Reconstruction of extended sources for the Helmholtz equation

KAUST Repository

Kress, Rainer

2013-02-26

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our inclusions are interior forces with compact support and our data consist of a single measurement of near-field Cauchy data on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler \\'equivalent point source\\' problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2013 IOP Publishing Ltd.

Modern solvers for Helmholtz problems

CERN Document Server

Tang, Jok; Vuik, Kees

2017-01-01

This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to b...

Optimal 25-Point Finite-Difference Subgridding Techniques for the 2D Helmholtz Equation

Directory of Open Access Journals (Sweden)

Tingting Wu

2016-01-01

Full Text Available We present an optimal 25-point finite-difference subgridding scheme for solving the 2D Helmholtz equation with perfectly matched layer (PML. This scheme is second order in accuracy and pointwise consistent with the equation. Subgrids are used to discretize the computational domain, including the interior domain and the PML. For the transitional node in the interior domain, the finite difference equation is formulated with ghost nodes, and its weight parameters are chosen by a refined choice strategy based on minimizing the numerical dispersion. Numerical experiments are given to illustrate that the newly proposed schemes can produce highly accurate seismic modeling results with enhanced efficiency.

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

Science.gov (United States)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

Polarization coupling of vector Bessel–Gaussian beams

International Nuclear Information System (INIS)

Takeuchi, Ryushi; Kozawa, Yuichi; Sato, Shunichi

2013-01-01

We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO 4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation. (paper)

Numerical solution of the helmholtz equation for the superellipsoid via the galerkin method

Directory of Open Access Journals (Sweden)

Hy Dinh

2013-01-01

Full Text Available The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation for a smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: $x=cos(xsin(y^{n},y=sin(xsin(y^{n},z=cos(y$ where $n$ varied from 0.5 to 4. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Dirichlet boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We are researching the feasibility of obtaining good convergence results for the superellipsoid surface. It was our view that smaller and lighter wave numbers would reduce computational costs associated with obtaining Galerkin coefficients. In addition, we hoped to significantly reduce the number of terms in the infinite series needed to modify the original integral equation, all of which were achieved in the analysis of the superellipsoid in a finite range. We used the Green's theorem to solve the integral equation for the boundary of the surface. Previously, multiple surfaces were used to test this method, such as the sphere, ellipsoid, and perturbation of the sphere, pseudosphere and the oval of Cassini Lin and Warnapala , Warnapala and Morgan .

Magnetohydrodynamic Kelvin-Helmholtz instability; Magnetohydrodynamische Kelvin-Helmholtz-Instabilitaet

Energy Technology Data Exchange (ETDEWEB)

Brett, Walter

2014-07-21

In the presented work the Kelvin-Helmholtz-Instability in magnetohydrodynamic flows is analyzed with the methods of Multiple Scales. The concerned fluids are incompressible or have a varying density perpendicular to the vortex sheet, which is taken into account using a Boussinesq-Approximation and constant Brunt-Vaeisaelae-Frequencies. The Multiple Scale Analysis leads to nonlinear evolution equations for the amplitude of the perturbations. Special solutions to these equations are presented and the effects of the magnetic fields are discussed.

Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation

International Nuclear Information System (INIS)

Wei, T; Qin, H H; Shi, R

2008-01-01

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a numerical algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimate and convergence analysis have also been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method

A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations

KAUST Repository

Poulson, Jack

2013-05-02

A parallelization of a sweeping preconditioner for three-dimensional Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are shown to be O(γ2N4/3) and O(γN logN), where γ(ω) denotes the modestly frequency-dependent number of grid points per perfectly matched layer. Several computational and memory improvements are introduced relative to using black-box sparse-direct solvers for the auxiliary problems, and competitive runtimes and iteration counts are reported for high-frequency problems distributed over thousands of cores. Two open-source packages are released along with this paper: Parallel Sweeping Preconditioner (PSP) and the underlying distributed multifrontal solver, Clique. © 2013 Society for Industrial and Applied Mathematics.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

Science.gov (United States)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Novel approach to the Helmholtz integral equation solution by Fourier series expansion for acoustic radiation and scattering problems

CSIR Research Space (South Africa)

Shatalov, MY

2006-01-01

Full Text Available -scale structure to guarantee the numerical accuracy of solution. In the present paper the authors propose to use a novel method of solution of the Helmholtz integral equation, which is based on expansion of the integrands in double Fourier series. The main...

Helmholtz algebraic solitons

Energy Technology Data Exchange (ETDEWEB)

Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2010-02-26

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

Helmholtz algebraic solitons

International Nuclear Information System (INIS)

Christian, J M; McDonald, G S; Chamorro-Posada, P

2010-01-01

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

Imaging of the internal structure of comet 67P/Churyumov-Gerasimenko from radiotomography CONSERT Data (Rosetta Mission) through a full 3D regularized inversion of the Helmholtz equations on functional spaces

Science.gov (United States)

Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie; Benna, Mehdi; Kofman, Wlodek; Herique, Alain

We investigate the inverse problem of imaging the internal structure of comet 67P/ Churyumov-Gerasimenko from radiotomography CONSERT data by using a coupled regularized inversion of the Helmholtz equations. A first set of Helmholtz equations, written w.r.t a basis of 3D Hankel functions describes the wave propagation outside the comet at large distances, a second set of Helmholtz equations, written w.r.t. a basis of 3D Zernike functions describes the wave propagation throughout the comet with avariable permittivity. Both sets are connected by continuity equations over a sphere that surrounds the comet. This approach, derived from GPS water vapor tomography of the atmosphere,will permit a full 3D inversion of the internal structure of the comet, contrary to traditional approaches that use a discretization of space at a fraction of the radiowave wavelength.

Solution of the Helmholtz-Poincare Wave Equation using the coupled boundary integral equations and optimal surface eigenfunctions

International Nuclear Information System (INIS)

Werby, M.F.; Broadhead, M.K.; Strayer, M.R.; Bottcher, C.

1992-01-01

The Helmholtz-Poincarf Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWECs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a bi-orthogonal expansion of the Green's function. However some freedom in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermitian operator. The methodology will be explained in detail and examples will be presented

Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids

Energy Technology Data Exchange (ETDEWEB)

Sheng, Qin, E-mail: Qin_Sheng@baylor.edu [Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, One Bear Place, Waco, TX 76798-7328 (United States); Sun, Hai-wei, E-mail: hsun@umac.mo [Department of Mathematics, University of Macau (Macao)

2016-11-15

This study concerns the asymptotic stability of an eikonal, or ray, transformation based Peaceman–Rachford splitting method for solving the paraxial Helmholtz equation with high wave numbers. Arbitrary nonuniform grids are considered in transverse and beam propagation directions. The differential equation targeted has been used for modeling propagations of high intensity laser pulses over a long distance without diffractions. Self-focusing of high intensity beams may be balanced with the de-focusing effect of created ionized plasma channel in the situation, and applications of grid adaptations are frequently essential. It is shown rigorously that the fully discretized oscillation-free decomposition method on arbitrary adaptive grids is asymptotically stable with a stability index one. Simulation experiments are carried out to illustrate our concern and conclusions.

Korteweg-de Vries description of Helmholtz-Kerr dark solitons

Energy Technology Data Exchange (ETDEWEB)

Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom) ; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom) ; Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2006-12-15

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schroedinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz-Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations.

Korteweg-de Vries description of Helmholtz-Kerr dark solitons

International Nuclear Information System (INIS)

Christian, J M; McDonald, G S; Chamorro-Posada, P

2006-01-01

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schroedinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz-Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations

Seafloor identification in sonar imagery via simulations of Helmholtz equations and discrete optimization

Science.gov (United States)

Engquist, Björn; Frederick, Christina; Huynh, Quyen; Zhou, Haomin

2017-06-01

We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial, and military applications. The forward model incorporates multiscale simulations, by coupling Helmholtz equations and geometrical optics for a wide range of spatial scales in the seafloor geometry. This allows for detailed recovery of seafloor parameters including material type. Simulated backscattered data is generated using numerical microlocal analysis techniques. In order to lower the computational cost of the large-scale simulations in the inversion process, we take advantage of a pre-computed library of representative acoustic responses from various seafloor parameterizations.

Helmholtz bright and boundary solitons

International Nuclear Information System (INIS)

Christian, J M; McDonald, G S; Chamorro-Posada, P

2007-01-01

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts

Helmholtz bright and boundary solitons

Energy Technology Data Exchange (ETDEWEB)

Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2007-02-16

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts.

Equation of state and Helmholtz free energy for the atomic system of the repulsive Lennard-Jones particles.

Science.gov (United States)

Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid

2017-12-07

Simple and accurate expressions are presented for the equation of state (EOS) and absolute Helmholtz free energy of a system composed of simple atomic particles interacting through the repulsive Lennard-Jones potential model in the fluid and solid phases. The introduced EOS has 17 and 22 coefficients for fluid and solid phases, respectively, which are regressed to the Monte Carlo (MC) simulation data over the reduced temperature range of 0.6≤T * ≤6.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. The average absolute relative percent deviation in fitting the EOS parameters to the MC data is 0.06 and 0.14 for the fluid and solid phases, respectively. The thermodynamic integration method is used to calculate the free energy using the MC simulation results. The Helmholtz free energy of the ideal gas is employed as the reference state for the fluid phase. For the solid phase, the values of the free energy at the reduced density equivalent to the close-packed of a hard sphere are used as the reference state. To check the validity of the predicted values of the Helmholtz free energy, the Widom particle insertion method and the Einstein crystal technique of Frenkel and Ladd are employed. The results obtained from the MC simulation approaches are well agreed to the EOS results, which show that the proposed model can reliably be utilized in the framework of thermodynamic theories.

Vector domain decomposition schemes for parabolic equations

Science.gov (United States)

Vabishchevich, P. N.

2017-09-01

A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and studied. A boundary value problem for a second-order parabolic equation is used as a model problem. The general approach to the construction of domain decomposition schemes is based on partition of unity. Specifically, a vector problem is set up for solving problems in individual subdomains. Stability conditions for vector regionally additive schemes of first- and second-order accuracy are obtained.

Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

Science.gov (United States)

Keefe, Laurence

2016-11-01

Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

Reduction of the state vector by a nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Pearle, P.

1976-01-01

It is hypothesized that the state vector describes the physical state of a single system in nature. Then it is necessary that the state vector of a macroscopic apparatus not assume the form of a superposition of macroscopically distinguishable state vectors. To prevent this, it is suggested that a nonlinear term be added to the Schrodinger equation, which rapidly drives the amplitude of one or another of the state vectors in such a superposition to one, and the rest to zero. It is proposed that it is the phase angles of the amplitudes immediately after a measurement which determine which amplitude is driven to one. A diffusion equation is arrived at to describe the reduction of an ensemble of state vectors corresponding to an ensemble of macroscopically identically prepared experiments. Then a nonlinear term to add to the Schrodinger equation is presented, and it is shown that this leads to the diffusion equation in a weak-coupling approximation

Application of the method of integral equations to calculating the electrodynamic characteristics of periodically corrugated waveguides

International Nuclear Information System (INIS)

Belov, V.E.; Rodygin, L.V.; Fil'chenko, S.E.; Yunakovskii, A.D.

1988-01-01

A method is described for calculating the electrodynamic characteristics of periodically corrugated waveguide systems. This method is based on representing the field as the solution of the Helmholtz vector equation in the form of a simple layer potential, transformed with the use of the Floquet conditions. Systems of compound integral equations based on a weighted vector function of the simple layer potential are derived for waveguides with azimuthally symmetric and helical corrugations. A numerical realization of the Fourier method is cited for seeking the dispersion relation of azimuthally symmetric waves of a circular corrugated waveguide

Helmholtz solitons in power-law optical materials

International Nuclear Information System (INIS)

Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.

2007-01-01

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified

Bistable Helmholtz solitons in cubic-quintic materials

International Nuclear Information System (INIS)

Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

2007-01-01

We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations

The Helmholtz Hierarchy: Phase Space Statistics of Cold Dark Matter

OpenAIRE

Tassev, Svetlin

2010-01-01

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the "Helmholtz Hierarchy") of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys...

Lagrangian vector field and Lagrangian formulation of partial differential equations

Directory of Open Access Journals (Sweden)

M.Chen

2005-01-01

Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.

Fractional vector calculus and fractional Maxwell's equations

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2008-01-01

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

The Helmholtz Hierarchy: phase space statistics of cold dark matter

International Nuclear Information System (INIS)

Tassev, Svetlin V.

2011-01-01

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the ''Helmholtz Hierarchy'') of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys causality to all orders. We present an interpretation of the hierarchy in terms of effective particle trajectories

Algebraic solution for the vector potential in the Dirac equation

Energy Technology Data Exchange (ETDEWEB)

Booth, H.S. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia); Centre for Mathematics and its Applications, Australian National University (Australia)]. E-mail: hbooth@wintermute.anu.edu.au; Legg, G.; Jarvis, P.D. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia)

2001-07-20

The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with attention to the additional constraints arising from non-maximality of the rank. The extension of the method to general spacetimes is illustrated by examples in diverse dimensions with both c- and a-number wavefunctions. (author)

Helmholtz's Kant revisited (Once more). The all-pervasive nature of Helmholtz's struggle with Kant's Anschauung.

Science.gov (United States)

De Kock, Liesbet

2016-04-01

In this analysis, the classical problem of Hermann von Helmholtz's (1821-1894) Kantianism is explored from a particular vantage point, that to my knowledge, has not received the attention it deserves notwithstanding its possible key role in disentangling Helmholtz's relation to Kant's critical project. More particularly, we will focus on Helmholtz's critical engagement with Kant's concept of intuition [Anschauung] and (the related issue of) his dissatisfaction with Kant's doctrinal dualism. In doing so, it soon becomes clear that both (i) crucially mediated Helmholtz's idiosyncratic appropriation and criticism of (certain aspects of) Kant's critical project, and (ii) can be considered as a common denominator in a variety of issues that are usually addressed separately under the general header of (the problem of) Helmholtz's Kantianism. The perspective offered in this analysis can not only shed interesting new light on some interpretive issues that have become commonplace in discussions on Helmholtz's Kantianism, but also offers a particular way of connecting seemingly unrelated dimensions of Helmholtz's engagement with Kant's critical project (e.g. Helmholtz's views on causality and space). Furthermore, it amounts to the rather surprising conclusion that Helmholtz's most drastic revision of Kant's project pertains to his assumption of free will as a formal condition of experience and knowledge. Copyright © 2015 Elsevier Ltd. All rights reserved.

Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations

International Nuclear Information System (INIS)

Bourdon, A; Pasko, V P; Liu, N Y; Celestin, S; Segur, P; Marode, E

2007-01-01

This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP 3 ) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by Segur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 O 2 O 2 is the partial pressure of molecular oxygen in air in units of Torr ( p O 2 = 150 Torr) at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP 3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of

Parallel Vector Fields and Einstein Equations of Gravity | Mahara ...

African Journals Online (AJOL)

In this paper, we prove that no nontrivial timelike or spacelike parallel vector field exists in a region where the gravitational field created by macroscopic bodies and governed by Einstein's equations does not vanish. In other words, we prove that the existence of such vector fields in a region implies the vanishing of the ...

Stability of Vector Functional Differential Equations: A Survey | Gil ...

African Journals Online (AJOL)

This paper is a survey of the recent results of the author on the stability of linear and nonlinear vector differential equations with delay. Explicit conditions for the exponential and absolute stabilities are derived. Moreover, solution estimates for the considered equations are established. They provide the bounds for the regions ...

Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation

Directory of Open Access Journals (Sweden)

Mitsuo Kato

2018-01-01

Full Text Available A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.

Use of Lanczos vectors in fluid/structure interaction problems

International Nuclear Information System (INIS)

Jeans, R.; Mathews, I.C.

1992-01-01

The goals of any numerical computational technique used for the solution of structural acoustics problems in the exterior infinite domain should be of accuracy with rapid convergence, robustness, and computational efficiency. A computer program has been developed to achieve each of these three goals. Accuracy and robustness in the numerical representation of the integral equations used to represent the infinite fluid was attained through the use of boundary element implementations of the surface Helmholtz integral equations. The computational efficiency was resolved through the use of Lanczos vectors to model the deformation characteristics of the structure. The authors have developed collocation and variational techniques to overcome the difficulties previously encountered in the numerical implementation of the hypersingular integral operator. The Cauchy singularity present in the integral formulation is made numerically amenable through the use of tangential derivatives in both the collocation and variational techniques. The variational approach has the advantage that the resulting added fluid mass term is symmetric and combines efficiently with a finite element approximation of the structural elastic response. Several different strategies making use of the Lanczos vectors have been investigated. The first involved the use of Lanczos vectors solely to characterize the structural response. This reduced form of the structural dynamical matrix was then substituted back into a Burton and Miller formulation of the acoustic problem. The second strategy investigated involved forming the complex Lanzcos vectors of the dynamical matrix formed from the addition of a symmetrical added fluid matrix to the structural mass matrix. The size of resultant matrix equation set solved at each frequency for this strategy is determined by the number of Lanczos vectors used. 19 refs., 10 figs., 2 tabs

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Algebraic inversion of the Dirac equation for the vector potential in the non-Abelian case

International Nuclear Information System (INIS)

Inglis, S M; Jarvis, P D

2012-01-01

We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell–Dirac equations, we set up the formalism for non-Abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-Abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-Abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series. (paper)

A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations

KAUST Repository

Zhang, Tao; Salama, Amgad; Sun, Shuyu; Zhong, Hua

2015-01-01

In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.

A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations

KAUST Repository

Zhang, Tao

2015-06-01

In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.

Effect of cold plasma on the Kelvin-Helmholtz instability

International Nuclear Information System (INIS)

Melander, B.G.

1978-01-01

The thesis studies the effect of a two-component plasma (hot and cold) on the shear driven Kelvin-Helmholtz instability. An ion distribution with a shear flow parallel to the ambient magnetic field and a density gradient parallel to the shear direction is used. Both the electrostatic and electromagnetic versions of the instability are studied in the limit of hydromagnetic frequencies. The dispersion relation is obtained in the electrostatic case by solving the Vlasov equation for the perturbed ion and electron densities and then using the quasineutrality condition. In the electromagnetic case the coupled Vlasov and Maxwell's equations are solved to obtain the dispersion relation

Computational issues and applications of line-elements to model subsurface flow governed by the modified Helmholtz equation

Science.gov (United States)

Bakker, Mark; Kuhlman, Kristopher L.

2011-09-01

Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks.

Formulas for detecting a spherical stiff inclusion from interior data: a sensitivity analysis for the Helmholtz equation

International Nuclear Information System (INIS)

McLaughlin, Joyce; Oberai, Assad; Yoon, Jeong-Rock

2012-01-01

In this paper, we establish sensitivity results that are relevant for imaging stiffness in tissue but may also be useful in other contexts. The data are the displacement at a single frequency throughout the imaging domain. The goal is to determine how the quantities—(1) amplitude of displacement, or alternatively (2) the displacement itself, the average displacement, the phase or the phase gradient—change within a homogeneous stiff inclusion embedded within a homogeneous background. The results are easily interpreted formulas that show the dependence on the radius of the inclusion, the frequency and the stiffness contrast between the inclusion and the background. Our assumptions are: (1) the displacement satisfies the Helmholtz equation with the variable stiffness parameter; (2) the experiment produces a plane wave in the absence of any inclusions; (3) in 3D, the inclusion is spherical; (4) in 2D the inclusion is a circular disc; and alternatively in 3D the inclusion is an infinite circular cylinder. Our method of analysis is to use series expansions of the solution expanded about the center of the inclusion. (paper)

Lie symmetries in differential equations

International Nuclear Information System (INIS)

Pleitez, V.

1979-01-01

A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt

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

Science.gov (United States)

Mullenmeister, Paul

1988-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)

2010-10-21

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

Numerical solution of integral equations, describing mass spectrum of vector mesons

International Nuclear Information System (INIS)

Zhidkov, E.P.; Nikonov, E.G.; Sidorov, A.V.; Skachkov, N.B.; Khoromskij, B.N.

1988-01-01

The description of the numerical algorithm for solving quasipotential integral equation in impulse space is presented. The results of numerical computations of the vector meson mass spectrum and the leptonic decay width are given in comparison with the experimental data

Solving large sets of coupled equations iteratively by vector processing on the CYBER 205 computer

International Nuclear Information System (INIS)

Tolsma, L.D.

1985-01-01

The set of coupled linear second-order differential equations which has to be solved for the quantum-mechanical description of inelastic scattering of atomic and nuclear particles can be rewritten as an equivalent set of coupled integral equations. When some type of functions is used as piecewise analytic reference solutions, the integrals that arise in this set can be evaluated analytically. The set of integral equations can be solved iteratively. For the results mentioned an inward-outward iteration scheme has been applied. A concept of vectorization of coupled-channel Fortran programs, based on this integral method, is presented for the use on the Cyber 205 computer. It turns out that, for two heavy ion nuclear scattering test cases, this vector algorithm gives an overall speed-up of about a factor of 2 to 3 compared to a highly optimized scalar algorithm for a one vector pipeline computer

Kelvin-Helmholtz instability in solar spicules

Directory of Open Access Journals (Sweden)

H Ebadi

2016-12-01

Full Text Available Magneto hydrodynamic waves, propagating along spicules, may become unstable and the expected instability is of Kelvin-Helmholtz type. Such instability can trigger the onset of wave turbulence leading to an effective plasma heating and particle acceleration. In present study, two-dimensional magneto hydrodynamic simulations performed on a Cartesian grid is presented in spicules with different densities, moving at various speeds depending on their environment. Simulations being applied in this study show the onset of Kelvin-Helmholtz type instability and transition to turbulent flow in spicules. Development of Kelvin-Helmholtz instability leads to momentum and energy transport, dissipation, and mixing of fluids. When magnetic fields are involved, field amplification is also possible to take place

Extraordinary acoustic transmission mediated by Helmholtz resonators

Directory of Open Access Journals (Sweden)

Vijay Koju

2014-07-01

Full Text Available We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.

Characterizing permanent magnet blocks with Helmholtz coils

Science.gov (United States)

Carnegie, D. W.; Timpf, J.

1992-08-01

Most of the insertion devices to be installed at the Advanced Photon Source will utilize permanent magnets in their magnetic structures. The quality of the spectral output is sensitive to the errors in the field of the device which are related to variations in the magnetic properties of the individual blocks. The Advanced Photon Source will have a measurement facility to map the field in the completed insertion devices and equipment to test and modify the magnetic strength of the individual magnet blocks. One component of the facility, the Helmholtz coil permanent magnet block measurement system, has been assembled and tested. This system measures the total magnetic moment vector of a block with a precision better than 0.01% and a directional resolution of about 0.05°. The design and performance of the system will be presented.

2013 CIME Course Vector-valued Partial Differential Equations and Applications

CERN Document Server

Marcellini, Paolo

2017-01-01

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

Stable chains and vortex equations on complex vector bundles

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we study an object on almost Hermitian manifold M consisting of a finite number of J i -holomorphic vector bundles E i over M and homomorphisms φ i :E 1 →E i-1 . We call such an object a J-holomorphic chain. We then prove a Hitchin-Kobayashi correspondence relating the existence of solutions to certain chain vortex equations and an appropriate notion of stability for the corresponding chains. (author)

Vacuum spacetimes with a spacelike, hypersurface-orthogonal Killing vector: reduced equations in a canonical frame

International Nuclear Information System (INIS)

Bonanos, S

2003-01-01

The Newman-Penrose equations for spacetimes having one spacelike Killing vector are reduced-in a geometrically defined 'canonical frame' - to a minimal set, and its differential structure is studied. Expressions for the frame vectors in an arbitrary coordinate basis are given, and coordinate-independent choices of the metric functions are suggested which make the components of the Ricci tensor in the direction of the Killing vector vanish

Preliminary analysis of resonance effect by Helmholtz-Schrödinger method

International Nuclear Information System (INIS)

Er-Yan, Yan; Fan-Bao, Meng; Hong-Ge, Ma; Chao-Yang, Chen

2010-01-01

The Helmholtz-Schrödinger method is employed to study the electric field standing wave caused by coupling through a simple slot. There is a good agreement between the numerical results and the resonant conditions presented by the Helmholtz—Schrödinger method. Thus, it can be used in similar cases where the amplitude of the electric field is the important quantity or eigenfunctions of the Schrödinger equation are needed for complicated quantum structures with hard wall boundary conditions. (general)

Integrability and symmetries for the Helmholtz oscillator with friction

International Nuclear Information System (INIS)

Almendral, Juan A; Sanjuan, Miguel A F

2003-01-01

This paper deals with the Helmholtz oscillator, which is a simple nonlinear oscillator whose equation presents a quadratic nonlinearity and the possibility of escape. When a periodic external force is introduced, the width of the stochastic layer, which is a region around the separatrix where orbits may exhibit transient chaos, is calculated. In the absence of friction and external force, it is well known that analytical solutions exist since it is completely integrable. When only friction is included, there is no analytical solution for all parameter values. However, by means of the Lie theory for differential equations we find a relation between parameters for which the oscillator is integrable. This is related to the fact that the system possesses a symmetry group and the corresponding symmetries are computed. Finally, the analytical explicit solutions are shown and related to the basins of attraction

Helmholtz and the psychophysiology of time.

Science.gov (United States)

Debru, C

2001-09-01

After having measured the velocity of the nervous impulse in the 1850s, Helmholtz began doing research on the temporal dimensions of visual perception. Experiments dealing with the velocity of propagation in nerves (as well as with aspects of perception) were carried out occasionally for some fifteen years until their final publication in 1871. Although the temporal dimension of perception seems to have interested Helmholtz less than problems of geometry and space, his experiments on the time of perception were technically rather subtle and seminal, especially compared with experiments performed by his contemporaries, such as Sigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann, and Wilhelm Wundt. Helmholtz's conception of the temporal aspects of perception reflects the continuity that holds between psychophysiological research and the Kantian philosophical background.

Incompressible spectral-element method: Derivation of equations

Science.gov (United States)

Deanna, Russell G.

1993-01-01

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

CFD simulation of Kelvin-Helmholtz instability

International Nuclear Information System (INIS)

Strubelj, L.; Tiselj, I.

2005-01-01

Kelvin-Helmholtz instability appears in stratified two-fluid flow at surface. When the relative velocity is higher than the critical relative velocity, the growth of waves occurs. The experiment of Thorpe [1] used as a benchmark in the present paper, is made in a rectangular glass tube filled with two immiscible fluids of various densities. We simulated the growth of instability with CFX-5.7 code and compared simulation with analytical solution. It was found that surface tension force, which stabilizes growth of waves, actually has a destabilizing effect in simulation, unless very small timestep and residual is used. In CFX code system of nonlinear Navier-Stokes equations is linearised and solved iterative in each timestep, until prescribed residual is achieved. On the other hand, simulation without surface tension force is more stable than analytical result predicts. (author)

ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

Institute of Scientific and Technical Information of China (English)

无

2011-01-01

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.

A new iterative solver for the time-harmonic wave equation

NARCIS (Netherlands)

Riyanti, C.D.; Erlangga, Y.A.; Plessix, R.E.; Mulder, W.A.; Vuik, C.; Oosterlee, C.

2006-01-01

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can

Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

Directory of Open Access Journals (Sweden)

Yang-Yang Chen

2016-01-01

Full Text Available The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure. The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method. The application of the present homoclinic solutions to the chaos prediction of the nonautonomous Helmholtz-Duffing oscillator is performed. Effectiveness and advantage of the present solutions are shown by comparisons.

The Kelvin-Helmholtz instability on the magnetopause

International Nuclear Information System (INIS)

Kivelson, M.G.; California Univ., Los Angeles; Pu, Z.-Y.

1984-01-01

Conditions for the development of Kelvin-Helmholtz (K-H) waves on the magnetopause have been known for more than 15 years; more recently, spacecraft observations have stimulated further examination of the properties of K-H waves. For a magnetopause with no boundary layer, two different modes of surface waves have been identified and their properties have been investigated for various assumed orientations of magnetic field and flow velocity vectors. The power radiated into the magnetosphere from the velocity shear at the boundary has been estimated. Other calculations have focused on the consequences of finite thickness boundary layers, both uniform and non-uniform. The boundary layer is found to modify the wave modes present at the magnetopause and to yield a criterion for the wavelength of the fastest growing surface waves. The paper concludes by questioning the extent to which the inferences from boundary layer models are model dependent and identifies areas where further work is needed or anticipated. (author)

Can Hall effect trigger Kelvin-Helmholtz instability in sub-Alfvénic flows?

Science.gov (United States)

Pandey, B. P.

2018-05-01

In the Hall magnetohydrodynamics, the onset condition of the Kelvin-Helmholtz instability is solely determined by the Hall effect and is independent of the nature of shear flows. In addition, the physical mechanism behind the super- and sub-Alfvénic flows becoming unstable is quite different: the high-frequency right circularly polarized whistler becomes unstable in the super-Alfvénic flows whereas low-frequency, left circularly polarized ion-cyclotron wave becomes unstable in the presence of sub-Alfvénic shear flows. The growth rate of the Kelvin-Helmholtz instability in the super-Alfvénic case is higher than the corresponding ideal magnetohydrodynamic rate. In the sub-Alfvénic case, the Hall effect opens up a new, hitherto inaccessible (to the magnetohydrodynamics) channel through which the partially or fully ionized fluid can become Kelvin-Helmholtz unstable. The instability growth rate in this case is smaller than the super-Alfvénic case owing to the smaller free shear energy content of the flow. When the Hall term is somewhat smaller than the advection term in the induction equation, the Hall effect is also responsible for the appearance of a new overstable mode whose growth rate is smaller than the purely growing Kelvin-Helmholtz mode. On the other hand, when the Hall diffusion dominates the advection term, the growth rate of the instability depends only on the Alfvén -Mach number and is independent of the Hall diffusion coefficient. Further, the growth rate in this case linearly increases with the Alfvén frequency with smaller slope for sub-Alfvénic flows.

Experimental realization of extraordinary acoustic transmission using Helmholtz resonators

Directory of Open Access Journals (Sweden)

Brian C. Crow

2015-02-01

Full Text Available The phenomenon of extraordinary acoustic transmission through a solid barrier with an embedded Helmholtz resonator (HR is demonstrated. The Helmholtz resonator consists of an embedded cavity and two necks that protrude, one on each side of the barrier. Extraordinary transmission occurs for a narrow spectral range encompassing the resonant frequency of the Helmholtz resonator. We show that an amplitude transmission of 97.5% is achieved through a resonator whose neck creates an open area of 6.25% of the total barrier area. In addition to the enhanced transmission, we show that there is a smooth, continuous phase transition in the transmitted sound as a function of frequency. The frequency dependent phase transition is used to experimentally realize slow wave propagation for a narrow-band Gaussian wave packet centered at the maximum transmission frequency. The use of parallel pairs of Helmholtz resonators tuned to different resonant frequencies is experimentally explored as a means of increasing the transmission bandwidth. These experiments show that because of the phase transition, there is always a frequency between the two Helmholtz resonant frequencies at which destructive interference occurs whether the resonances are close or far apart. Finally, we explain how the phase transition associated with Helmholtz-resonator-mediated extraordinary acoustic transmission can be exploited to produce diffractive acoustic components including sub-wavelength thickness acoustic lenses.

