Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata

We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.Comment: 11 pages (plain TeX), 4 figures (PostScript), preprint OUTP-92-51

Far-from-equilibrium growth of thin films in a temperature gradient

The irreversible growth of thin films under far-from-equilibrium conditions is studied in $(2+1)-$dimensional strip geometries. Across one of the transverse directions, a temperature gradient is applied by thermal baths at fixed temperatures between $T_1$ and $T_2$, where $T_1<T_c^{hom}<T_2$ and $T_c^{hom}=0.69(1)$ is the critical temperature of the system in contact with an homogeneous thermal bath. By using standard finite-size scaling methods, we characterized a continuous order-disorder phase transition driven by the thermal bath gradient with critical temperature $T_c=0.84(2)$ and critical exponents $\nu=1.53(6)$, $\gamma=2.54(11)$, and $\beta=0.26(8)$, which belong to a different universality class from that of films grown in an homogeneous bath. Furthermore, the effects of the temperature gradient are analyzed by means of a bond model that captures the growth dynamics. The interplay of geometry and thermal bath asymmetries leads to growth bond flux asymmetries and the onset of transverse ordering effects that explain qualitatively the shift in the critical temperature.Comment: 4 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1207.253

Universality in adsorbate ordering on nanotube surfaces

Numerically efficient transfer matrix technique for studying statistics of coherent adsorbates on small nanotubes has been developed. In the framework of a realistic microscopic model fitted to the data of ab initio calculations taken from literature sources, the ordering of potassium adsorbate on (6,0) single-walled carbon nanotube has been studied. Special attention has been payed to the phase transition-like abrupt changes seen in the adsorption isotherms at low temperature. It has been found that the behavior during the transitions conforms with the universality hypothesis of the theory of critical phenomena and is qualitatively the same as in the one dimensional Ising model. Quantitatively the critical behavior can be fully described by two parameters. Their qualitative connection with the properties of interphase boundaries is suggested but further research is needed to develop a quantitative theory.Comment: 11 pages, 6 figures; some typos correcte

On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems

In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with generalized aspect ratio $\rho > 1$ to a system with $\rho < 1$. The symmetry is formulated within a finite-size scaling theory, and expressions for several universal amplitude ratios are derived. The predictions are confirmed within the exactly solvable weakly anisotropic two-dimensional Ising model and are checked within the two-dimensional dipolar in-plane Ising model using Monte Carlo simulations. This model shows a strongly anisotropic phase transition with different correlation length exponents $\nu_{||} \neq \nu_\perp$ parallel and perpendicular to the spin axis.Comment: RevTeX4, 4 pages, 3 figure

No-go theorem on spontaneous parity breaking revisited

An essential assumption in the Vafa and Witten's theorem on P and CT realization in vector-like theories concerns the existence of a free energy density in Euclidean space in the presence of any external hermitian symmetry breaking source. We show how this requires the previous assumption that the symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is plausible, actually a theorem is still lacking.Comment: Talk presented at LATTICE99(Theoretical Developments),3 pages. Latex using espcrc2.st

Interfacial friction between semiflexible polymers and crystalline surfaces

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities the decay of the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.Comment: 31 pages, 12 figure

Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods near a liquid-liquid critical temperature $T_c$. Choosing equal chemical potentials for the two species, the SGMC switches identities (${\rm A} \to {\rm B} \to {\rm A}$) to generate well-equilibrated configurations of the system on the coexistence curve for $T<T_c$ and at the critical concentration, $x_c=1/2$, for $T>T_c$. A finite-size scaling analysis of the concentration susceptibility above $T_c$ and of the order parameter below $T_c$ is performed, varying the number of particles from N=400 to 12800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.Comment: 35 pages, 13 figure

Non-monotonous crossover between capillary condensation and interface localisation/delocalisation transition in binary polymer blends

Within self-consistent field theory we study the phase behaviour of a symmetric binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localisation/delocalisation transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. The crossover between these qualitatively different limiting behaviours occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field.Comment: to appear in Europhys.Let