Search results for "Equations"
showing 10 items of 955 documents
Thermodynamics of electrokinetic processes—I. Formulations
1990
Abstract The phenomenological equations of electrokinetic processes are studied according to five different formulations. Transformation matrices with Haase's formulation are given. A study of the measurable character of fluxes, forces and phenomenological coefficients in those formulations is also made. The extrinsic character, if so, of the formulations is examined and a general definition of formulations established only for binary solutions is given. Finally, a review of the literature is included, aiming to clarify the possible misunderstandings arising from the application of these five formulations.
Improved fast Gauss transform for meshfree electromagnetic transients simulations
2019
Abstract In this paper improved fast summations are introduced to enhance a meshfree solver for the evolution of the electromagnetic fields over time. The original method discretizes the time-domain Maxwell’s curl equations via Smoothed Particle Hydrodynamics requiring many summations on the first derivatives of the kernel function and field vectors at each time step. The improved fast Gauss transform is properly adopted picking up the computational cost and the memory requirement at an acceptable level preserving the accuracy of the computation. Numerical simulations in two-dimensional domains are discussed giving evidence of improvements in the computation compared to the standard formula…
Time-dependent Kohn-Sham approach to quantum electrodynamics
2010
We prove a generalization of the van Leeuwen theorem towards quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. Thereby we circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.
A Smoothed Particle Interpolation Scheme for Transient Electromagnetic Simulation
2006
In this paper, the fundamentals of a mesh-free particle numerical method for electromagnetic transient simulation are presented. The smoothed particle interpolation methodology is used by considering the particles as interpolation points in which the electromagnetic field components are computed. The particles can be arbitrarily placed in the problem domain: No regular grid, nor connectivity laws among the particles, have to be initially stated. Thus, the particles can be thickened only in distinct confined areas, where the electromagnetic field rapidly varies or in those regions in which objects of complex shape have to be simulated. Maxwell’s equations with the assigned boundary and initi…
The electromagnetic and Proca fields revisited: A unified quantization
1997
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μφ(x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U(1)(x, t), acquire dyn…
Motion of an electric charge in a terrestrial laboratory.
1995
The equation of motion for a charge in an electromagnetic field is written in the Fermi coordinates of an observer moving with a constant acceleration g=9.8 m/${\mathrm{s}}^{2}$ (${10}^{\mathrm{\ensuremath{-}}18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in units such that c=1). This is involved in the equation of motion not only as a Newtonian term g\ensuremath{\rightarrow}, but also as a relativistic correction of the form ``-2(g\ensuremath{\rightarrow}\ensuremath{\cdot}v\ensuremath{\rightarrow})v\ensuremath{\rightarrow}.'' We have studied the effect of this term under the conditions of an accelerator of particles. To this end, we have considered a constant and uniform magnetic field, a…
Noncoaxial Inductance Calculations Without the Vector Potential for Axisymmetric Coils and Planar Coils
2008
This paper presents an exact method for calculating the mutual inductance between a general axisymmetric coil and a second planar coil consisting of either a disk coil or a planar loop of essentially arbitrary shape. The approach is based directly on the magnetic field rather than the vector potential . The paper gives detailed results for two circular loops, a circular loop and an elliptic loop, and a circular loop and an annular disk coil. The method can be extended to cover the cases where all these loops and coils are extruded in the axial direction to give the corresponding solenoids. The method is also applicable to calculations for nuclear radiation detectors.
Exactly solvable relativistic model with the anomalous interaction
2010
A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron'ko-Stroganov model.
Corrective meshless particle formulations for time domain Maxwell's equations
2007
AbstractIn this paper a meshless approximation of electromagnetic (EM) field functions and relative differential operators based on particle formulation is proposed. The idea is to obtain numerical solutions for EM problems by passing up the mesh generation usually required to compute derivatives, and by employing a set of particles arbitrarily placed in the problem domain. The meshless Smoothed Particle Hydrodynamics method has been reformulated for solving the time domain Maxwell's curl equations. The consistency of the discretized model is investigated and improvements in the approximation are obtained by modifying the numerical process. Corrective algorithms preserving meshless consiste…
High order normal form construction near the elliptic orbit of the Sitnikov problem
2011
We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form up to 40th order in Cartesian coordinates.