178 research outputs found
Bimodality and hysteresis in systems driven by confined L\'evy flights
We demonstrate occurrence of bimodality and dynamical hysteresis in a system
describing an overdamped quartic oscillator perturbed by additive white and
asymmetric L\'evy noise. Investigated estimators of the stationary probability
density profiles display not only a turnover from unimodal to bimodal character
but also a change in a relative stability of stationary states that depends on
the asymmetry parameter of the underlying noise term. When varying the
asymmetry parameter cyclically, the system exhibits a hysteresis in the
occupation of a chosen stationary state.Comment: 4 pages, 5 figures, 30 reference
Memory beyond memory in heart beating: an efficient way to detect pathological conditions
We study the long-range correlations of heartbeat fluctuations with the
method of diffusion entropy. We show that this method of analysis yields a
scaling parameter that apparently conflicts with the direct evaluation
of the distribution of times of sojourn in states with a given heartbeat
frequency. The strength of the memory responsible for this discrepancy is given
by a parameter , which is derived from real data. The
distribution of patients in the (, )-plane yields a neat
separation of the healthy from the congestive heart failure subjects.Comment: submitted to Physical Review Letters, 5 figure
Superdiffusion in quasi-two-dimensional Yukawa liquids
The emergence and vanishing of superdiffusion in quasi-two-dimensional Yukawa
systems are investigated by molecular dynamics simulations. Using both the
asymptotic behaviour of the mean-squared displacement of the particles and the
long-time tail of the velocity autocorrelation function as indicators for
superdiffusion, we confirm the existence of a transition from normal diffusion
to superdiffusion in systems changing from a three-dimensional to a
two-dimensional character. A connection between superdiffusion and
dimensionality is established by the behaviour of the projected pair
distribution function
Levy flights in quenched random force fields
Levy flights, characterized by the microscopic step index f, are for f<2 (the
case of rare events) considered in short range and long range quenched random
force fields with arbitrary vector character to first loop order in an
expansion about the critical dimension 2f-2 in the short range case and the
critical fall-off exponent 2f-2 in the long range case. By means of a dynamic
renormalization group analysis based on the momentum shell integration method,
we determine flows, fixed point, and the associated scaling properties for the
probability distribution and the frequency and wave number dependent diffusion
coefficient. Unlike the case of ordinary Brownian motion in a quenched force
field characterized by a single critical dimension or fall-off exponent d=2,
two critical dimensions appear in the Levy case. A critical dimension (or
fall-off exponent) d=f below which the diffusion coefficient exhibits anomalous
scaling behavior, i.e, algebraic spatial behavior and long time tails, and a
critical dimension (or fall-off exponent) d=2f-2 below which the force
correlations characterized by a non trivial fixed point become relevant. As a
general result we find in all cases that the dynamic exponent z, characterizing
the mean square displacement, locks onto the Levy index f, independent of
dimension and independent of the presence of weak quenched disorder.Comment: 27 pages, Revtex file, 17 figures in ps format attached, submitted to
Phys. Rev.
Correlation Differences in Heartbeat Fluctuations During Rest and Exercise
We study the heartbeat activity of healthy individuals at rest and during
exercise. We focus on correlation properties of the intervals formed by
successive peaks in the pulse wave and find significant scaling differences
between rest and exercise. For exercise the interval series is anticorrelated
at short time scales and correlated at intermediate time scales, while for rest
we observe the opposite crossover pattern -- from strong correlations in the
short-time regime to weaker correlations at larger scales. We suggest a
physiologically motivated stochastic scenario to explain the scaling
differences between rest and exercise and the observed crossover patterns.Comment: 4 pages, 4 figure
A detection algorithm for the first jump time in sample trajectories of jump-diffusions driven by α-stable white noise
The purpose of this paper is to develop a detection algorithm for the first jump point in sampling trajectories of jump-diffusions which are described as solutions of stochastic differential equations driven by -stable white noise. This is done by a multivariate Lagrange interpolation approach. To this end, we utilise computer simulation algorithm in MATLAB to visualise the sampling trajectories of the jump-diffusions for various combinations of parameters arising in the modelling structure of stochastic differential equations
Multifractality in Human Heartbeat Dynamics
Recent evidence suggests that physiological signals under healthy conditions
may have a fractal temporal structure. We investigate the possibility that time
series generated by certain physiological control systems may be members of a
special class of complex processes, termed multifractal, which require a large
number of exponents to characterize their scaling properties. We report on
evidence for multifractality in a biological dynamical system --- the healthy
human heartbeat. Further, we show that the multifractal character and nonlinear
properties of the healthy heart rate are encoded in the Fourier phases. We
uncover a loss of multifractality for a life-threatening condition, congestive
heart failure.Comment: 19 pages, latex2e using rotate and epsf, with 5 ps figures; to appear
in Nature, 3 June, 199
Log-periodic route to fractal functions
Log-periodic oscillations have been found to decorate the usual power law
behavior found to describe the approach to a critical point, when the
continuous scale-invariance symmetry is partially broken into a discrete-scale
invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the
renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes
characterized by the amplitudes A(n) of the power law series expansion. These
two classes are separated by a novel ``critical'' point. Growth processes
(DLA), rupture, earthquake and financial crashes seem to be characterized by
oscillatory or bounded regular microscopic functions g(x) that lead to a slow
power law decay of A(n), giving strong log-periodic amplitudes. In contrast,
the regular function g(x) of statistical physics models with
``ferromagnetic''-type interactions at equibrium involves unbound logarithms of
polynomials of the control variable that lead to a fast exponential decay of
A(n) giving weak log-periodic amplitudes and smoothed observables. These two
classes of behavior can be traced back to the existence or abscence of
``antiferromagnetic'' or ``dipolar''-type interactions which, when present,
make the Green functions non-monotonous oscillatory and favor spatial modulated
patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new
demonstration of the source of strong log-periodicity and of a justification
of the general offered classification, update of reference lis
Oscillatory instability in super-diffusive reaction -- diffusion systems: fractional amplitude and phase diffusion equations
Nonlinear evolution of a reaction--super-diffusion system near a Hopf
bifurcation is studied. Fractional analogues of complex Ginzburg-Landau
equation and Kuramoto-Sivashinsky equation are derived, and some of their
analytical and numerical solutions are studied
Anomalous diffusion and the first passage time problem
We study the distribution of first passage time (FPT) in Levy type of
anomalous diffusion. Using recently formulated fractional Fokker-Planck
equation we obtain three results. (1) We derive an explicit expression for the
FPT distribution in terms of Fox or H-functions when the diffusion has zero
drift. (2) For the nonzero drift case we obtain an analytical expression for
the Laplace transform of the FPT distribution. (3) We express the FPT
distribution in terms of a power series for the case of two absorbing barriers.
The known results for ordinary diffusion (Brownian motion) are obtained as
special cases of our more general results.Comment: 25 pages, 4 figure
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