462 research outputs found
Survival of interacting Brownian particles in crowded 1D environment
We investigate a diffusive motion of a system of interacting Brownian
particles in quasi-one-dimensional micropores. In particular, we consider a
semi-infinite 1D geometry with a partially absorbing boundary and the hard-core
inter-particle interaction. Due to the absorbing boundary the number of
particles in the pore gradually decreases. We present the exact analytical
solution of the problem. Our procedure merely requires the knowledge of the
corresponding single-particle problem. First, we calculate the simultaneous
probability density of having still a definite number of surviving
particles at definite coordinates. Focusing on an arbitrary tagged particle, we
derive the exact probability density of its coordinate. Secondly, we present a
complete probabilistic description of the emerging escape process. The survival
probabilities for the individual particles are calculated, the first and the
second moments of the exit times are discussed. Generally speaking, although
the original inter-particle interaction possesses a point-like character, it
induces entropic repulsive forces which, e.g., push the leftmost (rightmost)
particle towards (opposite) the absorbing boundary thereby accelerating
(decelerating) its escape. More importantly, as compared to the reference
problem for the non-interacting particles, the interaction changes the
dynamical exponents which characterize the long-time asymptotic dynamics.
Interesting new insights emerge after we interpret our model in terms of a)
diffusion of a single particle in a -dimensional space, and b) order
statistics defined on a system of independent, identically distributed
random variables
Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions
Properties of the four families of recently introduced special functions of
two real variables, denoted here by , and , are studied. The
superscripts and refer to the symmetric and antisymmetric functions
respectively. The functions are considered in all details required for their
exploitation in Fourier expansions of digital data, sampled on square grids of
any density and for general position of the grid in the real plane relative to
the lattice defined by the underlying group theory. Quality of continuous
interpolation, resulting from the discrete expansions, is studied, exemplified
and compared for some model functions.Comment: 22 pages, 10 figure
Three variable exponential functions of the alternating group
New class of special functions of three real variables, based on the
alternating subgroup of the permutation group , is studied. These
functions are used for Fourier-like expansion of digital data given on lattice
of any density and general position. Such functions have only trivial analogs
in one and two variables; a connection to the functions of is shown.
Continuous interpolation of the three dimensional data is studied and
exemplified.Comment: 10 pages, 3 figure
Matrix permanent and quantum entanglement of permutation invariant states
We point out that a geometric measure of quantum entanglement is related to
the matrix permanent when restricted to permutation invariant states. This
connection allows us to interpret the permanent as an angle between vectors. By
employing a recently introduced permanent inequality by Carlen, Loss and Lieb,
we can prove explicit formulas of the geometric measure for permutation
invariant basis states in a simple way.Comment: 10 page
Probabilities in the inflationary multiverse
Inflationary cosmology leads to the picture of a "multiverse," involving an
infinite number of (spatially infinite) post-inflationary thermalized regions,
called pocket universes. In the context of theories with many vacua, such as
the landscape of string theory, the effective constants of Nature are
randomized by quantum processes during inflation. We discuss an analytic
estimate for the volume distribution of the constants within each pocket
universe. This is based on the conjecture that the field distribution is
approximately ergodic in the diffusion regime, when the dynamics of the fields
is dominated by quantum fluctuations (rather than by the classical drift). We
then propose a method for determining the relative abundances of different
types of pocket universes. Both ingredients are combined into an expression for
the distribution of the constants in pocket universes of all types.Comment: 18 pages, RevTeX 4, 2 figures. Discussion of the full probability in
Sec.VI is sharpened; the conclusions are strengthened. Note added explaining
the relation to recent work by Easther, Lim and Martin. Some references adde
Reconstructing sparticle mass spectra using hadronic decays
Most sparticle decay cascades envisaged at the Large Hadron Collider (LHC) involve hadronic decays of intermediate particles. We use state-of-the art techniques based on the K⊥ jet algorithm to reconstruct the resulting hadronic final states for simulated LHC events in a number of benchmark supersymmetric scenarios. In particular, we show that a general method of selecting preferentially boosted massive particles such as W±, Z0 or Higgs bosons decaying to jets, using sub-jets found by the K⊥ algorithm, suppresses QCD backgrounds and thereby enhances the observability of signals that would otherwise be indistinct. Consequently, measurements of the supersymmetric mass spectrum at the per-cent level can be obtained from cascades including the hadronic decays of such massive intermediate bosons
Approximating the monomer-dimer constants through matrix permanent
The monomer-dimer model is fundamental in statistical mechanics. However, it
is #P-complete in computation, even for two dimensional problems. A
formulation in matrix permanent for the partition function of the monomer-dimer
model is proposed in this paper, by transforming the number of all matchings of
a bipartite graph into the number of perfect matchings of an extended bipartite
graph, which can be given by a matrix permanent. Sequential importance sampling
algorithm is applied to compute the permanents. For two-dimensional lattice
with periodic condition, we obtain , where the exact value is
. For three-dimensional lattice with periodic condition,
our numerical result is , {which agrees with the best known
bound .}Comment: 6 pages, 2 figure
The Portevin-Le Chatelier effect in the Continuous Time Random Walk framework
We present a continuous time random walk model for the Portevin-Le Chatelier
(PLC) effect. From our result it is shown that the dynamics of the PLC band can
be explained in terms of the Levy Walk
Repetitions in beta-integers
Classical crystals are solid materials containing arbitrarily long periodic
repetitions of a single motif. In this paper, we study the maximal possible
repetition of the same motif occurring in beta-integers -- one dimensional
models of quasicrystals. We are interested in beta-integers realizing only a
finite number of distinct distances between neighboring elements. In such a
case, the problem may be reformulated in terms of combinatorics on words as a
study of the index of infinite words coding beta-integers. We will solve a
particular case for beta being a quadratic non-simple Parry number.Comment: 11 page
Eml1 loss impairs apical progenitor spindle length and soma shape in the developing cerebral cortex
The ventricular zone (VZ) of the developing cerebral cortex is a pseudostratified epithelium that contains progenitors undergoing precisely regulated divisions at its most apical side, the ventricular lining (VL). Mitotic perturbations can contribute to pathological mechanisms leading to cortical malformations. The HeCo mutant mouse exhibits subcortical band heterotopia (SBH), likely to be initiated by progenitor delamination from the VZ early during corticogenesis. The causes for this are however, currently unknown. Eml1, a microtubule (MT)-associated protein of the EMAP family, is impaired in these mice. We first show that MT dynamics are perturbed in mutant progenitor cells in vitro. These may influence interphase and mitotic MT mechanisms and indeed, centrosome and primary cilia were altered and spindles were found to be abnormally long in HeCo progenitors. Consistently, MT and spindle length regulators were identified in EML1 pulldowns from embryonic brain extracts. Finally, we found that mitotic cell shape is also abnormal in the mutant VZ. These previously unidentified VZ characteristics suggest altered cell constraints which may contribute to cell delamination
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