On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

International Nuclear Information System (INIS)

Zhao, J.M.; Tan, J.Y.; Liu, L.H.

2012-01-01

Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.

Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments

Science.gov (United States)

2010-09-01

that of the former is geared towards determining the transport amplitude, having found the eikonal by some other means. Among the principal...FOR MODELING RADIO TRANSMISSION LOSS 1761 We can then use the following asymptotic ansatz (10) where (11) and is the tunnel width [26]. The eikonal is a...equation and equating terms of the same order of , we can define the eikonal and find the vector PE [4] for the straight waveguide (12) where is the

Holomorphic Vector Bundles Corresponding to some Soliton Solutions of the Ward Equation

Energy Technology Data Exchange (ETDEWEB)

Zhu, Xiujuan, E-mail: yzzhuxiujuan@sina.com [Jiangsu Second Normal University, School of Mathematics and Information Technology (China)

2015-12-15

Holomorphic vector bundles corresponding to the static soliton solution of the Ward equation were explicitly presented by Ward in terms of a meromorphic framing. Bundles (for simplicity, “bundle” is to be taken throughout to mean “holomorphic vector bundle”) corresponding to all Ward k-soliton solutions whose extended solutions have only simple poles, and some Ward 2-soliton solutions whose extended solutions have only a second-order pole, were explicitly described by us in a previous paper. In this paper, we go on to present some bundles corresponding to soliton-antisoliton solutions of the Ward equation, and Ward 3-soliton solutions whose extended solutions have a simple pole and a double pole. To give some more interpretation of the bundles, we study the second Chern number of the corresponded bundles and find that it can be obtained directly from the patching matrices. We also point out some information about bundles corresponding to Ward soliton solutions whose extended solutions have general pole data at the end of the paper.

Singular vectors and invariant equations for the Schroedinger algebra in n ≥ 3 space dimensions. The general case

International Nuclear Information System (INIS)

Dobrev, V. K.; Stoimenov, S.

2010-01-01

The singular vectors in Verma modules over the Schroedinger algebra s(n) in (n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schroedinger algebras are constructed.

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering

KAUST Repository

AbdulJabbar, Mustafa Abdulmajeed; Al Farhan, Mohammed; Al-Harthi, Noha A.; Chen, Rui; Yokota, Rio; Bagci, Hakan; Keyes, David E.

2018-01-01

scattering, which uses FMM as a matrix-vector multiplication inside the GMRES iterative method. Our FMM Helmholtz kernels treat nontrivial singular and near-field integration points. We implement highly optimized kernels for both shared and distributed memory

Vectorized and multitasked solution of the few-group neutron diffusion equations

International Nuclear Information System (INIS)

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-01-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. For the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model

On separable Pauli equations

International Nuclear Information System (INIS)

Zhalij, Alexander

2002-01-01

We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

Relativistic energy eigenvalues for the Dirac equation in the presence of vector and scalar potentials via the simple similarity transformation

International Nuclear Information System (INIS)

Barakat, T

2012-01-01

Based on the simple similarity transformation, we were able to transform the Dirac equation whose potential contains vector V (r) = -A/r + B 1 r and scalar S(r) = B 2 r types into a form nearly identical to the Schrödinger equation. The transformed equation is so simple that one can solve it by means of the asymptotic iteration method. Moreover, within the same framework we were able to obtain the relativistic energy eigenvalues for the Dirac equation with vector Coulomb plus scalar linear, and with pure scalar linear potentials; V (r) = -A/r, S(r) = B 2 r, and V (r) = 0, S(r) = B 2 r, respectively.

Exact solutions of the vacuum Einstein's equations allowing for two noncommuting Killing vectors

International Nuclear Information System (INIS)

Aliev, V.N.; Leznov, A.N.

1990-01-01

Einstein's equations are written in the form of covariant gauge theory in two-dimensional space with binomial solvable gauge group, with respect to two noncommutative of Killing vectors. The theory is exact integrable in one-dimensional case and series of partial exact solutions are constructed in two-dimensional. 5 refs

Analytic solution of vector model kinetic equations with constant kernel and their applications

International Nuclear Information System (INIS)

Latyshev, A.V.

1993-01-01

For the first time exact solutions the heif-space boundary value problems for model kinetic equations is obtained. Here x > 0, μ is an element of (-∞, 0) union (0, +∞), Σ = diag {σ 1 , σ 2 }, C = [c ij ] - 2 x 2-matrix, Ψ (x, μ) is vector-column with elements ψ 1 and ψ 2 . Exact solution of the diffusion slip flow of the binary gas mixture as a application for the model Boltzmann equation with collision operator in the McCormack's form is found. 18 refs

Infinite-Dimensional Symmetry Algebras as a Help Toward Solutions of the Self-Dual Field Equations with One Killing Vector

Science.gov (United States)

Finley, Daniel; McIver, John K.

2002-12-01

The sDiff(2) Toda equation determines all self-dual, vacuum solutions of the Einstein field equations with one rotational Killing vector. Some history of the searches for non-trivial solutions is given, including those that begin with the limit as n → ∞ of the An Toda lattice equations. That approach is applied here to the known prolongation structure for the Toda lattice, hoping to use Bäcklund transformations to generate new solutions. Although this attempt has not yet succeeded, new faithful (tangent-vector) realizations of A∞ are described, and a direct approach via the continuum Lie algebras of Saveliev and Leznov is given.

Helmholtz resonance in a piezoelectric–hydraulic pump-based hybrid actuator

International Nuclear Information System (INIS)

Kim, Gi-Woo; Wang, K W

2011-01-01

This paper demonstrates that a hydraulically acting Helmholtz resonator can exist in a piezoelectric–hydraulic pump (PHP) based hybrid actuator, which in turn affects the volumetric efficiency of the PHP. The simulation and experimental results illustrate the effect of Helmholtz resonance on the flow rate performance of the PHP. The study also shows how to shift the Helmholtz resonant frequency to a higher value through changing parameters such as the cylinder diameter and the effective bulk modulus of the working fluid, which will improve the volumetric efficiency and broaden the operating frequency range of the PHP actuator

Simulation of Helmholtz Resonance Effects in Aircraft ECS

OpenAIRE

Pollok, Alexander; Schröffer, Andreas

2017-01-01

Helmholtz resonators are closed volumes that are connected to pipes. They exhibit a pronounced resonance frequency, where small boundary pressure excitations in the volume or the environment lead to large mass flow excitations in the pipe. Aircraft have a topology similar to Helmholtz resonators, the closed volume is represented by the cabin, while the pipe is represented by the Environmental Control System. Some discrepancies appear due to the non-zero mass-flow or friction effects in...

Equi-frequency contour of photonic crystals with the extended Dirichlet-to-Neumann wave vector eigenvalue equation method

International Nuclear Information System (INIS)

Jiang Bin; Zhang Yejing; Wang Yufei; Liu Anjin; Zheng Wanhua

2012-01-01

We present the extended Dirichlet-to-Neumann wave vector eigenvalue equation (DtN-WVEE) method to calculate the equi-frequency contour (EFC) of square lattice photonic crystals (PhCs). With the extended DtN-WVEE method and Snell's law, the effective refractive index of the mode with a circular EFC can be obtained, which is further validated with the refractive index weighted by the electric field or magnetic field. To further verify the EFC calculated by the DtN-WVEE method, the finite-difference time-domain method is also used. Compared with other wave vector eigenvalue equation methods that calculate EFC directly, the size of the eigenmatrix used in the DtN-WVEE method is much smaller, and the computation time is significantly reduced. Since the DtN-WVEE method solves wave vectors for given arbitrary frequencies, it can also find applications in studying the optical properties of a PhC with dispersive, lossy and magnetic materials. (paper)

Genus two finite gap solutions to the vector nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Woodcock, Thomas; Warren, Oliver H; Elgin, John N

2007-01-01

A recently published article presents a technique used to derive explicit formulae for odd genus solutions to the vector nonlinear Schroedinger equation. In another article solutions of genus two are derived using a different approach which assumes a separable ansatz. In this communication, the extension of the first technique to the even genus case is discussed, and this extension is carried out explicitly for genus two. Furthermore, a birational mapping is found between the spectral curves that arise in the two approaches. (fast track communication)

Reciprocity relationships in vector acoustics and their application to vector field calculations.

Science.gov (United States)

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

Kelvin-Helmholtz instability as a possible cause of edge localized modes

International Nuclear Information System (INIS)

Strauss, H.R.

1992-01-01

Edge localized modes may be a Kelvin-Helmholtz instability caused by the sheared rotation of H-mode plasmas. The Kelvin-Helmholtz instability is stabilized by coupling to Alfven waves. There is a critical velocity gradient, of the order of the Alfven velocity divided by the magnetic shear length. This is verified in a numerical simulation. The critical velocity shear is consistent with experiment. A non-linear simulation shows how the Kelvin-Helmholtz mode can cause oscillations of the velocity profile. (author). Letter-to-the-editor. 13 refs, 6 figs

Noise reduction efficiency of Helmholtz resonator in simulated channel of HVAC system

Directory of Open Access Journals (Sweden)

Hossein Ali Yousefi Rizi

2014-01-01

Conclusions: This research showed that the designed Helmholtz resonators at a certain frequency of low-frequency sound demonstrated the soundest decrease. The increase in the Helmholtz resonators′ chamber volume and their neck′s pass area are negatively associated with the rate of sound resonance. As a result, of determining the effective frequency range of the Helmholtz resonator, the designed resonator could be applied as an effective and efficient instrument of removing or decreasing noise.

Nonlinear perturbations of systems of partial differential equations with constant coefficients

Directory of Open Access Journals (Sweden)

Carmen J. Vanegas

2000-01-01

Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.

Helmholtz and Zoellner: nineteenth-century empiricism, spiritism, and the theory of space perception.

Science.gov (United States)

Stromberg, W H

1989-10-01

J. K. F. Zoellner began writing on "experimental proofs" of a fourth spatial dimension, and of the existence of spirits, in 1878. His arguments caused strong controversy, with rebuttal essays by Wilhelm Wundt and others. The author argues that Zoellner's case that these matters are experimental questions rested on arguments which Hermann von Helmholtz, inveighing against rationalist views of space and space perception, had recently published. Zoellner's use of Helmholtz's arguments to advance and defend his spiritist views occasioned strong criticism of Helmholtz, affected careers and reputations of scholars in Berlin and Leipzig, and caused enduring controversy over the credibility of Helmholtz's empiricist theory of space perception.

Nonlinearity, Viscosity and Air-Compressibility Effects on the Helmholtz Resonant Wave Motion Generated by an Oscillating Twin Body in a Free Surface

Science.gov (United States)

Ananthakrishnan, Palaniswamy

2012-11-01

The problem is of practical relevance in determining the motion response of multi-hull and air-cushion vehicles in high seas and in littoral waters. The linear inviscid problem without surface pressure has been well studied in the past. In the present work, the nonlinear wave-body interaction problem is solved using finite-difference methods based on boundary-fitted coordinates. The inviscid nonlinear problem is tackled using the mixed Eulerian-Lagrangian formulation and the solution of the incompressible Navier-Stokes equations governing the viscous problem using a fractional-step method. The pressure variation in the air cushion is modeled using the isentropic gas equation pVγ = Constant. Results show that viscosity and free-surface nonlinearity significantly affect the hydrodynamic force and the wave motion at the resonant Helmholtz frequency (at which the primary wave motion is the vertical oscillation of the mean surface in between the bodies). Air compressibility suppresses the Helmholtz oscillation and enhances the wave radiation. Work supported by the ONR under the grant N00014-98-1-0151.

Symmetry-breaking analysis for the general Helmholtz-Duffing oscillator

International Nuclear Information System (INIS)

Cao Hongjun; Seoane, Jesus M.; Sanjuan, Miguel A.F.

2007-01-01

The symmetry breaking phenomenon for a general Helmholtz-Duffing oscillator as a function of a symmetric parameter in the nonlinear force is investigated. Different values of this parameter convert the general oscillator into either the Helmholtz or the Duffing oscillator. Due to the variation of the symmetric parameter, the phase space patterns of the unperturbed Helmholtz-Duffing oscillator will cause a huge difference between the left-hand homoclinic orbit and the right-hand one. In particular, the area of the left-hand homoclinic orbits is a strictly monotonously decreasing function, while the area of the right-hand homoclinic orbit varies only in a very small range. There exist distinct local supercritical and subcritical saddle-node bifurcations at two different centers. The left-hand and the right-hand existing regions of the harmonic solutions of the Helmholtz-Duffing oscillator created by the left-hand and the right-hand saddle-node bifurcation curves will lead to different transition in the amplitude-frequency plane. There exists also a critical frequency which has the effect that the left-hand homoclinic bifurcation value is equal to the right-hand homoclinic bifurcation value. And, if the amplitude coefficient of the Helmholtz-Duffing oscillator is used as the control parameter, and it is larger than the same left-hand and right-hand homoclinic bifurcation, then the global stability of the system will be destroyed at a lowest cost. Besides this critical frequency, the left-hand and the right-hand homoclinic bifurcations are not only unequal, but also their effects for the system's stability are different. Among them, the effect resulting from the small homoclinic bifurcation for the system's stability is local and negligible, while the effect from the large homoclinic bifurcation is global but this is accomplished at a quite larger cost

The Determinate World Kant and Helmholtz on the Physical Meaning of Geometry

CERN Document Server

Hyder, David

2009-01-01

This study examines the place of Hermann von Helmholtz´s seminal papers on geometry in his philosophy of science. The arguments of these papers are traced back to his prior work on the theory of magnitudes, as well as to Helmholtz´s early, Kantian position. The author claims that Helmholtz should be understood not as opposing Kant, but as modifying the latter´s theory of magnitudes so as to remove obstacles to their common project of constructing a complete system of natural science.

Acoustic superlens using Helmholtz-resonator-based metamaterials

International Nuclear Information System (INIS)

Yang, Xishan; Yin, Jing; Yu, Gaokun; Peng, Linhui; Wang, Ning

2015-01-01

Acoustic superlens provides a way to overcome the diffraction limit with respect to the wavelength of the bulk wave in air. However, the operating frequency range of subwavelength imaging is quite narrow. Here, an acoustic superlens is designed using Helmholtz-resonator-based metamaterials to broaden the bandwidth of super-resolution. An experiment is carried out to verify subwavelength imaging of double slits, the imaging of which can be well resolved in the frequency range from 570 to 650 Hz. Different from previous works based on the Fabry-Pérot resonance, the corresponding mechanism of subwavelength imaging is the Fano resonance, and the strong coupling between the neighbouring Helmholtz resonators separated at the subwavelength interval leads to the enhanced sound transmission over a relatively wide frequency range

The Helmholtz legacy in physiological acoustics

CERN Document Server

Hiebert, Erwin

2014-01-01

This book explores the interactions between science and music in the late nineteenth- and early twentieth century. It examines and evaluates the work of Hermann von Helmholtz, Max Planck, Shohe Tanaka, and Adriaan Fokker, leading physicists and physiologists who were committed to understanding crucial aesthetic components of the art of music, including the standardization of pitch and the implementation of various types of intonations. With a mixture of physics, physiology, and aesthetics, author Erwin Hiebert addresses throughout the book how just intonation came to intersect with the history of keyboard instruments and exert an influence on the development of Western music. He begins with the work of Hermann von Helmholtz, a leading nineteenth-century physicist and physiologist who not only made important contributions in vision, optics, electrodynamics and thermodynamics, but also helped advanced the field of music theory as well. The author traces the Helmholtzian trends of thought that become inherently ...

An efficient Helmholtz solver for acoustic transversely isotropic media

KAUST Repository

Wu, Zedong

2017-11-11

The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and depend on less medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we propose to separate the quasi-P wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the non-elliptic-anisotropic components, which form a pseudo-differential operator. We, then, develop a separable approximation of the dispersion relation of non-elliptic-anisotropic components, specifically for transversely isotropic (TI) media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the non-elliptical terms represented in the Fourier domain. A frequency domain Helmholtz formulation of the approach renders the iterative implementation efficient as the cost is dominated by the Lower-Upper (LU) decomposition of the impedance matrix for the simpler elliptical anisotropic model. Also, the resulting wavefield is free of S-wave artifacts and has balanced amplitude. Numerical examples show that the method is reasonably accurate and efficient.

An efficient Helmholtz solver for acoustic transversely isotropic media

KAUST Repository

Wu, Zedong; Alkhalifah, Tariq Ali

2017-01-01

The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and depend on less medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we propose to separate the quasi-P wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the non-elliptic-anisotropic components, which form a pseudo-differential operator. We, then, develop a separable approximation of the dispersion relation of non-elliptic-anisotropic components, specifically for transversely isotropic (TI) media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the non-elliptical terms represented in the Fourier domain. A frequency domain Helmholtz formulation of the approach renders the iterative implementation efficient as the cost is dominated by the Lower-Upper (LU) decomposition of the impedance matrix for the simpler elliptical anisotropic model. Also, the resulting wavefield is free of S-wave artifacts and has balanced amplitude. Numerical examples show that the method is reasonably accurate and efficient.

Increase in effectiveness of low frequency acoustic liners by use of coupled Helmholtz resonators

Science.gov (United States)

Dean, L. W.

1977-01-01

Coupling of Helmholtz resonators in a low-frequency absorber array was studied as a means for increasing the effectiveness for absorbing low-frequency core engine noise. The equations for the impedance of the coupled-resonator systems were developed in terms of uncoupled-resonator parameters, and the predicted impedance for a parallel-coupled scheme is shown to compare favorably with measurements from a test model. In addition, attenuation measurements made in a flow duct on test coupled-resonator panels are shown to compare favorably with predicted values. Finally, the parallel-coupled concept is shown to give significantly more attenuation than that of a typical uncoupled resonator array of the same total volume.

Scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials in arbitrary dimension

International Nuclear Information System (INIS)

Chen Changyuan; Sun Dongsheng; Lu Falin

2004-01-01

Properties of scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials are investigated in an arbitrary dimension. Exact results of normalized wave functions of scattering states in the 'k/2π scale' and formula of phase shifts are presented

Harvesting energy from airflow with a michromachined piezoelectric harvester inside a Helmholtz resonator

NARCIS (Netherlands)

Matova, S.P.; Elfrink, R.; Vullers, R.J.M.; Schaijk, R. van

2011-01-01

In this paper we report an airflow energy harvester that combines a piezoelectric energy harvester with a Helmholtz resonator. The resonator converts airflow energy to air oscillations which in turn are converted into electrical energy by a piezoelectric harvester. Two Helmholtz resonators with

New correct solutions of the Dirac equation. 5

International Nuclear Information System (INIS)

Bagrov, V.G.; Byzov, N.N.; Gitman, D.M.; Klimenko, Yu.I.; Meshkov, A.G.; Shapovalov, V.N.; Shakhmatov, V.M.

1975-01-01

Some exact solutions for the Dirac equation, Klein-Gordon equation and classical relativistic equations of motion of an electron in external electromagnetic fields of a special type are considered. When fields E vector and H vector are related by the expression H vector=[n vector E vector]+n vector H 3 , where n vector is a constant unit vector, it turns out that among fields permitting the separation of variables in the Klein-Gordon equation more than half satisfy this relationship. For such fields the solution of the Dirac equation may be simplified considerably. Four specific kinds of fields are examined. The character of electron motion in such fields is peculiar but in the mathematical aspect, part of the problem is reduced to those considered previously

Another Look at Helmholtz's Model for the Gravitational Contraction of the Sun

Science.gov (United States)

Tort, A. C.; Nogarol, F.

2011-01-01

We take another look at the Helmholtz model for the gravitational contraction of the Sun. We show that there are two other pedagogically useful ways of rederiving Helmholtz's main results that make use of Gauss's law, the concept of gravitational field energy and the work-kinetic energy theorem. An account of the energy balance involved in the…

From Helmholtz to Schlick: The evolution of the sign-theory of perception.

Science.gov (United States)

Oberdan, Thomas

2015-08-01

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zurȕck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his 'method of coincidences', similar to the 'point-coincidences' featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism. Copyright © 2015 Elsevier Ltd. All rights reserved.

Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective

Science.gov (United States)

Bernard, Julien

2018-02-01

I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.

A highly accurate method to solve Fisher's equation

Indian Academy of Sciences (India)

The solution of the Helmholtz equation was approximated by a sixth-order compact finite difference. (CFD6) method in [29]. In [30], a CFD6 scheme has been presented to ... efficiency of the proposed method are reported in §3. Finally .... our discussion, one can apply the proposed method to solve the more general problem.

Elementary vectors

CERN Document Server

Wolstenholme, E Œ

1978-01-01

Elementary Vectors, Third Edition serves as an introductory course in vector analysis and is intended to present the theoretical and application aspects of vectors. The book covers topics that rigorously explain and provide definitions, principles, equations, and methods in vector analysis. Applications of vector methods to simple kinematical and dynamical problems; central forces and orbits; and solutions to geometrical problems are discussed as well. This edition of the text also provides an appendix, intended for students, which the author hopes to bridge the gap between theory and appl

Breather type solutions of the vector nonlinear Schroedinger equation with quasi-constant boundary conditions

International Nuclear Information System (INIS)

Makhan'kov, V.G.; Slavov, S.I.

1989-01-01

Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs

Harvesting energy from airflow with a michromachined piezoelectric harvester inside a Helmholtz resonator

International Nuclear Information System (INIS)

Matova, S P; Elfrink, R; Vullers, R J M; Van Schaijk, R

2011-01-01

In this paper we report an airflow energy harvester that combines a piezoelectric energy harvester with a Helmholtz resonator. The resonator converts airflow energy to air oscillations which in turn are converted into electrical energy by a piezoelectric harvester. Two Helmholtz resonators with adjustable resonance frequencies have been designed—one with a solid bottom and one with membrane on the bottom. The resonance frequencies of the resonators were matched to the complementing piezoelectric harvesters during harvesting. The aim of the presented work is a feasibility study on using packaged piezoelectric energy harvesters with Helmholtz resonators for airflow energy harvesting. The maximum energy we were able to obtain was 42.2 µW at 20 m s −1

Multimode Coupling Theory for Kelvin–Helmholtz Instability in Incompressible Fluid

International Nuclear Information System (INIS)

Li-Feng, Wang; Ying-Jun, Li; Wen-Hua, Ye; Zheng-Feng, Fan

2009-01-01

A weakly nonlinear model is proposed for multimode Kelvin–Helmholtz instability. The second-order mode coupling formula for Kelvin–Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not

Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: Polyampholyte and polyelectrolyte solutions

International Nuclear Information System (INIS)

Jiang, Hao; Adidharma, Hertanto

2014-01-01

The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions

Complex vector triads in spinor theory in Minkowski space

International Nuclear Information System (INIS)

Zhelnorovich, V.A.

1990-01-01

It is shown that tensor equations corresponding to the spinor Dirac equations represent a three-dimensional part of four-dimensional vector equations. The equations are formulated in an evidently invariant form in antisymmetric tensor components and in the corresponding components of a complex vector triad. A complete system of relativistically invariant tensor equations is ascertained

Vector mesons on the light front

International Nuclear Information System (INIS)

Naito, K.; Maedan, S.; Itakura, K.

2004-01-01

We apply the light-front quantization to the Nambu-Jona-Lasinio model with the vector interaction, and compute vector meson's mass and light-cone wavefunction in the large N limit. Following the same procedure as in the previous analyses for scalar and pseudo-scalar mesons, we derive the bound-state equations of a qq-bar system in the vector channel. We include the lowest order effects of the vector interaction. The resulting transverse and longitudinal components of the bound-state equation look different from each other. But eventually after imposing an appropriate cutoff, one finds these two are identical, giving the same mass and the same (spin-independent) light-cone wavefunction. Mass of the vector meson decreases as one increases the strength of the vector interaction

A comparison of high-order polynomial and wave-based methods for Helmholtz problems

Science.gov (United States)

Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien

2016-09-01

The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

Science.gov (United States)

Gunzburger, M. D.; Nicolaides, R. A.

1986-01-01

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

Science.gov (United States)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

The research reactor BER II at the Helmholtz-Center Berlin

Energy Technology Data Exchange (ETDEWEB)

Krohn, Herbert [Helmholtz-Zentrum Berlin (HZB), Berlin (Germany)

2012-10-15

For basic and application-oriented research assignments the Helmholtz-Center Berlin (Helmholtz Zentrum Berlin - HZB) runs a research reactor that operates as a source of neutron beams for a wide range of scientific investigations. At the end of the 1980{sup th} the BER II was completed renewed and fitted with new experimental facilities. The BER II is a light water cooled and moderated swimming pool type reactor to be operated at 10 MW thermal power. Six neutron guides deliver cold neutrons from the cold moderator cell to a neutron guide hall adjacent to the experiment hall. With its 24 experimental stations, experimenters at HZB have practically all neutron scattering or neutron radiography techniques at their disposal. (orig.)

The research reactor BER II at the Helmholtz-Center Berlin

International Nuclear Information System (INIS)

Krohn, Herbert

2012-01-01

For basic and application-oriented research assignments the Helmholtz-Center Berlin (Helmholtz Zentrum Berlin - HZB) runs a research reactor that operates as a source of neutron beams for a wide range of scientific investigations. At the end of the 1980 th the BER II was completed renewed and fitted with new experimental facilities. The BER II is a light water cooled and moderated swimming pool type reactor to be operated at 10 MW thermal power. Six neutron guides deliver cold neutrons from the cold moderator cell to a neutron guide hall adjacent to the experiment hall. With its 24 experimental stations, experimenters at HZB have practically all neutron scattering or neutron radiography techniques at their disposal. (orig.)

The electromagnetic field equations for moving media

International Nuclear Information System (INIS)

Ivezić, T

2017-01-01

In this paper a formulation of the field equation for moving media is developed by the generalization of an axiomatic geometric formulation of the electromagnetism in vacuum (Ivezić T 2005 Found. Phys. Lett. 18 401). First, the field equations with bivectors F ( x ) and ℳ ( x ) are presented and then these equations are written with the 4D vectors E ( x ), B ( x ), P ( x ) and M ( x ). The latter contain both the 4D velocity vector u of a moving medium and the 4D velocity vector v of the observers who measure E and B fields. They do not appear in previous literature. All these equations are also written in the standard basis and compared with Maxwell’s equations with 3D vectors. In this approach the Ampère-Maxwell law and Gauss’s law are inseparably connected in one law and the same happens with Faraday’s law and the law that expresses the absence of magnetic charge. It is shown that Maxwell’s equations with 3D vectors and the field equations with 4D geometric quantities are not equivalent in 4D spacetime (paper)

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

Cluster observations of reconnection due to the Kelvin-Helmholtz instability at the dawnside magnetospheric flank

Directory of Open Access Journals (Sweden)

K. Nykyri

2006-10-01

Full Text Available On 3 July 2001, the four Cluster satellites traversed along the dawnside magnetospheric flank and observed large variations in all plasma parameters. The estimated magnetopause boundary normals were oscillating in the z-direction and the normal component of the magnetic field showed systematic  2–3 min bipolar variations for 1 h when the IMF had a small positive b_z-component and a Parker-spiral orientation in the x,y-plane. Brief  33 s intervals with excellent deHoffman Teller frames were observed satisfying the Walén relation. Detailed comparisons with 2-D MHD simulations indicate that Cluster encountered rotational discontinuities generated by Kelvin-Helmholtz instability. We estimate a wave length of  6 R_E and a wave vector with a significant z-component.

On the equation of motion in electrodynamics

International Nuclear Information System (INIS)

Papas, C.H.

1975-01-01

A new vector equation of motion in electrodynamics is proposed by replacing the Schott term in the Lorentz-Dirac equation by an expression depending on the electro-magnetic field vectors E and B and the velocity vector V. It is argued that several conceptual difficulties in the Lorentz-Dirac equation disappear while the results remain the same except for extreme high fields and velocities as could be encountered in astrophysics

Gauge anomaly with vector and axial-vector fields in 6D curved space

Science.gov (United States)

Yajima, Satoshi; Eguchi, Kohei; Fukuda, Makoto; Oka, Tomonori

2018-03-01

Imposing the conservation equation of the vector current for a fermion of spin 1/2 at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial-vector fields in 6D curved space is expressed in tensorial form. The anomaly consists of terms that resemble the chiral U(1) anomaly and the commutator terms that disappear if the axial-vector field is Abelian.

Rayleigh-Taylor and Kelvin-Helmholtz instabilities in targets accelerated by laser ablation

International Nuclear Information System (INIS)

Emery, M.H.; Gardner, J.H.; Boris, J.P.

1982-01-01

With use of the fast2d laser-shell model, the acceleration of a 20-μm-thick plastic foil up to 160 km/s has been simulated. It is possible to follow the Rayleigh-Taylor bubble-and-spike development far into the nonlinear regime and beyond the point of foil fragmentation. Strong shear flow develops which evolves into the Kelvin-Helmholtz instability. The Kelvin-Helmholtz instability causes the tips of the spikes to widen and as a result reduce their rate of ''fall.''

Hybrid inverse problems for a system of Maxwell’s equations

International Nuclear Information System (INIS)

Bal, Guillaume; Zhou, Ting

2014-01-01

This paper concerns the quantitative step of the medical imaging modality thermo-acoustic tomography (TAT). We model the radiation propagation by a system of Maxwell’s equations. We show that the index of refraction of light and the absorption coefficient (conductivity) can be uniquely and stably reconstructed from a sufficiently large number of TAT measurements. Our method is based on verifying that the linearization of the inverse problem forms a redundant elliptic system of equations. We also observe that the reconstructions are qualitatively quite different from the setting where radiation is modeled by a scalar Helmholtz equation as in Bal G et al (2011 Inverse Problems 27 055007). (paper)

3-D transient eddy current calculations for the FELIX cylinder experiments

International Nuclear Information System (INIS)

Davey, K.R.; Turner, L.R.

1986-12-01

The three-dimensional eddy current transient field problem is formulated first using the U-V method. This method breaks the vector Helmholtz equation into two scalar Helmholtz equations. Null field integral equations and the appropriate boundary conditions are used to set up an identification matrix which is independent of null field point locations. Embedded in the identification matrix are the unknown eigenvalues of the problem representing its impulse response in time. These eigenvalues are found by equating the determinant of the identification matrix to zero. When this initial forcing function is Fourier decomposed into its spatial harmonics, each Fourier component can be associated with a unique eigenvalue by this technique. The true transient solution comes through a convolution of the impulse response so obtained with the particular external field decay governing the problem at hand. The technique is applied to the FELIX cylinder experiments; computed results are compared to data. A pseudoanalytic confirmation of the eigenvalues so obtained is formulated to validate the procedure

Optimization of field homogeneity of Helmholtz-like coils for measuring the balance of planar gradiometers

International Nuclear Information System (INIS)

Nordahn, M.A.; Holst, T.; Shen, Y.Q.

