131 research outputs found
Stochastic chaos: An analog of quantum chaos
Some intriging connections between the properties of nonlinear noise driven
systems and the nonlinear dynamics of a particular set of Hamilton's equation
are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger
equation, can exhibit a transition in their spectral statistics as a coupling
parameter is varied. This transition is connected to the transition to
non-integrability in the Hamilton's equations.Comment: Uuencoded compressed postscript file, 4 pages, 3 fig
Temporally Asymmetric Fluctuations are Sufficient for the Operation of a Correlation Ratchet
It has been shown that the combination of a broken spatial symmetry in the
potential (or ratchet potential) and time correlations in the driving are
crucial, and enough to allow transformation of the fluctuations into work. The
required broken spatial symmetry implies a specific molecular arrangement of
the proteins involved. Here we show that a broken spatial symmetry is not
required, and that temporally asymmetric fluctuations (with mean zero) can be
used to do work, even when the ratchet potential is completely symmetric.
Temporal asymmetry, defined as a lack of invariance of the statistical
properties under the operation to temporal inversion, is a generic property of
nonequilibrium fluctuation, and should therefore be expected to be quite common
in biological systems.Comment: 17 pages, ps figures on request, LaTeX Article Forma
Recovering ‘lost’ information in the presence of noise: application to rodent–predator dynamics.
A Hamiltonian approach is introduced for the reconstruction of trajectories and models of complex stochastic dynamics from noisy measurements. The method converges even when entire trajectory components are unobservable and the parameters are unknown. It is applied to reconstruct nonlinear models of rodent–predator oscillations in Finnish Lapland and high-Arctic tundra. The projected character of noisy incomplete measurements is revealed and shown to result in a degeneracy of the likelihood function within certain null-spaces. The performance of the method is compared with that of the conventional Markov chain Monte Carlo (MCMC) technique
Trans-membrane Signal Transduction and Biochemical Turing Pattern Formation
The Turing mechanism for the production of a broken spatial symmetry in an initially homogeneous system of reacting and diffusing substances has attracted much interest as a potential model for certain aspects of morphogenesis such as pre-patterning in the embryo, and has also served as a model for self-organization in more generic systems. The two features necessary for the formation of Turing patterns are short-range autocatalysis and long-range inhibition which usually only occur when the diffusion rate of the inhibitor is significantly greater than that of the activator. This observation has sometimes been used to cast doubt on applicability of the Turing mechanism to cellular patterning since many messenger molecules that diffuse between cells do so at more-or-less similar rates. Here we show that stationary, symmetry-breaking Turing patterns can form in physiologically realistic systems even when the extracellular diffusion coefficients are equal; the kinetic properties of the 'receiver' and 'transmitter' proteins responsible for signal transduction will be primary factors governing this process
Observable and hidden singular features of large fluctuations in nonequilibrium systems
We study local features, and provide a topological insight into the global
structure of the probability density distribution and of the pattern of the
optimal paths for large rare fluctuations away from a stable state. In contrast
to extremal paths in quantum mechanics, the optimal paths do {\it not}
encounter caustics. We show how this occurs, and what, instead of caustics, are
the experimentally observable singularities of the pattern. We reveal the
possibility for a caustic and a switching line to start at a saddle point, and
discuss the consequences.Comment: 10 pages, 3 ps figures by request, LaTeX Article Format (In press,
Phys. Lett. A
Applications of dynamical inference to the analysis of noisy biological time series with hidden dynamical variables.
We present a Bayesian framework for parameter inference in noisy, non-stationary, nonlinear, dynamical systems. The technique is implemented in two distinct ways: (i) Lightweight implementation: to be used for on-line analysis, allowing multiple parameter estimation, optimal compensation for dynamical noise, and reconstruction by integration of the hidden dynamical variables, but with some limitations on how the noise appears in the dynamics; (ii) Full scale implementation: of the technique with extensive numerical simulations (MCMC), allowing for more sophisticated reconstruction of hidden dynamical trajectories and dealing better with sources of noise external to the dynamics (measurements noise)
Realistic Models of Biological Motion
The origin of biological motion can be traced back to the function of
molecular motor proteins. Cytoplasmic dynein and kinesin transport organelles
within our cells moving along a polymeric filament, the microtubule. The motion
of the myosin molecules along the actin filaments is responsible for the
contraction of our muscles. Recent experiments have been able to reveal some
important features of the motion of individual motor proteins, and a new
statistical physical description - often referred to as ``thermal ratchets'' -
has been developed for the description of motion of these molecules. In this
approach the motors are considered as Brownian particles moving along
one-dimensional periodic structures due to the effect of nonequilibrium
fluctuations. Assuming specific types of interaction between the particles the
models can be made more realistic. We have been able to give analytic solutions
for our model of kinesin with elastically coupled Brownian heads and for the
motion of the myosin filament where the motors are connected through a rigid
backbone. Our theoretical predictions are in a very good agreement with the
various experimental results. In addition, we have considered the effects
arising as a result of interaction among a large number of molecular motors,
leading to a number of novel cooperative transport phenomena.Comment: 12 pages (5 figures). submitted to Elsevier Preprin
Rectification of Fluctuations in an Underdamped Ratchet
We investigate analytically the motion of underdamped particles subject to a
deterministic periodic potential and a periodic temperature. Despite the fact
that an underamped particle experiences the temperature oscillation many times
in its escape out of a well and in its motion along the potential, a net
directed current linear in the friction constant is found. If both the
potential and the temperature modulation are sinusoidal with a phase lag
, this current is proportional to .Comment: 4 pages REVTEX, 2 figures include
Cooperative Transport of Brownian Particles
We consider the collective motion of finite-sized, overdamped Brownian
particles (e.g., motor proteins) in a periodic potential. Simulations of our
model have revealed a number of novel cooperative transport phenomena,
including (i) the reversal of direction of the net current as the particle
density is increased and (ii) a very strong and complex dependence of the
average velocity on both the size and the average distance of the particles.Comment: 4 pages, 5 figure
- …