172 research outputs found
Stochastic resonance in electrical circuits—I: Conventional stochastic resonance.
No full textStochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory
Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.
No full textStochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate
From the potential of the mean force to a quasiparticle's effective potential in narrow ion channels
No full textWe consider the selective permeation of ions through narrow water-filled channels in the presence of strong interaction between the ions. These interactions lead to highly correlated ionic motion, which can conveniently be described via the concept of a quasiparticle. Here, we connect the quasiparticle's effective potential and the multi-ion potential of the mean force, found through molecular dynamics simulations, and we validate the method on an analytical toy model of the KcsA channel. Possible future applications of the method to the connection between molecular dynamical calculations and the experimentally measured current-voltage and current-concentration characteristics of the channel are discussed
Physics of selective conduction and point mutation in biological ion channels
No full textWe introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. We derive an effective grand-canonical ensemble and generalized Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K+ channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical
Polarization switches in vertical-cavity surface-emitting lasers
No full textThe polarization dynamics of a vertical cavity surface emitting laser is investigated as a nonlinear stochastic dynamical system. The polarization switches in the device are considered as activation processes in a two dimensional system with a saddle cycle; the optimal way of switching is determined as the solution of a boundary value problem. The theoretical results are in good agreement with the numerical simulations
Fluctuations and the energy-optimal control of chaos.
No full textThe energy-optimal entraining of the dynamics of a periodically driven oscillator, moving it from a chaotic attractor to a coexisting stable limit cycle, is investigated via analysis of fluctuational transitions between the two states. The deterministic optimal control function is identified with the corresponding optimal fluctuational force, which is found by numerical and analog simulations
Stochastic resonance : linear response and giant nonlinearity.
No full textThe response of a bistable system to a weak periodic force is investigated using linear response theory (LRT) and by analogue electronic experiment. For quasithermal systems the response, and in particular its increase with increasing noise intensity D, are described by the fluctuation dissipation relations. For small D the low-frequency susceptibility of the system chi(omega) has been found in explicit form allowing for both forced oscillations about the states and periodic modulation of the probabilities of fluctuational transitions between the states. It is shown, both theoretically and experimentally, that a phase lag phi between the force and the response passes through a maximum when D is tuned through the range where stochastic resonance (SR) occurs. A giant nonlinearity of the response is shown to arise for small D and small frequencies of the driving force. It results in the signal induced by a sinusoidal force being nearly rectangular. The range of applicability of LRT is established
Field-dependent dehydration and optimal ionic escape paths for C2N membranes
No full textMost analytic theories describing electrostatically driven ion transport through water-filled nanopores assume that the corresponding permeation barriers are bias-independent. While this assumption may hold for sufficiently wide pores under infinitely small bias, transport through subnanometer pores under finite bias is difficult to interpret analytically. Given recent advances in subnanometer pore fabrication and the rapid progress in detailed computer simulations, it is important to identify and understand the specific field-induced phenomena arising during ion transport. Here we consider an atomistic model of electrostatically driven ion permeation through subnanoporous C2N membranes. We analyze probability distributions of ionic escape trajectories and show that the optimal escape path switches between two different configurations depending on the bias magnitude. We identify two distinct mechanisms contributing to field-induced changes in transport-opposing barriers: a weak one arising from field-induced ion dehydration and a strong one due to the field-induced asymmetry of the hydration shells. The simulated current-voltage characteristics are compared with the solution of the 1D Nernst-Planck model. Finally, we show that the deviation of simulated currents from analytic estimates for large fields is consistent with the field-induced barriers and the observed changes in the optimal ion escape path
Zero-dispersion nonlinear resonance in dissipative systems.
No full textIt is shown theoretically and by analog electronic experiment that, in dissipative oscillatory systems for which the frequency of eigenoscillation displays an extremum as a function of energy, the dynamics of nonlinear resonance can differ markedly from the conventional case. Transitions between the conventional and novel types of nonlinear resonance, as parameters vary, correspond to changes in the topology of basins of attraction. With added noise, they can result in drastic changes in fluctuational transition rates between small- and large-amplitude regimes
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