184 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 $\omega$, 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

### The travelling salesman problem on randomly diluted lattices: results for small-size systems

If one places N cities randomly on a lattice of size L, we find that the
normalized optimal travel distances per city in the Euclidean and Manhattan
metrics vary monotonically with the city concentration p. We have studied such
optimal tours for visiting all the cities using a branch and bound algorithm,
giving exact optimized tours for small system sizes (N<100). Extrapolating the
results for N tending to infinity, we find that the normalized optimal travel
distances per city in the Euclidean and Manhattan metrics both equal unity for
p=1, and they reduce to about 0.74 and 0.94, respectively, as p tends to zero.
Although the problem is trivial for p=1, it certainly reduces to the standard
TSP on continuum (NP-hard problem) for p tending to zero. We did not observe
any irregular behaviour at any intermediate point. The crossover from the
triviality to the NP-hard problem seems to occur at p=1.Comment: 7 pages, 4 figures. Revised version with changes in text and figures
(to be published in Euro. Phys. Jour. B

### Fat tailed distributions for deaths in conflicts and disasters

We study the statistics of human deaths from wars, conflicts, similar
man-made conflicts as well as natural disasters. The probability distribution
of number of people killed in natural disasters as well as man made situations
show power law decay for the largest sizes, with similar exponent values.
Comparisons with natural disasters, when event sizes are measured in terms of
physical quantities (e.g., energy released in earthquake, volume of rainfall,
land area affected in forest fires, etc.) also show striking resemblances. The
universal patterns in their statistics suggest that some subtle similarities in
their mechanisms and dynamics might be responsible.Comment: 6 pages, 3 figs + 2 table

### 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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