Iterative solution of the Helmholtz equation
Energy Technology Data Exchange (ETDEWEB)
Larsson, E.; Otto, K. [Uppsala Univ. (Sweden)
1996-12-31
We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.
Reconstruction of extended sources for the Helmholtz equation
Kress, Rainer; Rundell, William
2013-01-01
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
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei
2012-07-01
We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.
Thin-Layer Solutions of the Helmholtz and Related Equations
Ockendon, J. R.
2012-01-01
This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.
Bistable dark solitons of a cubic-quintic Helmholtz equation
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2010-01-01
We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
Semi-analytic solution to planar Helmholtz equation
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Tukač M.
2013-06-01
Full Text Available Acoustic solution of interior domains is of great interest. Solving acoustic pressure fields faster with lower computational requirements is demanded. A novel solution technique based on the analytic solution to the Helmholtz equation in rectangular domain is presented. This semi-analytic solution is compared with the finite element method, which is taken as the reference. Results show that presented method is as precise as the finite element method. As the semi-analytic method doesn’t require spatial discretization, it can be used for small and very large acoustic problems with the same computational costs.
Reconstruction of extended sources for the Helmholtz equation
International Nuclear Information System (INIS)
Kress, Rainer; Rundell, William
2013-01-01
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. (paper)
Reconstruction of extended sources for the Helmholtz equation
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.
A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
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.
Transmission problems for the Helmholtz equation for a rectilinear-circular lune
Directory of Open Access Journals (Sweden)
Volodymyr Denysenko
2007-01-01
Full Text Available The question related to the construction of the solution of plane transmission problem for the Helmholtz equation in a rectilinear-circular lune is considered. An approach is proposed based on the method of partial domains and the principle of reflection for the solutions of the Helmholtz equation through the segment.
DEFF Research Database (Denmark)
Reck, Kasper; Thomsen, Erik Vilain; Hansen, Ole
2011-01-01
. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution......The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method...
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
Implicit Boundary Integral Methods for the Helmholtz Equation in Exterior Domains
2016-06-01
solve the Helmholtz equation as ∂Ω goes through significant change in its shape and topology — applications for which implicit representation of the...boundary-value problems for the wave equation and maxwell’s equations. Russian Math . Surv., 1965. [16] S. Reutskiy. The method of fundamental
Two numerical methods for an inverse problem for the 2-D Helmholtz equation
Gryazin, Y A; Lucas, T R
2003-01-01
Two solution methods for the inverse problem for the 2-D Helmholtz equation are developed, tested, and compared. The proposed approaches are based on a marching finite-difference scheme which requires the solution of an overdetermined system at each step. The preconditioned conjugate gradient method is used for rapid solutions of these systems and an efficient preconditioner has been developed for this class of problems. Underlying target applications include the imaging of land mines, unexploded ordinance, and pollutant plumes in environmental cleanup sites, each formulated as an inverse problem for a 2-D Helmholtz equation. The images represent the electromagnetic properties of the respective underground regions. Extensive numerical results are presented.
First-order system least-squares for the Helmholtz equation
Energy Technology Data Exchange (ETDEWEB)
Lee, B.; Manteuffel, T.; McCormick, S.; Ruge, J.
1996-12-31
We apply the FOSLS methodology to the exterior Helmholtz equation {Delta}p + k{sup 2}p = 0. Several least-squares functionals, some of which include both H{sup -1}({Omega}) and L{sup 2}({Omega}) terms, are examined. We show that in a special subspace of [H(div; {Omega}) {intersection} H(curl; {Omega})] x H{sup 1}({Omega}), each of these functionals are equivalent independent of k to a scaled H{sup 1}({Omega}) norm of p and u = {del}p. This special subspace does not include the oscillatory near-nullspace components ce{sup ik}({sup {alpha}x+{beta}y)}, where c is a complex vector and where {alpha}{sub 2} + {beta}{sup 2} = 1. These components are eliminated by applying a non-standard coarsening scheme. We achieve this scheme by introducing {open_quotes}ray{close_quotes} basis functions which depend on the parameter pair ({alpha}, {beta}), and which approximate ce{sup ik}({sup {alpha}x+{beta}y)} well on the coarser levels where bilinears cannot. We use several pairs of these parameters on each of these coarser levels so that several coarse grid problems are spun off from the finer levels. Some extensions of this theory to the transverse electric wave solution for Maxwell`s equations will also be presented.
DEFF Research Database (Denmark)
Miansari, Mo; Miansari, Me; Barari, Amin
2009-01-01
In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...
Directory of Open Access Journals (Sweden)
Ya-Juan Hao
2013-01-01
Full Text Available The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.
Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Sigmund, Ole
2009-01-01
The focus of the study in this article is on the use of a Helmholtz type differential equation as a filter for topology optimisation problems. Until now various filtering schemes have been utilised in order to impose mesh independence in this type of problems. The usual techniques require topology...... information about the neighbour sub-domains is an expensive operation. The proposed filtering technique requires only mesh information necessary for the finite element discretisation of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz type differential...... equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimisation problems in linear elasticity, solved on sequential and parallel computers....
Optimal 25-Point Finite-Difference Subgridding Techniques for the 2D Helmholtz Equation
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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.
On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
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.
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
Inverse random source scattering for the Helmholtz equation in inhomogeneous media
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.
Numerical solution of the helmholtz equation for the superellipsoid via the galerkin method
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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 .
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.
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.
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...
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
Vector domain decomposition schemes for parabolic equations
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.
On Helmholtz Problem for Plane Periodical Structures
International Nuclear Information System (INIS)
Akishin, P.G.; Vinitskij, S.I.
1994-01-01
The plane Helmholtz problem of the periodical disc structures with the phase shifts conditions of the solutions along the basis lattice vectors and the Dirichlet conditions on the basic boundaries is considered. The Green function satisfying the quasi periodical conditions on the lattice is constructed. The Helmholtz problem is reduced to the boundary integral equations for the simple layer potentials of this Green function. The methods of the discretization of the arising integral equations are proposed. The procedures of calculation of the matrix elements are discussed. The reality of the spectral parameter of the nonlinear continuous and discretized problems is shown. 8 refs., 2 figs
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.
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
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.
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
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.
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)
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.
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
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)
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 ...
Modern solvers for Helmholtz problems
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...
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.
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.
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.
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)
Maxwell Equations and the Redundant Gauge Degree of Freedom
Wong, Chun Wa
2009-01-01
On transformation to the Fourier space (k,[omega]), the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the…
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
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.
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.
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.
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
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
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
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.
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.
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.
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.
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
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.
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
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
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.
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.
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)
Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments
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
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
The Helmholtz Hierarchy: Phase Space Statistics of Cold Dark Matter
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...
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.
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
2013 CIME Course Vector-valued Partial Differential Equations and Applications
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.
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
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.
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
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.
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.
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)
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.
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.
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
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
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined......This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...
A vector field method on the distorted Fourier side and decay for wave equations with potentials
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).
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
Characterizing permanent magnet blocks with Helmholtz coils
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.
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.
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
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)
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.
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
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)
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
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)
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 ...
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.
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.
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.
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
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.
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
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.
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.
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.
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
Helmholtz and the psychophysiology of time.
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.
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
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.
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.
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.
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
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...
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)
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.
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
The Helmholtz legacy in physiological acoustics
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 ...
Capillary and viscous perturbations to Helmholtz flows
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.Â 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
Moore, M. R.
2014-02-21
Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p.Â 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.
A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
Poulson, Jack; Engquist, Bjö rn; Li, Siwei; Ying, Lexing
2013-01-01
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
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris; Darve, Eric
2013-01-01
bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
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.
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.
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)
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.
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.
An efficient Helmholtz solver for acoustic transversely isotropic media
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
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.
Gicquaud, Romain; Huneau, Cécile
2016-09-01
We construct solutions to the constraint equations in general relativity using the limit equation criterion introduced in Dahl et al. (2012). We focus on solutions over compact 3-manifolds admitting a S1-symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results.
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr nonlinearity, are shown to reduce...... the properties of Maxwell's equations in nonlinear optics, without resorting to the commonly used nonlinear Schr\\"odinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to nonlinear sideband wave interactions. This is important in femto......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...
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
Can Hall effect trigger Kelvin-Helmholtz instability in sub-Alfvénic flows?
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.
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
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.
Simulation of Helmholtz Resonance Effects in Aircraft ECS
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...
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.
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)
International Nuclear Information System (INIS)
Majumdar, A.; Makowitz, H.
1987-10-01
With the development of modern vector/parallel supercomputers and their lower performance clones it has become possible to increase computational performance by several orders of magnitude when comparing to the previous generation of scalar computers. These performance gains are not observed when production versions of current thermal-hydraulic codes are implemented on modern supercomputers. It is our belief that this is due in part to the inappropriateness of using old thermal-hydraulic algorithms with these new computer architectures. We believe that a new generation of algorithms needs to be developed for thermal-hydraulics simulation that is optimized for vector/parallel architectures, and not the scalar computers of the previous generation. We have begun a study that will investigate several approaches for designing such optimal algorithms. These approaches are based on the following concepts: minimize recursion; utilize predictor-corrector iterative methods; maximize the convergence rate of iterative methods used; use physical approximations as well as numerical means to accelerate convergence; utilize explicit methods (i.e., marching) where stability will permit. We call this approach the ''EPIC'' methodology (i.e., Explicit Predictor Iterative Corrector methods). Utilizing the above ideas, we have begun our work by investigating the one-dimensional transient heat conduction equation. We have developed several algorithms based on variations of the Hopscotch concept, which we discuss in the body of this report. 14 refs
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
Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering
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
Solution of the General Helmholtz Equation Starting from Laplace’s Equation
2002-11-01
infinity for the two dimensional case. For the 3D the general form case, this term does not exist, as the potential at infinity is zero. Hence the Green’s...companies. She has assisted the Comisi6n the Living System Laboratory, Interministerial de Ciencia y Tecnologia (National LG Electronics, From 1998 to 2000
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.
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
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
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
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)
Increase in effectiveness of low frequency acoustic liners by use of coupled Helmholtz resonators
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.
The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity
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.
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
Voluntarism in early psychology: the case of Hermann von Helmholtz.
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.
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)
Kelvin-Helmholtz instability in a weakly ionized layer
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...
Symbolic computer vector analysis
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.
A new iterative solver for the time-harmonic wave equation
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
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.
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
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.
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.
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.
Kelvin-Helmholtz Instability: Lessons Learned and Ways Forward
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.
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
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.
Helmholtz and Goethe -- controversies at the birth of modern neuroscience.
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.
Another Look at Helmholtz's Model for the Gravitational Contraction of the Sun
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…
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
Global Simulations of the Asymmetry in Forming Kelvin-Helmholtz Instability at Mercury
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.
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
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...
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...
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.
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
Directory of Open Access Journals (Sweden)
Hao Li
2016-01-01
Full Text Available 1,1,1,2,3,3,3-Heptafluoropropane (R227ea is a good refrigerant that reduces greenhouse effects and ozone depletion. In practical applications, we usually have to know the compressed liquid densities at different temperatures and pressures. However, the measurement requires a series of complex apparatus and operations, wasting too much manpower and resources. To solve these problems, here, Song and Mason equation, support vector machine (SVM, and artificial neural networks (ANNs were used to develop theoretical and machine learning models, respectively, in order to predict the compressed liquid densities of R227ea with only the inputs of temperatures and pressures. Results show that compared with the Song and Mason equation, appropriate machine learning models trained with precise experimental samples have better predicted results, with lower root mean square errors (RMSEs (e.g., the RMSE of the SVM trained with data provided by Fedele et al. [1] is 0.11, while the RMSE of the Song and Mason equation is 196.26. Compared to advanced conventional measurements, knowledge-based machine learning models are proved to be more time-saving and user-friendly.
