Non-Self-Similar Behavior in the LSW Theory of Ostwald Ripening

The classical Lifshitz–Slyozov–Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. Here we consider the long-time behavior of measure-valued solutions for systems in which particle size is uniformly bounded, i.e., for initial measures of compact support. We prove that the long-time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to other self-similar solutions, and conditional stability theorems for some such solutions. For a dense set of initial data, convergence to any self-similar solution is impossible.     

Influence of Quantal and Statistical Fluctuations on Phase Transitions in Finite Nuclei

Investigations on thermal evolution of pairing-phase transition and shape-phase transition in light nuclei are made as a function of pair gap, deformation, temperature and angular momentum using a finite temperature statistical approach with main emphasis to fluctuations. The occurrence of a peak structure in the specific heat predicted as signals of the pairing-phase and shape-phase transitions are reviewed and it is found that they are not actually true phase
transitions and it is only an artifact of the mean field models. Since quantal number and spin fluctuations and statistical fluctuations in pair gap, deformation degrees of freedom and energy when incorporated, it wash out the pairing-phase transition and smooth out the shape-phase transition. Phase transitions due to collapse of pair gap and deformation is discussed and a clear picture of pairing-phase transition in light nuclei is presented in which pairing transition is reconciled.     

Fluctuations induced extinction and stochastic resonance effect in a model of tumor growth with periodic treatment

We investigate a stochastic model of tumor growth derived from the catalytic Michaelis-Menten reaction with positional and environmental fluctuations under subthreshold periodic treatment. Firstly, the influences of environmental fluctuations on the treatable stage are analyzed numerically. Applying the standard theory of stochastic resonance derived from the two-state approach, we derive the signal-to-noise ratio (SNR) analytically, which is used to measure the stochastic resonance phenomenon. It is found that the weak environmental fluctuations could induce the extinction of tumor cells in the subthreshold periodic treatment. The positional stability is better in favor of the treatment of the tumor cells. Besides, the appropriate and feasible treatment intensity and the treatment cycle should be highlighted considered in the treatment of tumor cells.     

The Asymmetric Exclusion Process Revisited: Fluctuations and Dynamics in the Domain Wall Picture

We investigate the total asymmetric exclusion process by analyzing the dynamics of the shock. Within this approach we are able to calculate the fluctuations of the number of particles and density profiles not only in the stationary state but also in the transient regime. We find that the analytical predictions and the simulation results are in excellent agreement.     

Stochastic models of firstorder nonequilibrium phase transitions in chemical reactions

The steady states of a simple nonlinear chemical system kept far from equilibrium are analyzed. A standard macroscopic analysis shows that the nonlinearity introduces an instability causing a transition analogous to a thermodynamic first-order phase transition. Near this transition the system exhibits hysteresis between two alternative steady states. Fluctuations are introduced into this model using a stochastic master equation. The solution of this master equation is unique, preventing two alternative exactly stable states. However, a quasi-hysteresis occurs involving transitions between alternative metastable steady states on a time scale that is longer than that of the fluctuations around the mean steady state values by a factor of the forme , where ø is the height of a generalized thermodynamic potential barrier between the two states. In the thermodynamic limit this time scale tends to infinity and we have essentially two alternative stable steady states.     

On anomalous diffusion of fractal clusters under certain realistic physical conditions

Summary Diffusion of a fractal cluster of dimensiond _f in a three-dimensional space is investigated. The diffusion process is assumed to be modelled by a standard parabolic diffusion equation, although a more general case represented by the Fokker-Planck-Kolmogoroff equation is also introduced. The mean-square displacement of the cluster mass centre is analysed and its anomalous behaviour is presented and critically discussed. The results obtained can be applied to describe some effects which may occur during the diffusion-limited cluster-cluster aggregation process, especially when the viscosity of the solvent is changed in time and/or a directed transport of clusters is present in the system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

On the surface configuration of solids in relation to the surface free enthalpy excess and its consequences in phase transitions

Summary In previous studies the average number of neighbors (n _avrg) of an atom in the surface phase was found to increase by about (5÷20)% between 0 K and the melting temperature for all solid chemical elements in the periodic table. This increment makes the solid surface “geometrically impossible” to exist at the melting temperature. The latter results in the collapse of crystal structure, beginning with the formation of liquid in the surface layers. Ratio of critical and melting temperature is also discussed.     

On the Correspondence between Subshifts of Finite Type and Statistical Mechanics Models

Several classical problems in symbolic dynamics concern the characterization of the simplex of measures of maximal entropy. For subshifts of finite type in higher dimensions, methods of statistical mechanics are ideal for dealing with these problems. R. Burton and J. Steif developed a strategy to construct examples of strongly irreducible subshifts of finite type admitting several measures of maximal entropy. This strategy exploits a correspondence between equilibrium statistical mechanics and symbolic dynamics—a correspondence which was later formalized by O. Häggström. In this paper, we revisit and discuss this correspondence with the aim of presenting a simplified version of it and present some applications of rigorous results concerning the Potts model and the six-vertex model to symbolic dynamics, illustrating in this way the possibilities of this correspondence.     

