1,017 research outputs found
Deterministic SR in a Piecewise Linear Chaotic Map
The phenomenon of Stochastic Resonance (SR) is observed in a completely
deterministic setting - with thermal noise being replaced by one-dimensional
chaos. The piecewise linear map investigated in the paper shows a transition
from symmetry-broken to symmetric chaos on increasing a system parameter. In
the latter state, the chaotic trajectory switches between the two formerly
disjoint attractors, driven by the map's inherent dynamics. This chaotic
switching rate is found to `resonate' with the frequency of an externally
applied periodic perturbation (multiplicative or additive). By periodically
modulating the parameter at a specific frequency , we observe the
existence of resonance where the response of the system (in terms of the
residence-time distribution) is maximum. This is a clear indication of SR-like
behavior in a chaotic system.Comment: 6 pages LaTex, 4 figure
Statistical mechanics of money: How saving propensity affects its distribution
We consider a simple model of a closed economic system where the total money
is conserved and the number of economic agents is fixed. In analogy to
statistical systems in equilibrium, money and the average money per economic
agent are equivalent to energy and temperature, respectively. We investigate
the effect of the saving propensity of the agents on the stationary or
equilibrium money distribution.The equilibrium probablity distribution of money
becomes the usual Gibb's distribution, characteristic of non-interacting
agents, when the agents do not save. However with saving, even for local or
individual self-interest, the dynamics become cooperative and the resulting
asymmetric Gaussian-like stationary distribution acquires global ordering
properties. Intriguing singularities are observed in the stationary money
distribution in the market, as function of the ``marginal saving propensity''
of the agents.Comment: 9 pages, 5 figures. Revised version with major changes in the text
and figures (to appear in Euro. Phys. Jour. B
Dynamic transitions and hysteresis
When an interacting many-body system, such as a magnet, is driven in time by
an external perturbation, such as a magnetic field,the system cannot respond
instantaneously due to relaxational delay. The response of such a system under
a time-dependent field leads to many novel physical phenomena with intriguing
physics and important technological applications. For oscillating fields, one
obtains hysteresis that would not occur under quasistatic conditions in the
presence of thermal fluctuations. Under some extreme conditions of the driving
field, one can also obtain a non-zero average value of the variable undergoing
such dynamic hysteresis. This non-zero value indicates a breaking of symmetry
of the hysteresis loop, around the origin. Such a transition to the
spontaneously broken symmetric phase occurs dynamically when the driving
frequency of the field increases beyond its threshold value which depends on
the field amplitude and the temperature. Similar dynamic transitions also occur
for pulsed and stochastically varying fields. We present an overview of the
ongoing researches in this not-so-old field of dynamic hysteresis and
transitions.Comment: 30 Pages Revtex, 10 Postscript figures. To appear in Reviews of
Modern Physics, April, 199
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