Modelling the dynamics of stochastic local search on <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="SmallCaps">sat</Emphasis>

A new analytical tool is presented to provide a better understanding of the search space of k-sat. This tool, termed the local value distribution , describes the probability of finding assignments of any value q′ in the neighbourhood of assignments of value q. The local value distribution is then used to define a Markov model to model the dynamics of a corresponding stochastic local search algorithm for k-sat. The model is evaluated by comparing the predicted algorithm dynamics to experimental results. In most cases the fit of the model to the experimental results is very good, but limitations are also recognised.     

A Monte Carlo Estimation of the Entropy for Markov Chains

We introduce an estimate of the entropy of the marginal density p ^t of a (eventually inhomogeneous) Markov chain at time t≥1. This estimate is based on a double Monte Carlo integration over simulated i.i.d. copies of the Markov chain, whose transition density kernel is supposed to be known. The technique is extended to compute the external entropy , where the p ₁ ^t s are the successive marginal densities of another Markov process at time t. We prove, under mild conditions, weak consistency and asymptotic normality of both estimators. The strong consistency is also obtained under stronger assumptions. These estimators can be used to study by simulation the convergence of p ^t to its stationary distribution. Potential applications for this work are presented: (1) a diagnostic by simulation of the stability property of a Markovian dynamical system with respect to various initial conditions; (2) a study of the rate in the Central Limit Theorem for i.i.d. random variables. Simulated examples are provided as illustration.      

Local order, entropy and predictability of financial time series

We consider time series of financial data as the Dow Jones Index with respect to the existence of local order. The basic idea is that in spite of the high stochasticity in average there might be special local situations where there local order exist and the predictability is considerably higher than in average. In order to check this assumption we discretise the time series and investigate the frequency of the continuation of definite words of length n first. We prove the existence of relatively long-range correlations under special conditions. The higher order Shannon entropies and the conditional entropies (dynamical entropies) are calculated, characteristic fluctuations are found. Instead of the dynamic entropies which yield mean values of the uncertainty/predictability we finally investigate the local values of the uncertainty/predictability and the distribution of these quantities. Received 19 January 2000     

经验势能函数的改进

本文提出改进经验势能函数的一般方法,即构成改进后的势能函数V=WV′,校正函数W=exp{P[(γ_e/γ)^q-1]}。此法应用于改进Rydberg函数与PG函数,结果成功。     

多相移DFB激光器的单模稳定性分析

本文分析了多相移激光器的稳态特性.在我们的分析中,考虑了空间烧孔(SHB)及非线性增益的因素.在通用的传输矩阵法(TMM)的基础上,我们对TMM模型的输入进行向量处理(而不是用牛顿 拉斐森法(NR))来求阈值及高于阈值条件下的主模及次模,进而求出单模稳定性.这个方法也可用于其它DFB结构的模分析.     

Structure and size distribution of percolating clusters. Comparison with gelling systems

Dynamic properties of Brownian particles immersed in a periodic potential with two barriers V₁ and V₂ (symmetric bistable potential) are studied by using the Fokker-Planck equation which we solve numerically by the matrix continued fraction method. This study will therefore serve to demonstrate the influence of this form of potential, which is of great interest for superionic conductors and for many other solid systems, on the diffusion process. Thus, we have calculated the full width at half maximum (FWHM) ) of the quasi-elastic line of the dynamic structure factor, for a large range of values of the wave-vectors q. Our results show clearly that, by varying the ratio of the barriers strictly between and 1, the Fokker-Planck equation describes a diffusive process which has some characteristic of jump and liquid-like regimes. While in the limit cases, i.e. when tends to or 1, the diffusion process can be described only by a simple jump motion. However, the jump-lengths corresponding to each limit case are not equal. In general the change of the ratio is found to have a significant effect on the character of the diffusive motion. We have also performed Fokker-Planck dynamics calculations of the diffusion coefficient in a bistable potential. We have found a good agreement between numerical calculations and analytical approximation results obtained in the high friction limit. Received 25 May 1998 and Received in final form 15 November 1998     

