Publications by authors named "Jayanta K Bhattacharjee"

We show how a dynamical systems approach can, somewhat unexpectedly, be relevant in the quantum dynamics featuring oscillations and escape in the Morse potential. We compare the dynamics resulting from the approach with the results obtained from a direct numerical integration of the relevant Schrödinger equation to support our claim. An interesting finding of the numerical investigation is the marked increase in the probability of obtaining a significant fraction (more than 50%) of the wave packet in the classically forbidden range beyond a critical energy of the packet.

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Article Synopsis
  • * Surprisingly, exposing CrGeTe to air leads to the formation of a stable ferromagnetic phase (CrTe with T ≈ 160 K) alongside its original phase (T ≈ 69 K), revealing a complex coexistence of two magnetic states.
  • * The study uses Ginzburg-Landau theory to explain this coexistence and suggests these findings might help develop new air-stable materials with multiple magnetic phases, challenging the common notion of instability in
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A randomly stirred model, akin to the one used by DeDominicis and Martin for homogeneous isotropic turbulence, is introduced to study Bolgiano-Obukhov scaling in fully developed turbulence in a stably stratified fluid. The energy spectrum (), where is a wavevector in the inertial range, is expected to show the Bolgiano-Obukhov scaling at a large Richardson number (a measure of the stratification). We find that the energy spectrum is anisotropic.

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The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease.

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Nanomechanical oscillators have, over the last few years, started probing regimes where quantum fluctuations are important. Here we consider a nonlinear parametric oscillator in the quantum domain. We show that in the classical subharmonic resonance zone, the quantum fluctuations are finite but greatly magnified depending on the strength of the nonlinear coupling.

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We set up the scaling theory for stably stratified turbulent fluids. For a system having infinite extent in the horizontal directions, but with a finite width in the vertical direction, this theory predicts that the inertial range can display three possible scaling behavior, which are essentially parametrized by the buoyancy frequency N, or dimensionless horizontal Froude number F_{h}, and the vertical length scale l_{v} that sets the scale of variation of the velocity field in the vertical direction for a fixed Reynolds number. For very low N or very high Re_{b} or F_{h}, and with l_{v}≫l_{h}, the typical horizontal length scale, buoyancy forces are irrelevant and hence, unsurprisingly, the kinetic energy spectra show the well-known K41 scaling in the inertial range.

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It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré-Andronov-Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value.

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The frequency spectra of the entropy and kinetic energy along with the power spectrum of the thermal flux are computed from direct numerical simulations for turbulent Rayleigh-Bénard convection with uniform rotation about a vertical axis in low-Prandtl-number fluids (Pr<0.6). Simulations are done for convective Rossby numbers Ro≥0.

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We present results for entropy and kinetic energy spectra computed from direct numerical simulations for low-Prandtl-number (Pr < 1) turbulent flow in Rayleigh-Bénard convection with uniform rotation about a vertical axis. The simulations are performed in a three-dimensional periodic box for a range of the Taylor number (0 ≤ Ta ≤ 10(8)) and reduced Rayleigh number r = Ra/Ra(∘)(Ta,Pr) (1.0 × 10(2) ≤ r ≤ 5.

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A thermodynamic model including fluctuations of micelle sizes has been derived to describe solution properties of amphiphile systems close to the critical micelle concentration. Owing to the consideration of an affinity field in the free energy of the system, the model is capable of featuring experimental findings that are incorrectly reflected by established theories of the micelle formation and disintegration kinetics. In conformity with experiments, the thermodynamic theory predicts the onset of micellar structure formation already at amphiphile concentrations below the critical micelle concentration.

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Based on a thermodynamic model of amphiphile solutions derived in the first part of the paper, the ultrasonic attenuation of such systems has been considered theoretically, including fluctuations of local concentrations and micelle sizes. At amphiphile concentrations smaller than the critical micelle concentration (cmc), scaling behavior in terms of the concentration distance to the cmc is predicted by theory, in fair agreement with experimental evidence. The scaling function in the sound attenuation below the cmc reveals the unsymmetric broadening in the spectra that clearly emerges from measurements when approaching the cmc.

