) Poisson equations are solved using a semi-analytical method combined with an eigenfunction expansion method. Expressions for the potentials are obtained as special functions of infinite series expressions. A subthreshold drain current is proposed on the basis of the potential profile, and it accounts for the carriers’ drift diffusion and thermionic emission theory. The advantage of this work is that the two-dimensional treatment of the gate insulator region has resulted in physical consistency across a dielectric boundary. The proposed model not only offers physical insight into device physics but also provides the basic designing guideline for DDPG MOSFETs, enabling the designer to optimize the device in accordance with the application. Very good agreement for both the subthreshold surface potential and drain current is observed between the model calculations and the simulated results.
Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems
Tutu, Hiroki; Horita, Takehiko; Ouchi, Katsuya
2015-04-01
Within the context of the Brownian ratchet model, a molecular rotary system that can perform unidirectional rotations induced by linearly polarized ac fields and produce positive work under loads was studied. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to the torque. We propose a master equation for coarse-grained states, which takes into account the boundary motion between states, and develop a kinetic description to estimate the mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can enable us to predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.
The fractional Poisson process and the inverse stable subordinator
Meerschaert, Mark M; Vellaisamy, P
2010-01-01
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extends to a broad class of renewal processes that include models for tempered fractional diffusion, and distributed-order (e.g., ultraslow) fractional diffusion.
Interaction of two-dimensional magnetoexcitons
Dumanov, E. V.; Podlesny, I. V.; Moskalenko, S. A.; Liberman, M. A.
2017-04-01
We study interaction of the two-dimensional magnetoexcitons with in-plane wave vector k→∥ = 0 , taking into account the influence of the excited Landau levels (ELLs) and of the external electric field perpendicular to the surface of the quantum well and parallel to the external magnetic field. It is shown that the account of the ELLs gives rise to the repulsion between the spinless magnetoexcitons with k→∥ = 0 in the Fock approximation, with the interaction constant g decreasing inverse proportional to the magnetic field strength B (g (0) ∼ 1 / B) . In the presence of the perpendicular electric field the Rashba spin-orbit coupling (RSOC), Zeeman splitting (ZS) and nonparabolicity of the heavy-hole dispersion law affect the Landau quantization of the electrons and holes. They move along the new cyclotron orbits, change their Coulomb interactions and cause the interaction between 2D magnetoexcitons with k→∥ = 0 . The changes of the Coulomb interactions caused by the electrons and by the holes moving with new cyclotron orbits are characterized by some coefficients, which in the absence of the electric field turn to be unity. The differences between these coefficients of the electron-hole pairs forming the magnetoexcitons determine their affinities to the interactions. The interactions between the homogeneous, semihomogeneous and heterogeneous magnetoexcitons forming the symmetric states with the same signs of their affinities are attractive whereas in the case of different sign affinities are repulsive. In the heterogeneous asymmetric states the interactions have opposite signs in comparison with the symmetric states. In all these cases the interaction constant g have the dependence g (0) 1 /√{ B} .
Sadabadi, Mahdiye Sadat; Shafiee, Masoud; Karrari, Mehdi
2008-07-01
In this paper, parameter identification of two-dimensional continuous-time systems via two-dimensional modulating functions is proposed. In the proposed method, trigonometric functions and sine-cosine wavelets are used as modulating functions. By this, a partial differential equation on the finite-time intervals is converted into an algebraic equation linear in parameters. The parameters of the system can then be estimated using the least square algorithms. The underlying computations utilize a two-dimensional fast Fourier transform algorithm, without the need for estimating the unknown initial or boundary conditions, at the beginning of each finite-time interval. Numerical simulations are presented to show the effectiveness of the proposed algorithm.
USTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER'S TYPE
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A two-dimensional nonlinear shell model"of Koiter's type"has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the"small" parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the "small" parameter, the nonlinear shell model of Koiter's type considered here is thus justified, at least formally.
Numerical solution to the Vlasov equation: The 2D code
Fijalkow, Eric
1999-02-01
The present code solves the two-dimensional Vlasov equation for a periodic in space system, in presence of an external magnetic field B O. The self coherent electric field given by Poisson equation is computed by Fast Fourier Transform (FFT). The output of the code consist of a list of diagnostics, such as total mass conservation, total momentum and energies, and of projections of the distribution function in different subspaces as the x- v x space, the x- y space and so on.
