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We consider the trick of balancing a vertical stick on a horizontal plate. It is shown that the horizontal stochastic driving of the point of contact can prevent the stick from falling provided that the stochasticity is that of a coloured noise with a correlation strength stronger than a critical value., Comment: 5 pages, 1 figure

Turbulence in driven stratified active matter is considered. The relevant parameters characterizing the problem are the Reynolds number Re and an active matter Richardson-like number,R. In the mixing limit,Re>>1, R<<1, we show that the standard Kolmogorov energy spectrum 5/3 law is realized. On the other hand, in the stratified limit, Re>>1,R>>1, there is a new turbulence universality class with a 7/5 law. The crossover from one regime to the other is discussed in detail. Experimental predictions and probes are also discussed.

A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence., Comment: 12 pages, 11 figures

Work fluctuations and work probability distributions are fundamentally different in systems with short- ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with shortranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet , well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short-ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behaviour of the work probability distribution and the associated fluctuations is presented.

The propagation of an initially Gaussian wave packet of width $\Delta_0$ in a cubic non-linear Schrodinger equation with a negative coupling constant for the nonlinear term is considered . It is predicted analytically and verified numerically that for a free particle if $\Delta_0$ is less than a critical value $\Delta_c$, then the packet will propagate in time with linearly growing width but for $\Delta>\Delta_c$, the packet will start becoming narrow and cease to be a Gaussian . For a simple harmonic oscillator, we find that for $\Delta_0$ smaller than a critical value, there always exist a coupling strength for which the packet simply oscillates about the mean position without changing its shape., Comment: 14 figures

This paper presents the Discrete Wavelet based fusion techniques for combining perceptually important image features. SPIHT (Set Partitioning in Hierarchical Trees) algorithm is an efficient method for lossy and lossless coding of fused image. This paper presents some modifications on the SPIHT algorithm. It is based on the idea of insignificant correlation of wavelet coefficient among the medium and high frequency sub bands. In RE-MSPIHT algorithm, wavelet coefficients are scaled prior to SPIHT coding based on the sub band importance, with the goal of minimizing the MSE., Comment: 16 pages

We use the Bohr Sommerfeld quantization rule along with a perturbative evaluation of the action intergral to find exact energy levels for the P\"oschl-Teller potential (both hyperbolic and trigonometric forms), the Morse potential, and the Rosen Morse potential. Combining perturbation theory with the simplest asymptotic evaluation of the action integral allows us to obtain all the energy levels of the Lennard-Jones potential with an accuracy greater than 0.1 per cent and serves to confirm that the perturbation results for P\"oschl-Teller and Morse Potentials are exact., Comment: Use of perturbation theory and Bohr Sommerfeld quantisation to find energy eigenvalues of some potentials; Journal of Mathematical Chemistry online first Oct. 18, 2011

We investigate a population-imbalanced two-species fermionic system where the resonantly-paired fermions combine to form bosonic molecules via Feshbach interaction. We study the dynamics of the intrinsic quantum fluctuations of the system. It is shown that the natural fluctuations of the condensate fraction consists of a fixed number of periodic components : indicating that these oscillations do not die out, and are sustained in the mean field dynamics of the system. These frequency components bear distinct signatures of the nature of pairing present in the system. We describe how a time dependent external magnetic field can be used to locate these oscillation frequencies, and thus to explore the momentum space structure of the population imbalanced system. We propose that this method can be used as an indirect experimental probe for detecting exotic phases like the breached pair state, FFLO state, and a phase-separated state comprising of BCS and normal regions.

We show how the condition of isochronicity can be studied for two dimensional systems in the renormalization group (RG) context. We find a necessary condition for the isochronicity of the Cherkas and another class of cubic systems. Our conditions are satisfied by all the cases studied recently by Bardet et al \cite{bard} and Ghose Choudhury and Guha

From a linear stability analysis of the Gross Pitaevskii equation for binary Bose Einstein condensates, it is found that the uniform state becomes unstable to a periodic perturbation of wave number k if k exceeds a critical value kc. However we find that a stationary spatially periodic state does not exist. We show the existence of pulse type solutions, when the pulse structure for one condensate is strongly influenced by the presence of the other condensate., Comment: This paper has been withdrawn by the author due to significant calculation error

We propose a mean-field, phenomenological Ginzburg-Landau free energy functional with two competing order parameters for a two-component, spin-polarized Fermi gas. This free energy supports a tricritical point which is different from the conventional one and this change offers a correct understanding of the experimental phase diagram of imbalanced Fermi systems (Shin et al, Nature, 2008). The specific heat also happens to be different than in standard theory., Comment: Published version

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers.

