Dynamics of Inhomogeneous Chains of Coupled Quadratic Maps

A new effective local analysis method is elaborated for coupled map dynamics. In contrast to the previously suggested methods, it allows visually investigating the evolution of synchronization and complex-behavior domains for a distributed medium described by a set of maps. The efficiency of the method is demonstrated with examples of ring and flow models of diffusively coupled quadratic maps. An analysis of a ring chain in the presence of space defects reveals some new global-behavior phenomena.     

Adsorption thermodynamics of monomers on diluted-bonds triangular lattices

The surface of amorphous solids cannot be usually represented by a regular lattice of adsorbing sites. One of the main characteristics of such surfaces is a variable connectivity for each site. A simple model consisting of a triangular lattice where a fraction of bonds (interactions) is suppressed at random is used here to find out, by using Monte Carlo simulations, how the adsorption thermodynamics of repulsively interacting monomers is modified with respect to the same process in the regular lattice. Adsorption isotherm, differential heat of adsorption and adsorbed phase entropy calculations are carried out showing and interpreting the effects of the variable connectivity. In particular, it is found that the order-disorder phase transition observed for the regular lattice survives, though with modifications, above a critical mean connectivity.     

Resolution of conflicting views concerning frequency-response models for conducting materials with dispersive relaxation, and isomorphism of macroscopic and microscopic models

Possible errors in the widely used 1972–1973 macroscopic original-electric-modulus formalism are identified, corrected, and their consequences considered. These errors include misidentification of the high-frequency-limiting dielectric constant arising entirely from mobile charges, ε_C1∞, and the failure to treat properly the high-frequency-limiting dielectric constant associated with bulk dipolar and vibrionic effects, ε_D∞. It is shown that the corrected modulus formalism, which describes dispersed mobile-charge effects, is isomorphic in form with the 1973 microscopic continuous-time random-walk hopping model of Scher and Lax after a minor but significant correction is made to the latter's response function. This firmly established correction, which nevertheless could not be determined by Kronig–Kramers transformation, involved inversion of synthetic frequency-response data to determine a distribution of relaxation times and led to extension of the real part of the Scher–Lax dielectric response to higher frequencies by the inclusion of a nonzero limiting value. This isomorphism, along with excellent data fitting using the corrected modulus formalism, suggests that since the Scher–Lax stochastic model involves no explicit Coulomb interactions, cation motion in glasses is dominated by short-range interactions. Finally, two very-high-frequency processes, which each lead to a limiting plateau value of the real part of the conductivity at sufficiently high frequencies, are discussed in detail.     

Statistical physics, optimization and source coding

The combinatorial problem of satisfying a given set of constraints that depend on N discrete variables is a fundamental one in optimization and coding theory. Even for instances of randomly generated problems, the question “does there exist an assignment to the variables that satisfies all constraints?” may become extraordinarily difficult to solve in some range of parameters where a glass phase sets in. We shall provide a brief review of the recent advances in the statistical mechanics approach to these satisfiability problems and show how the analytic results have helped to design a new class of message-passing algorithms — the survey propagation (SP) algorithms — that can efficiently solve some combinatorial problems considered intractable. As an application, we discuss how the packing properties of clusters of solutions in randomly generated satisfiability problems can be exploited in the design of simple lossy data compression algorithms.     

Analogues of Non-Gibbsianness in Joint Measures of Disordered Mean Field Models

It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity properties of the conditional probabilities in finite volume of the following mean field models: (a) joint measures of random field Ising, (b) joint measures of dilute Ising, (c) decimation of ferromagnetic Ising. The conditional probabilities are functions of the empirical mean of the conditionings; so we look at the large volume behavior of these functions to discover non-trivial limiting objects. For (a) we find (1) discontinuous dependence for almost any realization and (2) dependence of the conditional probabilities on the phase. In contrast to that we see continuous behavior for (b) and (c), for almost any realization. This is in complete analogy to the behavior of the corresponding lattice models in high dimensions. It shows that non-Gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean-field models.     

Measuring the extent of phase separation during polymerization of composite latex particles using modulated temperature DSC

The morphological features of composite latex particles predominantly develop during the polymerization process and depend upon a significant number of variables. In this study, we have concentrated on the relative polarities of the two polymers in the particles and the rate at which we added the monomers during semibatch reactions containing the seed polymer latex. Our particular interest was to develop data that could reveal the extent of polymer phase separation as a function of the amount of monomer fed, and to characterize the morphology resulting from it. While TEM is the most common analytical technique employed, we show in this paper that modulated temperature DSC can generate data that allows us to follow the phase separation process as the monomer feed progresses. By considering the possibilities of having “phases” within the particles of pure polymer, homogeneously mixed (but nonequilibrium) polymers, gradient and interfacial polymer, we have been able to quite successfully simulate the DSC data. This results in quantitative estimates of the relative amounts of these “phases” and their polymer compositions. Combining these results with TEM photos showing the spatial characteristics of the morphology, we can achieve a much greater understanding of the physical structure of the composite latex particles. In many cases we find that phase separation is far from complete at the end of the reaction process. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2790–2806, 2005     

Ray aberrations of two-dimensional oblique lattices on the self-image plane

We extend the geometrical theory of aberration for a self-imaging system to the case of two-dimensional oblique lattices. In our approach, the fundamental translation vectors of the lattice are not restricted in both length and orientation. Evaluating the disturbance of light through the oblique lattice under coherent illumination, we find the conditions of constraint which limit the self-imaging of the oblique lattice. Various types of oblique lattices are shown to obey the self-imaging conditions. We derive the equations to trace the optical paths of self-imaging rays and then analyze the ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of the corresponding actual ray. The ray aberrations are shown to disappear when the periods of the lattice are large compared with the wavelength of light. We find that the ray aberrations carried by self-imaged oblique lattices are totally undercorrected and the aberrated image patches are displaced along the direction tangent vector of a chief ray.     

Electrical conduction and optical properties of amorphous (Sb2Se3)100−xSnx thin films

The variation of DC electrical conductivity and the optical properties of thermally evaporated a- (Sb₂Se₃)_100−xSn_x thin films with temperature have been studied. It is found that the thermal activation energy decreases, while the optical gap first increases (up to x=1) and then decreases, with the increase in Sn content. These results have been explained by taking into consideration the structural modifications induced by the incorporation of Sn into the parent alloy. The variation in the conductivity prefactor (σ_o) with Sn addition indicates a change in the dominant conduction transport mechanism from extended states to localized states. An experimental correlation between the activation energy and the pre-exponential factor has been observed, indicating the validity of Meyer–Neldel rule in the studied samples.     

Localization of a pair of bound particles in a random potential

We study the localization length l_c of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle. For a pair with many bound states N the localization length is proportional to N, independently of the form of the two particle interaction. For the case of two bound states, we present an exact solution for the corresponding Fokker–Planck equation and demonstrate that l_c depends sensitively on the shape of the interaction potential and the symmetry of the bound state wave functions.     

Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.