Biomedical subjects

Deb Shankar Ray

Publications and source records attributed to Deb Shankar Ray.

16 recordsLinked to original sources

PubMed2006

A parametric variant of resonant activation: two-state model approach.

Mean first passage time of a periodically driven particle for its escape over a fluctuating barrier with wells remaining unbiased exhibits a resonance when the frequency of the driving field is varied. This parametric variant of resonant activation and associated features of noise induced transition are realized in terms of a two-state model to estimate analytically several quantifiers of the escape event. Numerical simulation on a continuous double-well model collaborates our theoretical analysis.

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PubMed2006

Stochastic energetics of quantum transport.

We examine the stochastic energetics of directed quantum transport due to rectification of nonequilibrium thermal fluctuations. We calculate the quantum efficiency of a ratchet device both in presence and absence of an external load to characterize two quantifiers of efficiency. It has been shown that the quantum current as well as efficiency in absence of load (Stokes efficiency) is higher as compared to classical current and efficiency, respectively, at low temperature. The conventional efficiency of the device in presence of load on the other hand is higher for a classical system in contrast to its classical counterpart. The maximum conventional efficiency being independent of the nature of the bath and the potential remains the same for classical and quantum systems.

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PubMed2006

Electric field induced instabilities: waves and stationary patterns.

We examine a prototypical ionic reaction-diffusion system involving the well-known iodate-arsenous acid reaction in an electric field at a constant current density. By taking into consideration of the spatial inhomogeneities in electric field intensity and charge density due to ionic migration and diffusion using charge balance condition, we look for the different instability regions in the appropriate parameter space. We show that the model admits of both absolute and convective instability resulting in the development of propagating waves and also stationary spatial patterns at times.

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PubMed2005

Quantum escape kinetics over a fluctuating barrier.

The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.

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PubMed2005

Sustained simultaneous glycolytic and insulin oscillations in beta-cells.

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.

Adenosine Triphosphate↗

PubMed2005

Spiral pattern in chlorite-iodide-malonic acid reaction: a theoretical and numerical study.

The development of spiral pattern in a model representing chlorite-iodide-malonic acid reaction is investigated theoretically and numerically. We have carried out a multiple scale analysis of the model to identify the experimentally admissible parameter range and the appropriate perturbation for shifting Hopf bifurcation boundary towards the oscillating region. Our theoretical analysis is corroborated by numerical simulation.

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PubMed2005

Noise-induced quantum transport.

We analyze the problem of directed quantum transport induced by external exponentially correlated telegraphic noise. In addition to quantum nature of the heat bath, nonlinearity of the periodic system potential brings in quantum contribution. We observe that quantization, in general, enhances classical current at low temperature, while the differences become insignificant at higher temperature. Interplay of quantum diffusion and quantum correction to system potential is analyzed for various ranges of temperature, correlation time and strength of external noise and asymmetry parameters. A possible experimental realization of the observed quantum effects in a superionic conductor placed in a random asymmetric dichotomous electric field has been suggested.

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PubMed2005

Noise-induced instability: an approach based on higher-order moments.

Noise-induced transitions in the organization of systems far from equilibrium have been of vital interest. Although the effects of additive and multiplicative noise have been widely studied, it is only the multiplicative noise that can be dealt with within the scope of a linear analysis of first moments of the spatiotemporal perturbations, by the application of Novikov's theorem. For the case of additive noise, the corresponding straightforward linear analysis of the first moment throws no light on the effect of the noise on stability conditions. We propose here a simple approach based on higher-order moments to show how additive noise can give rise to noise-induced instability in spatially extended systems, at times leading to pattern formation. Our theoretical analysis is corroborated by numerical simulations on two simple one-component reaction-diffusion systems in two dimensions.

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PubMed2004

Mobility-induced instability and pattern formation in a reaction-diffusion system.

Ions undergoing a reaction-diffusion process are susceptible to electric field. We show that a constant external field may induce a kind of instability on the state stabilized by diffusion in a reaction-diffusion system giving rise to formation of pattern even when the diffusion coefficients of the reactants are equal. The origin of the pattern is due to the difference in mobilities of the two species and is thus markedly different from that of deformed Turing pattern in presence of the field. While this differential flow instability had been shown earlier to result in traveling waves, we realize in the context of stationary pattern formation in a typical reaction-diffusion-advective system. Our analysis is based on a numerical simulation of a generic model on a two-dimensional domain.

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PubMed2004

Anharmonic quantum contribution to vibrational dephasing.

Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of the potential makes a significant contribution to the rate and the frequency shift. We compare our theoretical estimates with those obtained from experiments for small diatomics N(2), O(2), and CO.

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PubMed2004

Solution of quantum Langevin equation: approximations, theoretical and numerical aspects.

Based on a coherent state representation of noise operator and an ensemble averaging procedure using Wigner canonical thermal distribution for harmonic oscillators, a generalized quantum Langevin equation has been recently developed [Phys. Rev. E 65, 021109 (2002); 66, 051106 (2002)] to derive the equations of motion for probability distribution functions in c-number phase-space. We extend the treatment to explore several systematic approximation schemes for the solutions of the Langevin equation for nonlinear potentials for a wide range of noise correlation, strength and temperature down to the vacuum limit. The method is exemplified by an analytic application to harmonic oscillator for arbitrary memory kernel and with the help of a numerical calculation of barrier crossing, in a cubic potential to demonstrate the quantum Kramers' turnover and the quantum Arrhenius plot.

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PubMed2003

Collapse and revival of glycolytic oscillation.

Glycolysis is the major source of metabolic energy in almost all living cells. A key feature of the glycolytic oscillations is their critical control by substrate injection rate. We show that in the limit of weak noise of the fluctuating substrate injection rate a new instability arises in the dynamics leading to collapse and revival of glycolytic oscillation reminiscent of "bursting" of action potential in nerve cells. The dynamical system in this limit also exhibits an interesting mirror image symmetry between growth and decay of fluctuations of the reaction product.

Allosteric Regulation↗

PubMed2002

Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime.

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value, which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.

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PubMed2002

Class of self-limiting growth models in the presence of nonlinear diffusion.

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand, are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.

Animals↗

PubMed2002

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

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PubMed2002

Approach to quantum Kramers' equation and barrier crossing dynamics.

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum-mechanical mean values of their co-ordinates and momenta we have derived a c number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of the temperature and friction. While almost all the earlier theories rest on quasiprobability distribution functions (e.g., Wigner function) and path integral methods, the present work is based on true probability distribution functions and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermally activated processes and tunneling.

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