Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input

We investigate with the help of analytical and numerical methods the reaction A+A->A on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for large x, the particle concentration c(x) behaves like As/x (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opposite direction the particle concentration behaves like Aa/sqrt(x). The constants As and Aa are independent of the input and the two coagulation rates. The universality of Aa comes as a surprise since in the asymmetric case the system has a massive spectrum.Comment: 27 pages, LaTeX, including three postscript figures, to appear in J. Stat. Phy

Concentration for One and Two Species One-Dimensional Reaction-Diffusion Systems

We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The coagulation (A + A -> A) or the annihilation (A + A -> 0) models can be mapped onto systems in which both processes are allowed. With the help of the coagulation-decoagulation model results for some death-decoagulation and annihilation-creation systems are given. We also find a reaction-diffusion system which is equivalent to the two species annihilation model (A + B ->0). Besides we present numerical results of Monte Carlo simulations. An accurate description of the effects of the reaction rates on the concentration in one-species diffusion-annihilation model is made. The asymptotic behavior of the concentration in the two species annihilation system (A + B -> 0) with symmetric initial conditions is studied.Comment: 20 pages latex, uuencoded figures at the en

Exactly solvable models through the empty interval method, for more-than-two-site interactions

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E_n(t)$'s, the probability that $n$ consecutive sites are empty at time $t$. The general method of solving the time evolution equation is discussed. As an example, a system with next-nearest-neighbor interaction is studied.Comment: 19 pages, LaTeX2

The duality relation between Glauber dynamics and the diffusion-annihilation model as a similarity transformation

In this paper we address the relationship between zero temperature Glauber dynamics and the diffusion-annihilation problem in the free fermion case. We show that the well-known duality transformation between the two problems can be formulated as a similarity transformation if one uses appropriate (toroidal) boundary conditions. This allow us to establish and clarify the precise nature of the relationship between the two models. In this way we obtain a one-to-one correspondence between observables and initial states in the two problems. A random initial state in Glauber dynamics is related to a short range correlated state in the annihilation problem. In particular the long-time behaviour of the density in this state is seen to depend on the initial conditions. Hence, we show that the presence of correlations in the initial state determine the dependence of the long time behaviour of the density on the initial conditions, even if such correlations are short-ranged. We also apply a field-theoretical method to the calculation of multi-time correlation functions in this initial state.Comment: 15 pages, Latex file, no figures. To be published in J. Phys. A. Minor changes were made to the previous version to conform with the referee's Repor

Yeast XRS2 and human NBN gene: Experimental evidence for homology using codon optimized cDNA

The genes, XRS2 in Saccharomyces cerevisiae and NBN in mammals, have little sequence identity at the amino acid level. Nevertheless, they are both found together with MRE11 and RAD50 in a highly conserved protein complex which functions in the repair of DNA double-strand breaks. Here, we have examined the evolutionary and functional relationship of these two genes by cross-complementation experiments. These experiments necessitated sequence correction for specific codon usage before they could be successfully conducted. We present evidence that despite extreme sequence divergence nibrin can, at least partially, replace Xrs2 in the cellular DNA damage response, and Xrs2 is able to promote nuclear localization of MRE11 in NBS cells. We discuss that the extreme sequence divergence reflects a unique adaptive pressure during evolution related to the specific eukaryotic role for both Xrs2 and nibrin in the subcellular localisation of the DNA repair complex. This, we suggest, is of particular relevance when cells are infected by viruses. The conflict hypothesis of co-evolution of DNA repair genes and DNA viruses may thus explain the very low sequence identity of these two homologous genes

Plasma zinc concentrations are depressed during the acute phase response in children with falciparum malaria

Plasma concentrations of some micronutrients are altered in the setting of acute infectious or inflammatory stress. Previous studies have provided conflicting evidence concerning the extent and direction of changes in plasma zinc concentrations during the acute phase response. We carried out an observational cohort study in 689 children enrolled in a randomized trial of zinc supplementation during acute falciparum malaria in order to evaluate the relation between plasma zinc concentration and the acute phase response. Plasma zinc was measured by atomic absorption spectrophotometry. On admission, 70% of all subjects had low plasma zinc (\u3c9.2 μmol/L). Multivariate analysis of predictors of admission plasma zinc showed that admission C-reactive protein (CRP), parasite density, and study site were the most important predictors. Predictors of changes in plasma zinc from admission to 72 h included baseline CRP, change in CRP, treatment group, study site, and baseline zinc concentration. In children with acute malaria infection, baseline plasma zinc concentrations were very low and were inversely correlated with CRP (r = -0.24, P \u3c 0.0001) and the degree of parasitemia (r = -0.19, P \u3c 0.0001). Even when CRP and time were taken into account, zinc supplementation increased plasma zinc concentration from admission to 72 h. When available, plasma zinc concentrations should be interpreted with concurrent measures of the acute phase response such as CRP. In children whose age, diet, and/or nutritional status place them at risk of zinc deficiency, those with low plasma zinc levels should be supplemented with oral zinc and followed for clinical and/or biochemical response. © 2005 American Society for Nutritional Sciences

Multispecies reaction-diffusion systems

Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large time behaviour of the average densities has also been obtained.Comment: LaTeX file, 15 pages, to appear in Phys. Rev.

EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and between stochastic and soluble {\em non-stochastic} models. The results agree with experiments on one-dimensional annihilation-coagulation processes.Comment: 15 pages, Latex. Some corrections made and an appendix adde

Phase transition in an asymmetric generalization of the zero-temperature Glauber model

An asymmetric generalization of the zero-temperature Glauber model on a lattice is introduced. The dynamics of the particle-density and specially the large-time behavior of the system is studied. It is shown that the system exhibits two kinds of phase transition, a static one and a dynamic one.Comment: LaTeX, 9 pages, to appear in Phys. Rev. E (2001