Stabilizing the intensity of a wave amplified by a beam of particles

The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles as in a free electron laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose a strategy to stabilize the intensity by re-shaping the macro-particle. This strategy involves the study of the linear stability (using the residue method) of selected periodic orbits of a mean-field model. As parameters of an additional perturbation are varied, bifurcations occur in the system which have drastic effect on the modification of the self-consistent dynamics, and in particular, of the macro-particle. We show how to obtain an appropriate tuning of the parameters which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.     

The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems

Many oscillatory biological systems show periodic travelling waves. These are often modelled using coupled reaction-diffusion equations. However, the effects of different movement rates (diffusion coefficients) of the interacting components on the predictions of these equations are largely unknown. Here we investigate the ways in which varying the diffusion coefficients in such equations alters the wave speed, time period, wavelength, amplitude and stability of periodic wave solutions. We focus on two sets of kinetics that are commonly used in ecological applications: lambda-omega equations, which are the normal form of an oscillatory coupled reaction-diffusion system close to a supercritical Hopf bifurcation, and a standard predator-prey model. Our results show that changing the ratio of the diffusion coefficients can significantly alter the shape of the one-parameter family of periodic travelling wave solutions. The position of the boundary between stable and unstable waves also depends on the ratio of the diffusion coefficients: in all cases, stability changes through an Eckhaus (‘sideband’) instability. These effects are always symmetrical in the two diffusion coefficients for the lambda-omega equations, but are asymmetric in the predator-prey equations, especially when the limit cycle of the kinetics is of large amplitude. In particular, there are two separate regions of stable waves in the travelling wave family for some parameter values in the predator-prey scenario. Our results also show the existence of a one-parameter family of travelling waves, but not necessarily a Hopf bifurcation, for all values of the diffusion coefficients. Simulations of the full partial differential equations reveals that varying the ratio of the diffusion coefficients can significantly change the properties of periodic travelling waves that arise from particular wave generation mechanisms, and our analysis of the travelling wave families assists in the understanding of these effects.     

(2 + 1)D exotic Newton-Hooke symmetry, duality and projective phase

A particle system with a (2 + 1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality transformation. In the flat limit, the system transforms into a free Galilean exotic particle on the noncommutative plane. The wave equations carrying projective representations of the exotic Newton-Hooke symmetry are constructed.     

A review of analytical methods, based on the wave approach, to compute partitions transmission loss

In this paper, various methods for calculating partition transparency are investigated. These methods are all based on the wave approach, yet they differ in the way of considering the incident field, partition leaf dimensions and the absorbing material, or absorbent, incorporated between the partition leaves. The method verification has been done through comparison with the experimental data available in the literature. Results are very convincing and the wave approach proves to be highly accurate. The basic wave approach is well suited for modeling of infinite single or double-leaf partitions, although the diffuse incident field requires spatial windowing to achieve agreement with experimental data. When porous material is incorporated inside double-leaf partitions, the model needs to be enhanced, based on the Biot theory, to ensure coincidence with experimental data. In the case of partitions, which cannot be considered infinite, spatial windowing is applied to the transparency to correct for the dimensional effect, especially in the low-frequency range. The final model turns out to be highly accurate, as long as spatial windowing is limited to the first coincidence frequency. The wave approach therefore proves to be a suitable method and calculation times are moreover acceptable.     

A Phase Space Transform Adapted to the Wave Equation

Wave packets emerged in recent years as a very useful tool in the study of nonlinear wave equations. In this article we introduce a phase space transform adapted to the geometry of wave packets, and use it to characterize and study the associated classes of pseudodifferential and Fourier integral operators.     

Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

Comparisons between predictions of a Biot-Allard model allowing for angle-dependent elasticity and angle-and-porosity dependent tortuosity and transmission data obtained at normal incidence on water-saturated replica bones are extended to oblique incidence. The model includes two parameters which are adjusted for best fit at normal incidence. Using the same parameter values, it is found that predictions of the variation of transmitted waveforms with angle through two types of bone replica are in reasonable agreement with data despite the fact that scattering is not included in the theory.     

On the paper “Symmetry analysis of wave equation on sphere” by H. Azad and M.T. Mustafa

Using the scalar curvature of the product manifold S²×R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave equation obtained by H. Azad and M.T. Mustafa [H. Azad, M.T. Mustafa, Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl. 333 (2007) 1180-1188] to nonlinear Klein-Gordon equations on the two-dimensional sphere.     

Dispersion of elastic waves in the contact-impact problem of a long cylinder

Numerical dispersion of two-dimensional finite elements was studied. The outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars. In accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones.     

Shell correction in Bohr stopping theory

Second-harmonic cross-correlation operates a selection in time-phase among the randomly de-phased contributions to an optical field that propagated through a scattering medium. It can thus be used to selectively detect the weak contribution remaining coherent with the incident field. Received 7 May 1999