Two-dimensional materials and their prospects in transistor electronics.
Schwierz, F; Pezoldt, J; Granzner, R
2015-05-14
During the past decade, two-dimensional materials have attracted incredible interest from the electronic device community. The first two-dimensional material studied in detail was graphene and, since 2007, it has intensively been explored as a material for electronic devices, in particular, transistors. While graphene transistors are still on the agenda, researchers have extended their work to two-dimensional materials beyond graphene and the number of two-dimensional materials under examination has literally exploded recently. Meanwhile several hundreds of different two-dimensional materials are known, a substantial part of them is considered useful for transistors, and experimental transistors with channels of different two-dimensional materials have been demonstrated. In spite of the rapid progress in the field, the prospects of two-dimensional transistors still remain vague and optimistic opinions face rather reserved assessments. The intention of the present paper is to shed more light on the merits and drawbacks of two-dimensional materials for transistor electronics and to add a few more facets to the ongoing discussion on the prospects of two-dimensional transistors. To this end, we compose a wish list of properties for a good transistor channel material and examine to what extent the two-dimensional materials fulfill the criteria of the list. The state-of-the-art two-dimensional transistors are reviewed and a balanced view of both the pros and cons of these devices is provided.
Directory of Open Access Journals (Sweden)
C. M.ª Piernas Sánchez
2010-04-01
Full Text Available Introduction: The excess of visceral abdominal adipose tissue is one of the major concerns in obesity and its clinical treatment. Objective: To apply the two-dimensional predictive equation proposed by Garaulet et al. to determine the abdominal fat distribution and to compare the results with the body composition obtained by multi-frequency bioelectrical impedance analysis (M-BIA. Subjects/methods: We studied 230 women, who underwent anthropometry and M-BIA. The predictive equation was applied. Multivariate lineal and partial correlation analyses were performed with control for BMI and % body fat, using SPSS 15.0 with statistical significance P Introducción: El exceso de tejido adiposo abdominal visceral es una de las mayores preocupaciones en la obesidad y su tratamiento clínico. Objetivo: Aplicar la ecuación predictiva bidimensional propuesta por Garaulet et al., para determinar la distribución de la grasa abdominal y comparar los resultados con la composición corporal obtenida mediante el análisis de impedancia bioeléctrica multi-frecuencia (M-BIA. Sujetos/métodos: Estudiamos a 230 mujeres a las que se sometió a antropometría y M-BIA. Se aplicó la ecuación predicitiva. Se realizaron correlaciones lineales multivariadas y parciales controlando el IMC y el % de grasa corporal, utilizando SPSS 15.0 con significación estadística P < 0,05. Resultados: En global, se consideró que las mujeres tenían una distribución subcutánea de la grasa abdominal. La grasa troncal, regional y la masa muscular se asociaron negativamente con VA/SApredicted, mientras que le índice visceral obtenido mediante M-BIA se correlacionó positivamente con VA/SApredicted. Discusión/conclusión: La ecuación predictiva puede ser útil en la práctica clínica para obtener una clasificación segura, barata y precisa de la obesidad abdominal.
Extended Poisson Exponential Distribution
Directory of Open Access Journals (Sweden)
Anum Fatima
2015-09-01
Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.
Johnson, D H
2009-01-01
What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of jointly Bernoulli processes. One intriguing consequence of these models is that jointly Poisson processes can only be positively correlated as measured by the correlation coefficient defined by cumulants of the probability generating functional.
Contravariant Gravity on Poisson Manifolds and Einstein Gravity
Kaneko, Yukio; Watamura, Satoshi
2016-01-01
A relation between a gravity on Poisson manifolds proposed in arXiv:1508.05706 and the Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein-Hilbert-type action includes couplings between the metric and the Poisson tensor. The Weyl transformation is studied to reveal properties of those interactions. It is argued that the theory can have an equivalent description in terms of the Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold has another description by a real scalar field coupling to the metric in a specific manner.
Ultrafast two dimensional infrared chemical exchange spectroscopy
Fayer, Michael
2011-03-01
The method of ultrafast two dimensional infrared (2D IR) vibrational echo spectroscopy is described. Three ultrashort IR pulses tuned to the frequencies of the vibrational transitions of interest are directed into the sample. The interaction of these pulses with the molecular vibrational oscillators produces a polarization that gives rise to a fourth pulse, the vibrational echo. The vibrational echo pulse is combined with another pulse, the local oscillator, for heterodyne detection of the signal. For fixed time between the second and third pulses, the waiting time, the first pulse is scanned. Two Fourier transforms of the data yield a 2D IR spectrum. The waiting time is increased, and another spectrum is obtained. The change in the 2D IR spectra with increased waiting time provides information on the time evolution of the structure of the molecular system under observation. In a 2D IR chemical exchange experiment, two species A and B, are undergoing chemical exchange. A's are turning into B's, and B's are turning into A's, but the overall concentrations of the species are not changing. The kinetics of the chemical exchange on the ground electronic state under thermal equilibrium conditions can be obtained 2D IR spectroscopy. A vibration that has a different frequency for the two species is monitored. At very short time, there will be two peaks on the diagonal of the 2D IR spectrum, one for A and one for B. As the waiting time is increased, chemical exchange causes off-diagonal peaks to grow in. The time dependence of the growth of these off-diagonal peaks gives the chemical exchange rate. The method is applied to organic solute-solvent complex formation, orientational isomerization about a carbon-carbon single bond, migration of a hydrogen bond from one position on a molecule to another, protein structural substate interconversion, and water hydrogen bond switching between ions and water molecules. This work was supported by the Air Force Office of Scientific
Molecular assembly on two-dimensional materials
Kumar, Avijit; Banerjee, Kaustuv; Liljeroth, Peter
2017-02-01
Molecular self-assembly is a well-known technique to create highly functional nanostructures on surfaces. Self-assembly on two-dimensional (2D) materials is a developing field driven by the interest in functionalization of 2D materials in order to tune their electronic properties. This has resulted in the discovery of several rich and interesting phenomena. Here, we review this progress with an emphasis on the electronic properties of the adsorbates and the substrate in well-defined systems, as unveiled by scanning tunneling microscopy. The review covers three aspects of the self-assembly. The first one focuses on non-covalent self-assembly dealing with site-selectivity due to inherent moiré pattern present on 2D materials grown on substrates. We also see that modification of intermolecular interactions and molecule–substrate interactions influences the assembly drastically and that 2D materials can also be used as a platform to carry out covalent and metal-coordinated assembly. The second part deals with the electronic properties of molecules adsorbed on 2D materials. By virtue of being inert and possessing low density of states near the Fermi level, 2D materials decouple molecules electronically from the underlying metal substrate and allow high-resolution spectroscopy and imaging of molecular orbitals. The moiré pattern on the 2D materials causes site-selective gating and charging of molecules in some cases. The last section covers the effects of self-assembled, acceptor and donor type, organic molecules on the electronic properties of graphene as revealed by spectroscopy and electrical transport measurements. Non-covalent functionalization of 2D materials has already been applied for their application as catalysts and sensors. With the current surge of activity on building van der Waals heterostructures from atomically thin crystals, molecular self-assembly has the potential to add an extra level of flexibility and functionality for applications ranging
Adaptive Algorithm for Estimation of Two-Dimensional Autoregressive Fields from Noisy Observations
Directory of Open Access Journals (Sweden)
Alimorad Mahmoudi
2014-01-01
Full Text Available This paper deals with the problem of two-dimensional autoregressive (AR estimation from noisy observations. The Yule-Walker equations are solved using adaptive steepest descent (SD algorithm. Performance comparisons are made with other existing methods to demonstrate merits of the proposed method.
Quantum mechanical treatment of a constrained particle on two dimensional sphere
Jahangiri, L.; Panahi, H.
2016-12-01
In this work, we study the motion of a particle on two dimensional sphere. By writing the Schrodinger equation, we obtain the wave function and energy spectra for three dimensional harmonic oscillator potential plus trigonometric Rosen-Morse non-central potential. By letting three special cases for intertwining operator, we investigate the energy spectra and wave functions for Smorodinsky-Winternitz potential model.
