Delay differential equations (DDE's) are a powerful modeling
tool used in several fields, such as optics, climatology,
and physiology. An important characteristic of these
equations is the presence of an effectively
infinite-dimensional phase space, which allows DDE's to
exhibit a high level of multistability. This multistability
can lead to unexpected results when DDE's are stochastically
driven, as illustrated by recent work on an overdamped
particle with delayed coupling to a quartic and
stochastically driven potential [S. Guillouzic, I.
L'Heureux, and A. Longtin, Phys. Rev. E 61, 4906
(2000)]. In this case, the presence of an attractor
characterized by unbounded oscillatory trajectories prevents
the stochastic process describing the position of the
particle from approaching a steady-state limit. In this
talk, we report on the study of the transition to this
peculiar attractor for a family of single-well potentials.
Of particular note is the fact that the transition rate is
found to follow Arrhenius' law when the noise amplitude is
small.
[C32.002] Lack of a Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System
G. Korniss (Rensselaer), P.A. Rikvold, M.A. Novotny (Florida State U.)
We discuss the subtle finite-size effects of the dynamic phase transition (DPT) in the two-dimensional kinetic Ising model in an oscillating external field. We present analytical and computational evidence that there is no finite-temperature tri-critical point in this spatially extended bistable system. This is in contrast with claims made by Acharyya(M. Acharyya, Phys. Rev. E 59), 218 (1999). for the existence of a tri-critical point in this system. Large-scale simulations reveal that the negative dip of the Binder cumulant and the corresponding three-peak order-parameter distribution (otherwise characteristics of a first order transition) are merely finite-size effects. When the DPT prevails in the thermodynamic limit, it is always continuous(G. Korniss, C.J. White, P.A. Rikvold, and M.A. Novotny, Phys.\ Rev.\ E 63) (2001), in press; e-print cond-mat/0008155.. The ``spurious" finite-size effects are related to the stochastic nature of the underlying metastable decay for ``small" systems(S.W. Sides, P.A. Rikvold, and M.A. Novotny, Phys.\ Rev.\ E 57), 6512 (1998); 59, 2710 (1999)..
[C32.003] Double Stochastic Resonance Peaks in Systems with Dynamic Phase Transitions
Beom Jun Kim, Petter Minnhagen (Dept. of Theoretical Physics, Umea University, Sweden), Hyun Jin Kim, M. Y. Choi (Dept. of Physics, Seoul National University, Korea), Gun Sang Jeon (Center for Strongly Correlated Materials Research, Seoul National University, Korea)
To probe the connection between the dynamic phase transition
and stochastic resonance, we study the mean-field kinetic
Ising model and the two-dimensional Josephson-junction array
in the presence of appropriate oscillating magnetic fields.
Observed in both systems are double stochastic
resonance peaks, one below and the other above the dynamic
transition temperature, the appearance of which is argued to
be a generic property of the system with a continuous
dynamic phase transition. In particular, the frequency
matching condition around the dynamic phase transition
between the external drive frequency and the internal
characteristic frequency of the system is identified as the
origin of such double peaks.
[C32.004] Noninvasive Control of Stochastic Resonance
Jonathan Mason (Georgia Institute of Technology), John Lindner (College of Wooster), Joseph Neff, Barbara Breen (Georgia Institute of Technology), Adi Bulsara (SPAWAR Systems Center), William Ditto (Georgia Institute of Technology)
External feedback can enhance (or depress) the response of a
noisy bistable system to monochromatic signals,
significantly magnifying its natural stochastic resonance.
We compare and contrast a variety of such feedback
strategies, using both numerical simulations and analog
electronic experiments. These noninvasive control techniques
are especially valuable for noisy bistable systems that are
difficult or impossible to modify internally.
[C32.005] Monostable array enhanced stochastic resonance
Barbara Breen (Georgia Institute of Technology), John Lindner, Meghan Wills (The College of Wooster), Adi Bulsara (Space and Naval Warfare Systems Center), William Ditto (Georgia Institute of Technology)
We present a simple nonlinear system that exhibits
arbitrarily many distinct stochastic resonances. By
adjusting the noise and coupling of an array of underdamped,
monostable oscillators, we modify the array’s natural
frequencies so that the spectral response of a typical
oscillator in an array of oscillators exhibits different
stochastic resonances. Such families of resonances may
elucidate and facilitate a variety of noise-mediated
cooperative phenomena, such as Noise Enhanced Propagation,
in a broad class of similar nonlinear systems.
[C32.006] Stochastic Resonance and Noise-Induced Phase Synchronization
Jan A. Freund, Lutz Schimansky-Geier (Institute of Physics, Humboldt-University at Berlin, Germany), Andre Longtin (Physics Department, University of Ottawa, Canada)
The phenomenon of stochastic resonance can be reformulated
in the framework of externally driven nonlinear oscillators.
Amplitude and phase descriptions of the latter mentioned
systems can be transferred to one of the paradigms for SR,
the two state system. The phenomena of frequency and phase
locking can thus be revisited in the context of SR which
reveals itself through the fact that both effects can be
enhanced by optimal noise. We present the idea of
noise-induced phase synchronization starting out from a
simple model system which allows for an entirely analytic
treatment. Bridging to the dynamics of neurons requires the
inclusion of memory kernels (semi-Markovian processes).
