New narrow <Emphasis Type="Italic">N</Emphasis>(1685) and <Emphasis Type="Italic">N</Emphasis>(1726)? Remarks on the interpretation of the neutron anomaly as an interference phenomenon

Different interpretations of narrow structures at W ~ 1.68 and 1.72 GeV observed in several reactions are discussed. It is questionable whether interference phenomena could explain the whole complex of experimental findings. More probable hypotheses would be the existence of one or two narrow resonances N(1685) and N(1726) and/or the sub-threshold virtual KΣ and ωp production (cusps).     

A DIAGONAL SPLIT-CELL MODEL FOR THE OVERLAPPING YEE FDTD METHOD

In this paper, we present a nonorthogonal overlapping Yee method for solv- ing Maxwell＇s equations using the diagonal split-cell model. When material interface is presented, the diagonal split-cell model does not require permittivity averaging so that better accuracy can be achieved. Our numerical results on optical force computation show that the standard FDTD method converges linearly, while the proposed method achieves quadratic convergence and better accuracy.     

Mach reflection for the two-dimensional Burgers equation

We study shock reflection for the two 2D Burgers equation. This model equation is an asymptotic limit of the Euler equations, and retains many of the features of the full equations. A von Neumann type analysis shows that the 2D Burgers equation has detachment, sonic, and Crocco points in complete analogy with gas dynamics. Numerical solutions support the detachment/sonic criterion for transition from regular to Mach reflection. There is also strong numerical evidence that the reflected shock in the 2D Burgers Mach reflection forms a smooth wave near the Mach stem, as proposed by Colella and Henderson in their study of the Euler equations.     

Book review

Gordon and Breach Science Publishers, Amsterdam, 1998, 418 pages. ISBN: 90-5699-107-8, $100.The book under review appeared in the Gordon and Breach series on stability and control that aims to promote useful mathematical techniques. The goal of the book is to generalize     

Rotationally invariant hyperbolic waves

We use weakly nonlinear asymptotics to derive a canonical asymptotic equation for rotationally invariant hyperbolic waves. The equation can include weak dissipative, dispersive, or diffractive effects. We give applications to equations from magnetohydrodynamics, elasticity, and viscoelasticity.     

Solitary waves, steepening and initial collapse in the Maxwell–Lorentz system

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 relation reveals various asymptotic regimes such as Schrödinger and KdV branches. Existence of soliton-type solutions in the Schrödinger regime and light bullets containing few optical cycles together with dark solitons are illustrated numerically. Envelope collapse regimes of the Schrödinger equation are compared to the full system and an arrest mechanism is clearly identified when the spectral width of the initial pulse broadens beyond the applicability of the asymptotic behavior. We show that beyond a certain threshold the carrier wave steepens into an infinite gradient similarly to the canonical Majda–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities.     

Generalization of the FDTD algorithm for simulations of hydrodynamic nonlinear Drude model

In this paper we present a numerical method for solving a three-dimensional cold-plasma system that describes electron gas dynamics driven by an external electromagnetic wave excitation. The nonlinear Drude dispersion model is derived from the cold-plasma fluid equations and is coupled to the Maxwell’s field equations. The Finite-Difference Time-Domain (FDTD) method is applied for solving the Maxwell’s equations in conjunction with the time-split semi-implicit numerical method for the nonlinear dispersion and a physics based treatment of the discontinuity of the electric field component normal to the dielectric-metal interface. The application of the proposed algorithm is illustrated by modeling light pulse propagation and second-harmonic generation (SHG) in metallic metamaterials (MMs), showing good agreement between computed and published experimental results.