准坐标下广义力学系统的Lie对称定理及其逆定理

研究准坐标下广义力学系统的Lie对称性与守恒量.首先,对准坐标下广义力学系统定义无限小生成元,并应用微分方程在无限小变换下不变性的Lie方法,建立系统的确定方程.其次,给出结构方程和守恒量的形式.最后,研究Lie对称性逆问题(由已知积分求Lie对称)并举例说明结果的应用. 关键词： 广义力学 准坐标 Lie对称 确定方程 结构方程 守恒量     

变质量单面完整约束系统Lie对称性的摄动与广义Hojman型绝热不变量

研究变质量单面完整约束系统Lie对称性的摄动与广义Hojman型绝热不变量.首先通过一般无限小变换下的Lie对称性得到广义Hojman型的守恒量；然后基于力学系统高阶绝热不变量的定义，研究小扰动作用下系统Lie对称性的摄动，得到系统广义Hojman型绝热不变量；最后举例说明结果的应用. 关键词： 变质量 单面完整约束 对称性 摄动 绝热不变量     

非完整力学系统的非Noether守恒量——Hojman守恒量

研究非完整力学系统的非Noether守恒量——Hojman守恒量. 在时间不变的特殊Lie对称变换下，给出非完整力学系统的Lie对称性确定方程、约束限制方程和附加限制方程，得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出一个例子说明本文结果的应用. 关键词： 分析力学 非完整系统 Lie对称性 非Noether守恒量     

带有附加项的广义Hamilton系统的Mei对称性

研究带附加项的广义Hamilton系统的Mei对称性的定义和判据，给出系统Mei对称性为Lie对称性的充分必要条件. 通过Lie对称性间接导出具有Mei对称性且带有附加项的广义Hamilton系统运动微分方程的Hojman守恒量. 举例说明结果的应用. 关键词： 附加项 广义Hamilton系统 Mei对称性 Hojman守恒量     

一类非完整系统运动微分方程的Lie对称性与Hojman型守恒量

研究一类非完整系统运动方程的Lie对称性与Hojman型守恒量.给出系统Lie对称性的确定方程和限制方程，存在守恒量的条件以及守恒量的形式.举例说明结果的应用. 关键词： 分析力学 非完整系统 对称性 Hojman型守恒量     

广义线性非完整力学系统的Hojman守恒量

研究广义线性非完整力学系统的Lie对称性导致的Hojman守恒量,在时间不变的特殊Lie对称变换下,给出系统的Lie对称性确定方程、约束限制方程和附加限制方程,得到相应完整系统的Hojman守恒量以及广义线性非完整力学系统的弱Hojman守恒量和强Hojman守恒量,并举一算例说明结果的应用.     

相空间中变质量力学系统的Hojman守恒量

研究一般的无限小变换下相空间中变质量力学系统Lie对称性的Hojman守恒量. 给出了相空 间中变质量力学系统Lie 对称性的确定方程和Hojman守恒量定理,并举例说明结果的应用. 关键词： 相空间 变质量系统 一般的无限小变换 Lie对称性 Hojman守恒量     

广义Hamilton系统的Lie对称性与守恒量

研究广义Hamilton系统Lie对称性导致的新型守恒量.首先,建立系统的微分方程.其次,研究一类特殊无限小变换下系统的Lie对称性.第三,将Hojman定理推广到广义Hamilton系统.最后,举例说明结果的应用. 关键词： 广义Hamilton系统 Lie对称性 守恒量     

相对运动动力学系统Nielsen方程的Lie对称性与Hojman守恒量

研究相对运动动力学系统Nielsen方程的Lie对称性和Lie对称性直接导致的Hojman守恒量.在群的无限小变换下,给出相对运动动力学系统Nielsen方程Lie对称性的定义和判据;得到相对运动动力学系统Nielsen方程Lie对称性的确定方程以及Lie对称性直接导致的Hojman守恒量的表达式.举例说明结果的应用. 关键词： 相对运动动力学 Nielsen方程 Lie对称性 Hojman守恒量     

广义经典力学系统的Hojman守恒定理

研究广义经典力学系统的对称性与守恒定理.利用常微分方程在无限小变换下的不变性，建 立了系统在高维增广相空间中仅依赖于正则变量的Lie对称变换，并直接由系统的Lie对称性得到了系统的一类守恒律.实际上，这是Hojman的守恒定理对广义经典力学系统的推广.举例说明结果的应用. 关键词： 广义经典力学 对称性 守恒定理     

