Monotonicity of the free energy in the stochastic Heisenberg model

The specific free energy of the state at timet of the stochastic Heisenberg model is shown to be non-increasing witht, and to strictly decrease whenever this state is not a Gibbs state of the Hamiltonian. The initial state is assumed to be translation invariant and suitably smooth. For such states a convergence theorem is obtained.This paper represents the second part of the author's thesis. The first part appeared as [5]     

关于自由能的一些讨论

给出了自由能函数的完整表达式,并说明了自由能展开式中各项的物理意义．指出了自由能展开式系数及自变量的共轭变量的意义,吉布斯自由能的一阶偏导数都是热力学变量;吉布斯自由能的二阶偏导数一律都是物性张量．讨论了相变过程中的自由能函数展开式应保留的项数等,还给出了相稳定性条件．     

Morphometric approach to the solvation free energy of complex molecules

We show that the solvation free energy of a complex molecule such as a protein can be calculated using only four geometrical measures of the molecular structure and corresponding thermodynamical coefficients. We compare results from this morphometric approach to those obtained by an elaborate statistical-mechanical theory in liquid state physics for a large variety of different structures of protein G and find excellent agreement. Since the computational time is drastically reduced, the new approach provides a practical and efficient way for calculating the solvation free energy which can be employed when this quantity has to be calculated for a large number of structures, as in a simulation study of protein folding.     

GaAs photoconductivity indicates native defect structure and metastability of Te complex

We present photoconductivity measurements at 77K and room temperature of various semi-insulating GaAs samples grown with the LEC technique in PBN. The presence of a sharp structure near mid-gap believed to be due to a native defect, is here explained as arising from dislocations in the sample. We also observe the presence of a metastable state in one of our samples containing Cr and Te dopants, and propose a tentative model involving lattice relaxation at a Te related complex.     

A stochastic ansatz and its relationship with the dichotomic Markov process

It is shown that a simple stochastic ansatz for the solution of a stochastic differential equation leads to exact results for the dichotomic Markov process. This has implications for more complex problems where the ansatz leads to a simplified approach to the solution of stochastic equations in engineering and applied physics.     

A definition of metastability for Markov processes with detailed balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach [1]. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.     

Baldovin-Stella stochastic volatility process and Wiener process mixtures

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a powerful and consistent way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distributions and show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, we show that the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The basic Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.     

Incompatible stochastic processes and complex probabilities

The definition of conditional probabilities is based upon the existence of a joint probability. However, a reconstruction of the joint probability from given conditional probabilities imposes certain constraints upon the latter, so that if several conditional probabilities are chosen arbitrarily, the corresponding joint probability may not exist. Such an incompleteness in conditional probabilities can be eliminated by introducing complex probabilities. The physical meaning of the new mathematical formalism, as well as its relation to quantum probabilities, is discussed.     

Twist free energy

One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two parallel limiting planes, generate an interface and a cost in free energy per unit area of the interface. For continuum symmetries the order parameter interpolates smoothly between the end planes carrying two different directions of the order parameter. The cost in free energy is then proportional to L^d-2 for a system of characteristic size L. The power of L is related to the lower critical dimension, and the coefficient of this additional free energy vanishes at the critical temperature. In this note it is shown within a loop expansion that one does find the expected behavior of this twist free energy. This is a preamble to the study of situations where the broken continuum symmetry is believed to be more complex, as in Parisi ansatz for the Edwards-Anderson spin glass. Received 11 June 2001     

Relative grain boundary free energy and surface free energy of some metals and alloys

By the method of thermal etching measurements were carried out of the ratio of grain boundary free energy _GB to the surface free energy _s in silver, copper, nickel, gamma-iron and cobalt of 99·999 pct. purity each, three copper-aluminium alloys and eight nickel-cobalt alloys, the total concentration of impurities in each alloy not exceeding 0·01 pct, as a function of the temperature and sometimes of the annealing medium.     

Williams-watts dielectric relaxation: A fractal time stochastic process

Dielectric relaxation in amorphous materials is treated in a defect-diffusion model where relaxation occurs when a mobile defect, such as a vacancy, reaches a frozen-in dipole. The random motion of the defect is assumed to be governed by a fractal time stochastic process where the mean duration between defect movements is infinite. When there are many more defects than dipoles, the Williams-Watts decaying fractional exponential relaxation law is derived. The argument of the exponential is related to the number of distinct sites visited by the random walk of the defect. For the same reaction dynamics but with more traps than walkers, an algebraically decaying relaxation is found.     

关于二元混合物体系的偏摩尔吉布斯自由能的表达式

利用Gibbs-Duhem方程证明了偏摩尔自由能的一个计算公式.     

Detecting the topologies of complex networks with stochastic perturbations

How to recover the underlying connection topology of a complex network from observed time series of a component variable of each node subject to random perturbations is studied. A new technique termed Piecewise Granger Causality is proposed. The validity of the new approach is illustrated with two FitzHugh-Nagumo neurobiological networks by only observing the membrane potential of each neuron, where the neurons are coupled linearly and nonlinearly, respectively. Comparison with the traditional Granger causality test is performed, and it is found that the new approach outperforms the traditional one. The impact of the network coupling strength and the noise intensity, as well as the data length of each partition of the time series, is further analyzed in detail. Finally, an application to a network composed of coupled chaotic Ro?ssler systems is provided for further validation of the new method.     

A study of metastability in the Ising model

We consider a two-dimensional Ising ferromagnet with (+) boundary conditions and negative external field, where a Markovian time evolution is assumed. We construct, suitably restricting the allowed configurations att=0, a non equilibrium state with positive magnetization such that:

1. only one phase is present,
2. the relaxation time for unit volume is finite and can be made very large.

These results are obtained following a general method for describing metastable states proposed by Lebowitz and Penrose and exploiting the analysis of the Ising-spin-configurations in terms of contours given by Minlos and Sinai.     

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

In this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of ‘delay fractioning’, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.     

The free energy of systems with net charge

For quite general domains, the free energy density of a system with net charge differs in the thermodynamic limit from that of a neutral system by an electrostatic correction.     

The SU(2) chiral model in an external field: A complex stochastic process on a non-abelian group

The principal chiral model in an external field has a complex action. Conventional methods for performing Monte Carlo simulations are therefore useless for strong fields or weak coupling (i.e. large lattices). We apply the Langevin equation to this action and generate a complex stochastic process on a non-abelian group. Nice agreement with the pertubative expansion is observed for strong fields. A clear verification of the second-order phase transition for weak fields proved by Polyakov and Wiegmann seems to require larger lattices and more computer time than we have available, but should be straightforward using the complex Langevin equation.     

Global synchronization of general delayed complex networks with stochastic disturbances

In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, It?'s differential rule and the linear matrix inequality (LMI) optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.