[C32.007] Delayed stochastic resonance with 1-D chain of binary elements
Toru Ohira (Sony Computer Science Laboratories, Tokyo, Japan)
We discuss a simple model of 1-dimensional chain of binary stochastic elements with delayed interaction. Each element makes transitions between its two states, with probabilities which depends on the fixed-interval-past state of the preceding element in the chain. We show that rather regular spiking behavior emerges with suitably tuned parameters. This can be seen as a stochastic resonance just from noise and delay coupling alone without external oscillatory signals. This phenomena is analyzed theoretically and its applications to communication systems or biological systems are discussed. This is an extension of previous woks on delayed stochastic resonance with single[1] and two units [2].
[1] Toru Ohira and Yuzuru Sato, "Resonance with noise and delay", PRL vol 82, pp.2811-2815 (1999).
[2] Toru Ohira and Yuzuru Sato, "Resonance in Delayed
Stochastic Dynamics", Statistical Physics, (Tokuyama and
Stanley, eds.) , AIP conference Proceedings 519, pp. 628-634
(2000).
[C32.008] Stochastic Resonance and Optimal Detection in Noise-Floor Limited Systems
Mario Inchiosa (SPAWAR Systems Center, San Diego (US Navy)), John Robinson (Defence Research Establishment, Stockholm, Sweden), Adi Bulsara (SPAWAR Systems Center, San Diego (US Navy))
We show that in systems whose output must compete with a
noise source, Stochastic Resonance (maximization of output
signal-noise separation as a nonmonotonic function of input
noise strength) exists even when measured in terms of
fundamental statistical measures and optimal\/
detector performance [Inchiosa, Robinson, and Bulsara, Phys.
Rev. Lett. 85 3369 (2000)]. This is in contrast to the
commonly considered scenario where, without the competing
noise, the system (e.g.\ a driven, overdamped particle
moving in a double well potential) is essentially invertible
and optimal detector performance monotonically deteriorates
with increasing input noise strength.
[C32.009] Enhanced Diffusion and Mobility of Brownian Particles in Periodic Potentials
Ethan H. Cannon, David Potashnik, Gerald J. Iafrate (Department of Electrical Engineering, University of Notre Dame)
We model the transport properties of Brownian particles in a
periodic potential with external forcing using the
Fokker-Planck equation. For time-independent forcing,
enhanced diffusion is indicated; while for time-periodic
forcing, enhanced mobility and directed diffusion in an
asymmetric potential are found. We discuss the dependence of
transport properties on the force strength and frequency,
and we explore ramifications of enhanced diffusion and
mobility for diffusion-based semiconductor devices.
[C32.010] Fluctuations and Onset of Coherence in a Thermoacoustic Engine
Young Sang Kwon, Orest Symko (University of Utah, Department of Physics)
We have investigated air pressure fluctuations in a
thermoacoustic engine which was operated as a prime mover
with heat producing sound in a resonator. A temperature
gradient was gradually applied across a stack in the
resonator and at some critical value pressure fluctuations
triggered the onset of acoustic oscillations which were then
sustained by heat from the stack. The pressure fluctuations
were amplified by the stack, which has a large surface area,
and were released at the end of the stack triggering
eventually the oscillations. Results show the growth of
coherence in resonator oscillations as induced by random
fluctuations in the presence of a temperature gradient.
[C32.011] Correlated noise and avalanches in combustion fronts
J. Maunuksela, M. Myllys, J. Merikoski, J. Timonen (Dept of Physics, Univ of Jyvaskyla, P.O. Box 35, FIN-40351 Jyvaskyla, Finland)
Slow combustion fronts propagating in paper have been shown previously to display kinetic roughening, which asymptotically is in the KPZ Universality class with white noise, but at short scale has definitely higher apparent scaling exponents as well as apparent multiscaling behavior. We will report new accurate results for measured fronts in which effective filtering methods are used to reduce digitizing errors and other erratic factors. Utilizing numerical solution of the KPZ equation with the real mass density of the paper as the input noise, we find that avalanches are responsible for the apparent multiscaling, and noise correlations for the higher apparent scaling exponents at short scales.
[1] J. Maunuksela, M. Myllys, O.-P. Kahkonen, N. Provatas, M. J. Alava, and T. Ala-Nissila, Phys. Rev. Lett. 79, 1515 (1997).
[2] M. Myllys, J. Maunuksela, M.J. Alava, T. Ala-Nissila,
and J. Timonen, Phys. Rev. Lett. 84, 1946 (2000).
[C32.012] Control of diffusion with optical tweezers
Lowell McCann (University of Wisconsin-River Falls)
A Brownian particle confined in a potential energy landscape moves from one local minimum to another by thermal activation over the intervening potential barrier. In a spatially symmetric potential, there is normally no preferential direction for this motion. We have shown experimentally that a Brownian particle in a symmetric potential will move in one preferential direction due to the presence of a weak zero-average periodic external field that is asymmetric in time. In these experiments, the diffusing object is a submicron colloidal sphere and the symmetric potential is created with a pair of single beam optical traps. A biharmonic modulation is applied to the system, allowing control of the direction of the hopping through adjustment of the phase angle between the harmonics. Controlling the direction of diffusion should prove useful in separating polydisperse suspensions.