1999-01-01

Measuring the balance of planar SQUID gradiometers using a relatively small Helmholtz-like coil system requires a careful design of the coils in order to have a high degree of field uniformity along the radial direction. The level to which planar gradiometers can be balanced will be affected by any misalignment of the gradiometer relative to the ideal central position. Therefore, the maximum degree of balancing possible is calculated numerically for the Helmholtz geometry under various perturbations, including misalignment of the gradiometer along the cylindrical and the radial axis, and angular tilting relative to the normal plane. Furthermore, if the ratio between the coil separation and coil radius is chosen to be less than unity, calculations show that the expected radial uniformity of the field can be improved considerably compared to the traditional Helmholtz geometry. The optimized coil geometry is compared to the Helmholtz geometry and is found to yield up to an order of magnitude improvement of the worst case error signal within a volume spanned by the uncertainty in the alignment. (author)

Square Helmholtz coil with homogeneous field for magnetic measurement of longer HTS tapes

Energy Technology Data Exchange (ETDEWEB)

Alamgir, A.K.M. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China)]. E-mail: alam643@hotmail.com; Fang, J. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China); Gu, C. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China); Han, Z. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China)

2005-08-01

Magnetic ac loss measurement of HTS tapes and films at various magnetic field orientations becomes a crucial issue from the view point of measurement precision. In principle, due to tiny loss component and anisotropic properties, longer HTS sample subjected to very good homogeneous field could facilitate the accuracy of this kind of measurement. We investigated field profile of Helmholtz coils with square winding as a magnetizer for HTS tape and films. It is found that square winding exhibits better field-homogeneity than that of conventional circular winding with the similar coil dimensions for ideal condition. Being apart from ideal condition, we investigated field profile of square Helmholtz coil with various combinations of coil parameters and made a conclusion for the best combination based on the field homogeneity and field intensity. The design also provides noise reduction facilities by allowing compact and identical pick up-compensation coil arrangement. In addition, we optimized the final design of Helmholtz coil to compensate the influence of difficulties in square winding on the field distribution. Finally, as small as 0.5% field variation was estimated for 50 mm long sample to be magnetized under a proper combination of fabrication parameters. Investigation of field homogeneity, noise effect and a practical design of square Helmholtz coil as a pick-up coil based magnetizer will be reported.

Square Helmholtz coil with homogeneous field for magnetic measurement of longer HTS tapes

International Nuclear Information System (INIS)

Alamgir, A.K.M.; Fang, J.; Gu, C.; Han, Z.

2005-01-01

Magnetic ac loss measurement of HTS tapes and films at various magnetic field orientations becomes a crucial issue from the view point of measurement precision. In principle, due to tiny loss component and anisotropic properties, longer HTS sample subjected to very good homogeneous field could facilitate the accuracy of this kind of measurement. We investigated field profile of Helmholtz coils with square winding as a magnetizer for HTS tape and films. It is found that square winding exhibits better field-homogeneity than that of conventional circular winding with the similar coil dimensions for ideal condition. Being apart from ideal condition, we investigated field profile of square Helmholtz coil with various combinations of coil parameters and made a conclusion for the best combination based on the field homogeneity and field intensity. The design also provides noise reduction facilities by allowing compact and identical pick up-compensation coil arrangement. In addition, we optimized the final design of Helmholtz coil to compensate the influence of difficulties in square winding on the field distribution. Finally, as small as 0.5% field variation was estimated for 50 mm long sample to be magnetized under a proper combination of fabrication parameters. Investigation of field homogeneity, noise effect and a practical design of square Helmholtz coil as a pick-up coil based magnetizer will be reported

Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulthén Potential

Directory of Open Access Journals (Sweden)

Altuğ Arda

2017-01-01

Full Text Available We find the exact bound state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass function m(x. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the nonrelativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of PT-symmetric forms of the present potential.

Nonperturbative Aspects of Axial Vector Vertex

Institute of Scientific and Technical Information of China (English)

ZONG Hong-Shi; CHEN Xiang-Song; WANG Fan; CHANG Chao-Hsi; ZHAO En-Guang

2002-01-01

It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model.Gluon dressing of the axial vector vertex and the quark self-energy functions are described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger Dyson equation in the rainbow approximation,respectively.

Conformal Killing vectors in Robertson-Walker spacetimes

International Nuclear Information System (INIS)

Maartens, R.; Maharaj, S.d.

1986-01-01

It is well known that Robertson-Walker spacetimes admit a conformal Killingl vector normal to the spacelike homogeneous hypersurfaces. Because these spacetimes are conformally flat, there are a further eight conformal Killing vectors, which are neither normal nor tangent to the homogeneous hypersurfaces. The authors find these further conformal Killing vectors and the Lie algebra of the full G 15 of conformal motions. Conditions on the metric scale factor are determined which reduce some of the conformal Killing vectors to homothetic Killing vectors or Killing vectors, allowing one to regain in a unified way the known special geometries. The non-normal conformal Killing vectors provide a counter-example to show that conformal motions do not, in general, map a fluid flow conformally. These non-normal vectors are also used to find the general solution of the null geodesic equation and photon Liouville equation. (author)

Kelvin-Helmholtz Instability: Lessons Learned and Ways Forward

Science.gov (United States)

Masson, A.; Nykyri, K.

2018-06-01

The Kelvin-Helmholtz instability (KHI) is a ubiquitous phenomenon across the Universe, observed from 500 m deep in the oceans on Earth to the Orion molecular cloud. Over the past two decades, several space missions have enabled a leap forward in our understanding of this phenomenon at the Earth's magnetopause. Key results obtained by these missions are first presented, with a special emphasis on Cluster and THEMIS. In particular, as an ideal instability, the KHI was not expected to produce mass transport. Simulations, later confirmed by spacecraft observations, indicate that plasma transport in Kelvin-Helmholtz (KH) vortices can arise during non-linear stage of its development via secondary process. In addition to plasma transport, spacecraft observations have revealed that KHI can also lead to significant ion heating due to enhanced ion-scale wave activity driven by the KHI. Finally, we describe what are the upcoming observational opportunities in 2018-2020, thanks to a unique constellation of multi-spacecraft missions including: MMS, Cluster, THEMIS, Van Allen Probes and Swarm.

Flows of non-smooth vector fields and degenerate elliptic equations with applications to the Vlasov-Poisson and semigeostrophic systems

CERN Document Server

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.

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering

KAUST Repository

AbdulJabbar, Mustafa Abdulmajeed

2018-03-27

Algorithmic and architecture-oriented optimizations are essential for achieving performance worthy of anticipated energy-austere exascale systems. In this paper, we present an extreme scale FMM-accelerated boundary integral equation solver for wave scattering, which uses FMM as a matrix-vector multiplication inside the GMRES iterative method. Our FMM Helmholtz kernels treat nontrivial singular and near-field integration points. We implement highly optimized kernels for both shared and distributed memory, targeting emerging Intel extreme performance HPC architectures. We extract the potential thread- and data-level parallelism of the key Helmholtz kernels of FMM. Our application code is well optimized to exploit the AVX-512 SIMD units of Intel Skylake and Knights Landing architectures. We provide different performance models for tuning the task-based tree traversal implementation of FMM, and develop optimal architecture-specific and algorithm aware partitioning, load balancing, and communication reducing mechanisms to scale up to 6,144 compute nodes of a Cray XC40 with 196,608 hardware cores. With shared memory optimizations, we achieve roughly 77% of peak single precision floating point performance of a 56-core Skylake processor, and on average 60% of peak single precision floating point performance of a 72-core KNL. These numbers represent nearly 5.4x and 10x speedup on Skylake and KNL, respectively, compared to the baseline scalar code. With distributed memory optimizations, on the other hand, we report near-optimal efficiency in the weak scalability study with respect to both the logarithmic communication complexity as well as the theoretical scaling complexity of FMM. In addition, we exhibit up to 85% efficiency in strong scaling. We compute in excess of 2 billion DoF on the full-scale of the Cray XC40 supercomputer.

Capillary and viscous perturbations to Helmholtz flows

KAUST Repository

Moore, M. R.; Ockendon, H.; Ockendon, J. R.; Oliver, J. M.

2014-01-01

Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p. 264506) relating to droplet impact, this paper presents an analysis of the perturbations to the free surface caused by small surface tension and viscosity in steady Helmholtz flows. In particular, we identify the regimes in which appreciable vorticity can be shed from the boundary layer to the bulk flow. © 2014 Cambridge University Press.

Capillary and viscous perturbations to Helmholtz flows

KAUST Repository

Moore, M. R.

2014-02-21

Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p. 264506) relating to droplet impact, this paper presents an analysis of the perturbations to the free surface caused by small surface tension and viscosity in steady Helmholtz flows. In particular, we identify the regimes in which appreciable vorticity can be shed from the boundary layer to the bulk flow. © 2014 Cambridge University Press.

Conservation Properties of the Hamiltonian Particle-Mesh method for the Quasi-Geostrophic Equations on a sphere

NARCIS (Netherlands)

H. Thorsdottir (Halldora)

2011-01-01

htmlabstractThe Hamiltonian particle-mesh (HPM) method is used to solve the Quasi-Geostrophic model generalized to a sphere, using the Spherepack modeling package to solve the Helmholtz equation on a colatitude-longitude grid with spherical harmonics. The predicted energy conservation of a

Mathematical Methods for Engineers and Scientists 2 Vector Analysis, Ordinary Differential Equations and Laplace Transforms

CERN Document Server

Tang, Kwong-Tin

2007-01-01

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

KAUST Repository

Fan, Xiaolin; Kou, Jisheng; Qiao, Zhonghua; Sun, Shuyu

2017-01-01

are applied to a functional minimization problem of the total Helmholtz free energy. Mass conservation constraints are enforced through Lagrange multipliers. A system of chemical equilibrium equations is obtained which is a set of second-order elliptic

A new complex vector method for balancing chemical equations: Nova kompleksna metoda za uravnoteženje kemičnih enačb:

OpenAIRE

Risteski, Ice B.

2010-01-01

In this article, the author discovers a paradox of balancing chemical equations. The many counterexamples illustrate that the considered procedure of balancing chemical equations given in the paper1 is inconsistent. A new complex vector method for paradox resolution is given too. V članku avtor opisuje paradoks pri uravnoteženju kemijskih reakcij. Več primerov dokazuje, da je procedura uravnoteženja kemijskih reakcij v viru1 inkonsistentna. Predstavljena je nova kompleksna vektorska metoda...

Magnetized Kelvin-Helmholtz instability: theory and simulations in the Earth's magnetosphere context

Science.gov (United States)

Faganello, Matteo; Califano, Francesco

2017-12-01

The Kelvin-Helmholtz instability, proposed a long time ago for its role in and impact on the transport properties at magnetospheric flanks, has been widely investigated in the Earth's magnetosphere context. This review covers more than fifty years of theoretical and numerical efforts in investigating the evolution of Kelvin-Helmholtz vortices and how the rich nonlinear dynamics they drive allow solar wind plasma bubbles to enter into the magnetosphere. Special care is devoted to pointing out the main advantages and weak points of the different plasma models that can be adopted for describing the collisionless magnetospheric medium and in underlying the important role of the three-dimensional geometry of the system.

Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations.

Science.gov (United States)

Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman

2015-04-01

The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.

A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

Science.gov (United States)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity

Science.gov (United States)

Orazzo, Annagrazia; Hoepffner, Jérôme

2012-11-01

At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.

Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions

International Nuclear Information System (INIS)

Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino

2006-01-01

The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

Energy Technology Data Exchange (ETDEWEB)

Okamoto, Kazuhisa [Nagoya University, Department of Physics, Nagoya (Japan); Nonaka, Chiho [Nagoya University, Department of Physics, Nagoya (Japan); Nagoya University, Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya (Japan); Duke University, Department of Physics, Durham, NC (United States)

2017-06-15

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions. (orig.)

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

Science.gov (United States)

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-01

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

Voluntarism in early psychology: the case of Hermann von Helmholtz.

Science.gov (United States)

De Kock, Liesbet

2014-05-01

The failure to recognize the programmatic similarity between (post-)Kantian German philosophy and early psychology has impoverished psychology's historical self-understanding to a great extent. This article aims to contribute to recent efforts to overcome the gaps in the historiography of contemporary psychology, which are the result of an empiricist bias. To this end, we present an analysis of the way in which Hermann von Helmholtz's theory of perception resonates with Johann Gottlieb Fichte's Ego-doctrine. It will be argued that this indebtedness is particularly clear when focusing on the foundation of the differential awareness of subject and object in perception. In doing so, the widespread reception of Helmholtz's work as proto-positivist or strictly empiricist is challenged, in favor of the claim that important elements of his theorizing can only be understood properly against the background of Fichte's Ego-doctrine. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Real-time optical laboratory solution of parabolic differential equations

Science.gov (United States)

Casasent, David; Jackson, James

1988-01-01

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Coupled Kelvin-Helmholtz and Tearing Mode Instabilities at the Mercury's Magnetopause

Science.gov (United States)

Ivanovski, S. L.; Milillo, A.; Kartalev, M.; Massetti, S.

2018-05-01

A MHD approach for numerical simulations of coupled Kelvin-Helmholtz and tearing mode instabilities has been applied to Mercury’s magnetopause and used to perform a physical parameters study constrained by the MESSENGER data.

Broad-aperture polarized proton target with arbitrary orientation of polarization vector

International Nuclear Information System (INIS)

Belyaev, A.A.; Get'man, V.A.; Derkach, A.Ya.; Karnaukhov, I.M.; Lukhanin, A.A.; Razumnyj, A.A.; Sorokin, P.V.; Sporov, E.A.; Telegin, Yu.N.; Trotsenko, V.I.

1985-01-01

Polarized proton target with the Helmholtz broad-aperture superconducting magnetic system is described. Axial aperture α=95 deg, inter-coil access angle β=23 deg. The structure of the target allows various versions of the installation what make sure an arbitrary orientation of polarization vector. The 0.1 W cold output 3 He evaporation cryostat was used to obtain the work temperature 0.5 K allowing quick transformation to a 3 He- 4 He dilution refrigerator. Results of the study are given on the dynamical proton polarization in 1,2-propylenglycol with various stable Cr 5 complexes

The outlooks of Helmholtz, Plank and Einstein on the unified physical theory

International Nuclear Information System (INIS)

Treder, G.Yu.

1982-01-01

The outlooks of Helmholtz, Planck and Einstein on the unified physical theory are exposed. Planck formulated the Einstein relativistic mechanics in the canonical form stemming from the suggested by Helmholtz approach that the principle of action is the unified formal principle of physics. Einstein and his companious proceeded from machroscopic fields in the attempts to prove the unified geometric field theory. The sense of Planck length as ''the smallest length in physics'' is determined, on the one hand, by the Heizenberg uncerntainty principle for the measurement process, and on the other hand by the universal proportionality between inertia and gravity. It results from geometrical nature and gravitational potential, i. e. from Einstein interpretation of the equivalence principle

Symbolic computer vector analysis

Science.gov (United States)

Stoutemyer, D. R.

1977-01-01

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Kochen-Specker vectors

International Nuclear Information System (INIS)

Pavicic, Mladen; Merlet, Jean-Pierre; McKay, Brendan; Megill, Norman D

2005-01-01

We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in an n-dimensional Hilbert space, H n , n≥3, to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R n , on algorithms that single out those diagrams on which algebraic (0)-(1) states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all four-dimensional KS vector systems containing up to 24 vectors were generated and described, all three-dimensional vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found

Complex Polynomial Vector Fields

DEFF Research Database (Denmark)

Dias, Kealey

vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...

Vector geometry

CERN Document Server

Robinson, Gilbert de B

2011-01-01

This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

Using the minimum principle for the Helmholtz free energy in the analysis of the equilibria of a van der Waals fluid

International Nuclear Information System (INIS)

Ascoli, Sergio; Malvestuto, Vincenzo

2004-01-01

For a fluid system, obeying a state equation of the van der Waals type, the gas and the liquid phases can coexist in equilibrium, at a given temperature, only if the volume of the system is kept fixed. Thus, in order to study the two-phase equilibria of a fluid system, it seemed quite natural to choose the molar volume as the independent variable, and, consequently, the Helmholtz free energy as the proper thermodynamic potential for the application of the minimum principle. Specific computations are here carried out for a single van der Waals fluid, namely, pure water at 300 0 C. As a result, the present treatment indicates a simple and effective way to identify the whole range of molar volumes where the equilibrium preferred by the system is a two-phase equilibrium. This range results to be wider than the interval of strict instability of the van der Waals isotherm. Finally, it is pointed out that all the results, obtained here for the van der Waals state equation, can be extended to all the state equations of the same type

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

KAUST Repository

Wu, Zedong

2018-04-05

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.

Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory

Directory of Open Access Journals (Sweden)

Zulfiqar Ali

2013-01-01

Full Text Available We find exact solutions of the Generalized Modified Boussinesq (GMB equation, the Kuromoto-Sivashinsky (KS equation the and, Camassa-Holm (CH equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.

A new approach to radiative transfer theory using Jones's vectors. I

International Nuclear Information System (INIS)

Fymat, A.L.; Vasudevan, R.

1975-01-01

Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing arbitrary polydispersion of particles is described using Jones's amplitude vectors and matrices. This novel approach exploits the close analogy between the quantum mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector, and draws on the methodology of such spin 1/2 systems. The complete equivalence between the transport equation for Jones's vectors and the classical radiative transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact operator formulation of the theory is provided, and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. Lastly, the integro-differential equations for the amplitude reflection and transmission matrices are derived, and related to the usual corresponding equations. The present formulation is the most succinct and the most convenient one for both theoretical and experimental studies. It yields a simpler analysis than the classical formulation since it reduces by a factor of two the dimensionality of transfer problems. It preserves information on phases, and thus can be used directly across the entire electromagnetic spectrum without any further conversion into intensities. (Auth.)

A vector field method on the distorted Fourier side and decay for wave equations with potentials

CERN Document Server

Donninger, Roland

2016-01-01

The authors study the Cauchy problem for the one-dimensional wave equation \\partial_t^2 u(t,x)-\\partial_x^2 u(t,x)+V(x)u(t,x)=0. The potential V is assumed to be smooth with asymptotic behavior V(x)\\sim -\\tfrac14 |x|^{-2}\\mbox{ as } |x|\\to \\infty. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t\\partial_t+x\\partial_x, where the latter are obtained by employing a vector field method on the âeoedistortedâe Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, âeoeCodimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski spaceâe, preprint arXiv:1310.5606 (2013).

A numerical solution to the radial equation of the tidal wave propagation

International Nuclear Information System (INIS)

Makarious, S.H.

1981-08-01

The tidal wave function y(x) is a solution to an inhomogeneous, linear, second-order differential equation with variable coefficient. Numerical values for the height-dependence terms, in the observed tides, have been utilized in finding y(x) as a solution to an initial-value problem. Complex Fast Fourier Transform technique is also used to obtain the solution in a complex form. Based on a realistic temperature structure, the atmosphere - below 110 km - has been divided into layers with distinct characteristics, and thus the technique of propagation in stratified media has been applied. The reduced homogeneous equation assumes the form of Helmholtz equation and with initial conditions the general solution is obtained. (author)

Understanding Vector Fields.

Science.gov (United States)

Curjel, C. R.

1990-01-01

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Benney's long wave equations

International Nuclear Information System (INIS)

Lebedev, D.R.

1979-01-01

Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

POSSOL, 2-D Poisson Equation Solver for Nonuniform Grid

International Nuclear Information System (INIS)

Orvis, W.J.

1988-01-01

1 - Description of program or function: POSSOL is a two-dimensional Poisson equation solver for problems with arbitrary non-uniform gridding in Cartesian coordinates. It is an adaptation of the uniform grid PWSCRT routine developed by Schwarztrauber and Sweet at the National Center for Atmospheric Research (NCAR). 2 - Method of solution: POSSOL will solve the Helmholtz equation on an arbitrary, non-uniform grid on a rectangular domain allowing only one type of boundary condition on any one side. It can also be used to handle more than one type of boundary condition on a side by means of a capacitance matrix technique. There are three types of boundary conditions that can be applied: fixed, derivative, or periodic

Quark-gluon plasma tomography by vector mesons

International Nuclear Information System (INIS)

Lovas, I.; Schram, Zs.; Csernai, L.P.; Hungarian Academy of Sciences, Budapest; Nyiri, A.

2001-01-01

The fireball formed in a heavy ion collision is characterized by the impact parameter vector b-vector, which can be determined from the multiplicity and the angular distribution of the reaction products. By appropriate rotations the b-vector vectors of each collision can be aligned into a fixed direction. Using the measured values of the momentum distributions independent integral equations can be formulated for the unknown emission densities (E M (r-vector)) and for the unknown absorption densities (Δμ(r-vector)) of the different vector mesons. (author)

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries

Science.gov (United States)

Paliathanasis, Andronikos; Vakili, Babak

2016-01-01

We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor a( t), a scalar field with potential function V(φ ) minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(φ ). Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace under the infinitesimal generator of the desired symmetries. It is shown that by applying the Lie symmetry condition the form of the coupling function and also the scalar field potential function may be explicitly determined so that we are able to solve the Wheeler-DeWitt equation. Finally, we show how we can use the Lie symmetries in order to construct conservation laws and exact solutions for the field equations.

Vector potential quantization and the photon wave-particle representation

International Nuclear Information System (INIS)

Meis, C; Dahoo, P R

2016-01-01

The quantization procedure of the vector potential is enhanced at a single photon state revealing the possibility for a simultaneous representation of the wave-particle nature of the photon. Its relationship to the quantum vacuum results naturally. A vector potential amplitude operator is defined showing the parallelism with the Hamiltonian of a massless particle. It is further shown that the quantized vector potential satisfies both the wave propagation equation and a linear time-dependent Schrödinger-like equation. (paper)

Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

KAUST Repository

Kou, Jisheng

2018-02-25

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager\\'s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2018-01-01

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager's reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

HNF - Helmholtz Nano Facility

Directory of Open Access Journals (Sweden)

Wolfgang Albrecht

2017-05-01

Full Text Available The Helmholtz Nano Facility (HNF is a state-of-the-art cleanroom facility. The cleanroom has ~1100 m2 with cleanroom classes of DIN ISO 1-3. HNF operates according to VDI DIN 2083, Good Manufacturing Practice (GMP and aquivalent to Semiconductor Industry Association (SIA standards. HNF is a user facility of Forschungszentrum Jülich and comprises a network of facilities, processes and systems for research, production and characterization of micro- and nanostructures. HNF meets the basic supply of micro- and nanostructures for nanoelectronics, fluidics. micromechanics, biology, neutron and energy science, etc.. The task of HNF is rapid progress in nanostructures and their technology, offering efficient access to infrastructure and equipment. HNF gives access to expertise and provides resources in production, synthesis, characterization and integration of structures, devices and circuits. HNF covers the range from basic research to application oriented research facilitating a broad variety of different materials and different sample sizes.

Deviation equation in spaces with affine connection. Pts. 3 and 4

International Nuclear Information System (INIS)

Iliev, B.Z.

1987-01-01

The concept of a parallel transport is used to define a class of displacement vectors in spaces with affine connection. The nonlocal deviation equation in such spaces is introduced using a definition of the deviation vector based on the displacement vector. It turns out to be a special of the generalized deviation equation, but having an appropriate physical interpretation. The equation of geodesic deviation is presented as an example

Complex Polynomial Vector Fields

DEFF Research Database (Denmark)

The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...

Fučík spectra for vector equations

Directory of Open Access Journals (Sweden)

Christian Fabry

2000-01-01

Full Text Available Let $L:\\hbox{dom} L\\subset L^2(\\Omega;R^N\\rightarrow L^2(\\Omega;R^N$ be a linear operator, $\\Omega$ being open and bounded in $R^M$. The aim of this paper is to study the Fu\\v c\\'\\i k spectrum for vector problems of the form $Lu=\\alpha Au^+ -\\beta Au^-$, where $A$ is an $N\\times N$ matrix, $\\alpha, \\beta$ are real numbers, $u^+$ a vector defined componentwise by $(u^+_i=\\max\\{u_i,0\\}$, $u^-$ being defined similarly. With $\\lambda^*$ an eigenvalue for the problem $Lu=\\lambda Au$, we describe (locally curves in the Fučík spectrum passing through the point $(\\lambda^*,\\lambda^*$, distinguishing different cases illustrated by examples, for which Fučík curves have been computed numerically.

A third note: Helmholtz, Palestrina, and the Early History of Musicology

NARCIS (Netherlands)

Kursell, J.

2015-01-01

This contribution focuses on Hermann von Helmholtz’s work on Renaissance composer Giovanni Pierluigi da Palestrina. Helmholtz used his scientific concept of distortion to analyze this music and, reversely, to find corroboration for the concept in his musical analyses. In this, his work interlocked

Fractional Vector Calculus and Fractional Special Function

OpenAIRE

Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

2010-01-01

Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions.

Calibration of Helmholtz Coils for the characterization of MEMS magnetic sensor using fluxgate magnetometer with DAS1 magnetic range data acquisition system

Science.gov (United States)

Ahmad, Farooq; Dennis, John Ojur; Md Khir, Mohd Haris; Hamid, Nor Hisham

2012-09-01

This paper presents the calibration of Helmholtz coils for the characterization of MEMS Magnetic sensor using Fluxgate magnetometer with DAS1 Magnetic Range Data Acquisition System. The Helmholtz coils arrangement is often used to generate a uniform magnetic field in space. In the past, standard magnets were used to calibrate the Helmholtz coils. A method is presented here for calibrating these coils using a Fluxgate magnetometer and known current source, which is easier and results in greater accuracy.

Spinor formalism and complex-vector formalism of general relativity

International Nuclear Information System (INIS)

Han-ying, G.; Yong-shi, W.; Gendao, L.

1974-01-01

In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra

Kelvin-Helmholtz instability in a weakly ionized layer

OpenAIRE

Shadmehri, Mohsen; Downes, Turlough P.

2007-01-01

We study the linear theory of Kelvin-Helmholtz instability in a layer of ions and neutrals with finite thickness. In the short wavelength limit the thickness of the layer has a negligible effect on the growing modes. However, perturbations with wavelength comparable to layer's thickness are significantly affected by the thickness of the layer. We show that the thickness of the layer has a stabilizing effect on the two dominant growing modes. Transition between the modes not only depends on th...

Analysis of 2H(d vector, p)3H reaction at 30-90 keV by four-body Faddeev-Yakubovsky equation

International Nuclear Information System (INIS)

Uzu, Eizo; Oryu, Shinsho; Tanifuji, Makoto.

1993-01-01

Low-energy 2 H(d vector, p) 3 H reactions are investigated by the four-body Faddeev-Yakubovsky equations. Cross sections and tensor analyzing powers are calculated at 30-90 keV energies. The PEST-1 potentials are used for nucleon-nucleon interactions. The [2+2] and [3+1] subamplitudes are treated by the Hilbert-Schmidt expansions. Numerical results give qualitative explanation of experimental data. (author)

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

Science.gov (United States)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I

International Nuclear Information System (INIS)

Tsuchida, Takayuki; Wolf, Thomas

2005-01-01

We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made

Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I

Energy Technology Data Exchange (ETDEWEB)

Tsuchida, Takayuki [Department of Physics, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337 (Japan); Wolf, Thomas [Department of Mathematics, Brock University, St Catharines, ON L2S 3A1 (Canada)

2005-09-02

We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.

Calculation of normal modes of the closed waveguides in general vector case

Science.gov (United States)

Malykh, M. D.; Sevastianov, L. A.; Tiutiunnik, A. A.

2018-04-01

The article is devoted to the calculation of normal modes of the closed waveguides with an arbitrary filling ɛ, μ in the system of computer algebra Sage. Maxwell equations in the cylinder are reduced to the system of two bounded Helmholtz equations, the notion of weak solution of this system is given and then this system is investigated as a system of ordinary differential equations. The normal modes of this system are an eigenvectors of a matrix pencil. We suggest to calculate the matrix elements approximately and to truncate the matrix by usual way but further to solve the truncated eigenvalue problem exactly in the field of algebraic numbers. This approach allows to keep the symmetry of the initial problem and in particular the multiplicity of the eigenvalues. In the work would be presented some results of calculations.

Topological invariants and the dynamics of an axial vector torsion field

International Nuclear Information System (INIS)

Drechsler, W.

1983-01-01

A generalized throry of gravitation is discussed which is based on a Riemann-Cartan space-time, U 4 , with an axial vector torsion field. Besides Einstein's equations determining the metric of the U 4 a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for the U 4 space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic. (author)

Conservative rigid body dynamics by convected base vectors with implicit constraints

DEFF Research Database (Denmark)

Krenk, Steen; Nielsen, Martin Bjerre

2014-01-01

of differential equations without additional algebraic constraints on the base vectors. A discretized form of the equations of motion is obtained by starting from a finite time increment of the Hamiltonian, and retracing the steps of the continuous formulation in discrete form in terms of increments and mean...... of the base vectors. Orthogonality and unit length of the base vectors are imposed by constraining the equivalent Green strain components, and the kinetic energy is represented corresponding to rigid body motion. The equations of motion are obtained via Hamilton’s equations including the zero...... values over each integration time increment. In this discrete form the Lagrange multipliers are given in terms of a representative value within the integration time interval, and the equations of motion are recast into a conservative mean-value and finite difference format. The Lagrange multipliers...

Problems and worked solutions in vector analysis

CERN Document Server

Shorter, LR

2014-01-01

""A handy book like this,"" noted The Mathematical Gazette, ""will fill a great want."" Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis for undergraduate and graduate students of applied mathematics.Opening chapters define vector addition and subtraction, show how to resolve and determine the direction of two or more vectors, and explain systems of coordinates, vector equations of a plane and straight line, relative velocity and acceleration, and infinitely small vectors. The following chapters deal with scalar and vect

[Scientific theoretical founding of medicine as a natural science by Hermann von Helmholtz (1821-1894)].

Science.gov (United States)

Neumann, J N

1994-01-01

In this study an attempt will be made to discuss the epistemological problems in the theory and practice of modern technical medicine in the writings of Hermann von Helmholz. An inquiry into the relationship between von Helmholtz' thinking and the critical philosophy of Immanuel Kant is followed by the characteristics of von Helmholtz' philosophy of science which he himself called "empirical theory". The question of medicine as a science finally leads to the main problem of medical epistemology, viz., the relationship between theoretical knowledge and practice in medicine. In this context the anthropological dimension is brought into consideration.

