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Sample records for maxwell equations consists

  1. Generation of static solutions of self-consistent system of Einstein-Maxwell equations

    International Nuclear Information System (INIS)

    Anchikov, A.M.; Daishev, R.A.

    1988-01-01

    The theorem, according to which the static solution of the self-consistent system of the Einstein-Maxwell equations is assigned to energy static solution of the Einstein equations with the arbitrary energy-momentum tensor in the right part, is proved. As a consequence of this theorem, the way of the generation of the static solutions of the self-consistent system of the Einstein-Maxwell equations with charged dust as a source of the vacuum solutions of the Einstein equations is shown

  2. Generation of static solutions of the self-consistent system of Einstein-Maxwell equations

    International Nuclear Information System (INIS)

    Anchikov, A.M.; Daishev, R.A.

    1988-01-01

    A theorem is proved, according to which to each solution of the Einstein equations with an arbitrary momentum-energy tensor in the right hand side there corresponds a static solution of the self-consistent system of Einstein-Maxwell equations. As a consequence of this theorem, a method is established of generating static solutions of the self-consistent system of Einstein-Maxwell equations with a charged grain as a source of vacuum solutions of the Einstein equations

  3. Green`s function of Maxwell`s equations and corresponding implications for iterative methods

    Energy Technology Data Exchange (ETDEWEB)

    Singer, B.S. [Macquarie Univ., Sydney (Australia); Fainberg, E.B. [Inst. of Physics of the Earth, Moscow (Russian Federation)

    1996-12-31

    Energy conservation law imposes constraints on the norm and direction of the Hilbert space vector representing a solution of Maxwell`s equations. In this paper, we derive these constrains and discuss the corresponding implications for the Green`s function of Maxwell`s equations in a dissipative medium. It is shown that Maxwell`s equations can be reduced to an integral equation with a contracting kernel. The equation can be solved using simple iterations. Software based on this algorithm have successfully been applied to a wide range of problems dealing with high contrast models. The matrix corresponding to the integral equation has a well defined spectrum. The equation can be symmetrized and solved using different approaches, for instance one of the conjugate gradient methods.

  4. Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations

    International Nuclear Information System (INIS)

    Brizard, Alain J.

    2000-01-01

    A new variational principle for the nonlinear gyrokinetic Vlasov--Maxwell equations is presented. This Eulerian variational principle uses constrained variations for the gyrocenter Vlasov distribution in eight-dimensional extended phase space and turns out to be simpler than the Lagrangian variational principle recently presented by H. Sugama [Phys. Plasmas 7, 466 (2000)]. A local energy conservation law is then derived explicitly by the Noether method. In future work, this new variational principle will be used to derive self-consistent, nonlinear, low-frequency Vlasov--Maxwell bounce-gyrokinetic equations, in which the fast gyromotion and bounce-motion time scales have been eliminated

  5. Geometric Implications of Maxwell's Equations

    Science.gov (United States)

    Smith, Felix T.

    2015-03-01

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

  6. Static Einstein--Maxwell field equations

    International Nuclear Information System (INIS)

    Das, A.

    1979-01-01

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

  7. Maxwell's equations, quantum physics and the quantum graviton

    International Nuclear Information System (INIS)

    Gersten, Alexander; Moalem, Amnon

    2011-01-01

    Quantum wave equations for massless particles and arbitrary spin are derived by factorizing the d'Alembertian operator. The procedure is extensively applied to the spin one photon equation which is related to Maxwell's equations via the proportionality of the photon wavefunction Ψ to the sum E + iB of the electric and magnetic fields. Thus Maxwell's equations can be considered as the first quantized one-photon equation. The photon wave equation is written in two forms, one with additional explicit subsidiary conditions and second with the subsidiary conditions implicitly included in the main equation. The second equation was obtained by factorizing the d'Alembertian with 4×4 matrix representation of 'relativistic quaternions'. Furthermore, scalar Lagrangian formalism, consistent with quantization requirements is developed using derived conserved current of probability and normalization condition for the wavefunction. Lessons learned from the derivation of the photon equation are used in the derivation of the spin two quantum equation, which we call the quantum graviton. Quantum wave equation with implicit subsidiary conditions, which factorizes the d'Alembertian with 8×8 matrix representation of relativistic quaternions, is derived. Scalar Lagrangian is formulated and conserved probability current and wavefunction normalization are found, both consistent with the definitions of quantum operators and their expectation values. We are showing that the derived equations are the first quantized equations of the photon and the graviton.

  8. 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.

  9. How to obtain the covariant form of Maxwell's equations from the continuity equation

    International Nuclear Information System (INIS)

    Heras, Jose A

    2009-01-01

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

  10. Magnetic monopoles, Galilean invariance, and Maxwell's equations

    International Nuclear Information System (INIS)

    Crawford, F.S.

    1992-01-01

    Maxwell's equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell's equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb's law, Biot and Savart's law, Ampere's law, Faraday's law, Maxwell's displacement current, etc., are introduced independently, ''as demanded by experiment.'' Instead a conceptual path that deduces all of Maxwell's equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton's laws hold, to a first approximation; (b) the laws of electrodynamics are Galilean invariant---i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities v much-lt c are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula

  11. Unconditionally stable integration of Maxwell's equations

    NARCIS (Netherlands)

    J.G. Verwer (Jan); M.A. Botchev

    2008-01-01

    htmlabstractNumerical integration of Maxwell''s equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction

  12. Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates

    International Nuclear Information System (INIS)

    Brizard, A.

    1988-09-01

    A gyrokinetic formalism using magnetic coordinates is used to derive self-consistent, nonlinear Maxwell-Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic coordinates is an important feature of this work as it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the Action-variational Lie perturbation method of Cary and Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfven perturbations in slab geometry, or electrostatic perturbations in toroidal geometry. In this present work, fully electromagnetic perturbations in toroidal geometry are considered. 26 refs

  13. Chaotic dynamics in the Maxwell-Bloch equations

    International Nuclear Information System (INIS)

    Holm, D.D.; Kovacic, G.

    1992-01-01

    In the slowly varying envelope approximation and the rotating wave approximation for the Maxwell-Bloch equations, we describe how the presence of a small-amplitude probe laser in an excited, two-level, resonant medium leads to homoclinic chaos in the laser-matter dynamics. We also describe a derivation of the Maxwell-Bloch equations from an action principle

  14. Modified Maxwell equations in quantum electrodynamics

    CERN Document Server

    Harmuth, Henning F; Meffert, Beate

    2001-01-01

    Divergencies in quantum field theory referred to as "infinite zero-point energy" have been a problem for 70 years. Renormalization has always been considered an unsatisfactory remedy. In 1985 it was found that Maxwell's equations generally do not have solutions that satisfy the causality law. An additional term for magnetic dipole currents corrected this shortcoming. Rotating magnetic dipoles produce magnetic dipole currents, just as rotating electric dipoles in a material like barium titanate produce electric dipole currents. Electric dipole currents were always part of Maxwell's equations. T

  15. Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories

    International Nuclear Information System (INIS)

    Niu Chao; Tian Yu; Wu Xiaoning; Ling Yi

    2012-01-01

    The dual fluid description for a general cutoff surface at radius r=r c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε 2 ). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff r c but dependent on the charge density of the black brane.

  16. Maxwell Equations and the Redundant Gauge Degree of Freedom

    Science.gov (United States)

    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…

  17. How to obtain the covariant form of Maxwell's equations from the continuity equation

    Energy Technology Data Exchange (ETDEWEB)

    Heras, Jose A [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico D. F. (Mexico); Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D. F. 01210 (Mexico)

    2009-07-15

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

  18. Comparison of different Maxwell solvers coupled to a PIC resolution method of Maxwell-Vlasov equations

    International Nuclear Information System (INIS)

    Fochesato, Ch.; Bouche, D.

    2007-01-01

    The numerical solution of Maxwell equations is a challenging task. Moreover, the range of applications is very wide: microwave devices, diffraction, to cite a few. As a result, a number of methods have been proposed since the sixties. However, among all these methods, none has proved to be free of drawbacks. The finite difference scheme proposed by Yee in 1966, is well suited for Maxwell equations. However, it only works on cubical mesh. As a result, the boundaries of complex objects are not properly handled by the scheme. When classical nodal finite elements are used, spurious modes appear, which spoil the results of simulations. Edge elements overcome this problem, at the price of rather complex implementation, and computationally intensive simulations. Finite volume methods, either generalizing Yee scheme to a wider class of meshes, or applying to Maxwell equations methods initially used in the field of hyperbolic systems of conservation laws, are also used. Lastly, 'Discontinuous Galerkin' methods, generalizing to arbitrary order of accuracy finite volume methods, have recently been applied to Maxwell equations. In this report, we more specifically focus on the coupling of a Maxwell solver to a PIC (Particle-in-cell) method. We analyze advantages and drawbacks of the most widely used methods: accuracy, robustness, sensitivity to numerical artefacts, efficiency, user judgment. (authors)

  19. Maxwell-Like Equations for Free Dirac Electrons

    Science.gov (United States)

    Bruce, S. A.

    2018-03-01

    In this article, we show that the wave equation for a free Dirac electron can be represented in a form that is analogous to Maxwell's electrodynamics. The electron bispinor wavefunction is explicitly expressed in terms of its real and imaginary components. This leads us to incorporate into it appropriate scalar and pseudo-scalar fields in advance, so that a full symmetry may be accomplished. The Dirac equation then takes on a form similar to that of a set of inhomogeneous Maxwell's equations involving a particular self-source. We relate plane wave solutions of these equations to waves corresponding to free Dirac electrons, identifying the longitudinal component of the electron motion, together with the corresponding Zitterbewegung ("trembling motion").

  20. MAXWELL EQUATIONS FOR A GENERALISED LAGRANGIAN FUNCTIONAL ECUACIONES DE MAXWELL PARA UNA FUNCIONAL DE LAGRANGE GENERALIZADA

    Directory of Open Access Journals (Sweden)

    Héctor Torres-Silva

    2008-11-01

    Full Text Available This work deals with the problem of the construction of the Lagrange functional for an electromagnetic field. The generalised Maxwell equations for an electromagnetic field in free space are introduced. The main idea relies on the change of Lagrange function under the integral action. Usually, the Lagrange functional which describes the electromagnetic field is built with the quadrate of the electromagnetic field tensor . Such a quadrate term is the reason, from a mathematical point of view, for the linear form of the Maxwell equations in free space. The author does not make this assumption and nonlinear Maxwell equations are obtained. New material parameters of free space are established. The equations obtained are quite similar to the well-known Maxwell equations. The energy tensor of the electromagnetic field from a chiral approach to the Born Infeld Lagrangian is discussed in connection with the cosmological constant.Se aborda el problema de la construcción de la funcional de Lagrange de un campo electromagnético. Se introducen las ecuaciones generalizadas de Maxwell de un campo electromagnético en el espacio libre. La idea principal se basa en el cambio de función de Lagrange en virtud de la acción integral. Por lo general, la funcional de lagrange, que describe el campo electromagnético, se construye con el cuadrado del tensor de campo electromagnético. Ese término cuadrático es la razón, desde un punto de vista matemático, de la forma lineal de las ecuaciones de Maxwell en el espacio libre. Se obtienen las ecuaciones no lineales de Maxwell sin considerar esta suposición. Las ecuaciones de Maxwell obtenidas son bastante similares a las conocidas ecuaciones de Maxwell. Se analiza el tensor de energía del campo electromagnético en un enfoque quiral de la Lagrangiana de Born Infeld en relación con la constante cosmológica.

  1. Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals

    International Nuclear Information System (INIS)

    Takeda, Hiroyuki; John, Sajeev

    2011-01-01

    We theoretically demonstrate the population switching of quantum dots (QD's), modeled as two-level atoms in idealized one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) by self-consistent solution of the Maxwell-Bloch equations. In our semiclassical theory, energy states of the electron are quantized, and electron dynamics is described by the atomic Bloch equation, while electromagnetic waves satisfy the classical Maxwell equations. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states (LDOS) and spontaneous emission rates exhibit abrupt changes with frequency, enabling large QD population inversion driven by both continuous and pulsed optical fields. We recapture and generalize this ultrafast population switching using the Maxwell-Bloch equations. Radiative emission from the QD is obtained directly from the surrounding PC geometry using finite-difference time-domain simulation of the electromagnetic field. The atomic Bloch equations provide a source term for the electromagnetic field. The total electromagnetic field, consisting of the external input and radiated field, drives the polarization components of the atomic Bloch vector. We also include a microscopic model for phonon dephasing of the atomic polarization and nonradiative decay caused by damped phonons. Our self-consistent theory captures stimulated emission and coherent feedback effects of the atomic Mollow sidebands, neglected in earlier treatments. This leads to remarkable high-contrast QD-population switching with relatively modest (factor of 10) jump discontinuities in the electromagnetic LDOS. Switching is demonstrated in three separate models of QD's placed (i) in the vicinity of a band edge of a 1D PC, (ii) near a cutoff frequency in a bimodal waveguide channel of a 2D PC, and (iii) in the vicinity of a localized defect mode side coupled to a single-mode waveguide channel in a 2D PC.

  2. Mathematics and Maxwell's equations

    Energy Technology Data Exchange (ETDEWEB)

    Boozer, Allen H, E-mail: ahb17@columbia.ed [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States)

    2010-12-15

    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.

  3. Stationary axisymmetric Einstein--Maxwell field equations

    International Nuclear Information System (INIS)

    Catenacci, R.; Diaz Alonso, J.

    1976-01-01

    We show the existence of a formal identity between Einstein's and Ernst's stationary axisymmetric gravitational field equations and the Einstein--Maxwell and the Ernst equations for the electrostatic and magnetostatic axisymmetric cases. Our equations are invariant under very simple internal symmetry groups, and one of them appears to be new. We also obtain a method for associating two stationary axisymmetric vacuum solutions with every electrostatic known

  4. Classes of general axisymmetric solutions of Einstein-Maxwell equations

    International Nuclear Information System (INIS)

    Krori, K.D.; Choudhury, T.

    1981-01-01

    An exact solution of the Einstein equations for a stationary axially symmetric distribution of mass composed of all types of multipoles is obtained. Following Ernst (1968), from this vacuum solution the corresponding solution of the coupled Einstein-Maxwell equations is derived. A solution of Einstein-Maxwell fields for a static axially symmetric system composed of all types of multipoles is also obtained. (author)

  5. Second order guiding-center Vlasov–Maxwell equations

    DEFF Research Database (Denmark)

    Madsen, Jens

    2010-01-01

    Second order gyrogauge invariant guiding-center coordinates with strong E×B-flow are derived using the Lie transformation method. The corresponding Poisson bracket structure and equations of motion are obtained. From a variational principle the explicit Vlasov–Maxwell equations are derived...

  6. 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

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

    International Nuclear Information System (INIS)

    Kambe, Tsutomu

    2010-01-01

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

  8. Squeezing of open boundaries by Maxwell-consistent real coordinate transformation

    DEFF Research Database (Denmark)

    Shyroki, Dzmitry

    2006-01-01

    To emulate open boundaries within a finite computational domain, real-function coordinate transformation consistent with generally covariant Maxwell equations is proposed. The mapping-realized with arctangent function here-has a transparent geometric meaning of pure squeezing of coordinates, does...... not introduce artificially lossy layers (or "lossy coordinates") to absorb outgoing radiation, nor lead to spurious non-Maxwellian fields. In finite-difference frequency-domain calculations on staggered grid, clear superiority over perfectly matched layers is demonstrated by the proposed technique, at a lower...

  9. Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

    International Nuclear Information System (INIS)

    Kramer, D.; Neugebauer, G.

    1981-01-01

    The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. Using the method of Wahlquist and Estabrook (J. Math Phys.; 16:1 (1975)) it is shown that the prolongation structure of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found. (author)

  10. Generalization of the Biot--Savart law to Maxwell's equations using special relativity

    International Nuclear Information System (INIS)

    Neuenschwander, D.E.; Turner, B.N.

    1992-01-01

    Maxwell's equations are obtained by generalizing the laws of magnetostatics, which follow from the Biot--Savart law and superposition, to be consistent with special relativity. The Lorentz force on a charged particle and its rate of energy change also follow by making Newton's second law for a particle in a magnetostatic field consistent with special relativity

  11. Unconditionally stable integration of Maxwell's equations

    NARCIS (Netherlands)

    Verwer, J.G.; Bochev, Mikhail A.

    Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit finite difference

  12. Comparison of different Maxwell solvers coupled to a PIC resolution method of Maxwell-Vlasov equations; Evaluation de differents solveurs Maxwell pour la resolution de Maxwell-Vlasov par une methode PIC

    Energy Technology Data Exchange (ETDEWEB)

    Fochesato, Ch. [CEA Bruyeres-le-Chatel, Dept. de Conception et Simulation des Armes, Service Simulation des Amorces, Lab. Logiciels de Simulation, 91 (France); Bouche, D. [CEA Bruyeres-le-Chatel, Dept. de Physique Theorique et Appliquee, Lab. de Recherche Conventionne, Centre de Mathematiques et Leurs Applications, 91 (France)

    2007-07-01

    The numerical solution of Maxwell equations is a challenging task. Moreover, the range of applications is very wide: microwave devices, diffraction, to cite a few. As a result, a number of methods have been proposed since the sixties. However, among all these methods, none has proved to be free of drawbacks. The finite difference scheme proposed by Yee in 1966, is well suited for Maxwell equations. However, it only works on cubical mesh. As a result, the boundaries of complex objects are not properly handled by the scheme. When classical nodal finite elements are used, spurious modes appear, which spoil the results of simulations. Edge elements overcome this problem, at the price of rather complex implementation, and computationally intensive simulations. Finite volume methods, either generalizing Yee scheme to a wider class of meshes, or applying to Maxwell equations methods initially used in the field of hyperbolic systems of conservation laws, are also used. Lastly, 'Discontinuous Galerkin' methods, generalizing to arbitrary order of accuracy finite volume methods, have recently been applied to Maxwell equations. In this report, we more specifically focus on the coupling of a Maxwell solver to a PIC (Particle-in-cell) method. We analyze advantages and drawbacks of the most widely used methods: accuracy, robustness, sensitivity to numerical artefacts, efficiency, user judgment. (authors)

  13. Maxwell-Vlasov equations as a continuous Hamiltonian system

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1980-09-01

    The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion

  14. FDTD for Hydrodynamic Electron Fluid Maxwell Equations

    Directory of Open Access Journals (Sweden)

    Yingxue Zhao

    2015-05-01

    Full Text Available In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG from metallic split-ring resonator (SRR.

  15. On fictitious domain formulations for Maxwell's equations

    DEFF Research Database (Denmark)

    Dahmen, W.; Jensen, Torben Klint; Urban, K.

    2003-01-01

    We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formu...

  16. CSR Fields: Direct Numerical Solution of the Maxwell's Equation

    International Nuclear Information System (INIS)

    Novokhatski, Alexander

    2011-01-01

    We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in (1). Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in (2). We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields (3).

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

    Science.gov (United States)

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

    1994-01-01

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

  18. Reformulation of Maxwell's equations to incorporate near-solute solvent structure.

    Science.gov (United States)

    Yang, Pei-Kun; Lim, Carmay

    2008-09-04

    Maxwell's equations, which treat electromagnetic interactions between macroscopic charged objects in materials, have explained many phenomena and contributed to many applications in our lives. Derived in 1861 when no methods were available to determine the atomic structure of macromolecules, Maxwell's equations assume the solvent to be a structureless continuum. However, near-solute solvent molecules are highly structured, unlike far-solute bulk solvent molecules. Current methods cannot treat both the near-solute solvent structure and time-dependent electromagnetic interactions in a macroscopic system. Here, we derive "microscopic" electrodynamics equations that can treat macroscopic time-dependent electromagnetic field problems like Maxwell's equations and reproduce the solvent molecular and dipole density distributions observed in molecular dynamics simulations. These equations greatly reduce computational expense by not having to include explicit solvent molecules, yet they treat the solvent electrostatic and van der Waals effects more accurately than continuum models. They provide a foundation to study electromagnetic interactions between molecules in a macroscopic system that are ubiquitous in biology, bioelectromagnetism, and nanotechnology. The general strategy presented herein to incorporate the near-solute solvent structure would enable studies on how complex cellular protein-ligand interactions are affected by electromagnetic radiation, which could help to prevent harmful electromagnetic spectra or find potential therapeutic applications.

  19. Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrödinger Equations using the FDTD Method

    Directory of Open Access Journals (Sweden)

    I. Ahmed

    2012-09-01

    Full Text Available Maxwell and Schrödinger equations are coupled to incorporate quantum effects for the simulation of plasmonics nanodevices. Maxwell equations with Lorentz-Drude (LD dispersive model are applied to large size plasmonics components, whereas coupled Maxwell and Schrödinger equations are applied to components where quantum effects are needed. The finite difference time domain method (FDTD is applied to simulate these coupled equations.

  20. Resolution of unsteady Maxwell equations with charges in non convex domains

    International Nuclear Information System (INIS)

    Garcia, Emmanuelle

    2002-01-01

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

  1. The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

    Science.gov (United States)

    Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

    2018-04-01

    The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

  2. New and old symmetries of the Maxwell and Dirac equations

    International Nuclear Information System (INIS)

    Fushchich, V.I.; Nikitin, A.G.

    1983-01-01

    The symmetry properties of Maxwell's equations for the electromagnetic field and also of the Dirac and Kemmer-Duffin-Petiau equations are analyzed. In the framework of a ''non-Lie'' approach it is shown that, besides the well-known invariance with respect to the conformal group and the Heaviside-Larmor-Rainich transformations, Maxwell's equations have an additional symmetry with respect to the group U(2)xU(2) and with respect to the 23-dimensional Lie algebra A 23 . The transformations of the additional symmetry are given by nonlocal (integro-differential) operators. The symmetry of the Dirac equation in the class of differential and integro-differential transformations is investigated. It is shown that this equation is invariant with respect to an 18-parameter group, which includes the Poincare group as a subgroup. A 28-parameter invariance group of the Kemmer-Duffin-Petiau equation is found. Finite transformations of the conformal group for a massless field with arbitrary spin are obtained. The explicit form of conformal transformations for the electromagnetic field and also for the Dirac and Weyl fields is given

  3. The covariant formulation of Maxwell's equations expressed in a form independent of specific units

    International Nuclear Information System (INIS)

    Heras, Jose A; Baez, G

    2009-01-01

    The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants α, β and γ into these equations. Maxwell's equations involving these constants are then specialized to the most commonly used systems of units: Gaussian, SI and Heaviside-Lorentz by giving the constants α, β and γ the values appropriate to each system

  4. On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave

    Directory of Open Access Journals (Sweden)

    Arbab A. I.

    2009-04-01

    Full Text Available We have formulated the basic laws of electromagnetic theory in quaternion form. The formalism shows that Maxwell equations and Lorentz force are derivable from just one quaternion equation that only requires the Lorentz gauge. We proposed a quaternion form of the continuity equation from which we have derived the ordinary continuity equation. We introduce new transformations that produces a scalar wave and generalize the continuity equation to a set of three equations. These equations imply that both current and density are waves. Moreover, we have shown that the current can not cir- culate around a point emanating from it. Maxwell equations are invariant under these transformations. An electroscalar wave propagating with speed of light is derived upon requiring the invariance of the energy conservation equation under the new transforma- tions. The electroscalar wave function is found to be proportional to the electric field component along the charged particle motion. This scalar wave exists with or without considering the Lorentz gauge. We have shown that the electromagnetic fields travel with speed of light in the presence or absence of free charges.

  5. Mathematical and numerical methods for Vlasov-Maxwell equations: the contributions of data mining

    International Nuclear Information System (INIS)

    Assous, F.; Chaskalovic, J.

    2014-01-01

    There exist a lot of formulations that can model plasma physics or particle accelerators problems as the Vlasov- Maxwell equations. This paper deals with the applications of data mining techniques in the evaluation of numerical solutions of Vlasov-Maxwell models. This is part of the topic of characterizing the model and approximation errors via learning techniques. We give two examples of application. The first one aims at comparing two Vlasov-Maxwell approximate models. In the second one, a scheme based on data mining techniques is proposed to characterize the errors between a P1 and a P2 finite element Particle-In-Cell approach. Beyond these examples, this original approach should operate in all cases where intricate numerical simulations like for the Vlasov-Maxwell equations take a central part. (authors)

  6. On new and old symmetries of Maxwell and Dirac equations

    International Nuclear Information System (INIS)

    Fushchich, V.I.; Nikitin, A.G.

    1983-01-01

    Symmetry properties of the Maxwell equation for the electromagnetic field are analysed as well as of the Dirac and Kemmer-Duffin-Petiau one. In the frame of the non-geometrical approach it is demonstrated, that besides to the well-known invariance under the conformal group and Heaviside-Larmor-Rainich transformation, Maxwell equation possess the additional symmetry under the group U(2)xU(2) and under the 23-dimensional Lie algebra A 23 . The additional symmetry transformations are realized by the non-local (integro-differential) operators. The symmetry of the Dirac. equation under the differential and integro-differential transformations is investio.ated. It is shown that this equation is invariant under the 18-parametrical group, which includes the Poincare group as a subgroup. The 28-parametrical invariance group of the Kemmer-Duffin-Petiau equation is found. The finite conformal group transformations for a massless field of any spin are obtained. The explicit form of the conformal transformations for the electromagnetic field as well as for the Dirac and Weyl fields is given

  7. Algorithm development for Maxwell's equations for computational electromagnetism

    Science.gov (United States)

    Goorjian, Peter M.

    1990-01-01

    A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.

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

    Science.gov (United States)

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

    1995-01-01

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

  9. Gravitational and electromagnetic potentials of the stationary Einstein-Maxwell field equations

    International Nuclear Information System (INIS)

    Jones, T.C.

    1979-01-01

    Associated with the stationary Einstein-Maxwell field equations is an infinite hierarchy of potentials. The basic characteristics of these potentials are examined in general and then in greater detail for the particular case of the Reissner-Nordstrom metric. Thier essential utility in the process of solution generation is elucidated, and the necessary equations for solution generation are developed. Appropriate generating functions, which contain the complete infinite hierarchy of potentials, are developed and analyzed. Particular attention is paid to the inherent gauge freedom of these generating functions. Two methods of solution generation, which yield asymptotically flat solutions in vacuum, are generalized to include electromagnetism. One method, using potentials consistent with the Harrison transformation and the Reissner-Nordstrom metric, is discussed in detail, and its resultant difficulties are explored

  10. Isomonodromic deformations and self-similar solutions of the Einstein-Maxwell equations

    International Nuclear Information System (INIS)

    Kitaev, A.V.

    1992-01-01

    It is shown that the self-similar solutions of the Einstein-Maxwell equations in the cylindrical case describe the isomonodromic deformations of ordinary linear differential equations with rational coefficients. New types of such solutions, expressed in terms of the fifth Painleve transcendent, are found. 24 refs

  11. The square root of the Dirac operator on superspace and the Maxwell equations

    Science.gov (United States)

    Bzdak, Adam; Hadasz, Leszek

    2004-02-01

    We re-consider the procedure of "taking a square root of the Dirac equation" on superspace and show that it leads to the well-known superfield Wα and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.

  12. q-deformed Weinberg-Salam model and q-deformed Maxwell equations

    International Nuclear Information System (INIS)

    Alavi, S.A.; Sarbishaei, M.; Mokhtari, A.

    2000-01-01

    We study the q-deformation of the gauge part of the Weinberg-Salam model and show that the q-deformed theory involves new interactions. We then obtain q-deformed Maxwell equations from which magnetic monopoles appear naturally. (author)

  13. An elementary solution of the Maxwell equations for a time-dependent source

    International Nuclear Information System (INIS)

    Rivera, R; Villarroel, D

    2002-01-01

    We present an elementary solution of the Maxwell equations for a time-dependent source consisting of an infinite solenoid with a current density that increases linearly with time. The geometrical symmetries and the time dependence of the current density make possible a mathematical treatment that does not involve the usual technical difficulties, thus making this presentation suitable for students that are taking a first course in electromagnetism. We also show that the electric field generated by the solenoid can be used to construct an exact solution of the relativistic equation of motion of the electron that takes into account the effect of the radiation. In particular, we derive, in an almost trivial way, the formula for the radiation rate of an electron in circular motion

  14. The square root of the Dirac operator on superspace and the Maxwell equations

    International Nuclear Information System (INIS)

    Bzdak, Adam; Hadasz, Leszek

    2004-01-01

    We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W α and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation

  15. The covariant formulation of Maxwell's equations expressed in a form independent of specific units

    Energy Technology Data Exchange (ETDEWEB)

    Heras, Jose A; Baez, G [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200 Mexico DF (Mexico)], E-mail: herasgomez@gmail.com, E-mail: gbaez@correo.azc.uam.mx

    2009-01-15

    The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants {alpha}, {beta} and {gamma} into these equations. Maxwell's equations involving these constants are then specialized to the most commonly used systems of units: Gaussian, SI and Heaviside-Lorentz by giving the constants {alpha}, {beta} and {gamma} the values appropriate to each system.

  16. The square root of the Dirac operator on superspace and the Maxwell equations

    Energy Technology Data Exchange (ETDEWEB)

    Bzdak, Adam; Hadasz, Leszek

    2004-02-26

    We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W{sub {alpha}} and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.

  17. New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

    International Nuclear Information System (INIS)

    Goyal, Nisha; Gupta, R.K.

    2012-01-01

    The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein—Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions

  18. Axiomatic field theory and quantum electrodynamics: the massive case. [Gauge invariance, Maxwell equations, high momentum behavior

    Energy Technology Data Exchange (ETDEWEB)

    Steinmann, O [Bielefeld Univ. (F.R. Germany). Fakultaet fuer Physik

    1975-01-01

    Massive quantum electrodynamics of the electron is formulated as an LSZ theory of the electromagnetic field F(..mu nu..) and the electron-positron fields PSI. The interaction is introduced with the help of mathematically well defined subsidiary conditions. These are: 1) gauge invariance of the first kind, assumed to be generated by a conserved current j(..mu..); 2) the homogeneous Maxwell equations and a massive version of the inhomogeneous Maxwell equations; 3) a minimality condition concerning the high momentum behaviour of the theory. The inhomogeneous Maxwell equation is a linear differential equation connecting Fsub(..mu nu..) with the current Jsub(..mu..). No Lagrangian, no non-linear field equations, and no explicit expression of Jsub(..mu..) in terms of PSI, anti-PSI are needed. It is shown in perturbation theory that the proposed conditions fix the physically relevant (i.e. observable) quantities of the theory uniquely.

  19. Maxwell equations in conformal invariant electrodynamics

    International Nuclear Information System (INIS)

    Fradkin, E.S.; AN SSSR, Novosibirsk. Inst. Avtomatiki i Ehlektrometrii); Kozhevnikov, A.A.; Palchik, M.Ya.; Pomeransky, A.A.

    1983-01-01

    We consider a conformal invariant formulation of quantum electrodynamics. Conformal invariance is achieved with a specific mathematical construction based on the indecomposable representations of the conformal group associated with the electromagnetic potential and current. As a corolary of this construction modified expressions for the 3-point Green functions are obtained which both contain transverse parts. They make it possible to formulate a conformal invariant skeleton perturbation theory. It is also shown that the Euclidean Maxwell equations in conformal electrodynamics are manifestations of its kinematical structure: in the case of the 3-point Green functions these equations follow (up to constants) from the conformal invariance while in the case of higher Green functions they are equivalent to the equality of the kernels of the partial wave expansions. This is the manifestation of the mathematical fast of a (partial) equivalence of the representations associated with the potential, current and the field tensor. (orig.)

  20. Self-consistent Maxwell-Bloch model of quantum-dot photonic-crystal-cavity lasers

    Science.gov (United States)

    Cartar, William; Mørk, Jesper; Hughes, Stephen

    2017-08-01

    We present a powerful computational approach to simulate the threshold behavior of photonic-crystal quantum-dot (QD) lasers. Using a finite-difference time-domain (FDTD) technique, Maxwell-Bloch equations representing a system of thousands of statistically independent and randomly positioned two-level emitters are solved numerically. Phenomenological pure dephasing and incoherent pumping is added to the optical Bloch equations to allow for a dynamical lasing regime, but the cavity-mediated radiative dynamics and gain coupling of each QD dipole (artificial atom) is contained self-consistently within the model. These Maxwell-Bloch equations are implemented by using Lumerical's flexible material plug-in tool, which allows a user to define additional equations of motion for the nonlinear polarization. We implement the gain ensemble within triangular-lattice photonic-crystal cavities of various length N (where N refers to the number of missing holes), and investigate the cavity mode characteristics and the threshold regime as a function of cavity length. We develop effective two-dimensional model simulations which are derived after studying the full three-dimensional passive material structures by matching the cavity quality factors and resonance properties. We also demonstrate how to obtain the correct point-dipole radiative decay rate from Fermi's golden rule, which is captured naturally by the FDTD method. Our numerical simulations predict that the pump threshold plateaus around cavity lengths greater than N =9 , which we identify as a consequence of the complex spatial dynamics and gain coupling from the inhomogeneous QD ensemble. This behavior is not expected from simple rate-equation analysis commonly adopted in the literature, but is in qualitative agreement with recent experiments. Single-mode to multimode lasing is also observed, depending on the spectral peak frequency of the QD ensemble. Using a statistical modal analysis of the average decay rates, we also

  1. Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

    Science.gov (United States)

    Tweney, Ryan D.

    2011-01-01

    James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other…

  2. Local WKB dispersion relation for the Vlasov-Maxwell equations

    International Nuclear Information System (INIS)

    Berk, H.L.; Dominguez, R.R.

    1982-10-01

    A formalism for analyzing systems of integral equations, based on the Wentzel-Kramers-Brillouin (WKB) approximation, is applied to the Vlasov-Maxwell integral equations in an arbitrary-β, spatially inhomogenous plasma model. It is shown that when treating frequencies comparable with and larger than the cyclotron frequency, relevant new terms must be accounted for to treat waves that depend upon local spatial gradients. For a specific model, the response for very short wavelength and high frequency is shown to reduce to the straight-line orbit approximation when the WKB rules are correctly followed

  3. On the stationary Einstein-Maxwell-Klein-Gordon equations

    International Nuclear Information System (INIS)

    Gegenberg, J.D.

    1981-05-01

    The stationary Einstein-Maxwell-Klein-Gordon (EMKG) equations for interacting gravitational, electromagnetic and meson fields are examined. The theory is cast into the formalism of principal fiber bundles with a connection, wherein its relationship to current trends in theoretical physics is made manifest. The EMKG equations are shown to admit a Higgs-like mechanism for giving mass to the gauge field. A theorem specifying sufficient conditions for the stationarity of the spacetime metric to imply stationarity of the other fields is proved. By imposing additional constraints and symmetries, the EMKG equations are considerably simplified. An attempt is made to apply a solution-generation technique, and this meets with only partial success. Finally, a stationary but non-static solution is found, and the geometric and physical properties are discussed

  4. The square root of the Dirac operator on the superspace and the Maxwell equations

    OpenAIRE

    Bzdak, Adam; Hadasz, Leszek

    2003-01-01

    We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\\alpha and to the proper equations of motion for the components, i.e. the Maxwell equations and the massless Dirac equation.

  5. Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations

    International Nuclear Information System (INIS)

    Davidson, R.C.; Chen, C.

    1997-08-01

    A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B sol (rvec x) is developed. The analysis is carried out for a thin beam with characteristic beam radius r b much-lt S, and directed axial momentum γ b mβ b c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f b (rvec x,rvec p,t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B z (z) = B 0 = const. and for the case of a periodic solenoidal focusing field B z (z + S) = B z (z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field rvec B sol (rvec x) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria

  6. Twisting null geodesic congruences and the Einstein-Maxwell equations

    International Nuclear Information System (INIS)

    Newman, Ezra T; Silva-Ortigoza, Gilberto

    2006-01-01

    In a recent article, we returned to the study of asymptotically flat solutions of the vacuum Einstein equations with a rather unconventional point of view. The essential observation in that work was that from a given asymptotically flat vacuum spacetime with a given Bondi shear, one can find a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences where the class was uniquely given up to the arbitrary choice of a complex analytic 'worldline' in a four-dimensional complex space. By imitating certain terms in the Weyl tensor that are found in the algebraically special type II metrics, this complex worldline could be made unique and given-or assigned-the physical meaning as the complex centre of mass. Equations of motion for this case were found. The purpose of the present work is to extend those results to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically shear-free null geodesic congruences depending on a complex worldline in the same four-dimensional complex space. However in this case there will be, in general, two distinct but uniquely chosen worldlines, one of which can be assigned as the complex centre of charge while the other could be called the complex centre of mass. Rather than investigating the situation where there are two distinct complex worldlines, we study instead the special degenerate case where the two worldlines coincide, i.e., where there is a single unique worldline. This mimics the case of algebraically special Einstein-Maxwell fields where the degenerate principle null vector of the Weyl tensor coincides with a Maxwell principle null vector. Again we obtain equations of motion for this worldline-but explicitly found here only in an approximation. Though there are ambiguities in assigning physical meaning to different terms it appears as if reliance on the Kerr and charged Kerr metrics and classical electromagnetic radiation theory helps

  7. Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations

    Energy Technology Data Exchange (ETDEWEB)

    Després, Bruno, E-mail: despres@ann.jussieu.fr [Laboratory Jacques Louis Lions, University Pierre et Marie Curie, Paris VI, Boîte courrier 187, 75252 Paris Cedex 05 (France); Weder, Ricardo, E-mail: weder@unam.mx [Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, DF 01000 (Mexico)

    2016-03-22

    We study the long-time asymptotic of the solutions to Maxwell's equation in the case of an upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Després, L.M. Imbert-Gérard and R. Weder (2014) [15], where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas. - Highlights: • The upper-hybrid resonance in the cold plasma model is considered. • The long-time asymptotic of the solutions to Maxwell's equations is studied. • A method based in a singular limiting absorption principle is proposed.