Newell, Homer E
2006-01-01
When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts.Part I, the basic portion of the text, consists of a thorough treatment of vector algebra and the vector calculus. Part II presents the illustrative matter, demonstrating applications to kinematics, mechanics, and e
Hoffmann, Banesh
1975-01-01
From his unusual beginning in ""Defining a vector"" to his final comments on ""What then is a vector?"" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar p
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)
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.
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)
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
The Determinate World Kant and Helmholtz on the Physical Meaning of Geometry
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.
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
Introduction to matrices and vectors
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.
International Nuclear Information System (INIS)
Jin Yaqiu; Liang Zichang
2005-01-01
To solve the 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both vertical z and transversal (x,y) directions, to form very thin multi-boxes. The zeroth order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to derive high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer resolutions from inhomogeneous scatter model such as vegetation canopy and alien target beneath canopy are simulated and discussed
A Two-Dimensional Helmholtz Equation Solution for the Multiple Cavity Scattering Problem
2013-02-01
obtained by using the block Gauss – Seidel iterative meth- od. To show the convergence of the iterative method, we define the error between two...models to the general multiple cavity setting. Numerical examples indicate that the convergence of the Gauss – Seidel iterative method depends on the...variational approach. A block Gauss – Seidel iterative method is introduced to solve the cou- pled system of the multiple cavity scattering problem, where
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
2015-03-31
2.52) by finite differences, see Section 3.1.1. Building the matrix QH of (3.22) that enters into the BEP (3.4) (or, in the inhomogeneous case , (3.5...necessary for this study , but it may in some cases be convenient to allow the power series to have a more general form in which the exponent of r is...from this error estimate the tolerance σ can be set. The numerical case study of Section 5.2.2 provides evidence that taking σ equal to the overall
Knibbe, H.P.
2015-01-01
The oil and gas industry makes use of computational intensive algorithms to provide an image of the subsurface. The image is obtained by sending wave energy into the subsurface and recording the signal required for a seismic wave to reflect back to the surface from the Earth interfaces that may have
Fractional Vector Calculus and Fractional Special Function
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.
Coupled Kelvin-Helmholtz and Tearing Mode Instabilities at the Mercury's Magnetopause
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.
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...
Acoustic energy harvesting using an electromechanical Helmholtz resonator.
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.
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 evolution in subsonic cold streams feeding galaxies
Angulo, Adrianna; Coffing, S.; Kuranz, C.; Drake, R. P.; Klein, S.; Trantham, M.; Malamud, G.
2017-10-01
The most prolific star formers in cosmological history lie in a regime where dense filament structures carried substantial mass into the galaxy to sustain star formation without producing a shock. However, hydrodynamic instabilities present on the filament surface limit the ability of such structures to deliver dense matter deeply enough to sustain star formation. Simulations lack the finite resolution necessary to allow fair treatment of the instabilities present at the stream boundary. Using the Omega EP laser, we simulate this mode of galaxy formation with a cold, dense, filament structure within a hotter, subsonic flow and observe the interface evolution. Machined surface perturbations stimulate the development of the Kelvin-Helmholtz (KH) instability due to the resultant shear between the two media. A spherical crystal imaging system produces high-resolution radiographs of the KH structures along the filament surface. The results from the first experiments of this kind, using a rod with single-mode, long-wavelength modulations, will be discussed. This work is funded by the U.S. Department of Energy, through the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, Grant Number DE-NA0002956, and the National Laser User Facility Program, Grant Number DE-NA0002719, and through.
Reconstruction of propagating Kelvin-Helmholtz vortices at Mercury's magnetopause
Sundberg, Torbjörn; Boardsen, Scott A.; Slavin, James A.; Blomberg, Lars G.; Cumnock, Judy A.; Solomon, Sean C.; Anderson, Brian J.; Korth, Haje
2011-12-01
A series of quasi-periodic magnetopause crossings were recorded by the MESSENGER spacecraft during its third flyby of Mercury on 29 September 2009, likely caused by a train of propagating Kelvin-Helmholtz (KH) vortices. We here revisit the observations to study the internal structure of the waves. Exploiting MESSENGER's rapid traversal of the magnetopause, we show that the observations permit a reconstruction of the structure of a rolled-up KH vortex directly from the spacecraft's magnetic field measurements. The derived geometry is consistent with all large-scale fluctuations in the magnetic field data, establishes the non-linear nature of the waves, and shows their vortex-like structure. In several of the wave passages, a reduction in magnetic field strength is observed in the middle of the wave, which is characteristic of rolled-up vortices and is related to the increase in magnetic pressure required to balance the centrifugal force on the plasma in the outer regions of a vortex, previously reported in computer simulations. As the KH wave starts to roll up, the reconstructed geometry suggests that the vortices develop two gradual transition regions in the magnetic field, possibly related to the mixing of magnetosheath and magnetospheric plasma, situated at the leading edges from the perspectives of both the magnetosphere and the magnetosheath.
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
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.
Kelvin-Helmholtz instability: the ``atom'' of geophysical turbulence?
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.
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.
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.
Incompressible spectral-element method: Derivation of equations
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.
1989-04-13
DIMENSION HXU(N),HXV(NI), HYU (N),HYV(N) DIMENSION AA(N),AC(N),CC(N) DIMENSION Tl(N),T2(N),T3(N),T4(N) DIMENSION DUM3(M,N) C SET COEFFICIENTS OF DIFFERENCE...DELXSQ=DELX*DELX DELYSQ=DELY*DELY C DEFINE MAP FACTORS DO 10 J=1,N HXU(J)=COS(Y(J)/AR) HYU (J)=I.O 10 CONTINUE 31 DO 20 J-1,Nl HXV(J)-0.5*(HXU(J)+HXU(J+l...L.H.S. OF DIFFERENCE EQUATION. C COEFFICIENTS DEFINED IN INTERIOR OF DOMAIN ONLY. DO 25 J=2,N-1, AA(J)=( (HXU(J)*HXV(J-1) )/I(HYV(J.-1)* HYU (J
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.
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.
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.
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.
Brand, Louis
2006-01-01
The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brou
DEFF Research Database (Denmark)
2012-01-01
The present invention relates to a compact, reliable and low-cost vector velocimeter for example for determining velocities of particles suspended in a gas or fluid flow, or for determining velocity, displacement, rotation, or vibration of a solid surface, the vector velocimeter comprising a laser...
Slackline dynamics and the Helmholtz-Duffing oscillator
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.
From Helmholtz to Schlick: The evolution of the sign-theory of perception.
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.
Reciprocity in Vector Acoustics
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
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.
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
Guilfoyle, Richard A.; Smith, Lloyd M.
1994-01-01
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site.
Guilfoyle, R.A.; Smith, L.M.
1994-12-27
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site. 2 figures.
Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering
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.
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
Levine, Robert
2004-01-01
The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…
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.''
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.
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
Prominence Bubble Shear Flows and the Coupled Kelvin-Helmholtz — Rayleigh-Taylor Instability
Berger, Thomas; Hillier, Andrew
2017-08-01
Prominence bubbles are large arched structures that rise from below into quiescent prominences, often growing to heights on the order of 10 Mm before going unstable and generating plume upflows. While there is general agreement that emerging flux below pre-existing prominences causes the structures, there is lack of agreement on the nature of the bubbles and the cause of the instability flows. One hypothesis is that the bubbles contain coronal temperature plasma and rise into the prominence above due to both magnetic and thermal buoyancy, eventually breaking down via a magnetic Rayleigh-Taylor (RT) instability to release hot plasma and magnetic flux and helicity into the overlying coronal flux rope. Another posits that the bubbles are actually just “arcades” in the prominence indicating a magnetic separator line between the bipole and the prominence fields with the observed upflows and downflows caused by reconnection along the separator. We analyze Hinode/SOT, SDO/AIA, and IRIS observations of prominence bubbles, focusing on characteristics of the bubble boundary layers that may discriminate between the two hypotheses. We find speeds on the order of 10 km/s in prominence plasma downflows and lateral shear flows along the bubble boundary. Inflows to the boundary gradually increase the thickness and brightness of the layer until plasma drains from there, apparently around the dome-like bubble domain. In one case, shear flow across the bubble boundary develops Kelvin-Helmholtz (KH) vortices that we use to infer flow speeds in the low-density bubble on the order of 100 km/sec. IRIS spectra indicate that plasma flows on the bubble boundary at transition region temperatures achieve Doppler speeds on the order of 50 km/s, consistent with this inference. Combined magnetic KH-RT instability analysis leads to flux density estimates of 10 G with a field angle of 30° to the prominence, consistent with vector magnetic field measurements. In contrast, we find no evidence
Introduction to partial differential equations with applications
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.
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.
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)
Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
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.
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.
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
A third note: Helmholtz, Palestrina, and the Early History of Musicology
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
Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective
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.
Gauge anomaly with vector and axial-vector fields in 6D curved space
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.
Problems and worked solutions in vector analysis
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
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
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
Thomas, E. G. F.
2012-01-01
This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving
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
An introduction to vectors, vector operators and vector analysis
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.
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).
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)
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.
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
Hamlin, Nathaniel D; Newman, William I
2013-04-01
We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon such schemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numerical discretization renders them unstable. We include numerical viscosity to restore numerical stability. In relativistic flows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in our KH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbed velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining unperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in the nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvénic Mach number M(A). We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, and intermediate turbulence
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.)
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.)
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.
A low frequency acoustic insulator by using the acoustic metasurface to a Helmholtz resonator
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.
Magnetized Kelvin-Helmholtz instability: theory and simulations in the Earth's magnetosphere context
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.
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 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
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)
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))
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)
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
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)
Real-time optical laboratory solution of parabolic differential equations
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.
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.
Toward lattice fractional vector calculus
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.
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.
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.
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
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.)
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
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
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
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
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
A generalized nonlocal vector calculus
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.
Reciprocity relationships in vector acoustics and their application to vector field calculations.
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.
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)
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.
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.
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.
A Third Note: Helmholtz, Palestrina, and the Early History of Musicology.
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.
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.
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
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.
Introduction to partial differential equations
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.
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
Raster images vectorization system
Genytė, Jurgita
2006-01-01
The problem of raster images vectorization was analyzed and researched in this work. Existing vectorization systems are quite expensive, the results are inaccurate, and the manual vectorization of a large number of drafts is impossible. That‘s why our goal was to design and develop a new raster images vectorization system using our suggested automatic vectorization algorithm and the way to record results in a new universal vectorial file format. The work consists of these main parts: analysis...
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)
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
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
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.
Energy Technology Data Exchange (ETDEWEB)
Ferrari, A [Max-Planck-Institut fuer Extraterrestrische Physik, Garching b. Muenchen (Germany, F.R.); Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica); Trussoni, E; Zaninetti, L [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica
1981-09-01
This second paper of the series is devoted to Kelvin-Helmholtz instabilities in cylindrical boundary layer flows (jets). The vortex-sheet approximation is still used, and compressible flows are studied in subsonic, transonic, supersonic and relativistic regimes. Magnetic field effects are analysed, together with density contrast inside and outside the jet. The general result is that, due to the onset of a so-called reflection branch of resonant modes, jets are always unstable, both to pinching and helical perturbations with wavelengths of the order of the jet circumference. In particular the time-scales for instability are such that this certainly plays a significant part in the morphology and energetics of extended radio sources.
Sturner, A. P.; Eriksson, S.; Newman, D. L.; Lapenta, G.; Gershman, D. J.; Plaschke, F.; Ergun, R.; Wilder, F. D.; Torbert, R. B.; Giles, B. L.; Strangeway, R. J.; Russell, C. T.; Burch, J. L.