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

Science.gov (United States)

Sá, Lucas

2017-03-01

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

Collisionless Kelvin-Helmholtz instability and vortex-induced reconnection in the external region of the Earth magnetotail

International Nuclear Information System (INIS)

Pegoraro, F; Faganello, M; Califano, F

2008-01-01

In a magnetized plasma streaming with a non uniform velocity, the Kelvin-Helmholtz instability plays a major role in mixing different plasma regions and in stretching the magnetic field lines leading to the formation of layers with a sheared magnetic field where magnetic field line reconnection can take place. A relevant example is provided by the formation of a mixing layer between the Earth's magnetosphere and the solar wind at low latitudes during northward periods. In the considered configuration, in the presence of a magnetic field nearly perpendicular to the plane defined by the velocity field and its inhomogeneity direction, velocity shear drives a Kelvin-Helmholtz instability which advects and distorts the magnetic field configuration. If the Alfven velocity associated to the in-plane magnetic field is sufficiently weak with respect to the variation of the fluid velocity in the plasma, the Kelvin-Helmholtz instability generates fully rolled-up vortices which advect the magnetic field lines into a complex configuration, causing the formation of current layers along the inversion curves of the in-plane magnetic field component. Pairing of the vortices generated by the Kelvin-Helmholtz instability is a well know phenomenon in two-dimensional hydrodynamics. Here we investigate the development of magnetic reconnection during the vortex pairing process and show that completely different magnetic structures are produced depending on how fast the reconnection process develops on the time scale set by the pairing process.

Quantum nonlinear lattices and coherent state vectors

DEFF Research Database (Denmark)

Ellinas, Demosthenes; Johansson, M.; Christiansen, Peter Leth

1999-01-01

for the state vectors invokes the study of the Riemannian and symplectic geometry of the CSV manifolds as generalized phase spaces. Next, we investigate analytically and numerically the behavior of mean values and uncertainties of some physically interesting observables as well as the modifications...... (FP) model. Based on the respective dynamical symmetries of the models, a method is put forward which by use of the associated boson and spin coherent state vectors (CSV) and a factorization ansatz for the solution of the Schrodinger equation, leads to quasiclassical Hamiltonian equations of motion...... state vectors, and accounts for the quantum correlations of the lattice sites that develop during the time evolution of the systems. (C) 1999 Elsevier Science B.V. All rights reserved....

Drift-Diffusion Equation

Directory of Open Access Journals (Sweden)

K. Banoo

1998-01-01

equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

Painleve test and discrete Boltzmann equations

International Nuclear Information System (INIS)

Euler, N.; Steeb, W.H.

1989-01-01

The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

On Approximate Solutions of Functional Equations in Vector Lattices

Directory of Open Access Journals (Sweden)

Bogdan Batko

2014-01-01

Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.

Generalized Landau-Lifshitz-Gilbert equation for uniformly magnetized bodies

Energy Technology Data Exchange (ETDEWEB)

Serpico, C. [Dipartimento di Ingegneria Elettrica, Universita di Napoli ' FedericoII' , Via Claudio 21, I-80125 Naples (Italy)], E-mail: serpico@unina.it; Mayergoyz, I.D. [ECE Department and UMIACS, University of Maryland, College Park, MD 20742 (United States); Bertotti, G. [Istituto Nazionale di Ricerca Metrologica (INRiM), I-10135 Turin (Italy); D' Aquino, M. [Dipartimento per le Tecnologie, University of Napoli ' Parthenope' , I-80133 Naples (Italy); Bonin, R. [Istituto Nazionale di Ricerca Metrologica (INRiM), I-10135 Turin (Italy)

2008-02-01

We consider generalized Landau-Lifshitz-Gilbert (LLG) deterministic dynamics in uniformly magnetized bodies. The dynamics take place on the unit sphere {sigma}, and are characterized by a vector field v tangential to {sigma}. By using Helmholtz decomposition on {sigma}, it is proven that v is uniquely defined by two potentials {chi} and {psi}. Potential {chi} can be identified with the free energy of the system, while {psi} describes non-conservative interactions of the system with the environment. The presence of {psi} modifies the usual energy balance of LLG dynamics. Instead of purely relaxation dynamics we may have steady injection of energy through non-conservative interactions. The implications of the new form of the energy balance are discussed in detail.

Nuclear safety research in HGF 2012; Fortschrittsbericht 2012. Programm 'Nukleare Sicherheitsforschung' Helmholtz-Gemeinschaft

Energy Technology Data Exchange (ETDEWEB)

Anon.

2013-06-15

After the events at the Japanese nuclear power plant of Fukushima Daiichi, the German Federal government decided that Germany will give up electricity generation from nuclear power within a decade. The last reactor will be disconnected from the power grid in 2022. Helping to make this opt-out safe is one of the duties of the Helmholtz Association with its Nuclear Safety Research Program within the Energy Research Area. Also the demolition of nuclear power plants and the repository problem will keep society, and thus also research, busy for a number of decades to come. Giving up electricity production from nuclear power thus must not mean giving up the required nuclear technology competences. In the fields of reactor safety, demolition, final storage, radiation protection, and crisis management, in critical support of international developments, and for competent evaluation of nuclear facilities around Germany, these competences will be in demand far beyond the German opt-out. This is the reason why the final report by the Ethics Committee on 'Safe Energy Supply' emphasizes the importance of nuclear technology research. Close cooperation on national, European and international levels is indispensable in this effort. Also nuclear safety research in the Helmholtz Association is aligned with the challenges posed by the opt-out of the use of nuclear power. It is important that the high competences in the areas of plant safety and demolition, handling of radioactive waste, and safe final storage as well as radiation protection be preserved. The Nuclear Safety Research Program within the Energy Research Area of the Helmholtz Association therefore will continue studying scientific and technical aspects of the safety of nuclear reactors and the safety of nuclear waste management. These research activities are provident research conducted for society and must be preserved for a long period of time. The work is closely harmonized with the activities of the partners

Wave equations for pulse propagation

International Nuclear Information System (INIS)

Shore, B.W.

1987-01-01

Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

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

Science.gov (United States)

Shatalov, A.; Hafez, M.

2003-11-01

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

Thermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng-Robinson equation of state

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2017-01-01

In this paper, we consider a diffuse-interface gas-liquid two-phase flow model with inhomogeneous temperatures, in which we employ the Peng-Robinson equation of state and the temperature-dependent influence parameter instead of the van der Waals equation of state and the constant influence parameter used in the existing models. As a result, our model can characterize accurately the physical behaviors of numerous realistic gas-liquid fluids, especially hydrocarbons. Furthermore, we prove a relation associating the pressure gradient with the gradients of temperature and chemical potential, and thereby derive a new formulation of the momentum balance equation, which shows that gradients of the chemical potential and temperature become the primary driving force of the fluid motion. It is rigorously proved that the new formulations of the model obey the first and second laws of thermodynamics. To design efficient numerical methods, we prove that Helmholtz free energy density is a concave function with respect to the temperature under certain physical conditions. Based on the proposed modeling formulations and the convex-concave splitting of Helmholtz free energy density, we propose a novel thermodynamically stable numerical scheme. We rigorously prove that the proposed method satisfies the first and second laws of thermodynamics. Finally, numerical tests are carried out to verify the effectiveness of the proposed simulation method.

Thermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng-Robinson equation of state

KAUST Repository

Kou, Jisheng

2017-12-06

In this paper, we consider a diffuse-interface gas-liquid two-phase flow model with inhomogeneous temperatures, in which we employ the Peng-Robinson equation of state and the temperature-dependent influence parameter instead of the van der Waals equation of state and the constant influence parameter used in the existing models. As a result, our model can characterize accurately the physical behaviors of numerous realistic gas-liquid fluids, especially hydrocarbons. Furthermore, we prove a relation associating the pressure gradient with the gradients of temperature and chemical potential, and thereby derive a new formulation of the momentum balance equation, which shows that gradients of the chemical potential and temperature become the primary driving force of the fluid motion. It is rigorously proved that the new formulations of the model obey the first and second laws of thermodynamics. To design efficient numerical methods, we prove that Helmholtz free energy density is a concave function with respect to the temperature under certain physical conditions. Based on the proposed modeling formulations and the convex-concave splitting of Helmholtz free energy density, we propose a novel thermodynamically stable numerical scheme. We rigorously prove that the proposed method satisfies the first and second laws of thermodynamics. Finally, numerical tests are carried out to verify the effectiveness of the proposed simulation method.

Properties of vector and axial-vector mesons from a generalized Nambu-Jona-Lasinio model

International Nuclear Information System (INIS)

Bernard, V.; Meissner, U.G.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

1988-01-01

We construct a generalized Nambu-Jona-Lasinio lagrangian including scalar, pseudoscalar, vector and axial-vector mesons. We specialize to the two-flavor case. The properties of the structured vacuum as well as meson masses and coupling constants are calculated giving an overall agreement within 20% of the experimental data. We investigate the meson properties at finite density. In contrast to the mass of the scalar σ-meson, which decreases sharply with increasing density, the vector meson masses are almost independent of density. Furthermore, the vector-meson-quark coupling constants are also stable against density changes. We point out that these results imply a softening of the nuclear equation of state at high densities. Furthermore, we discuss the breakdown of the KFSR relation on the quark level as well as other deviations from phenomenological concepts such as universality and vector meson dominance. (orig.)

Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations

OpenAIRE

Kolev, Boris

2006-01-01

23 pages; International audience; This paper is a survey article on bi-Hamiltonian systems on the dual of the Lie algebra of vector fields on the circle. We investigate the special case where one of the structures is the canonical Lie-Poisson structure and the second one is constant. These structures called affine or modified Lie-Poisson structures are involved in the integrability of certain Euler equations that arise as models of shallow water waves.

Can really the electromagnetic transverse waves with E-vector parallel to B-vector and finite energy exist?

International Nuclear Information System (INIS)

Malinowski, S.

1984-01-01

It is shown that the total field energy for general solutions of the sourceless Maxwell's equations with E-vector parallel to B-vector is infinite. Moreover the action and/or the ''pseudoscalar charge'' must be infinite too in this case. Therefore the expected similarity to the instanton or meron solutions of nonabelian gauge theories is illusory. 5 refs. (author)

Effect of plasma density profile of tokamak on Kelvin-Helmholtz instability

International Nuclear Information System (INIS)

Tang Fulin

1984-01-01

The purpose of this paper is to study the effect of radial distribution of plasma density profile of tokamak on Kelvin-Helmholtz instability caused by toroidal rotation. The effect of radial distribution of plasma rotational velocity on stability is also examine for comparison. It is found that within the range of tokamak parameters the only radial distribution of plasma rotational velocity cannot induce Kelvin-Helmholtz instability. On the contrary, when there is a radial distribution of plasma density, i.e. P 01 =P 0 e -tx and V 0 1 = const, plasma becomes unstable, and instability will increase proportionally to the value of t. Meanwhile when the value of t remains constant, the instability growth rate will decrease if P 0 grows or the distance between plasma and wall of container decreases too. It shows that the Kelvin-Helmoltz instability is not only influenced by the steepness of density profile but also by the inertia of plasma in central region, which is helpful for depressing the instability. (author). 5 refs, 4 figs, 2 tabs

A low frequency acoustic insulator by using the acoustic metasurface to a Helmholtz resonator

Science.gov (United States)

Zhao, Xiang; Cai, Li; Yu, Dianlong; Lu, Zhimiao; Wen, Jihong

2017-06-01

Acoustic metasurfaces (AMSs) are able to manipulate wavefronts at an anomalous angle through a subwavelength layer. Their application provide a new way to control sound waves in addition to traditional materials. In this work, we introduced the AMS into the design of a Helmholtz resonator (HR) and studied the acoustic transmission through the modified HR in a pipe with one branch. The variation of sound insulation capacity with the phase gradient of the AMS was studied, and the results show that the AMS can remarkably lower the frequency band of the sound insulation without increasing the size. Our investigation provides a new degree of freedom for acoustic control with a Helmholtz resonator, which is of great significance in acoustic metasurface theory and sound insulation design.

The Common Data Acquisition Platform in the Helmholtz Association

International Nuclear Information System (INIS)

Kaever, P.; Balzer, M.; Kopmann, A.; Zimmer, M.; Rongen, H.

2017-01-01

Various centres of the German Helmholtz Association (HGF) started in 2012 to develop a modular data acquisition (DAQ) platform, covering the entire range from detector readout to data transfer into parallel computing environments. This platform integrates generic hardware components like the multi-purpose HGF-Advanced Mezzanine Card or a smart scientific camera framework, adding user value with Linux drivers and board support packages. Technically the scope comprises the DAQ-chain from FPGA-modules to computing servers, notably frontend-electronics-interfaces, microcontrollers and GPUs with their software plus high-performance data transmission links. The core idea is a generic and component-based approach, enabling the implementation of specific experiment requirements with low effort. This so called DTS-platform will support standards like MTCA.4 in hard- and software to ensure compatibility with commercial components. Its capability to deploy on other crate standards or FPGA-boards with PCI express or Ethernet interfaces remains an essential feature. Competences of the participating centres are coordinated in order to provide a solid technological basis for both research topics in the Helmholtz Programme ''Matter and Technology'': ''Detector Technology and Systems'' and ''Accelerator Research and Development''. The DTS-platform aims at reducing costs and development time and will ensure access to latest technologies for the collaboration. Due to its flexible approach, it has the potential to be applied in other scientific programs.

The Common Data Acquisition Platform in the Helmholtz Association

Science.gov (United States)

Kaever, P.; Balzer, M.; Kopmann, A.; Zimmer, M.; Rongen, H.

2017-04-01

Various centres of the German Helmholtz Association (HGF) started in 2012 to develop a modular data acquisition (DAQ) platform, covering the entire range from detector readout to data transfer into parallel computing environments. This platform integrates generic hardware components like the multi-purpose HGF-Advanced Mezzanine Card or a smart scientific camera framework, adding user value with Linux drivers and board support packages. Technically the scope comprises the DAQ-chain from FPGA-modules to computing servers, notably frontend-electronics-interfaces, microcontrollers and GPUs with their software plus high-performance data transmission links. The core idea is a generic and component-based approach, enabling the implementation of specific experiment requirements with low effort. This so called DTS-platform will support standards like MTCA.4 in hard- and software to ensure compatibility with commercial components. Its capability to deploy on other crate standards or FPGA-boards with PCI express or Ethernet interfaces remains an essential feature. Competences of the participating centres are coordinated in order to provide a solid technological basis for both research topics in the Helmholtz Programme ``Matter and Technology'': ``Detector Technology and Systems'' and ``Accelerator Research and Development''. The DTS-platform aims at reducing costs and development time and will ensure access to latest technologies for the collaboration. Due to its flexible approach, it has the potential to be applied in other scientific programs.

A methodology for uncertainty analysis of reference equations of state

DEFF Research Database (Denmark)

Cheung, Howard; Frutiger, Jerome; Bell, Ian H.

We present a detailed methodology for the uncertainty analysis of reference equations of state (EOS) based on Helmholtz energy. In recent years there has been an increased interest in uncertainties of property data and process models of thermal systems. In the literature there are various...... for uncertainty analysis is suggested as a tool for EOS. The uncertainties of the EOS properties are calculated from the experimental values and the EOS model structure through the parameter covariance matrix and subsequent linear error propagation. This allows reporting the uncertainty range (95% confidence...

On the solutions of the second heavenly and Pavlov equations

Science.gov (United States)

Manakov, S. V.; Santini, P. M.

2009-10-01

We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations connected with the commutation of multidimensional vector fields, such as the heavenly equation of Plebanski, the dispersionless Kadomtsev-Petviashvili (dKP) equation and the two-dimensional dispersionless Toda (2ddT) equation, as well as with the commutation of one-dimensional vector fields, such as the Pavlov equation. We also showed that the associated Riemann-Hilbert inverse problems are powerful tools to establish if the solutions of the Cauchy problem break at finite time, to construct their long-time behaviour and characterize classes of implicit solutions. In this paper, using the above theory, we concentrate on the heavenly and Pavlov equations, (i) establishing that their localized solutions evolve without breaking, unlike the cases of dKP and 2ddT; (ii) constructing the long-time behaviour of the solutions of their Cauchy problems; (iii) characterizing a distinguished class of implicit solutions of the heavenly equation.

On the solutions of the second heavenly and Pavlov equations

International Nuclear Information System (INIS)

Manakov, S V; Santini, P M

2009-01-01

We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations connected with the commutation of multidimensional vector fields, such as the heavenly equation of Plebanski, the dispersionless Kadomtsev-Petviashvili (dKP) equation and the two-dimensional dispersionless Toda (2ddT) equation, as well as with the commutation of one-dimensional vector fields, such as the Pavlov equation. We also showed that the associated Riemann-Hilbert inverse problems are powerful tools to establish if the solutions of the Cauchy problem break at finite time, to construct their long-time behaviour and characterize classes of implicit solutions. In this paper, using the above theory, we concentrate on the heavenly and Pavlov equations, (i) establishing that their localized solutions evolve without breaking, unlike the cases of dKP and 2ddT; (ii) constructing the long-time behaviour of the solutions of their Cauchy problems; (iii) characterizing a distinguished class of implicit solutions of the heavenly equation.

Calculation of the beam injector steering system using Helmholtz coils

International Nuclear Information System (INIS)

Passaro, A.; Sircilli Neto, F.; Migliano, A.C.C.

1991-03-01

In this work, a preliminary evaluation of the beam injector steering system of the IEAv electron linac is presented. From the existing injector configuration and with the assumptions of monoenergetic beam (100 keV) and uniform magnetic field, two pairs of Helmholtz coils were calculated for the steering system. Excitations of 105 A.turn and 37 A.turn were determined for the first and second coils, respectively. (author)

ON A PROLONGATION CONSTRUCTION FOR LOCAL NON-DIVERGENT VECTOR FIELDS ON Rn

Directory of Open Access Journals (Sweden)

A. M. Lukatsky

2015-01-01

Full Text Available The problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This construction allows to move from the Euler equations for the ideal incompressible fluid to the Euler equations on finite-dimensional Lie groups.

Vector-tensor interaction of gravitation

Energy Technology Data Exchange (ETDEWEB)

Zhang Yuan-zhong; Guo han-ying

1982-11-01

In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.

A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter

International Nuclear Information System (INIS)

Zhang Yufeng; Tam, Honwah; Feng Binlu

2011-01-01

Highlights: → A generalized Zakharov-Shabat equation is obtained. → The generalized AKNS vector fields are established. → The finite-band solution of the g-ZS equation is obtained. → By using a Lie algebra presented in the paper, a new soliton hierarchy with an arbitrary parameter is worked out. - Abstract: In this paper, a generalized Zakharov-Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G ∼ . From the stationary zero curvature equation we define the Lenard gradients {g j } and the corresponding generalized AKNS (g-AKNS) vector fields {X j } and X k flows. Employing the nonlinearization method, we obtain the generalized Zhakharov-Shabat Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the X k flows and the polynomial integrals {H k } are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel-Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an arbitrary parameter k are derived.

Resolution of unsteady Maxwell equations with charges in non convex domains

International Nuclear Information System (INIS)

Garcia, Emmanuelle

2002-01-01

This research thesis deals with the modelling and numerical resolution of problems related to plasma physics. The interaction of charged particles (electrons and ions) with electromagnetic fields is modelled with the system of unsteady Vlasov-Maxwell coupled equations (the Vlasov system describes the transport of charged particles and the Maxwell equations describe the wave propagation). The author presents definitions related to singular domains, establishes a Helmholtz decomposition in a space of electro-magnetostatic solutions. He reports a mathematical analysis of decompositions into a regular and a singular part of general functional spaces intervening in the investigation of the Maxwell system in complex geometries. The method is then implemented for bi-dimensional domains. A last part addressed the study and the numerical resolution of three-dimensional problems

Black and gray Helmholtz-Kerr soliton refraction

International Nuclear Information System (INIS)

Sanchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S.

2011-01-01

Refraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell's law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified, and predictions are verified by full numerical simulations. The existence of a unique total nonrefraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposal of positive or negative lensing operations on soliton arrays at planar boundaries.

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

International Nuclear Information System (INIS)

Sá, Lucas

2017-01-01

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

A low frequency acoustic insulator by using the acoustic metasurface to a Helmholtz resonator

Directory of Open Access Journals (Sweden)

Xiang Zhao

2017-06-01

Full Text Available Acoustic metasurfaces (AMSs are able to manipulate wavefronts at an anomalous angle through a subwavelength layer. Their application provide a new way to control sound waves in addition to traditional materials. In this work, we introduced the AMS into the design of a Helmholtz resonator (HR and studied the acoustic transmission through the modified HR in a pipe with one branch. The variation of sound insulation capacity with the phase gradient of the AMS was studied, and the results show that the AMS can remarkably lower the frequency band of the sound insulation without increasing the size. Our investigation provides a new degree of freedom for acoustic control with a Helmholtz resonator, which is of great significance in acoustic metasurface theory and sound insulation design.

Introduction to matrices and vectors

CERN Document Server

Schwartz, Jacob T

2001-01-01

In this concise undergraduate text, the first three chapters present the basics of matrices - in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition.

Field Equations for Abelian Vector Fields in the Bianchi Type I Metric in the Framework of Teleparallel Gravity

International Nuclear Information System (INIS)

Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.

2010-01-01

Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.

Vectorized Fokker-Planck package for the CRAY-1

International Nuclear Information System (INIS)

McCoy, M.G.; Mirin, A.A.; Killeen, J.

1979-08-01

A program for the solution of the time-dependent, two dimensional, nonlinear, multi-species Fokker-Planck equation is described. The programming is written such that the loop structure is highly vectorizable on the CRAY FORTRAN Compiler. A brief discussion of the Fokker-Planck equation itself is followed by a description of the procedure developed to solve the equation efficiently. The Fokker-Planck equation is a second order partial differential equation whose coefficients depend upon moments of the distribution functions. Both the procedure for the calculation of these coefficients and the procedure for the time advancement of the equation itself must be done efficiently if significant overall time saving is to result. The coefficients are calculated in a series of nested loops, while time advancement is accomplished by a choice of either a splitting or an ADI technique. Overall, timing tests show that the vectorized CRAY program realizes up to a factor of 12 advantage over an optimized CDC-7600 program and up to a factor of 365 over a non-vectorized version of the same program on the CRAY

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

International Nuclear Information System (INIS)

Himmetoglu, Burak; Peloso, Marco; Contaldi, Carlo R.

2009-01-01

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), and (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

Science.gov (United States)

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

Solutions of Navier-Stokes Equation with Coriolis Force

Directory of Open Access Journals (Sweden)

Sunggeun Lee

2017-01-01

Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.

A Third Note: Helmholtz, Palestrina, and the Early History of Musicology.

Science.gov (United States)

Kursell, Julia

2015-06-01

This contribution focuses on Hermann von Helmholtz's work on Renaissance composer Giovanni Pierluigi da Palestrina. Helmholtz used his scientific concept of distortion to analyze this music and, reversely, to find corroboration for the concept in his musical analyses. In this, his work interlocked with nineteenth-century aesthetic and scholarly ideals. His eagerness to use the latest products of historical scholarship in early music reveals a specific view of music history. Historical documents of music provide the opportunity for the discovery of new experimental research topics and thereby also reveal insights into hearing under different conditions. The essay argues that this work occupies a peculiar position in the history of musicology; it falls under the header of "systematic musicology," which eventually emerged as a discipline of musicology at the end of the nineteenth century. That this discipline has a history at all is easily overlooked, as many of its contributors were scientists with an interest in music. A history of musicology therefore must consider at least the following two caveats: parts of it take place outside the institutionalized field of musicology, and any history of musicology must, in the last instance, be embedded in a history of music.

Introduction to partial differential equations with applications

CERN Document Server

Zachmanoglou, E C

1988-01-01

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Simulating Photons and Plasmons in a Three-dimensional Lattice

International Nuclear Information System (INIS)

Pletzer, A.; Shvets, G.

2002-01-01

Three-dimensional metallic photonic structures are studied using a newly developed mixed finite element-finite difference (FE-FD) code, Curly3d. The code solves the vector Helmholtz equation as an eigenvalue problem in the unit cell of a triply periodic lattice composed of conductors and/or dielectrics. The mixed FE-FD discretization scheme ensures rapid numerical convergence of the eigenvalue and allows the code to run at low resolution. Plasmon and photonic band structure calculations are presented

Numerical investigation of renormalization group equations in a model of vector field advected by anisotropic stochastic environment

International Nuclear Information System (INIS)

Busa, J.; Ajryan, Eh.A.; Jurcisinova, E.; Jurcisin, M.; Remecky, R.

2009-01-01

Using the field-theoretic renormalization group, the influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of passive transverse vector field advected by an incompressible turbulent flow is investigated. The velocity field is taken to have a Gaussian statistics with zero mean and defined noise with finite time correlations. It is shown that the inertial-range scaling regimes are given by the existence of infrared stable fixed points of the corresponding renormalization group equations with some angle integrals. The analysis of integrals is given. The problem is solved numerically and the borderline spatial dimension d e (1,3] below which the stability of the scaling regime is not present is found as a function of anisotropy parameters

A generalized nonlocal vector calculus

Science.gov (United States)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

Survey on Dirac equation in general relativity theory

International Nuclear Information System (INIS)

Paillere, P.

1984-10-01

Starting from an infinitesimal transformation expressed with a Killing vector and using systematically the formalism of the local tetrades, we show that, in the area of the general relativity, the Dirac equation may be formulated only versus the four local vectors which determine the gravitational potentials, their gradients and the 4-vector potential of the electromagnetic field [fr

HelmholtzZentrum Muenchen Deutsches Forschungszentrum fuer Gesundheit und Umwelt. Annual report 2011; HelmholtzZentrum Muenchen Deutsches Forschungszentrum fuer Gesundheit und Umwelt. Jahresbericht 2011

Energy Technology Data Exchange (ETDEWEB)

NONE

2012-11-01

The contribution under consideration is the annual report 2011 of the German Research Centre for Environmental Health (HelmholtzZentrum Munich, Federal Republic of Germany). The most important component of this annual report are the scientific highlights according to the following topics: (1) Systems researches for the health (M. Hrabe de Angelis); (2) Mechanisms of the interaction between genes and environment (M. Goetz); (3) Research of the metabolism (M. Tschoep); (4) Research of lungs and allergies (O. Eickelberg); (5) Technologies for the bio medicine (V. Ntziachristos); (6) Natural basis of existence (J. Durner).

Boundary conditions for the numerical solution of elliptic equations in exterior regions

International Nuclear Information System (INIS)

Bayliss, A.; Gunzburger, M.; Turkel, E.

1982-01-01

Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used

On the separability of field equations in Myers-Perry spacetimes

International Nuclear Information System (INIS)

Murata, Keiju; Soda, Jiro

2008-01-01

We study the separability of scalar, vector and tensor fields in five-dimensional Myers-Perry spacetimes with equal angular momenta. In these spacetimes, there exists enlarged symmetry, U(2) ≅ SU(2) x U(1). Using the group theoretical method with a twist, we perform the dimensional reduction at the action level and show that both vector and tensor field equations can be reduced to coupled ordinary differential equations. We reveal the structure of couplings between variables. In particular, we have obtained the decoupled master equations for zero modes of a vector field. The same analysis can be done for zero modes of a tensor field. Therefore, our formalism gives a basis for studying of the stability of Myers-Perry black holes

Parabolic Equation Modeling of Propagation over Terrain Using Digital Elevation Model

Directory of Open Access Journals (Sweden)

Xiao-Wei Guan

2018-01-01

Full Text Available The parabolic equation method based on digital elevation model (DEM is applied on propagation predictions over irregular terrains. Starting from a parabolic approximation to the Helmholtz equation, a wide-angle parabolic equation is deduced under the assumption of forward propagation and the split-step Fourier transform algorithm is used to solve it. The application of DEM is extended to the Cartesian coordinate system and expected to provide a precise representation of a three-dimensional surface with high efficiency. In order to validate the accuracy, a perfectly conducting Gaussian terrain profile is simulated and the results are compared with the shift map. As a consequence, a good agreement is observed. Besides, another example is given to provide a theoretical basis and reference for DEM selection. The simulation results demonstrate that the prediction errors will be obvious only when the resolution of the DEM used is much larger than the range step in the PE method.

Helmholtz and Goethe -- controversies at the birth of modern neuroscience.

Science.gov (United States)

Kesselring, Jürg

2013-01-01

Hermann von Helmholtz (1821-1894), a great German scientist and philosopher, made his mark during the exciting twilight period from the Enlightenment and Romanticism to the beginnings of modern neuroscience and offered new perspectives through his work. His early inclination was for physics, which he found more attractive than purely geometric and algebraic studies, but his father was not able to make it possible for him to study physics, and so he studied medicine in order to earn a living. His lecture before the Physical Society in Berlin on July 23, 1847, 'about the conservation of the force' marked an epochal turn, even though his intention had been to deliver 'merely, some critical investigations and arrangement of facts in favor of the physiologists' as well as good arguments for the refusal of the theory of 'vitality'. Even though these new concepts were at first dismissed as fantastic speculation by some of the authorities in physics and philosophy of the day, they were enthusiastically welcomed by younger students of philosophy and the older men soon had to allow themselves to be persuaded that the effectiveness of vitality, though great and beautiful, is actually always dependent on some source of energy. Helmholtz critically assessed Goethe as a physical scientist but he did not dispute his great importance as a poet. Copyright © 2012 S. Karger AG, Basel.

From a world-sheet supersymmetry to the Dirac equation

International Nuclear Information System (INIS)

Mankoc Borstnik, N.

1991-10-01

Starting from a classical action for a point particle with a local world-sheet supersymmetry, the Dirac equation follows with operators α-vector, β-vector γ-vector being defined in the Grassmann space as differential operators and having all the properties of the corresponding Dirac matrices except that α-vector and β-vector are anti-Hermitian rather than Hermitian. Such a particle interacts with an external field as expected. (author). 7 refs

Archive of Geosample Information from the GEOMAR Helmholtz Centre for Ocean Research Kiel Core Repository

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — The GEOMAR Helmholtz Centre for Ocean Research Kiel made a one-time contribution to the Index to Marine and Lacustrine Geological Samples (IMLGS) database of...

Meromorphic Vector Fields and Circle Packings

DEFF Research Database (Denmark)

Dias, Kealey

The objective of the Ph.D. project is to initiate a classification of bifurcations of meromorphic vector fields and to clarify their relation to circle packings. Technological applications are to image analysis and to effective grid generation using discrete conformal mappings. The two branches...... of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions or meromorphic (allowing poles...... as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic vector fields. Restricting...

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

KAUST Repository

Wu, Zedong; Alkhalifah, Tariq Ali

2018-01-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods

Density-space potential phase difference in a Kelvin--Helmholtz instability

International Nuclear Information System (INIS)

Glowienka, J.C.; Jennings, W.C.; Hickok, R.L.

1974-01-01

The low-frequency instability found in a hollow cathode discharge in helium was studied using an ion beam probe as a primary diagnostic tool. Three aspects of the instability are discussed: the location and amplitude of the oscillation and its correlation with the shape of the space potential; the phase angle between density and space potential oscillations; and the comparison of the data with three known instability models: Kelvin--Helmholtz, Rayleigh--Taylor, and drift waves--for mode identification. (U.S.)