  8. Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains

    KAUST Repository

    Bonito, Andrea

    2013-12-01

    This note establishes regularity estimates for the solution of the Maxwell equations in Lipschitz domains with non-smooth coefficients and minimal regularity assumptions. The argumentation relies on elliptic regularity estimates for the Poisson problem with non-smooth coefficients. © 2013 Elsevier Ltd.

  9. Strong cosmic censorship for solutions of the Einstein-Maxwell field equations with polarized Gowdy symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Nungesser, Ernesto; Rendall, Alan D [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany)

    2009-05-21

    A proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this, it is seen that the deep results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.

  10. Strong cosmic censorship for solutions of the Einstein-Maxwell field equations with polarized Gowdy symmetry

    International Nuclear Information System (INIS)

    Nungesser, Ernesto; Rendall, Alan D

    2009-01-01

    A proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this, it is seen that the deep results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.

  11. Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation

    International Nuclear Information System (INIS)

    Davidson, Ronald C.; Lee, W. Wei-li; Hong Qin; Startsev, Edward

    2001-01-01

    This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed

  12. Orbiting the moons of Pluto complex solutions to the Einstein, Maxwell, Schroedinger and Dirac equations

    CERN Document Server

    Rauscher, Elizabeth A

    2011-01-01

    The Maxwell, Einstein, Schrödinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal

  13. On solution of Maxwell's equations in axisymmetric domains with edges. Part I: Theoretical aspects

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    In this paper we present the basic mathematical tools for treating boundary value problems for the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges by means of partial Fourier analysis. We consider the decomposition of the classical and regularized time-harmonic three-dimensional Maxwell's equations into variational equations in the plane meridian domain of the axisymmetric domain and define suitable weighted Sobolev spaces for their treatment. The trace properties of these spaces on the rotational axis and some properties of the solutions are proved, which are important for further numerical treatment, e.g. by the finite-element method. Particularly, a priori estimates of the solutions of the reduced system are given and the asymptotic behavior of these solutions near reentrant corners of the meridian domain is explicitly described by suitable singular functions. (author)

  14. Symplectic discretization for spectral element solution of Maxwell's equations

    International Nuclear Information System (INIS)

    Zhao Yanmin; Dai Guidong; Tang Yifa; Liu Qinghuo

    2009-01-01

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

  15. Theoretical and numerical study of the equations of Vlasov-Maxwell in the covariant formalism

    International Nuclear Information System (INIS)

    Back, A.

    2011-11-01

    A new point of view is proposed for the simulation of plasmas using the kinetic model which links the equations of Vlasov for the distribution of particles and the equations of Maxwell for the electromagnetic contribution of fields. We use the following principle: the equations of Physics are mathematical objects which put in relation geometrical objects. To preserve the geometrical properties of the various objects in an equation, we use, for the theoretical and numerical study, the differential geometry. All the equations of Physics can be written with differential forms and this point of view is not dependent on the choice of coordinates. We propose then a discretization of the differential forms by using B-Splines. To be coherent with the theory, we also propose a discretization of the various operations of the differential geometry. We test our scheme, first on the equations of Maxwell with several boundary conditions and since it does not depend on the system of coordinates, we also test it when we change coordinates. Finally, we apply the same method to the equations of Vlasov-Poisson in one-dimension and we propose several numerical schemes. (author)

  16. Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates

    NARCIS (Netherlands)

    Harutyunyan, D.; Izsak, F.; van der Vegt, Jacobus J.W.; Bochev, Mikhail A.

    For the adaptive solution of the Maxwell equations on three-dimensional domains with N´ed´elec edge finite element methods, we consider an implicit a posteriori error estimation technique. On each element of the tessellation an equation for the error is formulated and solved with a properly chosen

  17. Infinitely many large energy solutions of superlinear Schrodinger-Maxwell equations

    Directory of Open Access Journals (Sweden)

    Lin Li

    2012-12-01

    Full Text Available In this article we study the existence of infinitely many large energy solutions for the superlinear Schrodinger-Maxwell equations $$displaylines{ -Delta u+V(xu+ phi u=f(x,u quad hbox{in }mathbb{R}^3,cr -Delta phi=u^2, quad hbox{in }mathbb{R}^3, }$$ via the Fountain Theorem in critical point theory. In particular, we do not use the classical Ambrosetti-Rabinowitz condition.

  18. A negative-norm least-squares method for time-harmonic Maxwell equations

    KAUST Repository

    Copeland, Dylan M.

    2012-04-01

    This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.

  19. Application of the operator splitting to the Maxwell equations with the source term

    NARCIS (Netherlands)

    Bochev, Mikhail A.; Faragó, I.; Horváth, R.

    Motivated by numerical solution of the time-dependent Maxwell equations, we consider splitting methods for a linear system of differential equations $w'(t)=Aw(t)+f(t),$ $A\\in\\mathbb{R}^{n\\times n}$ split into two subproblems $w_1'(t)=A_1w_1(t)+f_1(t)$ and $w_2'(t)=A_2w_2(t)+f_2(t),$ $A=A_1+A_2,$

  20. Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

    Directory of Open Access Journals (Sweden)

    Boris V. Kapitonov

    2010-02-01

    Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

  1. Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

    Science.gov (United States)

    Tweney, Ryan D.

    2011-07-01

    James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

  2. Time-integration methods for finite element discretisations of the second-order Maxwell equation

    NARCIS (Netherlands)

    Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.

    This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic

  3. Reduced Vlasov-Maxwell simulations

    International Nuclear Information System (INIS)

    Helluy, P.; Navoret, L.; Pham, N.; Crestetto, A.

    2014-01-01

    The Maxwell-Vlasov system is a fundamental model in physics. It can be applied to plasma simulations, charged particles beam, astrophysics, etc. The unknowns are the electromagnetic field, solution to the Maxwell equations and the distribution function, solution to the Vlasov equation. In this paper we review two different numerical methods for Vlasov-Maxwell simulations. The first method is based on a coupling between a Discontinuous Galerkin (DG) Maxwell solver and a Particle-In-Cell (PIC) Vlasov solver. The second method only uses a DG approach for the Vlasov and Maxwell equations. The Vlasov equation is first reduced to a space-only hyperbolic system thanks to the finite-element method. The two numerical methods are implemented using OpenCL in order to achieve high performance on recent Graphic Processing Units (GPU). We obtained interesting speedups, but we also observe that the PIC method is the most expensive part of the computation. Therefore we propose another fully Eulerian approach. Thanks to a decomposition of the distribution function on velocity basis functions, we obtain a reduced Vlasov model, which appears to be a hyperbolic system of conservation laws written only in the (x,t) space. We can thus adapt very easily our DG solver to the reduced model

  4. Effective Hamiltonians, two level systems, and generalized Maxwell-Bloch equations

    International Nuclear Information System (INIS)

    Sczaniecki, L.

    1981-02-01

    A new method is proposed involving a canonical transformation leading to the non-secular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating wave approximation is written anew within the framework of our formalism. (author)

  5. Exact cosmological solutions of Einstein-Maxwell equations as perturbations of the Bertotti-Robinson model

    International Nuclear Information System (INIS)

    Portugal, R.; Soares, I.D.

    1985-01-01

    Two new classes of spatially homogeneous cosmological solutions of Einstein-Maxwell equations are obtained by considering a class of exact perturbations of the static Bertotti-Robinson (BR) model. The BR solution is shown to be unstable under these perturbations, being perturbed into exact cosmological solutions with perfect fluid (equations of state p = lambda rho, O [pt

  6. Nonlocal symmetries and nonlocal conservation laws of Maxwell's equations

    International Nuclear Information System (INIS)

    Anco, S.C.; Bluman, G.

    1997-01-01

    Nonlocal symmetries are obtained for Maxwell's equations in three space-time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the constants of motion arising from local conservation laws for space-time symmetries. These nine constants of motion represent additional conserved quantities for the electromagnetic field in three space endash time dimensions. copyright 1997 American Institute of Physics

  7. Particle-like solutions of the Einstein-Dirac-Maxwell equations

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    1999-08-01

    We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.

  8. A new perspective on relativistic transformation for Maxwell's equations of electrodynamics

    International Nuclear Information System (INIS)

    Huang, Y.-S.

    2009-01-01

    A new scheme for relativistic transformation of the electromagnetic fields is formulated through relativistic transformation in the wavevector space, instead of the space-time space. Maxwell's equations of electrodynamics are shown to be form-invariant among inertial frames in accordance with this new scheme of relativistic transformation. This new perspective on relativistic transformation not only fulfills the principle of relativity, but is also compatible with quantum theory.

  9. Limited-diffraction solutions to Maxwell and Schroedinger equations

    International Nuclear Information System (INIS)

    Lu, Jian-yu; Greenleaf, J.F.

    1996-10-01

    The authors have developed a new family of limited diffraction electromagnetic X-shaped waves based on the scalar X-shaped waves discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain their shape as they propagate to an infinite distance. The 'X waves' possess (theoretically) infinitely extended 'arms' and - at least, the ones studied in this paper - have an infinite total energy: therefore, they are not physically realizable. However, they can be truncated in both space and time and 'approximated' by means of a finite aperture radiator so to get a large enough depth of interest (depth of field). In addition to the Maxwell equations, X wave solutions to the free Schroedinger equation are also obtained. Possible applications of these new waves are discussed. Finally, the authors discuss the appearance of the X-shaped solutions from the purely geometric point of view of the special relativity theory

  10. A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations

    OpenAIRE

    Boudin , Laurent; Grec , Bérénice; Salvarani , Francesco

    2012-01-01

    International audience; We consider the Maxwell-Stefan model of diffusion in a multicomponent gaseous mixture. After focusing on the main differences with the Fickian diffusion model, we study the equations governing a three-component gas mixture. We provide a qualitative and quantitative mathematical analysis of the model. The main properties of the standard explicit numerical scheme are also analyzed. We eventually include some numerical simulations pointing out the uphill diffusion phenome...

  11. On symmetries and exact solutions of the Einstein–Maxwell field equations via the symmetry approach

    International Nuclear Information System (INIS)

    Kaur, Lakhveer; Gupta, R K

    2013-01-01

    Using the Lie symmetry approach, we have examined herein the system of partial differential equations corresponding to the Einstein–Maxwell equations for a static axially symmetric spacetime. The method used reduces the system of partial differential equations to a system of ordinary differential equations according to the Lie symmetry admitted. In particular, we found the relevant system of ordinary differential equations is all optimal subgroups. The system of ordinary differential equations is further solved in general to obtain exact solutions. Several new physically important families of exact solutions are derived. (paper)

  12. A new type of massive spin-one boson: And its relation with Maxwell equations

    International Nuclear Information System (INIS)

    Ahluwalia, D.V.

    1995-01-01

    First, the author showed that in the (1, 0) circle-plus (0, 1) representation space there exist not one but two theories for charged particles. In the Weinberg construct, the boson and its antiboson carry same relative intrinsic parity, whereas in the author's construct the relative intrinsic parities of the boson and its antiboson are opposite. These results originate from the commutativity of the operations of Charge conjugation and Parity in Weinberg's theory, and from the anti-commutativity of the operations of Charge conjugation and Parity in the author's theory. The author thus claims that he has constructed a first non-trivial quantum theory of fields for the Wigner-type particles. Second, the massless limit of both theories seems formally identical and suggests a fundamental modification of Maxwell equations. At its simplest level, the modification to Maxwell equations enters via additional boundary condition(s)

  13. Stochastic Levy Divergence and Maxwell's Equations

    Directory of Open Access Journals (Sweden)

    B. O. Volkov

    2015-01-01

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

  14. L2-stability of the Vlasov-Maxwell-Boltzmann system near global Maxwellians

    International Nuclear Information System (INIS)

    Ha, Seung-Yeal; Xiao, Qinghua; Xiong, Linjie; Zhao, Huijiang

    2013-01-01

    We present a L 2 -stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L 2 -distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., “A revisiting to the L 2 -stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L 2 stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on the L 2 -stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. [“Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space,” Commun. Pure Appl. Math. 24, 1497–1546 (2011)] and Guo [“The Vlasov-Maxwell-Boltzmann system near Maxwellians,” Invent. Math. 153(3), 593–630 (2003)] satisfy a uniform L 2 -stability estimate. This is the first result on the L 2 -stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions

  15. Exact solutions of Einstein and Einstein-Maxwell equations in higher-dimensional spacetime

    International Nuclear Information System (INIS)

    Xu Dianyan; Beijing Univ., BJ

    1988-01-01

    The D-dimensional Schwarzschild-de Sitter metric and Reissner-Nordstrom-de-Sitter metric are derived directly by solving the Einstein and Einstein-Maxwell equations. The D-dimensional Kerr metric is rederived by using the complex coordinate transformation method and the D-dimensional Kerr-de Sitter metric is also given. The conjecture about the D-dimensional metric of a rotating charged mass is given at the end of this paper. (author)

  16. Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

    Science.gov (United States)

    Chun, Sehun

    2017-07-01

    Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.

  17. Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law

    Institute of Scientific and Technical Information of China (English)

    Liu Changmao

    2005-01-01

    The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codifferential forms are pointed out: they represent the tangent surface and the normal surface fluxes of a tensor, respectively. The definitions of the divergence and the curl of a 2D surface flux of a tensor are obtained.Maxwell's equations, namely, the construction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law ( mass or fluid flux quantity and so on) and the feature of central field ( or its composition). By the feature of central field ( or its composition), the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory ( a magnetic monopole has no effect on electric current just like a couple basing no effect on the sum of forces) are presented: magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell's equations.

  18. Modular hp-FEM system HERMES and its application to Maxwell´s equations

    Czech Academy of Sciences Publication Activity Database

    Vejchodský, Tomáš; Šolín, P.; Zítka, M.

    2007-01-01

    Roč. 76, č. 2 (2007), s. 223-228 ISSN 0378-4754. [MODELLING 2005. Plzeň, 04.06.2005-08.06.2005] R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503 Keywords : hp-FEM * time-harmonic Maxwell´s equations * hierarchic higher-order edge elements Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007

  19. Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-01-01

    We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)

  20. Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

    International Nuclear Information System (INIS)

    Tanimura, Shogo

    1992-01-01

    R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs

  1. Numerical solution of the Maxwell-Vlasov equations in the periodic regime. Application to the study of isotope separation by ion cyclotron resonance; Resolution numerique des equations de Maxwell-Vlasov en regime periodique. Application a l'etude de la separation isotopique par resonance cyclotron ionique

    Energy Technology Data Exchange (ETDEWEB)

    Omnes, P

    1999-01-25

    This work is dedicated to the study of the behaviour of a magnetic confined plasma that is excited by a purely sinusoidal electric current delivered by an antenna. The response of the electrons to the electromagnetic field is considered as linear,whereas the ions of the plasma are represented by a non-relativistic Vlasov equation. In order to avoid transients, the coupled Maxwell-Vlasov equations are solved in a periodic mode and in a bounded domain. An equivalent electric conductivity tensor has been defined, this tensor is a linear operator that links the electric current generated by the movement of the particles to the electromagnetic field. Theoretical considerations can assure the existence and uniqueness of a periodical solution to Vlasov equations and of a solution to Maxwell equations in harmonic mode. The system of equations is periodical and has been solved by using an iterative method. The application of this method to the simulation of a isotopic separation device based on ionic cyclotron resonance has shown that the convergence is reached in a few iterations and that the solution is valid. Furthermore a method based on a finite-volume formulation of Maxwell equations in the time domain is presented. 2 new variables are defined in order to better take into account the Gauss' law and the conservation of the magnetic flux, the new system is still hyperbolic. The parallelization of the process has been successfully realized. (A.C.)

  2. Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

    KAUST Repository

    Huang, Yunqing

    2011-09-01

    Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell\\'s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

  3. Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions

    Directory of Open Access Journals (Sweden)

    A. Sakabekov

    2016-01-01

    Full Text Available We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.

  4. A family of solutions to the Einstein-Maxwell system of equations describing relativistic charged fluid spheres

    Science.gov (United States)

    Komathiraj, K.; Sharma, Ranjan

    2018-05-01

    In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordström space-time. By reducing the Einstein-Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

  5. Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations

    Science.gov (United States)

    Katkar, L. N.

    2015-03-01

    In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.

  6. A reconstruction of Maxwell model for effective thermal conductivity of composite materials

    International Nuclear Information System (INIS)

    Xu, J.Z.; Gao, B.Z.; Kang, F.Y.

    2016-01-01

    Highlights: • Deficiencies were found in classical Maxwell model for effective thermal conductivity. • Maxwell model was reconstructed based on potential mean-field theory. • Reconstructed Maxwell model was extended with particle–particle contact resistance. • Predictions by reconstructed Maxwell model agree excellently with experimental data. - Abstract: Composite materials consisting of high thermal conductive fillers and polymer matrix are often used as thermal interface materials to dissipate heat generated from mechanical and electronic devices. The prediction of effective thermal conductivity of composites remains as a critical issue due to its dependence on considerably factors. Most models for prediction are based on the analog between electric potential and temperature that satisfy the Laplace equation under steady condition. Maxwell was the first to derive the effective electric resistivity of composites by examining the far-field spherical harmonic solution of Laplace equation perturbed by a sphere of different resistivity, and his model was considered as classical. However, a close review of Maxwell’s derivation reveals that there exist several controversial issues (deficiencies) inherent in his model. In this study, we reconstruct the Maxwell model based on a potential mean-field theory to resolve these issues. For composites made of continuum matrix and particle fillers, the contact resistance among particles was introduced in the reconstruction of Maxwell model. The newly reconstructed Maxwell model with contact resistivity as a fitting parameter is shown to fit excellently to experimental data over wide ranges of particle concentration and mean particle diameter. The scope of applicability of the reconstructed Maxwell model is also discussed using the contact resistivity as a parameter.

  7. Scientific discussion | Unifying physics and technology in light of Maxwell's equations | Royal Society, London | 16-17 November

    CERN Multimedia

    2015-01-01

    Discussion meeting organised by Professor Anatoly Zayats, Professor John Ellis and Professor Roy Pike.   16-17 November 2015 at The Royal Society 6-9 Carlton House Terrace, London Event details The unification of electric and magnetic fields about 150 years ago in what is now known as electromagnetic theory expressed in Maxwell's Equations has enabled virtually all modern electrical, electronic, radio and photonic technologies. What new scientific breakthroughs and applications will unification with the other fields provide? This meeting brings together high-energy, optical, quantum and solid-state physicists to discuss recent developments enabled by Maxwell's Equations and will try to predict future innovations. Attending this event This event is intended for researchers in relevant fields and is free to attend. There are a limited number of places and registration is essential. For more information, visit the Royal Society event website.

  8. Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses

    Science.gov (United States)

    Joseph, Rose M.; Hagness, Susan C.; Taflove, Allen

    1991-01-01

    The initial results for femtosecond pulse propagation and scattering interactions for a Lorentz medium obtained by a direct time integration of Maxwell's equations are reported. The computational approach provides reflection coefficients accurate to better than 6 parts in 10,000 over the frequency range of dc to 3 x 10 to the 16th Hz for a single 0.2-fs Gaussian pulse incident upon a Lorentz-medium half-space. New results for Sommerfeld and Brillouin precursors are shown and compared with previous analyses. The present approach is robust and permits 2D and 3D electromagnetic pulse propagation directly from the full-vector Maxwell's equations.

  9. The usage of Maxwell fractional equations for the investigation of the waveguide processes

    International Nuclear Information System (INIS)

    Maksyuta, M.V.; Slinchenko, Yu.A.; Grygoruk, V.I.

    2016-01-01

    By means of nabla operator written down with using both of some differential operators with integer orders and fractional differential Caputo operators, gradient, divergence and rotor operators are determined, it is checked up the fulfillment of vector relations in fractional vector analysis, fractional Green, Stocks and Ostrogradsky-Gauss formulas. For a specific expression of nabla operator (nabla components along x and y axes have a unit order and along z axis, correspondingly, a fractional value in the interval from zero till unit) Maxwell fractional equations are written down. Based on the following from them some fractional wave equations, dissipative and polarization processes at electromagnetic waves distribution both in rectangular (planar) and in cylindrical waveguide structures are analyzed.

  10. A New Comment on Dyson's Exposition of Feynman's Proof of Maxwell Equations

    International Nuclear Information System (INIS)

    Pombo, Claudia

    2009-01-01

    A paper by Dyson, published nearly two decades ago, describing Feynman's proof of Maxwell equations, has generated many comments, analysis, discussions and generalizations of the proof. Feynman's derivation is assumed to be based on two main sets of equations. One is supposed to be the second law of Newton and the other a set of basic commutation relations from quantum physics.Here we present a new comment on this paper, focusing mainly on the initial arguments and applying a new method of analysis and interpretation of physics, named observational realism. The present discussion does not alter the technical steps of Feynman, but do clarify their basis. We show that Newton's physics is not a starting point in Feynman's derivation, neither is quantum physics involved in it, but the foundations of relativity only.

  11. Numerical solution of the Maxwell-Vlasov equations in the periodic regime. Application to the study of isotope separation by ion cyclotron resonance

    International Nuclear Information System (INIS)

    Omnes, P.

    1999-01-01

    This work is dedicated to the study of the behaviour of a magnetic confined plasma that is excited by a purely sinusoidal electric current delivered by an antenna. The response of the electrons to the electromagnetic field is considered as linear, whereas the ions of the plasma are represented by a non-relativistic Vlasov equation. In order to avoid transients, the coupled Maxwell-Vlasov equations are solved in a periodic mode and in a bounded domain. An equivalent electric conductivity tensor has been defined, this tensor is a linear operator that links the electric current generated by the movement of the particles to the electromagnetic field. Theoretical considerations can assure the existence and uniqueness of a periodical solution to Vlasov equations and of a solution to Maxwell equations in harmonic mode. The system of equations is periodical and has been solved by using an iterative method. The application of this method to the simulation of a isotopic separation device based on ionic cyclotron resonance has shown that the convergence is reached in a few iterations and that the solution is valid. Furthermore a method based on a finite-volume formulation of Maxwell equations in the time domain is presented. 2 new variables are defined in order to better take into account the Gauss' law and the conservation of the magnetic flux, the new system is still hyperbolic. The parallelization of the process has been successfully realized. (A.C.)

  12. Maxwell-Higgs vortices with internal structure

    Science.gov (United States)

    Bazeia, D.; Marques, M. A.; Menezes, R.

    2018-05-01

    Vortices are considered in relativistic Maxwell-Higgs systems in interaction with a neutral scalar field. The gauge field interacts with the neutral field via the presence of generalized permeability, and the charged and neutral scalar fields interact in a way dictated by the presence of first order differential equations that solve the equations of motion. The neutral field may be seen as the source field of the vortex, and we study some possibilities, which modify the standard Maxwell-Higgs solution and include internal structure to the vortex.

  13. Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics

    International Nuclear Information System (INIS)

    Le Bourdiec, S.

    2007-03-01

    Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

  14. J ames Clerk Maxwell and his Equations

    Indian Academy of Sciences (India)

    standing importance in the development of physical ideas. Maxwell has been ... mathematics teacher was William Hopkins, the famous 'Wran- ... union (like Faraday's) was child- ... bility or to use any influence when he unsuccessfully tried for.

  15. A Model for Solving the Maxwell Quasi Stationary Equations in a 3-Phase Electric Reduction Furnace

    Directory of Open Access Journals (Sweden)

    S. Ekrann

    1982-10-01

    Full Text Available A computer code has been developed for the approximate computation of electric and magnetic fields within an electric reduction furnace. The paper describes the numerical methods used to solve Maxwell's quasi-stationary equations, which are the governing equations for this problem. The equations are discretized by a staggered grid finite difference technique. The resulting algebraic equations are solved by iterating between computations of electric and magnetic quantities. This 'outer' iteration converges only when the skin depth is larger or of about the same magnitude as the linear dimensions of the computational domain. In solving for electric quantities with magnetic quantities being regarded as known, and vice versa, the central computational task is the solution of a Poisson equation for a scalar potential. These equations are solved by line successive overrelaxation combined with a rebalancing technique.

  16. On solution of Maxwell's equations in axisymmetric domains with edges. Part II: Numerical aspects

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    In this paper we consider the Fourier-finite-element method for treating the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges. By means of partial Fourier analysis, the 3D BVP is decomposed into an infinite sequence of 2D variational equations in the plane meridian domain of the axisymmetric domain, a finite number of which is considered and treated using nodal H 1 -conforming finite elements. For domains with reentrant edges, the singular field method is employed to compensate the singular behavior of the solutions. Emphases are given to estimates of the Fourier-finite-element approximation error and convergence analysis in the H 1 -norm under different regularity assumptions. (author)

  17. Dynamics of a magnetic monopole in matter, Maxwell equations in dyonic matter and detection of electric dipole moments

    International Nuclear Information System (INIS)

    Artru, X.; Fayolle, D.

    2001-01-01

    For a monopole, the analogue of the Lorentz equation in matter is shown to be f = g (H-v centre dot D). Dual-symmetric Maxwell equations, for matter containing hidden magnetic charge in addition to electric ones, are given. They apply as well to ordinary matter if the particles possess T-violating electric dipole moments. Two schemes of experiments for the detection of such moments in macroscopic pieces of matter are proposed

  18. Classes of exact Einstein Maxwell solutions

    Science.gov (United States)

    Komathiraj, K.; Maharaj, S. D.

    2007-12-01

    We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

  19. Discrete exterior calculus approach for discretizing Maxwell's equations on face-centered cubic grids for FDTD

    Science.gov (United States)

    Salmasi, Mahbod; Potter, Michael

    2018-07-01

    Maxwell's equations are discretized on a Face-Centered Cubic (FCC) lattice instead of a simple cubic as an alternative to the standard Yee method for improvements in numerical dispersion characteristics and grid isotropy of the method. Explicit update equations and numerical dispersion expressions, and the stability criteria are derived. Also, several tools available to the standard Yee method such as PEC/PMC boundary conditions, absorbing boundary conditions, and scattered field formulation are extended to this method as well. A comparison between the FCC and the Yee formulations is made, showing that the FCC method exhibits better dispersion compared to its Yee counterpart. Simulations are provided to demonstrate both the accuracy and grid isotropy improvement of the method.

  20. An efficient discontinuous Galerkin finite element method for highly accurate solution of maxwell equations

    KAUST Repository

    Liu, Meilin

    2012-08-01

    A discontinuous Galerkin finite element method (DG-FEM) with a highly accurate time integration scheme for solving Maxwell equations is presented. The new time integration scheme is in the form of traditional predictor-corrector algorithms, PE CE m, but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy. Numerical results demonstrate that the proposed DG-FEM uses larger time steps than DG-FEM with classical PE CE) m schemes when high accuracy, which could be obtained using high-order spatial discretization, is required. © 1963-2012 IEEE.

  1. An efficient discontinuous Galerkin finite element method for highly accurate solution of maxwell equations

    KAUST Repository

    Liu, Meilin; Sirenko, Kostyantyn; Bagci, Hakan

    2012-01-01

    A discontinuous Galerkin finite element method (DG-FEM) with a highly accurate time integration scheme for solving Maxwell equations is presented. The new time integration scheme is in the form of traditional predictor-corrector algorithms, PE CE m, but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy. Numerical results demonstrate that the proposed DG-FEM uses larger time steps than DG-FEM with classical PE CE) m schemes when high accuracy, which could be obtained using high-order spatial discretization, is required. © 1963-2012 IEEE.

  2. Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics; Methodes deterministes de resolution des equations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen

    Energy Technology Data Exchange (ETDEWEB)

    Le Bourdiec, S

    2007-03-15

    Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

  3. Variational Principles, Lie Point Symmetries, and Similarity Solutions of the Vector Maxwell Equations in Non-linear Optics

    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...

  4. Null canonical formalism 1, Maxwell field. [Poisson brackets, boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Wodkiewicz, K [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej

    1975-01-01

    The purpose of this paper is to formulate the canonical formalism on null hypersurfaces for the Maxwell electrodynamics. The set of the Poisson brackets relations for null variables of the Maxwell field is obtained. The asymptotic properties of the theory are investigated. The Poisson bracket relations for the news-functions of the Maxwell field are computed. The Hamiltonian form of the asymptotic Maxwell equations in terms of these news-functions is obtained.

  5. A discontinuous Galerkin method for solving transient Maxwell equations with nonlinear material properties

    KAUST Repository

    Sirenko, Kostyantyn

    2014-07-01

    Discontinuous Galerkin time-domain method (DGTD) has been used extensively in computational electromagnetics for analyzing transient electromagnetic wave interactions on structures described with linear constitutive relations. DGTD expands unknown fields independently on disconnected mesh elements and uses numerical flux to realize information exchange between fields on different elements (J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Method, 2008). The numerical flux of choice for \\'linear\\' Maxwell equations is the upwind flux, which mimics accurately the physical behavior of electromagnetic waves on discontinuous boundaries. It is obtained from the analytical solution of the Riemann problem defined on the boundary of two neighboring mesh elements.

  6. A discontinuous Galerkin method for solving transient Maxwell equations with nonlinear material properties

    KAUST Repository

    Sirenko, Kostyantyn; Asirim, Ozum Emre; Bagci, Hakan

    2014-01-01

    Discontinuous Galerkin time-domain method (DGTD) has been used extensively in computational electromagnetics for analyzing transient electromagnetic wave interactions on structures described with linear constitutive relations. DGTD expands unknown fields independently on disconnected mesh elements and uses numerical flux to realize information exchange between fields on different elements (J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Method, 2008). The numerical flux of choice for 'linear' Maxwell equations is the upwind flux, which mimics accurately the physical behavior of electromagnetic waves on discontinuous boundaries. It is obtained from the analytical solution of the Riemann problem defined on the boundary of two neighboring mesh elements.

  7. Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations

    Science.gov (United States)

    Alzahrani, Mohammed A.; Gauthier, Robert C.

    2015-02-01

    For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.

  8. Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

    Science.gov (United States)

    Asinari, Pietro

    2009-11-01

    A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

  9. Re-inventing electromagnetics - Supercomputing solution of Maxwell's equations via direct time integration on space grids

    International Nuclear Information System (INIS)

    Taflove, A.

    1992-01-01

    This paper summarizes the present state and future directions of applying finite-difference and finite-volume time-domain techniques for Maxwell's equations on supercomputers to model complex electromagnetic wave interactions with structures. Applications so far have been dominated by radar cross section technology, but by no means are limited to this area. In fact, the gains we have made place us on the threshold of being able to make tremendous contributions to non-defense electronics and optical technology. Some of the most interesting research in these commercial areas is summarized. 47 refs

  10. Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations

    Energy Technology Data Exchange (ETDEWEB)

    Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares

    2015-07-01

    This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)

  11. Maxwell electrodynamics subjected to quantum vacuum fluctuations

    International Nuclear Information System (INIS)

    Gevorkyan, A. S.; Gevorkyan, A. A.

    2011-01-01

    The propagation of electromagnetic waves in the vacuum is considered taking into account quantum fluctuations in the limits of Maxwell-Langevin (ML) equations. For a model of “white noise” fluctuations, using ML equations, a second order partial differential equation is found which describes the quantum distribution of virtual particles in vacuum. It is proved that in order to satisfy observed facts, the Lamb Shift etc, the virtual particles should be quantized in unperturbed vacuum. It is shown that the quantized virtual particles in toto (approximately 86 percent) are condensed on the “ground state” energy level. It is proved that the extension of Maxwell electrodynamics with inclusion of the vacuum quantum field fluctuations may be constructed on a 6D space-time continuum with a 2D compactified subspace. Their influence on the refraction indexes of vacuum is studied.

  12. Cylindrical and spherical space equivalents to the plane wave expansion technique of Maxwell's wave equations

    Science.gov (United States)

    Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed

    2015-02-01

    The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.

  13. Majumdar-Papapetrou class of nonstatic cylindrically symmetric Brans-Dicke-Maxwell fields

    International Nuclear Information System (INIS)

    Tiwari, R.N.; Rao, P.P.

    1979-01-01

    Relations have been obtained between certain components of the metric and the electromagnetic potentials for source-free Brans-Dicke-Maxwell fields described by a nonstatic cylindrically symmetric Einstein-Rosen metric. These are important, in the sense that they generate a class of solutions that in a way can be said to belong to the class generated by similar relations obtained by Majumdar (Phys. Rev.; 72: 390 (1947)) and Papapetrou (Proc. R. Ir. Acad. Sect. A.; 51: 191 (1947)) for generalized static Einstein-Maxwell fields. The relations have further been used to reduce the B-D Maxwell equations to B-D vacuum equations and vice versa. (author)

  14. The c equivalence principle and the correct form of writing Maxwell's equations

    International Nuclear Information System (INIS)

    Heras, Jose A

    2010-01-01

    It is well known that the speed c u =1/√(ε 0 μ 0 ) is obtained in the process of defining SI units via action-at-a-distance forces, like the force between two static charges and the force between two long and parallel currents. The speed c u is then physically different from the observed speed of propagation c associated with electromagnetic waves in vacuum. However, repeated experiments have led to the numerical equality c u = c, which we have called the c equivalence principle. In this paper we point out that ∇xE=-[1/(ε 0 μ 0 c 2 )]∂B/∂t is the correct form of writing Faraday's law when the c equivalence principle is not assumed. We also discuss the covariant form of Maxwell's equations without assuming the c equivalence principle.

  15. High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

    Science.gov (United States)

    Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

    2018-01-01

    High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.

  16. Resolution of the Vlasov-Maxwell system by PIC discontinuous Galerkin method on GPU with OpenCL

    Directory of Open Access Journals (Sweden)

    Crestetto Anaïs

    2013-01-01

    Full Text Available We present an implementation of a Vlasov-Maxwell solver for multicore processors. The Vlasov equation describes the evolution of charged particles in an electromagnetic field, solution of the Maxwell equations. The Vlasov equation is solved by a Particle-In-Cell method (PIC, while the Maxwell system is computed by a Discontinuous Galerkin method. We use the OpenCL framework, which allows our code to run on multicore processors or recent Graphic Processing Units (GPU. We present several numerical applications to two-dimensional test cases.

  17. Evaluating lightning hazards to building environments using explicit numerical solutions of Maxwell's equations

    Science.gov (United States)

    Collier, Richard S.; McKenna, Paul M.; Perala, Rodney A.

    1991-08-01

    The objective here is to describe the lightning hazards to buildings and their internal environments using advanced formulations of Maxwell's Equations. The method described is the Three Dimensional Finite Difference Time Domain Solution. It can be used to solve for the lightning interaction with such structures in three dimensions with the inclusion of a considerable amount of detail. Special techniques were developed for including wire, plumbing, and rebar into the model. Some buildings have provisions for lightning protection in the form of air terminals connected to a ground counterpoise system. It is shown that fields and currents within these structures can be significantly high during a lightning strike. Time lapse video presentations were made showing the electric and magnetic field distributions on selected cross sections of the buildings during a simulated lightning strike.

  18. A class of algebraically general solutions of the Einstein-Maxwell equations for non-null electromagnetic fields

    International Nuclear Information System (INIS)

    Tupper, B.O.J.

    1976-01-01

    In a previous article (Gen. Rel. Grav.; 6 : 345 (1975)) the Einstein-Maxwell field equations for non-null electromagnetic fields were studied under the conditions that the null tetrad is parallel-propagated along both principal null congruences. A solution with twist and shear, but no expansion, was found and was conjectured to be the only expansion-free solution. Here it is shown that this conjecture is false; the general expansion-free solution is found to be a family of space-times depending on a single constant parameter which is the ratio of the (constant) twists of the two principal null congruences. (author)

  19. Incompressible Einstein–Maxwell fluids with specified electric fields

    Indian Academy of Sciences (India)

    The Einstein–Maxwell equations describing static charged spheres with uniform density and variable electric field intensity are studied. The special case of constant electric field is also studied. The evolution of the model is governed by a hypergeometric differential equation which has a general solution in terms of special ...