2016-12-01
Kinetic simulations and observations of magnetic reconnection suggest the Hall term of Ohm's Law is necessary for understanding fast reconnection in the Earth's magnetosphere. During high (>1) guide field plasma conditions in the solar wind and in Earth's magnetopause, tripolar variations in the guide magnetic field are often observed during current sheet crossings, and have been linked to reconnection Hall magnetic fields. Two proposed mechanisms for these tripolar variations are the presence of multiple nearby X-lines and magnetic island coalescence. We present results of an investigation into the structure of the electron currents supporting tripolar guide magnetic field variations during Kelvin-Helmholtz wave current sheet crossings using the Magnetosphere Multiscale (MMS) Mission, and compare with bipolar magnetic field structures and with kinetic simulations to understand how these tripolar structures may be used as tracers for magnetic islands.
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)
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
Araujo, Saulo de Freitas
2014-02-01
Wilhelm Wundt's biography is one of the main domains in Wundt scholarship that deserves more detailed attention. The few existing biographical works present many problems, ranging from vagueness to chronological inaccuracies, among others. One of the important gaps concerns the so-called Heidelberg period (1852-1874), during which he went from being a medical student to holding a professorship at the University of Heidelberg. The aim of this article is to dispel a very common confusion in the secondary literature, which refers to Wundt's assistantship with Helmholtz at the Physiological Institute, by establishing the precise dates of his assistantship. Contrary to what is generally repeated in the secondary literature, the primary sources allow us to determine precisely this period from October 1858 to March 1865. I conclude by pointing out the indispensability of the primary sources not only to Wundt scholarship but also to the historiography of psychology in general.
Faganello, Matteo; Borgogno, Dario; Califano, Francesco; Pegoraro, Francesco
2015-11-01
In an almost collisionless MagnetoHydrodynamic plasma in a relatively strong magnetic field, stresses can be conveyed far from the region where they are exerted e.g., through the propagation of Alfvèn waves. The forced dynamics of line-tied magnetic structures in solar and stellar coronae is a paradigmatic case. We investigate how this action at a distance develops from the equatorial region of the Kelvin-Helmholtz unstable flanks of the Earth's magnetosphere leading to the onset, at mid latitude in both hemispheres, of correlated double magnetic field line reconnection events that can allow the solar wind plasma to enter the Earth's magnetosphere. This mid-latitude double reconnection process, first investigated in, has been confirmed here by following a large set of individual field lines using a method similar to a Poincarè map.
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.
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.
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
Directory of Open Access Journals (Sweden)
Mok Tik
2014-06-01
Full Text Available This study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.
Development of a Miniature, Two-Axis, Triple-Helmholtz-Driven Gimbal
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.
Blob Formation and Ejection in Coronal Jets due to the Plasmoid and Kelvin–Helmholtz Instabilities
Energy Technology Data Exchange (ETDEWEB)
Ni, Lei; Lin, Jun [Yunnan Observatories, Chinese Academy of Sciences, 396 Yangfangwang, Guandu District, Kunming, 650216 (China); Zhang, Qing-Min [Key Laboratory for Dark Matter and Space Science, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China); Murphy, Nicholas A., E-mail: leini@ynao.ac.cn [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 (United States)
2017-05-20
We perform 2D resistive magnetohydrodynamic simulations of coronal jets driven by flux emergence along the lower boundary. The reconnection layers are susceptible to the formation of blobs that are ejected in the jet. Our simulation with low plasma β (Case I) shows that magnetic islands form easily and propagate upward in the jet. These islands are multithermal and thus are predicted to show up in hot channels (335 Å and 211 Å) and the cool channel (304 Å) in observations by the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory . The islands have maximum temperatures of 8 MK, lifetimes of 120 s, diameters of 6 Mm, and velocities of 200 km s{sup −1}. These parameters are similar to the properties of blobs observed in extreme-ultraviolet (EUV) jets by AIA. The Kelvin–Helmholtz instability develops in our simulation with moderately high plasma β (Case II) and leads to the formation of bright vortex-like blobs above the multiple high magnetosonic Mach number regions that appear along the jet. These vortex-like blobs can also be identified in the AIA channels. However, they eventually move downward and disappear after the high magnetosonic Mach number regions disappear. In the lower plasma β case, the lifetime for the jet is shorter, the jet and magnetic islands are formed with higher velocities and temperatures, the current-sheet fragments are more chaotic, and more magnetic islands are generated. Our results show that the plasmoid instability and Kelvin–Helmholtz instability along the jet are both possible causes of the formation of blobs observed at EUV wavelengths.
Acoustic response of Helmholtz dampers in the presence of hot grazing flow
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.
Modeling animal movements using stochastic differential equations
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...
Structural Equation Modeling of Multivariate Time Series
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…
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)
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.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Fractional vector calculus for fractional advection dispersion
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.
Students' Difficulties with Vector Calculus in Electrodynamics
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…
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...
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.)
U.S. Department of Health & Human Services — VectorBase is a Bioinformatics Resource Center for invertebrate vectors. It is one of four Bioinformatics Resource Centers funded by NIAID to provide web-based...
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....
Generalization of concurrence vectors
International Nuclear Information System (INIS)
Yu Changshui; Song Heshan
2004-01-01
In this Letter, based on the generalization of concurrence vectors for bipartite pure state with respect to employing tensor product of generators of the corresponding rotation groups, we generalize concurrence vectors to the case of mixed states; a new criterion of separability of multipartite pure states is given out, for which we define a concurrence vector; we generalize the vector to the case of multipartite mixed state and give out a good measure of free entanglement
Ebrahimi, Javad; Fragouli, Christina
2010-01-01
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L X L coding matrices that play a similar role as coding coefficients in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector co...
Vector Network Coding Algorithms
Ebrahimi, Javad; Fragouli, Christina
2010-01-01
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L x L coding matrices that play a similar role as coding c in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector coding, our algori...
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
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...
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.
Convexity and Marginal Vectors
van Velzen, S.; Hamers, H.J.M.; Norde, H.W.
2002-01-01
In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex.This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity.An other result is that
DEFF Research Database (Denmark)
Becciolini, Diego; Franzosi, Diogo Buarque; Foadi, Roshan
2015-01-01
We analyze the Large Hadron Collider (LHC) phenomenology of heavy vector resonances with a $SU(2)_L\\times SU(2)_R$ spectral global symmetry. This symmetry partially protects the electroweak S-parameter from large contributions of the vector resonances. The resulting custodial vector model spectrum...
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...
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.)
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
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)
Rotations with Rodrigues' vector
International Nuclear Information System (INIS)
Pina, E
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears to be a fundamental matrix that is used to express the components of the angular velocity, the rotation matrix and the angular momentum vector. The Hamiltonian formalism of rotational dynamics in terms of this vector uses the same matrix. The quantization of the rotational dynamics is performed with simple rules if one uses Rodrigues' vector and similar formal expressions for the quantum operators that mimic the Hamiltonian classical dynamics.
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)
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.
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
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.
Understanding Kelvin-Helmholtz instability in paraffin-based hybrid rocket fuels
Petrarolo, Anna; Kobald, Mario; Schlechtriem, Stefan
2018-04-01
Liquefying fuels show higher regression rates than the classical polymeric ones. They are able to form, along their burning surface, a low viscosity and surface tension liquid layer, which can become unstable (Kelvin-Helmholtz instability) due to the high velocity gas flow in the fuel port. This causes entrainment of liquid droplets from the fuel surface into the oxidizer gas flow. To better understand the droplets entrainment mechanism, optical investigations on the combustion behaviour of paraffin-based hybrid rocket fuels in combination with gaseous oxygen have been conducted in the framework of this research. Combustion tests were performed in a 2D single-slab burner at atmospheric conditions. High speed videos were recorded and analysed with two decomposition techniques. Proper orthogonal decomposition (POD) and independent component analysis (ICA) were applied to the scalar field of the flame luminosity. The most excited frequencies and wavelengths of the wave-like structures characterizing the liquid melt layer were computed. The fuel slab viscosity and the oxidizer mass flow were varied to study their influence on the liquid layer instability process. The combustion is dominated by periodic, wave-like structures for all the analysed fuels. Frequencies and wavelengths characterizing the liquid melt layer depend on the fuel viscosity and oxidizer mass flow. Moreover, for very low mass flows, no wavelength peaks are detected for the higher viscosity fuels. This is important to better understand and predict the onset and development of the entrainment process, which is connected to the amplification of the longitudinal waves.
Kelvin-Helmholtz instability in type-1 comet tails and associated phenomena
International Nuclear Information System (INIS)
Ershkovich, A.I.
1980-01-01
Selected problems of the solar wind - comet tail coupling that are currently accessible to quantitative analysis are reviewed. The model of a comet tail as a plasma cylinder separated by a tangential discontinuity surface from the solar wind is discussed in detail. This model is compatible with the well-known Alfven mechanism of formation of the comet tail. The stability problem of the comet tail boundary (considered as a discontinuity surface) is solved. Under typical conditions a comet tail boundary can undergo the Kelvin-Helmholtz instability. With finite amplitude the stabilizing effect of the magnetic field increases, and waves become stabilized. This model supplies a detailed quantitative description of helical waves observed in type-1 comet tails. A more general model of the tail boundary as a transition layer with a continuous change of the plasma parameters within it is also considered. This theory, in principle, enables us to solve one of the fundamental problems of cometary physics: the magnetic field of the comet tail can be derived from the observations of helical waves. This field turns out to be of the order of the interplanetary field. Various other considerations, discussed in this review also support this conclusion. (orig.)
Sutanto, E.; Chandra, F.; Dinata, R.
2017-05-01
Leakage current measurement which can follow IEC standard for medical device is one of many challenges to be answered. The IEC 60601-1 has defined that the limit for a leakage current for Medical Device can be as low as 10 µA and as high as 500 µA, depending on which type of contact (applied part) connected to the patient. Most people are using ELCB (Earth-leakage circuit breaker) for safety purpose as this is the most common and available safety device in market. One type of ELCB devices is RCD (Residual Current Device) and this RCD type can measure the leakage current directly. This work will show the possibility on how Helmholtz Coil Configuration can be made to be like the RCD. The possibility is explored by comparing the magnetic field formula from each device, then it proceeds with a simulation using software EJS (Easy Java Simulation). The simulation will make sure the concept of magnetic field current cancellation follows the RCD concept. Finally, the possibility of increasing the measurement’s sensitivity is also analyzed. The sensitivity is needed to see the possibility on reaching the minimum leakage current limit defined by IEC, 0.01mA.
Energy Technology Data Exchange (ETDEWEB)
Ferraro, A [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Max-Planck-Institut fuer Extraterrestrische Physik, Garching (Germany, F.R.)); Massaglia, S [Turin Univ. (Italy). Ist. di Fisica; Trussoni, E [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica
1982-03-01
In this paper a discussion is presented on Kelvin-Helmholtz instabilities in pressure-confined two-dimensional flows (slabs) delimited by boundary layers with velocity and density gradients. It is found that the fastest growing modes in supersonic flows are produced by perturbations reflecting at the boundaries and have wavelengths of the order of the slab width; this peak of instability is even more evident than in the case of vortex-sheet cylindrical flows, discussed in a previous paper. From a comparison of the results for the two-dimensional slab and three-dimensional cylinder it is concluded that a two-dimensional treatment provides an adequate description of instabilities in fluid flows. In this analogy, symmetric and antisymmetric modes in the slab correspond to pinching and helical modes in the cylinder. In the final section a comparison is attempted of the results obtained with morphologies in collimated jets in extragalactic radio sources; general characteristics appear to be classifiable in terms of scale-lengths of the velocity and density gradients in the boundary layers.