Scalar-vector bootstrap

Energy Technology Data Exchange (ETDEWEB)

Rejon-Barrera, Fernando [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL, Amsterdam (Netherlands); Robbins, Daniel [Department of Physics, Texas A& M University,TAMU 4242, College Station, TX 77843 (United States)

2016-01-22

We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.

Helmholtz Natural Modes: the universal and discrete spatial fabric of electromagnetic wavefields

International Nuclear Information System (INIS)

El Gawhary, Omar

2017-01-01

The interaction of electromagnetic waves with matter is at the foundation of the way we perceive and explore the world around us. In fact, when a field interacts with an object, signatures on the object’s geometry and physical properties are recorded in the resulting scattered field and are transported away from the object, where they can eventually be detected and processed. An optical field can transport information through its spectral content, its polarization state, and its spatial distribution. Generally speaking, the field’s spatial structure is typically subjected to changes under free-space propagation and any information therein encoded gets reshuffled by the propagation process. We must ascribe to this fundamental reason the fact that spectroscopy was known to the ancient civilizations already, and founded as modern science in the middle of seventeenth century, while to date we do not have an established scientific of field of ‘spatial spectroscopy’ yet. In this work we tackle this issue and we show how any field, whose evolution is dictated by Helmholtz equation, contains a universal and invariant spatial structure. When expressed in the framework of this spatial fabric, the spatial information content carried by any field reveals its invariant nature. This opens the way to novel paradigms in optical digital communications, inverse scattering, materials inspection, nanometrology and quantum optics. (paper)

Global Simulations of the Asymmetry in Forming Kelvin-Helmholtz Instability at Mercury

Science.gov (United States)

Paral, J.; Rankin, R.

2013-12-01

MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) is the first spacecraft to provide data from the orbit of Mercury. After the probe's insertion into the orbit on March 2011, the in situ measurements revealed a dawn-dusk asymmetry in the observations of Kelvin-Helmholtz (KH) instability. This instability forms at the magnetopause boundary due to the high shear of the plasma flows. The asymmetry in the observations is unexpected and largely unexplained, although it has been speculated that finite ion gyroradius effect plays an important role. The large gyroradius implies that kinetic effects are important and thus must be taken into account. We employ global ion hybrid-kinetic simulations to obtain a 2D model of Mercury's magnetosphere. This code treats ions as particles and follows the full trajectory while electrons act as a charge neutralizing fluid. The planet is treated as the perfect conductor placed in the streaming solar wind to form a quasi steady state of the magnetosphere. By placing a virtual probe in the simulation domain we obtain time series of the plasma parameters which can be compared to the observations by the MESSENGER spacecraft. The comparison of the KH instability is remarkably close to the observations of MESSENGER; to within a factor of two. The model also confirms the asymmetry in the observations. The ion density obtained from the computer model is shown together with velocity vectors (represented by arrows). The solid line represents the trajectory of the third flyby of MESSENGER on September 29, 2009.

Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations

International Nuclear Information System (INIS)

Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian

2012-01-01

We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations

Science.gov (United States)

Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying

2012-12-01

We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

Killing vectors in algebraically special space-times

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1984-01-01

The form of the isometric, homothetic, and conformal Killing vectors for algebraically special metrics which admit a shear-free congruence of null geodesics is obtained by considering their complexification, using the existence of a congruence of null strings. The Killing equations are partially integrated and the reasons which permit this reduction are exhibited. In the case where the congruence of null strings has a vanishing expansion, the Killing equations are reduced to a single master equation

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications

Science.gov (United States)

W. Hasan, W. Z.

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

Science.gov (United States)

Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

Directory of Open Access Journals (Sweden)

A H Sabry

Full Text Available The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

International Nuclear Information System (INIS)

Anco, Stephen C

2006-01-01

Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps

Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

Energy Technology Data Exchange (ETDEWEB)

Anco, Stephen C [Department of Mathematics, Brock University, St Catharines, ON (Canada)

2006-03-03

Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps.

Energy preserving integration of bi-Hamiltonian partial differential equations

NARCIS (Netherlands)

Karasozen, B.; Simsek, G.

2013-01-01

The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the

Elliptic Painlevé equations from next-nearest-neighbor translations on the E_8^{(1)} lattice

Science.gov (United States)

Joshi, Nalini; Nakazono, Nobutaka

2017-07-01

The well known elliptic discrete Painlevé equation of Sakai is constructed by a standard translation on the E_8(1) lattice, given by nearest neighbor vectors. In this paper, we give a new elliptic discrete Painlevé equation obtained by translations along next-nearest-neighbor vectors. This equation is a generic (8-parameter) version of a 2-parameter elliptic difference equation found by reduction from Adler’s partial difference equation, the so-called Q4 equation. We also provide a projective reduction of the well known equation of Sakai.

An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa

International Nuclear Information System (INIS)

Tillner-Roth, R.; Yokozeki, A.

1997-01-01

A fundamental equation of state for the Helmholtz free energy of R-32 (difluoromethane) is presented which is valid from the triple point at 136.34 K to 435 K and pressures up to 70 MPa. It is based on accurate measurements of pressure-density-temperature (p,ρ,T), speed of sound, heat capacity, and vapor pressure currently available. New values for the isobaric heat capacity c p circ of the ideal gas calculated from spectroscopic data taking into account also first order anharmonicity corrections are presented. The Helmholtz free energy equation of state has 19 coefficients and represents all selected experimental data within their estimated accuracy with the exception for heat capacities and speed of sound in the region close to the critical point. Typical uncertainties are ±0.05% for density, ±0.02% for the vapor pressure and ±0.5%endash 1% for the heat capacity. This equation of state has been compared to equations developed by other research groups by Annex 18 of the International Energy Agency and has been selected as an international standard formulation for the thermodynamic properties of R-32 by this group. copyright 1997 American Institute of Physics and American Chemical Society

Generalized vector calculus on convex domain

Science.gov (United States)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

KAUST Repository

Potsepaev, R.

2010-09-06

Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

Modeling animal movements using stochastic differential equations

Science.gov (United States)

Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie

2004-01-01

We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...

INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

Directory of Open Access Journals (Sweden)

Elena N. Kushner

2018-01-01

Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations

KAUST Repository

Chavez, Gustavo Ivan

2017-07-10

This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.

The Use of Helmholtz Resonance for Measuring the Volume of Liquids and Solids

Directory of Open Access Journals (Sweden)

Clive E. Davies

2010-11-01

Full Text Available An experimental investigation was undertaken to ascertain the potential of using Helmholtz resonance for volume determination and the factors that may influence accuracy. The uses for a rapid non-interference volume measurement system range from agricultural produce and mineral sampling through to liquid fill measurements. By weighing the sample the density can also measured indirectly.

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

2009-01-01

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

Structural Equation Modeling of Multivariate Time Series

Science.gov (United States)

du Toit, Stephen H. C.; Browne, Michael W.

2007-01-01

The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…

Development of a high-sensitivity and portable cell using Helmholtz resonance for noninvasive blood glucose-level measurement based on photoacoustic spectroscopy.

Science.gov (United States)

Tachibana, K; Okada, K; Kobayashi, R; Ishihara, Y

2016-08-01

We describe the possibility of high-sensitivity noninvasive blood glucose measurement based on photoacoustic spectroscopy (PAS). The demand for noninvasive blood glucose-level measurement has increased due to the explosive increase in diabetic patients. We have developed a noninvasive blood glucose-level measurement based on PAS. The conventional method uses a straight-type resonant cell. However, the cell volume is large, which results in a low detection sensitivity and difficult portability. In this paper, a small-sized Helmholtz-type resonant cell is proposed to improve detection sensitivity and portability by reducing the cell dead volume. First, the acoustic property of the small-sized Helmholtz-type resonant cell was evaluated by performing an experiment using a silicone rubber. As a result, the detection sensitivity of the small-sized Helmholtz-type resonant cell was approximately two times larger than that of the conventional straight-type resonant cell. In addition, the inside volume was approximately 30 times smaller. Second, the detection limits of glucose concentration were estimated by performing an experiment using glucose solutions. The experimental results showed that a glucose concentration of approximately 1% was detected by the small-sized Helmholtz-type resonant cell. Although these results on the sensitivity of blood glucose-level measurement are currently insufficient, they suggest that miniaturization of a resonance cell is effective in the application of noninvasive blood glucose-level measurement.

Generalized reduced MHD equations

International Nuclear Information System (INIS)

Kruger, S.E.; Hegna, C.C.; Callen, J.D.

1998-07-01

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space

International Nuclear Information System (INIS)

Rodriguez D, R.

2007-01-01

In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)

Mutational analysis a joint framework for Cauchy problems in and beyond vector spaces

CERN Document Server

Lorenz, Thomas

2010-01-01

Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling.

Simulation of laser propagation in a plasma with a frequency wave equation

International Nuclear Information System (INIS)

Desroziers, S.; Nataf, F.; Sentis, R.

2008-01-01

The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this huge linear system, we use an iterative Krylov method preconditioned by a separable matrix. The corresponding linear system is solved with a block cyclic reduction method. Some enlightenments on the parallel implementation are also given. Lastly, numerical results are presented including some features concerning the scalability of the numerical method on a parallel architecture. (authors)

Higher-dimensional generalizations of the Watanabe–Strogatz transform for vector models of synchronization

Science.gov (United States)

Lohe, M. A.

2018-06-01

We generalize the Watanabe–Strogatz (WS) transform, which acts on the Kuramoto model in d  =  2 dimensions, to a higher-dimensional vector transform which operates on vector oscillator models of synchronization in any dimension , for the case of identical frequency matrices. These models have conserved quantities constructed from the cross ratios of inner products of the vector variables, which are invariant under the vector transform, and have trajectories which lie on the unit sphere S d‑1. Application of the vector transform leads to a partial integration of the equations of motion, leaving independent equations to be solved, for any number of nodes N. We discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on S d‑1. We further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball , and leaves invariant the cross ratios constructed from inner products of vectors in . This mapping can be used to partially integrate a system of vector oscillators with trajectories in , and for d  =  2 leads to an extension of the Kuramoto system to a system of oscillators with time-dependent amplitudes and trajectories in the unit disk. We find an inequivalent generalization of the Möbius map which also preserves but leaves invariant a different set of cross ratios, this time constructed from the vector norms. This leads to a different extension of the Kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations.

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

KAUST Repository

Fan, Xiaolin

2017-01-19

This paper presents a componentwise convex splitting scheme for numerical simulation of multicomponent two-phase fluid mixtures in a closed system at constant temperature, which is modeled by a diffuse interface model equipped with the Van der Waals and the Peng-Robinson equations of state (EoS). The Van der Waals EoS has a rigorous foundation in physics, while the Peng-Robinson EoS is more accurate for hydrocarbon mixtures. First, the phase field theory of thermodynamics and variational calculus are applied to a functional minimization problem of the total Helmholtz free energy. Mass conservation constraints are enforced through Lagrange multipliers. A system of chemical equilibrium equations is obtained which is a set of second-order elliptic equations with extremely strong nonlinear source terms. The steady state equations are transformed into a transient system as a numerical strategy on which the scheme is based. The proposed numerical algorithm avoids the indefiniteness of the Hessian matrix arising from the second-order derivative of homogeneous contribution of total Helmholtz free energy; it is also very efficient. This scheme is unconditionally componentwise energy stable and naturally results in unconditional stability for the Van der Waals model. For the Peng-Robinson EoS, it is unconditionally stable through introducing a physics-preserving correction term, which is analogous to the attractive term in the Van der Waals EoS. An efficient numerical algorithm is provided to compute the coefficient in the correction term. Finally, some numerical examples are illustrated to verify the theoretical results and efficiency of the established algorithms. The numerical results match well with laboratory data.

Reduced equations for finite beta tearing modes in tokamaks

International Nuclear Information System (INIS)

Izzo, R.; Monticello, D.A.; DeLucia, J.; Park, W.; Ryu, C.M.

1984-10-01

The equations of resistive magnetohydrodynamics (MHD) are recast in a form that is useful for studying the evolution of those toroidal systems where the fast magnetosonic wave plays no important role. The equations are exact and have nabla vector.B vector = O satisfied explicitly. From this set of equations it is a simple matter to derive the equations of reduced MHD to any order in the inverse aspect ratio epsilon of the torus, and for β approx. epsilon or smaller. We demonstrate this by deriving a reduced set of MHD equations that are correct to 5th order in epsilon. These equations contain the exact equilibrium relation and as such can be used to find 3-D stellarator equilibria. In addition, if a subsidiary ordering in eta, the resistivity, is made, the equations of Glasser, Greene, and Johnson are recovered. This set of reduced equations has been coded by extending the initial value code, HILO. Results obtained, for both ideal and resistive linear stability, from the reduced equations are compared with those obtained by solving the full set of MHD equations in a cylinder. The agreement is shown to be excellent for both zero and finite beta calculations. Comparisons are also made with analytic theory illuminating the present limitations of the latter

Generalized nonlinear Proca equation and its free-particle solutions

Energy Technology Data Exchange (ETDEWEB)

Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

2016-06-15

We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

Construction of alternative Hamiltonian structures for field equations

Energy Technology Data Exchange (ETDEWEB)

Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2001-08-10

We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)

A Boundary Element Solution to the Problem of Interacting AC Fields in Parallel Conductors

Directory of Open Access Journals (Sweden)

Einar M. Rønquist

1984-04-01

Full Text Available The ac fields in electrically insulated conductors will interact through the surrounding electromagnetic fields. The pertinent field equations reduce to the Helmholtz equation inside each conductor (interior problem, and to the Laplace equation outside the conductors (exterior problem. These equations are transformed to integral equations, with the magnetic vector potential and its normal derivative on the boundaries as unknowns. The integral equations are then approximated by sets of algebraic equations. The interior problem involves only unknowns on the boundary of each conductor, while the exterior problem couples unknowns from several conductors. The interior and the exterior problem are coupled through the field continuity conditions. The full set of equations is solved by standard Gaussian elimination. We also show how the total current and the dissipated power within each conductor can be expressed as boundary integrals. Finally, computational results for a sample problem are compared with a finite difference solution.

Vector fields in a tight laser focus: comparison of models.

Science.gov (United States)

Peatross, Justin; Berrondo, Manuel; Smith, Dallas; Ware, Michael

2017-06-26

We assess several widely used vector models of a Gaussian laser beam in the context of more accurate vector diffraction integration. For the analysis, we present a streamlined derivation of the vector fields of a uniformly polarized beam reflected from an ideal parabolic mirror, both inside and outside of the resulting focus. This exact solution to Maxwell's equations, first developed in 1920 by V. S. Ignatovsky, is highly relevant to high-intensity laser experiments since the boundary conditions at a focusing optic dictate the form of the focus in a manner analogous to a physical experiment. In contrast, many models simply assume a field profile near the focus and develop the surrounding vector fields consistent with Maxwell's equations. In comparing the Ignatovsky result with popular closed-form analytic vector models of a Gaussian beam, we find that the relatively simple model developed by Erikson and Singh in 1994 provides good agreement in the paraxial limit. Models involving a Lax expansion introduce a divergences outside of the focus while providing little if any improvement in the focal region. Extremely tight focusing produces a somewhat complicated structure in the focus, and requires the Ignatovsky model for accurate representation.

Multi-component WKI equations and their conservation laws

Energy Technology Data Exchange (ETDEWEB)

Qu Changzheng [Department of Mathematics, Northwest University, Xi' an 710069 (China) and Center for Nonlinear Studies, Northwest University, Xi' an 710069 (China)]. E-mail: qu_changzheng@hotmail.com; Yao Ruoxia [Department of Computer Sciences, East China Normal University, Shanghai 200062 (China); Department of Computer Sciences, Weinan Teacher' s College, Weinan 715500 (China); Liu Ruochen [Department of Mathematics, Northwest University, Xi' an 710069 (China)

2004-10-25

In this Letter, a two-component WKI equation is obtained by using the fact that when curvature and torsion of a space curve satisfy the vector modified KdV equation, a graph of the curve satisfies the two-component WKI equation, which is a natural generalization to the WKI equation. It is shown that the two-component WKI equation can be solved in terms of the extended WKI scheme, and it admits an infinite number of conservation laws. In the same vein, a n-component generalization to the WKI equation is proposed.

Efficient and Enhanced Diffusion of Vector Field for Active Contour Model

OpenAIRE

Liu, Guoqi; Sun, Lin; Liu, Shangwang

2015-01-01

Gradient vector flow (GVF) is an important external force field for active contour models. Various vector fields based on GVF have been proposed. However, these vector fields are obtained with many iterations and have difficulty in capturing the whole image area. On the other hand, the ability to converge to deep and complex concavity with these vector fields is also needed to improve. In this paper, by analyzing the diffusion equation of GVF, a normalized set is defined and a dynamically nor...

Conservation properties and potential systems of vorticity-type equations

International Nuclear Information System (INIS)

Cheviakov, Alexei F.

2014-01-01

Partial differential equations of the form divN=0, N t +curl M=0 involving two vector functions in R 3 depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R 4 (t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented

Comparison of ν-support vector regression and logistic equation for ...

African Journals Online (AJOL)

Due to the complexity and high non-linearity of bioprocess, most simple mathematical models fail to describe the exact behavior of biochemistry systems. As a novel type of learning method, support vector regression (SVR) owns the powerful capability to characterize problems via small sample, nonlinearity, high dimension ...

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.

2017-08-29

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.

2017-01-01

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

Stability theory for dynamic equations on time scales

CERN Document Server

Martynyuk, Anatoly A

2016-01-01

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...

Vector-Interaction-Enhanced Bag Model

Science.gov (United States)

Cierniak, Mateusz; Klähn, Thomas; Fischer, Tobias; Bastian, Niels-Uwe

2018-02-01

A commonly applied quark matter model in astrophysics is the thermodynamic bag model (tdBAG). The original MIT bag model approximates the effect of quark confinement, but does not explicitly account for the breaking of chiral symmetry, an important property of Quantum Chromodynamics (QCD). It further ignores vector repulsion. The vector-interaction-enhanced bag model (vBag) improves the tdBAG approach by accounting for both dynamical chiral symmetry breaking and repulsive vector interactions. The latter is of particular importance to studies of dense matter in beta-equilibriumto explain the two solar mass maximum mass constraint for neutron stars. The model is motivated by analyses of QCD based Dyson-Schwinger equations (DSE), assuming a simple quark-quark contact interaction. Here, we focus on the study of hybrid neutron star properties resulting from the application of vBag and will discuss possible extensions.

Stability and special metrics for complex vector bundles with global sections

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we study one kind of vortex equations on complex vector bundles over almost Hermitian manifolds and prove a Hitchin-Kobayashi type correspondence relating the existence of solutions of these vortex equations to a certain stability condition. (author)

Bethe-Salpeter equation for fermion-antifermion system in the ladder approximation

International Nuclear Information System (INIS)

Fukui, Ichio; Seto, Noriaki; Yoshida, Toshihiro.

1977-01-01

The Bethe-Salpeter (B-S) equation is important for studying hadron physics. Especially intensive investigation on the fermion-antifermion B-S equation is indispensable for the phenomenological studies of hardrons. However, many components of the B-S amplitude and the Wick-rotated integral kernel of non-Fredholm type have prevented from knowing details the solutions even in the ladder approximation. Some particular solutions are known in case of the vanishing four-momenta of bound states. The B-S equation for the bound state of fermion-anti-fermion system interacting through vector (axial-vector) particle exchange was studied in the ladder approximation with Feynman gauge. The reduced equations were obtained for suitably decomposed amplitude, and it is shown that, in the S-wave case, the coupled equations separate into two parts. In the nonrelativistic limit, large components of the amplitude satisfy the Wick-Cutkosky equation, and small components are expressed in terms of the large ones. Equations are derived for the equal-time amplitudes. (Kobatake, H.)

SIMULATIONS OF THE KELVIN–HELMHOLTZ INSTABILITY DRIVEN BY CORONAL MASS EJECTIONS IN THE TURBULENT CORONA

Energy Technology Data Exchange (ETDEWEB)

Gómez, Daniel O.; DeLuca, Edward E. [Harvard-Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA 02138 (United States); Mininni, Pablo D. [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires (Argentina)

2016-02-20

Recent high-resolution Atmospheric Imaging Assembly/Solar Dynamics Observatory images show evidence of the development of the Kelvin–Helmholtz (KH) instability, as coronal mass ejections (CMEs) expand in the ambient corona. A large-scale magnetic field mostly tangential to the interface is inferred, both on the CME and on the background sides. However, the magnetic field component along the shear flow is not strong enough to quench the instability. There is also observational evidence that the ambient corona is in a turbulent regime, and therefore the criteria for the development of the instability are a priori expected to differ from the laminar case. To study the evolution of the KH instability with a turbulent background, we perform three-dimensional simulations of the incompressible magnetohydrodynamic equations. The instability is driven by a velocity profile tangential to the CME–corona interface, which we simulate through a hyperbolic tangent profile. The turbulent background is generated by the application of a stationary stirring force. We compute the instability growth rate for different values of the turbulence intensity, and find that the role of turbulence is to attenuate the growth. The fact that KH instability is observed sets an upper limit on the correlation length of the coronal background turbulence.

Dirichlet problem for Hermitian-Einstein equations over almost Hermitian manifolds

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we investigate the Dirichlet problem for Hermitian-Einstein equations on complex vector bundle over almost Hermitian manifolds, and we obtain the unique solubility of the Dirichlet problem for Hermitian-Einstein equations. (author)

Introduction to partial differential equations

CERN Document Server

Borthwick, David

2016-01-01

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

On the use of the Kodama vector field in spherically symmetric dynamical problems

Energy Technology Data Exchange (ETDEWEB)

Racz, Istvan [MTA KFKI, Reszecske- es Magfizikai Kutatointezet, H-1121 Budapest, Konkoly Thege Miklos ut 29-33, (Hungary)

2006-01-07

It is shown that by making use of the Kodama vector field, as a preferred time evolution vector field, in spherically symmetric dynamical systems unexpected simplifications arise. In particular, the evolution equations relevant for the case of a massless scalar field minimally coupled to gravity are investigated. The simplest form of these equations in the 'canonical gauge' is known to possess the character of a mixed first-order elliptic-hyperbolic system. The advantages related to the use of the Kodama vector field are twofold although they show up simultaneously. First, it is found that the true degrees of freedom separate. Second, a subset of the field equations possessing the form of a first-order symmetric hyperbolic system for these preferred degrees of freedom is singled out. It is also demonstrated, in the appendix, that the above results generalize straightforwardly to the case of a generic self-interacting scalar field.

Hermitian-Einstein metrics on holomorphic vector bundles over Hermitian manifolds

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we prove the long-time existence of the Hermitian-Einstein flow on a holomorphic vector bundle over a compact Hermitian (non-kaehler) manifold, and solve the Dirichlet problem for the Hermitian-Einstein equations. We also prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete noncompact Hermitian manifolds. (author)

Wavelets for the stimulation of turbulent incompressible flows

International Nuclear Information System (INIS)

Deriaz, E.

2006-02-01

This PhD thesis presents original wavelet methods aimed at simulating incompressible fluids. In order to construct 2D and 3D wavelets designed for incompressible flows, we resume P-G Lemarie-Rieussets and K. Urbans works on divergence free wavelets. We show the existence of associated fast algorithms. In the following, we use divergence-free wavelet construction to define the Helmholtz decomposition of 2D and 3D vector fields. All these algorithms provide a new method for the numerical resolution of the incompressible Navier-Stokes equations. (author)

Frequency domain, waveform inversion of laboratory crosswell radar data

Science.gov (United States)

Ellefsen, Karl J.; Mazzella, Aldo T.; Horton, Robert J.; McKenna, Jason R.

2010-01-01

A new waveform inversion for crosswell radar is formulated in the frequency-domain for a 2.5D model. The inversion simulates radar waves using the vector Helmholtz equation for electromagnetic waves. The objective function is minimized using a backpropagation method suitable for a 2.5D model. The inversion is tested by processing crosswell radar data collected in a laboratory tank. The estimated model is consistent with the known electromagnetic properties of the tank. The formulation for the 2.5D model can be extended to inversions of acoustic and elastic data.

Phasor Alternatives to Friis’ Transmission Equation

DEFF Research Database (Denmark)

Franek, Ondrej

2018-01-01

Two alternatives to Friis’ transmission equation in terms of phasor voltage waves are presented. In one formulation antennas are characterized by the complex effective length vectors. An additional form introducing field gain, that serves effectively as a phasor counterpart to the power gain......, is proposed. Both forms show the same degree of symmetry and modularity as the original Friis’ equation, but thanks to using phasors instead of power quantities they allow for superposition of fields or voltages. Although the new transmission equations are formulated in frequency domain, they also constitute...

Geometric Implications of Maxwell's Equations

Science.gov (United States)

Smith, Felix T.

2015-03-01

Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.

Scalar-vector unitarity mixing in ξ gauge

International Nuclear Information System (INIS)

Kaloshin, A.E.; Radzhabov, A.E.

2003-01-01

The effect of unitary mixing of scalar and vector fields in general ξ gauge is studied. This effect takes place for nonconserved vector currents and ξ gauge generates some additional problems with unphysical scalar field. Solutions of Dyson-Schwinger equations and performed the renormalization of full propagators are obtained. The key feature of renormalization is the usage of Ward identity which relates some different Green functions. It is found that using of Ward identity leads to disappearing of ξ dependence in renormalization matrix element [ru

On the Reduction of Vector and Axial-Vector Fields in a Meson Effective Action at O(p4)

International Nuclear Information System (INIS)

Bel'kov, A.A.; Lanev, A.V.; Schaale, A.

1994-01-01

Starting from an effective NJL-type quark interaction we have derived an effective meson action for the pseudoscalar sector. The vector and axial-vector degrees of freedom have been integrated out, applying the static equations of motion. As the results we have found a (reduced) pseudoscalar meson Lagrangian of the Gasser-Leutwyler type with modified structure coefficients L i . This method has been also used to construct the reduced weak and electromagnetic-weak currents. The application of the reduced Lagrangian and currents has been considered in physical processes. 36 refs., 1 fig., 1 tab

Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Vector case

International Nuclear Information System (INIS)

Doicu, A.; Trautmann, T.

2009-01-01

The paper is devoted to the extension of the matrix-exponential formalism for the scalar radiative transfer to the vector case. Using basic results of the theory of matrix-exponential functions we provide a compact and versatile formulation of the vector radiative transfer. As in the scalar case, we operate with the concept of the layer equation incorporating the level values of the Stokes vector. The matrix exponentials which enter in the expression of the layer equation are computed by using the matrix eigenvalue method and the Pade approximation. A discussion of the computational efficiency of the proposed method for both an aerosol-loaded atmosphere as well as a cloudy atmosphere is also provided

Collision of bright vector solitons in two-component Bose-Einstein condensates

International Nuclear Information System (INIS)

Ramesh Kumar, V.; Radha, R.; Wadati, Miki

2010-01-01

We investigate the coupled Gross-Pitaevskii equation describing the dynamics of two hyperfine states of Bose-Einstein condensates and deduce the integrability condition for the propagation of bright vector solitons. We show how the transient trap and scattering length can be suitably tailored to bring about fascinating collisional dynamics of vector solitons.

Severe accident research activities at Helmholtz-Zentrum Dresden-Rossendorf (HZDR)

Energy Technology Data Exchange (ETDEWEB)

Wilhelm, Polina; Jobst, Matthias; Schaefer, Frank; Kliem, Soeren [Helmholtz-Zentrum Dresden-Rossendorf e.V., Dresden (Germany)

2016-05-15

In the frame of the nuclear safety research program of the Helmholtz Association HZDR performs fundamental and applied research to assess and to reduce the risks related to the nuclear fuel cycle and the production of electricity in nuclear power plants. One of the research topics focuses on the safety aspects of current and future reactor designs. This includes the development and application of methods for analyses of transients and postulated accidents, covering the whole spectrum from normal operation till severe accident sequences including core degradation. This paper gives an overview of the severe accident research activities at the Reactor Safety Division at the Institute of Resource Ecology.

Exact non-linear equations for cosmological perturbations

Energy Technology Data Exchange (ETDEWEB)

Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Wu, David Chan Lon; Yoo, Jaiyul, E-mail: jinn-ouk.gong@apctp.org, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: clwu@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, Universität Zürich, CH-8057 Zürich (Switzerland)

2017-10-01

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

Reciprocity in Vector Acoustics

Science.gov (United States)

2017-03-01

Green’s Theorem to the left hand side of Equation (3.2) converts it to a surface integral that vanishes for the impedance boundary conditions one...There are situations where this assumption does not hold, such as at boundaries between layers or in an inhomogeneous layer , because the density gradient...instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic

Connecting science and the musical arts in teaching tone quality: Integrating Helmholtz motion and master violin teachers' pedagogies

Science.gov (United States)

Collins, Cheri D.

Is it possible for students to achieve better tone quality from even their factory-made violins? All violins, regardless of cost, have a common capacity for good tone in certain frequencies. These signature modes outline the first position range of a violin (196-600 hertz). To activate this basic capacity of all violins, the string must fully vibrate. To accomplish this the bow must be pulled across the string with enough pressure (relative to its speed and contact point) for the horsehairs to catch. This friction permits the string to vibrate in Helmholtz Motion, which produces a corner that travels along the edge of the string between the bridge and the nut. Creating this corner is the most fundamental technique for achieving good tone. The findings of celebrated scientists Ernest Chladni, Hermann von Helmholtz, and John Schelleng will be discussed and the tone-production pedagogy of master teachers Carl Flesch, Ivan Galamian, Robert Gerle, and Simon Fischer will be investigated. Important connections between the insights of these scientists and master teachers are evident. Integrating science and art can provide teachers with a better understanding of the characteristics of good tone. This can help their students achieve the best possible sound from their instruments. In the private studio the master teacher may not use the words "Helmholtz Motion." Yet through modeling and listening students are able to understand and create a quality tone. Music teachers without experience in string performance may be assigned to teach strings in classroom and ensembles settings. As a result modeling good tone is not always possible. However, all teachers and conductors can understand the fundamental behavior of string vibration and adapt their instruction strategies towards student success. Better tonal quality for any string instrument is ultimately achieved. Mastery and use of the Helmholtz Motion benefits teachers and students alike. Simple practice exercises for teaching

Kelvin-Helmholtz instability for a bounded plasma flow in a longitudinal magnetic field

International Nuclear Information System (INIS)

Burinskaya, T. M.; Shevelev, M. M.; Rauch, J.-L.