  20. Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

    KAUST Repository

    Huang, Yunqing; Li, Jichun; Yang, Wei; Sun, Shuyu

    2011-01-01

    Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

  1. James Clerk Maxwell perspectives on his life and work

    CERN Document Server

    McCartney, Mark; Whitaker, Andrew

    2014-01-01

    James Clerk Maxwell (1831-1879) had a relatively brief, but remarkable life, lived in his beloved rural home of Glenlair, and variously in Edinburgh, Aberdeen, London and Cambridge. His scholarship also ranged wide - covering all the major aspects of Victorian natural philosophy. He was one of the most important mathematical physicists of all time, coming only after Newton and Einstein. In scientific terms his immortality is enshrined in electromagnetism and Maxwell's equations, but as this book shows, there was much more to Maxwell than electromagnetism, both in terms of his science and his wider life. Maxwell's life and contributions to science are so rich that they demand the expertise of a range of academics - physicists, mathematicians, and historians of science and literature - to do him justice. The various chapters will enable Maxwell to be seen from a range of perspectives. Chapters 1 to 4 deal with wider aspects of his life in time and place, at Aberdeen, King's College London and the Cavendish Labo...

  2. Comment on “Maxwell's equations and electromagnetic Lagrangian density in fractional form” [J. Math. Phys. 53, 033505 (2012)

    International Nuclear Information System (INIS)

    Rabei, Eqab M.; Al-Jamel, A.; Widyan, H.; Baleanu, D.

    2014-01-01

    In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)

  3. Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation

    Energy Technology Data Exchange (ETDEWEB)

    Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr; Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr [University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence (France)

    2016-08-15

    It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.

  4. From pure spinors to quantum physics and to some classical field equations like Maxwell's and gravitational

    International Nuclear Information System (INIS)

    Budinich, Paolo

    2009-03-01

    In a previous paper we proposed a purely mathematical way to quantum mechanics based on Cartan's simple spinors in their most elementary form of 2 components spinors. Here we proceed along that path proposing, this time, a symmetric tensor, quadrilinear in simple spinors, as a candidate for the symmetric tensor of general relativity. The procedure resembles closely that in which one builds bilinearly from simple spinors an asymmetric electromagnetic tensor, from which easily descend Maxwell's equations and the photon can be seen as a bilinear combination of neutrinos. Here Lorentzian spaces result compact, building up spheres, where hopefully the problems of the Standard Model could be solved. (author)

  5. Self-consistent Vlasov-Maxwell description of the longitudinal dynamics of intense charged particle beams

    Directory of Open Access Journals (Sweden)

    Ronald C. Davidson

    2004-02-01

    Full Text Available This paper describes a self-consistent kinetic model for the longitudinal dynamics of a long, coasting beam propagating in straight (linear geometry in the z direction in the smooth-focusing approximation. Starting with the three-dimensional Vlasov-Maxwell equations, and integrating over the phase-space (x_{⊥},p_{⊥} transverse to beam propagation, a closed system of equations is obtained for the nonlinear evolution of the longitudinal distribution function F_{b}(z,p_{z},t and average axial electric field ⟨E_{z}^{s}⟩(z,t. The primary assumptions in the present analysis are that the dependence on axial momentum p_{z} of the distribution function f_{b}(x,p,t is factorable, and that the transverse beam dynamics remains relatively quiescent (absence of transverse instability or beam mismatch. The analysis is carried out correct to order k_{z}^{2}r_{w}^{2} assuming slow axial spatial variations with k_{z}^{2}r_{w}^{2}≪1, where k_{z}∼∂/∂z is the inverse length scale of axial variation in the line density λ_{b}(z,t=∫dp_{z}F_{b}(z,p_{z},t, and r_{w} is the radius of the conducting wall (assumed perfectly conducting. A closed expression for the average longitudinal electric field ⟨E_{z}^{s}⟩(z,t in terms of geometric factors, the line density λ_{b}, and its derivatives ∂λ_{b}/∂z,… is obtained for the class of bell-shaped density profiles n_{b}(r,z,t=(λ_{b}/πr_{b}^{2}f(r/r_{b}, where the shape function f(r/r_{b} has the form specified by f(r/r_{b}=(n+1(1-r^{2}/r_{b}^{2}^{n} for 0≤r

  6. The free Maxwell field in curved spacetime

    International Nuclear Information System (INIS)

    Kueskue, M.

    2001-09-01

    The aim of this thesis is to discuss quantizations of the free Maxwell field in flat and curved spacetimes. First we introduce briefly some notions from tensor analysis and the causal structure of spacetime. As an introduction to the main topic, we review some aspects of the two axiomatic quantum field theories, Wightman theory and algebraic quantum field theory. We also give an introduction into concepts of the quantization of fields on curved spacetime backgrounds. Then the wave equation and quantization of the Maxwell field in flat spacetimes is discussed. It follows a review of J. Dimock's quantization of the Maxwell field on curved spacetimes and then we come to our main result: We show explicitly that the Maxwell field, defined by dF=0 and δF=0, has a well posed initial value formulation on arbitrary globally hyperbolic spacetime manifolds. We prove the existence and uniqueness of fundamental solutions without employing a vector potential. Thus our solution is also applicable to spacetimes not satisfying the Poincare lemma and should lead to a quantization of the Maxwell field on non-trivial spacetime backgrounds. This in turn provides the opportunity to investigate physical states on non-trivial spacetime-topologies and could lead to the discovery of new quantum phenomena. (orig.)

  7. MAXWELL3, 3-D FEM Electromagnetism

    International Nuclear Information System (INIS)

    Grant, J.B.

    2001-01-01

    1 - Description of program or function: MAXWELL3 is a linear, time domain, finite element code designed for simulation of electromagnetic fields interacting with three-dimensional objects. The simulation region is discretized into 6-sided, 8-nodded elements which need not form a logically regular grid. Scatterers may be perfectly conducting or dielectric. Restart capability and a Muer-type radiating boundary are included. MAXWELL3 can be run in a two-dimensional mode or on infinitesimally thin geometries. The output of time histories on surfaces, or shells, in addition to volumes, is allowed. Two post-processors are included - HIST2XY, which splits the MAXWELL3 history file into simple xy data files, and FFT A BS, which performs fast Fourier transformations on the xy data. 2 - Method of solution: The numerical method requires that the model be discretized with a mesh generator. MAXWELL3 then uses the mesh and computes the time domain electric and magnetic fields by integrating Maxwell's divergence-free curl equations over time. The output from MAXWELL3 can then be used with a post-processor to get the desired information in a graphical form. The explicit time integration is done with a leap-frog technique that alternates evaluating the electric and magnetic fields at half time steps. This allows for centered time differencing accurate in second order. The algorithm is naturally robust and requires no parameters. 3 - Restrictions on the complexity of the problem: MAXWELL3 has no mesh generation capabilities. Anisotropic, nonlinear, and magnetic materials cannot be modeled. Material interfaces only account for dielectric changes and neglect any surface charges that would be present at the surface of a partially conducting material. The radiation boundary algorithm is only accurate for normally incident fields and becomes less accurate as the angle of incidence increases. Thus, only models using scattered fields should use the radiation boundary. This limits MAXWELL3

  8. Maxwell's fish-eye lens and the mirage of perfect imaging

    International Nuclear Information System (INIS)

    Merlin, R

    2011-01-01

    Recent claims that Maxwell's fish-eye is a perfect lens, capable of providing images with deep subwavelength resolution, are examined. We show that the imaging properties of a dispersionless fish-eye are very similar to those of an ideal spherical cavity. Using this correspondence, we prove that the correct solution to Maxwell equations in the fish-eye gives image sizes that are consistent with the standard diffraction limit. Perfect focusing is an optical illusion that results from placing a time-reversed source at the position of the geometrical image which, when combined with the field due to the primary (object) source, mimics the behavior of a perfect drain. Issues of causality are briefly discussed. We also demonstrate that passive outlets are not a good alternative to time-reversed sources for broadband drain-like behavior and that, even if they were, they could not do a better job than conventional optical systems at providing high resolution

  9. Consistent three-equation model for thin films

    Science.gov (United States)

    Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

    2017-11-01

    Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

  10. About perfectly adapted layers for the temporal resolution of Maxwell's equations

    International Nuclear Information System (INIS)

    Le Potier, Ch.

    1995-01-01

    The major obstacle encountered in diffraction problems is the limitation in place memory. One solution is to approach the Sommerfeld condition by taking into account absorbing boundary conditions on a boundary surface surrounding the studied object. Many authors have studied these problems, but, unfortunately, the implementation of absorbing boundary conditions of order greater than two for 3-dimensional non-structural meshes in the temporal case is a still unresolved problem to our knowledge. Another way is to add a dummy absorbent layer around the computational domain. J.P. Berenger has revived this method and considerably improved the resolution of the problems of time diffraction. His idea is to split the Maxwell equations in their anisotropic version in a layer surrounding the computational domain. On the other hand, J.Y. Wu introduced a new system of anisotropic equations in the frequency case. The author shows that this new system possesses the same properties as that of Berenger and this idea has been generalized to the temporal case with discretization in space by finite volumes in 3 dimensions for a structured or not structured mesh. The report also presents the implementation of these new methods in the SUMER-T code and the accuracy of these is compared with conventional absorbing boundary conditions [fr

  11. Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations

    International Nuclear Information System (INIS)

    Esteban, M.J.; Georgiev, V.; Sere, E.

    1995-01-01

    The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+1)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model. (author). 32 refs

  12. On the Foundational Equations of the Classical Theory of ...

    Indian Academy of Sciences (India)

    IAS Admin

    ... Equations of the Classical. Theory of Electrodynamics ... most cherished notions of the Maxwell{Lorentz theory .... dia in the presence of the fields, in which case a self- consistent ..... could benefit from further experimental verification, we.

  13. Einstein-aether theory with a Maxwell field: General formalism

    Energy Technology Data Exchange (ETDEWEB)

    Balakin, Alexander B., E-mail: Alexander.Balakin@kpfu.ru [Department of General Relativity and Gravitation, Institute of Physics, Kazan Federal University, Kremlevskaya str. 18, Kazan 420008 (Russian Federation); Lemos, José P.S., E-mail: joselemos@ist.utl.pt [Centro Multidisciplinar de Astrofísica-CENTRA, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

    2014-11-15

    We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.

  14. Stability and Instability of the Sub-extremal Reissner-Nordström Black Hole Interior for the Einstein-Maxwell-Klein-Gordon Equations in Spherical Symmetry

    Science.gov (United States)

    Van de Moortel, Maxime

    2018-05-01

    We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole—approaching a sub-extremal Reissner-Nordström background fast enough—in presence of a massive and charged scalar field, motivated by the strong cosmic censorship conjecture in that setting: 1. Stability We prove that spherically symmetric characteristic initial data to the Einstein-Maxwell-Klein-Gordon equations approaching a Reissner-Nordström background with a sufficiently decaying polynomial decay rate on the event horizon gives rise to a space-time possessing a Cauchy horizon in a neighbourhood of time-like infinity. Moreover, if the decay is even stronger, we prove that the space-time metric admits a continuous extension to the Cauchy horizon. This generalizes the celebrated stability result of Dafermos for Einstein-Maxwell-real-scalar-field in spherical symmetry. 2. Instability We prove that for the class of space-times considered in the stability part, whose scalar field in addition obeys a polynomial averaged- L 2 (consistent) lower bound on the event horizon, the scalar field obeys an integrated lower bound transversally to the Cauchy horizon. As a consequence we prove that the non-degenerate energy is infinite on any null surface crossing the Cauchy horizon and the curvature of a geodesic vector field blows up at the Cauchy horizon near time-like infinity. This generalizes an instability result due to Luk and Oh for Einstein-Maxwell-real-scalar-field in spherical symmetry. This instability of the black hole interior can also be viewed as a step towards the resolution of the C 2 strong cosmic censorship conjecture for one-ended asymptotically flat initial data.

  15. Nonmaxwell relaxation in disordered media: Physical mechanisms and fractional relaxation equations

    International Nuclear Information System (INIS)

    Arkhincheev, V.E.

    2004-12-01

    The problem of charge relaxation in disordered systems has been solved. It is shown, that due to the inhomogeneity of the medium the charge relaxation has a non-Maxwell character. The two physical mechanisms of a such behavior have been founded. The first one is connected with the 'fractality' of conducting ways. The second mechanism of nonexponential non-Maxwell behavior is connected with the frequency dispersion of effective conductivity of heterogeneous medium, initially consisting of conducting phases without dispersion. The new generalized relaxation equations in the form of fractional temporal integro-differential equations are deduced. (author)

  16. Second order finite volume scheme for Maxwell's equations with discontinuous electromagnetic properties on unstructured meshes

    Energy Technology Data Exchange (ETDEWEB)

    Ismagilov, Timur Z., E-mail: ismagilov@academ.org

    2015-02-01

    This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.

  17. Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

    Science.gov (United States)

    Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.

    2018-01-01

    Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

  18. Nonlinear Maxwell's and Schrodinger equations for describing the volumetric interaction of femtosecond laser pulses with transparent solid dielectrics: effect of the boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Zhukov, V.P.; Bulgakova, Nadezhda M.; Fedoruk, M.P.

    2017-01-01

    Roč. 84, č. 7 (2017), s. 439-446 ISSN 1070-9762 R&D Projects: GA MŠk LO1602; GA ČR GA16-12960S Institutional support: RVO:68378271 Keywords : glass * femtosecond laser pulses * Maxwell's and Schrdinger equations Subject RIV: BH - Optics, Masers, Lasers OBOR OECD: Optics (including laser optics and quantum optics) Impact factor: 0.299, year: 2016

  19. Extremal Kähler metrics and Bach-Merkulov equations

    Science.gov (United States)

    Koca, Caner

    2013-08-01

    In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell equations. Inspired by the work of C. LeBrun on Einstein-Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach-Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein-Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.

  20. Maxwell and the classical wave particle dualism.

    Science.gov (United States)

    Mendonça, J T

    2008-05-28

    Maxwell's equations are one of the greatest theoretical achievements in physics of all times. They have survived three successive theoretical revolutions, associated with the advent of relativity, quantum mechanics and modern quantum field theory. In particular, they provide the theoretical framework for the understanding of the classical wave particle dualism.

  1. The 'strength' of a system of differential equations

    International Nuclear Information System (INIS)

    Hoenselaers, C.

    1977-01-01

    A review of Einstein's concept of ''strength'' of a system of differential equations is given. As an example the strength of the Einstein-Maxwell equations for non-null Maxwell field is calculated and shown to be the same as for the pure vacuum Einstein equations. (auth.)

  2. Maxwell's equations in axisymmetrical geometry: coupling H(curl) finite element in volume and H(div) finite element in surface. The numerical code FuMel

    International Nuclear Information System (INIS)

    Cambon, S.; Lacoste, P.

    2011-01-01

    We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)

  3. Analytical BPS Maxwell-Higgs Vortices

    International Nuclear Information System (INIS)

    Hora, E. da; Ferreira, M. M. Jr.; Santos, C. dos; Casana, R.

    2014-01-01

    We have established a prescription for the calculation of analytical vortex solutions in the context of generalized Maxwell-Higgs models whose overall dynamics is controlled by two positive functions of the scalar field, namely, f(|ϕ|) and w(|ϕ|). We have also determined a natural constraint between these functions and the Higgs potential U(|ϕ|), allowing the existence of axially symmetric Bogomol'nyi-Prasad-Sommerfield (BPS) solutions possessing finite energy. Furthermore, when the generalizing functions are chosen suitably, the nonstandard BPS equations can be solved exactly. We have studied some examples, comparing them with the usual Abrikosov-Nielsen-Olesen (ANO) solution. The overall conclusion is that the analytical self-dual vortices are well-behaved in all relevant sectors, strongly supporting the consistency of the respective generalized models. In particular, our results mimic well-known properties of the usual (numerical) configurations, as localized energy density, while contributing to the understanding of topological solitons and their description by means of analytical methods.

  4. The c equivalence principle and the correct form of writing Maxwell's equations

    Energy Technology Data Exchange (ETDEWEB)

    Heras, Jose A, E-mail: herasgomez@gmail.co [Universidad Autonoma Metropolitana Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico DF (Mexico)

    2010-09-15

    It is well known that the speed c{sub u}=1/{radical}({epsilon}{sub 0{mu}0}) is obtained in the process of defining SI units via action-at-a-distance forces, like the force between two static charges and the force between two long and parallel currents. The speed c{sub u} is then physically different from the observed speed of propagation c associated with electromagnetic waves in vacuum. However, repeated experiments have led to the numerical equality c{sub u} = c, which we have called the c equivalence principle. In this paper we point out that {nabla}xE=-[1/({epsilon}{sub 0}{mu}{sub 0}c{sup 2})]{partial_derivative}B/{partial_derivative}t is the correct form of writing Faraday's law when the c equivalence principle is not assumed. We also discuss the covariant form of Maxwell's equations without assuming the c equivalence principle.

  5. On the hidden maxwell superalgebra underlying D = 4 supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Penafiel, D.M. [Departamento de Fisica, Universidad de Concepcion (Chile); DISAT, Politecnico di Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino (Italy); Ravera, L. [DISAT, Politecnico di Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino (Italy)

    2017-09-15

    In this work, we expand the hidden AdS-Lorentz superalgebra underlying D = 4 supergravity, reaching a (hidden) Maxwell superalgebra. The latter can be viewed as an extension involving cosmological constant of the superalgebra underlying D = 4 supergravity in flat spacetime. We write the Maurer-Cartan equations in this context and we find some interesting extensions of the antisymmetric 3-form A{sup (3)} appearing in the Free Differential Algebra in Minkowski space. The structure of Free Differential Algebras is obtained by considering the zero curvature equations. We write the parametrization of A{sup (3)} in terms of 1-forms and we rend the topological features of its extensions manifest. We interestingly find out that the structure of these extensions, and consequently the structure of the corresponding boundary contribution dA{sup (3)}, strongly depends on the form of the extra fermionic generator appearing in the hidden Maxwell superalgebra. The model we develop in this work is defined in an enlarged superspace with respect to the ordinary one, and the extra bosonic and fermionic 1-forms required for the closure of the hidden Maxwell superalgebra must be considered as physical fields in this enlarged superspace. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  6. A Note of Extended Proca Equations and Superconductivity

    Directory of Open Access Journals (Sweden)

    Christianto V.

    2009-01-01

    Full Text Available It has been known for quite long time that the electrodynamics of Maxwell equations can be extended and generalized further into Proca equations. The implications of in- troducing Proca equations include an alternative description of superconductivity, via extending London equations. In the light of another paper suggesting that Maxwell equations can be written using quaternion numbers, then we discuss a plausible exten- sion of Proca equation using biquaternion number. Further implications and experi- ments are recommended.

  7. Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices

    Science.gov (United States)

    Zhu, Yan-Qing; Zhang, Dan-Wei; Yan, Hui; Xing, Ding-Yu; Zhu, Shi-Liang

    2017-09-01

    The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct two- and three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconventional integer pseudospin, beyond the Dirac-Weyl-Majorana fermions, are an exotic kind of fermions named as Maxwell fermions. We demonstrate that the systems have rich topological features. For instance, the threefold degenerate points called Maxwell points may have quantized Berry phases and anomalous quantum Hall effects with spin-momentum locking may appear in topological Maxwell insulators in the two-dimensional lattices. In three dimensions, Maxwell points may have nontrivial monopole charges of ±2 with two Fermi arcs connecting them, and the merging of the Maxwell points leads to topological phase transitions. Finally, we propose realistic schemes for realizing the model Hamiltonians and detecting the topological properties of the emergent Maxwell quasiparticles in optical lattices.

  8. 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)

  9. Action principles for the Vlasov equation

    International Nuclear Information System (INIS)

    Ye, H.; Morrison, P.J.

    1992-01-01

    Five action principles for the Vlasov--Poisson and Vlasov--Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov--Maxwell equations are altered so as to produce the Vlasov--Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov--Poisson equation is altered to produce the Vlasov--Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables

  10. Maxwell fields and shear-free null geodesic congruences

    International Nuclear Information System (INIS)

    Newman, Ezra T

    2004-01-01

    We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principal null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the worldline. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, the following strange interpretation can be given. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x a take complex values, i.e., x a → z a = x a + iy a with complex metric g η ab dz a dz b , the real vacuum Maxwell equations can be extended into the complex space and rewritten as curl W=i W radical, div W=0 with W=E+iB. This subcase of Maxwell fields can then be extended into the complex space so as to have as source, a complex analytic worldline, i.e., to now become complex Lienard-Wiechart fields. When viewed as real fields on the real Minkowski space (z a = x a ), they possess a real principal null vector that is shear-free but twisting and diverging. The twist is a measure of how far the complex worldline is from the real 'slice'. Most Maxwell fields in this subcase are asymptotically flat with a time-varying set of electric and magnetic moments, all depending on the complex displacements and the complex velocities

  11. Spontaneous compactification in six-dimensional Einstein-Maxwell theory

    International Nuclear Information System (INIS)

    Randjbar-Daemi, S.; Salam, A.; Strathdee, J.

    1982-10-01

    A discrete set of solutions to the classical Einstein-Maxwell equations in six-dimensional spacetime is considered. These solutions have the form of a product of four-dimensional constant curvature spacetime with a 2-sphere. The Maxwell field has support on the 2-sphere where it represents a monopole of magnetic charge, n = +-1, +-2,... The spectrum of massless and massive states is obtained for the special case of the flat 4-space, and the solution is shown to be classically stable. The limiting case where the radius of the 2-sphere becomes small is considered and a dimensionally reduced effective Lagrangian for the long range modes is derived. This turns out to be an SU(2) x U(1) gauge theory with chiral couplings. (author)

  12. Fourier rebinning and consistency equations for time-of-flight PET planograms.

    Science.gov (United States)

    Li, Yusheng; Defrise, Michel; Matej, Samuel; Metzler, Scott D

    2016-01-01

    Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms

  13. Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

    Science.gov (United States)

    Delzanno, G. L.

    2015-11-01

    A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

  14. Dyons in presence of gravitation and symmetrized field equations

    International Nuclear Information System (INIS)

    Rawat, A.S.; Negi, O.P.S.

    1999-01-01

    Combined theory of gravitation and electromagnetism associated with particles carrying electric and magnetic charges has been established from an invariant action principle. Corresponding field equations, equation of motion and Einstein Maxwell's equations are obtained in unique and consistent way. It is shown that weak field approximation of slowly moving particle in gravitational field leads the symmetry between electromagnetic and linear gravitational fields. Postulation of the existence of gravimagnetic monopole leads structural symmetry between generalized electromagnetic and gravielectromagnetic fields. Corresponding quantization conditions and angular momentum are also analysed. (author)

  15. The covariant form of Maxwell equations for the fast simulation of the eddy current non destructive testing of complex specimens

    International Nuclear Information System (INIS)

    Caire, Francois

    2014-01-01

    This PhD work concerns the development of fast numerical tools, dedicated to the computation of the electromagnetic interaction between a low frequency 3D current source and a complex conductor, presenting rough interfaces and/or conductivity variations. The main application concerns the simulation of the Eddy Current nondestructive testing process applied to complex specimens. Indeed, the semi-analytical models available today are restricted to canonical geometries. The proposed method is based on the covariant form of Maxwell's equations, which translates the physical equations and relationships in a non-orthogonal coordinate system depending on the geometry of the specimen. Historically, this method (Curvilinear Coordinate Method, CCM or C-method) has been developed in the framework of optical applications, particularly for the characterization of diffraction gratings. Here, we transpose this formalism into the quasi-static regime and we extend the Second Order Vector Potential formalism, initially dedicated to orthonormal curvilinear coordinates systems, to general curvilinear coordinate systems. Thanks to this change of base, we are able to determine numerically a set of modal solutions of the source-free Maxwell equations in the new coordinate system introduced, and this allows us to represent the unknown fields as modal expansions in source-free domains. Then, the coefficients of these expansions are computed by introducing the source fields and by enforcing the boundary conditions that the total fields must verify at interfaces between the different media. In order to tackle the case of a layered conductor presenting rough interfaces, the generalized SOVP formalism is coupled with a recursive routine called the S-matrix algorithm. On the other hand, the application case of a complex shape specimen with depth-varying physical properties is treated by coupling the modal method we developed with a high-order numerical method: pseudo-spectral method. The

  16. Null strings and complex Einstein-Maxwell fields with cosmological constant

    International Nuclear Information System (INIS)

    Garcia, A.; Plebanski, J.F.; Robinson, I.

    1977-01-01

    Previous results of Plebanski and Robinson (Phys. Rev. Lett.; 37:493 (1976)) concerning left-degenerate Einstein-flat complex space-times and preliminary results concerning the electromagnetic field, are here generalized and worked out in some detail for the system of Einstein-Maxwell equations with a cosmological constant. On the assumption that there exists a congruence of totally null surfaces, the system is reduced to a pair of equations for the two unknown functions. (author)

  17. On Understanding: Maxwell on the Methods of Illustration and Scientific Metaphor

    Science.gov (United States)

    Cat, Jordi

    In this paper I examine the notion and role of metaphors and illustrations in Maxwell's works in exact science as a pathway into a broader and richer philosophical conception of a scientist and scientific practice. While some of these notions and methods are still at work in current scientific research-from economics and biology to quantum computation and quantum field theory-, here I have chosen to attest to their entrenchment and complexity in actual science by attempting to make some conceptual sense of Maxwell's own usage; this endeavour includes situating Maxwell's conceptions and applications in his own culture of Victorian science and philosophy. I trace Maxwell's notions to the formulation of the problem of understanding, or interpreting, abstract representations such as potential functions and Lagrangian equations. I articulate the solution in terms of abstract-concrete relations, where the concrete, in tune with Victorian British psychology and engineering, includes the muscular as well as the pictorial. This sets the basis for a conception of understanding in terms of unification and concrete modelling, or representation. I examine the relation of illustration to analogies and metaphors on which this account rests. Lastly, I stress and explain the importance of context-dependence, its consequences for realism-instrumentalism debates, and Maxwell's own emphasis on method.

  18. Macroscopic self-consistent model for external-reflection near-field microscopy

    International Nuclear Information System (INIS)

    Berntsen, S.; Bozhevolnaya, E.; Bozhevolnyi, S.

    1993-01-01

    The self-consistent macroscopic approach based on the Maxwell equations in two-dimensional geometry is developed to describe tip-surface interaction in external-reflection near-field microscopy. The problem is reduced to a single one-dimensional integral equation in terms of the Fourier components of the field at the plane of the sample surface. This equation is extended to take into account a pointlike scatterer placed on the sample surface. The power of light propagating toward the detector as the fiber mode is expressed by using the self-consistent field at the tip surface. Numerical results for trapezium-shaped tips are presented. The authors show that the sharper tip and the more confined fiber mode result in better resolution of the near-field microscope. Moreover, it is found that the tip-surface distance should not be too small so that better resolution is ensured. 14 refs., 10 figs

  19. A class of exact solutions to the Einstein field equations

    International Nuclear Information System (INIS)

    Goyal, Nisha; Gupta, R K

    2012-01-01

    The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

  20. The Maxwell-Stefan description of mixture diffusion in nanoporous crystalline materials

    NARCIS (Netherlands)

    Krishna, R.

    2014-01-01

    The efficacy of nanoporous crystalline materials in separation applications is often influenced to a significant extent by diffusion of guest molecules within the pores of the structural frameworks. The Maxwell-Stefan (M-S) equations provide a fundamental and convenient description of mixture

  1. Fast Solutions of Maxwell's Equation for High Resolution Electromagnetic Imaging of Transport Pathways; TOPICAL

    International Nuclear Information System (INIS)

    DAY, DAVID M.; NEWMAN, GREGORY A.

    1999-01-01

    A fast precondition technique has been developed which accelerates the finite difference solutions of the 3D Maxwell's equations for geophysical modeling. The technique splits the electric field into its curl free and divergence free projections, and allows for the construction of an inverse operator. Test examples show an order of magnitude speed up compared with a simple Jacobi preconditioner. Using this preconditioner a low frequency Neumann series expansion is developed and used to compute responses at multiple frequencies very efficiently. Simulations requiring responses at multiple frequencies, show that the Neumann series is faster than the preconditioned solution, which must compute solutions at each discrete frequency. A Neumann series expansion has also been developed in the high frequency limit along with spectral Lanczos methods in both the high and low frequency cases for simulating multiple frequency responses with maximum efficiency. The research described in this report was to have been carried out over a two-year period. Because of communication difficulties, the project was funded for first year only. Thus the contents of this report are incomplete with respect to the original project objectives

  2. James Clerk Maxwell: Life and science

    International Nuclear Information System (INIS)

    Marston, Philip L.

    2016-01-01

    Maxwell's life and science are presented with an account of the progression of Maxwell's research on electromagnetic theory. This is appropriate for the International Year of Light and Light-based Technologies, 2015. Maxwell's own confidence in his 1865 electromagnetic theory of light is examined, along with some of the difficulties he faced and the difficulties faced by some of his followers. Maxwell's interest in radiation pressure and electromagnetic stress is addressed, as well as subsequent developments. Some of Maxwell's other contributions to physics are discussed with an emphasis on the kinetic and molecular theory of gases. Maxwell's theistic perspective on science is illustrated, accompanied by examples of perspectives on Maxwell and his science provided by his peers and accounts of his interactions with those peers. Appendices examine the peer review of Maxwell's 1865 electromagnetic theory paper and the naming of the Maxwell Garnett effective media approximation and provide various supplemental perspectives. From Maxwell's publications and correspondence there is evidence he had a high regard for Michael Faraday. Examples of Maxwell's contributions to electromagnetic terminology are noted. - Highlights: • Maxwell’s 1865 “Dynamical theory of the electromagnetic field” is examined. • Maxwell affirmed confidence in his electromagnetic wave theory in his 1873 Treatise. • Discussion includes views and unpublished correspondence of Maxwell's contemporaries. • His contemporaries noticed the depth and breadth of Maxwell’s thought. • Maxwell’s contemporaries noticed his theistic perspective concerning science.

  3. Fourier rebinning and consistency equations for time-of-flight PET planograms

    International Nuclear Information System (INIS)

    Li, Yusheng; Matej, Samuel; Metzler, Scott D; Defrise, Michel

    2016-01-01

    Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John’s equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations (FCEs) and the Fourier–John equation (FJE), which are the duals of the consistency equations and John’s equation, respectively. We then solve the FCEs and FJE using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give

  4. Multiplicative renormalizability and self-consistent treatments of the Schwinger-Dyson equations

    International Nuclear Information System (INIS)

    Brown, N.; Dorey, N.

    1989-11-01

    Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched quantum electrodynamics, (QED), checking the consistency of various approximations. In particular, we show that the much used 'ladder' approximation is self-consistent, provided that the coupling constant is renormalized in a particular way. We also propose another approximation which satisfies this self-consistency test, but requires that the coupling be unrenormalized, as should be the case in the full quenched approximation. This new approximation admits an exact solution, which also satisfies the renormalization group equation for the quenched approximation. (author)

  5. Ion diode simulation with a finite-volume PIC approach for the numerical solution of the Maxwell-Lorentz system

    Energy Technology Data Exchange (ETDEWEB)

    Munz, C D; Schneider, R; Stein, E; Voss, U [Forschungszentrum Karlsruhe (Germany). Institut fuer Neutronenphysik und Reaktortechnik; Westermann, T [FH Karlsruhe (Germany). Fachbereich Naturwissenschaften; Krauss, M [Forschungszentrum Karlsruhe (Germany). Hauptabteilung Informations- und Kommunikationstechik

    1997-12-31

    The numerical concept realized in the the Karlsruhe Diode Code KADI2D is briefly reviewed. Several new aspects concerning the Maxwell field solver based on high resolution finite-volume methods are presented. A new approach maintaining charge conservation numerically for the Maxwell-Lorentz equations is shortly summarized. (author). 2 figs., 12 refs.

  6. Ion diode simulation with a finite-volume PIC approach for the numerical solution of the Maxwell-Lorentz system

    International Nuclear Information System (INIS)

    Munz, C.D.; Schneider, R.; Stein, E.; Voss, U.; Westermann, T.; Krauss, M.

    1996-01-01

    The numerical concept realized in the the Karlsruhe Diode Code KADI2D is briefly reviewed. Several new aspects concerning the Maxwell field solver based on high resolution finite-volume methods are presented. A new approach maintaining charge conservation numerically for the Maxwell-Lorentz equations is shortly summarized. (author). 2 figs., 12 refs

  7. Incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time-dependent maxwell equations

    KAUST Repository

    Sirenko, Kostyantyn

    2013-01-01

    A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method\\'s superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. © 1963-2012 IEEE.

  8. Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

    International Nuclear Information System (INIS)

    Bhattacharyya Krishnendu; Hayat Tasawar; Alsaedi Ahmed

    2014-01-01

    An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations (PDEs) are converted into a nonlinear self-similar ordinary differential equation (ODE). For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  9. Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation

    Science.gov (United States)

    Gegenhasi; Li, Ya-Qian; Zhang, Duo-Duo

    2018-04-01

    In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the mKP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a Bäcklund transformation for the differential-difference KP equation with self-consistent sources. Supported by the National Natural Science Foundation of China under Grant Nos. 11601247 and 11605096, the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant Nos. 2016MS0115 and 2015MS0116 and the Innovation Fund Programme of Inner Mongolia University No. 20161115

  10. A one-to-one correspondence between the static Einstein-Maxwell and stationary Einstein-vacuum space-times

    International Nuclear Information System (INIS)

    Chandrasekhar, Subrahmanyan

    1989-01-01

    A one-to-one correspondence is established between the static solutions of the Einstein-Maxwell equations and the stationary solutions of the Einstein-vacuum equations, that enables one to directly write down a solution for the one from a known solution of the other, and conversely, by a simple transcription. The directness of the correspondence is achieved by writing the metric for static Einstein-Maxwell space-times in a coordinate system and a gauge adapted to the two-centre problem and the metric for stationary Einstein-vacuum space-times in a coordinate system and a gauge adapted to black holes with event horizons. (author)

  11. Maxwell: A new vision of the world

    Science.gov (United States)

    Maystre, Daniel

    2014-05-01

    The paper outlines the crucial contributions of James Clerk Maxwell to Physics and more generally to our vision of the world. He achieved 150 years ago a synthesis of the pioneering works in magnetostatics, electrostatics, induction and, by introducing the notion of displacement current, gave birth to Electromagnetics. Then, he deduced the existence of electromagnetic waves and identified light as one of them. Maxwell equations deeply changed a Newtonian conception of the world based on particle interactions by pointing out the vital role of waves in physics. This new conception had a strong influence on the development of quantum physics. Finally, the invariance of light velocity in Galilean frames led to Lorentz transformations, a key step toward the theory of relativity. Par ailleurs, les équations de Maxwell ont profondément changé une conception du monde newtonienne basée sur l'interaction entre particules en révélant le rôle essentiel des ondes en physique, ce qui eut une influence déterminante sur le développement de la physique quantique. Enfin, l'invariance de la vitesse de la lumière dans les repères galiléens a entraîné la découverte des transformations de Lorentz, une étape capitale vers la théorie de la relativité.

  12. Newton's second law, radiation reaction and type II Einstein-Maxwell fields

    International Nuclear Information System (INIS)

    Newman, Ezra T

    2011-01-01

    Considering perturbations of the Reissner-Nordstroem metric while keeping the perturbations in the class of type II Einstein-Maxwell metrics, we perform a spherical harmonic expansion of all the variables up to the quadrupole term. This leads to rather surprising results. Referring to the source of the metric as a type II particle (analogous to referring to a Schwarzschild-Reissner-Nordstroem or Kerr-Newman particle), we see immediately that the Bondi momentum of the particle takes the classical form of mass times velocity plus an electromagnetic radiation reaction term, while the Bondi mass loss equation becomes the classical gravitational and electromagnetic (electric and magnetic) dipole and quadrupole radiation. The Bondi momentum loss equation turns into Newton's second law of motion containing the Abraham-Lorentz-Dirac radiation reaction force plus a momentum recoil (rocket) force, while the reality condition on the Bondi mass aspect yields the conservation of angular momentum. Two things must be pointed out: (1) these results, (equations of motion, etc) take place, not in the spacetime of the type II metric but in an auxiliary space referred to as H-space, whose physical meaning is rather obscure and (2) this analysis of the type II field equations is a very special case of a similar analysis of the general asymptotically flat Einstein-Maxwell equations. Although the final results are similar (though not the same), the analysis uses different equations (specifically, the type II field equations) and is vastly simpler than the general case. Without a great deal of the technical structures needed in the general case, one can see rather easily where the basic results reside in the type II field equations. (paper)

  13. Maxwell's fishpond

    International Nuclear Information System (INIS)

    Kinsler, Paul; Tan Jiajun; Thio, Timothy C Y; Trant, Claire; Kandapper, Navin

    2012-01-01

    Most of us will have at some time thrown a pebble into water, and watched the ripples spread outwards and fade away. But now there is also a way to reverse the process, and make those ripples turn around and reconverge again, …and again, and again. To do this we have designed the Maxwell's fishpond, a water wave or ‘transformation aquatics’ version of the Maxwell's fisheye lens (Tyc et al 2011 New J. Phys. 13 115004; Luneburg 1964 Mathematical Theory of Optics). These are transformation devices where wave propagation on the surface of a sphere is modelled using a flat device with spatially varying properties. And just as for rays from a point source on a sphere, a wave disturbance in a Maxwell's fisheye or fishpond spreads out at first, but then reforms itself at its opposite (or complementary) point. Here we show how such a device can be made for water waves, partly in friendly competition with comparable electromagnetic devices (Ma et al 2011 New J. Phys. 13 033016) and partly as an accessible and fun demonstration of the power of transformation mechanics. To the eye, our Maxwell's fishpond was capable of reforming a disturbance up to five times, although such a feat required taking considerable care, close observation, and a little luck. (paper)

  14. Thermodynamically self-consistent integral equations and the structure of liquid metals

    International Nuclear Information System (INIS)

    Pastore, G.; Kahl, G.