MESSENGER Orbital Observations of Large-Amplitude Kelvin-Helmholtz Waves at Mercury's Magnetopause
Sundberg, Torbjorn; Boardsen, Scott A.; Slavin, James A.; Anderson, Brian J.; Korth, Haje; Zurbuchen, Thomas H.; Raines, Jim M.; Solomon, Sean C.
2012-01-01
We present a survey of Kelvi\\ n-Helmholtz (KH) waves at Mercury's magnetopause during MESSENGER's first Mercury year in orb it. The waves were identified on the basis of the well-established sawtooth wave signatures that are associated with non-linear KH vortices at the magnetopause. MESSENGER frequently observed such KH waves in the dayside region of the magnetosphere where the magnetosheath flow velocity is still sub -sonic, which implies that instability growth rates at Mercury's magnetopau are much larger than at Earth. We attribute these greater rates to the limited wave energy dissipation in Mercury's highly resistive regolith. The wave amplitude was often on the order of ' 00 nT or more, and the wave periods were - 10- 20 s. A clear dawn-dusk asymmetry is present in the data, in that all of the observed wave events occurred in the post-noon and dusk-side sectors of the magnetopause. This asymmetry is like ly related to finite Larmor-radius effects and is in agreement with results from particle-in-cell simulations of the instability. The waves were observed almost exclusively during periods when the north-south component of the magnetosheath magnetic field was northward, a pattern similar to that for most terrestrial KH wave events. Accompanying plasma measurements show that the waves were associated with the transport of magnetosheath plasma into the magnetosphere.
Kieokaew, Rungployphan; Foullon, Claire; Lavraud, Benoit
2018-01-01
Four-spacecraft missions are probing the Earth's magnetospheric environment with high potential for revealing spatial and temporal scales of a variety of in situ phenomena. The techniques allowed by these four spacecraft include the calculation of vorticity and the magnetic curvature analysis (MCA), both of which have been used in the study of various plasma structures. Motivated by curved magnetic field and vortical structures induced by Kelvin- Helmholtz (KH) waves, we investigate the robustness of the MCA and vorticity techniques when increasing (regular) tetrahedron sizes, to interpret real data. Here for the first time, we test both techniques on a 2.5-D MHD simulation of KH waves at the magnetopause. We investigate, in particular, the curvature and flow vorticity across KH vortices and produce time series for static spacecraft in the boundary layers. The combined results of magnetic curvature and vorticity further help us to understand the development of KH waves. In particular, first, in the trailing edge, the magnetic curvature across the magnetopause points in opposite directions, in the wave propagation direction on the magnetosheath side and against it on the magnetospheric side. Second, the existence of a "turnover layer" in the magnetospheric side, defined by negative vorticity for the duskside magnetopause, which persists in the saturation phase, is reminiscent of roll-up history. We found significant variations in the MCA measures depending on the size of the tetrahedron. This study lends support for cross-scale observations to better understand the nature of curvature and its role in plasma phenomena.
Energy Technology Data Exchange (ETDEWEB)
Cowee, Misa M [Los Alamos National Laboratory; Winske, Dan [Los Alamos National Laboratory; Gary, S Peter [Los Alamos National Laboratory
2009-01-01
Two-dimensional hybrid (kinetic ions, massless fluid electrons) simulations of the Kelvin Helmholtz Instability (KHI) for a magnetopause configuration with a magnetic shear across the boundary are carried out to examine how the transport of magnetosheath plasma into the magnetosphere is affected by the shear field. Low magnetic shear conditions where the magnetosheath magnetic field is within 30{sup o} of northward is included in the simulations because KHI is thought to be important for plasma transport only for northward or near-northward interplanetary magnetic field orientations. The simulations show that coherent vortices can grow for these near-northward angles, and that they are sometimes more coherent than for pure northward conditions because the turbulence which breaks-down these vortices is reduced when there are magnetic tension forces. With increasing magnetic shear angle, the growth rate is reduced, and the vortices do not grow to as large of size which reduces the plasma transport. By tracking the individual particle motions diffusion coefficients can be obtained for the system, where the diffusion is not classical in nature but instead has a time dependence resulting from both the increasingly large-scale vortex motion and the small-scale turbulence generated in the break-down of the instabilities. Results indicate that diffusion on the order of 10{sup 9} m{sup 2}/s could possibly be generated by KHI on the flanks of the magnetosphere.
Electron Debye scale Kelvin-Helmholtz instability: Electrostatic particle-in-cell simulations
International Nuclear Information System (INIS)
Lee, Sang-Yun; Lee, Ensang; Kim, Khan-Hyuk; Lee, Dong-Hun; Seon, Jongho; Jin, Ho
2015-01-01
In this paper, we investigated the electron Debye scale Kelvin-Helmholtz (KH) instability using two-dimensional electrostatic particle-in-cell simulations. We introduced a velocity shear layer with a thickness comparable to the electron Debye length and examined the generation of the KH instability. The KH instability occurs in a similar manner as observed in the KH instabilities in fluid or ion scales producing surface waves and rolled-up vortices. The strength and growth rate of the electron Debye scale KH instability is affected by the structure of the velocity shear layer. The strength depends on the magnitude of the velocity and the growth rate on the velocity gradient of the shear layer. However, the development of the electron Debye scale KH instability is mainly determined by the electric field generated by charge separation. Significant mixing of electrons occurs across the shear layer, and a fraction of electrons can penetrate deeply into the opposite side fairly far from the vortices across the shear layer
International Nuclear Information System (INIS)
Sutanto, E; Chandra, F; Dinata, R
2017-01-01
Leakage current measurement which can follow IEC standard for medical device is one of many challenges to be answered. The IEC 60601-1 has defined that the limit for a leakage current for Medical Device can be as low as 10 µA and as high as 500 µA, depending on which type of contact (applied part) connected to the patient. Most people are using ELCB (Earth-leakage circuit breaker) for safety purpose as this is the most common and available safety device in market. One type of ELCB devices is RCD (Residual Current Device) and this RCD type can measure the leakage current directly. This work will show the possibility on how Helmholtz Coil Configuration can be made to be like the RCD. The possibility is explored by comparing the magnetic field formula from each device, then it proceeds with a simulation using software EJS (Easy Java Simulation). The simulation will make sure the concept of magnetic field current cancellation follows the RCD concept. Finally, the possibility of increasing the measurement’s sensitivity is also analyzed. The sensitivity is needed to see the possibility on reaching the minimum leakage current limit defined by IEC, 0.01mA. (paper)
Observation of the Kelvin–Helmholtz Instability in a Solar Prominence
Yang, Heesu; Xu, Zhi; Lim, Eun-Kyung; Kim, Sujin; Cho, Kyung-Suk; Kim, Yeon-Han; Chae, Jongchul; Cho, Kyuhyoun; Ji, Kaifan
2018-04-01
Many solar prominences end their lives in eruptions or abrupt disappearances that are associated with dynamical or thermal instabilities. Such instabilities are important because they may be responsible for energy transport and conversion. We present a clear observation of a streaming kink-mode Kelvin–Helmholtz Instability (KHI) taking place in a solar prominence using the Hα Lyot filter installed at the New Vacuum Solar Telescope, Fuxian-lake Solar Observatory in Yunnan, China. On one side of the prominence, a series of plasma blobs floated up from the chromosphere and streamed parallel to the limb. The plasma stream was accelerated to about 20–60 km s‑1 and then undulated. We found that 2″- and 5″-size vortices formed, floated along the stream, and then broke up. After the 5″-size vortex, a plasma ejection out of the stream was detected in the Solar Dynamics Observatory/Atmospheric Imaging Assembly images. Just before the formation of the 5″-size vortex, the stream displayed an oscillatory transverse motion with a period of 255 s with the amplitude growing at the rate of 0.001 s‑1. We attribute this oscillation of the stream and the subsequent formation of the vortex to the KHI triggered by velocity shear between the stream, guided by the magnetic field and the surrounding media. The plasma ejection suggests the transport of prominence material into the upper layer by the KHI in its nonlinear stage.
Förner, K.; Polifke, W.
2017-10-01
The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.
Kelvin-Helmholtz instability and kinetic internal kink modes in tokamaks
International Nuclear Information System (INIS)
Naitou, H.; Kobayashi, T.; Yagi, M.; Matsumoto, T.; Tokuda, S.; Kishimoto, Y.
2003-01-01
The m=1 (poloidal mode number) and n=1 (toroidal mode number) kinetic internal kink (KIK) mode in the presence of a density gradient is studied with 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 included. The unstable KIK mode is observed in the parameter range in which the linear theory predicts complete stabilization due to the electron diamagnetic effect. The electrostatic potential profile in the linear stage of the KIK instability has the sheared poloidal flow with the m=1 mode structure. The vortexes are generated due to the Kelvin-Helmholtz (K-H) instability. The KIK is stabilized when the vortexes are formed, but it is destabilized again as the vortexes diminish due to the charge neutralizing electron motion along the magnetic field. These phenomena are observed in the early nonlinear stage of the KIK instability in which the width of the m=1 magnetic island is sufficiently small compared with the radial extent of the vortexes. The strong coupling between the vortexes and the KIK instability can be one of the candidates explaining the sudden onset of the sawtooth crash. (author)
Directory of Open Access Journals (Sweden)
M. G. G. T. Taylor
2012-06-01
Full Text Available The Kelvin-Helmholtz Instability (KHI can drive waves at the magnetopause. These waves can grow to form rolled-up vortices and facilitate transfer of plasma into the magnetosphere. To investigate the persistence and frequency of such waves at the magnetopause we have carried out a survey of all Double Star 1 magnetopause crossings, using a combination of ion and magnetic field measurements. Using criteria originally used in a Geotail study made by Hasegawa et al. (2006 (forthwith referred to as H2006, 17 candidate events were identified from the entire TC-1 mission (covering ~623 orbits where the magnetopause was sampled, a majority of which were on the dayside of the terminator. The relationship between density and shear velocity was then investigated, to identify the predicted signature of a rolled up vortex from H2006 and all 17 events exhibited some level of rolled up behavior. The location of the events had a clear dawn-dusk asymmetry, with 12 (71% on the post noon, dusk flank suggesting preferential growth in this region.
Global reconnection topology as inferred from plasma observations inside Kelvin-Helmholtz vortices
Directory of Open Access Journals (Sweden)
M. B. Bavassano Cattaneo
2010-04-01
Full Text Available During a long lasting period of northward interplanetary magnetic field and high solar wind speed (above 700 km/s, the Cluster spacecraft go across a number of very large rolled-up Kelvin-Helmholtz (KH vortices at the dusk magnetopause, close to the terminator. The peculiarity of the present event is a particular sequence of ions and electrons distribution functions observed repeatedly inside each vortex. In particular, whenever Cluster crosses the current layer inside the vortices, multiple field-aligned ion populations appear, suggesting the occurrence of reconnection. In addition, the ion data display a clear velocity filter effect both at the leading and at the trailing edge of each vortex. This effect is not present in the simultaneous electron data. Unlike other KH studies reported in the literature in which reconnection occurs within the vortices, in the present event the observations are not compatible with local reconnection, but are accounted for by lobe reconnection occurring along an extended X-line at the terminator in the Southern Hemisphere. The reconnected field lines "sink" across the magnetopause and then convect tailward-duskward where they become embedded in the vortices. Another observational evidence is the detected presence of solar wind plasma on the magnetospheric side of the vortices, which confirms unambiguously the occurrence of mass transport across the magnetopause already reported in the literature. The proposed reconnection scenario accounts for all the observational aspects, regarding both the transport process and the kinetic signatures.
