Exactly solvable models through the generalized empty interval method: multi-species and more-than-two-site interactions

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E^{\mathbf a}_n(t)$'s, the expectation value of the product of certain linear combination of the number operators on $n$ consecutive sites at time $t$.Comment: 10 pages, LaTe

Static- and dynamical-phase transition in multidimensional voting models on continua

A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of the system are such that two adjacent sites, one empty the other occupied, may evolve to a state where both of these sites are either empty or occupied. The continuum version of this model in a Ddimensional region with boundary is studied, and two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the relaxation of the system toward its stationary state. Based on the first behavior, the static phase transition (discontinuous changes in the stationary profiles of the system) is studied. Based on the second behavior, the dynamical phase transition (discontinuous changes in the relaxation-times of the system) is studied. It is shown that the static phase transition is induced by the bulk reactions only, while the dynamical phase transition is a result of both bulk reactions and boundary conditions.Comment: 10 pages, LaTeX2

Exactly solvable models through the empty interval method

The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the probability that $n$ consecutive sites are empty ($E_n$), has been exactly obtained. In the thermodynamic limit, the large-time behavior of the system has also been investigated. Releasing the translational invariance of the initial conditions, the evolution equation for the probability that $n$ consecutive sites, starting from the site $k$, are empty ($E_{k,n}$) is obtained. In the thermodynamic limit, the large time behavior of the system is also considered. Finally, the continuum limit of the model is considered, and the empty-interval probability function is obtained.Comment: 12 pages, LaTeX2

The Effect of Fertilizer Treatments at Three Compactness Levels on Qualitative Traits of Sport Lawn in Winter Season

Lawn quality, which introduces by good color, density, uniformity and texture varies depending on the species, maintenance operation, and time of the year. In the current study, the effect of organic fertilizers containing Leaf Mold (LM), Rice Husk (RH), manure, Spent Mushroom Compost (SMC), a mixture of LM, RH and SMC (mixture 1), a mixture of LM, RH and manure (mixture 2), with the ratio of 1:1:1 and control (no fertilizer) at three levels of soil compactness including roller weights of 36, 56, 76 kilograms on qualitative traits of sport lawn were investigated in winter season. Treatments were applied in a strip plot design with three replications, in research farm of Gorgan University of Agricultural Sciences and Natural Resources during fall 2008-2009. According to achieved results, manure and RH treatments in first and second compaction and manure treatment in third compaction level showed the highest amount of chlorophyll content. In visual assessment, the highest and lowest of lawn quality was observed in the manure and the control treatment respectively. In first and second compaction, the maximum height was observed in manure treatment. Control and LM treatments showed the minimum height. In third compaction, maximum and minimum heights were associated with manure and control treatment respectively

Phase transition in an asymmetric generalization of the zero-temperature q-state Potts model

An asymmetric generalization of the zero-temperature q-state Potts model on a one dimensional lattice, with and without boundaries, has been studied. The dynamics of the particle number, and specially the large time behavior of the system has been analyzed. In the thermodynamic limit, the system exhibits two kinds of phase transitions, a static and a dynamic phase transition.Comment: 11 pages, LaTeX2

Effect of Several Organic Fertilizers Along with Some Soil Compactness Levels on Nutrients Content of Sport Lawn in Fall Season

The lawn has an incredible role in designing and construction of landscape areas and lawn bed provides aeration, moisture and nutrients, which is essential for having an acceptance lawn, so the role of organic matter and degree of soil compactness need to be studied. In the current study, the effect of some bed mixtures including Leaf Mold (LM), Rice Husk (RH), manure, Spent Mushroom Compost (SMC), a mixture of LM, RH and SMC (mixture 1), a mixture of LM, RH and manure (mixture 2) with the ratio of 1:1:1 and control (no fertilizer), also the effect of some different soil compactness (roller weights of 36, 56 and 76 kilograms) on the content of some nutrients of sport lawn in fall season were investigated. Hence, an experiment was conducted at the strip plot design with three replications, in research farm of Gorgan University of Agricultural Sciences and Natural Resources during 2008-09. According to the results of this study, interaction of fertilizer and soil compactness was significant for most measured factors. The manure and control treatments showed the most and the least amount of nitrogen in all compactness treatments respectively. The manure and SMC treatments and also treatments containing these organic matters increased plant phosphorus content in comparing with RH, LM and control treatments. Also in three compactness, manure and SMC treatments showed more plant potassium in contrast to control

Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions

Autonomous multispecies systems with more-than-two-neighbor interactions are studied. Conditions necessary and sufficient for closedness of the evolution equations of the $n$-point functions are obtained. The average number of the particles at each site for one species and three-site interactions, and its generalization to the more-than-three-site interactions is explicitly obtained. Generalizations of the Glauber model in different directions, using generalized rates, generalized number of states at each site, and generalized number of interacting sites, are also investigated.Comment: 9 pages, LaTeX2

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