We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wave function as well as for the phonon field. We have shown that, the condensate wave function (which obeys the Gross-Pitaevskii equation) is responsible for the mean field part of Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force., Comment: Accepted in Journal of Physics B: Atomic, Molecular and Optical Physics

We show that the Lindstedt-Poincare perturbation theory is always a reliable technique in the region of small coupling constant. The harmonic balance result, on the other hand, if expanded in the perturbation parameter may lead to incorrect results., Comment: 15 pages, 1 figure

We consider a two dimensional Turing like system with two diffusing species which interact with each other. Considering the species to be charged, we include the effect of an electric field along a given direction which can lead to a drift induced instability found by A.B.Rovinsky and M.Menzinger\cite{9}. This allows one to study the competition between diffusion and drift as was done numerically by Riaz et al. We show here that an analytic formula can be found on the basis of a linear stability analysis that incorporates all the effects that are known for the system and also allows for some detailed predictions., Comment: 1 figure

An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where {\psi} vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed., Comment: 16 pages, 4 figures, v2 matches the journal version

The effect of an external noise on the Lorenz model is investigated near the onset of convection and near the Hopf bifurcation. We show the existence of a diverging time scale near the onset of convection and a resonance near the Hopf bifurcation. Our calculation provides an understanding of the noise induced stabilization of the limit cycle that had been observed numerically., Comment: 4 pages, one fig

We have considered the critical Casimir force on a $^4$He film below and above the bulk $\lambda$ point. We have explored the role of fluctuations around the mean field theory in a perturbative manner, and have substantially improved the mean field result of Zandi et al [Phys. Rev. E {\bf 76}, 030601(R) (2007)]. The Casimir scaling function obtained by us approaches a universal constant ($-\frac{\zeta(3)}{8\pi}$) for $T\lesssim 2.13~\text{K}$., Comment: The term $\frac{1}{4b}\xi_0^4k_BT_\lambda$ at the Fig.2-caption in the published version should be read as $\frac{1}{4b\xi_0^4k_BT_\lambda}$

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.

A form for the two-point third order structure function has been calculated for three dimensional homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalisation of the 3D incompressible turbulence owing to rotation., Comment: This revised version corrects some serious flaws in the discussions after the equation (2) and the equation (13) of the earlier version. Some typos are also corrected

We show, both analytically and numerically, that for a nonlinear system making a transition from one equilibrium state to another under the action of an external time dependent force, the work probability distribution is in general asymmetric., Comment: 7 pages, 5 figures

The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point that a point on the fixed point in the phase space should remain there forever, for, a fixed point can evolve as well! Under such considerations one can argue that a free-kicked football should be non-chaotic., Comment: This paper is a replaced version to modify the not-so-true claim, made unknowingly in the earlier version, of being first to propose the peculiar dynamical systems as described in the paper. With respect to the original workers, we present here our original findings

Lotka Volterra model and its modified forms have long become a major area of interest for periodic motions in nonlinear systems with competitive species. The model given by Volterra shows that its periodicity is dependent on initial condition. This characteristics allows us to calculate the effect of periodic seasonal changes on population densities of different species, Comment: 9 pages, 5 figures

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 figures

Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a saddle point and the inner one a centre type point. For the weakly viscous disc, there are four possible critical points, of which the outermost is a saddle point, while the next inner one is a spiral. Coupling the nature of the critical points with the outer boundary condition of the flow, gives us a complete understanding of all the important physical features of the flow solutions in the subsonic regions of the disc. In the inviscid disc, the physical realisability of the transonic solution passing through the saddle point is addressed by considering a temporal evolution of the flow, which is a very likely non-perturbative mechanism for selecting the transonic inflow solution from among a host of other possible stable solutions. For the weakly viscous disc, while a linearised time-dependent perturbation imposed on the steady mass inflow rate causes instability, the same perturbative analysis reveals that for the inviscid disc, there is a very close correspondence between the equation for the propagation of the perturbation and the metric of an acoustic black hole. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length scale is defined for the spatial extent of the inward rotational drift of matter., Comment: 14 pages, REVTeX, 3 figures