Mathematics and Maxwell's equations
International Nuclear Information System (INIS)
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Energy preserving integration of bi-Hamiltonian partial differential equations
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
Supergravity inspired vector curvaton
International Nuclear Information System (INIS)
Dimopoulos, Konstantinos
2007-01-01
It is investigated whether a massive Abelian vector field, whose gauge kinetic function is growing during inflation, can be responsible for the generation of the curvature perturbation in the Universe. Particle production is studied and it is shown that the vector field can obtain a scale-invariant superhorizon spectrum of perturbations with a reasonable choice of kinetic function. After inflation the vector field begins coherent oscillations, during which it corresponds to pressureless isotropic matter. When the vector field dominates the Universe, its perturbations give rise to the observed curvature perturbation following the curvaton scenario. It is found that this is possible if, after the end of inflation, the mass of the vector field increases at a phase transition at temperature of order 1 TeV or lower. Inhomogeneous reheating, whereby the vector field modulates the decay rate of the inflaton, is also studied
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)
Becciolini, Diego; Franzosi, Diogo Buarque; Foadi, Roshan; Frandsen, Mads T.; Hapola, Tuomas; Sannino, Francesco
2015-07-01
We analyze the Large Hadron Collider (LHC) phenomenology of heavy vector resonances with a S U (2 )L×S U (2 )R spectral global symmetry. This symmetry partially protects the electroweak S parameter from large contributions of the vector resonances. The resulting custodial vector model spectrum and interactions with the standard model fields lead to distinct signatures at the LHC in the diboson, dilepton, and associated Higgs channels.
HITZER, Eckhard MS
2002-01-01
This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...
Directory of Open Access Journals (Sweden)
Jean-François Degbomont
2010-10-01
Full Text Available This paper addresses the symbolic representation of non-convex real polyhedra, i.e., sets of real vectors satisfying arbitrary Boolean combinations of linear constraints. We develop an original data structure for representing such sets, based on an implicit and concise encoding of a known structure, the Real Vector Automaton. The resulting formalism provides a canonical representation of polyhedra, is closed under Boolean operators, and admits an efficient decision procedure for testing the membership of a vector.
International Nuclear Information System (INIS)
Brown, F.B.
1981-01-01
Examination of the global algorithms and local kernels of conventional general-purpose Monte Carlo codes shows that multigroup Monte Carlo methods have sufficient structure to permit efficient vectorization. A structured multigroup Monte Carlo algorithm for vector computers is developed in which many particle events are treated at once on a cell-by-cell basis. Vectorization of kernels for tracking and variance reduction is described, and a new method for discrete sampling is developed to facilitate the vectorization of collision analysis. To demonstrate the potential of the new method, a vectorized Monte Carlo code for multigroup radiation transport analysis was developed. This code incorporates many features of conventional general-purpose production codes, including general geometry, splitting and Russian roulette, survival biasing, variance estimation via batching, a number of cutoffs, and generalized tallies of collision, tracklength, and surface crossing estimators with response functions. Predictions of vectorized performance characteristics for the CYBER-205 were made using emulated coding and a dynamic model of vector instruction timing. Computation rates were examined for a variety of test problems to determine sensitivities to batch size and vector lengths. Significant speedups are predicted for even a few hundred particles per batch, and asymptotic speedups by about 40 over equivalent Amdahl 470V/8 scalar codes arepredicted for a few thousand particles per batch. The principal conclusion is that vectorization of a general-purpose multigroup Monte Carlo code is well worth the significant effort required for stylized coding and major algorithmic changes
Vectors and their applications
Pettofrezzo, Anthony J
2005-01-01
Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of two- and three-dimensional space. Its rigorous development includes a complete treatment of the algebra of vectors in the first two chapters.Among the text's outstanding features are numbered definitions and theorems in the development of vector algebra, which appear in italics for easy reference. Most of the theorems include proofs, and coordinate position vectors receive an in-depth treatment. Key concept
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
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
ON A PROLONGATION CONSTRUCTION FOR LOCAL NON-DIVERGENT VECTOR FIELDS ON Rn
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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.
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
Das, Subrata Kumar; Das, Siddarth Shankar; Saha, Korak; Murali Krishna, U. V.; Dani, K. K.
2018-04-01
Characteristics of Kelvin Helmholtz Instability (KHI) using Doppler wind lidar observation have rarely been reported during the Indian summer monsoon season. In this paper, we present a case study of KHI near planetary boundary layer using Doppler wind lidar and radiosonde measurements at Mahabubnagar, a tropical Indian station. The data was collected during the Integrated Ground Observation Campaign (June-October 2011) under the Cloud Aerosol Interaction and Precipitation Enhancement EXperiment-2011. The continuous wind lidar observation during 10-16 August 2011 shows there is an increase in carrier-to-noise ratio values near planetary boundary layer from 03:00 to 11:00 LT on 13 August; reveals the formation of KHI. There is a strong power bursts pattern corresponding to high turbulence characteristics in the early half of the day. The KHI temporal evolution from initial to dissipating stage is observed with clear variation in the carrier-to-noise ratio values. The observed KHI billows are in the height between 600 and 1200 m and lasted for about 7.5 h. The vertical velocity from Doppler lidar measurement shows the presence of updrafts after breaking of KHI in the boundary layer. The presence of strong wind shear, high stability parameter, low Richardson number and high relative humidity during the enhanced carrier-to-noise ratio period indicates the ideal condition for the formation and persistence of this dynamic instability. A typical characteristic of trapped humidity above the KHI billows suggest the presence of strong inversion. A wavelet analysis of 3-dimensional wind components show dominant periodicity of 45-65 min and the periodicity in vertical wind is more prominent.
INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS
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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
Vector-Vector Scattering on the Lattice
Romero-López, Fernando; Urbach, Carsten; Rusetsky, Akaki
2018-03-01
In this work we present an extension of the LüScher formalism to include the interaction of particles with spin, focusing on the scattering of two vector particles. The derived formalism will be applied to Scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass.
Selection vector filter framework
Lukac, Rastislav; Plataniotis, Konstantinos N.; Smolka, Bogdan; Venetsanopoulos, Anastasios N.
2003-10-01
We provide a unified framework of nonlinear vector techniques outputting the lowest ranked vector. The proposed framework constitutes a generalized filter class for multichannel signal processing. A new class of nonlinear selection filters are based on the robust order-statistic theory and the minimization of the weighted distance function to other input samples. The proposed method can be designed to perform a variety of filtering operations including previously developed filtering techniques such as vector median, basic vector directional filter, directional distance filter, weighted vector median filters and weighted directional filters. A wide range of filtering operations is guaranteed by the filter structure with two independent weight vectors for angular and distance domains of the vector space. In order to adapt the filter parameters to varying signal and noise statistics, we provide also the generalized optimization algorithms taking the advantage of the weighted median filters and the relationship between standard median filter and vector median filter. Thus, we can deal with both statistical and deterministic aspects of the filter design process. It will be shown that the proposed method holds the required properties such as the capability of modelling the underlying system in the application at hand, the robustness with respect to errors in the model of underlying system, the availability of the training procedure and finally, the simplicity of filter representation, analysis, design and implementation. Simulation studies also indicate that the new filters are computationally attractive and have excellent performance in environments corrupted by bit errors and impulsive noise.
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.; Nitta, Muneto; Veldhuis, T. ter; Xiong, C.
2009-01-01
Local oscillations of the brane world are manifested as massive vector fields. Their coupling to the Standard Model can be obtained using the method of nonlinear realizations of the spontaneously broken higher-dimensional space-time symmetries, and to an extent, are model independent. Phenomenological limits on these vector field parameters are obtained using LEP collider data and dark matter constraints
Vector-Interaction-Enhanced Bag Model
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.
Efficient and Enhanced Diffusion of Vector Field for Active Contour Model
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...
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)
Generalized vector calculus on convex domain
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.
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
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)
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms
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.
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.
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
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
Vectors, tensors and the basic equations of fluid mechanics
Aris, Rutherford
1962-01-01
Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
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.
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Minnesota Department of Natural Resources — This vector dataset is a detailed (1-acre minimum), hierarchically organized vegetation cover map produced by computer classification of combined two-season pairs of...
Sesquilinear uniform vector integral
Indian Academy of Sciences (India)
theory, together with his integral, dominate contemporary mathematics. ... directions belonging to Bartle and Dinculeanu (see [1], [6], [7] and [2]). ... in this manner, namely he integrated vector functions with respect to measures of bounded.
Kansas Data Access and Support Center — The Kansas Tagged Vector Contour (TVC) dataset consists of digitized contours from the 7.5 minute topographic quadrangle maps. Coverage for the state is incomplete....
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel
1991-01-01
Roč. 2, - (1991), s. 281-292 ISSN 0956-7925 Keywords : vector hysteresis operator * hysteresis potential * differential inequality Subject RIV: BA - General Mathematics http://www.math.cas.cz/~krejci/b15p.pdf
Support vector machines applications
Guo, Guodong
2014-01-01
Support vector machines (SVM) have both a solid mathematical background and good performance in practical applications. This book focuses on the recent advances and applications of the SVM in different areas, such as image processing, medical practice, computer vision, pattern recognition, machine learning, applied statistics, business intelligence, and artificial intelligence. The aim of this book is to create a comprehensive source on support vector machine applications, especially some recent advances.
International Nuclear Information System (INIS)
Akama, K.; Hattori, T.; Yasue, M.
1991-01-01
An exotic composite vector boson V is introduced in two dynamical models of composite quarks, leptons, W, and Z. One is based on four-Fermi interactions, in which composite vector bosons are regarded as fermion-antifermion bound states and the other is based on the confining SU(2) L gauge model, in which they are given by scalar-antiscalar bound states. Both approaches describe the same effective interactions for the sector of composite quarks, leptons, W, Z, γ, and V
Melillo Fenech, Tanya
2010-01-01
A vector-borne disease is one in which the pathogenic microorganism is transmitted from an infected individual to another individual by an arthropod or other agent. The transmission depends upon the attributes and requirements of at least three different Iiving organisms : the pathologic agent which is either a virus, protozoa, bacteria or helminth (worm); the vector, which is commonly an arthropod such as ticks or mosquitoes; and the human host.
Duality properties of Gorringe Leach equations
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.
Calculation of normal modes of the closed waveguides in general vector case
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.
International Nuclear Information System (INIS)
Yan, Zhenya
2011-01-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black–Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields. -- Highlights: ► We investigate the coupled nonlinear volatility and option pricing model. ► We analytically present vector financial rogue waves. ► The vector financial rogue waves may be used to describe the extreme events in financial markets. ► This results may excite the relative researches and potential applications of vector rogue waves.
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.
Geometric Implications of Maxwell's Equations
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.
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.
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...
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....
Differential Equations and Computational Simulations
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
Vectorization in quantum chemistry
International Nuclear Information System (INIS)
Saunders, V.R.
1987-01-01
It is argued that the optimal vectorization algorithm for many steps (and sub-steps) in a typical ab initio calculation of molecular electronic structure is quite strongly dependent on the target vector machine. Details such as the availability (or lack) of a given vector construct in the hardware, vector startup times and asymptotic rates must all be considered when selecting the optimal algorithm. Illustrations are drawn from: gaussian integral evaluation, fock matrix construction, 4-index transformation of molecular integrals, direct-CI methods, the matrix multiply operation. A cross comparison of practical implementations on the CDC Cyber 205, the Cray-IS and Cray-XMP machines is presented. To achieve portability while remaining optimal on a wide range of machines it is necessary to code all available algorithms in a machine independent manner, and to select the appropriate algorithm using a procedure which is based on machine dependent parameters. Most such parameters concern the timing of certain vector loop kernals, which can usually be derived from a 'bench-marking' routine executed prior to the calculation proper
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
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
Fractional gradient and its application to the fractional advection equation
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.
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 ...
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)
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 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.
