10 research outputs found
Dispersion of the time spent in a state: General expression for unicyclic model and dissipation-less precision
We compare the relation between dispersion and dissipation for two random
variables that can be used to characterize the precision of a Brownian clock.
The first random variable is the current between states. In this case, a
certain precision requires a minimal energetic cost determined by a known
thermodynamic uncertainty relation. We introduce a second random variable that
is a certain linear combination of two random variables, each of which is the
time a stochastic trajectory spends in a state. Whereas the first moment of
this random variable is equal to the average probability current, its
dispersion is generally different from the dispersion associated with the
current. Remarkably, for this second random variable a certain precision can be
obtained with an arbitrarily low energy dissipation, in contrast to the
thermodynamic uncertainty relation for the current. As a main technical
achievement, we provide an exact expression for the dispersion related to the
time that a stochastic trajectory spends in a cluster of states for a general
unicyclic network.Comment: 17 pages, 1 figur
Rate enhancement of gated drift-diffusion process by optimal resetting
`Gating' is a widely observed phenomenon in biochemistry that describes the
transition between the activated (or open) and deactivated (or closed) states
of an ion-channel, which makes transport through that channel highly selective.
In general, gating is a mechanism that imposes an additional restriction on a
transport, as the process ends only when the `gate' is open and continues
otherwise. When diffusion occurs in presence of a constant bias to a {\it
gated} target, i.e., to a target that switches between an open and a closed
state, the dynamics essentially slows down compared to {\it ungated}
drift-diffusion, resulting in an increase in the mean completion time. In this
work, we utilize stochastic resetting as an external protocol to counterbalance
the delay due to gating. We consider a particle that undergoes drift-diffusion
in the presence of a stochastically gated target and is moreover subjected to a
rate-limiting resetting dynamics. Calculating the minimal mean completion time
rendered by an optimal resetting for this exactly-solvable system, we construct
a phase diagram that owns three distinct phases: (i) where resetting can make
gated drift-diffusion faster even compared to the original ungated process,
(ii) where resetting still expedites gated drift-diffusion, but not beyond the
original ungated process, and (iii) where resetting fails to expedite gated
drift-diffusion. Gated drift-diffusion aptly models various stochastic
processes such as chemical reactions that exclusively take place for certain
activated state of the reactants. Our work predicts the conditions where
stochastic resetting can act as a useful strategy to enhance the rate of such
processes without compromising on their selectivity.Comment: 12 Pages, 8 Figure
The role of interplay between the potential and the ambient energies on the vibration energy harvesting
In this paper we have demonstrated how the conversion of the ambient energy into the electrical energy depends on the properties of the ambient energy and the mechanical oscillator. We have observed that the conversion of the vibration energy into the electrical energy may be good if the voltage can follow closely the evolution of of the amplitude of the oscillator. Thus if the voltage and the position fluctuate in a correlated manner then the conversion of the ambient energy into the electrical energy is good. Our another observation is that for a given capacitance, the power transferred (PT) from the oscillator to the transducer may be maximum in the variation of PT with increase in resistance, R. In other words, the power transferred changes with a maximum as the capacitance, C grows for a fixed value of the resistance. Along with these we have investigated how the other relevant quantities such as the efficiency of the energy transferred process depends on the characteristics of the oscillating systems, the environment and the piezoelectric dynamics
Synchronization of Nonidentical Coupled Phase Oscillators in the Presence of Time Delay and Noise
We have studied in this paper the dynamics of globally coupled phase oscillators having the Lorentzian
frequency distribution with zero mean in the presence of both time delay and noise. Noise may
be Gaussian or non-Gaussian in characteristics. In the limit of zero noise strength, we find that
the critical coupling strength (CCS) increases linearly as a function of time delay. Thus the role
of time delay in the dynamics for the deterministic system is qualitatively equivalent to the effect
of frequency fluctuations of the phase oscillators by additive white noise in absence of time delay.
But for the stochastic model, the critical coupling strength grows nonlinearly with the increase of
the time delay. The linear dependence of the critical coupling strength on the noise intensity also
changes to become nonlinear due to creation of additional phase difference among the oscillators
by the time delay. We find that the creation of phase difference plays an important role in the
dynamics of the system when the intrinsic correlation induced by the finite correlation time of the
noise is small. We also find that the critical coupling is higher for the non-Gaussian noise compared
to the Gaussian one due to higher effective noise strength