Jamming of directed traffic on a square lattice

Phase transition from a free-flow phase to a jammed phase is an important feature of traffic networks. We study this transition in the case of a simple square lattice network for different values of data posting rate $(\rho)$ by introducing a parameter $p$ which selects a neighbour for onward data transfer depending on queued traffic. For every $\rho$ there is a critical value of $p$ above which the system become jammed. The $\rho-p$ phase diagram shows some interesting features. We also show that the average load diverges logarithmically as $p$ approaches $p_c$ and the queue length distribution exhibits exponential and algebraic nature in different regions of the phase diagram.Comment: 12 pages, 9 figure

Biodiesel: Freedom from Dependence on Fossil Fuels?

In view of the depleting oil reserves and exponential rise in petroleum prices, the search for alternative sources of fuel is very timely and important. The present paper addresses the underlying issues in biodiesel production from biomaterials and sustainable production and supply of first-generation biofuels, especially the one from jatropha. The agencies and research institutions involved in the production of biofuels and the national and international efforts made in this regard are discussed here. There is also a dire need of a step towards large-scale production and supply of second-generation biofuels, although in infant stage, to strengthen the world economy in general and Indian economy in particular. However, the production of biofuels are likely to have serious socio-economic implications especially to the lesser developed societies. This needs serious attention from policy makers and public at large

Quantum phase transition in a disordered long-range transverse Ising antiferromagnet

We consider a long-range Ising antiferromagnet put in a transverse field (LRTIAF) with disorder. We have obtained the phase diagrams for both the classical and quantum case. For the pure case applying quantum Monte Carlo method, we study the variation of order parameter (spin correlation in the Trotter direction), susceptibility and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We discuss generally the phase diagram for the same LRTIAF model with perturbative Sherrington-Kirkpatrick (SK) type disorder. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the pure LRTIAF system, an infinitesimal SK spin glass disorder is enough to induce a stable glass order in the LRTIAF. This glass order eventually gets destroyed as the thermal or quantum fluctuations are increased beyond their threshold values and the transition to para phase occurs. Analytical studies for the phase transitions are discussed in detail in each case. These transitions have been confirmed by applying classical and quantum Monte Carlo methods. We show here that the disordered LRTIAF has a surrogate incubation property of the SK spin glass phase.Comment: 16 pages, 12 figures. accepted in PR

Multidimensional persistence behaviour in an Ising system

We consider a periodic Ising chain with nearest-neighbour and $r$-th neighbour interaction and quench it from infinite temperature to zero temperature. The persistence probability $P(t)$, measured as the probability that a spin remains unflipped upto time $t$, is studied by computer simulation for suitable values of $r$. We observe that as time progresses, $P(t)$ first decays as $t^{-0.22}$ (-the {\em first} regime), then the $P(t)-t$ curve has a small slope (in log-log scale) for some time (-the {\em second} regime) and at last it decays nearly as $t^{-3/8}$ (-the {\em third} regime). We argue that in the first regime, the persistence behaviour is the usual one for a two-dimensional system, in the second regime it is like that of a non-interacting (`zero-dimensional') system and in the third regime the persistence behaviour is like that of a one dimensional Ising model. We also provide explanations for such behaviour.Comment: 6 pages, 12 figure

Phase transitions and non-equilibrium relaxation in kinetic models of opinion formation

We review in details some recently proposed kinetic models of opinion dynamics. We discuss the several variants including a generalised model. We provide mean field estimates for the critical points, which are numerically supported with reasonable accuracy. Using non-equilibrium relaxation techniques, we also investigate the nature of phase transitions observed in these models. We study the nature of correlations as the critical points are approached, and comment on the universality of the phase transitions observed.Comment: 11 pages, 8 eps figures, 1 table. Contribution for proceedings of Statphys-Kolkata-VII 26-30 November, 201