Dynamic Scaling of an Adsorption-Diffusion Process on Fractals

A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic scaling law on fractal surfaces. The adsorption-diffusion process obeys the fracton dynamics on the fractal surfaces.Comment: 9 pages, 7 figure

Soluble two-species diffusion-limited Models in arbitrary dimensions

A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the equations of motion of the correlation functions close, are determined explicitly. This property allows to solve for the density and the two-point (two-time) correlation functions in arbitrary dimension for both, a translation invariant class and another one where translation invariance is broken. Systems with correlated as well as uncorrelated, yet random initial states can also be treated exactly by this approach. We discuss the asymptotic behavior of density and correlation functions in the various cases. The dynamics studied is very rich.Comment: 28 pages, 0 figure. To appear in Physical Review E (February 2001

Equilibrium Properties of A Monomer-Monomer Catalytic Reaction on A One-Dimensional Chain

We study the equilibrium properties of a lattice-gas model of an $A + B \to 0$ catalytic reaction on a one-dimensional chain in contact with a reservoir for the particles. The particles of species $A$ and $B$ are in thermal contact with their vapor phases acting as reservoirs, i.e., they may adsorb onto empty lattice sites and may desorb from the lattice. If adsorbed $A$ and $B$ particles appear at neighboring lattice sites they instantaneously react and both desorb. For this model of a catalytic reaction in the adsorption-controlled limit, we derive analytically the expression of the pressure and present exact results for the mean densities of particles and for the compressibilities of the adsorbate as function of the chemical potentials of the two species.Comment: 19 pages, 5 figures, submitted to Phys. Rev.

Coupled Maps on Trees

We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. As the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to effect. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatio-temporal structures. We find that a mean-field like treatment is valid on this (effectively infinite dimensional) lattice.Comment: latex file (25 pages), 4 figures included. To be published in Phys. Rev.

Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers

The center-bound excitonic diffusion on dendrimers subjected to several types of non-homogeneous funneling potentials, is considered. We first study the mean-first passage time (MFPT) for diffusion in a linear potential with different types of correlated and uncorrelated random perturbations. Increasing the funneling force, there is a transition from a phase in which the MFPT grows exponentially with the number of generations $g$, to one in which it does so linearly. Overall the disorder slows down the diffusion, but the effect is much more pronounced in the exponential compared to the linear phase. When the disorder gives rise to uncorrelated random forces there is, in addition, a transition as the temperature $T$ is lowered. This is a transition from a high-$T$ regime in which all paths contribute to the MFPT to a low-$T$ regime in which only a few of them do. We further explore the funneling within a realistic non-linear potential for extended dendrimers in which the dependence of the lowest excitonic energy level on the segment length was derived using the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT grows initially linearly with $g$ but crosses-over, beyond a molecular-specific and $T$-dependent optimal size, to an exponential increase. Finally we consider geometrical disorder in the form of a small concentration of long connections as in the {\it small world} model. Beyond a critical concentration of connections the MFPT decreases significantly and it changes to a power-law or to a logarithmic scaling with $g$, depending on the strength of the funneling force.Comment: 13 pages, 9 figure

A genetic contribution from the Far East into Ashkenazi Jews via the ancient Silk Road

Contemporary Jews retain a genetic imprint from their Near Eastern ancestry, but obtained substantial genetic components from their neighboring populations during their history. Whether they received any genetic contribution from the Far East remains unknown, but frequent communication with the Chinese has been observed since the Silk Road period. To address this issue, mitochondrial DNA (mtDNA) variation from 55,595 Eurasians are analyzed. The existence of some eastern Eurasian haplotypes in eastern Ashkenazi Jews supports an East Asian genetic contribution, likely from Chinese. Further evidence indicates that this connection can be attributed to a gene flow event that occurred less than 1.4 kilo-years ago (kya), which falls within the time frame of the Silk Road scenario and fits well with historical records and archaeological discoveries. This observed genetic contribution from Chinese to Ashkenazi Jews demonstrates that the historical exchange between Ashkenazim and the Far East was not confined to the cultural sphere but also extended to an exchange of genes

PCR array and protein array studies demonstrate that IL-1β (interleukin-1β) stimulates the expression and secretion of multiple cytokines and chemokines in human adipocytes

The role of IL-1β in regulating the expression and secretion of cytokines and chemokines by human adipocytes was examined. Adipocytes were incubated with human IL-1β for 4 or 24 h. The expression of a panel of 84 cytokine/chemokine genes was probed using PCR arrays. IL-1β stimulated the expression of >30 cytokine/chemokine genes on the arrays; 15 showed >100-fold increases in mRNA at 4 or 24 h including CSF3, CXCL1, CXCL2, CXCL12 and IL8. CSF3 exhibited a 10,000-fold increase in mRNA at 4 h. ADIPOQ was among the genes whose expression was inhibited. Protein arrays were used to examine the secretion of cytokines/chemokines from adipocytes. IL-1β stimulated the secretion of multiple cytokines/chemokines including MCP-1, IL-8, IP-10, MIP-1α and MCP-4. The most responsive was IP-10, which exhibited a 5,000-fold increase in secretion with IL-1β. IL-1β is likely to play a substantial role in stimulating the inflammatory response in human adipocytes in obesity

Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let

Influence of auto-organization and fluctuation effects on the kinetics of a monomer-monomer catalytic scheme

We study analytically kinetics of an elementary bimolecular reaction scheme of the Langmuir-Hinshelwood type taking place on a d-dimensional catalytic substrate. We propose a general approach which takes into account explicitly the influence of spatial correlations on the time evolution of particles mean densities and allows for the analytical analysis. In terms of this approach we recover some of known results concerning the time evolution of particles mean densities and establish several new ones.Comment: Latex, 25 pages, one figure, submitted to J. Chem. Phy

Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A + A -> A, despite differences between the two models in other statistical measures, such as the interparticle distribution function