14,045 research outputs found
Cooperative surmounting of bottlenecks
The physics of activated escape of objects out of a metastable state plays a
key role in diverse scientific areas involving chemical kinetics, diffusion and
dislocation motion in solids, nucleation, electrical transport, motion of flux
lines superconductors, charge density waves, and transport processes of
macromolecules, to name but a few. The underlying activated processes present
the multidimensional extension of the Kramers problem of a single Brownian
particle. In comparison to the latter case, however, the dynamics ensuing from
the interactions of many coupled units can lead to intriguing novel phenomena
that are not present when only a single degree of freedom is involved. In this
review we report on a variety of such phenomena that are exhibited by systems
consisting of chains of interacting units in the presence of potential
barriers.
In the first part we consider recent developments in the case of a
deterministic dynamics driving cooperative escape processes of coupled
nonlinear units out of metastable states. The ability of chains of coupled
units to undergo spontaneous conformational transitions can lead to a
self-organised escape. The mechanism at work is that the energies of the units
become re-arranged, while keeping the total energy conserved, in forming
localised energy modes that in turn trigger the cooperative escape. We present
scenarios of significantly enhanced noise-free escape rates if compared to the
noise-assisted case.
The second part deals with the collective directed transport of systems of
interacting particles overcoming energetic barriers in periodic potential
landscapes. Escape processes in both time-homogeneous and time-dependent driven
systems are considered for the emergence of directed motion. It is shown that
ballistic channels immersed in the associated high-dimensional phase space are
the source for the directed long-range transport
Equilibrium and dynamical properties of two dimensional self-gravitating systems
A system of N classical particles in a 2D periodic cell interacting via
long-range attractive potential is studied. For low energy density a
collapsed phase is identified, while in the high energy limit the particles are
homogeneously distributed. A phase transition from the collapsed to the
homogeneous state occurs at critical energy U_c. A theoretical analysis within
the canonical ensemble identifies such a transition as first order. But
microcanonical simulations reveal a negative specific heat regime near .
The dynamical behaviour of the system is affected by this transition : below
U_c anomalous diffusion is observed, while for U > U_c the motion of the
particles is almost ballistic. In the collapsed phase, finite -effects act
like a noise source of variance O(1/N), that restores normal diffusion on a
time scale diverging with N. As a consequence, the asymptotic diffusion
coefficient will also diverge algebraically with N and superdiffusion will be
observable at any time in the limit N \to \infty. A Lyapunov analysis reveals
that for U > U_c the maximal exponent \lambda decreases proportionally to
N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy,
in spite of a clear non ergodicity of the system, a common scaling law \lambda
\propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two
column version with included figures : less paper waste
Transport in finite size systems: an exit time approach
In the framework of chaotic scattering we analyze passive tracer transport in
finite systems. In particular, we study models with open streamlines and a
finite number of recirculation zones. In the non trivial case with a small
number of recirculation zones a description by mean of asymptotic quantities
(such as the eddy diffusivity) is not appropriate. The non asymptotic
properties of dispersion are characterized by means of the exit time
statistics, which shows strong sensitivity on initial conditions. This yields a
probability distribution function with long tails, making impossible a
characterization in terms of a unique typical exit time.Comment: 16 RevTeX pages + 6 eps-figures include
Coexistence of absolute negative mobility and anomalous diffusion
Using extensive numerical studies we demonstrate that absolute negative
mobility of a Brownian particle (i.e. the net motion into the direction
opposite to a constant biasing force acting around zero bias) does coexist with
anomalous diffusion. The latter is characterized in terms of a nonlinear
scaling with time of the mean-square deviation of the particle position. Such
anomalous diffusion covers "coherent" motion (i.e. the position dynamics x(t)
approaches in evolving time a constant dispersion), ballistic diffusion,
subdiffusion, superdiffusion and hyperdiffusion. In providing evidence for this
coexistence we consider a paradigmatic model of an inertial Brownian particle
moving in a one-dimensional symmetric periodic potential being driven by both
an unbiased time-periodic force and a constant bias. This very setup allows for
various sorts of different physical realizations
Chaotic Scattering Theory of Transport and Reaction-Rate Coefficients
The chaotic scattering theory is here extended to obtain escape-rate
expressions for the transport coefficients appropriate for a simple classical
fluid, or for a chemically reacting system. This theory allows various
transport coefficients such as the coefficients of viscosity, thermal
conductivity, etc., to be expressed in terms of the positive Lyapunov exponents
and Kolmogorov-Sinai entropy of a set of phase space trajectories that take
place on an appropriate fractal repeller. This work generalizes the previous
results of Gaspard and Nicolis for the coefficient of diffusion of a particle
moving in a fixed array of scatterers.Comment: 27 pages LaTeX, no figure
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