A note on the projecton of Gibbs measures

We give an example of a projection which maps two Gibbs measures for the same interaction into Gibbs measures for different interactions. As a corollary we find a case where by decimation a non-Gibbsian measure is transformed into a Gibbs measure.     

Equivalences of the large deviation principle for Gibbs measures and critical balance in the Ising model

In this paper we obtain the equivalence of the large deviation principle for Gibbs measures with and without an external field. For the Ising model, the equivalence allows us to study the result of competing influences of a positive external fieldh and a negative boundary condition in the cube ((B/h) ash0 for variousB. We find a critical balance at a valueB ₀ ofB.     

Evolution problems in spaces of probability measures

This is a short survey paper on the application of Monge’s theory of optimal mass transportation to evolution problems of a gradient type, in the case when the natural state space is the space of probability measures. This occurs for instance for Fokker-Planck equations, and optimal mass transportation methods provide, in this setting, very general existence and stability results.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

The Bohm criterion for a dusty plasma sheath

The formation of the sheath in a dusty plasma is investigated. The Bohm criterion is derived for two different cases: (a) when electrons are in thermodynamic equilibrium and dust grains provide the immobile, stationary background and (b) when both electrons and ions are in thermodynamic equilibrium and dust grains are moving. In the first case, Bohm criterion gets modified due to the fluctuation of the charge on the grain surface. In the second case, the collisional and Coulombic drag play important role in determining the Bohm criterion.     

Fractal Failure of Quasilocality for a Majority Rule Transformation on a Tree

We provide a transformation of the Ising model on a Cayley tree leading to non-Gibbsianness at any temperature, i.e. even within the uniqueness regime. We also introduce a new type of pathologies of renormalized Gibbs measures, called the fractal failure of quasilocality, and exhibit a concrete example.     

Dimension spectrum of axiom a diffeomorphisms. II. Gibbs measures

We compute the dimension spectrumf() of the singularity sets of a Gibbs measure defined on a two-dimensional compact manifold and invariant with respect to aC ² Axiom A diffeomorphism. This case is the generalization of the case where the measure studied is the Bowen-Margulis measure—the one that realizes the topological entropy. We obtain similar results; for example, the functionf is the Legendre-Fenchel transform of a free energy function which is real analytic (linear in the degenerate case). The functionf is also real analytic on its definition domain (defined in one point in the degenerate case) and is related to the Hausdorff dimensions of Gibbs measures singular with respect to each other and whose supports are the singularity sets, and we finally decompose these sets.     

Hausdorff Dimension of Sets of Generic Points for Gibbs Measures

For a translation invariant Gibbs measure on the configuration space X of a lattice finite spin system, we consider the set X of generic points. Using a Breiman type convergence theorem on the set X of generic points of an arbitrary translation invariant probability measure on X, we evaluate the Hausdorff dimension of the set X with respect to any metric out of a wide class of scale metrics on X (including Billingsley metrics generated by Gibbs measures).     

On Criticality for Competing Influences of Boundary and External Field in the Ising Model

We continue a study of Schonmann (1994), Schonmann and Shlosman (1996), and Greenwood and Sun (1997) regarding the competing influences of boundary conditions and external field for the Ising model. We find a critical point B ₀ in the competing influences for low temperature in dimension d 2A7E; 2.     

Gibbs Measures for Brownian Paths Under the Effect of an External and a Small Pair Potential

We consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure. Uniqueness of the Gibbs measure for two cases is shown. Also the typical path behaviour, the degree of mixing and some further properties are derived. We use cluster expansion in the small coupling parameter.     

Variational Principle for Some Renormalized Measures

We show that some measures suffering from the so-called renormalization group pathologies satisfy a variational principle and that the corresponding limit of the pressure, with boundary conditions in a set of measure 1, is equal to the pressure of the Ising model modulo a scale factor.     

The projection method for computing multidimensional absolutely continuous invariant measures

We present an algorithm for numerically computing an absolutely continuous invariant measure associated with a piecewiseC ² expanding mappingS: on a bounded region R ^N. The method is based on the Galerkin projection principle for solving an operator equation in a Banach space. With the help of the modern notion of functions of bounded variation in multidimension, we prove the convergence of the algorithm.     

热力学平衡态的涨落判据

任何热力学量的涨落在平衡态下都不能太大.特别地,要求熵和能量的涨落不大,就可以给出低温下热力学平衡态的普遍适用的判据.一些算例表明,低温下即使1023个粒子也不一定能达到热力学平衡态.     

Hardening measures for bipolar transistors against microwave-induced damage

In the present paper we study the influences of the bias voltage and the external components on the damage progress of a bipolar transistor induced by high-power microwaves. The mechanism is presented by analyzing the variation in the internal distribution of the temperature in the device. The findings show that the device becomes less vulnerable to damage with an increase in bias voltage. Both the series diode at the base and the relatively low series resistance at the emitter, Re, can obviously prolong the burnout time of the device. However, Re will aid damage to the device when the value is sufficiently high due to the fact that the highest hot spot shifts from the base-emitter junction to the base region. Moreover, the series resistance at the base Rb will weaken the capability of the device to withstand microwave damage.     

A comparison of criterion functions for fusion of multi-focus noisy images

In many practical applications, images are distorted by impulsive noise (IN) produced by image sensors and/or communication channels. This noise may cause miscalculation of sharpness values which, in turn, introduce significant errors in the results of image fusion. In this paper, conventional focus measures and frequency selective weighted median filter (FSWM) are evaluated for fusion of multi-focus images in the presence of IN. FSWM is also compared with other multi-focus fusion methods such as Laplacian Pyramid and wavelet. Experimental results are presented for several sets of images and the results show that FSWM can provide better performance than other focus measures and methods.     

The reversible measures for symmetric nearest-particle systems

Symmetric nearest-particle systems are certain spin systems on {0, 1}^z in which the flip rate is a function of the distances to the nearest particle of different type to the left and right. The process differs from the ordinary nearest-particle system in that the rates are preserved if zeros and ones are interchanged. The only reversible measure for the symmetric nearest-particle system is a renewaltype measure (the natural analog to the nonsymmetric case). Also as in the nonsymmetric case, reversibility only occurs when the rates are of a specific form. By imposing additional conditions on the rates it can be shown that the reversible measure is the only translation-invariant, invariant measure which concentrates on configurations having infinitely many zeros and ones to either side of the origin. This can be used to prove that for a large class of translation-invariant initial distributions, weak limits are reversible measures. Then we can conclude that the process is convergent for several examples of initial distributions.     

Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker–Planck equations

Using multiscale analysis and methods of statistical physics, we show that a solution to the N-atom Liouville equation can be decomposed via an expansion in terms of a smallness parameter , wherein the long scale time behavior depends upon a reduced probability density that is a function of slow-evolving order parameters. This reduced probability density is shown to satisfy the Smoluchowski equation up to O(²) for a given range of initial conditions. Furthermore, under the additional assumption that the nanoparticle momentum evolves on a slow time scale, we show that this reduced probability density satisfies a Fokker–Planck equation up to O(²). This approach has applications to a broad range of problems in the nanosciences.