Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions

The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.Comment: 8 pages, 6 figure

Plasmon induced transparency in graphene based terahertz metamaterials

Plasmon induced transparency (PIT) effect in a terahertz graphene metamaterial is numerically and theoretically analyzed. The proposed metamaterial comprises of a pair of graphene split ring resonators placed alternately on both sides of a graphene strip of nanometer scale. The PIT effect in the graphene metamaterial is studied for different vertical and horizontal configurations. Our results reveal that there is no PIT effect in the graphene metamaterial when the centers of both the split ring resonators and the graphene strip are collinear to each other. This is a noteworthy feature, as the PIT effect does not vanish for similar configuration in a metal-based metamaterial structure. We have further shown that the PIT effect can be tuned by varying the Fermi energy of graphene layer. A theoretical model using the three level plasmonic system is established in order to validate the numerical results. Our studies could be significant in designing graphene based frequency agile ultra-thin devices for terahertz applications

Cluster formation and anomalous fundamental diagram in an ant trail model

A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35, L573 (2002)}), motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability of evaporation of pheromone, and the average speed of the ants varies non-monotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatio-temporal organization of the ants. We find that the observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density.Comment: 11 pages, REVTEX, with 11 embedded EPS file

Flow properties of driven-diffusive lattice gases: theory and computer simulation

We develop n-cluster mean-field theories (0 < n < 5) for calculating the flow properties of the non-equilibrium steady-states of the Katz-Lebowitz-Spohn model of the driven diffusive lattice gas, with attractive and repulsive inter-particle interactions, in both one and two dimensions for arbitrary particle densities, temperature as well as the driving field. We compare our theoretical results with the corresponding numerical data we have obtained from the computer simulations to demonstrate the level of accuracy of our theoretical predictions. We also compare our results with those for some other prototype models, notably particle-hopping models of vehicular traffic, to demonstrate the novel qualitative features we have observed in the Katz-Lebowitz-Spohn model, emphasizing, in particular, the consequences of repulsive inter-particle interactions.Comment: 12 RevTex page

Genetic variability, characters association and path analysis for yield and fruit quality components in Brinjal

The experiment was done at AB District Seed Farm, BCKV, Kalyani Simanta, West-Bengal, India during autumn-winter 2013-14 and 2014-15. The characters that exhibited higher Phenotypic and Genotypic Co-efficient of variation values were number of fruits per plant (76.86, 75.63%), fruit weight (43.88, 41.34%), harvest index (23.57, 22.29%), fruit yield per plant (53.61, 51.17%), anthocyanin in peel, total phenols and DPPH (2,2-diphenyl-l-picryl hydrazyl) free radical scavenging (FRS) capacity indicating that a greater amount of genetic variability was present for these characters which provide greater scope for selection. High heritability coupled with high genetic advance as percent of mean was observed for the characters like plant height, days to 1st flowering, days to 50% flowering, number of fruits per plant, fruit weight, harvest index, fruit yield per plant, total sugar, anthocyanin in peel, total phenols and DPPH FRS capacity depicting that these traits were under the strong influence of additive gene action and hence simple selection based on phenotypic performance of these traits would be more effective. Fruit yield per plant showed highly positive significant correlation with number of primary branches per plant, number of fruits per plant, harvest index, vitamin-A and total phenols and significant negative correlation with days to 1st flowering, TSS, total sugars and total protein. Number of fruits per plant imparted the highest positive direct effect on yield followed by harvest index, fruit weight, days to 50% flowering and anthocyanin in peel. Number of fruits per plant and days to flowering were emerged as the main casual factors for positive or negative association of several characters with fruit yield per plant. Therefore, selection for fruit yield per plant based on these characters would be reliable

Hysteresis phenomenon in deterministic traffic flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow model being a straightforward generalization to the well known Nagel-Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the ``free-flowing'' (or ``gaseous'') phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the ``jammed'' (or ``liquid'') phase. Between the two critical values each of these phases may take place, which can be interpreted as an ``overcooled gas'' phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles.Comment: 22 pages, 6 figures, corrected and improved version, to appear in the Journal of Statistical Physic

Two-dimensional Burgers Cellular Automaton

A two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform dependent variables into discrete ones. Some exact solutions of the CA, such as shock wave solutions, are studied in detail.Comment: Latex2.09, 17 pages including 7 figure

Two-dimensional XY spin/gauge glasses on periodic and quasiperiodic lattices

Via Monte Carlo studies of the frustrated XY or classical planar model we demonstrate the possibility of a finite (nonzero) temperature spin/gauge glass phase in two dimensions. Examples of both periodic and quasiperiodic two dimensional lattices, where a high temperature paramagnetic phase changes to a spin/gauge glass phase with the lowering of temperature, are presented. The existence of the spin/gauge glass phase is substantiated by our study of the temperature dependence of the Edwards-Anderson order parameter, spin glass susceptibility, linear susceptibility and the specific heat. Finite size scaling analysis of spin glass susceptibility and order parameter yields a nonzero critical temperature and exponents that are in close agreement with those obtained by Bhatt and Young in their random ${\pm J}$ Ising model study on a square lattice. These results suggest that certain periodic and quasiperiodic two-dimensional arrays of superconducting grains in suitably chosen transverse magnetic fields should behave as superconducting glasses at low temperatures.Comment: RevTex, 25 pages. 11 epsf figures available upon request ([email protected] or [email protected]). Submitted to Phys. Rev.