1,236 research outputs found
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
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
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
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.
Characterization of the quasi-one-dimensional compounds δ-(EDT-TTF-CONMe2)2X, X=AsF6 and Br by vibrational spectroscopy and density functional theory calculations
We have investigated the infrared spectra of the quarter-filled charge-ordered insulators delta-(EDT-TTF-CONMe2)(2)X (X=AsF6, Br) along all three crystallographic directions in the temperature range from 300 to 10 K. DFT-assisted normal mode analysis of the neutral and ionic EDT-TTF-CONMe2 molecule allows us to assign the experimentally observed intramolecular modes and to obtain relevant information on the charge ordering and intramolecular interactions. From frequencies of charge-sensitive vibrations we deduce that the charge-ordered state is already present at room temperature and does not change on cooling, in agreement with previous NMR measurements. The spectra taken along the stacking direction clearly show features of vibrational overtones excited due to the anharmonic electronic molecule potential caused by the large charge disproportionation between the molecular sites. The shift of certain vibrational modes indicates the onset of the structural transition below 200 K. (C) 2014 AIP Publishing LLC
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
Molecular Spiders with Memory
Synthetic bio-molecular spiders with "legs" made of single-stranded segments
of DNA can move on a surface which is also covered by single-stranded segments
of DNA complementary to the leg DNA. In experimental realizations, when a leg
detaches from a segment of the surface for the first time it alters that
segment, and legs subsequently bound to these altered segments more weakly.
Inspired by these experiments we investigate spiders moving along a
one-dimensional substrate, whose legs leave newly visited sites at a slower
rate than revisited sites. For a random walk (one-leg spider) the slowdown does
not effect the long time behavior. For a bipedal spider, however, the slowdown
generates an effective bias towards unvisited sites, and the spider behaves
similarly to the excited walk. Surprisingly, the slowing down of the spider at
new sites increases the diffusion coefficient and accelerates the growth of the
number of visited sites.Comment: 10 pages, 3 figure
Ground State Energy of the One-Dimensional Discrete Random Schr\"{o}dinger Operator with Bernoulli Potential
In this paper, we show the that the ground state energy of the one
dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is
controlled asymptotically as the system size N goes to infinity by the random
variable \ell_N, the length the longest consecutive sequence of sites on the
lattice with potential equal to zero. Specifically, we will show that for
almost every realization of the potential the ground state energy behaves
asymptotically as in the sense that the ratio of
the quantities goes to one
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