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11.
胡亦钧 《武汉大学学报(理学版)》1995,(5)
设{Xn}n≥1是一列相互独立且具有相同分布、非负非退化的随机变量序列.S=X1+…+Xn,μEX1,a是X1的分布支撑的上确界.假设EeuX1<∞,u>0.对μ<Xn<a,本文分别讨论了1ogP{Sn≥nxn}及P{Sn≥nxn}J当n→∞时的渐近性质。 相似文献
12.
根据自治动力系统中周期跟踪性和极限跟踪性的定义,将其引入到非自治动力系统。研究了非自治动力系统中周期跟踪性和极限跟踪性的动力学性质,得到:(1)若F = { f i } i = 0 ∞ 拓扑共轭于G = { g i } i = 0 ∞ ,则F 具有周期跟踪性当且仅当G 具有周期跟踪性;(2)若F = { f i } i = 0 ∞ 拓扑共轭于G = { g i } i = 0 ∞ ,则F 具有极限跟踪性当且仅当G 具有极限跟踪性;(3)若乘积系统( X × Y , F × G ) 具有周期跟踪性,则( X , F ) 和( Y , G ) 具有周期跟踪性。 以上结论对非自治动力系统中跟踪性的发展有一定的促进作用。 相似文献
13.
We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing
free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the
classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution
function evolving under the classical Liouville's equation. The classical probability current so constructed matches with
the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth
transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values
are obtained in the limit of large mass of the particles. 相似文献
14.
T. A. Kaplan 《Journal of statistical physics》2006,122(6):1237-1260
The definition of the fundamental quantity, the chemical potential, is badly confused in the literature: there are at least
three distinct definitions in various books and papers. While they all give the same result in the thermodynamic limit, major
differences between them can occur for finite systems, in anomalous cases even for finite systems as large as a cm3. We resolve the situation by arguing that the chemical potential defined as the symbol μ conventionally appearing in the
grand canonical density operator is the uniquely correct definition valid for all finite systems, the grand canonical ensemble
being the only one of the various ensembles usually discussed (microcanonical, canonical, Gibbs, grand canonical) that is
appropriate for statistical thermodynamics, whenever the chemical potential is physically relevant. The zero–temperature limit
of this μ was derived by Perdew et al. for finite systems involving electrons, generally allowing for electron–electron interactions;
we extend this derivation and, for semiconductors, we also consider the zero–T limit taken after the thermodynamic limit.
The enormous finite size corrections (in macroscopic samples, e.g. 1 cm3) for one rather common definition of the c.p., found recently by Shegelski within the standard effective mass model of an
ideal intrinsic semiconductor, are discussed. Also, two very–small–system examples are given, including a quantum dot. 相似文献
15.
Leon Glass Theodore J. Perkins Jonathan Mason Hava T. Siegelmann Roderick Edwards 《Journal of statistical physics》2005,121(5-6):969-994
We consider dynamics in a class of piecewise-linear ordinary differential equations and in an electronic circuit that model
genetic networks. In these models, gene activity varies continuously in time. However, as in Boolean or discrete-time switching
networks, gene activity is driven high or low based only on whether the activities of the regulating genes are high or low
(i.e., above or below certain thresholds). Depending on the “regulatory logic”, these models can exhibit simple dynamics,
like stable fixed points or oscillation, or chaotic dynamics. The observed qualitative and quantitative differences between
the dynamics in the idealized equations and the dynamics in the electronic circuit lead us to focus attention on the analysis
of the dynamics as a function of parameter values. We propose new techniques for solving the inverse problem – the problem
of inferring the regulatory logic and parameters from time series data. We also give new symbolic and statistical methods
for characterizing dynamics in these networks. 相似文献
16.
This paper studies the stationary nonlinear Boltzmann equation for hard forces, in a Couette setting between two coaxial, rotating cylinders with given indata of Maxwellian type on the cylinders. A priori estimates are obtained mainly in L2, leading to multiple, isolated solutions together with a hydrodynamic limit control, based on asymptotic expansions together with a rest term. 相似文献
17.
