Non-linear representations of inhomogeneous groups

We classify the analytic actions, having a fixed point, of the classical inhomogeneous groups, such that the linear part of this action restricted to a Levi factor is the natural action defining this Levi factor as a classical simple group.     

Statistical properties of inhomogeneous waves

Statistical properties of inhomogeneous waves propagating in a randomly layered medium are simulated. It is shown that field instances can resonate near the interface and give shape to the averaged field.Pacific Institute of Oceanology, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 761–767, July, 1991.     

Oscillatory waves in inhomogeneous neural media

In this Letter we show that an inhomogeneous input can induce wave propagation failure in an excitatory neural network due to the pinning of a stationary front or pulse solution. A subsequent reduction in the strength of the input can lead to a Hopf instability of the stationary solution resulting in breatherlike oscillatory waves.     

Unitary and non-unitary representations of the complex inhomogeneous Lorentz group

We construct unitary and non-unitary representations of the complex inhomogeneous Lorentz group, including all its unitary, irreducible representations. We discuss the decomposition of these representations when they are restricted to the real inhomogeneous Lorentz group. We also discuss the representations of the Poincaré group for which the translation subgroup transforms under a not necessarily unitary representation. We summarize briefly the physical motivation for this study.Supported by the National Science Foundation (NSF-GP-58) while at Brandeis University and by the National Science Foundation, Grant NSF-GP-3465, while at the Courant Institute of Mathematical Sciences.     

Visual characteristics of inhomogeneous acoustic waves

Experimentally obtained visualizations of propagating inhomogeneous acoustic waves driven by zero-order antisymmetric Lamb waves (flexural waves) in water are presented. The inhomogeneous waves are visualized by optical holographic interferometry. A series of photographs show the evolution in time of instantaneous acoustic pressure distributions associated with propagating inhomogeneous waves. The photographs reveal characteristic features of flexurally driven inhomogeneous waves such as transversely attenuated wavefronts oriented perpendicularly to the plate boundary and a phase propagation velocity along the boundary approximately equal to the plate wave velocity (250 meters/second). Effects due to the dispersive nature of the flexural plate waves are also noted in the photographic series. Features distinguishing these subsonic, inhomogeneous surface waves (also called trapped or evanescent waves) from the leaky, lateral or head wave and also from incompressible fluid motions associated with low frequency vibrations of fluid loaded plates are identified. The relevance of inhomogeneous acoustic waves driven by subsonic flexural waves to practical sound-structure interaction problems is discussed.     

非均匀量子等离子体中的非线性波

本文探讨具有温度和密度梯度的非均匀量子等离子体系统, 获得了该系统在离子与中子碰撞频率较低情况下的二维非线性流体动力学方程． 求得了非均匀量子等离子体中的电势的冲击、爆炸和旋涡解．分析讨论了在致密天体物理环境中静电势的变化, 结果表明电势的冲击波的幅度和爆炸波的宽度,都随密度的增大(即随无维量子参量的减小)而增大, 但随漂移速度的增大(即随密度和温度梯度的增大)而减小; 静电势随时空相位的增大而趋向于稳定值, 系统最后达到稳定的状态． 旋涡解表明,旋涡静电势的时空分布呈现稳定的周期性的旋涡流．     

Strain solitary waves in inhomogeneous wave guides

The paper presents recent results of the research on strain solitary wave (soliton) evolution in elastic wave guides with different types of inhomogeneities. We analyze in calculations, numerical simulations and in experiments how physical or geometrical inhomogeneities affect the parameters of a density soliton propagating in it. In our experiments strain solitons are produced in a wave guide from an initial shock wave generated in the surrounding water by laser evaporation of a metallic target immersed into it nearby the input edge of the wave guide. Strain solitons are recorded in a desired part of the wave guide by means of holographic interferometry that allows to visualize the whole process and to obtain the complete set of data at different stages of the wave evolution.     

Cherenkov radiation waves in inhomogeneous dusty plasma

A kinetic theory is employed to study Cherenkov wave in an inhomogeneous dusty plasma. Two different frequency regimes are considered incorporating the plasma species temperatures. The dispersion relation for one-dimensional Cherenkov wave is derived and analyzed. The plasma species temperatures, their cyclotron frequencies, and the plasma density inhomogeneity effect the growth/damping of Cherenkov waves. It is shown that the plasma inhomogeneity contributes to damping of Cherenkov waves.     

Shock waves in periodically inhomogeneous active fibers

The dynamics of the pulse-envelope shock wave is studied in amplifying fibers whose gain, groupvelocity dispersion, and nonlinearity are nonuniform with respect to the fiber length. It is demonstrated that, in inhomogeneous fibers, picosecond pulses can exhibit a substantial steepening of the leading edge at lengths of less than 10 cm.