    1987-01-01

    We discuss the application of the new thermodynamically self-consistent integral equations for the determination of the structural properties of liquid metals. We present a detailed comparison of the structure (S(q) and g(r)) for models of liquid alkali metals as obtained from two thermodynamically self-consistent integral equations and some published exact computer simulation results; the range of states extends from the triple point to the expanded metal. The theories which only impose thermodynamic self-consistency without any fitting of external data show an excellent agreement with the simulation results, thus demonstrating that this new type of integral equation is definitely superior to the conventional ones (hypernetted chain, Percus-Yevick, mean spherical approximation, etc). (author)

  15. Parquet equations for numerical self-consistent-field theory

    International Nuclear Information System (INIS)

    Bickers, N.E.

    1991-01-01

    In recent years increases in computational power have provided new motivation for the study of self-consistent-field theories for interacting electrons. In this set of notes, the so-called parquet equations for electron systems are derived pedagogically. The principal advantages of the parquet approach are outlined, and its relationship to simpler self-consistent-field methods, including the Baym-Kadanoff technique, is discussed in detail. (author). 14 refs, 9 figs

  16. Enhanced Recovery in Tight Gas Reservoirs using Maxwell-Stefan Equations

    Science.gov (United States)

    Santiago, C. J. S.; Kantzas, A.

    2017-12-01

    Due to the steep production decline in unconventional gas reservoirs, enhanced recovery (ER) methods are receiving great attention from the industry. Wet gas or liquid rich reservoirs are the preferred ER candidates due to higher added value from natural gas liquids (NGL) production. ER in these reservoirs has the potential to add reserves by improving desorption and displacement of hydrocarbons through the medium. Nevertheless, analysis of gas transport at length scales of tight reservoirs is complicated because concomitant mechanisms are in place as pressure declines. In addition to viscous and Knudsen diffusion, multicomponent gas modeling includes competitive adsorption and molecular diffusion effects. Most models developed to address these mechanisms involve single component or binary mixtures. In this study, ER by gas injection is investigated in multicomponent (C1, C2, C3 and C4+, CO2 and N2) wet gas reservoirs. The competing effects of Knudsen and molecular diffusion are incorporated by using Maxwell-Stefan equations and the Dusty-Gas approach. This model was selected due to its superior properties on representing the physics of multicomponent gas flow, as demonstrated during the presented model validation. Sensitivity studies to evaluate adsorption, reservoir permeability and gas type effects are performed. The importance of competitive adsorption on production and displacement times is demonstrated. In the absence of adsorption, chromatographic separation is negligible. Production is merely dictated by competing effects between molecular and Knudsen diffusion. Displacement fronts travel rapidly across the medium. When adsorption effects are included, molecules with lower affinity to the adsorption sites will be produced faster. If the injected gas is inert (N2), an increase in heavier fraction composition occurs in the medium. During injection of adsorbing gases (CH4 and CO2), competitive adsorption effects will contribute to improved recovery of heavier

  17. Quantitative verification of ab initio self-consistent laser theory.

    Science.gov (United States)

    Ge, Li; Tandy, Robert J; Stone, A D; Türeci, Hakan E

    2008-10-13

    We generalize and test the recent "ab initio" self-consistent (AISC) time-independent semiclassical laser theory. This self-consistent formalism generates all the stationary lasing properties in the multimode regime (frequencies, thresholds, internal and external fields, output power and emission pattern) from simple inputs: the dielectric function of the passive cavity, the atomic transition frequency, and the transverse relaxation time of the lasing transition.We find that the theory gives excellent quantitative agreement with full time-dependent simulations of the Maxwell-Bloch equations after it has been generalized to drop the slowly-varying envelope approximation. The theory is infinite order in the non-linear hole-burning interaction; the widely used third order approximation is shown to fail badly.

  18. Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

    Directory of Open Access Journals (Sweden)

    Yu Bai

    2017-12-01

    Full Text Available This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

  19. Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

    Science.gov (United States)

    Bai, Yu; Jiang, Yuehua; Liu, Fawang; Zhang, Yan

    2017-12-01

    This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

  20. Quantum vacuum energy near a black hole: the Maxwell field

    International Nuclear Information System (INIS)

    Elster, T.

    1984-01-01

    A quantised Maxwell field is considered propagating in the gravitational field of a Schwarzschild black hole. The vector Hartle-Hawking propagator is defined on the Riemannian section of the analytically continued space-time and expanded in terms of four-dimensional vector spherical harmonics. The equations for the radial functions appearing in the expansion are derived for both odd and even parity. Using the expansion of the vector Hartle-Hawking propagator, the point-separated expectation value of the Maxwellian energy-momentum tensor in the Hartle-Hawking vacuum is derived. The renormalised values of radial pressure, tangential pressure and energy density are obtained near the horizon of the black hole. In contrast to the scalar field, the Maxwell field exhibits a positive energy density near the horizon in the Hartle-Hawking vacuum state. (author)

  1. Maxwell Air Force Base

    Science.gov (United States)

    most effective style of leadership. (Courtesy Photo, Air University Press) Air University Press Directory Maxwell Links Welcome Leadership Joint Land Use Study Heritage Pamphlet Maxwell Driving Tour (No releases 'A Discourse on Winning and Losing' "Developing Your Full Range of Leadership" focuses

  2. Coupled Dyson-Schwinger equations and effects of self-consistency

    International Nuclear Information System (INIS)

    Wu, S.S.; Zhang, H.X.; Yao, Y.J.

    2001-01-01

    Using the σ-ω model as an effective tool, the effects of self-consistency are studied in some detail. A coupled set of Dyson-Schwinger equations for the renormalized baryon and meson propagators in the σ-ω model is solved self-consistently according to the dressed Hartree-Fock scheme, where the hadron propagators in both the baryon and meson self-energies are required to also satisfy this coupled set of equations. It is found that the self-consistency affects the baryon spectral function noticeably, if only the interaction with σ mesons is considered. However, there is a cancellation between the effects due to the σ and ω mesons and the additional contribution of ω mesons makes the above effect insignificant. In both the σ and σ-ω cases the effects of self-consistency on meson spectral function are perceptible, but they can nevertheless be taken account of without a self-consistent calculation. Our study indicates that to include the meson propagators in the self-consistency requirement is unnecessary and one can stop at an early step of an iteration procedure to obtain a good approximation to the fully self-consistent results of all the hadron propagators in the model, if an appropriate initial input is chosen. Vertex corrections and their effects on ghost poles are also studied

  3. Unconditionally stable integration of Maxwell's equations

    NARCIS (Netherlands)

    J.G. Verwer (Jan); M.A. Botchev

    2009-01-01

    textabstractNumerical integration of Maxwell’s equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit –

  4. Self-consistent Maxwell-Bloch model of quantum-dot photonic-crystal-cavity lasers

    DEFF Research Database (Denmark)

    Cartar, William; Mørk, Jesper; Hughes, Stephen

    2017-01-01

    -level emitters are solved numerically. Phenomenological pure dephasing and incoherent pumping is added to the optical Bloch equations to allow for a dynamical lasing regime, but the cavity-mediated radiative dynamics and gain coupling of each QD dipole (artificial atom) is contained self-consistently within......-mode to multimode lasing is also observed, depending on the spectral peak frequency of the QD ensemble. Using a statistical modal analysis of the average decay rates, we also show how the average radiative decay rate decreases as a function of cavity size. In addition, we investigate the role of structural disorder...

  5. The free energy of Maxwell-Vlasov equilibria

    International Nuclear Information System (INIS)

    Morrison, P.J.; Pfirsch, D.

    1989-10-01

    A previously derived expression for the energy of arbitrary perturbations about arbitrary Vlasov-Maxwell equilibria is transformed into a very compact form. The new form is also obtained by a canonical transformation method for solving Vlasov's equation, which is based on Lie group theory. This method is simpler than the one used before and provides better physical insight. Finally a procedure is presented for determining the existence of negative-energy modes. In this context the question of why there is an accessibility constraint for the particles, but not for the fields, is discussed. 16 refs

  6. Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model

    International Nuclear Information System (INIS)

    Paschoal, Ricardo C.; Helayel Neto, Jose A.

    2003-01-01

    The magnetic field redefinition in Jain's composite fermion model for the fractional quantum Hall effect is shown to be effective described by a mean-field approximation of a model containing a Maxwell-Chern-Simons gauge field nominally coupled to matter. Also an explicit non-relativistic limit of the non-minimal (2+1) D Dirac's equation is derived. (author)

  7. Maxwell iteration for the lattice Boltzmann method with diffusive scaling

    Science.gov (United States)

    Zhao, Weifeng; Yong, Wen-An

    2017-03-01

    In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

  8. Exact solutions to the Mo-Papas and Landau-Lifshitz equations

    Science.gov (United States)

    Rivera, R.; Villarroel, D.

    2002-10-01

    Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

  9. Exact solutions to the Mo-Papas and Landau-Lifshitz equations

    International Nuclear Information System (INIS)

    Rivera, R.; Villarroel, D.

    2002-01-01

    Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics

  10. Maxwell superalgebras and Abelian semigroup expansion

    Directory of Open Access Journals (Sweden)

    P.K. Concha

    2014-09-01

    Full Text Available The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2 leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N. Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.

  11. Maxwell superalgebras and Abelian semigroup expansion

    Energy Technology Data Exchange (ETDEWEB)

    Concha, P.K.; Rodríguez, E.K. [Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Dipartimento di Scienza Applicata e Tecnologia (DISAT), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via Pietro Giuria, 1, 10125 Torino (Italy)

    2014-09-15

    The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2) leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM{sup (N)} recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N). Moreover, we show that new minimal Maxwell superalgebras type sM{sub m+2} and their N-extended generalization can be obtained using the S-expansion procedure.

  12. Consistency of a system of equations: What does that mean?

    NARCIS (Netherlands)

    Still, Georg J.; Kern, Walter; Koelewijn, Jaap; Bomhoff, M.J.

    2010-01-01

    The concept of (structural) consistency also called structural solvability is an important basic tool for analyzing the structure of systems of equations. Our aim is to provide a sound and practically relevant meaning to this concept. The implications of consistency are expressed in terms of

  13. Solution of degenerate hypergeometric system of Horn consisting of three equations

    Science.gov (United States)

    Tasmambetov, Zhaksylyk N.; Zhakhina, Ryskul U.

    2017-09-01

    The possibilities of constructing normal-regular solutions of a system consisting of three partial differential equations of the second order are studied by the Frobenius-Latysheva method. The method of determining unknown coefficients is shown and the relationship of the studied system with the system, which solution is Laguerre's polynomial of three variables is indicated. The generalization of the Frobenius-Latysheva method to the case of a system consisting of three equations makes it possible to clarify the relationship of such systems, which solutions are special functions of three variables. These systems include the functions of Whittaker and Bessel, 205 special functions of three variables from the list of M. Srivastava and P.W. Carlsson, as well as orthogonal polynomials of three variables. All this contributes to the further development of the analytic theory of systems consisting of three partial differential equations of the second order.

  14. Geology of Maxwell Montes, Venus

    Science.gov (United States)

    Head, J. W.; Campbell, D. B.; Peterfreund, A. R.; Zisk, S. A.

    1984-01-01

    Maxwell Montes represent the most distinctive topography on the surface of Venus, rising some 11 km above mean planetary radius. The multiple data sets of the Pioneer missing and Earth based radar observations to characterize Maxwell Montes are analyzed. Maxwell Montes is a porkchop shaped feature located at the eastern end of Lakshmi Planum. The main massif trends about North 20 deg West for approximately 1000 km and the narrow handle extends several hundred km West South-West WSW from the north end of the main massif, descending down toward Lakshmi Planum. The main massif is rectilinear and approximately 500 km wide. The southern and northern edges of Maxwell Montes coincide with major topographic boundaries defining the edge of Ishtar Terra.

  15. 21 CFR 886.1435 - Maxwell spot.

    Science.gov (United States)

    2010-04-01

    ... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Maxwell spot. 886.1435 Section 886.1435 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES OPHTHALMIC DEVICES Diagnostic Devices § 886.1435 Maxwell spot. (a) Identification. A Maxwell spot is an AC...

  16. Spontaneous symmetry breaking and self-consistent equations for the free-energy

    International Nuclear Information System (INIS)

    Lovesey, S.W.

    1980-03-01

    A variational procedure for the free-energy is used to derive self-consistent equations that allow for spontaneous symmetry breaking. For an N-component phi 4 -model the equations are identical to those obtained by summing all loops to order 1/N. (author)

  17. Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system

    DEFF Research Database (Denmark)

    Sørensen, Mads Peter; Brio, Moysey; Webb, Garry

    2002-01-01

    We present a numerical study of Maxwell's equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion......–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities....

  18. Global 3-D FDTD Maxwell's-Equations Modeling of Ionospheric Disturbances Associated with Earthquakes Using an Optimized Geodesic Grid

    Science.gov (United States)

    Simpson, J. J.; Taflove, A.

    2005-12-01

    We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A

  19. The electromagnetic Dirac-Fock-Podolsky problem and symplectic properties of the Maxwell and Yang-Mills type dynamical systems

    International Nuclear Information System (INIS)

    Bogolubov, N.N. Jr.; Prykarpatsky, A.K.; Taneri, U.; Prykarpatsky, Y.A.

    2009-01-01

    Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of a certain symmetry group, we construct the symplectic structures associated with connection forms on suitable principal fiber bundles. The application to the non-standard Hamiltonian analysis of the Maxwell and Yang-Mills type dynamical systems is presented. A symplectic reduction theory of the classical Maxwell electromagnetic field equations is formulated, the important Lorentz condition, ensuring the existence of electromagnetic waves, is naturally included into the Hamiltonian picture, thereby solving the well known Dirac, Fock and Podolsky problem. The symplectically reduced Poissonian structures and the related classical minimal interaction principle, concerning the Yang-Mills type equations, are considered. (author)

  20. Mass transfer simulation of nanofiltration membranes for electrolyte solutions through generalized Maxwell-Stefan approach

    International Nuclear Information System (INIS)

    Hoshyargar, Vahid; Fadaei, Farzad; Ashrafizadeh, Seyed Nezameddin

    2015-01-01

    A comprehensive mathematical model is developed for simulation of ion transport through nanofiltration membranes. The model is based on the Maxwell-Stefan approach and takes into account steric, Donnan, and dielectric effects in the transport of mono and divalent ions. Theoretical ion rejection for multi-electrolyte mixtures was obtained by numerically solving the 'hindered transport' based on the generalized Maxwell-Stefan equation for the flux of ions. A computer simulation has been developed to predict the transport in the range of nanofiltration, a numerical procedure developed linearization and discretization form of the governing equations, and the finite volume method was employed for the numerical solution of equations. The developed numerical method is capable of solving equations for multicomponent systems of n species no matter to what extent the system shows stiffness. The model findings were compared and verified with the experimental data from literature for two systems of Na 2 SO 4 +NaCl and MgCl 2 +NaCl. Comparison showed great agreement for different concentrations. As such, the model is capable of predicting the rejection of different ions at various concentrations. The advantage of such a model is saving costs as a result of minimizing the number of required experiments, while it is closer to a realistic situation since the adsorption of ions has been taken into account. Using this model, the flux of permeates and rejections of multi-component liquid feeds can be calculated as a function of membrane properties. This simulation tool attempts to fill in the gap in methods used for predicting nanofiltration and optimization of the performance of charged nanofilters through generalized Maxwell-Stefan (GMS) approach. The application of the current model may weaken the latter gap, which has arisen due to the complexity of the fundamentals of ion transport processes via this approach, and may further facilitate the industrial development of

  1. Solving Non-Isospectral mKdV Equation and Sine-Gordon Equation Hierarchies with Self-Consistent Sources via Inverse Scattering Transform

    International Nuclear Information System (INIS)

    Li Qi; Zhang Dajun; Chen Dengyuan

    2010-01-01

    N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. (general)

  2. Metamaterial characterization using Boltzmann's kinetic equation for electrons

    DEFF Research Database (Denmark)

    Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.

    2013-01-01

    Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows...

  3. The concept of coupling impedance in the self-consistent plasma wake field excitation

    International Nuclear Information System (INIS)

    Fedele, R.; Akhter, T.; De Nicola, S.; Migliorati, M.; Marocchino, A.; Massimo, F.; Palumbo, L.

    2016-01-01

    Within the framework of the Vlasov–Maxwell system of equations, we describe the self-consistent interaction of a relativistic charged-particle beam with the surroundings while propagating through a plasma-based acceleration device. This is done in terms of the concept of coupling (longitudinal) impedance in full analogy with the conventional accelerators. It is shown that also here the coupling impedance is a very useful tool for the Nyquist-type stability analysis. Examples of specific physical situations are finally illustrated.

  4. Alternative equations of gravitation

    International Nuclear Information System (INIS)

    Pinto Neto, N.

    1983-01-01

    It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt

  5. Comparing Teaching Approaches About Maxwell's Displacement Current

    Science.gov (United States)

    Karam, Ricardo; Coimbra, Debora; Pietrocola, Maurício

    2014-08-01

    Due to its fundamental role for the consolidation of Maxwell's equations, the displacement current is one of the most important topics of any introductory course on electromagnetism. Moreover, this episode is widely used by historians and philosophers of science as a case study to investigate several issues (e.g. the theory-experiment relationship). Despite the consensus among physics educators concerning the relevance of the topic, there are many possible ways to interpret and justify the need for the displacement current term. With the goal of understanding the didactical transposition of this topic more deeply, we investigate three of its domains: (1) The historical development of Maxwell's reasoning; (2) Different approaches to justify the term insertion in physics textbooks; and (3) Four lectures devoted to introduce the topic in undergraduate level given by four different professors. By reflecting on the differences between these three domains, significant evidence for the knowledge transformation caused by the didactization of this episode is provided. The main purpose of this comparative analysis is to assist physics educators in developing an epistemological surveillance regarding the teaching and learning of the displacement current.

  6. The cluster bootstrap consistency in generalized estimating equations

    KAUST Repository

    Cheng, Guang

    2013-03-01

    The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show that the cluster bootstrap yields a consistent approximation of the distribution of the regression estimate, and a consistent approximation of the confidence sets. We also show that a computationally more efficient one-step version of the cluster bootstrap provides asymptotically equivalent inference. © 2012.

  7. Self-consistence equations for extended Feynman rules in quantum chromodynamics

    International Nuclear Information System (INIS)

    Wielenberg, A.

    2005-01-01

    In this thesis improved solutions for Green's functions are obtained. First the for this thesis essential techniques and concepts of QCD as euclidean field theory are presented. After a discussion of the foundations of the extended approach for the Feynman rules of QCD with a systematic approach for the 4-gluon vertex a modified renormalization scheme for the extended approach is developed. Thereafter the resummation of the Dyson-Schwinger equations (DSE) by the appropriately modified Bethe-Salpeter equation is discussed. Then the leading divergences for the 1-loop graphs of the resummed DSE are determined. Thereafter the equation-of-motion condensate is defined as result of an operator-product expansion. Then the self-consistency equations for the extended approaches are defined and numerically solved. (HSI)

  8. Fully nonlinear phenomenology of the Berk-Breizman augmentation of the Vlasov-Maxwell system

    International Nuclear Information System (INIS)

    Vann, R.G.L.; Dendy, R.O.; Rowlands, G.; Arber, T.D.; D'Ambrumenil, N.

    2003-01-01

    The Berk-Breizman augmentation of the Vlasov-Maxwell system is widely used to model self-consistent resonant excitation and damping of wave fields by evolving energetic particle populations in magnetic fusion plasmas. The key model parameters are the particle annihilation rate ν a , which drives bump-on-tail structure, and the linear wave damping rate γ d . A code, based on the piecewise parabolic method, is used to integrate the fully nonlinear Berk-Breizman system of equations across the whole (ν a ,γ d ) parameter space. The results of this code show that the system's behavior can be classified into one of four types, each of which occurs in a well-defined region of parameter space: chaotic, periodic, steady state, and damped. The corresponding evolution in (x,v) phase space is also examined

  9. Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles

    Science.gov (United States)

    Elizondo-Aguilera, L. F.; Zubieta Rico, P. F.; Ruiz-Estrada, H.; Alarcón-Waess, O.

    2014-11-01

    A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, Fl m ,l m(k ,t ) and Flm ,l m S(k ,t ) , are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density nl m(k ,t ) and the translational (α =T ) and rotational (α =R ) current densities jlm α(k ,t ) . Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by Sl m ,l m(k ) . Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γT and γR, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

  10. Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

    Science.gov (United States)

    Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

    2014-11-01

    A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

  11. Consistency of lattice definitions of U(1) flux in Abelian projected SU(2) gauge theory

    International Nuclear Information System (INIS)

    Matsuki, Takayuki; Haymaker, Richard W.

    2004-01-01

    We reexamine the dual Abrikosov vortex under the requirement that the lattice averages of the fields satisfy exact Maxwell equations [ME]. The electric ME accounts for the total flux and the magnetic ME determines the shape of the confining string. This leads to unique and consistent definitions of flux and electric and magnetic currents at finite lattice spacing. The resulting modification of the standard DeGrand-Toussaint construction gives a magnetic current comprised of smeared monopoles

  12. Dynamical Mass Generation and Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics

    International Nuclear Information System (INIS)

    Sanchez Madrigal, S; Raya, A; Hofmann, C P

    2011-01-01

    We study the non-perturbative phenomena of Dynamical Mass Generation and Confinement by truncating at the non-perturbative level the Schwinger-Dyson equations in Maxwell-Chern-Simons planar quantum electrodynamics. We obtain numerical solutions for the fermion propagator in Landau gauge within the so-called rainbow approximation. A comparison with the ordinary theory without the Chern-Simons term is presented.

  13. Lorentz invariance violation and charge (non)conservation: A general theoretical frame for extensions of the Maxwell equations

    International Nuclear Information System (INIS)

    Laemmerzahl, Claus; Macias, Alfredo; Mueller, Holger

    2005-01-01

    All quantum gravity approaches lead to small modifications in the standard laws of physics which in most cases lead to violations of Lorentz invariance. One particular example is the extended standard model (SME). Here, a general phenomenological approach for extensions of the Maxwell equations is presented which turns out to be more general than the SME and which covers charge nonconservation (CNC), too. The new Lorentz invariance violating terms cannot be probed by optical experiments but need, instead, the exploration of the electromagnetic field created by a point charge or a magnetic dipole. Some scalar tensor theories and higher dimensional brane theories predict CNC in four dimensions and some models violating special relativity have been shown to be connected with CNC. Its relation to the Einstein Equivalence Principle has been discussed. Because of this upcoming interest, the experimental status of electric charge conservation is reviewed. Up to now there seem to exist no unique tests of charge conservation. CNC is related to the precession of polarization, to a modification of the 1/r-Coulomb potential, and to a time dependence of the fine structure constant. This gives the opportunity to describe a dedicated search for CNC

  14. Resolution of Maxwell equations within a 2D domain with inner corners. Part I: modelling with boundary conditions of the perfect conductor type

    International Nuclear Information System (INIS)

    Assous, F.; Ciarlet, P.; Sonnendruker, E.

    1996-01-01

    This study addresses the resolution of Maxwell equations in the case of a non-regular boundary and non-convex domain (presence of inner corners) which requires a notably locally refined mesh to obtain an acceptable numerical solution. The authors focus on a 2D problem which may physically correspond to a 3D problem, for example when the electromagnetic field is independent of one the three space variables (for example an infinite cylinder when the field does not depend on the variable associated with the cylinder axis). Model problems are presented: the steady problem, and the evolution problem. The solution is then decomposed into a regular part and a singular one. The authors report the solution calculation, and then the study of the model problems

  15. New variational formulation of Maxwell-Vlasov and guiding center theories

    International Nuclear Information System (INIS)

    Pfirsch, D.

    1983-07-01

    A new variational formulation of Maxwell-Vlasov and related theories is given in terms of a common Lagrangian density for both the 'Vlasov particles' and the Maxwell fields. This formulation is used to derive in a consistent way, on the one hand, correct charge and current densities and, on the other, corresponding energy and energy flux densities. All of these densities generally show in addition to particle like contributions electric polarization and magnetization terms. By some limiting procedure collisionless guiding center theories with polarization drifts included are also treated. In this way local energy conservation laws are formulated for such theories, which has not been possible up to now. (orig.)

  16. Integrable motion of curves in self-consistent potentials: Relation to spin systems and soliton equations

    Energy Technology Data Exchange (ETDEWEB)

    Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)

    2014-06-13

    Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.

  17. Electromagnetic equations based on the law of Biot and Savart

    International Nuclear Information System (INIS)

    Yan, C.-C.

    1983-01-01

    The law of Biot and Savart is given some interpretations that may be of some help in presenting the law. Some possible consequences and the whole set of Maxwell-Lorentz equations are shown to be derivable from the law of Biot and Savart. It is pointed out that the failure or success of deriving the set of Maxwell-Lorentz equation from the law of Biot and Savart is intimately connected to the basic ideas of the theory of special relativity of Einstein. (Author) [pt

  18. Consistent equations for interacting gauge fields of all spins in 3+1 dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Vasiliev, M A [AN SSSR, Moscow. Inst. Teoreticheskoj Fiziki (USSR)

    1990-07-05

    Consistent equations of motion of interacting gauge fields of all spins in 3+1 dimensions are formulated in a closed form. These equations are explicitly general coordinate invariant, possess all necessary higher spin gauge symmetries and reduce to the usual equations of free massless fields of all spins s=0, 1/2, 1, ..., {infinity} at the linearized level. In the spin-2 sector, the proposed equations are equivalent to the Einstein equations with the cosmological term. (orig.).

  19. High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

    International Nuclear Information System (INIS)

    Zhao Shan; Wei, G.W.

    2004-01-01

    This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite-difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 and 12 are achieved, respectively, in 1D and 2D. Detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded FDTD methods. As natural generalizations of the high-order FDTD schemes, the proposed derivative matching methods automatically reduce to the standard FDTD schemes when the material interfaces are absent. An interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code. Another feature of the present approach is that it can be robustly implemented with other high accuracy time-domain approaches, such as the multiresolution time-domain method and the local spectral time-domain method, to cope with material interfaces. Numerical experiments on both 1D and 2D problems are carried out to test the convergence, examine the stability, access the efficiency, and explore the limitation of the proposed methods. It is found that operating at their best capacity, the proposed high-order schemes could be over 2000 times more efficient than their fourth-order versions in 2D. In conclusion, the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high-order schemes for numerical solution of time-domain Maxwell's equations with material interfaces

  20. Yang–Mills equations on conformally connected torsion-free 4-manifolds with different signatures

    Directory of Open Access Journals (Sweden)

    Vyacheslav A. Luk'yanov

    2017-12-01

    Full Text Available In this paper we study spaces of conformal torsion-free connection of dimension 4 whose connection matrix satisfies the Yang–Mills equations. Here we generalize and strengthen the results obtained by us in previous articles, where the angular metric of these spaces had Minkowski signature. The generalization is that here we investigate the spaces of all possible metric signatures, and the enhancement is due to the fact that additional attention is paid to calculating the curvature matrix and establishing the properties of its components. It is shown that the Yang–Mills equations on 4-manifolds of conformal torsion-free connection for an arbitrary signature of the angular metric are reduced to Einstein's equations, Maxwell's equations and the equality of the Bach tensor of the angular metric and the energy-momentum tensor of the skew-symmetric charge tensor. It is proved that if the Weyl tensor is zero, the Yang–Mills equations have only self-dual or anti-self-dual solutions, i.e the curvature matrix of a conformal connection consists of self-dual or anti-self-dual external 2-forms. With the Minkowski signature (antiself-dual external 2-forms can only be zero. The components of the curvature matrix are calculated in the case when the angular metric of an arbitrary signature is Einstein, and the connection satisfies the Yang–Mills equations. In the Euclidean and pseudo-Euclidean 4-spaces we give some particular self-dual and anti-self-dual solutions of the Maxwell equations, to which all the Yang–Mills equations are reduced in this case.

  1. Inverse source problems for eddy current equations

    International Nuclear Information System (INIS)

    Rodríguez, Ana Alonso; Valli, Alberto; Camaño, Jessika

    2012-01-01

    We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by knowledge of the tangential components of the electromagnetic fields on the boundary, and we characterize the space of non-radiating sources. On the other hand, we prove that the inverse source problem has a unique solution if the source is supported on the boundary of a subdomain or if it is the sum of a finite number of dipoles. We address the applicability of this result for the localization of brain activity from electroencephalography and magnetoencephalography measurements. (paper)

  2. A multidimensionally consistent version of Hirota’s discrete KdV equation

    International Nuclear Information System (INIS)

    Atkinson, James

    2012-01-01

    A multidimensionally consistent generalization of Hirota’s discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as superposition principle are given. It is discussed how an important property of the defining polynomial, a factorization of discriminants, appears also in the few other known discrete integrable multi-quadratic models. (fast track communication)

  3. Generalized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-intensity Beams in a Coupled Transverse Focusing Lattice

    International Nuclear Information System (INIS)

    Qin, Hong; Chung, Moses; Davidson, Ronald C.

    2009-01-01

    In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.

  4. A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations

    Directory of Open Access Journals (Sweden)

    Wenhua Zhang

    2013-01-01

    Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.

  5. Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence

    International Nuclear Information System (INIS)

    Hahm, T.S.; Wang, Lu; Madsen, J.

    2008-01-01

    An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E x B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Our generalized ordering takes ρ i θi ∼ L E ∼ L p i is the thermal ion Larmor radius and ρ θi = B/B θ ρ i ), as typically observed in the tokamak H-mode edge, with L E and L p being the radial electric field and pressure gradient lengths. We take k # perpendicular# ρ i ∼ 1 for generality, and keep the relative fluctuation amplitudes e(delta)φ/T i ∼ (delta)B/B up to the second order. Extending the electrostatic theory in the presence of high E x B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pull-back transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation

  6. Modeling High Frequency Semiconductor Devices Using Maxwell's Equations

    National Research Council Canada - National Science Library

    El-Ghazaly, Samier

    1999-01-01

    .... In this research, we first replaced the conventional semiconductor device models, which are based on Poisson's Equation as a semiconductor model, with a new one that uses the full-wave electro...

  7. Quadrupole terms in the Maxwell equations: Debye-Hückel theory in quadrupolarizable solvent and self-salting-out of electrolytes.

    Science.gov (United States)

    Slavchov, Radomir I

    2014-04-28

    If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Hückel theory. The quadrupolar version of the Debye-Hückel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Hückel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient γ± known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally γ±. Comparison with experimental data for γ± for various electrolytes allows for the estimation of the quadrupolar length of water: LQ ≈ 2 Å, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy.

  8. El Dimoni de Maxwell

    OpenAIRE

    Monserrat, Bartomeu

    2010-01-01

    El dimoni de Maxwell és el resultat d'un experiment mental que va proposar el físic escocès James Clerk Maxwell (1831-1879), que si es complís amenaçaria la validesa de la segona llei de la termodinàmica. Segons aquest experiment, seria possible la transmissió de calor d'un cos a un altre de més calent sense cap altre canvi. S'hi ex- posen diverses solucions, que van des de la interacció entre la mesura i el sistema mesurat, fins a la teoria de la informació. Aquest article, origi...

  9. Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

    Science.gov (United States)

    Vogman, Genia

    Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space

  10. Supersymmetrization schemes of D=4 Maxwell algebra

    International Nuclear Information System (INIS)

    Kamimura, Kiyoshi; Lukierski, Jerzy

    2012-01-01

    The Maxwell algebra, an enlargement of Poincaré algebra by Abelian tensorial generators, can be obtained in arbitrary dimension D by the suitable contraction of O(D-1,1)⊕O(D-1,2) (Lorentz algebra ⊕ AdS algebra). We recall that in D=4 the Lorentz algebra O(3,1) is described by the realification Sp R (2|C) of complex algebra Sp(2|C)≃Sl(2|C) and O(3,2)≃Sp(4). We study various D=4N-extended Maxwell superalgebras obtained by the contractions of real superalgebras OSp R (2N-k;2|C)⊕OSp(k;4) (k=0,1,2,…,2N); (extended Lorentz superalgebra ⊕ extended AdS superalgebra). If N=1 (k=0,1,2) one arrives at three different versions of simple Maxwell superalgebra. For any fixed N we get 2N different superextensions of Maxwell algebra with n-extended Poincaré superalgebras (1⩽n⩽N) and the internal symmetry sectors obtained by suitable contractions of the real algebra O R (2N-k|C)⊕O(k). Finally the comments on possible applications of Maxwell superalgebras are presented.

  11. Geometric Integration Of The Valsov-Maxwell System With A Variational Particle-in-cell Scheme

    International Nuclear Information System (INIS)

    Squire, J.; Qin, H.; Tang, W.M.

    2012-01-01

    A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

  12. Pathological behavior of the open-shell restricted self-consistent-field equations

    International Nuclear Information System (INIS)

    Moscardo, F.; Alvarez-Collado, J.R.

    1979-01-01

    The possible solutions of open-shell restricted self-consistent-field equations for a doublet are studied for Li and Na atoms, according to the values of the parameters implied in those equations. A similar behavior, characterized by the presence of several variational solutions is observed in both atoms. Some of these solutions can be assigned to excited configurations. Excitation energies are in good agreement with experimental data. Doublet stability for the solutions obtained has been studied, discussing the saddle-point character present in those solutions associated to excited configurations

  13. Pathological behavior of the open-shell restricted self-consistent-field equations

    Energy Technology Data Exchange (ETDEWEB)

    Moscardo, F.; Alvarez-Collado, J.R.

    1979-02-01

    The possible solutions of open-shell restricted self-consistent-field equations for a doublet are studied for Li and Na atoms, according to the values of the parameters implied in those equations. A similar behavior, characterized by the presence of several variational solutions is observed in both atoms. Some of these solutions can be assigned to excited configurations. Excitation energies are in good agreement with experimental data. Doublet stability for the solutions obtained has been studied, discussing the saddle-point character present in those solutions associated to excited configurations.

  14. Interaction of magnetic field in flow of Maxwell nanofluid with convective effect

    Energy Technology Data Exchange (ETDEWEB)

    Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Chen, G.Q. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Laboratory of Systems Ecology, College of Engineering, Peking University, Beijing 100871 (China); Abbas, Ibrahim A. [Mathematics Department (Khulais), Faculty of Science and Arts, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)

    2015-09-01

    Magnetohydrodynamic (MHD) three-dimensional flow of Maxwell nanofluid subject to the convective boundary condition is investigated. The flow is generated by a bidirectional stretching surface. Thermophoresis and Brownian motion effects are present. Fluid is electrically conducted in the presence of a constant applied magnetic field. Unlike the previous cases even in the absence of nanoparticles, the correct formulation for the flow of Maxwell fluid in the presence of a magnetic field is established. Newly proposed boundary condition with the zero nanoparticles mass flux at the boundary is employed. The governing nonlinear boundary layer equations through appropriate transformations are reduced in the nonlinear ordinary differential system. The resulting nonlinear system has been solved for the velocities, temperature and nanoparticles concentration distributions. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt number are computed and analyzed. It is observed that the effects of magnetic parameter and the Biot number on the temperature and nanoparticles concentration are quite similar. Both the temperature and nanoparticles concentration are enhanced for the increasing value of magnetic parameter and Biot number. - Highlights: • Three-dimensional flow of Maxwell fluid. • Consideration of nanoparticles effect. • Formulation through convective condition. • Analysis in magnetohydrodynamic regime. • Utilization of new condition associated with mass flux.

  15. q-conformally covariant q-Minkowski space-time and invariant equations

    International Nuclear Information System (INIS)

    Dobrev, V.K.

    1997-09-01

    We present explicitly the covariant action of the q-conformal algebra on the q-Minkowski space we proposed earlier. We also present some q-conformally invariant equations, namely a hierarchy of q-Maxwell equations, and also a q-d'Alembert equation, proposed earlier by us, in a form different from the original . (author). 19 refs

  16. Inversion transformation in the Schroedinger equation

    International Nuclear Information System (INIS)

    Demkov, Yu.N.; Semenova, N.V.

