1,178 research outputs found
Steady-state selection in driven diffusive systems with open boundaries
We investigate the stationary states of one-dimensional driven diffusive
systems, coupled to boundary reservoirs with fixed particle densities. We argue
that the generic phase diagram is governed by an extremal principle for the
macroscopic current irrespective of the local dynamics. In particular, we
predict a minimal current phase for systems with local minimum in the
current--density relation. This phase is explained by a dynamical phenomenon,
the branching and coalescence of shocks, Monte-Carlo simulations confirm the
theoretical scenario.Comment: 6 pages, 5 figure
Current reversal and exclusion processes with history-dependent random walks
A class of exclusion processes in which particles perform history-dependent
random walks is introduced, stimulated by dynamic phenomena in some biological
and artificial systems. The particles locally interact with the underlying
substrate by breaking and reforming lattice bonds. We determine the
steady-state current on a ring, and find current-reversal as a function of
particle density. This phenomenon is attributed to the non-local interaction
between the walkers through their trails, which originates from strong
correlations between the dynamics of the particles and the lattice. We
rationalize our findings within an effective description in terms of
quasi-particles which we call front barriers. Our analytical results are
complemented by stochastic simulations.Comment: 5 pages, 6 figure
Molecular Spiders in One Dimension
Molecular spiders are synthetic bio-molecular systems which have "legs" made
of short single-stranded segments of DNA. Spiders move on a surface covered
with single-stranded DNA segments complementary to legs. Different mappings are
established between various models of spiders and simple exclusion processes.
For spiders with simple gait and varying number of legs we compute the
diffusion coefficient; when the hopping is biased we also compute their
velocity.Comment: 14 pages, 2 figure
Testing the Elliott-Yafet spin-relaxation mechanism in KC8; a model system of biased graphene
Temperature dependent electron spin resonance (ESR) measurements are reported
on stage 1 potassium doped graphite, a model system of biased graphene. The ESR
linewidth is nearly isotropic and although the g-factor has a sizeable
anisotropy, its majority is shown to arise due to macroscopic magnetization.
Albeit the homogeneous ESR linewidth shows an unusual, non-linear temperature
dependence, it appears to be proportional to the resistivity which is a
quadratic function of the temperature. These observations suggests the validity
of the Elliott-Yafet relaxation mechanism in KC8 and allows to place KC8 on the
empirical Beuneu-Monod plot among ordinary elemental metals.Comment: 6 pages, 4 figures, submitted to Phys. Rev.
Probability distribution of magnetization in the one-dimensional Ising model: Effects of boundary conditions
Finite-size scaling functions are investigated both for the mean-square
magnetization fluctuations and for the probability distribution of the
magnetization in the one-dimensional Ising model. The scaling functions are
evaluated in the limit of the temperature going to zero (T -> 0), the size of
the system going to infinity (N -> oo) while N[1-tanh(J/k_BT)] is kept finite
(J being the nearest neighbor coupling). Exact calculations using various
boundary conditions (periodic, antiperiodic, free, block) demonstrate
explicitly how the scaling functions depend on the boundary conditions. We also
show that the block (small part of a large system) magnetization distribution
results are identical to those obtained for free boundary conditions.Comment: 8 pages, 5 figure
Simulation studies of permeation through two-dimensional ideal polymer networks
We study the diffusion process through an ideal polymer network, using
numerical methods. Polymers are modeled by random walks on the bonds of a
two-dimensional square lattice. Molecules occupy the lattice cells and may jump
to the nearest-neighbor cells, with probability determined by the occupation of
the bond separating the two cells. Subjected to a concentration gradient across
the system, a constant average current flows in the steady state. Its behavior
appears to be a non-trivial function of polymer length, mass density and
temperature, for which we offer qualitative explanations.Comment: 8 pages, 4 figure
Isotropic Transverse XY Chain with Energy- and Magnetization Currents
The ground-state correlations are investigated for an isotropic transverse XY
chain which is constrained to carry either a current of magnetization J_M or a
current of energy J_E. We find that the effect of nonzero J_M on the
large-distance decay of correlations is twofold: i) oscillations are introduced
and ii) the amplitude of the power law decay increases with increasing current.
The effect of energy current is more complex. Generically, correlations in
current carrying states are found to decay faster than in the J_E=0 states,
contrary to expectations that correlations are increased by the presence of
currents. However, increasing the current, one reaches a special line where the
correlations become comparable to those of the J_E=0 states. On this line, the
symmetry of the ground state is enhanced and the transverse magnetization
vanishes. Further increase of the current destroys the extra symmetry but the
transverse magnetization remains at the high-symmetry, zero value.Comment: 7 pages, RevTex, 4 PostScript figure
A dynamically extending exclusion process
An extension of the totally asymmetric exclusion process, which incorporates
a dynamically extending lattice is explored. Although originally inspired as a
model for filamentous fungal growth, here the dynamically extending exclusion
process (DEEP) is studied in its own right, as a nontrivial addition to the
class of nonequilibrium exclusion process models. Here we discuss various
mean-field approximation schemes and elucidate the steady state behaviour of
the model and its associated phase diagram. Of particular note is that the
dynamics of the extending lattice leads to a new region in the phase diagram in
which a shock discontinuity in the density travels forward with a velocity that
is lower than the velocity of the tip of the lattice. Thus in this region the
shock recedes from both boundaries.Comment: 20 pages, 12 figure
Exact solution of a two-type branching process: Clone size distribution in cell division kinetics
We study a two-type branching process which provides excellent description of
experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The
model involves only a single type of progenitor cell, and does not require
support from a self-renewed population of stem cells. The progenitor cells
divide and may differentiate into post-mitotic cells. We derive an exact
solution of this model in terms of generating functions for the total number of
cells, and for the number of cells of different types. We also deduce large
time asymptotic behaviors drawing on our exact results, and on an independent
diffusion approximation.Comment: 16 page
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