Bunyavirus-Vector Interactions
Directory of Open Access Journals (Sweden)
Kate McElroy Horne
2014-11-01
Full Text Available The Bunyaviridae family is comprised of more than 350 viruses, of which many within the Hantavirus, Orthobunyavirus, Nairovirus, Tospovirus, and Phlebovirus genera are significant human or agricultural pathogens. The viruses within the Orthobunyavirus, Nairovirus, and Phlebovirus genera are transmitted by hematophagous arthropods, such as mosquitoes, midges, flies, and ticks, and their associated arthropods not only serve as vectors but also as virus reservoirs in many cases. This review presents an overview of several important emerging or re-emerging bunyaviruses and describes what is known about bunyavirus-vector interactions based on epidemiological, ultrastructural, and genetic studies of members of this virus family.
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Duality in vector optimization
Bot, Radu Ioan
2009-01-01
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the s
Multithreading in vector processors
Evangelinos, Constantinos; Kim, Changhoan; Nair, Ravi
2018-01-16
In one embodiment, a system includes a processor having a vector processing mode and a multithreading mode. The processor is configured to operate on one thread per cycle in the multithreading mode. The processor includes a program counter register having a plurality of program counters, and the program counter register is vectorized. Each program counter in the program counter register represents a distinct corresponding thread of a plurality of threads. The processor is configured to execute the plurality of threads by activating the plurality of program counters in a round robin cycle.
Eisenman, Richard L
2005-01-01
This outstanding text and reference applies matrix ideas to vector methods, using physical ideas to illustrate and motivate mathematical concepts but employing a mathematical continuity of development rather than a physical approach. The author, who taught at the U.S. Air Force Academy, dispenses with the artificial barrier between vectors and matrices--and more generally, between pure and applied mathematics.Motivated examples introduce each idea, with interpretations of physical, algebraic, and geometric contexts, in addition to generalizations to theorems that reflect the essential structur
Free topological vector spaces
Gabriyelyan, Saak S.; Morris, Sidney A.
2016-01-01
We define and study the free topological vector space $\\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\\mathbb{V}(X)$ is a $k_\\omega$-space if and only if $X$ is a $k_\\omega$-space. If $X$ is infinite, then $\\mathbb{V}(X)$ contains a closed vector subspace which is topologically isomorphic to $\\mathbb{V}(\\mathbb{N})$. It is proved that if $X$ is a $k$-space, then $\\mathbb{V}(X)$ is locally convex if and only if $X$ is discrete and countable. If $X$ is a metrizable space it is shown ...
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.
DEFF Research Database (Denmark)
2000-01-01
Using a pulsed ultrasound field, the two-dimensional velocity vector can be determined with the invention. The method uses a transversally modulated ultrasound field for probing the moving medium under investigation. A modified autocorrelation approach is used in the velocity estimation. The new...
Production of lentiviral vectors
Directory of Open Access Journals (Sweden)
Otto-Wilhelm Merten
2016-01-01
Full Text Available Lentiviral vectors (LV have seen considerably increase in use as gene therapy vectors for the treatment of acquired and inherited diseases. This review presents the state of the art of the production of these vectors with particular emphasis on their large-scale production for clinical purposes. In contrast to oncoretroviral vectors, which are produced using stable producer cell lines, clinical-grade LV are in most of the cases produced by transient transfection of 293 or 293T cells grown in cell factories. However, more recent developments, also, tend to use hollow fiber reactor, suspension culture processes, and the implementation of stable producer cell lines. As is customary for the biotech industry, rather sophisticated downstream processing protocols have been established to remove any undesirable process-derived contaminant, such as plasmid or host cell DNA or host cell proteins. This review compares published large-scale production and purification processes of LV and presents their process performances. Furthermore, developments in the domain of stable cell lines and their way to the use of production vehicles of clinical material will be presented.
Indian Academy of Sciences (India)
The Gram-Schmidt process is one of the first things one learns in a course ... We might want to stay as close to the experimental data as possible when converting these vectors to orthonormal ones demanded by the model. The process of finding the closest or- thonormal .... is obtained by writing the matrix A = [aI, an], then.
Champenois, Gilles
2007-01-01
The mnesor theory is the adaptation of vectors to artificial intelligence. The scalar field is replaced by a lattice. Addition becomes idempotent and multiplication is interpreted as a selection operation. We also show that mnesors can be the foundation for a linear calculus.
Treiman, Jay S
2014-01-01
Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...
Indian Academy of Sciences (India)
[G] Giannessi F, Theorems of alternative, quadratic programs and complementarity problems, in: Variational Inequalities and Complementarity Problems (eds) R W Cottle, F Giannessi and J L Lions (New York: Wiley) (1980) pp. 151±186. [K1] Kazmi K R, Existence of solutions for vector optimization, Appl. Math. Lett. 9 (1996).
Centers for Disease Control (CDC) Podcasts
2011-04-18
This podcast discusses emerging vector-borne pathogens, their role as prominent contributors to emerging infectious diseases, how they're spread, and the ineffectiveness of mosquito control methods. Created: 4/18/2011 by National Center for Emerging Zoonotic and Infectious Diseases (NCEZID). Date Released: 4/27/2011.
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.
A general comparison theorem for backward stochastic differential equations
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...
Progress toward Kelvin-Helmholtz instabilities in a High-Energy-Density Plasma on the Nike laser
Harding, E. C.; Drake, R. P.; Gillespie, R. S.; Grosskopf, M. J.; Huntington, C. M.; Aglitskiy, Y.; Weaver, J. L.; Velikovich, A. L.; Plewa, T.; Dwarkadas, V. V.
2008-04-01
In the realm of high-energy-density (HED) plasmas, there exist three primary hydrodynamic instabilities of concern: Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH). Although the RT and the RM instabilities have been readily observed and diagnosed in the laboratory, the KH instability remains relatively unexplored in HED plasmas. Unlike the RT and RM instabilities, the KH instability is driven by a lifting force generated by a strong velocity gradient in a stratified fluid. Understanding the KH instability mechanism in HED plasmas will provide essential insight into oblique shock systems, jets, mass stripping, and detailed RT-spike development. In addition, our KH experiment will help provide the groundwork for future transition to turbulence experiments. We present 2D FLASH simulations and experimental data from our initial attempts to create a pure KH system using the Nike laser at the Naval Research Laboratory.
International Nuclear Information System (INIS)
Borgogno, D.; Califano, F.; Pegoraro, F.; Faganello, M.
2015-01-01
In an almost collisionless magnetohydrodynamic plasma in a relatively strong magnetic field, stresses can be conveyed far from the region where they are exerted, e.g., through the propagation of Alfvèn waves. The forced dynamics of line-tied magnetic structures in solar and stellar coronae (see, e.g., A. F. Rappazzo and E. N. Parker, Astrophys. J. 773, L2 (2013) and references therein) is a paradigmatic case. Here, we investigate how this action at a distance develops from the equatorial region of the Kelvin-Helmholtz unstable flanks of the Earth's magnetosphere leading to the onset, at mid latitude in both hemispheres, of correlated double magnetic field line reconnection events that can allow the solar wind plasma to enter the Earth's magnetosphere
Extracting the potential-well of a near-field optical trap using the Helmholtz-Hodge decomposition
Zaman, Mohammad Asif; Padhy, Punnag; Hansen, Paul C.; Hesselink, Lambertus
2018-02-01
The non-conservative nature of the force field generated by a near-field optical trap is analyzed. A plasmonic C-shaped engraving on a gold film is considered as the trap. The force field is calculated using the Maxwell stress tensor method. The Helmholtz-Hodge decomposition is used to extract the conservative and the non-conservative component of the force. Due to the non-negligible non-conservative component, it is found that the conventional approach of extracting the potential by direct integration of the force is not accurate. Despite the non-conservative nature of the force field, it is found that the statistical properties of a trapped nanoparticle can be estimated from the conservative component of the force field alone. Experimental and numerical results are presented to support the claims.
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)
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)
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)
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
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
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)
Vectorization of Reed Solomon decoding and mapping on the EVP
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,
Transitive Lie algebras of vector fields: an overview
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
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)
Vector grammars and PN machines
Institute of Scientific and Technical Information of China (English)
蒋昌俊
1996-01-01
The concept of vector grammars under the string semantic is introduced.The dass of vector grammars is given,which is similar to the dass of Chomsky grammars.The regular vector grammar is divided further.The strong and weak relation between the vector grammar and scalar grammar is discussed,so the spectrum system graph of scalar and vector grammars is made.The equivalent relation between the regular vector grammar and Petri nets (also called PN machine) is pointed.The hybrid PN machine is introduced,and its language is proved equivalent to the language of the context-free vector grammar.So the perfect relation structure between vector grammars and PN machines is formed.
Elliptic Painlevé equations from next-nearest-neighbor translations on the E_8^{(1)} lattice
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.
Modern methods in topological vector spaces
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
Applications of the Local Algebras of Vector Fields to the Modelling of Physical Phenomena
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.
Spacelike conformal Killing vectors and spacelike congruences
International Nuclear Information System (INIS)
Mason, D.P.; Tsamparlis, M.
1985-01-01
Necessary and sufficient conditions are derived for space-time to admit a spacelike conformal motion with symmetry vector parallel to a unit spacelike vector field n/sup a/. These conditions are expressed in terms of the shear and expansion of the spacelike congruence generated by n/sup a/ and in terms of the four-velocity of the observer employed at any given point of the congruence. It is shown that either the expansion or the rotation of this spacelike congruence must vanish if Dn/sup a//dp = 0, where p denotes arc length measured along the integral curves of n/sup a/, and also that there exist no proper spacelike homothetic motions with constant expansion. Propagation equations for the projection tensor and the rotation tensor are derived and it is proved that every isometric spacelike congruence is rigid. Fluid space-times are studied in detail. A relation is established between spacelike conformal motions and material curves in the fluid: if a fluid space-time admits a spacelike conformal Killing vector parallel to n/sup a/ and n/sub a/u/sup a/ = 0, where u/sup a/ is the fluid four-velocity, then the integral curves of n/sup a/ are material curves in an irrotational fluid, while if the fluid vorticity is nonzero, then the integral curves of n/sup a/ are material curves if and only if they are vortex lines. An alternative derivation, based on the theory of spacelike congruences, of some of the results of Collins [J. Math. Phys. 25, 995 (1984)] on conformal Killing vectors parallel to the local vorticity vector in shear-free perfect fluids with zero magnetic Weyl tensor is given
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)
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.
Characterizations of Space Curves According to Bishop Darboux Vector in Euclidean 3-Space E3
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.
2015-09-28
buoyant underwater vehicle with an interior space in which a length of said underwater vehicle is equal to one tenth of the acoustic wavelength...underwater vehicle with an interior space in which a length of said underwater vehicle is equal to one tenth of the acoustic wavelength; an...unmanned underwater vehicle that can function as an acoustic vector sensor. (2) Description of the Prior Art [0004] It is known that a propagating
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
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)
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
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.
Numerical solutions of incompressible Navier-Stokes equations using modified Bernoulli's law
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.
Moving interfaces and quasilinear parabolic evolution equations
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...
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.)
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.
Hierarchal scalar and vector tetrahedra
International Nuclear Information System (INIS)
Webb, J.P.; Forghani, B.
1993-01-01
A new set of scalar and vector tetrahedral finite elements are presented. The elements are hierarchal, allowing mixing of polynomial orders; scalar orders up to 3 and vector orders up to 2 are defined. The vector elements impose tangential continuity on the field but not normal continuity, making them suitable for representing the vector electric or magnetic field. Further, the scalar and vector elements are such that they can easily be used in the same mesh, a requirement of many quasi-static formulations. Results are presented for two 50 Hz problems: the Bath Cube, and TEAM Problem 7
Leishmaniasis vector behaviour in Kenya
International Nuclear Information System (INIS)
Mutinga, M.J.