LiAr, LiKr and LiXe excimers: Photochemical formation of the - bands

We investigated the photochemical formation of lithium-rare-gas excimers in the 3 state through the reaction of Li₂(2(C)) and the ground-state rare-gas atom. Lithium-rare-gas vapor mixture was prepared in the heat-pipe oven. We populated the 2(C)state of the Li₂ molecule using the XeCl excimer laser wavelength at 308 nm or the PTP dye laser wavelength at about 335 nm. The 3-1 transitions were observed with peaks at 414, 420 and 435 nm for LiAr, LiKr and LiXe, respectively. We estimated thermally averaged rate constants for these photochemical reactions, which are cm³s^-1 for LiAr, cm ³ s^-1 for LiKr and cm³s^-1 for LiXe. Ab initio potential-energy curves and transition dipole moments for LiKr were calculated applying the SCF MRDCI method. Available data for the LiAr and LiKr excimers are presented, including potential-energy curves, electronic transition dipole moments, and spectroscopic constants. Possible photochemical formation of these molecules in the excited states is discussed. We performed the quantum-mechanical spectral simulations of the LiAr and LiKr 3-1 transitions, using ab initio potential-energy curves. Received: 2 October 1998 / Received in final form: 25 January 1999     

超布朗运动与无界区域上一类非线性微分方程

本文得到了超布朗运动的一个极限定理,并用超布朗运动给出了区域D上非线性微分方程的Dirichlet问题与随机Dirichlet问题非负有界解的精确表达式．     

Kinetic investigation of electronic energy transfer processes following the pulsed dye-laser generation of excited atomic barium, Ba[6s6p(P1)], in the presence of atomic strontium

The collisional behaviour of Ba[6s5d(³D_J)], 1.151 eV above the 6s²(¹S₀) electronic ground state, in the presence of atomic strontium, has been investigated in the ‘long-time domain' (ca. 100 μs–1 ms) following the pulsed dye-laser excitation of barium vapour at elevated temperature at λ = 553.5 nm (Ba[6s6p(¹P₁)] ← Ba[6s²(¹S₀)]. Ba(³D_J) is subsequently produced from the short-lived ¹P₁ state (τ_e = 8.37 ± 0.38 ns) by a number of radiative and collisional processes. It may then be monitored in the ‘long-time domain' by atomic spectroscopic marker methods involving either collisional activation of Ba(³D_J) by Ba(¹S₀) and He buffer gas to yield Ba[6s6p(³P_J)] with subsequent emission from the ³P₁ state (τ_e = 1.2 ± 0.1 μs): Ba[6s6p(³P₁)] → Ba[6s²(¹S₀)] + hv (λ = 791.1 nm). Alternatively, emission from Ba(¹P₁) may be monitored at long times following the generation of this short-lived state by energy pooling following self-annihilation of Ba(³D_J) + Ba(³D_J) from Ba[6s6p(¹P₁)] → Ba[6s²(¹S₀)] + hv (λ = 553.5 nm). The generation of Ba(³D_J) in the presence of atomic strontium yields emission in the long-time domain from Sr[5s5p(³P₁)] (τ_e = 19.6 μs): Sr[5s5p(³P₁)] → Sr[5s²(¹S₀)]  + hv (λ = 689.3 nm). Whilst the decay profiles at short times are complex in form, at long times all these atomic profiles show first-order kinetic removal with the decay coefficients for λ = 791.1 nm, 689.3 nm and 553.5 nm emissions in the ratio 1 : 2 : 2, consistent with overall third-order activation of the form: Ba(³D_J) + Ba(³D_J) + Sr(¹S₀) → Sr(³P_J) + 2Ba(¹S₀). The mechanism is modelled in detail, including measurement of integrated emission intensities, yielding kinetic data for fundamental collisional processes. The overall rate constant for the third-order collisional activation of Sr[5s5p(³P_J])from 2Ba[6s5d(³D_J)] + Sr[5s²(¹S₀)] takes the upper limit of 5.8 × 10⁻²⁷ cm⁶ atom⁻² s⁻¹ (T = 900 K). The rate constant for the two body collisional quenching of Ba[6s5d(³D_J)] by ground state atomic strontium, Sr[5s²(¹S₀)], is found to be (2.0 ± 0.1) × 10⁻¹² cm³ atom⁻¹ s⁻¹ (T = 900 K).