Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. It has been shown that in the case of a beam with uniform phase space density the Vlasov-Maxwell equations can be replaced exactly by the hydrodynamic equations with a triple ...

We consider high order methods for the one-dimensional Helmholtz equation and frequency-Maxwell system. We demand that the scheme be higher order even when the coefficients are discontinuous. We discuss the connection between schemes for the second-order scalar Helmholtz equation and the first-order system for the electromagnetic or acoustic applications. AMS subject classifications: 65N06, 78A...

This study examines the a brane Fuel Cell (PEMFC) b an approximatedmulti-co balance. Accuracy is assess and the correctedAMCmo does not permit the direct and to implications that C and mixture diffusion coe the maximum error betwe appropriate for PEMFC ap

We deal with the “nonrelativistic limit”, i.e. the limit c → ∞, where c is the speed of light, of the nonlinear PDE system obtained by coupling the Dirac equation for a 4-spinor to the Maxwell equations for the self-consistent field created by the “moving charge” of the spinor. This limit, sometimes also called “Post-Newtonian” limit, yields a SchrödingerPoisson system, where the spin and the m...

We consider a stationary two-phase Stefan problem with convection. The problem is governed by a coupled system involving a nonlinear Darcy law and the energy balance equation with second member in L 1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder xed point principle.

This setting can be generalized by replacing E by a differential 1-form ω, subject to the Maxwell-type equation (δd− k)ω = 0 [7]. Herein, d denotes the exterior derivative, and δ the co-derivative, its formal L adjoint [2,8]. The latter equation seamlessly extends to dimensions n other than 3. Moreover, it can be posed in Riemannian manifolds, while the original double curl equation relies on f...

We develop a spinor equation of the electromagnetic field, which is equivalent to the Maxwell equation and has a similar form as the Dirac equation. The spinor is the very conjugate momentum of the vector potential in the Lagrangian mechanics. In this framework the electromagnetic field described by the spinor exhibits the SU(2) internal symmetry. The quantization and the problem of longinal an...

In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

Correction: Lombard effect onset times reveal the speed of vocal plasticity in a songbird Samuel I. Hardman, Sue Anne Zollinger, Klemen Koselj, Stefan Leitner, Rupert C. Marshall and Henrik Brumm There was an error published in J. Exp. Biol. 220, 1065-1071. Eqn 2 was displayed incorrectly. The correct equation appears below. SPL increase 1⁄4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiff...