8 research outputs found
Winning combinations of history-dependent games
The Parrondo effect describes the seemingly paradoxical situation in which
two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24
(2000)]. Here we generalize this analysis to the case where both games are
history-dependent, i.e. there is an intrinsic memory in the dynamics of each
game. New results are presented for the cases of both random and periodic
switching between the two games.Comment: (6 pages, 7 figures) Version 2: Major cosmetic changes and some minor
correction
Breaking of general rotational symmetries by multi-dimensional classical ratchets
We demonstrate that a particle driven by a set of spatially uncorrelated,
independent colored noise forces in a bounded, multidimensional potential
exhibits rotations that are independent of the initial conditions. We calculate
the particle currents in terms of the noise statistics and the potential
asymmetries by deriving an n-dimensional Fokker-Planck equation in the small
correlation time limit. We analyze a variety of flow patterns for various
potential structures, generating various combinations of laminar and rotational
flows.Comment: Accepted, Physical Review
On the essential spectrum of Nadirashvili-Martin-Morales minimal surfaces
We show that the spectrum of a complete submanifold properly immersed into a
ball of a Riemannian manifold is discrete, provided the norm of the mean
curvature vector is sufficiently small. In particular, the spectrum of a
complete minimal surface properly immersed into a ball of is
discrete. This gives a positive answer to a question of Yau.Comment: This article is an improvement of an earlier version titled On the
spectrum of Martin-Morales minimal surfaces. 7 page
Nitrate leaching from a felled Sitka spruce plantation in Beddgelert Forest, North Wales
Simulation of circuits demonstrating stochastic resonance
In certain dynamical systems, the addition of noise can assist the detection of a signal and not degrade it as normally expected. This is possible via a phenomenon termed stochastic resonance (SR), where the response of a nonlinear system to a subthreshold periodic input signal is optimal for some non-zero value of noise intensity. We investigate the SR phenomenon in several circuits and systems. Although SR occurs in many disciplines, the sinusoidal signal by itself is not information bearing. To greatly enhance the practicality of SR, an (aperiodic) broadband signal is preferable. Hence, we employ aperiodic stochastic resonance (ASR) where noise can enhance the response of a nonlinear system to a weak aperiodic signal. We can characterize ASR by the use of cross-correlation-based measures. Using this measure, the ASR in a simple threshold system and in a FitzHugh-Nagumo neuronal model are compared using numerical simulations. Using both weak periodic and aperiodic signals, we show that the response of a nonlinear system is enhanced, regardless of the signal. © 2000 Elsevier Science Ltd. All rights reserved