Dispersion properties of electron acoustic waves in degenerate and non‐degenerate quantum plasmas

The longitudinal response functions are used to generalize the dispersion properties of electron acoustic waves (EAWs) in the presence of quantum recoil, for isotropic, non‐relativistic, degenerate/non‐degenerate plasmas. In order to study the EAWs, the constituents of non‐degenerate (thermal) plasma are considered to be of two groups of electrons having different number density and temperature, namely the cold electrons and the hot electrons. Similarly in degenerate (Fermi) plasma the two population of electrons are considered to be the thinly populated and the thickly populated electrons. The sparsely populated electrons are termed as cold electrons while the densely populated ones are termed as hot electrons. The ions are stationary which form the neutralizing background. The absorption coefficients for Landau damping with the inclusion of the quantum recoil in both plasmas are calculated and discussed. The results are discussed in the context of laser‐produced plasma.     

Radiation damping in an anharmonic oscillator

The effect of radiation damping in an anharmonic oscillator has been calculated using the technique of Kryloff and Bogolituboff. It is found that the intensity distribution of the emitted spectral line is asymmetric about its intensity maximum. The index of asymmetry agree with the experimental data on x-rayK _{a 1,2}lines.     

Elastic waves in a Timoshenko beam with boundary damping

In this paper we consider a Timoshenko beam with a damping moment applied to one of the endpoints. The elastic waves that develop from two sets of localised initial disturbances in the beam, are simulated and it is shown that properties of the spectrum adequately explain the features of the waves. We also show, using energy calculations, that the boundary moment is significantly more effective in reducing vibrations in the beam in one of the cases under consideration. The so-called second spectrum of the Timoshenko beam plays a prominent part in explaining this phenomenon.     

Multicomponent latex IPN materials: 2. Damping and mechanical behavior

The integrals of the linear loss shear modulus vs. temperature (loss area, LA) and linear tan δ vs. temperature (tan δ area, TA) were characterized for various core/shell latex particles with synthetic rubber, poly(butadiene-stat-styrene) [P (Bd/S), 90/10], and interpenetrating polymer networks (IPN) as the cores. The IPN cores were composed of P(Bd/S) (T_g ≃ − 70°C) and an acrylate based copolymer (T_g around 10°C) for potential impact and damping improvement in thermoplastics. Poly(styrene-stat-acrylonitrile) (SAN, 72/28) was the shell polymer for all these polymers. Under the same loading, for both toughening and damping controls, among the IPN core/shell, blend of separate core/shell, and multilayered core/shell polymers, the IPN core/shell polymers were the best dampers. However, the other core/shell polymers also showed higher LA values than P(Bd/S)/SAN core/shell polymer. A comparison of LA values via a group contribution analysis method was made, the effect of particle morphology and phase continuity on damping being studied. Inverted core/shell latex particles (glassy polymer SAN was synthesized first) showed much higher LA and TA values than normal core/shell ones (rubbery polymer was synthesized first). Models for maximum LA and TA behavior are proposed. The damping property was essentially controlled by the phase miscibility and morphology of the core/shell latex particles. The LA values for each peak in these multiphase materials provided some indication of the several fractional phase volumes. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1501–1514, 1997     

无穷维空间的牛顿法收敛域定理

本文对无穷维空间的映象给出了广义导数的概念,利用这种导数替代光滑映象的Frechet导数,给出了无穷维空间非光滑算子方程的阻尼牛顿法收敛域的一个定理。     

Exponential stability of wave equations with potential and indefinite damping

First, we consider the linear wave equation utt−uxx+a(x)ut+b(x)u=0 on a bounded interval (0,L)⊂R. The damping function a is allowed to change its sign. If is positive and the spectrum of the operator (_∂xx−b) is negative, exponential stability is proved for small . Explicit estimates of the decay rate ω are given in terms of and the largest eigenvalue of (_∂xx−b). Second, we show the existence of a global, small, smooth solution of the corresponding nonlinear wave equation utt−σx(ux)+a(x)ut+b(x)u=0, if, additionally, the negative part of a is small enough compared with ω.     

Existence and stability of planar diffusion waves for 2-D Euler equations with damping

To study the non-linear stability of a non-trivial profile for a multi-dimensional systems of gas dynamics, the combination of the Green function on estimating the lower order derivatives and the energy method for the higher order derivatives is shown to be not only useful but sometimes maybe also essential. In this paper, we study the stability of a planar diffusion wave for the isentropic Euler equations with damping in two-dimensional space. By introducing an approximate Green function for the linearized equations around the planar diffusion wave and by applying the energy method, we prove the global existence and the L₂ convergence rate of the solution when the initial data is a small perturbation of the planar diffusion wave. The decay rates of the perturbation and its lower order spatial derivatives obtained are optimal in the L₂ norm. Furthermore, the constructed approximate Green function in this paper can be used for the pointwise and the Lp estimates of the solutions concerned. In fact, the approach by combining of the Green function and energy method can be applied to other system especially when the derivatives of the coefficients in the system have certain time decay properties.     

带有记忆项和阻尼项的非线性双曲型方程的有限元方法

This paper studies the finite element method for some nonlinear hyperbolic partial differential equations with memory and dampling terms.A Crank-Nicolson approximation for this kind of equations is presented.By using the elliptic Ritz-Volterra projection,the analysis of the error estimates for the finite element numerical solutions and the optimal H1-norm error estimate are demonstrated.     

Relaxation oscillations and damping factors of 1.3 μm In(Ga)As/GaAs quantum-dot lasers

In(Ga)As/GaAs quantum-dot (QD) lasers with emission wavelength at 1295 nm at room temperature are fabricated. The laser active region contains a threefold stack of QD layers with surface dot density of 4.56 × 10¹⁰ cm^–2. The laser structure is aluminum-free with InGaP as cladding layers. Threshold current density of a narrow stripe laser of 8 m wide and 3.5 mm long is 152.5 A/cm². The highest relaxation oscillation frequency measured at room temperature is 1.8 GHz, corresponding to a modulation bandwidth of 2.8 GHz due to the small damping factor. From the above measurement, the differential gain and gain compression factor were extracted to be 4.3 × 10^–16 cm² and 3.4 × 10 ^–17 cm ³, respectively. Using these parameters, the maximum modulation bandwidth f _{3 dB max} is estimated as 7.9 GHz.