Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate

We present an \textit{exactly solvable} model of a monomer-monomer $A + B \to \emptyset$ reaction on a 2D inhomogeneous, catalytic substrate and study the equilibrium properties of the two-species adsorbate. The substrate contains randomly placed catalytic bonds of mean density $q$ which connect neighboring adsorption sites. The interacting $A$ and $B$ (monomer) species undergo continuous exchanges with corresponding adjacent gaseous reservoirs. A reaction $A + B \to \emptyset$ takes place instantaneously if $A$ and $B$ particles occupy adsorption sites connected by a catalytic bond. We find that for the case of \textit{annealed} disorder in the placement of the catalytic bonds the reaction model under study can be mapped onto the general spin $S = 1$ (GS1) model. Here we concentrate on a particular case in which the model reduces to an exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys. Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986)) and derive an exact expression for the disorder-averaged equilibrium pressure of the two-species adsorbate. We show that at equal partial vapor pressures of the $A$ and $B$ species this system exhibits a second-order phase transition which reflects a spontaneous symmetry breaking with large fluctuations and progressive coverage of the entire substrate by either one of the species.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Binary Reactive Adsorbate on a Random Catalytic Substrate

We study the equilibrium properties of a model for a binary mixture of catalytically-reactive monomers adsorbed on a two-dimensional substrate decorated by randomly placed catalytic bonds. The interacting $A$ and $B$ monomer species undergo continuous exchanges with particle reservoirs and react ($A + B \to \emptyset$) as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For the case of annealed disorder in the placement of the catalytic bonds this model can be mapped onto a classical spin model with spin values $S = -1,0,+1$, with effective couplings dependent on the temperature and on the mean density $q$ of catalytic bonds. This allows us to exploit the mean-field theory developed for the latter to determine the phase diagram as a function of $q$ in the (symmetric) case in which the chemical potentials of the particle reservoirs, as well as the $A-A$ and $B-B$ interactions are equal.Comment: 12 pages, 4 figure

Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain

We present an exact solution describing equilibrium properties of the catalytically-activated A + A \to 0 reaction taking place on a one-dimensional lattice, where some of the sites possess special "catalytic" properties. The A particles undergo continuous exchanges with the vapor phase; two neighboring adsorbed As react when at least one of them resides on a catalytic site (CS). We consider three situations for the CS distribution: regular, annealed random and quenched random. For all three CS distribution types, we derive exact results for the disorder-averaged pressure and present exact asymptotic expressions for the particles' mean density. The model studied here furnishes another example of a 1D Ising-type system with random multi-site interactions which admits an exact solution.Comment: 7 pages, 3 Figures, appearing in Europhysics Letter

Pattern Formation on Trees

Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the nodes of a tree is described by a nonlinear map, given rise to a coupled map lattice system. The coupling is expressed by a matrix whose eigenvectors constitute a basis on which spatial patterns on trees can be expressed by linear combination. The spectrum of eigenvalues of the coupling matrix exhibit a nonuniform distribution which manifest itself in the bifurcation structure of the spatially synchronized modes. These models may describe reaction-diffusion processes and several other phenomena occurring on heterogeneous media with hierarchical structure.Comment: Submitted to Phys. Rev. E, 15 pages, 9 fig

Analytical model of brittle destruction based on hypothesis of scale similarity

The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys the power law with the exponent between -4 and -1. The model of destruction has much in common with the fractal theory. The power exponent can be expressed in terms of the fractal dimension. Reasonable assumptions on the shape of fragments concretize the power exponent, and vice versa possible destruction laws can be inferred on the basis of measured size distributions.Comment: 10 pages, 3 figure

Ceria Entrapped Palladium Novel Composites for Hydrogen Oxidation Reaction in Alkaline Medium

A new heterogeneous catalyst for hydrogen oxidation reaction (HOR), metallic palladium within which nanoparticles of ceria are entrapped, CeO2@Pd, is described. Its preparation is based on a new materials methodology of molecular doping of metals. The metallic matrix, which encages the nanoparticles, is prepared in foam architecture, to ensure easy molecular diffusion. Characterization of the structural properties of the CeO2@Pd composite using SEM, STEM, TEM, XRD, EXAFS and nitrogen adsorption reveals its morphological architecture, which leads to improved catalytic activity. In-situ electrochemical and H2 temperature-programmed reduction (H2-TPR) spectra provide direct experimental evidence of the weakening of Pd‒H bond in the CeO2@Pd composites, relative to pure (undoped) Pd catalysts. Gas diffusion electrodes based on the entrapped CeO2@Pd catalysts demonstrated one order of magnitude higher activity than pure Pd analog in the HOR reaction in an alkaline medium

How the geometry makes the criticality in two - component spreading phenomena?

We study numerically a two-component A-B spreading model (SMK model) for concave and convex radial growth of 2d-geometries. The seed is chosen to be an occupied circle line, and growth spreads inside the circle (concave geometry) or outside the circle (convex geometry). On the basis of generalised diffusion-annihilation equation for domain evolution, we derive the mean field relations describing quite well the results of numerical investigations. We conclude that the intrinsic universality of the SMK does not depend on the geometry and the dependence of criticality versus the curvature observed in numerical experiments is only an apparent effect. We discuss the dependence of the apparent critical exponent $\chi_{a}$ upon the spreading geometry and initial conditions.Comment: Uses iopart.cls, 11 pages with 8 postscript figures embedde

On the robustness of scale invariance in SOC models

A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The system is critical only at a special point Jc in the coupling parameter space. However, the critical region around this point, where approximate scale invariance holds, is very large, suggesting a mechanism for explaining the ubiquity of scale invariance in Nature.Comment: 6 pages, 4 figures; submitted to Physical Review E; http://link.aps.org/doi/10.1103/PhysRevE.59.496

Numerical study of multilayer adsorption on fractal surfaces

We report a numerical study of van der Waals adsoprtion and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distributin of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to crossover effects, consistent with the findings of recent experiments. The effects of pore coupling and curvature dependent surface tension were also studied.Comment: 11 pages, 3 figure

Fractal Nanotechnology

Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces