1,721,036 research outputs found
Dynamic importance sampling for the escape problem in nonequilibrium systems: Observation of shifts in optimal paths
No full textThe activation problem is investigated in two-dimensional nonequilibrium systems. A numerical approach based on dynamic importance sampling (DIMS) is introduced. DIMS accelerates the simulations and allows the investigation to access noise intensities that were previously forbidden. The escape path is observed to be shifted compared to a heteroclinic trajectory calculated in the limit of zero-noise intensity. A theory to account for such shifts is presented and shown to agree with the simulations for a wide range of noise intensities
Noise in nonlinear dynamical systems.
No full textNoise is commonly regarded as having a destructive but relatively innocuous effect, blurring our view of a system but having no effect on the underlying processes involved. In this paper we show, using examples from stochastic nonlinear dynamics, that these intuitive ideas about noise can be very misleading. For example, an effect known as stochastic resonance means that the addition of extra noise to a system can actually improve the signal-to-noise ratio
Dynamics importance sampling for the collection of switching events in vertical-cavity surface-emitting lasers
No full textA numerical approach based on dynamic importance sampling (DIMS) is applied to investigate polarization switches in vertical-cavity surface-emitting lasers. A polarization switch is described as an activation process in a two-dimensional nonequilibrium system. DIMS accelerates the simulations and allows access to noise intensities that were previously forbidden, revealing qualitative changes in the shape of the transition paths with noise intensity
STOCHASTIC RESONANCE IN THE LINEAR AND NONLINEAR RESPONSES OF A BISTABLE SYSTEM TO A PERIODIC FIELD
No full textEFFECT OF NOISE AND INERTIA ON MODULATION-INDUCED NEGATIVE DIFFERENTIAL RESISTANCE
No full textIt is demonstrated that modulation-induced negative differential resistance can survive in the presence of noise and inertia. In the limit of large periodic forcing, by perturbing about the overdamped, noise-free system, analytic predictions for the effects of weak noise or small inertia are obtained. These are shown to compare well with the results of detailed numerical simulations
Experiments on critical phenomena in a noisy exit problem
No full textWe consider a noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable exit path as the parameters of the system are changed, and a corresponding nonanalyticity of the generalized activation energy. We also investigate the extent to which the bifurcation is related to the local breaking of time-reversal invariance. [S0031-9007(97)04333-0]
Optimal fluctuations and the control of chaos
No full textThe energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel-Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identified with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms
ANALOG STOCHASTIC QUANTIZATION FOR A ONE-DIMENSIONAL BINARY ALLOY
No full textThe technique of analog stochastic quantization (ASQ), originally introduced in relation to the quantum harmonic oscillator, is applied to a more complicated quantum system: namely, a one-dimensional binary alloy. The results from an electronic analog simulator are compared with those obtained from numerical solutions of the Schrodinger equation, with which they are shown to be in agreement. It is argued on this basis that the ASQ technique can in principle be applied to one-dimensional quantum systems with arbitrary potentials
Comment on "Influence of Noise on Force Measurements"
Full text linkSUMMARY In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a
colloidal particle near a wall in the presence of a gravitational field for
which they study the influence of noise on the measurement of force. Their
central result is a striking discrepancy between the forces derived from
experimental drift measurements via their Eq. (1), and from the equilibrium
distribution. From this discrepancy they infer the stochastic calculus realised
in the system.
We comment, however: (a) that Eq. (1) does not hold for space-dependent
diffusion, and corrections should be introduced; and (b) that the "force"
derived from the drift need not coincide with the "force" obtained from the
equilibrium distribution
THE EFFECT OF MULTIPLICATIVE NOISE ON THE RELAXATION-TIME OF A REAL NONLINEAR PHYSICAL SYSTEM - A COMPARISON OF EXPERIMENT AND THEORY FOR THE RANDOM GROWING RATE MODEL (RGRM)
No full text- …