    1984-01-01

    Using the inversion with respect to a sphere in the coordinate space, the equivalence between the Schroedinger equations with different potentials is established. It is shown that the zero-energy equation for a spherically symmetric potential is equivalent to the equation with an axially symmetric potential of a special form. The particular exact solutions of the zero-energy problem for the motion of a particle in the field of two Maxwell ''fish-eye'' potentials and potentials with the two Coulomb singularities are found

  17. Nonlinear heat conduction equations with memory: Physical meaning and analytical results

    Science.gov (United States)

    Artale Harris, Pietro; Garra, Roberto

    2017-06-01

    We study nonlinear heat conduction equations with memory effects within the framework of the fractional calculus approach to the generalized Maxwell-Cattaneo law. Our main aim is to derive the governing equations of heat propagation, considering both the empirical temperature-dependence of the thermal conductivity coefficient (which introduces nonlinearity) and memory effects, according to the general theory of Gurtin and Pipkin of finite velocity thermal propagation with memory. In this framework, we consider in detail two different approaches to the generalized Maxwell-Cattaneo law, based on the application of long-tail Mittag-Leffler memory function and power law relaxation functions, leading to nonlinear time-fractional telegraph and wave-type equations. We also discuss some explicit analytical results to the model equations based on the generalized separating variable method and discuss their meaning in relation to some well-known results of the ordinary case.

  18. New family of Maxwell like algebras

    International Nuclear Information System (INIS)

    Concha, P.K.; Durka, R.; Merino, N.; Rodríguez, E.K.

    2016-01-01

    We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

  19. New family of Maxwell like algebras

    Energy Technology Data Exchange (ETDEWEB)

    Concha, P.K., E-mail: patillusion@gmail.com [Departamento de Ciencias, Facultad de Artes y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia (Chile); Durka, R., E-mail: remigiuszdurka@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Merino, N., E-mail: nemerino@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Rodríguez, E.K., E-mail: everodriguezd@gmail.com [Departamento de Ciencias, Facultad de Artes y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia (Chile)

    2016-08-10

    We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

  20. 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

  1. Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity

    Science.gov (United States)

    Ravera, Lucrezia

    2018-03-01

    The purpose of this paper is to show that the so-called Maxwell superalgebra in four dimensions, which naturally involves the presence of a nilpotent fermionic generator, can be interpreted as a hidden superalgebra underlying N=1, {D}=4 supergravity extended to include a 2-form gauge potential associated to a 2-index antisymmetric tensor. In this scenario, the theory is appropriately discussed in the context of Free Differential Algebras (an extension of the Maurer-Cartan equations to involve higher-degree differential forms). The study is then extended to the Free Differential Algebra describing D = 11 supergravity, showing that, also in this case, there exists a super-Maxwell algebra underlying the theory. The same extra spinors dual to the nilpotent fermionic generators whose presence is crucial for writing a supersymmetric extension of the Maxwell algebras, both in the D = 4 and in the D = 11 case, turn out to be fundamental ingredients also to reproduce the D = 4 and D = 11 Free Differential Algebras on ordinary superspace, whose basis is given by the supervielbein. The analysis of the gauge structure of the supersymmetric Free Differential Algebras is carried on taking into account the gauge transformations from the hidden supergroup-manifold associated with the Maxwell superalgebras.

  2. Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program

    International Nuclear Information System (INIS)

    Sharp, W.M.; Yu, S.S.; Lee, E.P.

    1987-01-01

    A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations

  3. A kinetic equation for irreversible aggregation

    International Nuclear Information System (INIS)

    Zanette, D.H.

    1990-09-01

    We introduce a kinetic equation for describing irreversible aggregation in the ballistic regime, including velocity distributions. The associated evolution for the macroscopic quantities is studied, and the general solution for Maxwell interaction models is obtained in the Fourier representation. (author). 23 refs

  4. Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell p-form theory

    Czech Academy of Sciences Publication Activity Database

    Kuchynka, Martin; Pravdová, Alena

    2017-01-01

    Roč. 49, č. 5 (2017), č. článku 71. ISSN 0001-7701 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : Einstein–Maxwell equations * Weyl type N spacetimes * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.618, year: 2016 https://link.springer.com/article/10.1007/s10714-017-2234-7

  5. On the hydrodynamic limit of self-consistent field equations

    International Nuclear Information System (INIS)

    Pauli, H.C.

    1980-01-01

    As an approximation to the nuclear many-body problem, the hydrodynamical limit of self-consistent field equations is worked out and applied to the treatment of vibrational and rotational motion. Its validity is coupled to the value of a smallness parameter, behaving as 20Asup(-2/3) with the number of nucleons. For finite nuclei, this number is not small enough as compared to 1, and indeed one observes a discrepancy of roughly a factor of 5 between the hydrodynamic frequencies and the relevant experimental numbers. (orig.)

  6. The Maxwell-Chern-Simons gravity, and its cosmological implications

    Energy Technology Data Exchange (ETDEWEB)

    Haghani, Zahra; Shahidi, Shahab [Damghan University, School of Physics, Damghan (Iran, Islamic Republic of); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom)

    2017-08-15

    We consider the cosmological implications of a gravitational theory containing two vector fields coupled via a generalized Chern-Simons term. One of the vector fields is the usual Maxwell field, while the other is a constrained vector field with constant norm included in the action via a Lagrange multiplier. The theory admits a de Sitter type solution, with healthy cosmological perturbations. We also show that there are seven degrees of freedom that propagate on top of de Sitter space-time, consisting of two tensor polarizations, four degrees of freedom related to the two vector fields, and a scalar degree of freedom that makes one of the vector fields massive. We investigate the cosmological evolution of Bianchi type I space-time, by assuming that the matter content of the Universe can be described by the stiff and dust. The cosmological evolution of the Bianchi type I Universe strongly depends on the initial conditions of the physical quantities, as well as on the model parameters. The mean anisotropy parameter, and the deceleration parameter, are also studied, and we show that independently of the matter equation of state the cosmological evolution of the Bianchi type I Universe always ends in an isotropic de Sitter type phase. (orig.)

  7. Dynamic simulation of electromechanical systems: from Maxwell's theory to common-rail diesel injection.

    Science.gov (United States)

    Kurz, S; Becker, U; Maisch, H

    2001-05-01

    This paper describes the state-of-the-art of dynamic simulation of electromechanical systems. Electromechanical systems can be split into electromagnetic and mechanical subsystems, which are described by Maxwell's equations and by Newton's law, respectively. Since such systems contain moving parts, the concepts of Lorentz and Galilean relativity are briefly addressed. The laws of physics are formulated in terms of (partial) differential equations. Numerical methods ultimately aim at linear systems of equations, which can be solved efficiently on digital computers. The various discretization methods for performing this task are discussed. Special emphasis is placed on domain decomposition as a framework for the coupling of different numerical methods such as the finite element method and the boundary element method. The paper concludes with descriptions of some applications of industrial relevance: a high performance injection valve and an electromechanical relay.

  8. A one-dimensional analysis of real and complex turbulence and the Maxwell set for the stochastic Burgers equation

    International Nuclear Information System (INIS)

    Neate, A D; Truman, A

    2005-01-01

    The inviscid limit of the Burgers equation, with body forces white noise in time, is discussed in terms of the level surfaces of the minimizing Hamilton-Jacobi function and the classical mechanical caustic and their algebraic pre-images under the classical mechanical flow map. The problem is analysed in terms of a reduced (one-dimensional) action function using a circle of ideas due to Arnol'd, Cayley and Klein. We characterize those parts of the caustic which are singular, and give an explicit expression for the cusp density on caustics and level surfaces. By considering the double points of level surfaces we find an explicit formula for the Maxwell set in the two-dimensional polynomial case, and we extend this to higher dimensions using a double discriminant of the reduced action, solving a long-standing problem for Hamiltonian dynamical systems. When the pre-level surface touches the pre-caustic, the geometry (number of cusps) on the level surface changes infinitely rapidly causing 'real turbulence'. Using an idea of Klein, it is shown that the geometry (number of swallowtails) on the caustic also changes infinitely rapidly when the real part of the pre-caustic touches its complex counterpart, causing 'complex turbulence'. These are both inherently stochastic in nature, and we determine their intermittence in terms of the recurrent behaviour of two processes

  9. Maxwell's Multipole Vectors and the CMB

    OpenAIRE

    Weeks, Jeffrey R.

    2004-01-01

    The recently re-discovered multipole vector approach to understanding the harmonic decomposition of the cosmic microwave background traces its roots to Maxwell's Treatise on Electricity and Magnetism. Taking Maxwell's directional derivative approach as a starting point, the present article develops a fast algorithm for computing multipole vectors, with an exposition that is both simpler and better motivated than in the author's previous work. Tests show the resulting algorithm, coded up as a ...

  10. Effective evolution equations from quantum mechanics

    OpenAIRE

    Leopold, Nikolai

    2018-01-01

    The goal of this thesis is to provide a mathematical rigorous derivation of the Schrödinger-Klein-Gordon equations, the Maxwell-Schrödinger equations and the defocusing cubic nonlinear Schrödinger equation in two dimensions. We study the time evolution of the Nelson model (with ultraviolet cutoff) in a limit where the number N of charged particles gets large while the coupling of each particle to the radiation field is of order N^{−1/2}. At time zero it is assumed that almost all charges a...

  11. On Some Unusual Properties of Wave Solutions of Free Maxwell Equations

    Directory of Open Access Journals (Sweden)

    Augusto Espinoza

    2006-01-01

    Full Text Available Se descubren algunas propiedades inusuales de las soluciones de las llamadas ecuaciones libres de Maxwell. Mostramos la existencia de soluciones que representan las ondas electromagnéticas en el vacío para los cuales el vector de Poynting no coincide con el vector de Umov. Se presentan soluciones que corresponden a ondas magnéticas estacionarias de una configuración inusual en el vacío, que describen en el vacio formaciones estables anulares y esféricas de campo. Se demuestra que en el vacío, de acuerdo a las soluciones obtenidas el campo eléctrico E puede ser un vector polar así como un vector axial; y el campo magnético B, en su turno, puede ser un vector axial así como también un vector polar. Se muestra que tales soluciones existen cuando los vectores E y B, no son vectores polares ni axiales. Además, estas soluciones corresponden a ondas electromagnéticas que no transfieren energía ni momentos en cualquier punto del vacío.

  12. Dirac equation on a curved surface

    Energy Technology Data Exchange (ETDEWEB)

    Brandt, F.T., E-mail: fbrandt@usp.br; Sánchez-Monroy, J.A., E-mail: antosan@usp.br

    2016-09-07

    The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein–Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles. - Highlights: • The thin-layer method is employed to derive the Dirac equation on a curved surface. • A geometric potential is absent at least to first-order in the perturbative expansion. • The effects of the extrinsic curvature are included to rescue the non-relativistic limit. • The resulting Dirac equation is consistent with the Heisenberg uncertainty principle.

  13. Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

    Science.gov (United States)

    Kolesnichenko, A. V.; Marov, M. Ya.

    2018-01-01

    The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan-Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman-Enskog procedure using Sonine polynomial expansions. The modified Stefan-Maxwell relations are used for the description of ambipolar diffusion in the Earth's ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

  14. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme

    Energy Technology Data Exchange (ETDEWEB)

    Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)

    2012-08-15

    A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

  15. Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov-Maxwell system

    CERN Document Server

    Huot, F; Bertrand, P; Sonnendrücker, E; Coulaud, O

    2003-01-01

    The Time Splitting Scheme (TSS) has been examined within the context of the one-dimensional (1D) relativistic Vlasov-Maxwell model. In the strongly relativistic regime of the laser-plasma interaction, the TSS cannot be applied to solve the Vlasov equation. We propose a new semi-Lagrangian scheme based on a full 2D advection and study its advantages over the classical Splitting procedure. Details of the underlying integration of the Vlasov equation appear to be important in achieving accurate plasma simulations. Examples are given which are related to the relativistic modulational instability and the self-induced transparency of an ultra-intense electromagnetic pulse in the relativistic regime.

  16. Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

  17. Electromagnetic-field equations in the six-dimensional space-time R6

    International Nuclear Information System (INIS)

    Teli, M.T.; Palaskar, D.

    1984-01-01

    Maxwell's equations (without monopoles) for electromagnetic fields are obtained in six-dimensional space-time. The equations possess structural symmetry in space and time, field and source densities. Space-time-symmetric conservation laws and field solutions are obtained. The results are successfully correlated with their four-dimensional space-time counterparts

  18. Self-dual Maxwell-Chern-Simons theory on a cylinder

    International Nuclear Information System (INIS)

    Han, Jongmin; Kim, Seongtag

    2011-01-01

    In this paper, we study the relativistic Maxwell-Chern-Simons vortices on an asymptotically flat cylinder. A topological multivortex solution is constructed by variational methods, and the Maxwell and the Chern-Simons limits are verified.

  19. Consistency of direct integral estimator for partially observed systems of ordinary differential equations

    NARCIS (Netherlands)

    Vujačić, Ivan; Dattner, Itai

    In this paper we use the sieve framework to prove consistency of the ‘direct integral estimator’ of parameters for partially observed systems of ordinary differential equations, which are commonly used for modeling dynamic processes.

  20. An integral equation-based numerical solver for Taylor states in toroidal geometries

    Science.gov (United States)

    O'Neil, Michael; Cerfon, Antoine J.

    2018-04-01

    We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

  1. Solutions of the spin coefficient equations with nongeodesic eigenrays

    International Nuclear Information System (INIS)

    Kota, J.; Lukacs, B.; Perjes, Z.

    1982-01-01

    Among the many significant results obtained by spin coefficient techniques in general relativity, the exact integrals of gravitational equations have enjoyed particular attention. These integration procedures were first carried out with respect to a congruence of null geodesic curves. The authors show that spin coefficient equations can sometimes be exactly solved when the selected null congruence is nongeodesic. They derive metrics with this property and, among them, a new solution of the coupled Einstein-Maxwell equations. (Auth.)

  2. Light scattering by multiple spheres: comparison between Maxwell theory and radiative-transfer-theory calculations.

    Science.gov (United States)

    Voit, Florian; Schäfer, Jan; Kienle, Alwin

    2009-09-01

    We present a methodology to compare results of classical radiative transfer theory against exact solutions of Maxwell theory for a high number of spheres. We calculated light propagation in a cubic scattering region (20 x 20 x 20 microm(3)) consisting of different concentrations of polystyrene spheres in water (diameter 2 microm) by an analytical solution of Maxwell theory and by a numerical solution of radiative transfer theory. The relative deviation of differential as well as total scattering cross sections obtained by both approaches was evaluated for each sphere concentration. For the considered case, we found that deviations due to radiative transfer theory remain small, even for concentrations up to ca. 20 vol. %.

  3. New finite volume methods for approximating partial differential equations on arbitrary meshes

    International Nuclear Information System (INIS)

    Hermeline, F.

    2008-12-01

    This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)

  4. Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density

    Science.gov (United States)

    Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.

    1988-01-01

    The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.

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

    Directory of Open Access Journals (Sweden)

    Yang Zhao

    2013-01-01

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

  6. Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

    Science.gov (United States)

    Kassandrov, Vladimir V.; Rizcallah, Joseph A.

    We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.

  7. The many faces of Maxwell, Dirac and Einstein equations a Clifford bundle approach

    CERN Document Server

    Rodrigues, Jr, Waldyr A

    2016-01-01

    This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solut...

  8. Laplace's equation and Faraday's lines of force

    Energy Technology Data Exchange (ETDEWEB)

    Narasimhan, T.N.

    2007-06-01

    Boundary-value problems involve two dependent variables: a potential function, and a stream function. They can be approached in two mutually independent ways. The first, introduced by Laplace, involves spatial gradients at a point. Inspired by Faraday, Maxwell introduced the other, visualizing the flow domain as a collection of flow tubes and isopotential surfaces. Boundary-value problems intrinsically entail coupled treatment (or, equivalently, optimization) of potential and stream functions Historically, potential theory avoided the cumbersome optimization task through ingenious techniques such as conformal mapping and Green's functions. Laplace's point-based approach, and Maxwell's global approach, each provides its own unique insights into boundary-value problems. Commonly, Laplace's equation is solved either algebraically, or with approximate numerical methods. Maxwell's geometry-based approach opens up novel possibilities of direct optimization, providing an independent logical basis for numerical models, rather than treating them as approximate solvers of the differential equation. Whereas points, gradients, and Darcy's law are central to posing problems on the basis of Laplace's approach, flow tubes, potential differences, and the mathematical form of Ohm's law are central to posing them in natural coordinates oriented along flow paths. Besides being of philosophical interest, optimization algorithms can provide advantages that complement the power of classical numerical models. In the spirit of Maxwell, who eloquently spoke for a balance between abstract mathematical symbolism and observable attributes of concrete objects, this paper is an examination of the central ideas of the two approaches, and a reflection on how Maxwell's integral visualization may be practically put to use in a world of digital computers.

  9. Self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the Δ distribution function

    International Nuclear Information System (INIS)

    Mao, G.; Li, Z.; Zhuo, Y.

    1996-01-01

    We derive the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) equation for the delta distribution function within the framework which we have done for nucleon close-quote s. In our approach, the Δ isobars are treated in essentially the same way as nucleons. Both mean field and collision terms of Δ close-quote s RBUU equation are derived from the same effective Lagrangian and presented analytically. We calculate the in-medium NΔ elastic and inelastic scattering cross sections up to twice nuclear matter density and the results show that the in-medium cross sections deviate substantially from Cugnon close-quote s parametrization that is commonly used in the transport model. copyright 1996 The American Physical Society

  10. Anisotropic spheres with Van der Waals-type equation of state

    Indian Academy of Sciences (India)

    2014-07-02

    Jul 2, 2014 ... Einstein–Maxwell system; anisotropic matter; equation of state; relativistic star. ... the temperature-dominated phase in the early Universe or in ..... of Lobo [22], the de Sitter isotropic model and Einstein's model can be regained ...

  11. Comment on the consistency of truncated nonlinear integral equation based theories of freezing

    International Nuclear Information System (INIS)

    Cerjan, C.; Bagchi, B.; Rice, S.A.

    1985-01-01

    We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions

  12. Swarm analysis by using transport equations

    International Nuclear Information System (INIS)

    Dote, Toshihiko.

    1985-01-01

    As the basis of weak ionization plasma phenomena, the motion, i.e. swarm, of charged particles in the gas is analyzed by use of the transport equations, from which basic nature of the swarm is discussed. The present report is an overview of the studies made in the past several years. Described are principally the most basic aspects concerning behaviors of the electrons and positive ions, that is, the basic equations and their significance, characteristics of the behaviors of the electron and positive ion swarms as revealed by solving the equations, and various characteristics of the swarm parameters. Contents are: Maxwell-Boltzmann's transport equations, behavior of the electron swarm, energy loss of the electrons, and behavior of the positive ion swarm. (Mori, K.)

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

    Science.gov (United States)

    Sá, Lucas

    2017-03-01

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

  14. Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger-Maxwell systems

    Science.gov (United States)

    Chen, Qiang; Qin, Hong; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei

    2017-11-01

    An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schrödinger-Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. This new numerical capability enables us to carry out first-principle based simulation study of important photon-matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.

  15. Maxwell-Stefan based modelling of ion exchange systems containing common species (Cd"2"+, Na"+) and distinct sorbents (ETS-4, ETS-10)

    International Nuclear Information System (INIS)

    Lito, P. F.; Aniceto, J. P. S.; Silva, C. M.

    2015-01-01

    Cadmium(II) is a toxic hazardous cation, whose presence in the environment causes great concern because of its bioaccumulation in organisms and bio amplification along food chain. Hence, the removal of cadmium compounds from industrial waters and wastewaters is particularly essential, which requires intensive experimental and modelling studies to deal with the problem. In this work, the ion exchange of Cd"2"+ ions from aqueous solution using microporous titanosilicates (ETS-4 and ETS-10) has been modelled using adapted Maxwell-Stefan equations for the ions transport inside the sorbent particles. The fundamentals of the Maxwell-Stefan equations along with correlations for the convective mass transfer coefficients have been used with advantage to reduce the number of model parameters. In the whole, the model was able to represent successfully the kinetic behaviour of 11 independent and very distinct curves of both studied systems (Cd2"+"/Na"+/ETS-4 and Cd"2"+/Na"+/ ETS-10). The predictive capability of the model has been also shown, since several uptake curves were accurately predicted with parameters fitted previously to different sets of experimental data.

  16. Exact solution for heat transfer free convection flow of Maxwell nanofluids with graphene nanoparticles

    Science.gov (United States)

    Aman, Sidra; Zuki Salleh, Mohd; Ismail, Zulkhibri; Khan, Ilyas

    2017-09-01

    This article focuses on the flow of Maxwell nanofluids with graphene nanoparticles over a vertical plate (static) with constant wall temperature. Possessing high thermal conductivity, engine oil is useful to be chosen as base fluid with free convection. The problem is modelled in terms of PDE’s with boundary conditions. Some suitable non-dimensional variables are interposed to transform the governing equations into dimensionless form. The generated equations are solved via Laplace transform technique. Exact solutions are evaluated for velocity and temperature. These solutions are significantly controlled by some parameters involved. Temperature rises with elevation in volume fraction while Velocity decreases with increment in volume fraction. A comparison with previous published results are established and discussed. Moreover, a detailed discussion is made for influence of volume fraction on the flow and heat profile.

  17. Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

    International Nuclear Information System (INIS)

    Li Li

    2011-01-01

    From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.

  18. Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

    Energy Technology Data Exchange (ETDEWEB)

    Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

    2011-03-14

    From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.

  19. The exact solution of self-consistent equations in the scanning near-field optic microscopy problem

    DEFF Research Database (Denmark)

    Lozovski, Valeri; Bozhevolnyi, Sergey I.

    1999-01-01

    The macroscopic approach that allows one to obtain an exact solution of the self-consistent equation of the Lippmann-Schwinger type is developed. The main idea of our method consist in usage of diagram technque for exact summation of the infinite series corresponding to the iteration procedure fo...

  20. A modified KdV equation with self-consistent sources in non-uniform media and soliton dynamics

    International Nuclear Information System (INIS)

    Zhang Dajun; Bi Jinbo; Hao Honghai

    2006-01-01

    Two non-isospectral modified KdV equations with self-consistent sources are derived, which correspond to the time-dependent spectral parameter λ satisfying λ t = λ and λ t = λ 3 , respectively. Gauge transformation between the first non-isospectral equation (corresponding to λ t = λ) and its isospectral counterpart is given, from which exact solutions and conservation laws for the non-isospectral one are easily listed. Besides, solutions to the two non-isospectral modified KdV equations with self-consistent sources are derived by means of the Hirota method and the Wronskian technique, respectively. Non-isospectral dynamics and source effects, including one-soliton characteristics in non-uniform media, two-solitons scattering and special behaviours related to sources (for example, the 'ghost' solitons in the degenerate two-soliton case), are investigated analytically

  1. Thermodynamic consistency test procedure using orthogonal collocation and the Peng-Robinson equation of state

    International Nuclear Information System (INIS)

    Hamm, L.L.; Van Brunt, V.

    1982-08-01

    The Christiansen and Fredenslund programs for calculating vapor-liquid equilibria have been modified by replacing the Soave-Redlich-Kwong equation of state with the newly developed Peng-Robinson equation of state. This modification was shown to be a decided improvement for high pressure systems, especially in the critical and upper retrograde regions. Thermodynamic consistency tests were developed and used to evaluate and compare calculated values from both the modified and unmodified programs with reported experimental data for several vapor-liquid systems

  2. Evolution equations for Killing fields

    International Nuclear Information System (INIS)

    Coll, B.

    1977-01-01

    The problem of finding necessary and sufficient conditions on the Cauchy data for Einstein equations which insure the existence of Killing fields in a neighborhood of an initial hypersurface has been considered recently by Berezdivin, Coll, and Moncrief. Nevertheless, it can be shown that the evolution equations obtained in all these cases are of nonstrictly hyperbolic type, and, thus, the Cauchy data must belong to a special class of functions. We prove here that, for the vacuum and Einstein--Maxwell space--times and in a coordinate independent way, one can always choose, as evolution equations for the Killing fields, a strictly hyperbolic system: The above theorems can be thus extended to all Cauchy data for which the Einstein evolution problem has been proved to be well set

  3. Generalized nonlinear Proca equation and its free-particle solutions

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-06-15

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

  4. EINSTEIN EQUATIONS FOR TETRAD FIELDS ECUACIONES DE EINSTEIN PARA CAMPOS TETRADOS

    Directory of Open Access Journals (Sweden)

    Héctor Torres-Silva

    2008-11-01

    Full Text Available Every metric tensor can be expressed by the inner product of tetrad fields. We prove that Einstein's equations for these fields have the same form as the stress-energy tensor of electromagnetism if the total external current . Using the Evans' unified field theory, we show that the true unification of gravity and electromagnetism is with source-free Maxwell equations.Todo tensor métrico puede ser expresado por el producto interno de campos tetrados. Se prueba que las ecuaciones de Einstein para esos campos tienen la misma forma que el tensor electromagnético de momento-energía si la corriente externa total es igual a cero. Usando la teoría de campo unificado de Evans se muestra que la verdadera unificación de la gravedad y el electromagnetismo es con las ecuaciones de Maxwell sin fuentes.

  5. New two- and three-parameter solutions of the MPST equation

    International Nuclear Information System (INIS)

    Krori, K.D.; Chaudhury, T.; Bhattacharjee, R.

    1981-01-01

    Some new two- and three-parameter solutions of the MPST (Misra et al. Phys. Rev.; D7:1587 (1973)) equation are presented. All the three-parameter solutions are physical in the sense of asymptotic flatness. The simplest member of the three-parameter series of solutions is identical with a three-parameter solution of the static Einstein-Maxwell equations recently discovered by Bonnor (J. Phys. A.; 12:853 (1979)). (author)

  6. On separable Pauli equations

    International Nuclear Information System (INIS)

    Zhalij, Alexander

    2002-01-01

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

  7. Operational derivation of Boltzmann distribution with Maxwell's demon model.

    Science.gov (United States)

    Hosoya, Akio; Maruyama, Koji; Shikano, Yutaka

    2015-11-24

    The resolution of the Maxwell's demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of statistical mechanics and to derive results therein in an operational manner. Here, we present a derivation of the Boltzmann distribution in equilibrium as an example, without hypothesizing the principle of maximum entropy. Further, since the model can be applied to non-equilibrium processes, in principle, we demonstrate the dissipation-fluctuation relation to show the possibility in this direction.

  8. The electrically charged BTZ black hole with self (anti-self) dual Maxwell field

    International Nuclear Information System (INIS)

    Kamata, M.; Koikawa, T.

    1995-04-01

    The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensions discussed by Banados, Teitelboim and Zanelli are solved by assuming a self (anti-self) dual equation E r-circumflex = ± B -circumflex , which is imposed on the orthonormal basis components of the electric field E r-circumflex and the magnetic field B -circumflex . This solution describes an electrically charged extra black hole with mass M=8πGQ 2 e , angular momentum J = ±8πGQ 2 e / modul Λ 1/2 and electric charge Q e . Although the coordinate components of the electric field E r and the magnetic field B have singularities on the horizon at r (4πGQ 2 e / modul Λ) 1/2 , the spacetime has the same value of constant negative curvature R = 6Λ as that of Banados et al. (author). 5 refs

  9. Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

    Science.gov (United States)

    Horowitz, Jordan M

    2015-07-28

    The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

  10. Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

    Science.gov (United States)

    Raju, Thokala Soloman; Pal, Ritu

    2018-05-01

    We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

  11. The Principle of Energetic Consistency: Application to the Shallow-Water Equations

    Science.gov (United States)

    Cohn, Stephen E.

    2009-01-01

    If the complete state of the earth's atmosphere (e.g., pressure, temperature, winds and humidity, everywhere throughout the atmosphere) were known at any particular initial time, then solving the equations that govern the dynamical behavior of the atmosphere would give the complete state at all subsequent times. Part of the difficulty of weather prediction is that the governing equations can only be solved approximately, which is what weather prediction models do. But weather forecasts would still be far from perfect even if the equations could be solved exactly, because the atmospheric state is not and cannot be known completely at any initial forecast time. Rather, the initial state for a weather forecast can only be estimated from incomplete observations taken near the initial time, through a process known as data assimilation. Weather prediction models carry out their computations on a grid of points covering the earth's atmosphere. The formulation of these models is guided by a mathematical convergence theory which guarantees that, given the exact initial state, the model solution approaches the exact solution of the governing equations as the computational grid is made more fine. For the data assimilation process, however, there does not yet exist a convergence theory. This book chapter represents an effort to begin establishing a convergence theory for data assimilation methods. The main result, which is called the principle of energetic consistency, provides a necessary condition that a convergent method must satisfy. Current methods violate this principle, as shown in earlier work of the author, and therefore are not convergent. The principle is illustrated by showing how to apply it as a simple test of convergence for proposed methods.

  12. Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

    International Nuclear Information System (INIS)

    Fischer, E.

    1977-01-01

    Various families of exact solutions to the Einstein and Einstein--Maxwell field equations of general relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations. The physical situations in which such equations arise include: the external gravitational field of an axisymmetric, uncharged steadily rotating body, cylindrical gravitational waves with two degrees of freedom, colliding plane gravitational waves, the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein--Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa. The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables

  13. Lectures on nonlinear evolution equations initial value problems

    CERN Document Server

    Racke, Reinhard

    2015-01-01

    This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

  14. Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

    Directory of Open Access Journals (Sweden)

    Matt Challacombe

    2014-03-01

    Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.

  15. Consistent initial conditions for the Saint-Venant equations in river network modeling

    Directory of Open Access Journals (Sweden)

    C.-W. Yu

    2017-09-01

    Full Text Available Initial conditions for flows and depths (cross-sectional areas throughout a river network are required for any time-marching (unsteady solution of the one-dimensional (1-D hydrodynamic Saint-Venant equations. For a river network modeled with several Strahler orders of tributaries, comprehensive and consistent synoptic data are typically lacking and synthetic starting conditions are needed. Because of underlying nonlinearity, poorly defined or inconsistent initial conditions can lead to convergence problems and long spin-up times in an unsteady solver. Two new approaches are defined and demonstrated herein for computing flows and cross-sectional areas (or depths. These methods can produce an initial condition data set that is consistent with modeled landscape runoff and river geometry boundary conditions at the initial time. These new methods are (1 the pseudo time-marching method (PTM that iterates toward a steady-state initial condition using an unsteady Saint-Venant solver and (2 the steady-solution method (SSM that makes use of graph theory for initial flow rates and solution of a steady-state 1-D momentum equation for the channel cross-sectional areas. The PTM is shown to be adequate for short river reaches but is significantly slower and has occasional non-convergent behavior for large river networks. The SSM approach is shown to provide a rapid solution of consistent initial conditions for both small and large networks, albeit with the requirement that additional code must be written rather than applying an existing unsteady Saint-Venant solver.

  16. Temperature waves and the Boltzmann kinetic equation for phonons

    International Nuclear Information System (INIS)

    Urushev, D.; Borisov, M.; Vavrek, A.

    1988-01-01

    The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs

  17. Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle

    Energy Technology Data Exchange (ETDEWEB)

    Barletti, Luigi, E-mail: luigi.barletti@unifi.it [Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze (Italy)

    2014-08-15

    The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.

  18. Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group

    Science.gov (United States)

    Ardentov, Andrei A.; Sachkov, Yuri L.

    2017-12-01

    We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kinematic models of a car with a trailer). On the other hand, this is the simplest sub-Riemannian structure of step three. We describe the global structure of the cut locus (the set of points where geodesics lose their global optimality), the Maxwell set (the set of points that admit more than one minimizer), and the intersection of the cut locus with the caustic (the set of conjugate points along all geodesics). The group of symmetries of the cut locus is described: it is generated by a one-parameter group of dilations R+ and a discrete group of reflections Z2 × Z2 × Z2. The cut locus admits a stratification with 6 three-dimensional strata, 12 two-dimensional strata, and 2 one-dimensional strata. Three-dimensional strata of the cut locus are Maxwell strata of multiplicity 2 (for each point there are 2 minimizers). Two-dimensional strata of the cut locus consist of conjugate points. Finally, one-dimensional strata are Maxwell strata of infinite multiplicity, they consist of conjugate points as well. Projections of sub-Riemannian geodesics to the 2-dimensional plane of the distribution are Euler elasticae. For each point of the cut locus, we describe the Euler elasticae corresponding to minimizers coming to this point. Finally, we describe the structure of the optimal synthesis, i. e., the set of minimizers for each terminal point in the Engel group.

  19. Use of the SSF equations in the Kojima-Moon-Ochi thermodynamic consistency test of isothermal vapour-liquid equilibrium data

    Directory of Open Access Journals (Sweden)

    SLOBODAN P. SERBANOVIC

    2000-12-01

    Full Text Available The Kojima-Moon-Ochi (KMO thermodynamic consistency test of vapour–liquid equilibrium (VLE measurements for 32 isothermal data sets of binary systems of various complexity was applied using two fitting equations: the Redlich-Kister equation and the Sum of Symmetrical Functions. It was shown that the enhanced reliability of the fitting of the experimental data can change the conclusions drawn on their thermodynamic consistency in those cases of VLE data sets that are estimated to be near the border of consistency.

  20. On the classical Maxwell-Lorentz electrodynamics, the electron inertia problem, and the Feynman proper time paradigm

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Bogolubov, J.R.

    2016-01-01

    The classical Maxwell electromagnetic field and the Lorentz-type force equations are rederived in the framework of the Feynman proper time paradigm and the related vacuum field theory approach. The classical Ampere law origin is rederived, and its relationship with the Feynman proper time paradigm is discussed. The electron inertia problem is analyzed in detail within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle of stochastic electrodynamics. The modified Abraham-Lorentz damping radiation force is derived and the electromagnetic electron mass origin is argued

  1. Interference-exact radiative transfer equation

    DEFF Research Database (Denmark)

    Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani

    2017-01-01

    Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....

  2. Self-consistent expansion for the molecular beam epitaxy equation.

    Science.gov (United States)

    Katzav, Eytan

    2002-03-01

    Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(r-r('),t-t('))=2D(0)[r-->-r(')](2rho-d)delta(t-t(')). I find a lower critical dimension d(c)(rho)=4+2rho, above which the linear MBE solution appears. Below the lower critical dimension a rho-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.

  3. Anisotropic charged physical models with generalized polytropic equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Nasim, A.; Azam, M. [University of Education, Division of Science and Technology, Lahore (Pakistan)

    2018-01-15

    In this paper, we found the exact solutions of Einstein-Maxwell equations with generalized polytropic equation of state (GPEoS). For this, we consider spherically symmetric object with charged anisotropic matter distribution. We rewrite the field equations into simple form through transformation introduced by Durgapal (Phys Rev D 27:328, 1983) and solve these equations analytically. For the physically acceptability of these solutions, we plot physical quantities like energy density, anisotropy, speed of sound, tangential and radial pressure. We found that all solutions fulfill the required physical conditions. It is concluded that all our results are reduced to the case of anisotropic charged matter distribution with linear, quadratic as well as polytropic equation of state. (orig.)

  4. Singular limits of the equations of magnetohydrodynamics

    Czech Academy of Sciences Publication Activity Database

    Kukučka, Peter

    2011-01-01

    Roč. 13, č. 2 (2011), s. 173-189 ISSN 1422-6928 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier system * Oberbeck -Boussinesq approximation * Maxwell equations Subject RIV: BA - General Mathematics Impact factor: 0.768, year: 2011 http://www.springerlink.com/content/e14w1h5x188142n6/

  5. The Simon and Simon-Mars tensors for stationary Einstein-Maxwell fields

    International Nuclear Information System (INIS)

    Bini, Donato; Cherubini, Christian; Jantzen, Robert T; Miniutti, Giovanni

    2004-01-01

    Modulo conventional scale factors, the Simon and Simon-Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein-Maxwell equations, the expression for the Simon tensor in the Kerr-Newman-Taub-NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing-Yano tensor

  6. A self-consistent nodal method in response matrix formalism for the multigroup diffusion equations

    International Nuclear Information System (INIS)

    Malambu, E.M.; Mund, E.H.

    1996-01-01

    We develop a nodal method for the multigroup diffusion equations, based on the transverse integration procedure (TIP). The efficiency of the method rests upon the convergence properties of a high-order multidimensional nodal expansion and upon numerical implementation aspects. The discrete 1D equations are cast in response matrix formalism. The derivation of the transverse leakage moments is self-consistent i.e. does not require additional assumptions. An outstanding feature of the method lies in the linear spatial shape of the local transverse leakage for the first-order scheme. The method is described in the two-dimensional case. The method is validated on some classical benchmark problems. (author)

  7. Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory

    International Nuclear Information System (INIS)

    Janda, A.