The Shear‐Dependent Phase Separation Behavior of the Ternary Blend Polystyrene/Polyvinyl Methyl Ether/Styrene–Acrylonitrile Copolymer

The phase behavior and phase separation dynamics of a PS/PVME/SAN ternary blend using light scattering under a shear rate range of 0.1～40 s^?1 were investigated. The cloud point temperature first increases and then decreases with the increase of shear rates. At higher shear rates, the cloud point temperature again increases. The phase separation behavior in the early and later stages under shear field can be explained by the Cahn–Hilliard theory and the exponential growth law, respectively. The delay time τ _d ?, the apparent diffusion coefficient D _app, the growth rate R(q), and the exponent term show strong dependence on the difference between the experimental temperature and the cloud point temperature (ΔT), and on the shear rates. Compared with PS/PVME binary blends at lower shear rates, τ _d for a PS/PVME/SAN ternary blend is smaller, while at higher shear rates τ _d is larger. At higher shear rates, the introduction of the third component SAN to a PS/PVME binary blends slows the phase separation process.     

On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ _Q of the charge Q and the energy relaxation time τ _E . If τ _Q ? τ _E , the perturbed system relaxes first to the state with the ODLRO, which persists for a long time and finally relaxes to the full equilibrium static state. In the limit τQ → ∞, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time translation symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid ⁴He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.     

The concept of screening length in lifetime and relaxation semiconductors

It is shown that, contrary to normal practice, the most appropriate criterion for distinguishing between lifetime and relaxation semiconductors in the presence of traps is the ratio of the screening length L_s, to the ambipolar diffusion length L_Da,. L_s, is calculated. Its significance is not limited to zero current, even though it reduces to the conventional Debye length L_D when the trap concentration is zero. (With traps, we always have L_s < L_D.) The dielectric relaxation time itself is unaffected by traps, but in steady state situations, a material behaves as if it had an effective lifetime τ_0s = τ₀η, where η depends on the concentration and energetic position of the traps. τ_o, may be orders of magnitude greater than τ₀, the conventional diffusion length lifetime. Typical values of L_s, are presented as a function of trapping parameters. L_s>L_Da leads to relaxation behavior; L_s < L_Da, to lifetime behavior.     

Carrier concentration dependence and temperature dependence of mobility in silicon (100) N-channel inversion layers at low temperatures

The carrier concentration (N_s) dependence of electron mobility in Si (100) inversion layers has been measured at temperatures T = 1.5?70K for high- and low-mobility MOSFETs. An extrinsic term is observed in the T-dependent part of the scattering probability, τ^?1_T. At T = 4.4 K, τ^?1_T depends on N_s as N^?1.9_s in low mobility samples. In high-mobility samples, τ^?1_T increases with increasing N_s in high N_s region while τ^?1_T ∝ N^?1.6_s in low N_s region. The N_s-dependence of τ^?1_T becomes weaker with increasing T in both of low- and high-mobility samples. At N_s = 3 × 10¹² cm^?2, τ^?1_T depends on T as T^1.8 in low-mobility samples and τ^?1_T ∝ T^2.0 in high- mobility samples at T 5 K.     

弛豫表面的晶格振动不稳定性

Pietronero等人从一个简单模型出发,数值计算了表面的晶格振动不稳定性温度τ_s,但他们的计算是不完全的。本文找到一个可大大减少计算量的程序方案,给出完整的数值计算,并给出了准确地确定τ_s值的方法及精度更高的τ_s值,然后将结果进一步推广,讨论了固体表面发生弛豫时τ_s的变化。 关键词：     

Ionization Dynamics in a Pulse Disturbed Magnetically Confined Helium Plasma

The equilibrium of a magnetized Helium plasma is disturbed by a pulsed Trivelpiece-Gouldwave. The electrons obtain the energy by linear collisionless wave absorption. The relaxation phenomena of density and energy are explained in terms of two relaxation times τ_E, τ₁ and a quantity giving the additional ionization. These quantities are derived from a small signal fluid model based upon energy and particle balance equations. In the experiment they are taken from the transient curves of Langmuir-probe current, optical line radiation and the noise power at the electron cyclotron frequency. The experimental conditions are: Helium-gas, p = 1 …? 5 Pa, T_e = 4 eV, n = 1 …? 5 · 10¹⁰ cm^?3, B = 6,5 · 10^?2 T, 27 MHz rf plasma source, low frequency fluctuation level < 1%, classical losses. The energy relaxation time …?_E = 10 …? 15 μs is given by inelastic collision losses. The ionization time constant τ₁ is related to the instantaneous ionization frequency during the transient state. It shows a high value at the very beginning of the pulse which must be explained by a tail formation in the distribution function and enhanced radial losses becoming Bohm-like in the transition phase.     