On the phase stability of charged colloidal solutions modelled in terms of a simplified rigid-ion potential

Summary The phase stability of ionic multicomponent fluids is investigated through the Mean Spherical Approximation in the framework of the well-known Restricted Primitive Model of electrolytes. Phase stability conditions are obtained by studying the behaviour of the isothermal compressibility which diverges at the liquid-vapour spinodal. The model parameters are chosen so as to represent charged colloidal solutions with a big polyion and small counterions; the case in which a third neutral-particle species is present, possibly modelling the solvent, is also investigated. The MSA predictions turn out to be in good qualitative agreement with previous hypernetted-chain calculations for the same system; the simplicity and flexibility of the theory also allows a determination of the stability conditions for various assignments of the physical parameters which can reasonably mimic realistic configurations of charged colloidal solutions. Possible extensions and improvements of the present theoretical study, and a systematic procedure to assess its predictions for practical applications, are also shortly discussed. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

On the Becker/Döring Theory of Nucleation of Liquid Droplets in Solids

Nucleation of liquid precipitates in semi-insulating GaAs is accompanied by deviatoric stresses resulting from the liquid/solid misfit. A competition of surface tension and stress deviators at the interface determines the nucleation barrier.The evolution of liquid precipitates in semi-insulating GaAs is due to diffusional processes in the vicinity of the droplet. The diffusion flux results from a competition of chemical and mechanical driving forces.The size distribution of the precipitates is determined by a Becker--Dö-ring system. The study of its properties in the presence of deviatoric stresses is the subject of this study. The main tasks of this study are: (i) We propose a new Becker/Döring model that takes thermomechanical coupling into account. (ii) We compare the current model with already existing models from the literature. Irrespective of the incorporation of mechanical stresses, the various models differ due to different environments where the evolution of precipitates takes place. (iii) We determine the structure of equilibrium solutions according to the Becker/Döring model, and we compare these solutions with those that result from equilibrium thermodynamics.     

Fluctuations and finite-size effect in the Bak-Sneppen model

The self-organized criticality in the nearest-neighbor version of the Bak-Sneppen model is investigated from the event-by-event fluctuations of the mean fitness. The finite-size effect on the evolution of the critical state is shown, and a scaling solution to the gap equation for an infinite one-dimensional lattice is given numerically for the first time. The mean lifetime of avalanches is presented as a function of the gap from the solution. The critical value of the gap and an exponent are calculated from the solution. Received 10 December 2000 and Received in final form 18 January 2001     

On phase diagrams and on cBN formation in the system BN-Ca3B2N4

Abstract

The phase diagrams of Ca₃B₂N₄ and of the system BN-Ca₃B₂N₄ has been studied by high pressure differential thermal analysis Ca₃B₂N₄ has 3 structural phases and melts at higher temperature. The system BN-Ca₃B₂N₄ formes an eutectic melt and cBN is synthesized by nucleation and crystal growth.     

Fluctuations and correlations in the string clustering approach

The fluctuations due to the clustering of color sources can explain the behaviour of the scaled multiplicity variance and transverse momentum fluctuations with centrality. They also predict a nonmonotonic behaviour with centrality for the multiplicity associated to high-p_T events. The clustering of color sources gives rise to an increase in the long-range correlations with centrality as well as to a supression at high centrality with respect to superposition models.     

Novel approaches to parallelism in soft-matter problems

Summary We outline a novel method of exploiting distributed computational resources to study problems in soft-matter science. We have applied our method to simulations of polymers, including hydrodynamic effects. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Properties of exceptional points in some many body models

The Lipkin model is a popular toy model, first used in nuclear physics, to understand quantum phase transitions including symmetry breaking. However, the thermodynamic limit, that is the limit of large particle numbers, appears rather elusive. The pattern of the exceptional points of the model, in particular their behavior with increasing particle numbers, is presented. They may give a clue as to the properties of the Lipkin Hamiltonian in the thermodynamic limit. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

The processes of ordering and formation of two-dimensional glasses at metal surfaces

Using the experimental results obtained for the Dy-Mo(1 1 2) system, we discuss the possibilities and mechanisms of formation of two-dimensional (2D) glasses on metal surfaces. It has been found that in the coverage range 0.07 < θ < 0.58, ordered Dy superstructures formed and observed at T < 400 K are irreversibly destroyed by annealing to higher temperatures and turn into an amorphous (glass) structure on cooling. It is supposed that this conversion is caused by the formation, at T > 400 K, of a Dy-Mo surface alloy in which the rate of Dy surface diffusion is strongly reduced in comparison with its value in the absence of alloying. As a result, the mobility of Dy adatoms becomes too low at the temperatures corresponding to the ordered equilibrium state of the surface, and this state cannot be achieved in reasonable relaxation time. This interpretation is corroborated by the experimental data on substantial suppression of surface diffusion in some coadsorbed layers. Since surface glasses contact with ordered (crystalline) substrates, their structure may have a peculiar character different from that of “conventional” metal glasses. Surface glasses can find a number of applications as rather stable systems that combine low dimensionality, specific electronic structure of their constituents and extremely high density of defects.