    2006-01-01

    We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)

  8. Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory

    International Nuclear Information System (INIS)

    Soda, Jiro.

    1989-08-01

    On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)

  9. Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

    International Nuclear Information System (INIS)

    Cherny, A.Yu.; Brand, J.

    2004-01-01

    A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial

  10. The scientific papers of James Clerk Maxwell, vol.I

    CERN Document Server

    Maxwell, James Clerk

    2014-01-01

    One of the greatest theoretical physicists of the 19th century, James Clerk Maxwell is best known for his studies of the electromagnetic field. The 101 scientific papers of this two-volume set, arranged chronologically, testify to Maxwell's profound scientific legacy and include the preliminary explorations that culminated in his most famous work, A Treatise on Electricity and Magnetism. One of the nineteenth century's most significant papers, "A Dynamical Theory of the Electromagnetic Field," appears here, along with similarly influential expositions of Maxwell's dynamical theory of gases. The author's extensive range of interests is well represented, from his discussions of color blindness and the composition of Saturn's rings to his essays on geometrical optics, ether, and protecting buildings from lightning. His less technical writings are featured as well, including items written for the Encyclopedia Britannica and Nature magazine, book reviews, and popular lectures. Striking in their originality, these ...

  11. Swarm analysis by using transport equations, 1

    International Nuclear Information System (INIS)

    Dote, Toshihiko; Shimada, Masatoshi

    1980-01-01

    By evolving Maxwell-Boltzmann transport equations, various quantities on swarm of charged particles have been analyzed. Although this treatment is properly general, and common transport equations for charged particles ought to be given, in particular, equations only for electrons were presented here. The relation between the random energy and the drift energy was first derived and the general expression of the electron velocity was deduced too. For a simple example, one dimensional steady-state electron swarm in a uniform medium was treated. Electron swarm characteristics numerically calculated in He, Ne or Ar exhibited some interesting properties, which were physically clearly elucidated. These results were also compared with several data already published. Agreements between them were qualitatively rather well in detailed structures. (author)

  12. How one can construct a consistent relativistic quantum mechanics on the base of a relativistic wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Gavrilov, S.P. [Universidade Federal de Sergipe (UFS), Aracaju, SE (Brazil); Gitman, D.M. [Sao Paulo Univ. (USP), SP (Brazil). Inst. de Fisica

    2000-07-01

    Full text follows: There is a common opinion that the construction of a consistent relativistic quantum mechanics on the base of a relativistic wave equation meets well-known difficulties related to the existence of infinite number of negative energy levels, to the existence of negative vector norms, and so on, which may be only solved in a second-quantized theory, see, for example, two basic papers devoted to the problem L.Foldy, S.Wouthuysen, Phys. Rep.78 (1950) 29; H.Feshbach, F.Villars, Rev. Mod. Phys. 30 (1958) 24, whose arguments are repeated in all handbooks in relativistic quantum theory. Even Dirac trying to solve the problem had turned last years to infinite-component relativistic wave equations, see P.A.M. Dirac, Proc. R. Soc. London, A328 (1972) 1. We believe that a consistent relativistic quantum mechanics may be constructed on the base of an extended (charge symmetric) equation, which unite both a relativistic wave equation for a particle and for an antiparticle. We present explicitly the corresponding construction, see for details hep-th/0003112. We support such a construction by two demonstrations: first, in course of a careful canonical quantization of the corresponding classical action of a relativistic particle we arrive just to such a consistent quantum mechanics; second, we demonstrate that a reduction of the QFT of a corresponding field (scalar, spinor, etc.) to one-particle sector, if such a reduction may be done, present namely this quantum mechanics. (author)

  13. 77 FR 46116 - Notice of Inventory Completion: Maxwell Museum of Anthropology, University of New Mexico...

    Science.gov (United States)

    2012-08-02

    ... Inventory Completion: Maxwell Museum of Anthropology, University of New Mexico, Albuquerque, NM AGENCY: National Park Service, Interior. ACTION: Notice. SUMMARY: The Maxwell Museum of Anthropology has completed... has a cultural affiliation with the human remains should contact the Maxwell Museum of Anthropology at...

  14. 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.)

  15. Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy

    Directory of Open Access Journals (Sweden)

    T. Sajid

    2018-03-01

    Full Text Available The present article is about the study of Darcy-Forchheimer flow of Maxwell nanofluid over a linear stretching surface. Effects like variable thermal conductivity, activation energy, nonlinear thermal radiation is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method and MATLAB built-in bvp4c solver. The impact of different physical parameters like Brownian motion, thermophoresis parameter, Reynolds number, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, activation energy and Biot number on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that both thermophoresis parameter and activation energy parameter has ascending effect on the concentration profile.

  16. 77 FR 65403 - Notice of Inventory Completion: Maxwell Museum of Anthropology, University of New Mexico...

    Science.gov (United States)

    2012-10-26

    ... Inventory Completion: Maxwell Museum of Anthropology, University of New Mexico, Albuquerque, NM AGENCY... affiliated with the human remains may contact the Maxwell Museum of Anthropology. Repatriation of the human..., Maxwell Museum of Anthropology, MSC01 1050, University of New Mexico, Albuquerque, NM 87131-0001...

  17. 76 FR 56468 - Notice of Inventory Completion: Maxwell Museum of Anthropology, University of New Mexico...

    Science.gov (United States)

    2011-09-13

    ...: Maxwell Museum of Anthropology, University of New Mexico, Albuquerque, NM AGENCY: National Park Service, Interior. ACTION: Notice. SUMMARY: The Maxwell Museum of Anthropology, University of New Mexico has... contact the Maxwell Museum of Anthropology, University of New Mexico. Repatriation of the human remains to...

  18. 77 FR 65404 - Notice of Inventory Completion: Maxwell Museum of Anthropology, University of New Mexico...

    Science.gov (United States)

    2012-10-26

    ... Inventory Completion: Maxwell Museum of Anthropology, University of New Mexico, Albuquerque, NM; Correction... affiliated with the human remains may contact the Maxwell Museum of Anthropology. Repatriation of the human..., Maxwell Museum of Anthropology, MSC01 1050, University of New Mexico, Albuquerque, NM 87131-0001...

  19. Generalized isothermal models with strange equation of state

    Indian Academy of Sciences (India)

    intention to study the Einstein–Maxwell system with a linear equation of state with ... It is our intention to model the interior of a dense realistic star with a general ... The definition m(r) = 1. 2. ∫ r. 0 ω2ρ(ω)dω. (14) represents the mass contained within a radius r which is a useful physical quantity. The mass function (14) has ...

  20. Maxwell's color statistics: from reduction of visible errors to reduction to invisible molecules.

    Science.gov (United States)

    Cat, Jordi

    2014-12-01

    This paper presents a cross-disciplinary and multi-disciplinary account of Maxwell's introduction of statistical models of molecules for the composition of gases. The account focuses on Maxwell's deployment of statistical models of data in his contemporaneous color researches as established in Cambridge mathematical physics, especially by Maxwell's seniors and mentors. The paper also argues that the cross-disciplinary, or cross-domain, transfer of resources from the natural and social sciences took place in both directions and relied on the complex intra-disciplinary, or intra-domain, dynamics of Maxwell's researches in natural sciences, in color theory, physical astronomy, electromagnetism and dynamical theory of gases, as well as involving a variety of types of communicating and mediating media, from material objects to concepts, techniques and institutions.

  1. Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca theories obtained using only Noether's theorem

    International Nuclear Information System (INIS)

    Montesinos, M.; Flores, E.

    2006-01-01

    The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)

  2. Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

    2013-01-01

    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

  3. Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong-coupling regime

    Science.gov (United States)

    Strasberg, Philipp; Schaller, Gernot; Schmidt, Thomas L.; Esposito, Massimiliano

    2018-05-01

    We establish a theoretical method which goes beyond the weak-coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.

  4. Semiempirical equations for modeling solid-state kinetics based on a Maxwell-Boltzmann distribution of activation energies: applications to a polymorphic transformation under crystallization slurry conditions and to the thermal decomposition of AgMnO4 crystals.

    Science.gov (United States)

    Skrdla, Peter J; Robertson, Rebecca T

    2005-06-02

    Many solid-state reactions and phase transformations performed under isothermal conditions give rise to asymmetric, sigmoidally shaped conversion-time (x-t) profiles. The mathematical treatment of such curves, as well as their physical interpretation, is often challenging. In this work, the functional form of a Maxwell-Boltzmann (M-B) distribution is used to describe the distribution of activation energies for the reagent solids, which, when coupled with an integrated first-order rate expression, yields a novel semiempirical equation that may offer better success in the modeling of solid-state kinetics. In this approach, the Arrhenius equation is used to relate the distribution of activation energies to a corresponding distribution of rate constants for the individual molecules in the reagent solids. This distribution of molecular rate constants is then correlated to the (observable) reaction time in the derivation of the model equation. In addition to providing a versatile treatment for asymmetric, sigmoidal reaction curves, another key advantage of our equation over other models is that the start time of conversion is uniquely defined at t = 0. We demonstrate the ability of our simple, two-parameter equation to successfully model the experimental x-t data for the polymorphic transformation of a pharmaceutical compound under crystallization slurry (i.e., heterogeneous) conditions. Additionally, we use a modification of this equation to model the kinetics of a historically significant, homogeneous solid-state reaction: the thermal decomposition of AgMnO4 crystals. The potential broad applicability of our statistical (i.e., dispersive) kinetic approach makes it a potentially attractive alternative to existing models/approaches.

  5. Self-consistent nonlinear transmission line model of standing wave effects in a capacitive discharge

    International Nuclear Information System (INIS)

    Chabert, P.; Raimbault, J.L.; Rax, J.M.; Lieberman, M.A.

    2004-01-01

    It has been shown previously [Lieberman et al., Plasma Sources Sci. Technol. 11, 283 (2002)], using a non-self-consistent model based on solutions of Maxwell's equations, that several electromagnetic effects may compromise capacitive discharge uniformity. Among these, the standing wave effect dominates at low and moderate electron densities when the driving frequency is significantly greater than the usual 13.56 MHz. In the present work, two different global discharge models have been coupled to a transmission line model and used to obtain the self-consistent characteristics of the standing wave effect. An analytical solution for the wavelength λ was derived for the lossless case and compared to the numerical results. For typical plasma etching conditions (pressure 10-100 mTorr), a good approximation of the wavelength is λ/λ 0 ≅40 V 0 1/10 l -1/2 f -2/5 , where λ 0 is the wavelength in vacuum, V 0 is the rf voltage magnitude in volts at the discharge center, l is the electrode spacing in meters, and f the driving frequency in hertz

  6. 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)

  7. Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

    KAUST Repository

    Bonito, Andrea; Guermond, Jean-Luc

    2011-01-01

    We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

  8. Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories

    International Nuclear Information System (INIS)

    Osborn, H.

    1991-01-01

    A local renormalisation group equation which realises infinitesimal Weyl rescalings of the metric and which is an extension of the usual Callan-Symanzik equation is described. In order to ensure that any local composite operators, with dimensions so that on addition to the basic lagrangian they preserve renormalisability, are well defined for arbitrarily many insertions into correlation functions the couplings are assumed to depend on χ. Local operators are then defined by functional differentiation with respect to the couplings just as the energy-momentum tensor is given by functional differentiation with respect to the metric. The local renormalisation group equation contains terms depending on derivatives of the couplings as well as the curvature tensor formed from the metric, constrained by power counting. Various consistency relations arising from the commutativity of Weyl transformations are derived, extending previous one-loop results for the trace anomaly to all orders. In two dimensions the relations give an alternative derivation of the c-theorem and similar extensions are obtained in four dimensions. The equations are applied in detail to general renormalisable σ-models in two dimensions. The Curci-Paffuti relation is derived without any commitment to a particular regularisation scheme and further equations used to construct an action for the vanishing of the β-functions are also obtained. The discussion is also extended to σ-models with a boundary, as appropriate for open strings, and relations for the additional β-functions present in such models are obtained. (orig.)

  9. The contributions of Faraday and Maxwell to electrical science

    CERN Document Server

    Tricker, R A R

    1966-01-01

    The Contributions of Faraday and Maxwell to Electrical Science deals with the development of electromagnetic theory following the establishment of the basis for the first law of circulation relating to the magnetic fields generated by steady currents. This book is organized into two parts encompassing nine chapters that specifically treat the provision of the basis for the second law of circulation, the law that deals with the induction of currents, which was predominantly the work of British physicists, Michael Faraday and James Clerk Maxwell. Part I highlights their life, career, and contri

  10. Moving interfaces and quasilinear parabolic evolution equations

    CERN Document Server

    Prüss, Jan

    2016-01-01

    In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...

  11. Octonionic matrix representation and electromagnetism

    Energy Technology Data Exchange (ETDEWEB)

    Chanyal, B. C. [Kumaun University, S. S. J. Campus, Almora (India)

    2014-12-15

    Keeping in mind the important role of octonion algebra, we have obtained the electromagnetic field equations of dyons with an octonionic 8 x 8 matrix representation. In this paper, we consider the eight - dimensional octonionic space as a combination of two (external and internal) four-dimensional spaces for the existence of magnetic monopoles (dyons) in a higher-dimensional formalism. As such, we describe the octonion wave equations in terms of eight components from the 8 x 8 matrix representation. The octonion forms of the generalized potential, fields and current source of dyons in terms of 8 x 8 matrix are discussed in a consistent manner. Thus, we have obtained the generalized Dirac-Maxwell equations of dyons from an 8x8 matrix representation of the octonion wave equations in a compact and consistent manner. The generalized Dirac-Maxwell equations are fully symmetric Maxwell equations and allow for the possibility of magnetic charges and currents, analogous to electric charges and currents. Accordingly, we have obtained the octonionic Dirac wave equations in an external field from the matrix representation of the octonion-valued potentials of dyons.

  12. Deciphering the embedded wave in Saturn's Maxwell ringlet

    Science.gov (United States)

    French, Richard G.; Nicholson, Philip D.; Hedman, Mathew M.; Hahn, Joseph M.; McGhee-French, Colleen A.; Colwell, Joshua E.; Marouf, Essam A.; Rappaport, Nicole J.

    2016-11-01

    The eccentric Maxwell ringlet in Saturn's C ring is home to a prominent wavelike structure that varies strongly and systematically with true anomaly, as revealed by nearly a decade of high-SNR Cassini occultation observations. Using a simple linear "accordion" model to compensate for the compression and expansion of the ringlet and the wave, we derive a mean optical depth profile for the ringlet and a set of rescaled, background-subtracted radial wave profiles. We use wavelet analysis to identify the wave as a 2-armed trailing spiral, consistent with a density wave driven by an m = 2 outer Lindblad resonance (OLR), with a pattern speed Ωp = 1769.17° d-1 and a corresponding resonance radius ares = 87530.0 km. Estimates of the surface mass density of the Maxwell ringlet range from a mean value of 11g cm-2 derived from the self-gravity model to 5 - 12gcm-2 , as inferred from the wave's phase profile and a theoretical dispersion relation. The corresponding opacity is about 0.12 cm2 g-1, comparable to several plateaus in the outer C ring (Hedman, M.N., Nicholson, P.D. [2014]. Mont. Not. Roy. Astron. Soc. 444, 1369-1388). A linear density wave model using the derived wave phase profile nicely matches the wave's amplitude, wavelength, and phase in most of our observations, confirming the accuracy of the pattern speed and demonstrating the wave's coherence over a period of 8 years. However, the linear model fails to reproduce the narrow, spike-like structures that are prominent in the observed optical depth profiles. Using a symplectic N-body streamline-based dynamical code (Hahn, J.M., Spitale, J.N. [2013]. Astrophys. J. 772, 122), we simulate analogs of the Maxwell ringlet, modeled as an eccentric ringlet with an embedded wave driven by a fictitious satellite with an OLR located within the ring. The simulations reproduce many of the features of the actual observations, including strongly asymmetric peaks and troughs in the inward-propagating density wave. We argue that

  13. Static and time-dependent solutions of Einstein-Maxwell-Yukawa fields

    International Nuclear Information System (INIS)

    Lal, K.B.; Khan, M.Q.

    1977-01-01

    An exact solution of Einstein-Maxwell-Yukawa field equations has been obtained in a space-time with a static metric. A critical analysis reveals that the results previously obtained by Patel (Tensor New Sci.; 29:237 (1975)), Singh (Gen. Rel. Grav.; 6:657 (1974)), and Taub (Ann. Math.; 53:472 (1951)) are particular cases of the present solution. The singular behaviour of the solution is also discussed in this paper. Further, extending the technique developed by Janis et al (Phys. Rev.; 186:1729 (1969)), for static fields, to the case of nonstatic fields, an exact time-dependent axially symmetric solution of EMY fields has been obtained. The present solution in the nonstatic case is nonsingular in the sense of Bonnor (J. Math. Mech.; 6:203 (1957)) and presents a generalization of the results obtained by Misra (Proc. Cambridge Philos. Soc.; 58:711 (1962)) to the case when a zero-mass scalar field coexists with a source free electromagnetic field. (author)

  14. On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

    Science.gov (United States)

    Sarna, Neeraj; Torrilhon, Manuel

    2018-01-01

    We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.

  15. Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

    Science.gov (United States)

    Zhang, Yue; Zhu, Lianhua; Wang, Ruijie; Guo, Zhaoli

    2018-05-01

    Recently a discrete unified gas kinetic scheme (DUGKS) in a finite-volume formulation based on the Boltzmann model equation has been developed for gas flows in all flow regimes. The original DUGKS is designed for flows of single-species gases. In this work, we extend the DUGKS to flows of binary gas mixtures of Maxwell molecules based on the Andries-Aoki-Perthame kinetic model [P. Andries et al., J. Stat. Phys. 106, 993 (2002), 10.1023/A:1014033703134. A particular feature of the method is that the flux at each cell interface is evaluated based on the characteristic solution of the kinetic equation itself; thus the numerical dissipation is low in comparison with that using direct reconstruction. Furthermore, the implicit treatment of the collision term enables the time step to be free from the restriction of the relaxation time. Unlike the DUGKS for single-species flows, a nonlinear system must be solved to determine the interaction parameters appearing in the equilibrium distribution function, which can be obtained analytically for Maxwell molecules. Several tests are performed to validate the scheme, including the shock structure problem under different Mach numbers and molar concentrations, the channel flow driven by a small gradient of pressure, temperature, or concentration, the plane Couette flow, and the shear driven cavity flow under different mass ratios and molar concentrations. The results are compared with those from other reliable numerical methods. The results show that the proposed scheme is an effective and reliable method for binary gas mixtures in all flow regimes.

  16. Longitudinal motion in high current ion beams: a self-consistent phase space distribution with an envelope equation

    International Nuclear Information System (INIS)

    Neuffer, D.

    1979-03-01

    Many applications of particle acceleration, such as heavy ion fusion, require longitudinal bunching of a high intensity particle beam to extremely high particle currents with correspondingly high space charge forces. This requires a precise analysis of longitudinal motion including stability analysis. Previous papers have treated the longitudinal space charge force as strictly linear, and have not been self-consistent; that is, they have not displayed a phase space distribution consistent with this linear force so that the transport of the phase space distribution could be followed, and departures from linearity could be analyzed. This is unlike the situation for transverse phase space where the Kapchinskij--Vladimirskij (K--V) distribution can be used as the basis of an analysis of transverse motion. In this paper a self-consistent particle distribution in longitudinal phase space is derived which is a solution of the Vlasov equation and an envelope equation for this solution is derived

  17. Maxwell-Chern-Simons Casimir effect

    International Nuclear Information System (INIS)

    Milton, K.A.; Ng, Y.J.

    1990-01-01

    The topology of (2+1)-dimensional space permits the construction of quantum electrodynamics with the usual Maxwell action augmented by a gauge-invariant, but P- and T-violating, Chern-Simons mass term. We discuss the Casimir effect between parallel lines in such a theory. The effect of finite temperature is also considered. In principle, our results provide a way to measure the topological mass of the photon

  18. Hyperbolicity of the Nonlinear Models of Maxwell's Equations

    Science.gov (United States)

    Serre, Denis

    . We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.

  19. Non-linear effects in the Boltzmann equation

    International Nuclear Information System (INIS)

    Barrachina, R.O.

    1985-01-01

    The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

  20. Comments on Dirac-like monopole, Maxwell and Maxwell-Chern-Simons electrodynamics in D=(2+1)

    Energy Technology Data Exchange (ETDEWEB)

    Moura-Melo, Winder A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: winder@cbpf.br; Helayel Neto, J.A. [Universidade Catolica de Petropolis, RJ (Brazil). Grupo de Fisica Teorica. E-mail: helayel@cbpf.br

    2000-05-01

    Classical Maxwell and Maxwell-Chern-Simons Electrodynamics in (2+1) D are studied in some details. General expressions for the potential and fields are obtained for both models, and some particular cases are explicitly solved. Conceptual and technical difficulties arise, however, for accelerated charges. The propagation of electromagnetic signals is also studied and their reverberation is worked out and discussed. Furthermore, we show that a Dirac-like monopole yields a (static) tangential electric field. We also discuss some classical and quantum consequences of the field created by such a monopole when acting upon an usual electric charge. In particular, we show that at large distances, the dynamics of one single charged particle under the action of such a potential and a constant (external) magnetic field as well, reduces to that of one central harmonic oscillator, presenting, however, an interesting angular sector which admits energy-eigenvalues. For example, the quantisation of these eigenvalues yields a Dirac-like condition on the product of the charges. Moreover, such eigenvalues are shown to feel (and respond) to discrete shift of the angle variable. We also raise the question on the possibility of the formation pf bound states in this system. (author)

  1. Euler's pioneering equation the most beautiful theorem in mathematics

    CERN Document Server

    Wilson, Robin

    2018-01-01

    In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

  2. Construction of a new wastewater treatment plant, building 676, route Maxwell

    CERN Multimedia

    SC Unit

    2008-01-01

    A new wastewater treatment plant is being constructed on Route Maxwell to treat the effluents from the TS/MME/CCS surface treatment workshops. For this purpose, excavation work is being performed in two separate locations along Route Maxwell, causing a slight disruption to traffic in these areas. Site access through Gate C should, however, be maintained. The work is scheduled to continue through until February 2009.

  3. Classical electromagnetic field theory in the presence of magnetic sources

    OpenAIRE

    Chen, Wen-Jun; Li, Kang; Naón, Carlos

    2001-01-01

    Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell's equation and the equation of motion of a dyon moving in the electro-magnetic field.

  4. Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

    Energy Technology Data Exchange (ETDEWEB)

    Hahn, Y.K., E-mail: ykhahn22@verizon.net

    2014-12-15

    The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the

  5. Anisotropic power-law inflation for a conformal-violating Maxwell model

    Science.gov (United States)

    Do, Tuan Q.; Kao, W. F.

    2018-05-01

    A set of power-law solutions of a conformal-violating Maxwell model with a non-standard scalar-vector coupling will be shown in this paper. In particular, we are interested in a coupling term of the form X^{2n} F^{μ ν }F_{μ ν } with X denoting the kinetic term of the scalar field. Stability analysis indicates that the new set of anisotropic power-law solutions is unstable during the inflationary phase. The result is consistent with the cosmic no-hair conjecture. We show, however, that a set of stable slowly expanding solutions does exist for a small range of parameters λ and n. Hence a small anisotropy can survive during the slowly expanding phase.

  6. The mathematics of geometrical and physical optics. The k-funktion and its ramifications

    Energy Technology Data Exchange (ETDEWEB)

    Stavroudis, O.N. [Centro de Investigaciones en Optica, Leon, Guanajuato (Mexico)

    2006-07-01

    In this sequel to his book, 'The Optics of Rays, Wavefronts, and Caustics', Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen's principle, and Maxwell's model of Gauss' perfect lens. From the contents: Part I: Preliminaries - Calculus of variations - Calculus of variations: differential geometry of space curves (helix and ellipse) - Fermat's principle and the ray equation for inhomogeneous isotropic media - Hilbert integral, the derivation of the Hamilton-Jacobi theory, and the eikonal equation - First-order partial differential equations. Part II: The k-Function - Calculation of surface differential geometry parameters - Ray tracing - Refraction of wavefronts at surfaces - Solution of the Maxwell equation in the context of the k-function. Part III: Applications - Pseudo Maxwell equations - Derivation and discussion of the Cartesian oval - The modern Schiefspiegler - Huygen's principle - Maxwell's model of Gauss' perfect lens. (orig.)

  7. Time-independent integral equation for Maxwell's system. Application of radar cross section computation

    International Nuclear Information System (INIS)

    Pujols, Agnes

    1991-01-01

    We prove that the scattering operator for the wave equation in the exterior of an non-homogeneous obstacle exists. Its distribution kernel is represented by a time-dependent boundary integral equation. A space-time integral variational formulation is developed for determining the current induced by the scattering of an electromagnetic wave by an homogeneous object. The discrete approximation of the variational problem using a finite element method in both space and time leads to stable convergent schemes, giving a numerical code for perfectly conducting cylinders. (author) [fr

  8. Does the Higgs mechanism favour electron-electron bound states in Maxwell-Chern-Simons QED3?

    International Nuclear Information System (INIS)

    Belich, Humberto; Helayeel-Neto, Jose Abdalla; Ferreira Junior, Manoel Messias

    2000-01-01

    Full text follows: We show that low-energy electron-electron bound states appear in the Maxwell-Chern-Simons (MCS) planar QED. In spite of the repulsive interaction mediated by the MCS gauge field, a net attractive interaction stems due to the Higgs mechanism through an Yukawa-type interaction. The spontaneous breaking of a local U(1)-symmetry is realized by a γ 6 -type potential. We conclude, by using the Schroedinger equation associated to the net attractive scattering potential, that electron-electron bound states arise in the model. Therefore, the Higgs mechanism overcomes the difficulties found out by Girotti et al. (Phys. Rev. Lett. 69 (1992) 2623) in searching for bound states in the MCS planar QED. (author)

  9. 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)

  10. Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov–Maxwell equations

    Energy Technology Data Exchange (ETDEWEB)

    Qin, Hong; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei; Sun, Yajuan; Burby, Joshua W.; Ellison, Leland; Zhou, Yao

    2015-12-14

    Particle-in-cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretising its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g. 10(9), degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.

  11. Vlasov-Maxwell equilibrium solutions for Harris sheet magnetic field with Kappa velocity distribution

    International Nuclear Information System (INIS)

    Fu, W.-Z.; Hau, L.-N.

    2005-01-01

    An exact solution of the steady-state, one-dimensional Vlasov-Maxwell equations for a plasma current sheet with oppositely directed magnetic field was found by Harris in 1962. The so-called Harris magnetic field model assumes Maxwellian velocity distributions for oppositely drifting ions and electrons and has been widely used for plasma stability studies. This paper extends Harris solutions by using more general κ distribution functions that incorporate Maxwellian distribution in the limit of κ→∞. A new functional form for the plasma pressure as a function of the magnetic vector potential p(A) is found and the magnetic field is a modified tanh z function. In the extended solutions the effective temperature is no longer spatially uniform like in the Harris model and the thickness of the current layer decreases with decreasing κ

  12. 77 FR 19697 - Notice of Intent to Repatriate Cultural Items: Maxwell Museum of Anthropology, University of New...

    Science.gov (United States)

    2012-04-02

    ... Cultural Items: Maxwell Museum of Anthropology, University of New Mexico, Albuquerque, NM AGENCY: National Park Service, Interior. ACTION: Notice. SUMMARY: The Maxwell Museum of Anthropology, in consultation... with the cultural items may contact the Maxwell Museum of Anthropology. DATES: Representatives of any...

  13. Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

    International Nuclear Information System (INIS)

    Mukhopadhyay, Swati; Arif, M. Golam; Pk M Wazed Ali

    2013-01-01

    The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell (UCM) model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration (suction) and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration (suction) and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  14. WE-AB-207A-02: John’s Equation Based Consistency Condition and Incomplete Projection Restoration Upon Circular Orbit CBCT

    International Nuclear Information System (INIS)

    Ma, J; Qi, H; Wu, S; Xu, Y; Zhou, L; Yan, H

    2016-01-01

    Purpose: In transmitted X-ray tomography imaging, projections are sometimes incomplete due to a variety of reasons, such as geometry inaccuracy, defective detector cells, etc. To address this issue, we have derived a direct consistency condition based on John’s Equation, and proposed a method to effectively restore incomplete projections based on this consistency condition. Methods: Through parameter substitutions, we have derived a direct consistency condition equation from John’s equation, in which the left side is only projection derivative of view and the right side is projection derivative of other geometrical parameters. Based on this consistency condition, a projection restoration method is proposed, which includes five steps: 1) Forward projecting reconstructed image and using linear interpolation to estimate the incomplete projections as the initial result; 2) Performing Fourier transform on the projections; 3) Restoring the incomplete frequency data using the consistency condition equation; 4) Performing inverse Fourier transform; 5) Repeat step 2)∼4) until our criteria is met to terminate the iteration. Results: A beam-blocking-based scatter correction case and a bad-pixel correction case were used to demonstrate the efficacy and robustness of our restoration method. The mean absolute error (MAE), signal noise ratio (SNR) and mean square error (MSE) were employed as our evaluation metrics of the reconstructed images. For the scatter correction case, the MAE is reduced from 63.3% to 71.7% with 4 iterations. Compared with the existing Patch’s method, the MAE of our method is further reduced by 8.72%. For the bad-pixel case, the SNR of the reconstructed image by our method is increased from 13.49% to 21.48%, with the MSE being decreased by 45.95%, compared with linear interpolation method. Conclusion: Our studies have demonstrated that our restoration method based on the new consistency condition could effectively restore the incomplete projections

  15. Maxwell's electromagnetic theory and special relativity.

    Science.gov (United States)

    Hall, Graham

    2008-05-28

    This paper presents a brief history of electromagnetic theory from ancient times up to the work of Maxwell and the advent of Einstein's special theory of relativity. It is divided into five convenient periods and the intention is to describe these developments for the benefit of a lay scientific audience and with the minimum of technical detail.

  16. Why history matters: Ab initio rederivation of Fresnel equations confirms microscopic theory of refractive index

    Science.gov (United States)

    Starke, R.; Schober, G. A. H.

    2018-03-01

    We provide a systematic theoretical, experimental, and historical critique of the standard derivation of Fresnel's equations, which shows in particular that these well-established equations actually contradict the traditional, macroscopic approach to electrodynamics in media. Subsequently, we give a rederivation of Fresnel's equations which is exclusively based on the microscopic Maxwell equations and hence in accordance with modern first-principles materials physics. In particular, as a main outcome of this analysis being of a more general interest, we propose the most general boundary conditions on electric and magnetic fields which are valid on the microscopic level.

  17. The Maxwell-Einstein system, Ward identities and the Vilkovisky construction

    DEFF Research Database (Denmark)

    Nielsen, N. K.

    2012-01-01

    The gauge fixing dependence of the one-loop effective action of quantum gravity in the proper-time representation is investigated for a space of arbitrary curvature, and the investigation is extended to Maxwell-Einstein theory. The construction of Vilkovisky and DeWitt for removal of this depende......The gauge fixing dependence of the one-loop effective action of quantum gravity in the proper-time representation is investigated for a space of arbitrary curvature, and the investigation is extended to Maxwell-Einstein theory. The construction of Vilkovisky and DeWitt for removal...

  18. Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca theories obtained using only Noether's theorem

    Energy Technology Data Exchange (ETDEWEB)

    Montesinos, M. [CINVESTAV-IPN, 07360 Mexico D.F. (Mexico); Flores, E. [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)]. E-mail: merced@fis.cinvestav.mx

    2006-07-01

    The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)

  19. A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

    International Nuclear Information System (INIS)

    Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho

    2016-01-01

    In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is

  20. A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

    Energy Technology Data Exchange (ETDEWEB)

    Balsara, Dinshaw S., E-mail: dbalsara@nd.edu [Physics Department, University of Notre Dame (United States); Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, University of Tokyo, Tokyo 113-0033 (Japan); Garain, Sudip, E-mail: sgarain@nd.edu [Physics Department, University of Notre Dame (United States); Kim, Jinho, E-mail: jkim46@nd.edu [Physics Department, University of Notre Dame (United States)

    2016-08-01

    In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is

  1. Simulating variable-density flows with time-consistent integration of Navier-Stokes equations

    Science.gov (United States)

    Lu, Xiaoyi; Pantano, Carlos

    2017-11-01

    In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.

  2. Prolongation Loop Algebras for a Solitonic System of Equations

    Directory of Open Access Journals (Sweden)

    Maria A. Agrotis

    2006-11-01

    Full Text Available We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.

  3. 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.

  4. Construction of a new waste-water treatment plant, building 676, route Maxwell

    CERN Multimedia

    TS Department

    2008-01-01

    A new waste-water treatment plant is being constructed on Route Maxwell to treat the effluents from the TS/MME/CCS surface treatment workshops. For this purpose, excavation work is being performed in two separate locations along Route Maxwell, causing a slight disruption to traffic in these areas. Site access through Gate C should, however, be maintained. The work is scheduled to continue until February 2009.

  5. The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces

    International Nuclear Information System (INIS)

    Bergqvist, Goeran; Eriksson, Ingemar

    2007-01-01

    In this paper, we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces

  6. Aligned Magnetic Field Effects on Flow and Heat Transfer of the Upper-Convected Maxwell Fluid over a Stretching/Shrinking Sheet

    Directory of Open Access Journals (Sweden)

    Waini Iskandar

    2017-01-01

    Full Text Available In this paper, the effect of aligned magnetic field towards the flow and heat transfer of the upper-convected Maxwell (UCM fluid over a stretching/shrinking sheet is numerically studied. The governing partial differential equations are reduced into a system of ordinary differential equations using a similarity transformation, which are then solved numerically using the shooting method. The skin friction and heat transfer coefficients, the velocity, as well as the temperature profiles of the fluid are presented and discussed. Results indicate that an increase in the aligned angle strengthens the applied magnetic field which decrease the velocity and increase the temperature profiles of the fluid. This implies that an increase in the aligned angle increases the skin friction coefficient and decreases the heat transfer coefficients.

  7. Infinite sets of conservation laws for linear and nonlinear field equations

    International Nuclear Information System (INIS)

    Mickelsson, J.

    1984-01-01

    The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the 'coupling constant') the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant under the group of space-time symmetries. As an example, our method is applied to the Korteweg-de Vries equation and to the massless Thirring model. (orig.)

  8. Use of the Boltzmann equation for calculating the scattering law in gas mixtures

    International Nuclear Information System (INIS)

    Eder, O.J.; Lackner, T.

    1989-01-01

    A new approach is presented for the calculation of the dynamical incoherent structure factor S s (q, ω) for a dilute binary gas mixture. The starting point is the linearized one-dimensional Boltzmann equation for a mixture of particles interacting via a quasi-Maxwell potential (V(r) ≅ 1/r ν , ν=4). It is shown how - in the Fourier-Laplace space (q, ω) - the solution of the Boltzman equation can be expressed as an infinite continued fraction. The well known hydrodynamic limit (q→0) and the free gas limit (q→∞) are correctly reproduced as the appropriate limits of the continued fraction. A brief comparison between S s (q, ω) for two interaction potentials (quasi-Maxwell potential, ν=4, and hard core potential, ν=∞) is presented, and it is found that, after scaling the variables to the respective diffusion coefficients, only little dependence on the potential remains. Furthermore, for a one-component system in three dimensions results are summarized for the dynamical incoherent and coherent structure factor. (orig.) [de

  9. Observation of distorted Maxwell-Boltzmann distribution of epithermal ions in LHD

    Science.gov (United States)

    Ida, K.; Kobayashi, T.; Yoshinuma, M.; Akiyama, T.; Tokuzawa, T.; Tsuchiya, H.; Itoh, K.; LHD Experiment Group

    2017-12-01

    A distorted Maxwell-Boltzmann distribution of epithermal ions is observed associated with the collapse of energetic ions triggered by the tongue shaped deformation. The tongue shaped deformation is characterized by the plasma displacement localized in the toroidal, poloidal, and radial directions at the non-rational magnetic flux surface in toroidal plasma. Moment analysis of the ion velocity distribution measured with charge exchange spectroscopy is studied in order to investigate the impact of tongue event on ion distribution. A clear non-zero skewness (3rd moment) and kurtosis (4th moment -3) of ion velocity distribution in the epithermal region (within three times of thermal velocity) is observed after the tongue event. This observation indicates the clear evidence of the distortion of ion velocity distribution from Maxwell-Boltzmann distribution. This distortion from Maxwell-Boltzmann distribution is observed in one-third of plasma minor radius region near the plasma edge and disappears in the ion-ion collision time scale.

  10. A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

    Science.gov (United States)

    Lei, Dong; Liang, Yingjie; Xiao, Rui

    2018-01-01

    We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.

  11. Thermodynamic inconsistency of the modified Saha equation at high pressures

    International Nuclear Information System (INIS)

    Sweeney, M.A.