The properties of liquid nitrogen

Measurements are reported of the nitrogen-nucleus spin-lattice relaxation time, T ₁, in liquid nitrogen ¹⁴N₂ and liquid nitrogen ¹⁵N₂ along the liquid-vapour coexistence line from 77·3 K up to the critical temperature and for the fluid at the critical density up to 145 K. Values of the molecular reorientational correlation time, τ _Q , and the molecular angular momentum correlation time, τ _sr , are determined. The values of τ _Q and τ _sr and the relation between them are discussed in terms of various theories of molecular reorientation in molecular liquids. The values of τ _Q and τ _sr are also compared with those predicted by computer simulation methods. It is concluded that the molecular reorientation in liquid nitrogen is not by classical reorientational diffusion except possibly at temperatures near the triple point. It is suggested that at higher temperatures the reorientation is on average by rather large angles and that the process may be quantum mechanical to some extent. (For paper I in this series see reference [8].)     

Relaxationsphänomene in Mössbauerspektren von Magnetisierten paramagnetischen Substanzen. I [(Fe x,Al1-x )NH4(SO4)2· 12H2O]

The Fe³⁺-spin in alums of type (Fe _x , A1_1-x )NH₄(SO₄)₂ · 12 H₂O interacts (i) with the crystal lattice viaLS-coupling, and (ii) with the spins of the adjacent Fe³⁺-ions via magnetic dipole-dipole interaction. These interactions lead to a time fluctuation of the spin direction, characterized by correlation times τ _c and τ′ _c of increasing order. The times may be deduced from the⁵⁷Fe-Mössbauer spectra of the alums, τ _c from the width, and τ′ _c ≈τ _c from the position of the hyperfine structure lines. The theoretical interpretation of the Mössbauer spectra is relatively simple, when (i) the spin-lattice interaction gets frozen in, and (ii) a strong applied magnetic fieldH _a decouples the spins of the Fe³⁺-ion and the⁵⁷Fe-nucleus. The spectra were taken, therefore, at 4.2 °K and 8 kOe≦H _a ≦ 54 kOe. According to the 1/r ³-dependence of the magnetic dipole-dipole interaction τ _c should be related tox, the Fe-concentration, τ _c ·x≈τ₀=const. Forx≧0.5 our experimental results are in agreement with this rule when τ₀=(1.5±0.5) · 10^?9 s. For an alum withx=0.26, however, the observed spectra cannot be explained in terms of temporal spin fluctuations, at least not in the framework of the models which are available now. Here, presumedly, the electron spins of adjacent Fe³⁺-ions are coupled to more or less isolated and, consequently, relatively stationary spin clusters of various sizes, leading to many time independent internal magnetic fields. A treatment of this proposal is in preparation.     

Disorder effect on the traffic flow behavior

The effects of some disorders, on the traffic flow behavior, are studied numerically. Especially, the effect of mixture of vehicles of different velocities and/or lengths, the effects of different drivers reactions, the position and the extraction rate of off-ramp in the free way. Using a generalized optimal velocity model, for a mixture of fast and slow vehicles, we have investigated the effect of delay times τ _f and τ _s on the fundamental diagram. It is Found that the small delay times have almost no effect, while, for sufficiently large delay time τ _s , the current profile displays qualitatively five different forms, depending on τ _f , τ _s and the fractions f _f and f _s of the fast and slow cars, respectively. The velocity (current) exhibits first-order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to a jamming one, respectively. The minimal current appears in intermediate values of τ _s . Furthermore there exist, a critical value of τ _f above which the meta-stability and hysteresis appear. The effects of disorder due to drivers behaviors have been introduced through a random delay time τ allowing the car to reach its optimal velocity traffic flow models with open boundaries. In the absence of the variation of the delay time Δτ, it is found that the transition from unstable to meta-stable and from meta-stable to stable state occur under the effect of the injecting and the extracting rate probabilities α and β respectively. Moreover, the perturbation of the traffic flow behavior due to the off-ramp has been studied using numerical simulations in the one dimensional cellular automaton traffic flow model with open boundaries. When the off-ramp is located between two critical positions i _c1 and i _c2 the current remains constant (plateau) for β_0c1 < β₀ < β_0c2, and the density undergoes two successive first order transitions: from high density to plateau current phase and from average density to the low one. In the case of two off-ramps, these transitions occur only when the distance between ramps, is smaller than a critical value.