Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

唐家河自然保护区扭角羚种群动态及稳定性研究

１９８６年唐家河自然保护区内扭角羚的实际数量为４８０－５２０头,作者通过Ｌｅｓｌｉｅ矩阵的方法,预测了该保护区的内扭角羚种群１９８６－２００４年每隔３年各年份的理论数量分别为７１５,９６４,１３５８,１８４１,２５６４,３５８４头。讨论了该保护区扭角羚最适数量的应控制在１９９２年的９６４头,最大维持量不得超过１９９５年１３５８头。     

KCaF3结构相变的分子动力学模拟

基于无调节参数的Ｇｏｒｄｏｎ－Ｋｉｍ势和一种检测离子运动的新技术,以ＫＣａＦ３的分子动力学模拟结果为例,对钙钛矿ＡＢＸ３的离子分子固体的结构相变作了探讨．包括对阱势、折叠结构、能垒、超离子态、稳定性骨架和离子分子集团ＢＸ６的“尺寸”和“形状”．以期对离子分子固体的结构相变有一个基本了解．     

Distance distributions and dynamics of a zinc finger peptide from fluorescence resonance energy transfer measurements

Time-resolved fluorescence resonance energy transfer (FRET) measurements were used to measure distance distributions and intramolecular dynamics (site-to-site diffusion) of a 28-residue single-domain zinc finger peptide in the absence and presence of zinc ion. Energy transfer was measured between TRP₁₄ and a N-terminal DNS group. As expected, the TRP-to-DNS distance distribution for zinc-bound peptide is shorter and narrower (R _av=11.2 Å,hw=2.8 Å) than the metal-free peptide (R _av=20.1 Å,hw=14.5 Å). The degree of mutual donor-to-acceptor diffusion (D) was also determined for these distributions. For zinc-bound peptide there is no detectible diffusion (D0.2 Ų/ns), whereas for metal-free peptide a considerable amount of motion is occurring between the donor and the acceptor (D=12 Ų/ns). These results indicate that the zinc-bound peptide folds into a unique, well-defined conformation, whereas the metal-free conformation is flexible and rapidly changing. The absence of detectible mutual site-to-site diffusion between the donor and the acceptor in the metal-bound zinc finger peptide indicates that intramolecular motion is essentially frozen out, on the FRET time scale, as a consequence of zinc coordination.Dedicated to the memory of Barbara D. Wells.     

Nonequilibrium dynamics of a diffusion-limited reaction driven by a cluster-memory mechanism

The diffusion-limited reaction A+AA+B is studied in general dimension. The asymptotic decay of the system is found to depend nontrivially upon the initial concentration of A particles for certain ranges of the diffusion constant, backward reaction rate, and total concentration of particles. This nonequilibrium behavior is due to the formation of clusters centered about the initial A particles. A perturbative analysis ind=1 shows that the transition to the nonequilibrium dynamics is sharp and is quite similar to another previously studied reaction A+AA. Ford>1, a scaling argument is presented which describes the dependence of the asymptotic decay on the initial concentration of A particles and the equilibrium concentration for large backward reaction rates. Monte Carlo data are shown which confirm the analytic work ind=1, 2, and 3.     

Droplet dynamics for asymmetric Ising model

Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet.     

Theoretical studies on the reaction path and dynamics of the reaction CH_3+H_2O→CH_4+OH

The reaction path, the dynamical properties along the reaction path and CVT rate constants are computed by the ab initio MO method, the reaction path Hamiltonian theory and the variational transition state theory. The results show that the effect of the electron correlation energy on activation barrier is large, the recrossing and tunneling effects exist in the reaction.     

Structure and Dynamics of Methyl-substituted Beryllocene: [Be(C5Me5)2]

In this paper we study theoretically the molecular structure of [Be(C₅Me₅)₂], with special interest in similarities and differences found in the computed geometric parameters, depending on the treatment of the electron correlation used. Given the low energy differences found between the different configurations studied (less than 4 kcal mol⁻¹), and the high fluxionality found in experimental studies for this compound, we analyzed the dynamics of the system by means of first principles molecular dynamics calculations. A complex dynamics is found and analyzed in terms of two molecular rearrangement processes: 1,2-sigmatropic intraring rearrangement and a ring inversion mechanism that interchanges the roles (with regard to their coordination to the central Be atom) of the two rings.Dedicated to Dr. Jeal Paul Malrieu on occasion of his 65th birthday.     

Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)