Energy Technology Data Exchange (ETDEWEB)
Mota, R.D. [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, Mexico DF (Mexico)]. E-mail: mota@gina.esfm.ipn.mx; ravelo@esfm.ipn.mx; Granados, V.D.; Queijeiro, A.; Garcia, J. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Mexico DF (Mexico)
2002-03-29
For the quantum two-dimensional isotropic harmonic oscillator we show that the Infeld-Hull radial operators, as well as those of the supersymmetric approach for the radial equation, are contained in the constants of motion of the problem. (author)
Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrodinger model
DEFF Research Database (Denmark)
Schjødt-Eriksen, Jens; Gaididei, Yuri Borisovich; Christiansen, Peter Leth
2001-01-01
Collapse of (2 + 1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrodinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may...
Self-focusing instability of two-dimensional solitons and vortices
DEFF Research Database (Denmark)
Kuznetsov, E.A.; Juul Rasmussen, J.
1995-01-01
The instability of two-dimensional solitons and vortices is demonstrated in the framework of the three-dimensional nonlinear Schrodinger equation (NLSE). The instability can be regarded as the analog of the Kadomtsev-Petviashvili instability [B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl...
DEFF Research Database (Denmark)
Eilbeck, J. C; Lomdahl, P.S.; Olsen, O.H.
1985-01-01
A two-dimensional model of Josephson junction of overlap type is presented. The energy input is provided through induced magnetic fields modeled by a set of boundary conditions. In the limit of a very narrow junction, this model reduces to the one-dimensional model. Further, an equation derived f...
Jansen, Thomas la Cour; Knoester, Jasper
2007-01-01
We combine numerical Langevin simulations with numerical integration of the Schrodinger equation to calculate two-dimensional infrared spectra of ultrafast chemical exchange. This provides a tool to model and interpret such spectra of molecules undergoing chemical processes, such as isomerization an
A Solvable Model in Two-Dimensional Gravity Coupled to a Nonlinear Matter Field
Institute of Scientific and Technical Information of China (English)
YAN Jun; WANG Shun-Jin; TAO Bi-You
2001-01-01
The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.``
Coherent electron dynamics in a two-dimensional random system with mobility edges
de Moura, F. A. B. F.; Lyra, M. L.; Dominguez-Adame, F.; Malyshev, V.A.
2007-01-01
We study numerically the dynamics of a one-electron wavepacket in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schrodinger equation is used for this purpose. We find that the wavepacket displays Bloch-li
Klein Paradox of Two-Dimensional Dirac Electrons in Circular Well Potential
Institute of Scientific and Technical Information of China (English)
黄海; 付星球; 韩榕生
2012-01-01
We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation： For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.
Thermodynamics of Two-Dimensional Electron Gas in a Magnetic Field
Directory of Open Access Journals (Sweden)
V. I. Nizhankovskii
2011-01-01
Full Text Available Change of the chemical potential of electrons in a GaAs-AlGa1−As heterojunction was measured in magnetic fields up to 6.5 T at several temperatures from 2.17 to 12.3 K. A thermodynamic equation of state of two-dimensional electron gas well describes the experimental results.
A two-dimensional mathematical model of percutaneous drug absorption
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Kubota K
2004-06-01
Full Text Available Abstract Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1 the flow rate of the drug, (2 the flux and the cumulative amount of drug eliminated into the receptor cell, (3 the steady-state value of the flux, (4 the time to reach the steady
Directory of Open Access Journals (Sweden)
Carlos A Bustamante Chaverra
2013-03-01
are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation diﬀerential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is veriﬁed by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same results are obtained for all the non-linear solvers tested, but better convergence rates are attained with the Newton Raphson method in a double iteration scheme.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Energy Technology Data Exchange (ETDEWEB)
Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)
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.
On t-local solvability of inverse scattering problems in two-dimensional layered media
Baev, A. V.
2015-06-01
The solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form of an energy conservation law. It is shown that the inverse problems are solvable only in the class of potentials for which the stationary Navier-Stokes equation is solvable.