Phase Transition in Two Species Zero-Range Process

We study a zero-range process with two species of interacting particles. We show that the steady state assumes a simple factorised form, provided the dynamics satisfy certain conditions, which we derive. The steady state exhibits a new mechanism of condensation transition wherein one species induces the condensation of the other. We study this mechanism for a specific choice of dynamics.Comment: 8 pages, 3 figure

Tackling Salinity in Sustainable Agriculture—What Developing Countries May Learn from Approaches of the Developed World

Soil salinity is a common problem of the developing world as well as the developed world. However, the pace to reduce salinity is much slower in the developing world. The application of short-term approaches with an unsustainable supply of funds are the major reasons of low success. In contrast, the developed world has focused on long-term and sustainable techniques, and considerable funds per unit area have been allocated to reduce soil salinity. Here, we review the existing approaches in both worlds. Approaches like engineering and nutrient use were proven to be unsustainable, while limited breeding and biosaline approaches had little success in the developing countries. In contrast, advanced breeding and genetics tools were implemented in the developed countries to improve the salinity tolerance of different crops with more success. Resultantly, developed countries not only reduced the area for soil salinity at a higher rate, but more sustainable and cheaper ways to resolve the issue were implemented at the farmers’ field. Similarly, plant microbial approaches and the application of fertigation through drip irrigation have great potential for both worlds, and farmer participatory approaches are required to obtain fruitful outcomes. In this regard, a challenging issue is the transition of sustainable approaches from developed countries to developing ones, and possible methods for this are discussed

Conditional Distribution of Heavy Tailed Random Variables on Large Deviations of their Sum

It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of their sum is observed.Comment: Results on local conditioning adde

Analytic study of clustering in shaken granular material using zero-range processes

We show that models used to described granular clustering due to vertical shaking belong to the class of zero-range processes. This correspondence allows us to derive exactly in a very easy and straightforward manner a number of properties of the models like particle distribution functions, phase diagram, and characteristic time of clusterization.Comment: 4 pages, 3 figures submitted to PR

Factorised steady states for multi-species mass transfer models

A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and sufficient conditions on the mass transfer dynamics under which the steady state factorises. We generalise the model to mass transfer on arbitrary lattices and present sufficient conditions for factorisation. In both cases, explicit results for random sequential update and continuous time limits are given.Comment: 11 page

Condensation for a fixed number of independent random variables

A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal density \rho_c<\infty. The distribution of particles conditioned on the total number of particles equal to n does not depend on \phi (canonical ensemble). For fixed m, as n goes to infinity the canonical ensemble measure behave as follows: removing the site with the maximal number of particles, the distribution of particles in the remaining sites converges to the grand canonical measure with density \rho_c; the remaining particles concentrate (condensate) on a single site.Comment: 6 page

Rigorous results on spontaneous symmetry breaking in a one-dimensional driven particle system

We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting from an empty initial lattice, the system enters a symmetry broken state after some time T_1 through an amplification loop of initial fluctuations. It remains in the symmetry broken state for a time T_2 through a traffic jam effect. Applying a simple martingale argument, we obtain rigorous asymptotic estimates for the expected times ~ L ln(L) and ln() ~ L, where L is the system size. The actual value of T_1 depends strongly on the initial fluctuation in the amplification loop. Numerical simulations suggest that T_2 is exponentially distributed with a mean that grows exponentially in system size. For the phase transition line we argue and confirm by simulations that the flipping time between sign changes of the difference of particle numbers approaches an algebraic distribution as the system size tends to infinity.Comment: 23 pages, 7 figure

UV-B Exposure of Black Carrot (<i>Daucus carota</i> ssp. <i>sativus</i> var. <i>atrorubens</i>) Plants Promotes Growth, Accumulation of Anthocyanin, and Phenolic Compounds

© The Author(s).Black carrot (Daucus carota L. ssp. sativus var. atroburens) is a root vegetable with anthocyanins as major phenolic compounds. The accumulation of phenolic compounds is a common response to UV-B exposure, acting as protective compounds and as antioxidants. In the present study, black carrot plants grown under a 12-h photoperiod were supplemented with UV-B radiation (21.6 kj m−2 day−1) during the last two weeks of growth. Carrot taproots and tops were harvested separately, and the effect of the UV-B irradiance was evaluated in terms of size (biomass and length), total monomeric anthocyanin content (TMC), total phenolic content (TPC), and phytohormones levels. The results showed that UV-B irradiance promoted plant growth, as shown by the elevated root (30%) and top (24%) biomass, the increased TMC and TPC in the root (over 10%), and the increased TPC of the top (9%). A hormone analysis revealed that, in response to UV-B irradiance, the levels of abscisic acid (ABA), jasmonic acid (JA), and salicylic acid (SA) decreased in tops while the level of the cytokinins cis-zeatin (cZ) and trans-zeatinriboside (tZR) increased in roots, which correlated with an amplified growth and the accumulation of anthocyanins and phenolic compounds. Beyond the practical implications that this work may have, it contributes to the understanding of UV-B responses in black carrotThis research was funded by the Danish Ministry of Science, Innovation, and Education grant number 6111-00240B and “Fundación Séneca” of the Agency of Science and Technology of the Region of Murcia grant number 20405/SF/17.Peer reviewe