Relation between Stochastic Resonance and Synchronization of Passages in a Double-Well System

We calculate, numerically, the residence times (and their distribution) of a Brownian particle in a two-well system under the action of a periodic, saw-tooth type, external field. We define hysteresis in the system. The hysteresis loop area is shown to be a good measure of synchronization of passages from one well to the other. We establish connection between this stochastic synchronization and stochastic resonance in the system.Comment: To appear in PRE May 1997, figures available on reques

Asymmetric motion in a double-well under the action of zero-mean Gaussian white noise and periodic forcing

Residence times of a particle in both the wells of a double-well system, under the action of zero-mean Gaussian white noise and zero-averaged but temporally asymmetric periodic forcings, are recorded in a numerical simulation. The difference between the relative mean residence times in the two wells shows monotonic variation as a function of asymmetry in the periodic forcing and for a given asymmetry the difference becomes largest at an optimum value of the noise strength. Moreover, the passages from one well to the other become less synchronous at small noise strength as the asymmetry parameter (defined below) differs from zero, but at relatively larger noise strengths the passages become more synchronous with asymmetry in the field sweep. We propose that asymmetric periodic forcing (with zero mean) could provide a simple but sensible physical model for unidirectional motion in a symmetric periodic system aided by a symmetric Gaussian white noise.Comment: Appeared in PRE March 1997, figures available on reques

Aperiodic tumbling of microrods advected in a microchannel flow

We report on an experimental investigation of the tumbling of microrods in the shear flow of a microchannel (40 x 2.5 x 0.4 mm). The rods are 20 to 30 microns long and their diameters are of the order of 1 micron. Images of the centre-of-mass motion and the orientational dynamics of the rods are recorded using a microscope equipped with a CCD camera. A motorised microscope stage is used to track individual rods as they move along the channel. Automated image analysis determines the position and orientation of a tracked rods in each video frame. We find different behaviours, depending on the particle shape, its initial position, and orientation. First, we observe periodic as well as aperiodic tumbling. Second, the data show that different tumbling trajectories exhibit different sensitivities to external perturbations. These observations can be explained by slight asymmetries of the rods. Third we observe that after some time, initially periodic trajectories lose their phase. We attribute this to drift of the centre of mass of the rod from one to another stream line of the channel flow.Comment: 14 pages, 8 figures, as accepted for publicatio

Brownian rectifiers in the presence of temporally asymmetric unbiased forces

The efficiency of energy transduction in a temporally asymmetric rocked ratchet is studied. Time asymmetry favours current in one direction and suppresses it in the opposite direction due to which large efficiency ~ 50% is readily obtained. The spatial asymmetry in the potential together with system inhomogeneity may help in further enhancing the efficiency. Fine tuning of system parameters considered leads to multiple current reversals even in the adiabatic regime

Reliability of fluctuation-induced transport in a Maxwell-demon-type engine

We study the transport properties of an overdamped Brownian particle which is simultaneously in contact with two thermal baths. The first bath is modeled by an additive thermal noise at temperature $T_A$. The second bath is associated with a multiplicative thermal noise at temperature $T_B$. The analytical expressions for the particle velocity and diffusion constant are derived for this system, and the reliability or coherence of transport is analyzed by means of their ratio in terms of a dimensionless P\'{e}clet number. We find that the transport is not very coherent, though one can get significantly higher currents.Comment: 14 pages, 5 figure

Online) An Open Access

ABSTRACT Wetlands of the many areas of kachchh region are reduced day to day by the natural processes as well as developmental activities and as a result the population of birds depend upon these wetlands are under threat. This paper was attempted to assess the composition of avifauna in Lakhara, a fragmented wetland inside the Kachchh Biosphere Reserve. Regular survey was made in year 2009 to observe and identifying the avifauna using standard field guide and field equipments. A total of 57 species of bird recorded during the whole survey period and their feeding and threatened status was also analyzed. A good number of birds recorded in Lakhara wetland in spite of the small area. Most of the recorded birds of this wetland were belong to the Least Concern category of IUCN red list, 2010 and Schedule IV of the Indian Wildlife (Protection) Act, 1972. Lakhara wetland is also proved to be an important bird area of Kachchh for conservation aspects

Energetics of rocked inhomogeneous ratchets

We study the efficiency of frictional thermal ratchets driven by finite frequency driving force and in contact with a heat bath. The efficiency exhibits varied behavior with driving frequency. Both nonmonotonic and monotonic behavior have been observed. In particular the magnitude of efficiency in finite frequency regime may be more than the efficiency in the adiabatic regime. This is our central result for rocked ratchets. We also show that for the simple potential we have chosen, the presence of only spatial asymmetry (homogeneous system) or only frictional ratchet (symmetric potential profile), the adiabatic efficiency is always more than in the nonadiabatic case.Comment: 5 figure

Energy fluctuations in a biharmonically driven nonlinear system

We study the fluctuations of work done and dissipated heat of a Brownian particle in a symmetric double well system. The system is driven by two periodic input signals that rock the potential simultaneously. Confinement in one preferred well can be achieved by modulating the relative phase between the drives. We show that in the presence of pumping the stochastic resonance signal is enhanced when analyzed in terms of the average work done on the system per cycle. This is in contrast to the case when pumping is achieved by applying an external static bias, which degrades resonance. We analyze the nature of work and heat fluctuations and show that the steady state fluctuation theorem holds in this system.Comment: 13 pages, 14 figures, revised manuscrip

Stochastic Hysteresis and Resonance in a Kinetic Ising System

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.Comment: 35 pages. Submitted to Phys. Rev. E Minor revisions to the text and updated reference

Hydrodynamics of R-charged D1-branes

We study the hydrodynamic properties of strongly coupled $SU(N)$ Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to $1/4\pi$. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.Comment: 57 pages, 12 figure