Stochastic self-assembly of incommensurate clusters

We examine the classic problem of homogeneous nucleation and growth by deriving and analyzing a fully discrete stochastic master equation. Upon comparison with results obtained from the corresponding mean-field Becker-D\"{o}ring equations we find striking differences between the two corresponding equilibrium mean cluster concentrations. These discrepancies depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass incommensurability arises, a single remainder particle can "emulsify" or "disperse" the system by significantly broadening the mean cluster size distribution. This finite-sized broadening effect is periodic in the total mass of the system and can arise even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. For such finite ratios we show that homogeneous nucleation in the limit of large, closed systems is not accurately described by classical mean-field mass-action approaches.Comment: 5 pages, 4 figures, 1 tabl

Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.Comment: 12 pages, 4 figure

Climate Change Effects on Apple and Sour Cherry Phenology in a Gene Bank Plantation of Hungary

The trees observed were grown at Újfehértó, Eastern Hungary in a gene bank with 586 apple and 3 sour cherry cultivars. Each of the cultivars was monitored for its dates of: the beginning of bloom, main bloom and the end of bloom phenophases separately. In the present study, the interactions between the above mentioned phenomena are presented and numerically defined. Results presented proved that the dynamics of weather variables exert measurable effects on the development of fruits. We can find significant correlation between the maximum temperature of March and blooming time of the apple and sour cherry cultivars. If the temperature is increasing in the future the development stages of fruit trees will also shift to an earlier time. It is a serious problem in fruit farming, because the early climatic risk of frost occurrence is generally higher than that of in later times of a year. So, we will need to use more effective protection technologies and new extreme weather tolerant fruit varieties in the future. We should also pay more attention to the time intervals between the blooming and maturity, because the length and appearance of phenological phases have significant influences on quantitative and qualitative parameters of fruits