    1978-01-01

    The inclusion of a pressure ionization term in the Saha equation violates the thermodynamic Maxwell identities if corresponding changes are not made to the expressions for entropy and pressure. It is demonstrated that the usual application of the Rouse and Stewart-Pyatt modesl suffers from this limitation. Negative values of the adiabatic gradient in the degenerate dwarf models of Boehm and Straka are explained in terms of this thermodynamic inconsistency

  12. Historic Landscape Survey, Maxwell AFB, Alabama

    Science.gov (United States)

    2013-08-01

    signifies Maxwell AFB’s historic landscapes. 2.1 The pre-military landscape Prehistory in the southeastern United States is generally designated as...the period of Native American occupation before Spanish explorers made contact in the fifteenth and sixteenth centuries. In Alabama, the prehistory ... prehistory or history is made clear.56 A historic property is determined to be either significant or not significant by applying standardized National

  13. CFDTD Solution For Large Waveguide Slot Arrays

    National Research Council Canada - National Science Library

    Ho, T. Q; Hewett, C. A; Hunt, L. N; Ready, T. G; Baugher, M. C; Mikoleit, K. E

    2005-01-01

    The Finite Difference Time Domain (FDTD) technique consists of simulating time varying electromagnetic fields in various media with Maxwell's curl equations in the form of finite difference equations, which are then used in a leapfrog...

  14. Conserved quantities for stationary Einstein-Maxwell space-times

    International Nuclear Information System (INIS)

    Esposito, F.P.; Witten, L.

    1978-01-01

    It is shown that every stationary Einstein-Maxwell space-time has eight divergence-free vector fields and these are isolated in general form. The vector fields and associated conserved quantities are calculated for several families of space-times. (Auth.)

  15. James Clerk Maxwell 1831-1879

    International Nuclear Information System (INIS)

    Anon.

    1979-01-01

    Earlier this year saw the centenary of the birth of Albert Einstein. It is highly apt that 1979, which has been marked by further consolidation of the unified theory of weak and electromagnetic interactions and its recognition in the award of the Nobel Prize to Glashow, Salam and Weinberg, is also the centenary of the death of the great Scottish physicist who first formulated a unified theory of electric and magnetic fields. We are grateful to Abdus Salam for drawing our attention to the Maxwell anniversary

  16. James Clerk Maxwell 1831-1879

    Energy Technology Data Exchange (ETDEWEB)

    Anon.

    1979-12-15

    Earlier this year saw the centenary of the birth of Albert Einstein. It is highly apt that 1979, which has been marked by further consolidation of the unified theory of weak and electromagnetic interactions and its recognition in the award of the Nobel Prize to Glashow, Salam and Weinberg, is also the centenary of the death of the great Scottish physicist who first formulated a unified theory of electric and magnetic fields. We are grateful to Abdus Salam for drawing our attention to the Maxwell anniversary.

  17. The road to Maxwell's demon conceptual foundations of statistical mechanics

    CERN Document Server

    Hemmo, Meir

    2012-01-01

    Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.

  18. ‘…a paper …I hold to be great guns’: a commentary on Maxwell (1865) ‘A dynamical theory of the electromagnetic field’

    Science.gov (United States)

    Longair, Malcolm

    2015-01-01

    Maxwell's great paper of 1865 established his dynamical theory of the electromagnetic field. The origins of the paper lay in his earlier papers of 1856, in which he began the mathematical elaboration of Faraday's researches into electromagnetism, and of 1861–1862, in which the displacement current was introduced. These earlier works were based upon mechanical analogies. In the paper of 1865, the focus shifts to the role of the fields themselves as a description of electromagnetic phenomena. The somewhat artificial mechanical models by which he had arrived at his field equations a few years earlier were stripped away. Maxwell's introduction of the concept of fields to explain physical phenomena provided the essential link between the mechanical world of Newtonian physics and the theory of fields, as elaborated by Einstein and others, which lies at the heart of twentieth and twenty-first century physics. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750155

  19. Black hole dynamics in Einstein-Maxwell-dilaton theory

    Science.gov (United States)

    Hirschmann, Eric W.; Lehner, Luis; Liebling, Steven L.; Palenzuela, Carlos

    2018-03-01

    We consider the properties and dynamics of black holes within a family of alternative theories of gravity, namely Einstein-Maxwell-dilaton theory. We analyze the dynamical evolution of individual black holes as well as the merger of binary black hole systems. We do this for a wide range of parameter values for the family of Einstein-Maxwell-dilaton theories, investigating, in the process, the stability of these black holes. We examine radiative degrees of freedom, explore the impact of the scalar field on the dynamics of merger, and compare with other scalar-tensor theories. We argue that the dilaton can largely be discounted in understanding merging binary systems and that the end states essentially interpolate between charged and uncharged, rotating black holes. For the relatively small charge values considered here, we conclude that these black hole systems will be difficult to distinguish from their analogs within General Relativity.

  20. Systematic homogenization and self-consistent flux and pin power reconstruction for nodal diffusion methods. 1: Diffusion equation-based theory

    International Nuclear Information System (INIS)

    Zhang, H.; Rizwan-uddin; Dorning, J.J.

    1995-01-01

    A diffusion equation-based systematic homogenization theory and a self-consistent dehomogenization theory for fuel assemblies have been developed for use with coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is based on a multiple-scales asymptotic expansion carried out through second order in a small parameter, the ratio of the average diffusion length to the reactor characteristic dimension. By starting from the neutron diffusion equation for a three-dimensional heterogeneous medium and introducing two spatial scales, the development systematically yields an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections and assembly-surface-flux discontinuity factors. The rector eigenvalue 1/k eff is shown to be obtained to the second order in the small parameter, and the heterogeneous diffusion theory flux is shown to be obtained to leading order in that parameter. The latter of these two results provides a natural procedure for the reconstruction of the local fluxes and the determination of pin powers, even though homogenized assemblies are used in the global nodal diffusion calculation

  1. Effects of backreaction on power-Maxwell holographic superconductors in Gauss-Bonnet gravity

    Energy Technology Data Exchange (ETDEWEB)

    Salahi, Hamid Reza; Montakhab, Afshin [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Sheykhi, Ahmad [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha (Iran, Islamic Republic of)

    2016-10-15

    We analytically and numerically investigate the properties of s-wave holographic superconductors by considering the effects of scalar and gauge fields on the background geometry in five-dimensional Einstein-Gauss-Bonnet gravity. We assume the gauge field to be in the form of the power-Maxwell nonlinear electrodynamics. We employ the Sturm-Liouville eigenvalue problem for analytical calculation of the critical temperature and the shooting method for the numerical investigation. Our numerical and analytical results indicate that higher curvature corrections affect condensation of the holographic superconductors with backreaction. We observe that the backreaction can decrease the critical temperature of the holographic superconductors, while the power-Maxwell electrodynamics and Gauss-Bonnet coefficient term may increase the critical temperature of the holographic superconductors. We find that the critical exponent has the mean-field value β = 1/2, regardless of the values of Gauss-Bonnet coefficient, backreaction and power-Maxwell parameters. (orig.)

  2. Ultrashort optical solitons in the cubic-quintic complex Ginzburg-Landau equation with higher-order terms

    International Nuclear Information System (INIS)

    Fewo, Serge I.; Kofane, Timoleon C.; Ngabireng, Claude M.

    2008-01-01

    With the help of the Maxwell equations, a basic equation modeling the propagation of ultrashort optical solitons in optical fiber is derived, namely the higher-order complex Ginzburg-Landau equation (HCGLE). Considering this one-dimensional HCGLE, we obtain a set of differential equations characterizing the variation of the pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fiber optic-links. Equations obtained are investigated numerically in order to observe the behaviour of pulse parameters along the optical fiber. A fully numerical simulation of the one-dimensional HCGLE finally tests the results of the CV theory. A good agreement between both methods is observed. Among various behaviours, chaotic pulses, attenuate pulses and stable pulses can be obtained under certain parameter values. (author)

  3. An analytical theory of a scattering of radio waves on meteoric ionization - II. Solution of the integro-differential equation in case of backscatter

    Science.gov (United States)

    Pecina, P.

    2016-12-01

    The integro-differential equation for the polarization vector P inside the meteor trail, representing the analytical solution of the set of Maxwell equations, is solved for the case of backscattering of radio waves on meteoric ionization. The transversal and longitudinal dimensions of a typical meteor trail are small in comparison to the distances to both transmitter and receiver and so the phase factor appearing in the kernel of the integral equation is large and rapidly changing. This allows us to use the method of stationary phase to obtain an approximate solution of the integral equation for the scattered field and for the corresponding generalized radar equation. The final solution is obtained by expanding it into the complete set of Bessel functions, which results in solving a system of linear algebraic equations for the coefficients of the expansion. The time behaviour of the meteor echoes is then obtained using the generalized radar equation. Examples are given for values of the electron density spanning a range from underdense meteor echoes to overdense meteor echoes. We show that the time behaviour of overdense meteor echoes using this method is very different from the one obtained using purely numerical solutions of the Maxwell equations. Our results are in much better agreement with the observations performed e.g. by the Ondřejov radar.

  4. Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity

    CERN Document Server

    Chiodaroli, Marco; Johansson, Henrik; Roiban, Radu

    2015-01-01

    We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which th...

  5. On the consistent solution of the gap-equation for spontaneously broken λΦ4-theory

    International Nuclear Information System (INIS)

    Nachbagauer, H.

    1994-10-01

    A self-consistent solution of the finite temperature gap-equation for λΦ 4 theory beyond the Hartree-Fock approximation is presented using a composite operator effective action. It was found that in a spontaneously broken theory not only the so-called daisy and super daisy graphs contribute to the re summed mass, but also re summed non-local diagrams are of the same order, thus altering the effective mass for small values of the latter. (author). 10 refs., 3 figs., 1 tab

  6. Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in non-smooth axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, B.

    2005-10-01

    Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)

  7. Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

    International Nuclear Information System (INIS)

    Ayissi, Raoul Domingo; Noutchegueme, Norbert

    2015-01-01

    Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

  8. Intermediate modeling between kinetic equations and hydrodynamic limits: derivation, analysis and simulations

    International Nuclear Information System (INIS)

    Parisot, M.

    2011-01-01

    This work is dedicated study of a problem resulting from plasma physics: the thermal transfer of electrons in a plasma close to equilibrium Maxwellian. Firstly, a dimensional study of the Vlasov-Fokker-Planck-Maxwell system is performed, allowing one hand to identify a physically relevant parameter of scale and also to define mathematically the contours of validity domain. The asymptotic regime called Spitzer-Harm is studied for a relatively general class of collision operator. The following part of this work is devoted to the derivation and study of the hydrodynamic limit of the system of Vlasov-Maxwell-Landau outside the strictly asymptotic. A model proposed by Schurtz and Nicolais located in this context and analyzed. The particularity of this model lies in the application of a delocalization operation in the heat flux. The link with non-local models of Luciani and Mora is established as well as mathematics properties as the principle of maximum and entropy dissipation. Then a formal derivation from the Vlasov equations with a simplified collision operator, is proposed. The derivation, inspired by the recent work of D. Levermore, involves decomposition methods according to the spherical harmonics and methods of closing called diffusion methods. A hierarchy of intermediate models between the kinetic equations and the hydrodynamic limit is described. In particular a new hydrodynamic system integro-differential by nature, is proposed. The Schurtz and Nicolai model appears as a simplification of the system resulting from the derivation, assuming a steady flow of heat. The above results are then generalized to account for the internal energy dependence which appears naturally in the equation establishment. The existence and uniqueness of the solution of the nonstationary system are established in a simplified framework. The last part is devoted was the implementation of a specific numerical scheme to solve these models. We propose a finite volume approach can be

  9. Electron-electron attractive interaction in Maxwell-Chern-Simons QED3 at zero temperature

    International Nuclear Information System (INIS)

    Belich, H.; Ferreira Junior, M.M.; Helayel-Neto, J.A.; Ferreira Junior, M.M.

    2001-04-01

    One discusses the issue of low-energy electron-electron bound states in the Maxwell-Chern-Simons model coupled to QED 3 with spontaneous breaking of a local U(1)-symmetry. The scattering potential, in the non-relativistic limit, steaming from the electron-electron Moeller scattering, mediated by the Maxwell-Chern-Simons-Proca gauge field and the Higgs scalar, might be attractive by fine-tuning properly the physical parameters of the model. (author)

  10. Computational analysis of magnetohydrodynamic Casson and Maxwell flows over a stretching sheet with cross diffusion

    Science.gov (United States)

    Kumaran, G.; Sandeep, N.; Ali, M. E.

    This paper reports the magnetohydrodynamic chemically reacting Casson and Maxwell fluids past a stretching sheet with cross diffusion, non-uniform heat source/sink, thermophoresis and Brownian motion effects. Numerical results are obtained by employing the R-K based shooting method. Effects of pertinent parameters on flow, thermal and concentration fields are discussed with graphical illustrations. We presented the tabular results to discuss the nature of the skin friction coefficient, reduced Nusselt and Sherwood numbers. Dual nature is observed in the solution of Casson and Maxwell fluids. It is also observed a significant increase in heat and mass transfer rate of Maxwell fluid when compared with the Casson fluid.

  11. Reading Maxwell in Conceptual Physics

    Science.gov (United States)

    Bonham, Scott W.

    2018-05-01

    An important aspect of science education involves helping students learn to read and communicate scientific information and arguments. In this note, I would like to share a resource that I have come across which I have found to be a useful tool for helping students improve those skills, learn content material, and acquaint them with a great scientist. Specifically, this is having non-science college students in my course Light, Color and Vision read and discuss a letter by James Clerk Maxwell entitled "On the Theory of Colours in Relation to Colour-Blindness" (see Fig. 1).

  12. The polaron problem and the Boltzmann equation

    International Nuclear Information System (INIS)

    Devreese, J.

    1979-01-01

    A mobility theory for the Feynman polaron is developed. It is shown that the Boltzmann equation for polarons is valid for weak coupling and not too high electric fields. The analytical results indicate that for E → 0 the relaxation time approximation is valid. A comparison is made of three methods to calculate the mobility in a linear electron transport theory. An approximation to the Kubo formula, a mobility calculation using path integrals by Feynman and a calculation based on the displaced Maxwell distribution function are considered. The three methods lead to equivalent results in the weak scattering and small electric field limit

  13. An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

    Science.gov (United States)

    Subramanian, Ramanathan Vishnampet Ganapathi

    , with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited only by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Though the gradient from our fully discrete adjoint is formally exact, it does include sensitivity to numerical solutions that are only an artifact of the discretization. These are typically saw-tooth type features, such as seen in under-resolved numerical simulations. Since these have no physical analog, for physical analysis or design of realistic actuators, such solutions are in a sense spurious. This has been addressed without sacrificing accuracy by redesigning the basic discretization to be dual-consistent, for which the discrete-adjoint is consistent with the adjoint of the continuous system, and thus, free from spurious numerical sensitivity modes. We extend our exact discrete-adjoint to a spatially dual-consistent discretization of the compressible flow equations and demonstrate its practical application for aeroacoustic control of a Mach 1.3 turbulent jet. The formulation admits a broad class of finite-difference schemes that satisfy a summation by-parts rule, and extends to multi-block curvilinear grids for efficient handling of complex geometries. The formulation is developed for several boundary conditions commonly used in simulation of free-shear and wall-bounded flows. In addition, the proposed discretization leads to superconvergent approximations of functionals

  14. The effective action in Einstein-Maxwell theory

    OpenAIRE

    Bastianelli, Fiorenzo; Davila, Jose Manuel; Schubert, Christian

    2008-01-01

    Considerable work has been done on the one-loop effective action in combined electromagnetic and gravitational fields, particularly as a tool for determining the properties of light propagation in curved space. After a short review of previous work, I present some recent results obtained using the worldline formalism. In particular, I will discuss various ways of generalizing the QED Euler-Heisenberg Lagrangian to the Einstein-Maxwell case.

  15. Translationally invariant self-consistent field theories

    International Nuclear Information System (INIS)

    Shakin, C.M.; Weiss, M.S.

    1977-01-01

    We present a self-consistent field theory which is translationally invariant. The equations obtained go over to the usual Hartree-Fock equations in the limit of large particle number. In addition to deriving the dynamic equations for the self-consistent amplitudes we discuss the calculation of form factors and various other observables

  16. Iterative methods for the solution of very large complex symmetric linear systems of equations in electrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Clemens, M.; Weiland, T. [Technische Hochschule Darmstadt (Germany)

    1996-12-31

    In the field of computational electrodynamics the discretization of Maxwell`s equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extended to a whole class of methods for complex-symmetric algorithms SCBiCG(T, n), which only require one matrix vector multiplication per iteration step. In this class the well-known conjugate orthogonal conjugate gradient (COCG) method for complex-symmetric systems corresponds to the case n = 0. The case n = 1 yields the BiCGCR method which corresponds to the conjugate residual algorithm for the real-valued case. These methods in combination with a minimal residual smoothing process are applied separately to practical 3D electro-quasistatical and eddy-current problems in electrodynamics. The practical performance of the SCBiCG methods is compared with other methods such as QMR and TFQMR.

  17. No actual measurement … was required: Maxwell and Cavendish's null method for the inverse square law of electrostatics.

    Science.gov (United States)

    Falconer, Isobel

    In 1877 James Clerk Maxwell and his student Donald MacAlister refined Henry Cavendish's 1773 null experiment demonstrating the absence of electricity inside a charged conductor. This null result was a mathematical prediction of the inverse square law of electrostatics, and both Cavendish and Maxwell took the experiment as verifying the law. However, Maxwell had already expressed absolute conviction in the law, based on results of Michael Faraday's. So, what was the value to him of repeating Cavendish's experiment? After assessing whether the law was as secure as he claimed, this paper explores its central importance to the electrical programme that Maxwell was pursuing. It traces the historical and conceptual re-orderings through which Maxwell established the law by constructing a tradition of null tests and asserting the superior accuracy of the method. Maxwell drew on his developing 'doctrine of method' to identify Cavendish's experiment as a member of a wider class of null methods. By doing so, he appealed to the null practices of telegraph engineers, diverted attention from the flawed logic of the method, and sought to localise issues around the mapping of numbers onto instrumental indications, on the grounds that 'no actual measurement … was required'. Copyright © 2017 Elsevier Ltd. All rights reserved.

  18. The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

    International Nuclear Information System (INIS)

    Pfirsch, D.; Morrison, P.J.; Texas Univ., Austin

    1990-02-01

    A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any kind of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated - which need not be the same for all particle species in a plasma - are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. (orig.)

  19. The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

    International Nuclear Information System (INIS)

    Pfirsch, D.; Morrison, P.J.

    1990-02-01

    A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any king of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated --- which need not be the same for all particle species in a plasma --- are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. 11 refs

  20. Generalized phase transformations of spinor fields

    International Nuclear Information System (INIS)

    Mikhov, S.G.

    1993-09-01

    In this paper some generalized four parameter phase transformations of a Dirac spinor are considered. It is shown that a corresponding compensating transformation of the electromagnetic field which restores the invariance of the Dirac-Maxwell equation might exist, provided some consistency conditions are satisfied by the parameters of the transformations. These transformations are used further to consider the Maxwell equations under the assumption that a Bosonization takes place. Only one of the considered cases proves to have a solution (the other cases show to be trivial) which although unphysical is obtained explicitly. (author). 10 refs

  1. Thermodynamics of charged rotating dilaton black branes with power-law Maxwell field

    International Nuclear Information System (INIS)

    Zangeneh, M.K.; Sheykhi, A.; Dehghani, M.H.

    2015-01-01

    In this paper, we construct a new class of charged rotating dilaton black brane solutions, with a complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime, such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both the canonical and the grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of the Maxwell field on the thermal stability of the solutions. We find that, for α ≤ 1, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For α > 1, the solutions can encounter an unstable phase depending on the metric parameters. (orig.)

  2. Efficient 3D/1D self-consistent integral-equation analysis of ICRH antennae

    International Nuclear Information System (INIS)

    Maggiora, R.; Vecchi, G.; Lancellotti, V.; Kyrytsya, V.

    2004-01-01

    This work presents a comprehensive account of the theory and implementation of a method for the self-consistent numerical analysis of plasma-facing ion-cyclotron resonance heating (ICRH) antenna arrays. The method is based on the integral-equation formulation of the boundary-value problem, solved via a weighted-residual scheme. The antenna geometry (including Faraday shield bars and a recess box) is fairly general and three-dimensional (3D), and the plasma is in the one-dimensional (1D) 'slab' approximation; finite-Larmor radius effects, as well as plasma density and temperature gradients, are considered. Feeding via the voltages in the access coaxial lines is self consistently accounted throughout and the impedance or scattering matrix of the antenna array obtained therefrom. The problem is formulated in both the dual space (physical) and spectral (wavenumber) domains, which allows the extraction and simple handling of the terms that slow the convergence in the spectral domain usually employed. This paper includes validation tests of the developed code against measured data, both in vacuo and in the presence of plasma. An example of application to a complex geometry is also given. (author)

  3. One-dimensional free-electron laser equations without the slowly varying envelope approximation

    Directory of Open Access Journals (Sweden)

    C. Maroli

    2011-07-01

    Full Text Available A set of one-dimensional equations has been deduced in the time domain from the Maxwell-Lorentz system with the aim of describing the free-electron laser radiation without using the slowly varying envelope approximation (SVEA. These equations are valid even in the case of arbitrarily short electron bunches and of current distributions with ripples on the scale of or shorter than the wavelength. Numerical examples are presented, showing that for long homogeneous bunches the new set of equations gives results in agreement with the SVEA free-electron laser theory and that the use of short or prebunched electron beams leads to a decrease of the emission lethargy. Furthermore, we demonstrate that in all cases in which the backward low frequency wave has negligible effects, these equations can be reduced to a form similar to the usual 1D SVEA equations but with a different definition of the bunching term.

  4. Equations of motion in general relativity of a small charged black hole

    International Nuclear Information System (INIS)

    Futamase, T.; Hogan, P. A.; Itoh, Y.

    2008-01-01

    We present the details of a model in general relativity of a small charged black hole moving in an external gravitational and electromagnetic field. The importance of our model lies in the fact that we can derive the equations of motion of the black hole from the Einstein-Maxwell vacuum field equations without encountering infinities. The key assumptions which we base our results upon are that (a) the black hole is isolated and (b) near the black hole the wave fronts of the radiation generated by its motion are smoothly deformed spheres. The equations of motion which emerge fit the pattern of the original DeWitt and Brehme equations of motion (after they 'renormalize'). Our calculations are carried out in a coordinate system in which the null hypersurface histories of the wave fronts can be specified in a simple way, with the result that we obtain a new explicit form, particular to our model, for the well-known ''tail term'' in the equations of motion.

  5. Exact self-consistent solutions to the interacting spinor and scalar field equations in Bianchi type-I space-time

    International Nuclear Information System (INIS)

    Alvarado, R.; Rybakov, Yu.P.; Shikin, G.N.; Saha, B.

    1995-01-01

    Self-consistent solutions to the system of spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time. The absence of initial singularity should be emphasized for some types of solutions and also the isotropic mode of space-time expansion in some special cases. 3 refs

  6. Notes on solving Maxwell equations, part 2, Green's function for stratified media

    OpenAIRE

    Rook, R.

    2011-01-01

    In the previous report (part 1), the problem and its governing equations are described and is discarded in this report. The finite element method in part 1, or any other method for that matter, determines the fields in and close to the scatterer (near-field) that is used to construct the fields in the far-field. The goal of part 2 is to find far-field expressions formulated as total fields or the Radar Cross Section (RCS) of the scattered fields. The far-field is calculated from the scatterer...

  7. Geometric properties of static Einstein-Maxwell dilaton horizons with a Liouville potential

    International Nuclear Information System (INIS)

    Abdolrahimi, Shohreh; Shoom, Andrey A.

    2011-01-01

    We study nondegenerate and degenerate (extremal) Killing horizons of arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with a Liouville potential (the EMdL model) in d-dimensional (d≥4) static space-times. Using Israel's description of a static space-time, we construct the EMdL equations and the space-time curvature invariants: the Ricci scalar, the square of the Ricci tensor, and the Kretschmann scalar. Assuming that space-time metric functions and the model fields are real analytic functions in the vicinity of a space-time horizon, we study the behavior of the space-time metric and the fields near the horizon and derive relations between the space-time curvature invariants calculated on the horizon and geometric invariants of the horizon surface. The derived relations generalize similar relations known for horizons of static four- and five-dimensional vacuum and four-dimensional electrovacuum space-times. Our analysis shows that all the extremal horizon surfaces are Einstein spaces. We present the necessary conditions for the existence of static extremal horizons within the EMdL model.

  8. 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

  9. Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

    Science.gov (United States)

    Holst, Michael; Meier, Caleb; Tsogtgerel, G.

    2018-01-01

    In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (Class Quantum Gravity 30:205011, 2013), and Holst et al. (Phys Rev Lett 100(16):161101, 2008, Commun Math Phys 288(2):547-613, 2009), and also on the work of Maxwell (J Hyperbolic Differ Eqs 2(2):521-546, 2005a, Commun Math Phys 253(3):561-583, 2005b, Math Res Lett 16(4):627-645, 2009) and Dain (Class Quantum Gravity 21(2):555-573, 2004), under reasonable assumptions on the data we prove existence of both near- and far-from-constant mean curvature (CMC) solutions for a class of Robin boundary conditions commonly used in the literature for modeling black holes, with a third existence result for CMC appearing as a special case. Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the CMC setting, with interior boundary conditions representing excised interior black hole regions. Holst and Tsogtgerel compiled the interior boundary results covered by Dain and Maxwell, and then developed general interior conditions to model the apparent horizon boundary conditions of Dainand Maxwell for compact manifolds with boundary, and subsequently proved existence of solutions to the Lichnerowicz equation on compact manifolds with such boundary conditions. This paper picks up where Holst and Tsogtgerel left off, addressing the general non-CMC case for compact manifolds with boundary. As in our previous articles, our focus here is again on low regularity data and on the interaction between different types of boundary conditions. While our work here serves primarily to extend the solution theory for the compact with boundary case, we also develop several technical tools that have

  10. Consistent guiding center drift theories

    International Nuclear Information System (INIS)

    Wimmel, H.K.

    1982-04-01

    Various guiding-center drift theories are presented that are optimized in respect of consistency. They satisfy exact energy conservation theorems (in time-independent fields), Liouville's theorems, and appropriate power balance equations. A theoretical framework is given that allows direct and exact derivation of associated drift-kinetic equations from the respective guiding-center drift-orbit theories. These drift-kinetic equations are listed. Northrop's non-optimized theory is discussed for reference, and internal consistency relations of G.C. drift theories are presented. (orig.)

  11. Electron-electron attractive interaction in Maxwell-Chern-Simons QED{sub 3} at zero temperature

    Energy Technology Data Exchange (ETDEWEB)

    Belich, H.; Ferreira Junior, M.M.; Helayel-Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: belich@cbpf.br; manojr@cbpf.br; helayel@gft.ucp.br; Ferreira Junior, M.M. [Universidade Catolica de Petropolis, RJ (Brazil). Grupo de Fisica Teorica. E-mail: delcima@gft.ucp.br

    2001-04-01

    One discusses the issue of low-energy electron-electron bound states in the Maxwell-Chern-Simons model coupled to QED{sub 3} with spontaneous breaking of a local U(1)-symmetry. The scattering potential, in the non-relativistic limit, steaming from the electron-electron Moeller scattering, mediated by the Maxwell-Chern-Simons-Proca gauge field and the Higgs scalar, might be attractive by fine-tuning properly the physical parameters of the model. (author)

  12. Nonlinear Delta-f Particle Simulations of Collective Effects in High-Intensity Bunched Beams

    CERN Document Server

    Qin, Hong; Hudson, Stuart R; Startsev, Edward

    2005-01-01

    The collective effects in high-intensity 3D bunched beams are described self-consistently by the nonlinear Vlasov-Maxwell equations.* The nonlinear delta-f method,** a particle simulation method for solving the nonlinear Vlasov-Maxwell equations, is being used to study the collective effects in high-intensity 3D bunched beams. The delta-f method, as a nonlinear perturbative scheme, splits the distribution function into equilibrium and perturbed parts. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by equations of motion in the focusing field and self-consistent fields, and the particle weights are advanced by the coupling between the perturbed fields and the zero-order distribution function. The nonlinear delta-f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. A self-consistent 3D kinetic equilibrium is first established for high intensity bunched beams. The...

  13. New exact solutions of the(2+1-dimensional Broer-Kaup equation by the consistent Riccati expansion method

    Directory of Open Access Journals (Sweden)

    Jiang Ying

    2017-01-01

    Full Text Available In this work, we study the (2+1-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models

  14. Loading relativistic Maxwell distributions in particle simulations

    Energy Technology Data Exchange (ETDEWEB)

    Zenitani, Seiji, E-mail: seiji.zenitani@nao.ac.jp [National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan)

    2015-04-15

    Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms.

  15. Loading relativistic Maxwell distributions in particle simulations

    International Nuclear Information System (INIS)

    Zenitani, Seiji

    2015-01-01

    Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms

  16. Stochastic stimulated electronic x-ray Raman spectroscopy

    Directory of Open Access Journals (Sweden)

    Victor Kimberg

    2016-05-01

    → π * transition. Our theoretical model describes the evolution of the spectral and temporal characteristics of the transmitted x-ray radiation, by solving the equation of motion for the electronic and vibrational degrees of freedom of the system self consistently with the propagation by Maxwell equations.

  17. 77 FR 46114 - Notice of Intent to Repatriate Cultural Items: Maxwell Museum of Anthropology, University of New...

    Science.gov (United States)

    2012-08-02

    ... Intent to Repatriate Cultural Items: Maxwell Museum of Anthropology, University of New Mexico... Anthropology, in consultation with the Pueblo of Santa Ana, New Mexico, has determined that a collection of... cultural affiliation with the cultural items should contact the Maxwell Museum of Anthropology at the...

  18. Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

    Science.gov (United States)

    Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua

    2018-01-01

    The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified. Support of National Natural Science Foundation of China under Grant Nos. 11475028, 11772064, and 11502117 Science Challenge Project under Grant Nos. JCKY2016212A501 and TZ2016002

  19. Preliminary electromagnetic analysis of Helium Cooled Solid Blanket for CFETR by MAXWELL

    Energy Technology Data Exchange (ETDEWEB)

    Jin, Cheng; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn

    2016-11-15

    Highlights: • A FEM model of the blanket and magnetic system was built. • Electromagnetic forces and moments of the typical blanket for ferromagnetic and non-ferromagnetic materials were computed and analyzed. • Maxwell forces and Lorentz forces were computed and compared. • Eddy current in the blanket was analyzed under MD condition. - Abstract: A Helium Cooled Solid Blanket (HCSB) for CFETR (Chinese Fusion Engineering Test Reactor) was designed by USTC. The structural and thermal-hydraulic analysis has been carried out, while electromagnetic analysis was not carefully researched. In this paper, a FEM (finite element method) model of the HCSB was developed and electromagnetic forces as well as moments was computed by a FEM software called MAXWELL integrated in ANSYS Workbench. In the geometrical model, flow channels and small connecting parts were neglected because of the extreme complication and the reasonable conservative assumption by neglecting these circumstantial details. As for electromagnetic (EM) analysis, Lorentz forces due to eddy currents caused by main disruption and Maxwell forces due to the magnetization of RAFM steel (i.e. EUROFER97) were computed. Since the unavailability of the details of the plasma in CFETR, when disruptions happen, the condition where a linear current quench of main disruption occurs was assumed. The maximum magnitude of the electromagnetic forces was 356.45 kN and the maximum value of the coupled electromagnetic moments was 1899.40 N m around the radial direction. It is feasible to couple electromagnetic analysis, structural analysis and thermal-hydraulic analysis in the future since MAXWELL has good channels to exchange data between different analytic parts.

  20. Dynamic load mitigation using dissipative elastic metamaterials with multiple Maxwell-type oscillators

    Science.gov (United States)

    Alamri, Sagr; Li, Bing; Tan, K. T.

    2018-03-01

    Dissipative elastic metamaterials have attracted increased attention in recent times. This paper presents the development of a dissipative elastic metamaterial with multiple Maxwell-type resonators for stress wave attenuation. The mechanism of the dissipation effect on the vibration characteristics is systematically investigated by mass-spring-damper models with single and dual resonators. Based on the parameter optimization, it is revealed that a broadband wave attenuation region (stopping band) can be obtained by properly utilizing interactions from resonant motions and viscoelastic effects of the Maxwell-type oscillators. The relevant numerical verifications are conducted for various cases, and excellent agreement between the numerical and theoretical frequency response functions is shown. The design of this dissipative metamaterial system is further applied for dynamic load mitigation and blast wave attenuation. Moreover, the transient response in the continuum model is designed and analyzed for more robust design. By virtue of the bandgap merging effect induced by the Maxwell-type damper, the transient blast wave can be almost completely suppressed in the low frequency range. A significantly improved performance of the proposed dissipative metamaterials for stress wave mitigation is verified in both time and frequency domains.

  1. Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

    International Nuclear Information System (INIS)

    Li, Fei; Yu, Peicheng; Xu, Xinlu; Fiuza, Frederico; Decyk, Viktor K.

    2017-01-01

    In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1^ direction). We show that this eliminates the main NCI modes with moderate |k_1|, while keeps additional main NCI modes well outside the range of physical interest with higher |k_1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1^ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.

  2. One-Dimensional Vlasov-Maxwell Equilibrium for the Force-Free Harris Sheet

    International Nuclear Information System (INIS)

    Harrison, Michael G.; Neukirch, Thomas

    2009-01-01

    In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet

  3. Thermodynamic consistency of viscoplastic material models involving external variable rates in the evolution equations for the internal variables

    International Nuclear Information System (INIS)

    Malmberg, T.

    1993-09-01

    The objective of this study is to derive and investigate thermodynamic restrictions for a particular class of internal variable models. Their evolution equations consist of two contributions: the usual irreversible part, depending only on the present state, and a reversible but path dependent part, linear in the rates of the external variables (evolution equations of ''mixed type''). In the first instance the thermodynamic analysis is based on the classical Clausius-Duhem entropy inequality and the Coleman-Noll argument. The analysis is restricted to infinitesimal strains and rotations. The results are specialized and transferred to a general class of elastic-viscoplastic material models. Subsequently, they are applied to several viscoplastic models of ''mixed type'', proposed or discussed in the literature (Robinson et al., Krempl et al., Freed et al.), and it is shown that some of these models are thermodynamically inconsistent. The study is closed with the evaluation of the extended Clausius-Duhem entropy inequality (concept of Mueller) where the entropy flux is governed by an assumed constitutive equation in its own right; also the constraining balance equations are explicitly accounted for by the method of Lagrange multipliers (Liu's approach). This analysis is done for a viscoplastic material model with evolution equations of the ''mixed type''. It is shown that this approach is much more involved than the evaluation of the classical Clausius-Duhem entropy inequality with the Coleman-Noll argument. (orig.) [de

  4. Energy-momentum tensor of the electromagnetic field

    International Nuclear Information System (INIS)

    Horndeski, G.W.; Wainwright, J.

    1977-01-01

    In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources

  5. Modeling of heat conduction via fractional derivatives

    Science.gov (United States)

    Fabrizio, Mauro; Giorgi, Claudio; Morro, Angelo

    2017-09-01

    The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not.

  6. Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity

    Czech Academy of Sciences Publication Activity Database

    Consiglieri, L.; Nečasová, Šárka; Sokolowski, J.

    2009-01-01

    Roč. 38, č. 4 (2009), s. 1193-1215 ISSN 0324-8569 R&D Projects: GA ČR GA201/05/0005; GA ČR GA201/08/0012 Institutional research plan: CEZ:AV0Z10190503 Keywords : Maxwell-Boussinesq approximation Subject RIV: BA - General Mathematics Impact factor: 0.378, year: 2009

  7. Ito terms and the Maxwell field on the lattice

    International Nuclear Information System (INIS)

    D'Olivo, J.C.; Socolovsky, M.

    1988-01-01

    If lattice renormalization effects are ignored and the number of space-time dimensions is less than four, it is explicitly shown that the effective continuum action for the Maxwell field does not contain the so-called Ito terms. As is known, the qualitative reason for this result is the flat character of the integration measure

  8. A Full-Maxwell Approach for Large-Angle Polar Wander of Viscoelastic Bodies

    Science.gov (United States)

    Hu, H.; van der Wal, W.; Vermeersen, L. L. A.

