Persistence of a Brownian particle in a Time Dependent Potential

We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times -- leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the confinement, an exponential and an algebraic decay. Analytical calculations and numerical simulations show, that for the case of the exponential relaxation, the dynamics of Brownian particle at short and long times are independent of the parameters of the relaxation. On the contrary, for the algebraic decay of the confinement, the dynamics at long times is determined by the exponent of the decay. Finally, using the two-time correlation function for the position of the Brownian particle, we construct the persistence probability for the Brownian walker in such a scenario.Comment: 7 pages, 5 figures, Accepted for publication in Phys. Rev.

Global Persistence Exponent in Critical Dynamics: Finite Size induced Crossover

We extend the definition of a global order parameter to the case of a critical system confined between two infinite parallel plates separated by a finite distance $L$. For a quench to the critical point we study the persistence property of the global order parameter and show that there is a crossover behaviour characterized by a non universal exponent which depends on the ratio of the system size to a dynamic length scale

PGPR in Managing Root Rot Disease and Enhancing Growth in Mandarin (Citrus reticulata Blanco.) Seedlings

Decline in general plant-health and fruit production in mandarin influenced by abiotic and biotic factors is a major threat to cultivars grown in Darjeeling and Sikkim hills. Fusarium root rot, caused by F. oxysporum, is one of the most serious diseases afflicted during early plant growth stage in Citrus. To address this, seven PGPR isolates - Pseudomonas poae (RMK03), Bacillus stratosphericus (RHS/CL-01), Ochrobactrum anthropi, Paenibacillus lentimorbus, Bacillus pumilus, Bacillus megaterium and Bacillus amyloliquefaciens were isolated from the rhizosphere of Citrus reticulata, C. limonia and Camellia sinensis, and used for evaluating their effect on growth of mandarin seedlings. Pseudomonas poae showed in vitro antagonism to Fusarium oxysporum. Better growth enhancement was noticed with P. poae, B. stratosphericus, O. anthropi and B. pumilus. Enhanced activity of chlorophyll, total protein, phenol, four major defense enzymeschitinase, β-1, 3-glucanase, peroxidase and phenyalanine ammonia lyase was observed upon application of PGPR. P. poae also suppressed root rot caused by Fusarium oxysporum. Use of PGPR, which promote growth besides reducing disease severity to some extent, may lead to use of eco-friendly approaches for controlling plant diseases

Finite Size Effect in Persistence

We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially decaying function.The particle here is trapped with in a box of size $L$ . We have also considered the problem when the particle in trapped in a potential. Direct calculation and numerical result show that the scaling function here also an exponentially decaying function. We also present numerical works on harmonically trapped randomly accelerated particle and randomly accelerated particle with viscous drag.Comment: revtex4, 4 pages, 4 figure

Temperature dependence of spin polarizations at higher Landau Levels

We report our results on temperature dependence of spin polarizations at $\nu=1$ in the lowest as well as in the next higher Landau level that compare well with recent experimental results. At $\nu=3$, except having a much smaller magnitude the behavior of spin polarization is not much influenced by higher Landau levels. In sharp contrast, for filling factor $\nu=\frac83$ we predict that unlike the case of $\nu=\frac23$ the system remains fully spin polarized even at vanishingly small Zeeman energies.Comment: 4 pages, REVTEX, and 3 .ps files, To be published in Physical Review Letter

On the Complexity of Temporal-Logic Path Checking

Given a formula in a temporal logic such as LTL or MTL, a fundamental problem is the complexity of evaluating the formula on a given finite word. For LTL, the complexity of this task was recently shown to be in NC. In this paper, we present an NC algorithm for MTL, a quantitative (or metric) extension of LTL, and give an NCC algorithm for UTL, the unary fragment of LTL. At the time of writing, MTL is the most expressive logic with an NC path-checking algorithm, and UTL is the most expressive fragment of LTL with a more efficient path-checking algorithm than for full LTL (subject to standard complexity-theoretic assumptions). We then establish a connection between LTL path checking and planar circuits, which we exploit to show that any further progress in determining the precise complexity of LTL path checking would immediately entail more efficient evaluation algorithms than are known for a certain class of planar circuits. The connection further implies that the complexity of LTL path checking depends on the Boolean connectives allowed: adding Boolean exclusive or yields a temporal logic with P-complete path-checking problem

Persistence in Advection of Passive Scalar

We consider the persistence phenomenon in advectecd passive scalar equation in 1-dimension. The velocity field is random with the $\sim |k|^{-(2+\alpha)}$. In presence of the non-linearity the complete Green's function becomes $G^{-1}=-i\omega+Dk^2+\Sigma$. We determine $\Sigma$ self-consistently from the correlation function which gives $\Sigma \sim k^{\beta}$, with $\beta=(1-\alpha)/2$. The effect of the non-linear term in the equation in the $\mathcal{O}(\epsilon^2)$ is to replace the diffusion term due to molecular viscosity by an effective term of the form $\Sigma_0 k^{\beta}$. The stationary correlator for this system is $[\mathrm{Sech}(T/2)]^{1/\beta}$. Using the self-consistent theory we have determined the relation between $\beta$ and $\alpha$. Finally, IIA is used to determine the persistent exponent.Comment: 4 page

Reduction of Chromite ore at different flow rates of inert gas

Pre-reduction of chromite outside the submerged-arc furnace(SAF) can significantly lower the specific power consumption in the SAF process. Conventional processes for the pre-reduction of the ore operate at relatively high temperatures, at 1400-1500°C. It is possible to enhance the rate of reduction at low temperatures by optimizing the flow rate of inert gas over the reaction site. The influence of the flow rate of inert gas on the rate of reduction of chromite ore was investigated. The rate of reduction initially decreased wit the flow rate of the gas. It increased subsequently at higher flow rates to be followed by a decrease again. There was an optimum flow rate at which maximum reduction could be obtained. It was possible to achieve high levels of reduction at 1200°C by optimising the flow rate of the gas. The degree of reduction obtained was comparable to that obtained at 1400-1500°C, by conventional process routes

High-spin structure and Band Termination in 103^{103}Cd

Excited states of the neutron deficient $^{103}$Cd nucleus have been investigated via the $^{72}$Ge($^{35}$Cl, p3n) reaction at beam energy of 135 MeV by use of in-beam spectroscopic methods. Gamma rays depopulating the excited states were detected using the Gammasphere spectrometer with high-fold $\gamma$-ray coincidences. A quadrupole $\gamma$-ray coincidence analysis ($\gamma^{4}$) has been used to extend the known level scheme. The positive parity levels have been established up to $J = 35/2\hbar$ and $E_{x} = 7.071$ MeV. In addition to the observation of highly-fragmented level scheme belonging to the positive-parity sequences at E$_{x}\sim$ 5 MeV, the termination of a negative-parity sequence connected by $E2$ transitions has been established at $J = 47/2 \hbar$ and $E_{x} = 11.877$ MeV. The experimental results corresponding to both the positive- and negative-parity sequences have been theoretically interpreted in the framework of the core particle coupling model. Evidence is presented for a shape change from collective prolate to non-collective oblate above the $J^{\pi} = 39/2^{-}$ (8011 keV) level and for a smooth termination of the negative-parity band.Comment: 19 pages, 8 figures. Submitted to Phys. Rev.