2011-01-01

Kelvin-Helmholtz MHD instability in a plane three-layer plasma is investigated. A general dispersion relation for the case of arbitrarily orientated magnetic fields and flow velocities in the layers is derived, and its solutions for a bounded plasma flow in a longitudinal magnetic field are studied numerically. Analysis of Kelvin-Helmholtz instability for different ion acoustic velocities shows that perturbations with wavelengths on the order of or longer than the flow thickness can grow in an arbitrary direction even at a zero temperature. Oscillations excited at small angles with respect to the magnetic field exist in a limited range of wavenumbers even without allowance for the finite width of the transition region between the flow and the ambient plasma. It is shown that, in a low-temperature plasma, solutions resulting in kink-like deformations of the plasma flow grow at a higher rate than those resulting in quasi-symmetric (sausage-like) deformations. The transverse structure of oscillatory-damped eigenmodes in a low-temperature plasma is analyzed. The results obtained are used to explain mechanisms for the excitation of ultra-low-frequency long-wavelength oscillations propagating along the magnetic field in the plasma sheet boundary layer of the Earth’s magnetotail penetrated by fast plasma flows.

A classification system for one Killing vector solutions of Einstein's equations

International Nuclear Information System (INIS)

Hoenselaers, C.

1978-01-01

A double classification system for one Killing vector solutions in terms of the eigenvectors and eigenvalues of the Ricci and Bach tensor of the associated three manifold is proposed. The calculations of the Bach tensor are carried out for special cases. (author)

General Navier–Stokes-like momentum and mass-energy equations

Energy Technology Data Exchange (ETDEWEB)

Monreal, Jorge, E-mail: jmonreal@mail.usf.edu

2015-03-15

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.

Generalized reduced magnetohydrodynamic equations

International Nuclear Information System (INIS)

Kruger, S.E.

1999-01-01

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics

Perfect fluid cosmological Universes: One equation of state and the ...

Indian Academy of Sciences (India)

Anadijiban Das

2018-01-04

Jan 4, 2018 ... equation of state, one may calculate the geometric vari- ables, such as the ... connected by any analytic function ψ, the evolutions equations, mainly ... [3] J E Marsden and A J Tromba, Vector calculus, 3rd edn. (W. H. Freeman ...

An Equation of State for the Thermodynamic Properties of Cyclohexane

Energy Technology Data Exchange (ETDEWEB)

Zhou, Yong, E-mail: Yong.Zhou2@honeywell.com; Liu, Jun [Honeywell Integrated Technology China Co. Ltd., 430 Li Bing Road, Zhangjiang Hi-Tech Park, Shanghai 201203 (China); Penoncello, Steven G. [Center for Applied Thermodynamic Studies, College of Engineering, University of Idaho, Moscow, Idaho 83844 (United States); Lemmon, Eric W. [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)

2014-12-15

An equation of state for cyclohexane has been developed using the Helmholtz energy as the fundamental property with independent variables of density and temperature. Multi-property fitting technology was used to fit the equation of state to data for pρT, heat capacities, sound speeds, virial coefficients, vapor pressures, and saturated densities. The equation of state was developed to conform to the Maxwell criteria for two-phase vapor-liquid equilibrium states, and is valid from the triple-point temperature to 700 K, with pressures up to 250 MPa and densities up to 10.3 mol dm{sup −3}. In general, the uncertainties (k = 2, indicating a level of confidence of 95%) in density for the equation of state are 0.1% (liquid and vapor) up to 500 K, and 0.2% above 500 K, with higher uncertainties within the critical region. Between 283 and 473 K with pressures lower than 30 MPa, the uncertainty is as low as 0.03% in density in the liquid phase. The uncertainties in the speed of sound are 0.2% between 283 and 323 K in the liquid, and 1% elsewhere. Other uncertainties are 0.05% in vapor pressure and 2% in heat capacities. The behavior of the equation of state is reasonable within the region of validity and at higher and lower temperatures and pressures. A detailed analysis has been performed in this article.

Toward lattice fractional vector calculus

International Nuclear Information System (INIS)

Tarasov, Vasily E

2014-01-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)

Toward lattice fractional vector calculus

Science.gov (United States)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

On vector analogs of the modified Volterra lattice

Energy Technology Data Exchange (ETDEWEB)

Adler, V E; Postnikov, V V [L D Landau Institute for Theoretical Physics, 1a Semenov pr, 142432 Chernogolovka (Russian Federation); Sochi Branch of Peoples' Friendship University of Russia, 32 Kuibyshev str, 354000 Sochi (Russian Federation)], E-mail: adler@itp.ac.ru, E-mail: postnikovvv@rambler.ru

2008-11-14

The zero curvature representations, Baecklund transformations, nonlinear superposition principle and the simplest explicit solutions of soliton and breather type are presented for two vector generalizations of modified Volterra lattice. The relations with some other integrable equations are established.

MATRIX-VECTOR ALGORITHMS OF LOCAL POSTERIORI INFERENCE IN ALGEBRAIC BAYESIAN NETWORKS ON QUANTA PROPOSITIONS

Directory of Open Access Journals (Sweden)

A. A. Zolotin

2015-07-01

Full Text Available Posteriori inference is one of the three kinds of probabilistic-logic inferences in the probabilistic graphical models theory and the base for processing of knowledge patterns with probabilistic uncertainty using Bayesian networks. The paper deals with a task of local posteriori inference description in algebraic Bayesian networks that represent a class of probabilistic graphical models by means of matrix-vector equations. The latter are essentially based on the use of tensor product of matrices, Kronecker degree and Hadamard product. Matrix equations for calculating posteriori probabilities vectors within posteriori inference in knowledge patterns with quanta propositions are obtained. Similar equations of the same type have already been discussed within the confines of the theory of algebraic Bayesian networks, but they were built only for the case of posteriori inference in the knowledge patterns on the ideals of conjuncts. During synthesis and development of matrix-vector equations on quanta propositions probability vectors, a number of earlier results concerning normalizing factors in posteriori inference and assignment of linear projective operator with a selector vector was adapted. We consider all three types of incoming evidences - deterministic, stochastic and inaccurate - combined with scalar and interval estimation of probability truth of propositional formulas in the knowledge patterns. Linear programming problems are formed. Their solution gives the desired interval values of posterior probabilities in the case of inaccurate evidence or interval estimates in a knowledge pattern. That sort of description of a posteriori inference gives the possibility to extend the set of knowledge pattern types that we can use in the local and global posteriori inference, as well as simplify complex software implementation by use of existing third-party libraries, effectively supporting submission and processing of matrices and vectors when

Of the Helmholtz Club, South-Californian seedbed for visual and cognitive neuroscience, and its patron Francis Crick.

Science.gov (United States)

Aicardi, Christine

2014-03-01

Taking up the view that semi-institutional gatherings such as clubs, societies, research schools, have been instrumental in creating sheltered spaces from which many a 20th-century project-driven interdisciplinary research programme could develop and become established within the institutions of science, the paper explores the history of one such gathering from its inception in the early 1980s into the 2000s, the Helmholtz Club, which brought together scientists from such various research fields as neuroanatomy, neurophysiology, psychophysics, computer science and engineering, who all had an interest in the study of the visual system and of higher cognitive functions relying on visual perception such as visual consciousness. It argues that British molecular biologist turned South Californian neuroscientist Francis Crick had an early and lasting influence over the Helmholtz Club of which he was a founding pillar, and that from its inception, the club served as a constitutive element in his long-term plans for a neuroscience of vision and of cognition. Further, it argues that in this role, the Helmholtz Club served many purposes, the primary of which was to be a social forum for interdisciplinary discussion, where 'discussion' was not mere talk but was imbued with an epistemic value and as such, carefully cultivated. Finally, it questions what counts as 'doing science' and in turn, definitions of success and failure-and provides some material evidence towards re-appraising the successfulness of Crick's contribution to the neurosciences. Copyright © 2013 The Author. Published by Elsevier Ltd.. All rights reserved.

Development of a Miniature, Two-Axis, Triple-Helmholtz-Driven Gimbal

Science.gov (United States)

Sharif, Boz; Joscelyn, Ed; Wilcox, Brian; Johnson, Michael R.

2000-01-01

This paper details the development of a Helmholtz-driven, 2-axis gimbal to position a flat mirror within 50 microradian (fine positioning) in a space environment. The gimbal is intended to travel on a deep space mission mounted on a miniature "rover" vehicle. The gimbal will perform both pointing and scanning functions. The goal for total mass of the gimbal was 25 grams. The primary challenge was to design and build a bearing system that would achieve the required accuracy in addition to supporting the relatively large mass of the mirror and the outer gimbal. The mechanism is subjected to 100-G loading without the aid of any additional caging mechanism. Additionally, it was desired to have the same level of accuracy during Earth-bound, 1-G testing. Due to the inherent lack of damping in a zero-G, vacuum environment; the ability of the gimbal to respond to very small amounts of input energy is paramount. Initial testing of the first prototype revealed exceedingly long damping times required even while exposed to the damping effects of air and 1-G friction. It is envisioned that fine positioning of the gimbal will be accomplished in very small steps to avoid large disturbances to the mirror. Various bearing designs, including materials, lubrication options and bearing geometry will be discussed. In addition various options for the Helmholtz coil design will be explored with specific test data given. Ground testing in the presence of 1-G was compounded by the local magnetic fields due to the "compass" effect on the gimbal. The test data will be presented and discussed. Additionally, rationale for estimating gimbal performance in a zero-G environment will be presented and discussed.

Dynamical creation of complex vector solitons in spinor Bose-Einstein condensates

International Nuclear Information System (INIS)

Xiong Bo; Gong Jiangbin

2010-01-01

By numerical simulations of the Gross-Pitaevskii mean-field equations, we show that the dynamical creation of stable complex vector solitons in a homogeneous spin-1 Bose-Einstein condensate can be achieved by applying a localized magnetic field for a certain duration, with the initial uniform density prepared differently for the formation of different vector solitons. In particular, it is shown that stable dark-bright-dark vector solitons, dark-bright-bright vector solitons, and other analogous solutions can be dynamically created. It is also found that the peak intensity and the group velocity of the vector solitons thus generated can be tuned by adjusting the applied magnetic field. Extensions of our approach also allow for the creation of vector-soliton chains or the pumping of many vector solitons. The results can be useful for possible vector-soliton-based applications of dilute Bose-Einstein condensates.

The time dependent Schrodinger equation revisited I: quantum field and classical Hamilton-Jacobi routes to Schrodinger's wave equation

International Nuclear Information System (INIS)

Scully, M O

2008-01-01

The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation

Advanced electromagnetics and scattering theory

CERN Document Server

2015-01-01

This book present the lecture notes used in two courses that the late Professor Kasra Barkeshli had offered at Sharif University of Technology, namely, Advanced Electromagnetics and Scattering Theory. The prerequisite for the sequence is vector calculus and electromagnetic fields and waves. Some familiarity with Green's functions and integral equations is desirable but not necessary. The book  provides a brief but concise introduction to classical topics in the field. It is divided into three parts including annexes. Part I covers principle of electromagnetic theory. The discussion starts with a review of the Maxwell's equations in differential and integral forms and basic boundary conditions. The solution of inhomogeneous wave equation and various field representations including Lorentz's potential functions and the Green's function method are discussed next. The solution of Helmholtz equation and wave harmonics follow. Next, the book presents plane wave propagation in dielectric and lossy media and various...

Computing with linear equations and matrices

International Nuclear Information System (INIS)

Churchhouse, R.F.

1983-01-01

Systems of linear equations and matrices arise in many disciplines. The equations may accurately represent conditions satisfied by a system or, more likely, provide an approximation to a more complex system of non-linear or differential equations. The system may involve a few or many thousand unknowns and each individual equation may involve few or many of them. Over the past 50 years a vast literature on methods for solving systems of linear equations and the associated problems of finding the inverse or eigenvalues of a matrix has been produced. These lectures cover those methods which have been found to be most useful for dealing with such types of problem. References are given where appropriate and attention is drawn to the possibility of improved methods for use on vector and parallel processors. (orig.)

An introduction to vectors, vector operators and vector analysis

CERN Document Server

Joag, Pramod S

2016-01-01

Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.

Polarization speckles and generalized Stokes vector wave: a review [invited

DEFF Research Database (Denmark)

Takeda, Mitsuo; Wang, Wei; Hanson, Steen Grüner

2010-01-01

We review some of the statistical properties of polarization-related speckle phenomena, with an introduction of a less known concept of polarization speckles and their spatial degree of polarization. As a useful means to characterize twopoint vector field correlations, we review the generalized...... Stokes parameters proposed by Korotkova and Wolf, and introduce its time-domain representation to describe the space-time evolution of the correlation between random electric vector fields at two different space-time points. This time-domain generalized Stokes vector, with components similar to those...... of the beam coherence polarization matrix proposed by Gori, is shown to obey the wave equation in exact analogy to a coherence function of scalar fields. Because of this wave nature, the time-domain generalized Stokes vector is referred to as generalized Stokes vector wave in this paper....

A systematic approach to sketch Bethe-Salpeter equation

Directory of Open Access Journals (Sweden)

Qin Si-xue

2016-01-01

Full Text Available To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark–anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD’s gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB. The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.

Students' Difficulties with Vector Calculus in Electrodynamics

Science.gov (United States)

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-01-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

Nonlinear evolution-type equations and their exact solutions using inverse variational methods

International Nuclear Information System (INIS)

Kara, A H; Khalique, C M

2005-01-01

We present the role of invariants in obtaining exact solutions of differential equations. Firstly, conserved vectors of a partial differential equation (p.d.e.) allow us to obtain reduced forms of the p.d.e. for which some of the Lie point symmetries (in vector field form) are easily concluded and, therefore, provide a mechanism for further reduction. Secondly, invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. In this latter case, the reductions carry all the usual advantages regarding Noether symmetries and double reductions. The examples we consider are nonlinear evolution-type equations such as the Korteweg-deVries equation, but a detailed analysis is made on the Fisher equation (which describes reaction-diffusion waves in biology, inter alia). Other diffusion-type equations lend themselves well to the method we describe (e.g., the Fitzhugh Nagumo equation, which is briefly discussed). Some aspects of Painleve properties are also suggested

Entropy-Based Video Steganalysis of Motion Vectors

Directory of Open Access Journals (Sweden)

Elaheh Sadat Sadat

2018-04-01

Full Text Available In this paper, a new method is proposed for motion vector steganalysis using the entropy value and its combination with the features of the optimized motion vector. In this method, the entropy of blocks is calculated to determine their texture and the precision of their motion vectors. Then, by using a fuzzy cluster, the blocks are clustered into the blocks with high and low texture, while the membership function of each block to a high texture class indicates the texture of that block. These membership functions are used to weight the effective features that are extracted by reconstructing the motion estimation equations. Characteristics of the results indicate that the use of entropy and the irregularity of each block increases the precision of the final video classification into cover and stego classes.

Enhancing DC Glow Discharge Tube Museuum Displays using a Theremin Controlled Helmholtz Coil to Demonstrate Magnetic Confinement

Science.gov (United States)

Siu, Theodore; Wissel, Stephanie; Guttadora, Larry; Liao, Susan; Zwicker, Andrew

2010-11-01

Since their discovery in the mid 1800's, DC glow discharge apparatuses have commonly been used for spectral analysis, the demonstration of the Frank-Hertz experiment, and to study plasma breakdown voltages following from the Paschen Curve. A DC glow discharge tube museum display was outfitted with a Helmholtz Coil electromagnet in order to demonstrate magnetic confinement for a science museum display. A device commonly known as a ``theremin'' was designed and built in order to externally control the Helmholtz Coil current and the plasma current. Originally a musical instrument, a theremin has two variable capacitors connected to two radio frequency oscillators which determine pitch and volume. Using a theremin to control current and ``play'' the plasma adds appeal and durability by providing a new innovative means of interacting with a museum exhibit. Educationally, students can use the display to not only learn about plasma properties but also electronic properties of the human body.

A new formulation of equations of compressible fluids by analogy with Maxwell's equations

International Nuclear Information System (INIS)

Kambe, Tsutomu

2010-01-01

A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.

A general comparison theorem for backward stochastic differential equations

OpenAIRE

Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.

2010-01-01

A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...

Material parameters and vector scaling in transformation acoustics

International Nuclear Information System (INIS)

Cummer, Steven A; Rahm, Marco; Schurig, David

2008-01-01

The degree to which the coordinate transformation concept first demonstrated for electromagnetic waves can be applied to other classes of waves remains an open question. In this work, we thoroughly examine the coordinate transformation invariance of acoustic waves. We employ a purely physical argument to show how the acoustic velocity vector must transform differently than the E and H fields in Maxwell's equations, which explains why acoustic coordinate transformation invariance was not found in some previous analyses. A first principles analysis of the acoustic equations under arbitrary coordinate transformations confirms that the divergence operator is preserved only if velocity transforms in this physically correct way. This analysis also yields closed-form expressions for the bulk modulus and mass density tensor of the material required to realize an arbitrary coordinate transformation on the acoustic fields, which we show are equivalent to forms presented elsewhere. We demonstrate the computation of these material parameters in two specific cases and show that the change in velocity and pressure gradient vectors under a nonorthogonal coordinate transformation is precisely how these vectors must change from purely physical arguments. This analysis confirms that all of the electromagnetic devices and materials that have been conceived using the coordinate transformation approach are also in principle realizable for acoustic waves. Together with previous work, this analysis also shows how the curl, divergence and gradient operators maintain form under arbitrary coordinate transformations, opening the door to analyzing other wave systems built on these three vector operators.

Solution of Fokker–Planck equation by finite element and finite ...

Indian Academy of Sciences (India)

The response of a structural system to white noise excitation (delta-correlated) constitutes a Markov vector process whose transitional probability density function (TPDF) is governed by both the forward Fokker–Planck and backward Kolmogorov equations. Numerical solution of these equations by finite element and finite ...

Kelvin-Helmholtz instability: the ``atom'' of geophysical turbulence?

Science.gov (United States)

Smyth, William

2017-11-01

Observations of small-scale turbulence in Earth's atmosphere and oceans have most commonly been interpreted in terms of the Kolmogorov theory of isotropic turbulence, despite the fact that the observed turbulence is significantly anisotropic due to density stratification and sheared large-scale flows. I will describe an alternative picture in which turbulence consists of distinct events that occur sporadically in space and time. The simplest model for an individual event is the ``Kelvin-Helmholtz (KH) ansatz'', in which turbulence relieves the dynamic instability of a localized shear layer. I will summarize evidence that the KH ansatz is a valid description of observed turbulence events, using microstructure measurements from the equatorial Pacific ocean as an example. While the KH ansatz has been under study for many decades and is reasonably well understood, the bigger picture is much less clear. How are the KH events distributed in space and time? How do different events interact with each other? I will describe some tentative steps toward a more thorough understanding.

Self-dual solutions to Euclidean Yang-Mills equations

International Nuclear Information System (INIS)

Corrigan, E.

1979-01-01

The paper provides an introduction to two approaches towards understanding the classical Yang-Mills field equations. On the one hand, the work of Atiyah and Ward showed that the self-dual equations, which are non-linear, could be regarded as a set of linear equations which turned out to be related to each other by Baecklund transformations. Fundamental to their procedure was the observation that the information carried by the vector potential could be coded into the structure of certain analytic vector bundles over a three dimensional projective space. The classification of these bundles and the subsequent recovery of the gauge field led to the infinite set of ansaetze, corresponding to the sets of linear equation mentioned already. On the other hand, Atiyah, Hitchin, Drinfeld and Manin have recently constructed, completely algebraically, the bundles of interest and indicated how the Yang-Mills potential may be obtained. Remarkably, their construction differs very little as the gauge group is changed (to any of the classical compact groups) and, uses only the elementary operations of linear algebra to yield potentials as rational functions of the spatial coordinates. (Auth.)

The Integration Order of Vector Autoregressive Processes

DEFF Research Database (Denmark)

Franchi, Massimo

We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2...

Fractional vector calculus for fractional advection dispersion

Science.gov (United States)

Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

2006-07-01

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

The Wertheim integral equation theory with the ideal chain approximation and a dimer equation of state: Generalization to mixtures of hard-sphere chain fluids

International Nuclear Information System (INIS)

Chang, J.; Sandler, S.I.

1995-01-01

We have extended the Wertheim integral equation theory to mixtures of hard spheres with two attraction sites in order to model homonuclear hard-sphere chain fluids, and then solved these equations with the polymer-Percus--Yevick closure and the ideal chain approximation to obtain the average intermolecular and overall radial distribution functions. We obtain explicit expressions for the contact values of these distribution functions and a set of one-dimensional integral equations from which the distribution functions can be calculated without iteration or numerical Fourier transformation. We compare the resulting predictions for the distribution functions with Monte Carlo simulation results we report here for five selected binary mixtures. It is found that the accuracy of the prediction of the structure is the best for dimer mixtures and declines with increasing chain length and chain-length asymmetry. For the equation of state, we have extended the dimer version of the thermodynamic perturbation theory to the hard-sphere chain mixture by introducing the dimer mixture as an intermediate reference system. The Helmholtz free energy of chain fluids is then expressed in terms of the free energy of the hard-sphere mixture and the contact values of the correlation functions of monomer and dimer mixtures. We compared with the simulation results, the resulting equation of state is found to be the most accurate among existing theories with a relative average error of 1.79% for 4-mer/8-mer mixtures, which is the worst case studied in this work. copyright 1995 American Institute of Physics

Parallelization of pressure equation solver for incompressible N-S equations

International Nuclear Information System (INIS)

Ichihara, Kiyoshi; Yokokawa, Mitsuo; Kaburaki, Hideo.

1996-03-01

A pressure equation solver in a code for 3-dimensional incompressible flow analysis has been parallelized by using red-black SOR method and PCG method on Fujitsu VPP500, a vector parallel computer with distributed memory. For the comparison of scalability, the solver using the red-black SOR method has been also parallelized on the Intel Paragon, a scalar parallel computer with a distributed memory. The scalability of the red-black SOR method on both VPP500 and Paragon was lost, when number of processor elements was increased. The reason of non-scalability on both systems is increasing communication time between processor elements. In addition, the parallelization by DO-loop division makes the vectorizing efficiency lower on VPP500. For an effective implementation on VPP500, a large scale problem which holds very long vectorized DO-loops in the parallel program should be solved. PCG method with red-black SOR method applied to incomplete LU factorization (red-black PCG) has more iteration steps than normal PCG method with forward and backward substitution, in spite of same number of the floating point operations in a DO-loop of incomplete LU factorization. The parallelized red-black PCG method has less merits than the parallelized red-black SOR method when the computational region has fewer grids, because the low vectorization efficiency is obtained in red-black PCG method. (author)

Unsteady Stokes equations: Some complete general solutions

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes flow in the absence of body forces is derived. Keywords. Complete ...

A note on the super AKNS equations

International Nuclear Information System (INIS)

Li Yishen; Zhang Lining.

1986-10-01

We find some relationships between the usual AKNS scheme with the super one, when its elements take value from the Grassmann algebra on a two-dimensional vector space. The solutions of these super AKNS equations are discussed. (author)

Double gauge invariance and covariantly-constant vector fields in Weyl geometry

Science.gov (United States)

Kassandrov, Vladimir V.; Rizcallah, Joseph A.

2014-08-01

The wave equation and equations of covariantly-constant vector fields (CCVF) in spaces with Weyl nonmetricity turn out to possess, in addition to the canonical conformal-gauge, a gauge invariance of another type. On a Minkowski metric background, the CCVF system alone allows us to pin down the Weyl 4-metricity vector, identified herein with the electromagnetic potential. The fundamental solution is given by the ordinary Lienard-Wiechert field, in particular, by the Coulomb distribution for a charge at rest. Unlike the latter, however, the magnitude of charge is necessarily unity, "elementary", and charges of opposite signs correspond to retarded and advanced potentials respectively, thus establishing a direct connection between the particle/antiparticle asymmetry and the "arrow of time".

Vectorization, parallelization and porting of nuclear codes on the VPP500 system (vectorization). Progress report fiscal 1997

International Nuclear Information System (INIS)

Kawasaki, Nobuo; Ogasawara, Shinobu; Adachi, Masaaki; Kume, Etsuo; Ishizuki, Shigeru; Tanabe, Hidenobu; Nemoto, Toshiyuki; Kawai, Wataru; Watanabe, Hideo

1999-05-01

Several computer codes in the nuclear field have been vectorized, parallelized and transported on the FUJITSU VPP500 system and/or the AP3000 system at Center for Promotion of Computational Science and Engineering in Japan Atomic Energy Research Institute. We dealt with 14 codes in fiscal 1997. These results are reported in 3 parts, i.e., the vectorization part, the parallelization part and the porting part. In this report, we describe the vectorization. In this vectorization part, the vectorization of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations, statistical decay code SD and three-dimensional thermal analysis code for in-core test section (T2) of HENDEL SSPHEAT are described. In the parallelization part, the parallelization of cylindrical direct numerical simulation code CYLDNS44N, worldwide version of system for prediction of environmental emergency dose information code WSPEEDI, extension of quantum molecular dynamics code EQMD and three-dimensional non-steady compressible fluid dynamics code STREAM are described. In the porting part, the porting of transient reactor analysis code TRAC-BF1 and Monte Carlo radiation transport code MCNP4A on the AP3000 are described. In addition, a modification of program libraries for command-driven interactive data analysis plotting program IPLOT is described. (author)

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

International Nuclear Information System (INIS)

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

2007-01-01

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic

Maxwell’s Equations on Cantor Sets: A Local Fractional Approach

Directory of Open Access Journals (Sweden)

Yang Zhao

2013-01-01

Full Text Available Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.

Unsteady analytical solutions to the Poisson–Nernst–Planck equations

International Nuclear Information System (INIS)

Schönke, Johannes

2012-01-01

It is shown that the Poisson–Nernst–Planck equations for a single ion species can be formulated as one equation in terms of the electric field. This previously not analyzed equation shows similarities to the vector Burgers equation and is identical with it in the one dimensional case. Several unsteady exact solutions for one and multidimensional cases are presented. Besides new mathematical insights which these first known unsteady solutions give, they can serve as test cases in computer simulations to analyze numerical algorithms and to verify code. (paper)

Poiseuille equation for steady flow of fractal fluid

Science.gov (United States)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

A q-Schroedinger algebra, its lowest weight representations and generalized q-deformed heat equations

International Nuclear Information System (INIS)

Dobrev, V.K.; Doebner, H.D.; Mrugalla, C.

1995-12-01

We give a q-deformation S-perpendicular q of the centrally extended Schroedinger algebra. We construct the lowest weight representations of S-perpendicular q , starting from the Verma modules over S-perpendicular q , finding their singular vectors and factoring the Verma submodules built on the singular vectors. We also give a vector-field realization of S-perpendicular q which provides polynomial realization of the lowest weight representations and an infinite hierarchy of q-difference equations which may be called generalized q-deformed heat equations. We also apply our methods to the on-shell q-Schroedinger algebra proposed by Floreanini and Vinet. (author). 12 refs

Kelvin-Helmholtz instability and kinetic internal kink modes in tokamaks

International Nuclear Information System (INIS)

Naitou, H.

2002-01-01

The m=1 and n=1 kinetic internal kink (KIK) mode with a nonuniform density profile is studied by the cylindrical version of the gyro-reduced-MHD code which is one of the extended MHD codes being able to treat the physics beyond resistive MHD. Electron inertia and electron finite temperature effects are crucial. The linear mode structure of KIK mode includes the sheared poloidal flow with m=1, which excites the vortexes due to the Kelvin-Helmholtz (K-H) instability. We have found that there is a strong coupling between the KIK mode and the K-H mode even in the early nonlinear stage of KIK instability in which the width of the m=1 magnetic island is sufficiently small. (author)

Solution of the chemical master equation by radial basis functions approximation with interface tracking

NARCIS (Netherlands)

Kryven, I.; Röblitz, S; Schütte, C.

2015-01-01

Background: The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents

POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity

International Nuclear Information System (INIS)

Colman, J.

2001-01-01

1 - Description of program or function: POISSON, SUPERFISH is a group of (1) codes that solve Poisson's equation and are used to compute field quality for both magnets and fixed electric potentials and (2) RF cavity codes that calculate resonant frequencies and field distributions of the fundamental and higher modes. The group includes: POISSON, PANDIRA, SUPERFISH, AUTOMESH, LATTICE, FORCE, MIRT, PAN-T, TEKPLOT, SF01, and SHY. POISSON solves Poisson's (or Laplace's) equation for the vector (scalar) potential with nonlinear isotropic iron (dielectric) and electric current (charge) distributions for two-dimensional Cartesian or three-dimensional cylindrical symmetry. It calculates the derivatives of the potential, the stored energy, and performs harmonic (multipole) analysis of the potential. PANDIRA is similar to POISSON except it allows anisotropic and permanent magnet materials and uses a different numerical method to obtain the potential. SUPERFISH solves for the accelerating (TM) and deflecting (TE) resonant frequencies and field distributions in an RF cavity with two-dimensional Cartesian or three-dimensional cylindrical symmetry. Only the azimuthally symmetric modes are found for cylindrically symmetric cavities. AUTOMESH prepares input for LATTICE from geometrical data describing the problem, (i.e., it constructs the 'logical' mesh and generates (x,y) coordinate data for straight lines, arcs of circles, and segments of hyperbolas). LATTICE generates an irregular triangular (physical) mesh from the input data, calculates the 'point current' terms at each mesh point in regions with distributed current density, and sets up the mesh point relaxation order needed to write the binary problem file for the equation-solving POISSON, PANDIRA, or SUPERFISH. FORCE calculates forces and torques on coils and iron regions from POISSON or PANDIRA solutions for the potential. MIRT optimizes magnet profiles, coil shapes, and current densities from POISSON output based on a

Complete factorisation and analytic solutions of generalized Lotka-Volterra equations

Science.gov (United States)

Brenig, L.

1988-11-01

It is shown that many systems of nonlinear differential equations of interest in various fields are naturally imbedded in a new family of differential equations. This family is invariant under nonlinear transformations based on the concept of matrix power of a vector. Each equation belonging to that family can be brought into a factorized canonical form for which integrable cases can be easily identified and solutions can be found by quadratures.

Vector-Parallel processing of the successive overrelaxation method

International Nuclear Information System (INIS)

Yokokawa, Mitsuo

1988-02-01

Successive overrelaxation method, called SOR method, is one of iterative methods for solving linear system of equations, and it has been calculated in serial with a natural ordering in many nuclear codes. After the appearance of vector processors, this natural SOR method has been changed for the parallel algorithm such as hyperplane or red-black method, in which the calculation order is modified. These methods are suitable for vector processors, and more high-speed calculation can be obtained compared with the natural SOR method on vector processors. In this report, a new scheme named 4-colors SOR method is proposed. We find that the 4-colors SOR method can be executed on vector-parallel processors and it gives the most high-speed calculation among all SOR methods according to results of the vector-parallel execution on the Alliant FX/8 multiprocessor system. It is also shown that the theoretical optimal acceleration parameters are equal among five different ordering SOR methods, and the difference between convergence rates of these SOR methods are examined. (author)

All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector

Science.gov (United States)

Chudecki, Adam

2016-12-01

Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant Λ equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with Λ≠0 admitting a nonnull Killing vector are found.

Applications of the Local Algebras of Vector Fields to the Modelling of Physical Phenomena

OpenAIRE

Bayak, Igor V.