Derivation of two point spread functions PSFs suitable for infrared thermograms analysis is illustrated, based on two unique approaches, one based on depth decaying limit and one on diffusion limit. Experimental work using PMMA sample with back drilled holes and pulsed thermographic routine is utilized to show the effectiveness of deconvoluting pixel temperature transient history with suggested PSF’s. Synthetic second time derivative thermograms are utilized for comparison and the signal to noise ratio is used as a figure of merit for quantification. 相似文献
18.
Dmytro Iurashev Giovanni Campa Vyacheslav V. Anisimov Ezio Cosatto 《Combustion Theory and Modelling》2017,21(6):1148-1175
Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damages to combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. This work presents a three-step method to find stability margins within which gas turbines can be operated without going into self-excited pressure oscillations. As a first step, a set of unsteady Reynolds-averaged Navier–Stokes simulations with the Flame Speed Closure (FSC) model implemented in the OpenFOAM® environment are performed to obtain the flame describing function of the combustor set-up. The standard FSC model is extended in this work to take into account the combined effect of strain and heat losses on the flame. As a second step, a linear three-time-lag-distributed model for a perfectly premixed swirl-stabilized flame is extended to the nonlinear regime. The factors causing changes in the model parameters when applying high-amplitude velocity perturbations are analysed. As a third step, time-domain simulations employing a low-order network model implemented in Simulink® are performed. In this work, the proposed method is applied to a laboratory test rig. The proposed method permits not only the unsteady frequencies of acoustic oscillations to be computed, but the amplitudes of such oscillations as well. Knowing the amplitudes of unstable pressure oscillations, it is possible to determine how these oscillations are harmful to the combustor equipment. The proposed method has a low cost because it does not require any license for computational fluid dynamics software. 相似文献
19.
Analysis of detection limit to time-resolved coherent anti-Stokes Raman scattering nanoscopy 下载免费PDF全文
In the implementation of CARS nanoscopy, signal strength decreases with focal volume size decreasing. A crucial problem that remains to be solved is whether the reduced signal generated in the suppressed focal volume can be detected. Here reported is a theoretical analysis of detection limit (DL) to time-resolved CARS (T-CARS) nanoscopy based on our proposed additional probe-beam-induced phonon depletion (APIPD) method for the low concentration samples. In order to acquire a detailed shot-noise limited signal-to-noise (SNR) and the involved parameters to evaluate DL, the T-CARS process is described with full quantum theory to estimate the extreme power density levels of the pump and Stokes beams determined by saturation behavior of coherent phonons, which are both actually on the order of ~ 109 W/cm2. When the pump and Stokes intensities reach such values and the total intensity of the excitation beams arrives at a maximum tolerable by most biological samples in a certain suppressed focal volume (40-nm suppressed focal scale in APIPD method), the DL correspondingly varies with exposure time, for example, DL values are 103 and 102 when exposure times are 20 ms and 200 ms respectively. 相似文献
20.
Theoretical study of the electronic structure of LiNa and LiNa<Superscript>+</Superscript> molecules
Neji Khelifi Riadh Dardouri Omar Marzook Al-Dossary Brahim Oujia 《Journal of Russian Laser Research》2009,30(2):172-186
Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels of the lowest electronic states
of the alkali dimer LiNa molecule dissociating into Na (3s, 3p, 4s, 3d, and 4p) + Li (2s, 2p, 3s, and 3p) in 1,3Σ, 1,3Π, and 1,3Δ symmetries are presented. Adiabatic results are also reported for 2Σ, 2Π, and 2Δ electronic states of the molecular ion LiNa+ dissociating into Li (2s, 2p, 3s, and 3p) + Na+ and Li+ + Na(3s, 3p, 4s, 3d, and 4p). We use an ab initio approach involving a non-empirical pseudopotential for the Li (1s2) and Na (1s22s22p6) cores and core valence correlation correction. A very good agreement is obtained for some lowest states of the LiNa and
LiNa+ molecules for spectroscopic constants with the available theoretical works. The existence of numerous avoided crossings between
electronic states of 2Σ and 2Π symmetries is related to the charge transfer process between the two ionic systems Li+Na and LiNa+. 相似文献