1980-01-01
Leishmaniasis in Kenya exists in two forms: cutaneous and visceral. The vectors of visceral leishmaniasis have been the subject of investigation by various researchers since World War II, when the outbreak of the disease was first noticed. The vectors of cutaneous leishmaniasis were first worked on only a decade ago after the discovery of the disease focus in Mt. Elgon. The vector behaviour of these diseases, namely Phlebotomus pedifer, the vector of cutaneous leishmaniasis, and Phlebotomus martini, the vector of visceral leishmaniasis, are discussed in detail. P. pedifer has been found to breed and bite inside caves, whereas P. martini mainly bites inside houses. (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...
Mutational analysis a joint framework for Cauchy problems in and beyond vector spaces
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.
The Cauchy problem for the Pavlov equation
International Nuclear Information System (INIS)
Grinevich, P G; Santini, P M; Wu, D
2015-01-01
Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs that arise in various problems of mathematical physics and have been intensively studied in recent literature. This report aims to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data. (paper)
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.)
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
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
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Multifractal vector fields and stochastic Clifford algebra.
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.
DEFF Research Database (Denmark)
More, Simon J.; Bicout, Dominique; Bøtner, Anette
2017-01-01
After a request from the Europea n Commission, EFSA’s Panel on Animal Health and Welfaresummarised the main characteristics of 36 vector-borne disease s (VBDs) in 36 web-based storymaps.The risk of introduction in the EU through movement of livestock or pets was assessed for eac h of the36 VBDs......-agents for which the rate of introduction wasestimated to be very low, no further asse ssments were made. Due to the uncertainty related to someparameters used for the risk assessment or the instable or unpredictability disease situation in some ofthe source regions, it is recommended to update the assessment when...
International Nuclear Information System (INIS)
Otsason, J.
1998-01-01
The Vector Pipeline project linking the Chicago supply hub to markets in eastern Canada, the northeastern U.S. and the Mid-Atlantic states, is described. Subsidiary objectives of the promoters are to match market timing to upstream pipelines and market requirements, and to provide low cost expandability to complement upstream expandability. The presentation includes description of the project, costs, leased facilities, rates and tariffs, right of way considerations, storage facilities and a project schedule. Construction is to begin in March 1999 and the line should be in service in November 1999
ESTUDO DA INSTABILIDADE KELVIN-HELMHOLTZ ATRAVÉS DE SIMULAÇÕES COM O CÓDIGO ATHENA
Directory of Open Access Journals (Sweden)
Priscila Freitas-Lemes
2013-12-01
Full Text Available As instabilidades Kelvin-Helmholtz são comuns em sistemas astrofísicos e vão desde jatos deburacos negros até disco de acreção protoplantário. Um objeto astrofísico com fortes características da instabilidade de Kelvin-Helmholtz é a Nebulosa de Caraguejo, na qual a expansão do material foi ocasionado pela explosão de uma supernova há, aproximadamente, 1000 anos. Essa instabilidade ocorre no limite entre dois fluidos de diferentes densidades, quando um dos fluidos é acelerado com relação ao outro. Com o objetivo de estudar essa instabilidade, realizamos uma simulação com o código de malha euleriana ATHENA. Para essasimulação, consideramos um domínio quadrado com limites periódicos sobre as laterais, e, refletindo na fronteirada parte superior e inferior. A região superior da caixa é preenchida com um gás de densidade ρ=1,0, pressãoP1=1,0, índice adiabático γ=5/3 e velocidade u1=0,03 na direção x (para direita. A parte inferior tem densidadeρ=2,0, mesma pressão, velocidade e índice adiabático, só que no sentido contrário, para a esquerda. A velocidade é definida como uma função senoidal, que cria a perturbação inicial. Como resultado, observamos o princípio da instabilidade e a formação dos vórtices, com as cristas bem definidas. A nitidez da fronteira entre o material de alta e de baixa densidade está bem conservada, devido à difusão relativamente baixa do algoritmo. Notamos, ainda, que, evoluindo a simulação, os vórtices formados a partir da turbulência fundem-se.
Hellweg, C. E.; Gerzer, R.; Reitz, G.
2011-05-01
In the field of space life sciences, the demand of an interdisciplinary and specific training of young researchers is high due to the complex interaction of medical, biological, physical, technical and other questions. The Helmholtz Space Life Sciences Research School (SpaceLife) offers an excellent interdisciplinary training for doctoral students from different fields (biology, biochemistry, biotechnology, physics, psychology, nutrition or sports sciences and related fields) and any country. SpaceLife is coordinated by the Institute of Aerospace Medicine at the German Aerospace Center (DLR) in Cologne. The German Universities in Kiel, Bonn, Aachen, Regensburg, Magdeburg and Berlin, and the German Sports University (DSHS) in Cologne are members of SpaceLife. The Universities of Erlangen-Nürnberg, Frankfurt, Hohenheim, and the Beihang University in Beijing are associated partners. In each generation, up to 25 students can participate in the three-year program. Students learn to develop integrated concepts to solve health issues in human spaceflight and in related disease patterns on Earth, and to further explore the requirements for life in extreme environments, enabling a better understanding of the ecosystem Earth and the search for life on other planets in unmanned and manned missions. The doctoral candidates are coached by two specialist supervisors from DLR and the partner university, and a mentor. All students attend lectures in different subfields of space life sciences to attain an overview of the field: radiation and gravitational biology, astrobiology and space physiology, including psychological aspects of short and long term space missions. Seminars, advanced lectures, laboratory courses and stays at labs at the partner institutions or abroad are offered as elective course and will provide in-depth knowledge of the chosen subfield or allow to appropriate innovative methods. In Journal Clubs of the participating working groups, doctoral students learn
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
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.
Vector-vector production in photon-photon interactions
International Nuclear Information System (INIS)
Ronan, M.T.
1988-01-01
Measurements of exclusive untagged /rho/ 0 /rho/ 0 , /rho//phi/, K/sup *//bar K//sup */, and /rho/ω production and tagged /rho/ 0 /rho/ 0 production in photon-photon interactions by the TPC/Two-Gamma experiment are reviewed. Comparisons to the results of other experiments and to models of vector-vector production are made. Fits to the data following a four quark model prescription for vector meson pair production are also presented. 10 refs., 9 figs
Vector fields in a tight laser focus: comparison of models.
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.
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)
Somoano, Brian; Chan, Joanna; Morganroth, Greg
2011-01-01
Facial rejuvenation using local anesthesia has evolved in the past decade as a safer option for patients seeking fewer complications and minimal downtime. Mini- and short-scar face lifts using more conservative incision lengths and extent of undermining can be effective in the younger patient with lower face laxity and minimal loose, elastotic neck skin. By incorporating both an anterior and posterior approach and using an incision length between the mini and more traditional face lift, the Vertical Vector Face Lift can achieve longer-lasting and natural results with lesser cost and risk. Submentoplasty and liposuction of the neck and jawline, fundamental components of the vertical vector face lift, act synergistically with superficial musculoaponeurotic system plication to reestablish a more youthful, sculpted cervicomental angle, even in patients with prominent jowls. Dramatic results can be achieved in the right patient by combining with other procedures such as injectable fillers, chin implants, laser resurfacing, or upper and lower blepharoplasties. © 2011 Wiley Periodicals, Inc.
Vector control in leishmaniasis.
Kishore, K; Kumar, V; Kesari, S; Dinesh, D S; Kumar, A J; Das, P; Bhattacharya, S K
2006-03-01
Indoor residual spraying is a simple and cost effective method of controlling endophilic vectors and DDT remains the insecticide of choice for the control of leishmaniasis. However resistance to insecticide is likely to become more widespread in the population especially in those areas in which insecticide has been used for years. In this context use of slow release emulsified suspension (SRES) may be the best substitute. In this review spraying frequencies of DDT and new schedule of spray have been discussed. Role of biological control and environment management in the control of leishmaniasis has been emphasized. Allethrin (coil) 0.1 and 1.6 per cent prallethrin (liquid) have been found to be effective repellents against Phlebotomus argentipes, the vector of Indian kalaazar. Insecticide impregnated bednets is another area which requires further research on priority basis for the control of leishmaniasis. Role of satellite remote sensing for early prediction of disease by identifying the sandflygenic conditions cannot be undermined. In future synthetic pheromons can be exploited in the control of leishmaniasis.
Experimental demonstration of vector E x vector B plasma divertor
International Nuclear Information System (INIS)
Strait, E.J.; Kerst, D.W.; Sprott, J.C.
1977-01-01
The vector E x vector B drift due to an applied radial electric field in a tokamak with poloidal divertor can speed the flow of plasma out of the scrape-off region, and provide a means of externally controlling the flow rate and thus the width of the density fall-off. An experiment in the Wisconsin levitated toroidal octupole, using vector E x vector B drifts alone, demonstrates divertor-like behavior, including 70% reduction of plasma density near the wall and 40% reduction of plasma flux to the wall, with no adverse effects on confinement of the main plasma
Application of Stochastic Partial Differential Equations to Reservoir Property Modelling
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.
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.)
On the solutions of the second heavenly and Pavlov equations
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.
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)
International Nuclear Information System (INIS)
Kardjilov, Nikolay
2012-01-01
Neutron imaging is a non-destructive investigation method with a fast growing application field in materials research and fundamental science. The method is used broadly in the cultural heritage research as complementary technique to x-ray imaging. The ability of neutron beam to transmit thick layers of metal and the sensitivity to light elements makes the technique unique for detection of organic substances in metal and stone matrices. The high penetration power of neutrons allows for investigation of samples with real dimensions of about 100 cm3. The neutron imaging in cultural heritage helps to provide information about manufacturing processes and material properties which is very important for further restoration and conservation of the objects. The development of new methods like energy selective imaging and grating interferometry and the application of autoradiography increase the potential of the method for characterization of cultural heritage samples. The neutron tomography instrument CONRAD has been in operation since 2005 at the Hahn-Meitner research reactor at Helmholtz-Zentrum Berlin (HZB). Over the last 5 years, significant development work has been performed to expand the radiographic and tomographic capabilities of the beamline. New techniques have been implemented, including imaging with polarized neutrons, Bragg-edge mapping, high-resolution neutron imaging and grating interferometry. These methods together with the autoradiography have been provided to the user community as tools to help address scientific problems particularly in the field of cultural heritage and palaeontology. Descriptions and parameters of the facilities are given
Mahavarkar, Prasanna; John, Jacob; Dhapre, Vijay; Dongre, Varun; Labde, Sachin
2018-04-01
A tri-axial square Helmholtz coil system for the study of palaeomagnetic studies, manufactured by GEOFYZIKA (former Czechoslovakia), was successfully commissioned at the Alibag Magnetic Observatory (IAGA code: ABG) in the year 1985. This system was used for a few years, after which the system encountered technical problems with the control unit. Rectification of the unit could not be undertaken, as the information document related to this system was not available, and as a result the system had been lying in an unused state for a long time, until 2015, when the system was recommissioned and upgraded to a test facility for calibrating the magnetometer sensors. We have upgraded the system with a constant current source and a data-logging unit. Both of these units have been designed and developed in the institute laboratory. Also, re-measurements of the existing system have been made thoroughly. The upgraded system is semi-automatic, enabling non-specialists to operate it after a brief period of instruction. This facility is now widely used at the parent institute and external institutions to calibrate magnetometers and it also serves as a national facility. Here the design of this system with the calibration results for the space-borne fluxgate magnetometers is presented.