2015-01-01

In this paper we discuss the local algebras of linear vector fields that can be used in the mathematical modelling of physical space by building the dynamical flows of vector fields on eight-dimensional cylindrical or toroidal manifolds. It is shown that the topological features of the vector fields obey the Dirac equation when moving freely within the surface of a pseudo-sphere in the eight-dimensional pseudo-Euclidean space.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions.

Science.gov (United States)

Latella, Ivan; Pérez-Madrid, Agustín

2013-10-01

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Spectral element method for vector radiative transfer equation

International Nuclear Information System (INIS)

Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.

2010-01-01

A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.

Numerical experiments using CHIEF to treat the nonuniqueness in solving acoustic axisymmetric exterior problems via boundary integral equations

Directory of Open Access Journals (Sweden)

Adel A.K. Mohsen

2010-07-01

Full Text Available The problem of nonuniqueness (NU of the solution of exterior acoustic problems via boundary integral equations is discussed in this article. The efficient implementation of the CHIEF (Combined Helmholtz Integral Equations Formulation method to axisymmetric problems is studied. Interior axial fields are used to indicate the solution error and to select proper CHIEF points. The procedure makes full use of LU-decomposition as well as the forward solution derived in the solution. Implementations of the procedure for hard spheres are presented. Accurate results are obtained up to a normalised radius of ka = 20.983, using only one CHIEF point. The radiation from a uniformly vibrating sphere is also considered. Accurate results for ka up to 16.927 are obtained using two CHIEF points.

The Fokker-Planck equation for ray dispersion in gyrotropic stratified media

NARCIS (Netherlands)

Golynski, S.M.

1984-01-01

The Hamilton equations of geometrical optics determine the rays of the relevant wave field in the short wavelength. We give a systematic derivation of the Fokker-Planck equation for the joint probability density of the position and unit direction vector of rays propagating in a gyrotropic stratified

Traditional vectors as an introduction to geometric algebra

International Nuclear Information System (INIS)

Carroll, J E

2003-01-01

The 2002 Oersted Medal Lecture by David Hestenes concerns the many advantages for education in physics if geometric algebra were to replace standard vector algebra. However, such a change has difficulties for those who have been taught traditionally. A new way of introducing geometric algebra is presented here using a four-element array composed of traditional vector and scalar products. This leads to an explicit 4 x 4 matrix representation which contains key requirements for three-dimensional geometric algebra. The work can be extended to include Maxwell's equations where it is found that curl and divergence appear naturally together. However, to obtain an explicit representation of space-time algebra with the correct behaviour under Lorentz transformations, an 8 x 8 matrix representation has to be formed. This leads to a Dirac representation of Maxwell's equations showing that space-time algebra has hidden within its formalism the symmetry of 'parity, charge conjugation and time reversal'

Null vectors in superconformal quantum field theory

International Nuclear Information System (INIS)

Huang Chaoshang

1993-01-01

The superspace formulation of the N=1 superconformal field theory and superconformal Ward identities are used to give a precise definition of fusion. Using the fusion procedure, superconformally covariant differential equations are derived and consequently a complete and straightforward algorithm for finding null vectors in Verma modules of the Neveu-Schwarz algebra is given. (orig.)

Stochastic Levy Divergence and Maxwell's Equations

Directory of Open Access Journals (Sweden)

B. O. Volkov

2015-01-01

Full Text Available One of the main reasons for interest in the Levy Laplacian and its analogues such as Levy d'Alembertian is a connection of these operators with gauge fields. The theorem proved by Accardi, Gibillisco and Volovich stated that a connection in a bundle over a Euclidean space or over a Minkowski space is a solution of the Yang-Mills equations if and only if the corresponding parallel transport to the connection is a solution of the Laplace equation for the Levy Laplacian or of the d'Alembert equation for the Levy d'Alembertian respectively (see [5, 6]. There are two approaches to define Levy type operators, both of which date back to the original works of Levy [7]. The first is that the Levy Laplacian (or Levy d'Alembertian is defined as an integral functional generated by a special form of the second derivative. This approach is used in the works [5, 6], as well as in the paper [8] of Leandre and Volovich, where stochastic Levy-Laplacian is discussed. Another approach to the Levy Laplacian is defining it as the Cesaro mean of second order derivatives along the family of vectors, which is an orthonormal basis in the Hilbert space. This definition of the Levy Laplacian is used for the description of solutions of the Yang-Mills equations in the paper [10].The present work shows that the definitions of the Levy Laplacian and the Levy d'Alembertian based on Cesaro averaging of the second order directional derivatives can be transferred to the stochastic case. In the article the values of these operators on a stochastic parallel transport associated with a connection (vector potential are found. In this case, unlike the deterministic case and the stochastic case of Levy Laplacian from [8], these values are not equal to zero if the vector potential corresponding to the stochastic parallel transport is a solution of the Maxwell's equations. As a result, two approaches to definition of the Levy Laplacian in the stochastic case give different operators. This

KELVIN-HELMHOLTZ INSTABILITY OF A CORONAL STREAMER

Energy Technology Data Exchange (ETDEWEB)

Feng, L.; Gan, W. Q. [Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210008 Nanjing (China); Inhester, B., E-mail: lfeng@pmo.ac.cn [Max-Planck-Institut fuer Sonnensystemforschung, Max-Planck-Str.2, D-37191 Katlenburg-Lindau (Germany)

2013-09-10

Shear-flow-driven instability can play an important role in energy transfer processes in coronal plasma. We present for the first time the observation of a kink-like oscillation of a streamer that is probably caused by the streaming kink-mode Kelvin-Helmholtz instability (KHI). The wave-like behavior of the streamer was observed by the Large Angle and Spectrometric Coronagraph Experiment C2 and C3 on board the SOlar and Heliospheric Observatory. The observed wave had a period of about 70-80 minutes, and its wavelength increased from 2 R{sub Sun} to 3 R{sub Sun} in about 1.5 hr. The phase speeds of its crests and troughs decreased from 406 {+-} 20 to 356 {+-} 31 km s{sup -1} during the event. Within the same heliocentric range, the wave amplitude also appeared to increase with time. We attribute the phenomena to the MHD KHI, which occurs at a neutral sheet in a fluid wake. The free energy driving the instability is supplied by the sheared flow and sheared magnetic field across the streamer plane. The plasma properties of the local environment of the streamer were estimated from the phase speed and instability threshold criteria.

On parasupersymmetric oscillators and relativistic vector mesons in constant magnetic fields

Science.gov (United States)

Debergh, Nathalie; Beckers, Jules

1995-01-01

Johnson-Lippmann considerations on oscillators and their connection with the minimal coupling schemes are visited in order to introduce a new Sakata-Taketani equation describing vector mesons in interaction with a constant magnetic field. This new proposal, based on a specific parasupersymmetric oscillator-like system, is characterized by real energies as opposed to previously pointed out relativistic equations corresponding to this interacting context.

The spinodal constraint on the equation of state of expanded fluids

International Nuclear Information System (INIS)

Brosh, Eli; Makov, Guy; Shneck, Roni Z

2003-01-01

The spinodal is a locus in the P-V diagram, which is the limit of metastability of a substance with respect to a phase transition. In particular, it is the limit to the negative (tensile) pressure exerted on a liquid, at which the liquid may still be metastable with respect to the gas phase. By requiring that the Helmholtz free energy should be analytic at the spinodal, it is possible to derive the limiting behaviour of thermodynamic properties near the spinodal. In the present paper we show how this analyticity requirement may be used to choose between available equations of state (EOSs). In particular it is shown that the universal equation of state (UEOS) proposed by Vinet et al, complies with the analyticity requirement and may be used to locate the spinodal by extrapolation from within the stable region. The Baonza or 'pseudospinodal' EOS, which is apparently based on the functional form of thermodynamic properties near the spinodal, actually contradicts the analyticity requirement and indeed yields manifestly wrong results in locating the spinodal. However it is shown that the Baonza equation may be viewed as an approximation to the UEOS in states of compression. Its technical importance, which stems from its algebraic simplicity, is also stressed in the present work

Equations of motion for free-flight systems of rotating-translating bodies

International Nuclear Information System (INIS)

Hodapp, A.E. Jr.

1976-09-01

General vector differential equations of motion are developed for a system of rotating-translating, unbalanced, constant mass bodies. Complete flexibility is provided in placement of the reference coordinates within the system of bodies and in placement of body fixed axes within each body. Example cases are presented to demonstrate the ease in reduction of these equations to the equations of motion for systems of interest

Scale invariance, killing vectors, and the size of the fifth dimension

International Nuclear Information System (INIS)

Ross, D.K.

1986-01-01

An analysis is made of the classical five-dimensional sourceless Kaluza-Klein equations with the existence of the usual α/α/PSI/ Killing vector not assumed, where /PSI/ is the coordinate of the fifth dimension. The physical distance around the fifth dimension D 5 , needed for the calculation of the fine structure constant α, is not calculable in the usual theory because the equations have a global scale invariance. In the present case, the Killing vector and the global scale invariance are not present, but it is found rather generally that D 5 = 0. This indicates that quantum gravity is a necessary ingredient if α is to be calculated. It also provides an alternate explanation of why the universe appears four-dimensional

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

Toro, Eleuterio F.

2015-09-30

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.

Transitive Lie algebras of vector fields: an overview

NARCIS (Netherlands)

Draisma, J.

2011-01-01

This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on

Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: From fluid to kinetic modeling

Czech Academy of Sciences Publication Activity Database

Henri, P.; Cerri, S.S.; Califano, F.; Pegoraro, F.; Rossi, C.; Faganello, M.; Šebek, Ondřej; Trávníček, Pavel M.; Hellinger, Petr; Frederiksen, J. T.; Nordlund, A.; Markidis, S.; Keppens, R.; Lapenta, G.

2013-01-01

Roč. 20, č. 10 (2013), 102118/1-102118/13 ISSN 1070-664X R&D Projects: GA MŠk(CZ) 7E11053 EU Projects: European Commission(XE) 263340 - SWIFF Grant - others:European Commission(XE) HPC-EUROPA2 - No. 228398; EU(XE) RI-283493; NASA (US) NNX11A1164G Institutional support: RVO:67985815 ; RVO:68378289 Keywords : Kelvin-Helmholtz instability * plasma kinetic theory * plasma magnetohydrodynamics Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics; BL - Plasma and Gas Discharge Physics (UFA-U) Impact factor: 2.249, year: 2013

Exact, multiple soliton solutions of the double sine Gordon equation

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact, particular solutions of the double sine Gordon equation in n dimensional space are constructed. Under certain restrictions these solutions are N solitons, where N <= 2q - 1 and q is the dimensionality of space-time. The method of solution, known as the base equation technique, relates solutions of nonlinear partial differential equations to solutions of linear partial differential equations. This method is reviewed and its applicability to the double sine Gordon equation shown explicitly. The N soliton solutions have the remarkable property that they collapse to a single soliton when the wave vectors are parallel. (author)

New formulation of Hardin-Pope equations for aeroacoustics

DEFF Research Database (Denmark)

Ekaterinaris, J.A.

1999-01-01

Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented....... The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives...... of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic...

Applying the Helmholtz Illusion to Fashion: Horizontal Stripes Won't Make You Look Fatter

Directory of Open Access Journals (Sweden)

Peter Thompson

2011-01-01

Full Text Available A square composed of horizontal lines appears taller and narrower than an identical square made up of vertical lines. Reporting this illusion, Hermann von Helmholtz noted that such illusions, in which filled space seems to be larger than unfilled space, were common in everyday life, adding the observation that ladies' frocks with horizontal stripes make the figure look taller. As this assertion runs counter to modern popular belief, we have investigated whether vertical or horizontal stripes on clothing should make the wearer appear taller or fatter. We find that a rectangle of vertical stripes needs to be extended by 7.1% vertically to match the height of a square of horizontal stripes and that a rectangle of horizontal stripes must be made 4.5% wider than a square of vertical stripes to match its perceived width. This illusion holds when the horizontal or vertical lines are on the dress of a line drawing of a woman. We have examined the claim that these effects apply only for 2-dimensional figures in an experiment with 3-D cylinders and find no support for the notion that horizontal lines would be ‘fattening’ on clothes. Significantly, the illusion persists when the horizontal or vertical lines are on pictures of a real half-body mannequin viewed stereoscopically. All the evidence supports Helmholtz's original assertion.

Static Einstein--Maxwell field equations

International Nuclear Information System (INIS)

Das, A.

1979-01-01

The static Einstein--Maxwell field equations are investigated in the presence of both electric and magnetic fields. The sources or bodies are assumed to be of finite size and to not affect the connectivity of the associated space. Furthermore, electromagnetic and metric fields are assumed to have reasonable differentiabilities. It is then proved that the electric and magnetic field vectors are constant multiples of one another. Moreover, the static Einstein--Maxwell equations reduce to the static magnetovac case. If, furthermore, the variational derivation of the Einstein--Maxwell equations is assumed, then both the total electric and magnetic charge of each body must vanish. As a physical consequence it is pointed out that if a suspended magnet be electrically charged then it must experience a purely general relativistic torque

Fractional gradient and its application to the fractional advection equation

OpenAIRE

D'Ovidio, M.; Garra, R.

2013-01-01

In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional fractional differential equations. A first application is discussed in relation to the d-dimensional fractional advection-dispersion equation. We also study the connection with multidimensional L\\'evy processes.

The (ℎ/2π)-expansion for Regge-trajectories. 2. Relativistic equations

International Nuclear Information System (INIS)

Stepanov, S.S.; Tutik, R.S.

1992-01-01

The (h/2π)-expansion method, proposed earlier for deriving Regge trajectories for bound states of central potentials in the Schroedinger equation framework, is extended to the Klein-Gordon and Dirac equations with potentials having vector and scalar components. The simple recursion formulae, with the same form both for the parent and daughter Regge trajectories, are obtained. They provide, in principle, the calculation of the (h/2π)-expansion terms up to an arbitrary order. As an illustration, a superposition of the vector and scalar Coulomb potentials, and the funnel-shaped potential are treated with the technique developed. 20 refs.; 3 figs.; 1 table. (author)

Incoherent and coherent backscattering of light by a layer of densely packed random medium

Energy Technology Data Exchange (ETDEWEB)

Tishkovets, Victor P. [Institute of Radio Astronomy of NASU, 4 Chervonopraporna Street, Kharkiv 61002 (Ukraine)], E-mail: tishkovets@ira.kharkov.ua

2007-12-15

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.

Acoustic response of Helmholtz dampers in the presence of hot grazing flow

Science.gov (United States)

Ćosić, B.; Wassmer, D.; Terhaar, S.; Paschereit, C. O.

2015-01-01

Thermoacoustic instabilities are high amplitude instabilities of premixed gas turbine combustors. Cooled passive dampers are used to attenuate or suppress these instabilities in the combustion chamber. For the first time, the influence of temperature differences between the grazing flow in the combustor and the cross-flow emanating from the Helmholtz damper is comprehensively investigated in the linear and nonlinear amplitude regime. The flow field inside the resonator and in the vicinity of the neck is measured with high-speed particle image velocimetry for various amplitudes and at different momentum-flux ratios of grazing and purging flow. Seeding is used as a tracer to qualitatively assess the mixing of the grazing and purging flow as well as the ingestion into the neck of the resonator. Experimentally, the acoustic response for various temperature differences between grazing and purging flow is investigated. The multi-microphone method, in combination with two microphones flush-mounted in the resonator volume and two microphones in the plane of the resonator entrance, is used to determine the impedance of the Helmholtz resonator in the linear and nonlinear amplitude regime for various temperatures and different momentum-flux ratios. Additionally, a thermocouple was used to measure the temperature in the neck. The acoustic response and the temperature measurements are used to obtain the virtual neck length and the effective area jump from a detailed impedance model. This model is extended to include the observed acoustic energy dissipation caused by the density gradients at the neck vicinity. A clear correlation between temperature differences and changes of the mass end-correction is confirmed. The capabilities of the impedance model are demonstrated.

Monolithically integrated Helmholtz coils by 3-dimensional printing

Energy Technology Data Exchange (ETDEWEB)

Li, Longguang [Department of Electrical Engineering, University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Abedini-Nassab, Roozbeh; Yellen, Benjamin B., E-mail: yellen@duke.edu [Department of Electrical Engineering, University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Mechanical Engineering and Materials Science, Duke University, P.O. Box 90300, Hudson Hall, Durham, North Carolina 27708 (United States)

2014-06-23

3D printing technology is of great interest for the monolithic fabrication of integrated systems; however, it is a challenge to introduce metallic components into 3D printed molds to enable broader device functionality. Here, we develop a technique for constructing a multi-axial Helmholtz coil by injecting a eutectic liquid metal Gallium Indium alloy (EGaIn) into helically shaped orthogonal cavities constructed in a 3D printed block. The tri-axial solenoids each carry up to 3.6 A of electrical current and produce magnetic field up to 70 G. Within the central section of the coil, the field variation is less than 1% and is in agreement with theory. The flow rates and critical pressures required to fill the 3D cavities with liquid metal also agree with theoretical predictions and provide scaling trends for filling the 3D printed parts. These monolithically integrated solenoids may find future applications in electronic cell culture platforms, atomic traps, and miniaturized chemical analysis systems based on nuclear magnetic resonance.

Monolithically integrated Helmholtz coils by 3-dimensional printing

International Nuclear Information System (INIS)

Li, Longguang; Abedini-Nassab, Roozbeh; Yellen, Benjamin B.

2014-01-01

3D printing technology is of great interest for the monolithic fabrication of integrated systems; however, it is a challenge to introduce metallic components into 3D printed molds to enable broader device functionality. Here, we develop a technique for constructing a multi-axial Helmholtz coil by injecting a eutectic liquid metal Gallium Indium alloy (EGaIn) into helically shaped orthogonal cavities constructed in a 3D printed block. The tri-axial solenoids each carry up to 3.6 A of electrical current and produce magnetic field up to 70 G. Within the central section of the coil, the field variation is less than 1% and is in agreement with theory. The flow rates and critical pressures required to fill the 3D cavities with liquid metal also agree with theoretical predictions and provide scaling trends for filling the 3D printed parts. These monolithically integrated solenoids may find future applications in electronic cell culture platforms, atomic traps, and miniaturized chemical analysis systems based on nuclear magnetic resonance.

Kelvin-Helmholtz instability in a bounded plasma flow

International Nuclear Information System (INIS)

Burinskaya, T. M.

2008-01-01

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfven velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth's magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfven velocity.

Oscillatory regime in the multidimensional homogeneous cosmological models induced by a vector field

International Nuclear Information System (INIS)

Benini, R; Kirillov, A A; Montani, Giovanni

2005-01-01

We show that in multidimensional gravity, vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all homogeneous models. By analysing the Hamiltonian equations we derive the Poincare return map associated with the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a four-dimensional spacetime, the oscillatory regime here constructed overlaps the usual Belinski-Khalatnikov-Liftshitz one

ASTEM, Evaluation of Gibbs, Helmholtz and Saturation Line Function for Thermodynamics Calculation

International Nuclear Information System (INIS)

Moore, K.V.; Burgess, M.P.; Fuller, G.L.; Kaiser, A.H.; Jaeger, D.L.

1974-01-01

1 - Description of problem or function: ASTEM is a modular set of FORTRAN IV subroutines to evaluate the Gibbs, Helmholtz, and saturation line functions as published by the American Society of Mechanical Engineers (1967). Any thermodynamic quantity including derivative properties can be obtained from these routines by a user-supplied main program. PROPS is an auxiliary routine available for the IBM360 version which makes it easier to apply the ASTEM routines to power station models. 2 - Restrictions on the complexity of the problem: Unless re-dimensioned by the user, the highest derivative allowed is order 9. All arrays within ASTEM are one-dimensional to save storage area

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

Science.gov (United States)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Numerical investigation on an array of Helmholtz resonators for the reduction of micro-pressure waves in modern and future high-speed rail tunnel systems

Science.gov (United States)

Tebbutt, J. A.; Vahdati, M.; Carolan, D.; Dear, J. P.

2017-07-01

Previous research has proposed that an array of Helmholtz resonators may be an effective method for suppressing the propagation of pressure and sound waves, generated by a high-speed train entering and moving in a tunnel. The array can be used to counteract environmental noise from tunnel portals and also the emergence of a shock wave in the tunnel. The implementation of an array of Helmholtz resonators in current and future high-speed train-tunnel systems is studied. Wave propagation in the tunnel is modelled using a quasi-one-dimensional formulation, accounting for non-linear effects, wall friction and the diffusivity of sound. A multi-objective genetic algorithm is then used to optimise the design of the array, subject to the geometric constraints of a demonstrative tunnel system and the incident wavefront in order to attenuate the propagation of pressure waves. It is shown that an array of Helmholtz resonators can be an effective countermeasure for various tunnel lengths. In addition, the array can be designed to function effectively over a wide operating envelope, ensuring it will still function effectively as train speeds increase into the future.

Linear Einstein equations and Kerr-Schild maps

International Nuclear Information System (INIS)

Gergely, Laszlo A

2002-01-01

We prove that given a solution of the Einstein equations g ab for the matter field T ab , an autoparallel null vector field l a and a solution (l a l c , T ac ) of the linearized Einstein equation on the given background, the Kerr-Schild metric g ac + λl a l c (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor T ac + λT ac + λ 2 l (a T c)b l b . The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed spacetime due to Guerses and Guersey

Self-dual metrics with self-dual Killing vectors

International Nuclear Information System (INIS)

Tod, K.P.; Ward, R.S.

1979-01-01

Twistor methods are used to derive a class of solutions to Einstein's vacuum equations, with anti-self dual Weyl tensor. In particular, all metrics with a Killing vector whose derivative is anti-self-dual and which admit a real positive-definite section are exhibited and shown to coincide with the metrics of Hawking. (author)

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

Science.gov (United States)

Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming

1996-01-01

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

DEFF Research Database (Denmark)

Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

1994-01-01

perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...

On the population dynamics of the malaria vector

International Nuclear Information System (INIS)

Ngwa, G.A.

2005-10-01

A deterministic differential equation model for the population dynamics of the human malaria vector is derived and studied. Conditions for the existence and stability of a non-zero steady state vector population density are derived. These reveal that a threshold parameter, the vectorial basic reproduction number, exist and the vector can establish itself in the community if and only if this parameter exceeds unity. When a non-zero steady state population density exists, it can be stable but it can also be driven to instability via a Hopf Bifurcation to periodic solutions, as a parameter is varied in parameter space. By considering a special case, an asymptotic perturbation analysis is used to derive the amplitude of the oscillating solutions for the full non-linear system. The present modelling exercise and results show that it is possible to study the population dynamics of disease vectors, and hence oscillatory behaviour as it is often observed in most indirectly transmitted infectious diseases of humans, without recourse to external seasonal forcing. (author)

Characterizations of Space Curves According to Bishop Darboux Vector in Euclidean 3-Space E3

OpenAIRE

Huseyin KOCAYIGIT; Ali OZDEMIR

2014-01-01

In this paper, we obtained some characterizations of space curves according to Bihop frame in Euclidean 3-space E3 by using Laplacian operator and Levi-Civita connection. Furthermore, we gave the general differential equations which characterize the space curves according to the Bishop Darboux vector and the normal Bishop Darboux vector.

Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states

International Nuclear Information System (INIS)

Moodley, Mervlyn; Nsio Nzundu, T; Paul, S

2012-01-01

We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)

Parameters assessment of the inductively-coupled circuit for wireless power transfer

Science.gov (United States)

Isaev, Yu N.; Vasileva, O. V.; Budko, A. A.; Lefebvre, S.

2017-02-01

In this paper, a wireless power transfer model through the example of inductively-coupled coils of irregular shape in software package COMSOL Multiphysics is studied. Circuit parameters, such as inductance, coil resistance and self-capacitance were defined through electromagnetic energy by the finite-element method. The study was carried out according to Helmholtz equation. Spatial distribution of current per unit depending on frequency and the coupling coefficient for analysis of resonant frequency and spatial distribution of the vector magnetic potential at different distances between coils were presented. The resulting algorithm allows simulating the wireless power transfer between the inductively coupled coils of irregular shape with the assessment of the optimal parameters.

Some fundamental considerations of the equation of radiative transfer

International Nuclear Information System (INIS)

Kuriyan, J.G.; Sudarshan, E.C.G.

1978-10-01

The radiation transfer of the vector electromagnetic field was first formulated by Chandrasekhar while deriving the polarization characteristics of a sunlit sky. There are two subtle problems underlying this treatment. The first concerns the crucial identification of a Stokes parameter with the specific intensity of radiation. While both depend on position in 3-D space, the latter has, intrinsic to it, an additional angular dependence defining the flow of the radiation field. How can this inadequacy be remedied without damaging the results obtained heretofore from Chandrasekhar's formalism. The second problem arises from the fact that the radiative transfer equation describes the transport of an incoherent radiation field through space. This, however, seems to contradict the results of the Van Cittert-Zernike-Wolf theorem which implies that an incoherent field develops coherence as it passes through free space implying, of course, that the radiative transfer equation must involve not incoherent but partially coherent fields. The vector transfer equation of the direct beam (Beer's law) is derived from first principles. The analysis of this equation provides a satisfactory resolution of these two problems. The result also shows that the Beer's law will have to be modified to a matrix law to accommodate systems that are not spherically symmetric. 13 references

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

Fushchich, W.I.; Zhdanov, R.Z.

1989-01-01

This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua

2009-01-01

The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.

Numerical simulation using vorticity-vector potential formulation

Science.gov (United States)

Tokunaga, Hiroshi

1993-01-01

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

Vectorization of Reed Solomon decoding and mapping on the EVP

NARCIS (Netherlands)

Kumar, A.; Berkel, van C.H.

2008-01-01

Reed Solomon (RS) codes are used in a variety of (wireless) communication systems. Although commonly implemented in dedicated hardware, this paper explores the mapping of high-throughput RS decoding on vector DSPs. The four modules of such a decoder, viz. Syndrome Computation, Key Equation Solver,

Decay of MHD-scale Kelvin-Helmholtz vortices mediated by parasitic electron dynamics

International Nuclear Information System (INIS)

Nakamura, T.K.M.; Hayashi, D.; Fujimoto, M.; Shinohara, I.

2004-01-01

We have simulated nonlinear development of MHD-scale Kelvin-Helmholtz (KH) vortices by a two-dimensional two-fluid system including finite electron inertial effects. In the presence of moderate density jump across a shear layer, in striking contrast to MHD results, MHD KH vortices are found to decay by the time one eddy turnover is completed. The decay is mediated by smaller vortices that appear within the parent vortex and stays effective even when the shear layer width is made larger. It is shown that the smaller vortices are basically of MHD nature while the seeding for these is achieved by the electron inertial effect. Application of the results to the magnetotail boundary layer is discussed

Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2015-01-01

the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....

Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

International Nuclear Information System (INIS)

Clarkson, Chris; Osano, Bob

2011-01-01

Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second and higher order because perturbative modes are sourced by products of lower order modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second order. We perform much of our analysis using an index-free 'vector-calculus' approach which makes manipulating tensor equations considerably simpler. (papers)

Solution of single linear tridiagonal systems and vectorization of the ICCG algorithm on the Cray 1

International Nuclear Information System (INIS)

Kershaw, D.S.

1981-01-01

The numerical algorithms used to solve the physics equation in codes which model laser fusion are examined, it is found that a large number of subroutines require the solution of tridiagonal linear systems of equations. One dimensional radiation transport, thermal and suprathermal electron transport, ion thermal conduction, charged particle and neutron transport, all require the solution of tridiagonal systems of equations. The standard algorithm that has been used in the past on CDC 7600's will not vectorize and so cannot take advantage of the large speed increases possible on the Cray-1 through vectorization. There is however, an alternate algorithm for solving tridiagonal systems, called cyclic reduction, which allows for vectorization, and which is optimal for the Cray-1. Software based on this algorithm is now being used in LASNEX to solve tridiagonal linear systems in the subroutines mentioned above. The new algorithm runs as much as five times faster than the standard algorithm on the Cray-1. The ICCG method is being used to solve the diffusion equation with a nine-point coupling scheme on the CDC 7600. In going from the CDC 7600 to the Cray-1, a large part of the algorithm consists of solving tridiagonal linear systems on each L line of the Lagrangian mesh in a manner which is not vectorizable. An alternate ICCG algorithm for the Cray-1 was developed which utilizes a block form of the cyclic reduction algorithm. This new algorithm allows full vectorization and runs as much as five times faster than the old algorithm on the Cray-1. It is now being used in Cray LASNEX to solve the two-dimensional diffusion equation in all the physics subroutines mentioned above

On the Efficiency of Algorithms for Solving Hartree–Fock and Kohn–Sham Response Equations

DEFF Research Database (Denmark)

Kauczor, Joanna; Jørgensen, Poul; Norman, Patrick

2011-01-01

The response equations as occurring in the Hartree–Fock, multiconfigurational self-consistent field, and Kohn–Sham density functional theory have identical matrix structures. The algorithms that are used for solving these equations are discussed, and new algorithms are proposed where trial vectors...

Quark-gluon plasma tomography by vector mesons

International Nuclear Information System (INIS)

Lovas, I.

2001-01-01

Full text: The most important aim of relativistic heavy ion experiments is the observation f the quark-gluon plasma formation. In order to detect the transition into the plasma state it is desirable to map the density profile of the fireball formed in the collision. Here we investigate the possibility of this mapping by tomography. The fireball is characterized by the impact parameter vector b, which can be determined from the multiplicity and the angular distribution of the reaction products. By appropriate rotations the b vectors of each collision can be aligned into a fixed direction. Using the measured values of the momentum distributions independent integral equations can be formulated for the unknown emission densities (EM(r) and for the unknown absorption densities (Δ μ M (r)) of the different vector mesons M(≡ ω 0 , ρ 0 , φ 0 , ψ 0 , ψ 0' , Υ). At a fixed value of M and b the number of detected mesons N M (p,b) with momentum p, can be expressed by the following formula: N M (p,b) = ∫ V(b) dr EM(r) exp[-μ M (p)L(r,p o )] V(b) R(r, po)] exp[- ∫ from r until R(r,p 0 ) dl ' Δ μ M (r ' ,p)], where the average value of the absorption coefficient having no r dependence is denoted by μ(p), while Δ μM is defined as Δ μM = μ M - μ- M . The meson arrives to the surface of the fireball at R(r, p 0 ). The length of the path between r and R is denoted by L(r, po). The equation given above can be considered as an integral equation. Unfortunately it can not be transformed into an exact system of linear equations. However an iterative procedure can be constructed in such a way that in every iterative step a linear system of equations must be solved. N M (p,b) = ∫ V(b) dr exp[- μ M (p) L(r,p o )] [E M n (r) Σ from k=O until (n-1) (1/k !) (- ∫ from r until R (r, p 0 ) dl ' Δ μM n-1 (r ' , p) k + E M n-1 (r) (1/n !) (- ∫ from r until R(r, p 0 ) dl ' Δ μM n-1 (r ' , p)) (n-1) (- ∫ from r until R(r, p 0 ) dl ' Δ μM (n) (r ' , p))]. Since

Framework for non-coherent interface models at finite displacement jumps and finite strains

Science.gov (United States)

Ottosen, Niels Saabye; Ristinmaa, Matti; Mosler, Jörn

2016-05-01

This paper deals with a novel constitutive framework suitable for non-coherent interfaces, such as cracks, undergoing large deformations in a geometrically exact setting. For this type of interface, the displacement field shows a jump across the interface. Within the engineering community, so-called cohesive zone models are frequently applied in order to describe non-coherent interfaces. However, for existing models to comply with the restrictions imposed by (a) thermodynamical consistency (e.g., the second law of thermodynamics), (b) balance equations (in particular, balance of angular momentum) and (c) material frame indifference, these models are essentially fiber models, i.e. models where the traction vector is collinear with the displacement jump. This constraints the ability to model shear and, in addition, anisotropic effects are excluded. A novel, extended constitutive framework which is consistent with the above mentioned fundamental physical principles is elaborated in this paper. In addition to the classical tractions associated with a cohesive zone model, the main idea is to consider additional tractions related to membrane-like forces and out-of-plane shear forces acting within the interface. For zero displacement jump, i.e. coherent interfaces, this framework degenerates to existing formulations presented in the literature. For hyperelasticity, the Helmholtz energy of the proposed novel framework depends on the displacement jump as well as on the tangent vectors of the interface with respect to the current configuration - or equivalently - the Helmholtz energy depends on the displacement jump and the surface deformation gradient. It turns out that by defining the Helmholtz energy in terms of the invariants of these variables, all above-mentioned fundamental physical principles are automatically fulfilled. Extensions of the novel framework necessary for material degradation (damage) and plasticity are also covered.

Duality properties of Gorringe Leach equations

Science.gov (United States)

Grandati, Yves; Bérard, Alain; Mohrbach, Hervé

2009-02-01

In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold Vassiliev type. The specific associated conserved quantities (Laplace Runge Lenz vector and Fradkin Jauch Hill tensor) are then dual reflections of each other.

Diffusion at the Earth magnetopause: enhancement by Kelvin-Helmholtz instability

Directory of Open Access Journals (Sweden)

R. Smets

2007-02-01

Full Text Available Using hybrid simulations, we examine how particles can diffuse across the Earth's magnetopause because of finite Larmor radius effects. We focus on tangential discontinuities and consider a reversal of the magnetic field that closely models the magnetopause under southward interplanetary magnetic field. When the Larmor radius is on the order of the field reversal thickness, we show that particles can cross the discontinuity. We also show that with a realistic initial shear flow, a Kelvin-Helmholtz instability develops that increases the efficiency of the crossing process. We investigate the distribution functions of the transmitted ions and demonstrate that they are structured according to a D-shape. It accordingly appears that magnetic reconnection at the magnetopause is not the only process that leads to such specific distribution functions. A simple analytical model that describes the built-up of these functions is proposed.

ON ASYMTOTIC APPROXIMATIONS OF FIRST INTEGRALS FOR DIFFERENTIAL AND DIFFERENCE EQUATIONS

Directory of Open Access Journals (Sweden)

W.T. van Horssen

2007-04-01

Full Text Available In this paper the concept of integrating factors for differential equations and the concept of invariance factors for difference equations to obtain first integrals or invariants will be presented. It will be shown that all integrating factors have to satisfya system of partial differential equations, and that all invariance factors have to satisfy a functional equation. In the period 1997-2001 a perturbation method based on integrating vectors was developed to approximate first integrals for systems of ordinary differential equations. This perturbation method will be reviewed shortly. Also in the paper the first results in the development of a perturbation method for difference equations based on invariance factors will be presented.

A local-global problem for linear differential equations

NARCIS (Netherlands)

Put, Marius van der; Reversat, Marc

An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

A local-global problem for linear differential equations

NARCIS (Netherlands)

Put, Marius van der; Reversat, Marc

2008-01-01

An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

Liouville equation of relativistic charged fermion

International Nuclear Information System (INIS)

Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

1991-01-01

As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

On coupled development of MHD instabilities of Rayleigh-Taylor and Kelvin-Helmholtz types in nonuniform gas-plasmas flows

International Nuclear Information System (INIS)

Likhachev, A P; Medin, S A

2010-01-01

The simultaneous development of the MHD instabilities of Raylegh-Taylor and Kelvin-Helmholtz types at the interface between high-conducting plasmoid and surrounding non- or low-conducting gas is considered. The linear stage of the RTI development is studied analytically for incompressible and compressible fluids. The nonlinear stage of the individual development of the RTI and the coupled development of both instabilities has been investigated numerically. The time-dependent two-dimensional numerical model based on the solution of the Euler gasdynamic equations with body momentum and energy sources of MHD origin has been developed and used in calculations. A disturbance introducing in the background flow has been periodic with varied assignment type and wave length. Fundamental difference between the results of linear and nonlinear analysis has been revealed. In particular, the increment of the RTI development at nonlinear stage is one-two order of magnitude less than that predicted by linear theory and rather weakly depends on initial disturbance mode. In linear analysis the coupled development of the RTI and the KHI is determined by simple summing of the two effects in the expression of wave increment, whereas in nonlinear case the mutual influence of the instabilities leads to essential alterations in their development, main of which is the intensive 'layer-by-layer' destruction of the plasmoid surface.

Novel method for solution of coupled radial Schrödinger equations

International Nuclear Information System (INIS)

Ershov, S. N.; Vaagen, J. S.; Zhukov, M. V.

2011-01-01

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.

Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum

International Nuclear Information System (INIS)

Chen Changyuan; Sun Dongsheng; Lu Falin

2007-01-01

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given

Hairy black hole solutions in U(1) gauge-invariant scalar-vector-tensor theories

Science.gov (United States)

Heisenberg, Lavinia; Tsujikawa, Shinji

2018-05-01

In U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ → ϕ + c, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.

Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

International Nuclear Information System (INIS)

Wang Ling; Dong Zhongzhou; Liu Xiqiang

2008-01-01

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation (ANNV). Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.

Magnetohydrodynamic Kelvin-Helmholtz instabilities in astrophysics. 4. Single shear layer in MHD flows

Energy Technology Data Exchange (ETDEWEB)

Ferrari, A [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Turin Univ. (Italy). Ist. di Fisica Generale); Trussoni, E [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Max-Planck-Institut fuer Physik und Astrophysik, Garching (Germany, F.R.). Inst. fuer Extraterrestrische Physik)

1983-11-01

In this further paper on the physics of Kelvin-Helmholtz instabilities the case in which the fluids in relative motion are magnetized and separated by a shear layer is investigated. The present study points out, with respect to previous treatments, that different velocity profiles affect perturbations of short wavelength (as compared to the scale of the shear). Another new result is in the destabilizing effect, even in the subsonic regime, of the magnetic field on modes neutrally stable in the vortex sheet approximation. Such a behaviour is analogous to that found in the fluid case for Mach numbers >approx. = to 2. Possible astrophysical implications are also discussed.

Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

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Gijs Kant

2012-10-01

Full Text Available Parameterised Boolean Equation Systems (PBESs are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal mu-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG, a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically.

Equation of motion for string operators in quantum chromodynamics

International Nuclear Information System (INIS)

Suura, H.

1979-04-01

I derive from the QCD Lagrangian differential laws describing motions and interactions of an infinite set of string operators - locally gaugeinvariant color-singlet operators. By truncating the set, I obtain a q-anti q wave equation with a confinement potential, and also a jet-fragmentation equation which describes splitting of a q-anti q string and creation of I = O vector mesons. I argue for the validity of the perturbative treatment of the string operators. (orig.) [de

Exact solution of the N-dimensional generalized Dirac-Coulomb equation

International Nuclear Information System (INIS)

Tutik, R.S.

1992-01-01

An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)

The Dirac equation in external fields: Variable separation in Cartesian coordinates

International Nuclear Information System (INIS)

Shishkin, G.V.; Cabos, W.D.

1991-01-01

The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper

Magnetohydrodynamic Kelvin-Helmholtz instabilities in astrophysics. 1. Relativistic flows-plane boundary layer in vortex sheet approximation

Energy Technology Data Exchange (ETDEWEB)

Ferrari, A; Trussoni, E; Zaninetti, L [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Turin Univ. (Italy). Ist. di Fisica)

1980-11-01

In this paper some unsolved problems of the linear MHD Kelvin-Helmholtz instability are re-examined, starting from the analysis of relativistic (and non-relativistic) flows in the approximation of a plane vortex sheet, for the contact layer between the fluids in relative motion. Results are discussed for a range of physical parameters in specific connection with application to models of jets in extragalactic radio sources. Other physical aspects of the instability will be considered in forthcoming papers.

Vector calculus in non-integer dimensional space and its applications to fractal media

Science.gov (United States)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

Minimal parameter solution of the orthogonal matrix differential equation

Science.gov (United States)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1990-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

A vector matching method for analysing logic Petri nets

Science.gov (United States)

Du, YuYue; Qi, Liang; Zhou, MengChu

2011-11-01

Batch processing function and passing value indeterminacy in cooperative systems can be described and analysed by logic Petri nets (LPNs). To directly analyse the properties of LPNs, the concept of transition enabling vector sets is presented and a vector matching method used to judge the enabling transitions is proposed in this article. The incidence matrix of LPNs is defined; an equation about marking change due to a transition's firing is given; and a reachable tree is constructed. The state space explosion is mitigated to a certain extent from directly analysing LPNs. Finally, the validity and reliability of the proposed method are illustrated by an example in electronic commerce.

Generalized decompositions of dynamic systems and vector Lyapunov functions

Science.gov (United States)

Ikeda, M.; Siljak, D. D.

1981-10-01

The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.

A Chargeless Complex Vector Matter Field in Supersymmetric Scenario

Directory of Open Access Journals (Sweden)

L. P. Colatto

2015-01-01

Full Text Available We construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two nochiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms into matter fields by a global U1 gauge symmetry. For the aim of dealing with consistent terms without breaking the global U1 symmetry we imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminates the extra degrees of freedom which is consistent with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca’s type field for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the first steps to extend the analysis of charged massive vector field in a supersymmetric scenario.

Multifractal vector fields and stochastic Clifford algebra.

Science.gov (United States)

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2015-12-01

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

Multifractal vector fields and stochastic Clifford algebra

Energy Technology Data Exchange (ETDEWEB)

Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr [University Paris-Est, Ecole des Ponts ParisTech, Hydrology Meteorology and Complexity HM& Co, Marne-la-Vallée (France)

2015-12-15

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

Quaternion wave equations in curved space-time

Science.gov (United States)

Edmonds, J. D., Jr.

1974-01-01

The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

Modeling of Dielectric Properties of Aqueous Salt Solutions with an Equation of State

DEFF Research Database (Denmark)

Maribo-Mogensen, Bjørn; Kontogeorgis, Georgios; Thomsen, Kaj

2013-01-01

The static permittivity is the most important physical property for thermodynamic models that account for the electrostatic interactions between ions. The measured static permittivity in mixtures containing electrolytes is reduced due to kinetic depolarization and reorientation of the dipoles...... methodology for obtaining the static permittivity over wide ranges of temperatures, pressures, and compositions for use within an equation of state for mixed solvents containing salts. The static permittivity is calculated from a new extension of the framework developed by Onsager, Kirkwood, and Fröhlich...... to associating mixtures. Wertheim’s association model as formulated in the statistical associating fluid theory is used to account for hydrogen-bonding molecules and ion–solvent association. Finally, we compare the Debye–Hückel Helmholtz energy obtained using an empirical model with the new physical model...

Structural equations for Killing tensors of order two. II

International Nuclear Information System (INIS)

Hauser, I.; Malhiot, R.J.

1975-01-01

In a preceding paper, a new form of the structural equations for any Killing tensor of order two have been derived; these equations constitute a system analogous to the Killing vector equations Nabla/sub alpha/ K/sub beta/ = ω/sub alpha beta/ = -ω/sub beta alpha/ and Nabla/sub gamma/ ω/sub alpha beta = R/sub alpha beta gamma delta/ K/sup delta/. The first integrability condition for the Killing tensor structural equations is now derived. The structural equations and the integrability condition have forms which can readily be expressed in terms of a null tetrad to furnish a Killing tensor parallel of the Newman--Penrose equations; this is briefly described. The integrability condition implies the new result, for any given space--time, that the dimension of the set of second-order Killing tensors attains its maximum possible value of 50 only if the space--time is of constant curvature. Potential applications of the structural equations are discussed

Moving interfaces and quasilinear parabolic evolution equations

CERN Document Server

Prüss, Jan

2016-01-01

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...

Overcritical PT-symmetric square well potential in the Dirac equation

OpenAIRE

Cannata, Francesco; Ventura, Alberto

2007-01-01

We study scattering properties of a PT-symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the (1+1)-dimensional Dirac equation.

On Multiple Hall-Like Electron Currents and Tripolar Guide Magnetic Field Perturbations During Kelvin-Helmholtz Waves

Science.gov (United States)

Sturner, Andrew P.; Eriksson, Stefan; Nakamura, Takuma; Gershman, Daniel J.; Plaschke, Ferdinand; Ergun, Robert E.; Wilder, Frederick D.; Giles, Barbara; Pollock, Craig; Paterson, William R.; Strangeway, Robert J.; Baumjohann, Wolfgang; Burch, James L.

2018-02-01

Two magnetopause current sheet crossings with tripolar guide magnetic field signatures were observed by multiple Magnetosphere Multiscale (MMS) spacecraft during Kelvin-Helmholtz wave activity. The two out-of-plane magnetic field depressions of the tripolar guide magnetic field are largely supported by the observed in-plane electron currents, which are reminiscent of two clockwise Hall current loop systems. A comparison with a three-dimensional kinetic simulation of Kelvin-Helmholtz waves and vortex-induced reconnection suggests that MMS likely encountered the two Hall magnetic field depressions on either side of a magnetic reconnection X-line. Moreover, MMS observed an out-of-plane current reversal and a corresponding in-plane magnetic field rotation at the center of one of the current sheets, suggesting the presence of two adjacent flux ropes. The region inside one of the ion-scale flux ropes was characterized by an observed decrease of the total magnetic field, a strong axial current, and significant enhancements of electron density and parallel electron temperature. The flux rope boundary was characterized by currents opposite this axial current, strong in-plane and converging electric fields, parallel electric fields, and weak electron-frame Joule dissipation. These return current region observations may reflect a need to support the axial current rather than representing local reconnection signatures in the absence of any exhausts.

Modern methods in topological vector spaces

CERN Document Server

Wilansky, Albert

2013-01-01

Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect

Universal centers in the cubic trigonometric Abel equation

Directory of Open Access Journals (Sweden)

Jaume Giné

2014-02-01

Full Text Available We study the center problem for the trigonometric Abel equation $d \\rho/ d \\theta= a_1 (\\theta \\rho^2 + a_2(\\theta \\rho^3,$ where $a_1(\\theta$ and $a_2(\\theta$ are cubic trigonometric polynomials in $\\theta$. This problem is closely connected with the classical Poincaré center problem for planar polynomial vector fields. A particular class of centers, the so-called universal centers or composition centers, is taken into account. An example of non-universal center and a characterization of all the universal centers for such equation are provided.

Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

Full Text Available The skew-circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra of n×n complex skew-circulant matrices are displayed in this paper.

Diffraction of Electromagnetic Waves on a Waveguide Joint

Directory of Open Access Journals (Sweden)

Malykh Mikhail

2018-01-01

Full Text Available In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn’t reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the “Hamiltonian form” to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage.

Scalar and vector Galileons

International Nuclear Information System (INIS)

Rodríguez, Yeinzon; Navarro, Andrés A.

2017-01-01

An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to make the Hamiltonian bounded from below, as long as the action is not degenerate, the Galileon construction is a way to avoid pathologies both at the classical and quantum levels. Galileon actions are, therefore, of great interest in many branches of physics, specially in high energy physics and cosmology. This proceedings contribution presents the generalities of the construction of both scalar and vector Galileons following two different but complimentary routes. (paper)

Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes.

Science.gov (United States)

Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David; Santos, Jorge E

2018-06-08

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.

Covariant Derivatives and the Renormalization Group Equation

Science.gov (United States)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

Directory of Open Access Journals (Sweden)

Mehmet Ali Akinlar

2013-01-01

Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.

Three Interpretations of the Matrix Equation Ax = b

Science.gov (United States)

Larson, Christine; Zandieh, Michelle

2013-01-01

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

The usage of Maxwell fractional equations for the investigation of the waveguide processes

International Nuclear Information System (INIS)

Maksyuta, M.V.; Slinchenko, Yu.A.; Grygoruk, V.I.

2016-01-01

By means of nabla operator written down with using both of some differential operators with integer orders and fractional differential Caputo operators, gradient, divergence and rotor operators are determined, it is checked up the fulfillment of vector relations in fractional vector analysis, fractional Green, Stocks and Ostrogradsky-Gauss formulas. For a specific expression of nabla operator (nabla components along x and y axes have a unit order and along z axis, correspondingly, a fractional value in the interval from zero till unit) Maxwell fractional equations are written down. Based on the following from them some fractional wave equations, dissipative and polarization processes at electromagnetic waves distribution both in rectangular (planar) and in cylindrical waveguide structures are analyzed.

Acoustic energy harvesting using an electromechanical Helmholtz resonator.

Science.gov (United States)

Liu, Fei; Phipps, Alex; Horowitz, Stephen; Ngo, Khai; Cattafesta, Louis; Nishida, Toshikazu; Sheplak, Mark

2008-04-01

This paper presents the development of an acoustic energy harvester using an electromechanical Helmholtz resonator (EMHR). The EMHR consists of an orifice, cavity, and a piezoelectric diaphragm. Acoustic energy is converted to mechanical energy when sound incident on the orifice generates an oscillatory pressure in the cavity, which in turns causes the vibration of the diaphragm. The conversion of acoustic energy to electrical energy is achieved via piezoelectric transduction in the diaphragm of the EMHR. Moreover, the diaphragm is coupled with energy reclamation circuitry to increase the efficiency of the energy conversion. Lumped element modeling of the EMHR is used to provide physical insight into the coupled energy domain dynamics governing the energy reclamation process. The feasibility of acoustic energy reclamation using an EMHR is demonstrated in a plane wave tube for two power converter topologies. The first is comprised of only a rectifier, and the second uses a rectifier connected to a flyback converter to improve load matching. Experimental results indicate that approximately 30 mW of output power is harvested for an incident sound pressure level of 160 dB with a flyback converter. Such power level is sufficient to power a variety of low power electronic devices.

MHD Kelvin-Helmholtz instability in non-hydrostatic equilibrium

International Nuclear Information System (INIS)

Laghouati, Y; Bouabdallah, A; Zizi, M; Alemany, A

2007-01-01

The present work deals with the linear stability of a magnetohydrodynamic shear flow so that a stratified inviscid fluid rotating about a vertical axis when a uniform magnetic field is applied in the direction of the streaming or zonal flow. In geophysical flow, the stability of the flow is determined by taking into account the nonhydrostatic condition depending on Richardson number R i and the deviation δ from hydrostatic equilibrium. According to Stone (Stone P H 1971 J. Fluid. Mech. 45 659), it is shown that such deviation δ decreases the growth rates of three kinds of instability which can appear as geostrophic (G), symmetric (S) and Kelvin-Helmholtz (K-H) instabilities. To be specific, the evolution of the flow is therefore considered in the light of the influence of magnetic field, particularly, on K-H instability. The results of this study are presented by the linear stability of a magnetohydrodynamic, with horizontal free-shear flow of stratified fluid, subject to rotation about the vertical axis and uniform magnetic field in the zonal direction. Results are discussed and compared to previous works as Chandrasekhar (Chandrasekhar S 1961 Hydrodynamic and hydromagnetic stability (Oxford: Clarendon Press) chapter 11 pp 481-513) and Stone

Anomaly equations and the persistent mass condition

International Nuclear Information System (INIS)

Cohen, E.; Frishman, Y.

1982-01-01

Vector SU(Nsub(c)) gauge theories with nsub(f) flavors in the fundamental representation are considered. We prove that if the persistent mass condition is assumed, the two anomaly equations are identical and flavor independent for nsub(f) >= 3. Integer solutions exist only for nsub(f) = 2. The necessity of a separate discussion for 2 <= nsub(f) <= Nsub(c) is explained. (orig.)

Graphical Approach to Fresnel's Equations for Reflection and Refraction of Light.

Science.gov (United States)

Doyle, William T.

1980-01-01

Develops a coordinate-free approach to Fresnel's equations for the reflection and refraction of light at a plane interface. Describes a graphical construction for finding the vector amplitudes of the reflected and transmitted waves. (Author/CS)

Modified Einstein and Navier–Stokes Equations

Science.gov (United States)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Modified Einstein and Navier-Stokes Equations

Science.gov (United States)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

The Cauchy problem for non-linear Klein-Gordon equations

International Nuclear Information System (INIS)

Simon, J.C.H.; Taflin, E.

1993-01-01

We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)

Efficient solution of parabolic equations by Krylov approximation methods

Science.gov (United States)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Structure and properties of Hughston's stochastic extension of the Schroedinger equation

International Nuclear Information System (INIS)

Adler, Stephen L.; Horwitz, Lawrence P.

2000-01-01

Hughston has recently proposed a stochastic extension of the Schroedinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics. (c) 2000 American Institute of Physics

Interactions between two magnetohydrodynamic Kelvin-Helmholtz instabilities

International Nuclear Information System (INIS)

Lai, S. H.; Ip, W.-H.

2011-01-01

Kelvin-Helmholtz instability (KHI) driven by velocity shear is a generator of waves found away from the vicinity of the velocity-shear layers since the fast-mode waves radiated from the surface perturbation can propagate away from the transition layer. Thus the nonlinear evolution associated with KHI is not confined near the velocity-shear layer. To understand the physical processes in multiple velocity-shear layers, the interactions between two KHIs at a pair of tangential discontinuities are studied by two-dimensional magnetohydrodynamic simulations. It is shown that the interactions between two neighboring velocity-shear layers are dominated by the propagation of the fast-mode waves radiated from KHIs in a nonuniform medium. That is, the fast-mode Mach number of the surface waves M Fy , a key factor of the nonlinear evolution of KHI, will vary with the nonuniform background plasma velocity due to the existence of two neighboring velocity-shear layers. As long as the M Fy observed in the plasma rest frame across the neighboring velocity-shear layer is larger than one, newly formed fast-mode Mach-cone-like (MCL) plane waves generated by the fast-mode waves can be found in this region. As results of the interactions of two KHIs, reflection and distortion of the MCL plane waves generate the turbulence and increase the plasma temperature, which provide possible mechanisms of heating and accelerating local plasma between two neighboring velocity-shear layers.

Slackline dynamics and the Helmholtz-Duffing oscillator

Science.gov (United States)

Athanasiadis, Panos J.

2018-01-01

Slacklining is a new, rapidly expanding sport, and understanding its physics is paramount for maximizing fun and safety. Yet, compared to other sports, very little has been published so far on slackline dynamics. The equations of motion describing a slackline are fundamentally nonlinear, and assuming linear elasticity, they lead to a form of the Duffing equation. Following this approach, characteristic examples of slackline motion are simulated, including trickline bouncing, leash falls and longline surfing. The time-dependent solutions of the differential equations describing the system are acquired by numerical integration. A simple form of energy dissipation (linear drag) is added in some cases. It is recognized in this study that geometric nonlinearity is a fundamental aspect characterizing the dynamics of slacklines. Sports, and particularly slackline, is an excellent way of engaging young people with physics. A slackline is a simple yet insightful example of a nonlinear oscillator. It is very easy to model in the laboratory, as well as to rig and try on a university campus. For instructive purposes, its behaviour can be explored by numerically integrating the respective equations of motion. A form of the Duffing equation emerges naturally in the analysis and provides a powerful introduction to nonlinear dynamics. The material is suitable for graduate students and undergraduates with a background in classical mechanics and differential equations.

Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces

Directory of Open Access Journals (Sweden)

Gia Avalishvili

2016-01-01

Full Text Available Nonclassical problem for ultraparabolic equation with nonlocal initial condition with respect to one time variable is studied in abstract Hilbert spaces. We define the space of square integrable vector-functions with values in Hilbert spaces corresponding to the variational formulation of the nonlocal problem for ultraparabolic equation and prove trace theorem, which allows one to interpret initial conditions of the nonlocal problem. We obtain suitable a priori estimates and prove the existence and uniqueness of solution of the nonclassical problem and continuous dependence upon the data of the solution to the nonlocal problem. We consider an application of the obtained abstract results to nonlocal problem for ultraparabolic partial differential equation with second-order elliptic operator and obtain well-posedness result in Sobolev spaces.

Superfield generating equation of field-antifield formalism as a hyper-gauge theory

Energy Technology Data Exchange (ETDEWEB)

Batalin, Igor A. [P.N. Lebedev Physics Institute, Moscow (Russian Federation); Tomsk State Pedagogical University, Tomsk (Russian Federation); Lavrov, Peter M. [Tomsk State Pedagogical University, Tomsk (Russian Federation); National Research Tomsk State University, Tomsk (Russian Federation)

2017-02-15

Within a superfield approach, we formulate a simple quantum generating equation of the field-antifield formalism. Then we derive the Schroedinger equation with the Hamiltonian whose Δ-exact part serves as a generator to the quantum master transformations. We show that these generators do satisfy a nice composition law in terms of the quantum antibrackets. We also present an Sp(2) symmetric extension to the main construction, with specific features caused by the principal fact that all basic equations become Sp(2) vector-valued ones. (orig.)

Euler's fluid equations: Optimal control vs optimization

International Nuclear Information System (INIS)

Holm, Darryl D.

2009-01-01

An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.

Chiral equations and fiber bundles

International Nuclear Information System (INIS)

Mateos, T.; Becerril, R.

1992-01-01

Using the hypothesis g = g (lambda i ), the chiral equations (rhog, z g -1 ), z -bar + (rhog, z -barg -1 ), z = 0 are reduced to a Killing equation of a p-dimensional space V p , being lambda i lambda i (z, z-bar) 'geodesic' parameters of V p . Supposing that g belongs to a Lie group G, one writes the corresponding Lie algebra elements (F) in terms of the Killing vectors of V p and the generators of the subalgebra of F of dimension d = dimension of the Killing space. The elements of the subalgebras belong to equivalence classes which in the respective group form a principal fiber bundle. This is used to integrate the matrix g in terms of the complex variables z and z-bar ( Author)

On the relation between the Einstein field equations and the Jacobi–Ricci–Bianchi system

International Nuclear Information System (INIS)

Van den Bergh, N

2013-01-01

The 1 + 3 covariant equations, embedded in an extended tetrad formalism and describing a spacetime with an arbitrary energy–momentum distribution, are reconsidered. It is shown that, provided the 1 + 3 splitting is performed with respect to a generic time-like congruence with a tangent vector u, the Einstein field equations can be regarded as the integrability conditions for the Jacobi and Bianchi equations together with the Ricci equations for u. The same conclusion holds for a generic null congruence in the Newman–Penrose framework. (paper)

Using trees to compute approximate solutions to ordinary differential equations exactly

Science.gov (United States)

Grossman, Robert

1991-01-01

Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.

Anisotropic cosmological solutions in massive vector theories

Energy Technology Data Exchange (ETDEWEB)

Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji, E-mail: Lavinia.heisenberg@googlemail.com, E-mail: r.kase@rs.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)

2016-11-01

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v {sup 2} || φ{sup 2} are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w {sub DE} in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w {sub DE}{sup (iso)} typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

Anisotropic cosmological solutions in massive vector theories

International Nuclear Information System (INIS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-01-01

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v 2 || φ 2 are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w DE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w DE (iso) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

Fast computation of the characteristics method on vector computers

International Nuclear Information System (INIS)

Kugo, Teruhiko

2001-11-01

Fast computation of the characteristics method to solve the neutron transport equation in a heterogeneous geometry has been studied. Two vector computation algorithms; an odd-even sweep (OES) method and an independent sequential sweep (ISS) method have been developed and their efficiency to a typical fuel assembly calculation has been investigated. For both methods, a vector computation is 15 times faster than a scalar computation. From a viewpoint of comparison between the OES and ISS methods, the followings are found: 1) there is a small difference in a computation speed, 2) the ISS method shows a faster convergence and 3) the ISS method saves about 80% of computer memory size compared with the OES method. It is, therefore, concluded that the ISS method is superior to the OES method as a vectorization method. In the vector computation, a table-look-up method to reduce computation time of an exponential function saves only 20% of a whole computation time. Both the coarse mesh rebalance method and the Aitken acceleration method are effective as acceleration methods for the characteristics method, a combination of them saves 70-80% of outer iterations compared with a free iteration. (author)

Differential Equations and Computational Simulations

Science.gov (United States)

1999-06-18

given in (6),(7) in Taylor series of e. Equating coefficients of same power of e in both side of equity , we obtain a sequence of linear boundary value...fields, 3). structural instability and block stability of divergence-free vector fields on 2D compact manifolds with nonzero genus , and 4). structural...circle bands. Definition 3.1 Let N be a compact manifold without boundary and with genus k > 0. A closed domain fi C N is called a pseudo-manifold

Determination of multiple solutions of load flow equations

Indian Academy of Sciences (India)

This paper is concerned with the problem of finding all the real solutions (all components of the solution vector must be real values) of load flow equations. Solutions in which some of the components are complex values are of no interest as they have no physical significance as a load flow solution. This problem issignificant ...

Spinors, tensors and the covariant form of Dirac's equation

International Nuclear Information System (INIS)

Chen, W.Q.; Cook, A.H.

1986-01-01

The relations between tensors and spinors are used to establish the form of the covariant derivative of a spinor, making use of the fact that certain bilinear combinations of spinors are vectors. The covariant forms of Dirac's equation are thus obtained and examples in specific coordinate systems are displayed. (author)

Green`s function of Maxwell`s equations and corresponding implications for iterative methods

Energy Technology Data Exchange (ETDEWEB)

Singer, B.S. [Macquarie Univ., Sydney (Australia); Fainberg, E.B. [Inst. of Physics of the Earth, Moscow (Russian Federation)

1996-12-31

Energy conservation law imposes constraints on the norm and direction of the Hilbert space vector representing a solution of Maxwell`s equations. In this paper, we derive these constrains and discuss the corresponding implications for the Green`s function of Maxwell`s equations in a dissipative medium. It is shown that Maxwell`s equations can be reduced to an integral equation with a contracting kernel. The equation can be solved using simple iterations. Software based on this algorithm have successfully been applied to a wide range of problems dealing with high contrast models. The matrix corresponding to the integral equation has a well defined spectrum. The equation can be symmetrized and solved using different approaches, for instance one of the conjugate gradient methods.

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

International Nuclear Information System (INIS)

Chang, Jing; Gao, Yixian; Li, Yong

2015-01-01

Consider the one dimensional nonlinear beam equation u tt + u xxxx + mu + u 3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.