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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 相似文献
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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 相似文献
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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 相似文献
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Caihong Lei Guangxian Li Qi Yang Dahua Chen 《Journal of Macromolecular Science: Physics》2013,52(5):957-967
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. 相似文献
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G. E. Volovik 《JETP Letters》2013,98(8):491-495
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. 相似文献
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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 Ls, to the ambipolar diffusion length LDa,. Ls, is calculated. Its significance is not limited to zero current, even though it reduces to the conventional Debye length LD when the trap concentration is zero. (With traps, we always have Ls < LD.) The dielectric relaxation time itself is unaffected by traps, but in steady state situations, a material behaves as if it had an effective lifetime τ0s = τ0η, where η depends on the concentration and energetic position of the traps. τo, may be orders of magnitude greater than τ0, the conventional diffusion length lifetime. Typical values of Ls, are presented as a function of trapping parameters. Ls>LDa leads to relaxation behavior; Ls < LDa, to lifetime behavior. 相似文献
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The carrier concentration (Ns) 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?1T. At T = 4.4 K, τ?1T depends on Ns as N?1.9s in low mobility samples. In high-mobility samples, τ?1T increases with increasing Ns in high Ns region while τ?1T ∝ N?1.6s in low Ns region. The Ns-dependence of τ?1T becomes weaker with increasing T in both of low- and high-mobility samples. At Ns = 3 × 1012 cm?2, τ?1T depends on T as T1.8 in low-mobility samples and τ?1T ∝ T2.0 in high- mobility samples at T 5 K. 相似文献
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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].) 相似文献
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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 τE, 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, Te = 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. 相似文献
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The Fe3+-spin in alums of type (Fe x , A11-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. 相似文献
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H. Ez-Zahraouy A. Benyoussef 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,64(3-4):573-583
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 β0c1 < β0 < β0c2, 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. 相似文献