Directory of Open Access Journals (Sweden)
P. Mahavarkar
2018-04-01
Full Text Available A tri-axial square Helmholtz coil system for the study of palaeomagnetic studies, manufactured by GEOFYZIKA (former Czechoslovakia, was successfully commissioned at the Alibag Magnetic Observatory (IAGA code: ABG in the year 1985. This system was used for a few years, after which the system encountered technical problems with the control unit. Rectification of the unit could not be undertaken, as the information document related to this system was not available, and as a result the system had been lying in an unused state for a long time, until 2015, when the system was recommissioned and upgraded to a test facility for calibrating the magnetometer sensors. We have upgraded the system with a constant current source and a data-logging unit. Both of these units have been designed and developed in the institute laboratory. Also, re-measurements of the existing system have been made thoroughly. The upgraded system is semi-automatic, enabling non-specialists to operate it after a brief period of instruction. This facility is now widely used at the parent institute and external institutions to calibrate magnetometers and it also serves as a national facility. Here the design of this system with the calibration results for the space-borne fluxgate magnetometers is presented.
Tsubouchi, K.
2017-12-01
A discovery of "IBEX ribbon", localized bright emission of energetic neutral atoms, has brought new insights into the plasma environment of its source region beyond the heliosphere. It has been basically established that its geometrical property is associated with the local interstellar magnetic field draped on the heliopause, and pickup ions (PUIs) in the outer heliosheath (OHS) must be its primary source particles. Understanding the PUI dynamics in OHS more in detail is our motivation for this study. We performed two-dimensional hybrid simulations to evaluate the response of PUIs to the structural variation in the heliosheath. We assumed the simulation system such that the background plasma is hot solar wind in the inner heliosheath and cold interstellar plasma in OHS, and the directions of these flows are tangential to the heliopause. Such a situation leads to the growth of Kelvin-Helmholtz instability (KHI), where the plasma mixing and turbulence excitation takes place. We identified that non-stationarity and non-uniformity emerges in the PUI density structure in a specific energy range as KHI process advances. Relevance of these results to the expected observation like IBEX ribbon will be discussed.
THE ROLE OF KELVIN–HELMHOLTZ INSTABILITY FOR PRODUCING LOOP-TOP HARD X-RAY SOURCES IN SOLAR FLARES
Energy Technology Data Exchange (ETDEWEB)
Fang, Xia; Yuan, Ding; Xia, Chun; Doorsselaere, Tom Van; Keppens, Rony [Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven (Belgium)
2016-12-10
We propose a model for the formation of loop-top hard X-ray (HXR) sources in solar flares through the inverse Compton mechanism, scattering the surrounding soft X-ray (SXR) photons to higher energy HXR photons. We simulate the consequences of a flare-driven energy deposit in the upper chromosphere in the impulsive phase of single loop flares. The consequent chromosphere evaporation flows from both footpoints reach speeds up to hundreds of kilometers per second, and we demonstrate how this triggers Kelvin–Helmholtz instability (KHI) in the loop top, under mildly asymmetric conditions, or more toward the loop flank for strongly asymmetric cases. The KHI vortices further fragment the magnetic topology into multiple magnetic islands and current sheets, and the hot plasma within leads to a bright loop-top SXR source region. We argue that the magnetohydrodynamic turbulence that appears at the loop apex could be an efficient accelerator of non-thermal particles, which the island structures can trap at the loop-top. These accelerated non-thermal particles can upscatter the surrounding thermal SXR photons emitted by the extremely hot evaporated plasma to HXR photons.
Energy Technology Data Exchange (ETDEWEB)
Vandenboomgaerde, M.; Bonnefille, M.; Gauthier, P. [CEA, DAM, DIF, F-91297 Arpajon (France)
2016-05-15
Highly resolved radiation-hydrodynamics FCI2 simulations have been performed to model laser experiments on the National Ignition Facility. In these experiments, cylindrical gas-filled hohlraums with gold walls are driven by a 20 ns laser pulse. For the first time, simulations show the appearance of Kelvin-Helmholtz (KH) vortices at the interface between the expanding wall material and the gas fill. In this paper, we determine the mechanisms which generate this instability: the increase of the gas pressure around the expanding gold plasma leads to the aggregation of an over-dense gold layer simultaneously with shear flows. At the surface of this layer, all the conditions are met for a KH instability to grow. Later on, as the interface decelerates, the Rayleigh-Taylor instability also comes into play. A potential scenario for the generation of a mixing zone at the gold-gas interface due to the KH instability is presented. Our estimates of the Reynolds number and the plasma diffusion width at the interface support the possibility of such a mix. The key role of the first nanosecond of the laser pulse in the instability occurrence is also underlined.
Supresión de modos de vibración acústicos con un resonador Helmholtz
Directory of Open Access Journals (Sweden)
Guiguet Andrés
2003-01-01
Full Text Available La inserción de un Resonador Helmholtz (RH en las paredes laterales de un tubo, con ondas estacionarias en su interior, logra suprimir uno o más de sus modos resonantes si se elige adecuadamente la frecuencia del resonador. El RH puede actuar también como filtro de ondas propagantes.' En este caso, el RH atenua las ondas en un rango de frecuencia muy selectivo. En la mayoría de los textos de acústica, solamente se desarrolla la teoría que explica el filtrado de ondas propagantes. Sin embargo, en los laboratorios de física basica, donde se dispone solamente de tubos de Kundt de pequeña longitud, no es simple realizar un arreglo experimental que asegure la presencia de ondas propagantes puras en su interior. La falta de una teoría para ondas estacionarias y las dificultades experimentales que señalamos han producido algunas confusiones en trabajos que tratan sobre el tema. En este artículo se presenta un modelo teórico que describe satisfactoriamente el comportamiento del RH cuando funciona como filtro de ondas estacionarias y se marcan las diferencias con la situación en que opera como filtro de ondas propagantes.
Barbulescu, M.; Erdélyi, R.
2018-06-01
Recent observations have shown that bulk flow motions in structured solar plasmas, most evidently in coronal mass ejections (CMEs), may lead to the formation of Kelvin-Helmholtz instabilities (KHIs). Analytical models are thus essential in understanding both how the flows affect the propagation of magnetohydrodynamic (MHD) waves, and what the critical flow speed is for the formation of the KHI. We investigate both these aspects in a novel way: in a steady magnetic slab embedded in an asymmetric environment. The exterior of the slab is defined as having different equilibrium values of the background density, pressure, and temperature on either side. A steady flow and constant magnetic field are present in the slab interior. Approximate solutions to the dispersion relation are obtained analytically and classified with respect to mode and speed. General solutions and the KHI thresholds are obtained numerically. It is shown that, generally, both the KHI critical value and the cut-off speeds for magnetoacoustic waves are lowered by the external asymmetry.
Video Vectorization via Tetrahedral Remeshing.
Wang, Chuan; Zhu, Jie; Guo, Yanwen; Wang, Wenping
2017-02-09
We present a video vectorization method that generates a video in vector representation from an input video in raster representation. A vector-based video representation offers the benefits of vector graphics, such as compactness and scalability. The vector video we generate is represented by a simplified tetrahedral control mesh over the spatial-temporal video volume, with color attributes defined at the mesh vertices. We present novel techniques for simplification and subdivision of a tetrahedral mesh to achieve high simplification ratio while preserving features and ensuring color fidelity. From an input raster video, our method is capable of generating a compact video in vector representation that allows a faithful reconstruction with low reconstruction errors.
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
Extended vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
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
A vector matching method for analysing logic Petri nets
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.
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
Generalized decompositions of dynamic systems and vector Lyapunov functions
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.
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.
Optimality Conditions in Vector Optimization
Jiménez, Manuel Arana; Lizana, Antonio Rufián
2011-01-01
Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions have been written by some of the most eminent researchers in this field of mathematical programming. The Ebook is considered essential for researchers and students in this field.
Symmetric vectors and algebraic classification
International Nuclear Information System (INIS)
Leibowitz, E.
1980-01-01
The concept of symmetric vector field in Riemannian manifolds, which arises in the study of relativistic cosmological models, is analyzed. Symmetric vectors are tied up with the algebraic properties of the manifold curvature. A procedure for generating a congruence of symmetric fields out of a given pair is outlined. The case of a three-dimensional manifold of constant curvature (''isotropic universe'') is studied in detail, with all its symmetric vector fields being explicitly constructed
Vector continued fractions using a generalized inverse
International Nuclear Information System (INIS)
Haydock, Roger; Nex, C M M; Wexler, Geoffrey
2004-01-01
A real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
International Nuclear Information System (INIS)
Nelson, Ann E.; Walsh, Jonathan
2008-01-01
We show that for a force mediated by a vector particle coupled to a conserved U(1) charge, the apparent range and strength can depend on the size and density of the source, and the proximity to other sources. This chameleon effect is due to screening from a light charged scalar. Such screening can weaken astrophysical constraints on new gauge bosons. As an example we consider the constraints on chameleonic gauged B-L. We show that although Casimir measurements greatly constrain any B-L force much stronger than gravity with range longer than 0.1 μm, there remains an experimental window for a long-range chameleonic B-L force. Such a force could be much stronger than gravity, and long or infinite range in vacuum, but have an effective range near the surface of the earth which is less than a micron.
Architecture and Vector Control
DEFF Research Database (Denmark)
von Seidlein, Lorenz; Knols, Bart GJ; Kirby, Matthew
2012-01-01
, closing of eaves and insecticide treated bednets. All of these interventions have an effect on the indoor climate. Temperature, humidity and airflow are critical for a comfortable climate. Air-conditioning and fans allow us to control indoor climate, but many people in Africa and Asia who carry the brunt...... of vector-borne diseases have no access to electricity. Many houses in the hot, humid regions of Asia have adapted to the environment, they are built of porous materials and are elevated on stilts features which allow a comfortable climate even in the presence of bednets and screens. In contrast, many...... buildings in Africa and Asia in respect to their indoor climate characteristics and finally, show how state-of-the-art 3D modelling can predict climate characteristics and help to optimize buildings....
International Nuclear Information System (INIS)
Ginelli, Francesco; Politi, Antonio; Chaté, Hugues; Livi, Roberto
2013-01-01
Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets’ theorem for the properties of the CLVs. We then present a detailed description of a ‘dynamical’ algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi–Pasta–Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (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 connection between the Einstein and Yang-Mills equations
International Nuclear Information System (INIS)
Mason, L.J.; Newman, E.T.
1989-01-01
It is our purpose here to show an unusual relationship between the Einstein equations and the Yang-Mills equations. We give a correspondence between solutions of the self-dual Einstein vacuum equations and the self-dual Yang-Mills equations with a special choice of gauge group. The extension of the argument to the full Yang-Mills equations yields Einstein's unified equations. We try to incorporate the full Einstein vacuum equations, but the approach is incomplete. We first consider Yang-Mills theory for an arbitrary Lie-algebra with the condition that the connection 1-form and curvature are constant on Minkowski space. This leads to a set of algebraic equations on the connection components. We then specialize the Lie-algebra to be the (infinite dimensional) Lie algebra of a group of diffeomorphisms of some manifold. The algebraic equations then become differential equations for four vector fields on the manifold on which the diffeomorphisms act. In the self-dual case, if we choose the connection components from the Lie-algebra of the volume preserving 4-dimensional diffeomorphism group, the resulting equations are the same as those obtained by Ashtekar, Jacobsen and Smolin, in their remarkable simplification of the self-dual Einstein vacuum equations. (An alternative derivation of the same equations begins with the self-dual Yang-Mills connection now depending only on the time, then choosing the Lie-algebra as that of the volume preserving 3-dimensional diffeomorphisms). When the reduced full Yang-Mills equations are used in the same context, we get Einstein's equations for his unified theory based on absolute parallelism. To incorporate the full Einstein vacuum equations we use as the Lie group the semi-direct product of the diffeomorphism group of a 4-dimensional manifold with the group of frame rotations of an SO(1, 3) bundle over the 4-manifold. This last approach, however, yields equations more general than the vacuum equations. (orig.)
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