    2017-12-01

    For large-angle long-term true polar wander (TPW) there are currently two types of nonlinear methods which give approximated solutions: those assuming that the rotational axis coincides with the axis of maximum moment of inertia (MoI), which simplifies the Liouville equation, and those based on the quasi-fluid approximation, which approximates the Love number. Recent studies show that both can have a significant bias for certain models. Therefore, we still lack an (semi)analytical method which can give exact solutions for large-angle TPW for a model based on Maxwell rheology. This paper provides a method which analytically solves the MoI equation and adopts an extended iterative procedure introduced in Hu et al. (2017) to obtain a time-dependent solution. The new method can be used to simulate the effect of a remnant bulge or models in different hydrostatic states. We show the effect of the viscosity of the lithosphere on long-term, large-angle TPW. We also simulate models without hydrostatic equilibrium and show that the choice of the initial stress-free shape for the elastic (or highly viscous) lithosphere of a given model is as important as its thickness for obtaining a correct TPW behavior. The initial shape of the lithosphere can be an alternative explanation to mantle convection for the difference between the observed and model predicted flattening. Finally, it is concluded that based on the quasi-fluid approximation, TPW speed on Earth and Mars is underestimated, while the speed of the rotational axis approaching the end position on Venus is overestimated.

  9. A new approach to hull consistency

    Directory of Open Access Journals (Sweden)

    Kolev Lubomir

    2016-06-01

    Full Text Available Hull consistency is a known technique to improve the efficiency of iterative interval methods for solving nonlinear systems describing steady-states in various circuits. Presently, hull consistency is checked in a scalar manner, i.e. successively for each equation of the nonlinear system with respect to a single variable. In the present poster, a new more general approach to implementing hull consistency is suggested which consists in treating simultaneously several equations with respect to the same number of variables.

  10. Cattaneo-Christov Heat Flux Model for MHD Three-Dimensional Flow of Maxwell Fluid over a Stretching Sheet.

    Science.gov (United States)

    Rubab, Khansa; Mustafa, M

    2016-01-01

    This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.

  11. Ice bridges and ridges in the Maxwell-EB sea ice rheology

    Directory of Open Access Journals (Sweden)

    V. Dansereau

    2017-09-01

    Full Text Available This paper presents a first implementation of a new rheological model for sea ice on geophysical scales. This continuum model, called Maxwell elasto-brittle (Maxwell-EB, is based on a Maxwell constitutive law, a progressive damage mechanism that is coupled to both the elastic modulus and apparent viscosity of the ice cover and a Mohr–Coulomb damage criterion that allows for pure (uniaxial and biaxial tensile strength. The model is tested on the basis of its capability to reproduce the complex mechanical and dynamical behaviour of sea ice drifting through a narrow passage. Idealized as well as realistic simulations of the flow of ice through Nares Strait are presented. These demonstrate that the model reproduces the formation of stable ice bridges as well as the stoppage of the flow, a phenomenon occurring within numerous channels of the Arctic. In agreement with observations, the model captures the propagation of damage along narrow arch-like kinematic features, the discontinuities in the velocity field across these features dividing the ice cover into floes, the strong spatial localization of the thickest, ridged ice, the presence of landfast ice in bays and fjords and the opening of polynyas downstream of the strait. The model represents various dynamical behaviours linked to an overall weakening of the ice cover and to the shorter lifespan of ice bridges, with implications in terms of increased ice export through narrow outflow pathways of the Arctic.

  12. Ice bridges and ridges in the Maxwell-EB sea ice rheology

    Science.gov (United States)

    Dansereau, Véronique; Weiss, Jérôme; Saramito, Pierre; Lattes, Philippe; Coche, Edmond

    2017-09-01

    This paper presents a first implementation of a new rheological model for sea ice on geophysical scales. This continuum model, called Maxwell elasto-brittle (Maxwell-EB), is based on a Maxwell constitutive law, a progressive damage mechanism that is coupled to both the elastic modulus and apparent viscosity of the ice cover and a Mohr-Coulomb damage criterion that allows for pure (uniaxial and biaxial) tensile strength. The model is tested on the basis of its capability to reproduce the complex mechanical and dynamical behaviour of sea ice drifting through a narrow passage. Idealized as well as realistic simulations of the flow of ice through Nares Strait are presented. These demonstrate that the model reproduces the formation of stable ice bridges as well as the stoppage of the flow, a phenomenon occurring within numerous channels of the Arctic. In agreement with observations, the model captures the propagation of damage along narrow arch-like kinematic features, the discontinuities in the velocity field across these features dividing the ice cover into floes, the strong spatial localization of the thickest, ridged ice, the presence of landfast ice in bays and fjords and the opening of polynyas downstream of the strait. The model represents various dynamical behaviours linked to an overall weakening of the ice cover and to the shorter lifespan of ice bridges, with implications in terms of increased ice export through narrow outflow pathways of the Arctic.

  13. Maxwell-Cattaneo Heat Convection and Thermal Stresses Responses of a Semi-Infinite Medium to High-Speed Laser Heating due to High Speed Laser Heating

    Directory of Open Access Journals (Sweden)

    Abdallah I. A.

    2009-07-01

    Full Text Available Based on Maxwell-Cattaneo convection equation, the thermoelasticity problem is in- vestigated in this paper. The analytic solution of a boundary value problem for a semi- infinite medium with traction free surface heated by a high-speed laser-pulses have Dirac temporal profile is solved. The temperature, the displacement and the stresses distributions are obtained analytically using the Laplace transformation, and discussed at small time duration of the laser pulses. A numerical study for Cu as a target is performed. The results are presented graphically. The obtained results indicate that the small time duration of the laser pulses has no e ect on the finite velocity of the heat con- ductivity, but the behavior of the stress and the displacement distribution are affected due to the pulsed heating process and due to the structure of the governing equations.

  14. Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

    Science.gov (United States)

    Zhu, Ying; Herbert, John M.

    2018-01-01

    The "real time" formulation of time-dependent density functional theory (TDDFT) involves integration of the time-dependent Kohn-Sham (TDKS) equation in order to describe the time evolution of the electron density following a perturbation. This approach, which is complementary to the more traditional linear-response formulation of TDDFT, is more efficient for computation of broad-band spectra (including core-excited states) and for systems where the density of states is large. Integration of the TDKS equation is complicated by the time-dependent nature of the effective Hamiltonian, and we introduce several predictor/corrector algorithms to propagate the density matrix, one of which can be viewed as a self-consistent extension of the widely used modified-midpoint algorithm. The predictor/corrector algorithms facilitate larger time steps and are shown to be more efficient despite requiring more than one Fock build per time step, and furthermore can be used to detect a divergent simulation on-the-fly, which can then be halted or else the time step modified.

  15. The solution of the Poisson-Boltzmann's equation for self-consistent potential of infinite, random, nonlinear and non-uniform system

    International Nuclear Information System (INIS)

    Rasulova, M.Yu

    1998-01-01

    A study has been made of a system of charged particles and inhomogeneities randomly distributed in accordance with the same law in the neighborhoods of corresponding sites of a planar crystal lattice. The existence and uniqueness of the solution of the generalized Poisson-Boltzmann's equation for the average self-consistent potential and average density of surface charges are proved. (author)

  16. A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

    Science.gov (United States)

    Herschlag, Gregory J; Mitran, Sorin; Lin, Guang

    2015-06-21

    We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.

  17. Ampère–Maxwell law for a conducting wire: a topological perspective

    International Nuclear Information System (INIS)

    Ferreira, J M; Anacleto, Joaquim

    2013-01-01

    The integral form of Ampère–Maxwell's law for an arbitrarily-shaped wire is recast from a topological perspective, eliminating the need to use conduction current and displacement current terms to determine the magnetic field circulation around an arbitrarily-shaped loop. A generalized flux of the electric field is defined, enabling Ampère–Maxwell's law for magnetic field circulation to be written in a form which parallels that in the absence of conduction current. It is hoped that this work has educational interest since it provides an example of how topology can simplify the formulation of physical laws. The ideas presented herein are primarily intended for undergraduate students of electromagnetism, but may also be of interest to graduate students and teachers. (paper)

  18. Critical Combinations of Higher-Order Terms in Einstein-Maxwell Theory and Compactification

    Directory of Open Access Journals (Sweden)

    Nahomi Kan

    2015-01-01

    Full Text Available We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, particularly in the background of spontaneous compactification. Two classes of theories are proposed in this paper. The first model as a generalization of the critical gravity with the Maxwell field could have a de Sitter solution. We consider the Lanczos-Lovelock term and Horndeski term as well as the higher-order Maxwell term for the second model, which contains a possible longer expansion time for the inflationary phase. It is interesting that both models can be regarded as the generalization of the Randjbar-Daemi, Salam and Strathdee (RSS model and give the well behavior for inflation stage under the specific assumptions.

  19. Fractional Bhatnagar-Gross-Krook kinetic equation

    Science.gov (United States)

    Goychuk, Igor

    2017-11-01

    The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

  20. A comparison of Fick and Maxwell-Stefan diffusion formulations in PEMFC gas diffusion layers

    Science.gov (United States)

    Lindstrom, Michael; Wetton, Brian

    2017-01-01

    This paper explores the mathematical formulations of Fick and Maxwell-Stefan diffusion in the context of polymer electrolyte membrane fuel cell cathode gas diffusion layers. The simple Fick law with a diagonal diffusion matrix is an approximation of Maxwell-Stefan. Formulations of diffusion combined with mass-averaged Darcy flow are considered for three component gases. For this application, the formulations can be compared computationally in a simple, one dimensional setting. Despite the models' seemingly different structure, it is observed that the predictions of the formulations are very similar on the cathode when air is used as oxidant. The two formulations give quite different results when the Nitrogen in the air oxidant is replaced by helium (this is often done as a diagnostic for fuel cells designs). The two formulations also give quite different results for the anode with a dilute Hydrogen stream. These results give direction to when Maxwell-Stefan diffusion, which is more complicated to implement computationally in many codes, should be used in fuel cell simulations.

  1. Inverse problems for Maxwell's equations

    CERN Document Server

    Romanov, V G

    1994-01-01

    The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

  2. A NEW RELATIVISTIC FIELD THEORY OF THE ELECTRON UNA NUEVA TEORÍA RELATIVÍSTICA DE CAMPO PARA EL ELECTRÓN

    Directory of Open Access Journals (Sweden)

    Héctor Torres-Silva

    2008-11-01

    Full Text Available In this paper we present a qualitative discussion of a new General Relativistic Field Theory for the electron, obtaining the Dirac equation from electromagnetic fields with the electric field parallel to the magnetic field. The guiding principle is that of general relativity, and the main hypothesis is that the fundamental equations embrace the Dirac theory and the Maxwell-Lorentz theory as of two special cases respectively. We concern ourselves with the consistency and compatibility among those conditions under which the fundamental equations are reduced to the Dirac equation and the Maxwell-Lorentz equations. We expect that the present investigation will shed some light on those perplexing difficulties which we encounter in comprehending the behavior of an electron solely according to the Dirac equation and the Maxwell-Lorentz equations. Beyond this, we aim to investigate the possibility that other elementary particles are governed by the same fundamental equations under varied restrictive conditions.En este trabajo, se presenta un examen cualitativo sobre una nueva Teoría General Relativística para el electrón, con la obtención de la ecuación de Dirac a partir de los campos electromagnéticos con el campo eléctrico paralelo al campo magnético. El principio rector es el de la relatividad general, y la principal hipótesis es que de las ecuaciones fundamentales se desprende la teoría de Dirac y la teoría de Maxwell - Lorentz como de dos casos especiales cuidando la coherencia y compatibilidad entre las condiciones en las que las ecuaciones fundamentales se reducen a la ecuación de Dirac y las ecuaciones de Maxwell - Lorentz. Se espera que la presente investigación arroje alguna luz sobre las desconcertantes dificultades a las que nos encontramos en la comprensión del comportamiento de un electrón exclusivamente en función de la ecuación de Dirac y las ecuaciones de Maxwell - Lorentz. Más allá de esto, se puede investigar la

  3. Symmetry breaking in six-dimensional Einstein-Maxwell-Sigma theory

    International Nuclear Information System (INIS)

    Shin, H.J.

    1985-11-01

    The mass spectrum of six-dimensional gravity theory coupled with U(1) Maxwell and non-linear sigma field is analyzed. It is shown that this electroweak-gravity model can have perturbatively stable ground state and low mass gauge bosons of SU(2). Except the graviton, photon, low mass scalar triplet and three gauge bosons, all other states acquire masses of Planck scale. (author)

  4. Maxwell's demon, Szilard's engine and quantum measurements

    International Nuclear Information System (INIS)

    Zorek, W.H.

    1986-01-01

    The author proposes and analyzes a quantum version of Szilard's one-molecule engine. In particular, the author recovers, in the quantum context, Szilard's conclusion concerning the free energy ''cost'' of measurements (delta /sub F/ is greater than or equal to k/sub b/T1n2) per bit of information. A cycle of Szilard's engine is illustrated for both the original and quantum versions. The measurement of the location of the molecule is essential in the process of extracting work in both classical and quantum design. Measurements are made by the classical Maxwell's demon

  5. Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity

    International Nuclear Information System (INIS)

    Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu

    2015-01-01

    We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at tree-level and one loop. The double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.

  6. A Hybrid DGTD-MNA Scheme for Analyzing Complex Electromagnetic Systems

    KAUST Repository

    Li, Peng

    2015-01-07

    A hybrid electromagnetics (EM)-circuit simulator for analyzing complex systems consisting of EM devices loaded with nonlinear multi-port lumped circuits is described. The proposed scheme splits the computational domain into two subsystems: EM and circuit subsystems, where field interactions are modeled using Maxwell and Kirchhoff equations, respectively. Maxwell equations are discretized using a discontinuous Galerkin time domain (DGTD) scheme while Kirchhoff equations are discretized using a modified nodal analysis (MNA)-based scheme. The coupling between the EM and circuit subsystems is realized at the lumped ports, where related EM fields and circuit voltages and currents are allowed to “interact’’ via numerical flux. To account for nonlinear lumped circuit elements, the standard Newton-Raphson method is applied at every time step. Additionally, a local time-stepping scheme is developed to improve the efficiency of the hybrid solver. Numerical examples consisting of EM systems loaded with single and multiport linear/nonlinear circuit networks are presented to demonstrate the accuracy, efficiency, and applicability of the proposed solver.

  7. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    We generate two newexact models for the Einstein–Maxwell field equations. In our models, we consider the stellar object that is anisotropic and charged with linear equation of state consistent with quark stars. We have a new choice of measure of anisotropy that is physically reasonable. It is interesting that in our models we ...

  8. Statistical mechanics of stochastic neural networks: Relationship between the self-consistent signal-to-noise analysis, Thouless-Anderson-Palmer equation, and replica symmetric calculation approaches

    International Nuclear Information System (INIS)

    Shiino, Masatoshi; Yamana, Michiko

    2004-01-01

    We study the statistical mechanical aspects of stochastic analog neural network models for associative memory with correlation type learning. We take three approaches to derive the set of the order parameter equations for investigating statistical properties of retrieval states: the self-consistent signal-to-noise analysis (SCSNA), the Thouless-Anderson-Palmer (TAP) equation, and the replica symmetric calculation. On the basis of the cavity method the SCSNA can be generalized to deal with stochastic networks. We establish the close connection between the TAP equation and the SCSNA to elucidate the relationship between the Onsager reaction term of the TAP equation and the output proportional term of the SCSNA that appear in the expressions for the local fields

  9. A Simple and Consistent Equation of State for Sodium in the Single Phase and Two Phase Regions

    International Nuclear Information System (INIS)

    Breton, J.P.

    1976-01-01

    An equation of state valid over an extended temperature and density range has been derived. Then, the following properties have been deduced: coefficient of thermal expansion, isothermal coefficient of bulk compressibility, thermal pressure coefficient, heat capacity at constant pressure, at constant volume, along the saturation curve for liquid, for vapor, heat of vaporization, speed of sound, and finally the Mollier diagram and the entropy diagram. All the obtained properties are thermodynamically consistent and satisfy the basic relations of thermodynamics for both single phase and two-phase regions. Experimental results were always used when available

  10. A simple and consistent equation of state for sodium in the single phase and two phase regions

    International Nuclear Information System (INIS)

    Breton, J.P.

    1976-01-01

    An equation of state valid over an extended temperature and density range has been derived. Then, the following properties have been deduced : coefficient of thermal expansion, isothermal coefficient of bulk compressibility, thermal pressure coefficient, heat capacity at constant pressure, at constant volume, along the saturation curve for liquid, for vapor, heat of vaporization, speed of sound, and finally the Mollier diagram and the entropy diagram. All the obtained properties are thermodynamically consistent and satisfy the basic relations of thermodynamics for both single phase and two-phase regions. Experimental results were always used when available. (auth.)

  11. Perbandingan Regresi Binomial Negatif dan Regresi Conway-Maxwell-Poisson dalam Mengatasi Overdispersi pada Regresi Poisson

    Directory of Open Access Journals (Sweden)

    Lusi Eka Afri

    2017-03-01

    Full Text Available Regresi Binomial Negatif dan regresi Conway-Maxwell-Poisson merupakan solusi untuk mengatasi overdispersi pada regresi Poisson. Kedua model tersebut merupakan perluasan dari model regresi Poisson. Menurut Hinde dan Demetrio (2007, terdapat beberapa kemungkinan terjadi overdispersi pada regresi Poisson yaitu keragaman hasil pengamatan keragaman individu sebagai komponen yang tidak dijelaskan oleh model, korelasi antar respon individu, terjadinya pengelompokan dalam populasi dan peubah teramati yang dihilangkan. Akibatnya dapat menyebabkan pendugaan galat baku yang terlalu rendah dan akan menghasilkan pendugaan parameter yang bias ke bawah (underestimate. Penelitian ini bertujuan untuk membandingan model Regresi Binomial Negatif dan model regresi Conway-Maxwell-Poisson (COM-Poisson dalam mengatasi overdispersi pada data distribusi Poisson berdasarkan statistik uji devians. Data yang digunakan dalam penelitian ini terdiri dari dua sumber data yaitu data simulasi dan data kasus terapan. Data simulasi yang digunakan diperoleh dengan membangkitkan data berdistribusi Poisson yang mengandung overdispersi dengan menggunakan bahasa pemrograman R berdasarkan karakteristik data berupa , peluang munculnya nilai nol (p serta ukuran sampel (n. Data dibangkitkan berguna untuk mendapatkan estimasi koefisien parameter pada regresi binomial negatif dan COM-Poisson.   Kata Kunci: overdispersi, regresi binomial negatif, regresi Conway-Maxwell-Poisson Negative binomial regression and Conway-Maxwell-Poisson regression could be used to overcome over dispersion on Poisson regression. Both models are the extension of Poisson regression model. According to Hinde and Demetrio (2007, there will be some over dispersion on Poisson regression: observed variance in individual variance cannot be described by a model, correlation among individual response, and the population group and the observed variables are eliminated. Consequently, this can lead to low standard error

  12. Symmetry breaking in six-dimensional Einstein-Maxwell-sigma theory

    International Nuclear Information System (INIS)

    Shin, H.J.

    1986-01-01

    The mass spectrum of a six-dimensional gravity theory coupled with the U(1) Maxwell and nonlinear sigma fields is analyzed. It is shown that this electroweak-gravity model can have a perturbatively stable ground state and low-mass gauge bosons of SU(2). Except for the graviton, photon, low-mass scalar triplet, and three gauge bosons, all other states acquire masses of the Planck scale

  13. Split Octonion electrodynamics and unified fields of dyons

    International Nuclear Information System (INIS)

    Bisht, P.S.

    2004-01-01

    Split octonion electrodynamics has been developed in terms of Zorn's vector matrix realization by reformulating electromagnetic potential, current, field tensor and other dynamical quantities. Corresponding field equation (Unified Maxwell's equations) and equation of motion have been reformulated by means of split octonion and its Zorn vector realization in unique, simpler and consistent manner. It has been shown that this theory reproduces the dyon field equations in the absence of gravito-dyons and vice versa

  14. The plasma transport equations derived by multiple time-scale expansions and turbulent transport. I. General theory

    International Nuclear Information System (INIS)

    Edenstrasser, J.W.

    1995-01-01

    A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics

  15. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Keywords. Weber's electrodynamics; Maxwell's equations; Lorentz's force; classical electromagnetism. Abstract. We present the main aspects of Weber's electrodynamics and of Maxwell's equations. We discuss Maxwell's point of view related to Weber's electrodynamics. We compare Weber's force with Lorentz's force.

  16. Boltzmann equation for a mixture of gases with non-conservative processes

    International Nuclear Information System (INIS)

    Martiarena, M.L.

    1989-01-01

    The nonlinear and non-isotropic Boltzmann equation (NLBE) including several molecular species, non-conservative channels and external forces. The general solution of that equation is obtained for a spatially homogeneous mixture of L gases, consisting of Maxwell particles, as a Generalized Laguerre expansion, within a Hilbert space. Removal and self-generation effects are included in presence of a time-dependent external force. An exact particular solution is studied generalizing the well-known BKW-mode for a mixture of L gases with inelastic processes. An homogeneous gas of test particles, in d dimension, is considered which interacts with a background host medium in the presence of an external space and time dependent force. Scattering, removal and self-generation collisions are included. The inhomogeneous Boltzmann equation for this system to an homogeneous one is reduced without background or external forces, using a generalized Nilkoskii transform. It is shown that a background of field particles can confine the test gas, even in absence of external forces. Furthermore, the solution of NLBE with non-isotropic singular initial conditions, is analyzed. The NLBE is transformed into an integral equation which is solved iteratively. The evolution of delta and step singularities in the distribution function is discussed during the initial layer and compared with the isotropic case. As an application of the methods abovementioned, the collision of a beam of ions or neutral atoms with a carbon-foil is considered. The electron experimental spectra from a transport equation is described. It is supposed that convoy electron may be produced inside the solid by single ion-atom collisions as ELC or ECC. The produced electrons lost energy by collision with the atoms of the material, which are considered at rest. The electron distribution function is numerically calculated. The ratio between the intrinsic convoy electron peak height to the background electron intensity

  17. Quadrupole terms in the Maxwell equations: Born energy, partial molar volume, and entropy of ions.

    Science.gov (United States)

    Slavchov, Radomir I; Ivanov, Tzanko I

    2014-02-21

    A new equation of state relating the macroscopic quadrupole moment density Q to the gradient of the field ∇E in an isotropic fluid is derived: Q = αQ(∇E - U∇·E/3), where the quadrupolarizability αQ is proportional to the squared molecular quadrupole moment. Using this equation of state, a generalized expression for the Born energy of an ion dissolved in quadrupolar solvent is obtained. It turns out that the potential and the energy of a point charge in a quadrupolar medium are finite. From the obtained Born energy, the partial molar volume and the partial molar entropy of a dissolved ion follow. Both are compared to experimental data for a large number of simple ions in aqueous solutions. From the comparison the value of the quadrupolar length LQ is determined, LQ = (αQ/3ɛ)(1/2) = 1-4 Å. Data for ion transfer from aqueous to polar oil solution are analyzed, which allowed for the determination of the quadrupolarizability of nitrobenzene.

  18. Derivation of special relativity from Maxwell and Newton.

    Science.gov (United States)

    Dunstan, D J

    2008-05-28

    Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the -c(-2) term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.

  19. Simulation studies of hydrodynamic aspects of magneto-inertial fusion and high order adaptive algorithms for Maxwell equations

    Science.gov (United States)

    Wu, Lingling

    composite deuterium - xenon liners reduce the energy gain due to lower target compression rates. The effect of heating of targets by alpha particles on the fusion energy gain has also been investigated. The study of the dependence of the ram pressure amplification on radial compressibility showed a good agreement with the theory. The study concludes that a liner with higher Mach number and lower adiabatic index gamma (the radio of specific heats) will generate higher ram pressure amplification and higher fusion energy gain. We implemented a second order embedded boundary method for the Maxwell equations in geometrically complex domains. The numerical scheme is second order in both space and time. Comparing to the first order stair-step approximation of complex geometries within the FDTD method, this method can avoid spurious solution introduced by the stair step approximation. Unlike the finite element method and the FE-FD hybrid method, no triangulation is needed for this scheme. This method preserves the simplicity of the embedded boundary method and it is easy to implement. We will also propose a conservative (symplectic) fourth order scheme for uniform geometry boundary.

  20. Self-Consistent System of Equations for a Kinetic Description of the Low-Pressure Discharges Accounting for the Nonlocal and Collisionless Electron Dynamics

    International Nuclear Information System (INIS)

    Kaganovich, Igor D.; Polomarov, Oleg

    2003-01-01

    In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated

  1. Effect of deviations from the Maxwell distribution on neutron production in laser targets

    International Nuclear Information System (INIS)

    Henderson, D.B.; Petschek, A.G.

    1978-11-01

    Because of the brief duration of laser implosions and the small size of the pellets, one may be concerned that the ions never reach a Maxwell distribution or that the tail is lost by diffusion. This might have a large effect on , which depends heavily on the tail. We have calculated the ion distribution and the DT . Results are presented for the ratio of for a monoenergetic isotropic distribution to that for a Maxwell distribution, for the rate of approach of to the equilibrium value, and for the decay of due to fast ion losses. The main effect in the last case is due to energy losses, not to non-Maxwellian distribution. The effect is substantially different than previously reported

  2. Generalized Killing-Yano equations in D=5 gauged supergravity

    International Nuclear Information System (INIS)

    Kubiznak, David; Kunduri, Hari K.; Yasui, Yukinori

    2009-01-01

    We propose a generalization of the (conformal) Killing-Yano equations relevant to D=5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form *F, couples naturally to particles in the background as a 'torsion'. Killing-Yano tensors in the presence of torsion preserve most of the properties of the standard Killing-Yano tensors - exploited recently for the higher-dimensional rotating black holes of vacuum gravity with cosmological constant. In particular, the generalized closed conformal Killing-Yano 2-form gives rise to the tower of generalized closed conformal Killing-Yano tensors of increasing rank which in turn generate the tower of Killing tensors. An example of a generalized Killing-Yano tensor is found for the Chong-Cvetic-Lue-Pope black hole spacetime [Z.W. Chong, M. Cvetic, H. Lu, C.N. Pope, (hep-th/0506029)]. Such a tensor stands behind the separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in this background.

  3. Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations

    Directory of Open Access Journals (Sweden)

    Liping Gao

    2017-01-01

    Full Text Available In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.

  4. Spontaneous compactification of D=10 Maxwell-Einstein theory leads to SU(3) X SU(2) X U(1) gauge symmetry

    International Nuclear Information System (INIS)

    Watamura, S.

    1983-01-01

    Solutions of ten-dimensional Maxwell-Einstein theory and a bosonic part of N = 2, D = 10 supergravity theory are examined. It is shown that there is a solution for which six-dimensional internal space is compactified into CP 2 x S 2 . The gauge symmetry of the effective four-dimensional theory is SU(3) x SU(2) x U(1). The introduction of fermions is also considered. The requirement of consistency in introducing a spinsup(C) structure on CP 2 results in a U(1) charge quantization condition. (orig.)

  5. Charged anti-de Sitter BTZ black holes in Maxwell-f(T) gravity

    Science.gov (United States)

    Nashed, G. G. L.; Capozziello, S.

    2018-05-01

    Inspired by the Bañados, Teitelboim and Zanelli (BTZ) formalism, we discuss the Maxwell-f(T) gravity in (2 + 1) dimensions. The main task is to derive exact solutions for a special form of f(T) = T + 𝜖T2, with T being the torsion scalar of Weitzenböck geometry. To this end, a triad field is applied to the equations of motion of charged f(T) and sets of circularly symmetric noncharged and charged solutions have been derived. We show that, in the charged case, the monopole-like and the ln terms are linked by a correlative constant despite the known results in teleparallel geometry and its extensions.39 Furthermore, it is possible to show that the event horizon is not identical with the Cauchy horizon due to such a constant. The singularities and the horizons of these black holes are examined: they are new and have no analogue in the literature due to the fact that their curvature singularities are soft. We calculate the energy content of these solutions by using the general vector form of the energy-momentum within the framework of f(T) gravity. Finally, some thermodynamical quantities, like entropy and Hawking temperature, are derived.

  6. A Maxwell elasto-brittle rheology for sea ice modelling

    Science.gov (United States)

    Dansereau, Véronique; Weiss, Jérôme; Saramito, Pierre; Lattes, Philippe

    2016-07-01

    A new rheological model is developed that builds on an elasto-brittle (EB) framework used for sea ice and rock mechanics, with the intent of representing both the small elastic deformations associated with fracturing processes and the larger deformations occurring along the faults/leads once the material is highly damaged and fragmented. A viscous-like relaxation term is added to the linear-elastic constitutive law together with an effective viscosity that evolves according to the local level of damage of the material, like its elastic modulus. The coupling between the level of damage and both mechanical parameters is such that within an undamaged ice cover the viscosity is infinitely large and deformations are strictly elastic, while along highly damaged zones the elastic modulus vanishes and most of the stress is dissipated through permanent deformations. A healing mechanism is also introduced, counterbalancing the effects of damaging over large timescales. In this new model, named Maxwell-EB after the Maxwell rheology, the irreversible and reversible deformations are solved for simultaneously; hence drift velocities are defined naturally. First idealized simulations without advection show that the model reproduces the main characteristics of sea ice mechanics and deformation: strain localization, anisotropy, intermittency and associated scaling laws.

  7. On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

    Energy Technology Data Exchange (ETDEWEB)

    Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

    2005-01-28

    Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

  8. On Bianchi-I cosmic strings coupled with Maxwell fields in bimetric ...

    Indian Academy of Sciences (India)

    Axially symmetric Bianchi-I model is studied with source cosmic cloud strings coupled with electromagnetic field in Rosen's bimetric theory of relativity and observed that there is no contribution from cosmic strings and Maxwell fields in this theory.

  9. Self-consistent description of the SHFB equations for 112Sn

    Science.gov (United States)

    Ghafouri, M.; Sadeghi, H.; Torkiha, M.

    2018-03-01

    The Hartree-Fock (HF) method is an excellent approximation of the closed shell magic nuclei. Pair correlation is essential for the description of open shell nuclei and has been derived for even-even, odd-odd and even-odd nuclei. These effects are reported by Hartree-Fock with BCS (HFBCS) or Hartree-Fock-Bogolyubov (HFB). These issues have been investigated, especially in the nuclear charts, and such studies have been compared with the observed information. We compute observations such as total binding energy, charge radius, densities, separation energies, pairing gaps and potential energy surfaces for neutrons and protons, and compare them with experimental data and the result of the spherical codes. In spherical even-even neutron-rich nuclei are considered in the Skyrme-Hartree-Fock-Bogolyubov (SHFB) method with density-dependent pairing interaction. Zero-range density-dependent interactions is used in the pairing channel. We solve SHF or SHFB equations in the spatial coordinates with spherical symmetry for tin isotopes such as 112Sn. The numerical accuracy of solving equations in the coordinate space is much greater than the fundamental extensions, which yields almost precise results.

  10. Numerical study of magnetohydrodynamics (MHD boundary layer slip flow of a Maxwell nanofluid over an exponentially stretching surface with convective boundary condition

    Directory of Open Access Journals (Sweden)

    P.BalaAnki Reddy

    2017-12-01

    Full Text Available This paper focuses on a theoretical analysis of a steady two-dimensional magnetohydrodynamic boundary layer flow of a Maxwell fluid over an exponentially stretching surface in the presence of velocity slip and convective boundary condition. This model is used for a nanofluid, which incorporates the effects of Brownian motion and thermophoresis. The resulting non-linear partial differential equations of the governing flow field are converted into a system of coupled non-linear ordinary differential equations by using suitable similarity transformations, and the resultant equations are then solved numerically by using Runge-Kutta fourth order method along with shooting technique. A parametric study is conducted to illustrate the behavior of the velocity, temperature and concentration. The influence of significant parameters on velocity, temperature, concentration, skin friction coefficient and Nusselt number has been studied and numerical results are presented graphically and in tabular form. The reported numerical results are compared with previously published works on various special cases and are found to be an in excellent agreement. It is found that momentum boundary layer thickness decreases with the increase of magnetic parameter. It can also be found that the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters.

  11. Revisiting the phase transition of AdS-Maxwell-power-Yang-Mills black holes via AdS/CFT tools

    Science.gov (United States)

    El Moumni, H.

    2018-01-01

    In the present work we investigate the Van der Waals-like phase transition of AdS black hole solution in the Einstein-Maxwell-power-Yang-Mills gravity (EMPYM) via different approaches. After reconsidering this phase structure in the entropy-thermal plane, we recall the nonlocal observables such as holographic entanglement entropy and two point correlation function to show that the both observables exhibit a Van der Waals-like behavior as the case of the thermal entropy. By checking the Maxwell's equal area law and calculating the critical exponent for different values of charge C and nonlinearity parameter q we confirm that the first and the second order phases persist in the holographic framework. Also the validity of the Maxwell law is governed by the proximity to the critical point.

  12. Applications of 3-D Maxwell solvers to accelerator design

    International Nuclear Information System (INIS)

    Chou, W.

    1990-01-01

    This paper gives a brief discussion on various applications of 3-D Maxwell solvers to accelerator design. The work is based on our experience gained during the design of the storage ring of the 7-GeV Advanced Photon Source (APS). It shows that 3-D codes are not replaceable in many cases, and that a lot of work remains to be done in order to establish a solid base for 3-D simulations

  13. Nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model

    International Nuclear Information System (INIS)

    Han, Jongmin; Jang, Jaeduk

    2005-01-01

    In this paper we prove the existence of the radially symmetric nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model. We also verify the Chern-Simons limit for those solutions

  14. Doubly stratified mixed convection flow of Maxwell nanofluid with heat generation/absorption

    Energy Technology Data Exchange (ETDEWEB)

    Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Hayat, T. [Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000 (Pakistan); NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia); Ahmad, B. [NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)

    2016-04-15

    Magnetohydrodynamic (MHD) doubly stratified flow of Maxwell nanofluid in presence of mixed convection is analyzed in this article. Effects of thermophoresis, Brownian motion and heat generation/absorption are present. The flow is induced due to linear stretching of sheet. Mathematical formulation is made under boundary layer approach. Expressions of velocity, temperature and nanoparticles concentration are developed. The obtained results are plotted and discussed to examine the variations in temperature and nanoparticles concentration due to different physical parameters. Numerical computations are made to obtain the values of local Nusselt and Sherwood numbers. Impact of sundry parameters on the flow quantities is analyzed graphically. - Highlights: • Double stratified flow of Maxwell nanofluid with mixed convection is modeled. • Thermophoresis and Brownian motion effects are encountered. • Computations are made to obtain the solution expressions. • Numerical values of local Nusselt and Sherwood numbers are computed and examined.

  15. Lifting particle coordinate changes of magnetic moment type to Vlasov-Maxwell Hamiltonian dynamics

    International Nuclear Information System (INIS)

    Morrison, P. J.; Vittot, M.; Guillebon, L. de

    2013-01-01

    Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to the field theoretic level, by transforming the noncanonical Poisson bracket and Hamiltonian structure of the Vlasov-Maxwell dynamics. Several examples are given including magnetic coordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of spherical velocity coordinates. An example of the lifting procedure is performed to obtain a simplified version of gyrokinetics, where the magnetic moment is used as a coordinate and the dynamics is reduced by elimination of the electric field energy in the Hamiltonian.

  16. Quantum criticality in Einstein-Maxwell-dilaton gravity

    International Nuclear Information System (INIS)

    Wen, Wen-Yu

    2012-01-01

    We investigate the quantum Lifshitz criticality in a general background of Einstein-Maxwell-dilaton gravity. In particular, we demonstrate the existence of critical point with dynamic critical exponent z by tuning a nonminimal coupling to its critical value. We also study the effect of nonminimal coupling and exponent z to the Efimov states and holographic RG flow in the overcritical region. We have found that the nonminimal coupling increases the instability for a probe scalar to condensate and its back reaction is discussed. At last, we give a quantum mechanics treatment to a solvable system with z=2, and comment for generic z>2.

  17. Hybrid quantum-classical master equations

    International Nuclear Information System (INIS)

    Diósi, Lajos

    2014-01-01

    We discuss hybrid master equations of composite systems, which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested. Its consistency is derived from the consistency of Lindblad quantum master equations. We emphasize that quantum measurement is a natural example of exact hybrid systems. We derive a heuristic hybrid master equation of time-continuous position measurement (monitoring). (paper)

  18. Traffic restrictions on Routes Bloch, Maxwell and Bohr

    CERN Multimedia

    IT Department

    2008-01-01

    Excavation and pipework is being carried out in the framework of the transfer of the waste water treatment plant for the effluents from the surface treatment workshops from Building 254 to Building 676, currently under construction. This work may encroach onto Routes Bloch, Maxwell and Bohr and disrupt the flow of traffic. Users are requested to comply with the road signs that will be erected. The work is expected to last until the beginning of December 2008. Thank you for your understanding. TS/CE and TS/FM Groups Tel.7 4188 or 16 4314

  19. Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics

    International Nuclear Information System (INIS)

    Niven, Robert K.

    2005-01-01

    The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a 'binary decision', exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems

  20. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

    International Nuclear Information System (INIS)

    Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Qin, Hong; Sun, Yajuan

    2015-01-01

    Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave