75,284 research outputs found
Binary Mixtures of Particles with Different Diffusivities Demix
The influence of size differences, shape, mass and persistent motion on phase
separation in binary mixtures has been intensively studied. Here we focus on
the exclusive role of diffusivity differences in binary mixtures of equal-sized
particles. We find an effective attraction between the less diffusive
particles, which are essentially caged in the surrounding species with the
higher diffusion constant. This effect leads to phase separation for systems
above a critical size: A single close-packed cluster made up of the less
diffusive species emerges. Experiments for testing of our predictions are
outlined.Comment: 5 figures in main text, 8 figures in Supplemental Materia
Directed chaos in a billiard chain with transversal magnetic field
In generic Hamiltonian systems with a mixed phase space chaotic transport may
be directed and ballistic rather than diffusive. We investigate one particular
model showing this behaviour, namely a spatially periodic billiard chain in
which electrons move under the influence of a perpendicular magnetic field. We
analyze the phase-space structure and derive an explicit expression for the
chaotic transport velocity. Unlike previous studies of directed chaos our model
has a parameter regime in which the dispersion of an ensemble of chaotic
trajectories around its moving center of mass is essentially diffusive. We
explain how in this limit the deterministic chaos reduces to a biased random
walk in a billiard with a rough surface. The diffusion constant for this
simplified model is calculated analytically
Do interactions increase or reduce the conductance of disordered electrons? It depends!
We investigate the influence of electron-electron interactions on the
conductance of two-dimensional disordered spinless electrons. By using an
efficient numerical method which is based on exact diagonalization in a
truncated basis of Hartree-Fock states we are able to determine the exact
low-energy properties of comparatively large systems in the diffusive as well
as in the localized regimes. We find that weak interactions increase the d.c.
conductance in the localized regime while they decrease the d.c. conductance in
the diffusive regime. Strong interactions always decrease the conductance. We
also study the localization of single-particle excitations close to the Fermi
energy which turns out to be only weakly influenced by the interactions.Comment: final version as publsihed, 4 pages REVTEX, 6 EPS figures include
Influence of stochastic domain growth on pattern nucleation for diffusive systems with internal noise
Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport. However, self-organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity, as illustrated by the behavior of the French-flag model in response to intrinsic noise and Turing’s model when subjected to fluctuations in initial conditions. Domain growth is known to be a stabilizing factor for the latter, though the interaction of intrinsic noise and domain growth is underexplored, even in the simplest of biophysical settings. Previously, we developed analytical Fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems. In this paper we extend our analysis to encompass stochastically growing domains. This form of growth can be used only to link the meso- and macroscopic domains as the “box-splitting” form of growth on the microscopic scale has an ill-defined thermodynamic limit. The extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain, while stochastically controlling the length of each discretized compartment. Due to the dependence of diffusion on the domain discretization, we find that the description of diffusion cannot be uniquely derived. We apply these analytical methods to two justified descriptions, where it is shown that, under certain conditions, diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium, without additional kinetics. Finally, a logistically growing domain is considered. Not only does this show that we can deal with nonmonotonic descriptions of stochastic growth, but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary “on average.
Coherent quantum transport in disordered systems I: The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems
Excitonic transport in static disordered one dimensional systems is studied
in the presence of thermal fluctuations that are described by the
Haken-Strobl-Reineker model. For short times, non-diffusive behavior is
observed that can be characterized as the free-particle dynamics in the
Anderson localized system. Over longer time scales, the environment-induced
dephasing is sufficient to overcome the Anderson localization caused by the
disorder and allow for transport to occur which is always seen to be diffusive.
In the limiting regimes of weak and strong dephasing quantum master equations
are developed, and their respective scaling relations imply the existence of a
maximum in the diffusion constant as a function of the dephasing rate that is
confirmed numerically. In the weak dephasing regime, it is demonstrated that
the diffusion constant is proportional to the square of the localization length
which leads to a significant enhancement of the transport rate over the
classical prediction. Finally, the influence of noise and disorder on the
absorption spectrum is presented and its relationship to the transport
properties is discussed.Comment: 23 pages, 7 figure
A measure of individual role in collective dynamics
Identifying key players in collective dynamics remains a challenge in several
research fields, from the efficient dissemination of ideas to drug target
discovery in biomedical problems. The difficulty lies at several levels: how to
single out the role of individual elements in such intermingled systems, or
which is the best way to quantify their importance. Centrality measures
describe a node's importance by its position in a network. The key issue
obviated is that the contribution of a node to the collective behavior is not
uniquely determined by the structure of the system but it is a result of the
interplay between dynamics and network structure. We show that dynamical
influence measures explicitly how strongly a node's dynamical state affects
collective behavior. For critical spreading, dynamical influence targets nodes
according to their spreading capabilities. For diffusive processes it
quantifies how efficiently real systems may be controlled by manipulating a
single node.Comment: accepted for publication in Scientific Report
Effect of boundary conditions on diffusion in two-dimensional granular gases
We analyze the influence of boundary conditions on numerical simulations of
the diffusive properties of a two dimensional granular gas. We show in
particular that periodic boundary conditions introduce unphysical correlations
in time which cause the coefficient of diffusion to be strongly dependent on
the system size. On the other hand, in large enough systems with hard walls at
the boundaries, diffusion is found to be independent of the system size. We
compare the results obtained in this case with Langevin theory for an elastic
gas. Good agreement is found. We then calculate the relaxation time and the
influence of the mass for a particle of radius in a sea of particles of
radius . As granular gases are dissipative, we also study the influence of
an external random force on the diffusion process in a forced dissipative
system. In particular, we analyze differences in the mean square velocity and
displacement between the elastic and inelastic cases.Comment: 15 figures eps figures, include
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