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Somrita Ray

Bio: Somrita Ray is an academic researcher from Tel Aviv University. The author has contributed to research in topics: Brownian motion & Magnetic field. The author has an hindex of 10, co-authored 28 publications receiving 313 citations. Previous affiliations of Somrita Ray include Indian Association for the Cultivation of Science & University of Calcutta.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary is quantified and the transition is governed by the P-eclet number, the ratio between the rates of advective and diffusive transport.
Abstract: First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the P\\'eclet number ($Pe$) --- the ratio between the rates of advective and diffusive transport. When $Pe>1$ the process is drift-controlled and restart can only hinder its completion. In contrast, when $0\\leq~Pe<1$ the process is diffusion-controlled and restart can speed-up its completion by a factor of $\\sim1/Pe$. Such speedup occurs when the process is restarted at an optimal rate $r^{\\star}\\simeq r_0^{\\star}\\left(1-Pe\\right)$, where $r_0^{\\star}$ stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions --- some of its central features are completely generic.

76 citations

Journal ArticleDOI
TL;DR: In this article, the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary is quantified and the transition is governed by the P\'eclet number.
Abstract: First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the P\'eclet number ($Pe$) --- the ratio between the rates of advective and diffusive transport. When $Pe>1$ the process is drift-controlled and restart can only hinder its completion. In contrast, when $0\leq~Pe<1$ the process is diffusion-controlled and restart can speed-up its completion by a factor of $\sim1/Pe$. Such speedup occurs when the process is restarted at an optimal rate $r^{\star}\simeq r_0^{\star}\left(1-Pe\right)$, where $r_0^{\star}$ stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions --- some of its central features are completely generic.

72 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of resetting on diffusion in a logarithmic potential was studied, where a particle diffusing in a potential U(x) = U0 log |x| is reset, i.e., taken back to its initial position, with a constant rate r. The results presented in this paper generalize the results for simple diffusion with resetting.
Abstract: We study the effect of resetting on diffusion in a logarithmic potential. In this model, a particle diffusing in a potential U(x) = U0 log |x| is reset, i.e., taken back to its initial position, with a constant rate r. We show that this analytically tractable model system exhibits a series of transitions as a function of a single parameter, βU0, the ratio of the strength of the potential to the thermal energy. For βU0 −1, the potential is either weakly repulsive or attractive, and the diffusing particle eventually reaches the origin. In this case, we provide a closed-form expression for the subsequent first-passage time distribution and show that a resetting transition occurs at βU0 = 5. Namely, we find that resetting can expedite arrival to the origin when −1 5. The results presented herein generalize the results for simple diffusion with resetting—a widely applicable model that is obtained from ours by setting U0 = 0. Extending to general potential strengths, our work opens the door to theoretical and experimental investigation of a plethora of problems that bring together resetting and diffusion in logarithmic potential.

71 citations

Journal ArticleDOI
TL;DR: The ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na(3) cluster and the adiabatic PESs for the electronic states 2( 2)E' and 1(2)A(1)', and the non-adiabatic coupling (NAC) terms among those states are presented.
Abstract: We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na3 cluster and present the adiabatic PESs for the electronic states 22E′ and 12A1′, and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 22E′ and 12A1′ demonstrate the numerical validity of so called “Curl Condition,” such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the “adiabatic-diabatic transformation (ADT)” equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na3 cluster and thereby, to explore the numerical validity of the theoretical development o...

38 citations

Journal ArticleDOI
TL;DR: It is found that resetting can expedite arrival to the origin when -1 <βU0 < 5, but not when βU0 > 5, and the results presented herein generalize the results for simple diffusion with resetting.
Abstract: We study the effect of resetting on diffusion in a logarithmic potential. In this model, a particle diffusing in a potential $U(x) = U_0\log|x|$ is reset, i.e., taken back to its initial position, with a constant rate $r$. We show that this analytically tractable model system exhibits a series of phase transitions as a function of a single parameter, $\beta U_0$, the ratio of the strength of the potential to the thermal energy. For $\beta U_0 -1$ the potential is either weakly repulsive or attractive and the diffusing particle eventually reaches the origin. In this case, we provide a closed form expression for the subsequent first-passage time distribution and show that a resetting transition occurs at $\beta U_0=5$. Namely, we find that resetting can expedite arrival to the origin when $-1 5$. The results presented herein generalize results for simple diffusion with resetting -- a widely applicable model that is obtained from ours by setting $U_0=0$. Extending to general potential strengths, our work opens the door to theoretical and experimental investigation of a plethora of problems that bring together resetting and diffusion in logarithmic potential.

33 citations


Cited by
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Journal ArticleDOI
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

3,424 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider stochastic processes under resetting, which have attracted a lot of attention in recent years, and discuss multiparticle systems as well as extended systems, such as fluctuating interfaces.
Abstract: In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Levy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field. PACS numbers: 05.40.-a, 05.70.Fh, 02.50.Ey, 64.60.-i arXiv:1910.07993v2 [cond-mat.stat-mech]

361 citations

Journal ArticleDOI
20 Sep 2017-EPL
TL;DR: Gingrich et al. as discussed by the authors generalize the thermodynamic uncertainty relation, providing an entropic upper bound for average fluxes in time-continuous steady-state systems.
Abstract: We generalize the thermodynamic uncertainty relation, providing an entropic upper bound for average fluxes in time-continuous steady-state systems (Gingrich T. R. et al., Phys. Rev. Lett., 116 (2016) 120601), to time-discrete Markov chains and to systems under time-symmetric, periodic driving.

187 citations