We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers' time. We also describe the connection between stochastic processes and quantum mechanics., Comment: 20 pages, 3 figures

We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization scheme., Comment: 3 pages

Problems in non equilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia and Rose. We show that instead of using the response field, one can, following the stochastic quantization of Parisi and Wu, introduce a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in non equilibrium statistical physics., Comment: 4 pages

For a potential function (in one dimension) which evolves from a specified initial form $V_{i}(x)$ to a different $V_{f}(x)$ asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibeium.There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form $V(x,t)=V_{f}(x)+(V_{i}-V_{f})e^{-\lambda t}$. For a $V_{f}(x)$, which is double welled and a $V_{i}(x)$ which is simple harmonic, we show that, in particular, if the evolution is adiabatic, the results in a decrease in the Kramers time characteristics of $V_{f}(x)$. Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when $V_{i}(x)$ and $V_{f}(x)$ are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterising the potential variation and the Kramers time., Comment: This paper contains 5 pages

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been given., Comment: 9 pages, REVTeX, Additional treatment on travelling waves. Extensively revised in the publised version. Contains a full new section on the role of nonlinearity

The role of turbulence in a spherically symmetric accreting system has been studied on very large spatial scales of the system. This is also a highly subsonic flow region and here the accreting fluid has been treated as nearly incompressible. It has been shown here that the coupling of the mean flow and the turbulent fluctuations, gives rise to a scaling relation for an effective "turbulent viscosity". This in turn leads to a dynamic scaling for sound propagation in the accretion process. As a consequence of this scaling, the sonic horizon of the transonic inflow solution is shifted inwards, in comparison with the inviscid flow., Comment: 17 pages, AASTeX

The inviscid and thin accretion disc is a simple and well understood model system in accretion studies. In this work, modelling such a disc like a dynamical system, we analyse the nature of the fixed points of the stationary solutions of the flow. We show that of the two fixed points, one is a saddle and the other is a centre type point. We then demonstrate, using a simple but analogous mathematical model, that a temporal evolution of the flow is a very likely non-perturbative mechanism for the selection of an inflow solution that passes through the saddle type critical point., Comment: 7 pages, 2 figures. Corrected, altered and expanded version of what has been published in the Proceedings of the First National Conference on Nonlinear Systems and Dynamics (NCNSD 2003), held at Indian Institute of Technology, Kharagpur, India, in December, 2003

The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow., Comment: 4 pages in REVTeX with 2 figures. Typos have been corrected and some alterations have been made in the version published in Physical Review E

In a two species reaction diffusion system,we show that it is possible to generate a set of wavelength doubling bifuractions leading to spatially chaotic state.The wavelength doubling bifurcations are preceded by a symmetry breaking transition which acts as a precursor.

We consider photoemission from a two-electron quantum dot and find analytic expression for the cross-section. We show that the emission cross-section from the ground state as a function of magnetic field has sharp discontinuities corresponding to the singlet-triplet transitions for low magnetic fields and the transitions between magic numbers (2J+1) for high magnetic field. We also find the corrections to the photoemission cross-section from a more realistic quantum dot having a finite thickness due to nonvanishing extent of electron wave function in the direction perpendicular to the plane in which 2-D dot electrons are usually confined., Comment: 14 pages, 7 figures

A variational treatment for a two-electron quantum dot (the artificial helium atom) is proposed which leads to exact answer for the ground state energy. Depending on the magnetic field value the singlet-triplet and triplet-triplet transitions of the ground state take place, which are captured in our solution. Using the same variational technique we find corrections to wave function and energy and the transition field strengths in a realistic dot where electron wave function has a finite extent in the direction perpendicular to the x-y plane in which usually 2-D dot electrons are confined. Using the variational wave function we show that photoemission cross-section as a function of magnetic field has sharp discontinuities, which can be used for experimental verification of the singlet-triplet transitions., Comment: 12 pages, 5 figures

We treat the double well quantum oscillator from the standpoint of the Ehrenfest equation but in a manner different from Pattanayak and Schieve. We show that for short times there can be chaotic motion due to quantum fluctuations, but over sufficiently long times the behaviour is normal., Comment: Titlepage + 5 pages + Bibiliography,Submitted To Phys.Lett A