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We analyze the statistical properties of three-dimensional (3D) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field v. We obtain the master equation from the Navier-Stokes equation in a rotating frame and thence a set of exact hierarchical equations for the velocity structure functions for arbitrary angular velocity Ω.

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The heat flux in rotating Rayleigh-Bénard convection in a fluid of Prandtl number Pr=0.1 enclosed between free-slip top and bottom boundaries is investigated using direct numerical simulation in a wide range of Rayleigh numbers (10(4)≤Ra≤10(8)) and Taylor numbers (0≤Ta≤10(8)). The Nusselt number Nu scales with the Rayleigh number Ra as Ra(β) with β=2/7 for values of Nu greater than a critical value Nu(c), which occurs for Ta/Ra∼1.

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In addition to a previous theory on the coupling between noncritical concentration fluctuations and elementary chemical processes, an alternative treatment is presented which allows for a closed-form solution of ultrasonic attenuation spectra. This analytical form is first compared to a previous model and also to experimental spectra of binary liquid mixtures. The broadening of the spectra is briefly discussed in terms of molecular interactions and of the ratio of the relaxation times of the chemical equilibrium and of the diffusion of fluctuations.

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We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for the Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modeling other physical phenomena where rare events play an important role.

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Large deviations play a significant role in many branches of nonequilibrium statistical physics. They are difficult to handle because their effects, though small, are not amenable to perturbation theory. Even the Gaussian model, which is the usual initial step for most perturbation theories, fails to be a starting point while discussing intermittency in fluid turbulence, where large deviations dominate.

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The hydrodynamical equations and the notion of a frequency dependent complex specific heat near the critical point of binary liquids are used to obtain an expression for the low-frequency bulk viscosity. In this way the interrelations between different theoretical models, treating the critical sound attenuation from either a specific heat or a bulk viscosity approach, are made evident. The general structure of the bulk viscosity relation agrees with that of Onuki [Phys.

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We study the logistic mapping with the nonlinearity parameter varied through a delayed feedback mechanism. This history dependent modulation through a phaselike variable offers an enhanced possibility for stabilization of periodic dynamics. Study of the system as a function of nonlinearity and modulation parameters reveals new phenomena: In addition to period-doubling and tangent bifurcations, there can be bifurcations where the period increases by unity.

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The frequency and shear dependent critical viscosity at a correlation length xi= kappa(-1) has the form eta= eta(0) kappa(- x(eta) ) G ( z(1) , z(2) ) , where z(1) and z(2) are the independent dimensionless numbers in the problem defined as z(1) =-iomega/2 Gamma(0) kappa(3) and z(2) =-iomega/2 Gamma(0) kappa(3)(c) . The decay rate of critical fluctuations of correlation length kappa(-1) is Gamma(0) kappa(3) and k(c) is the effective wave number for which Gamma(0) k(3)(c) =S , the shear rate. The function G ( z(1) , z(2) ) is calculated in a one-loop self-consistent theory.

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A self-consistent mode-coupling calculation of the critical viscosity exponent z(eta) for classical fluids is performed by including the memory effect and the vertex corrections. The incorporation of the memory effect is through a self-consistency procedure that evaluates the order parameter and shear momentum relaxation rates at nonzero frequencies, thereby taking their frequency dependence into account. This approach offers considerable simplification and efficiency in the calculation.

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The long-wavelength diffusion coefficient of a critical fluid confined between two parallel plates, separated by a distance L, is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion coefficient as xi(-1) for xi<>L. We show that this is not strictly true.

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We arrange the loopwise perturbation theory for the critical viscosity exponent x(eta), which happens to be very small, as a power series in x(eta) itself, and argue that the effect of loops beyond two is negligible. We claim that the critical viscosity exponent should be very closely approximated by x(eta)=(8/15pi(2))(1+8/3pi(2)) approximately 0.0685.

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