798 research outputs found
Random walks reaching against all odds the other side of the quarter plane
For a homogeneous random walk in the quarter plane with nearest-neighbor
transitions, starting from some state , we study the event that the
walk reaches the vertical axis, before reaching the horizontal axis. We derive
an exact expression for the probability of this event, and derive an asymptotic
expression for the case when becomes large, a situation in which the
event becomes highly unlikely. The exact expression follows from the solution
of a boundary value problem and is in terms of an integral that involves a
conformal gluing function. The asymptotic expression follows from the
asymptotic evaluation of this integral. Our results find applications in a
model for nucleosome shifting, the voter model and the asymmetric exclusion
process.Comment: 18 pages, 2 figures, to appear in Journal of Applied Probabilit
Phase diagram of a generalized ABC model on the interval
We study the equilibrium phase diagram of a generalized ABC model on an
interval of the one-dimensional lattice: each site is occupied by a
particle of type \a=A,B,C, with the average density of each particle species
N_\a/N=r_\a fixed. These particles interact via a mean field
non-reflection-symmetric pair interaction. The interaction need not be
invariant under cyclic permutation of the particle species as in the standard
ABC model studied earlier. We prove in some cases and conjecture in others that
the scaled infinite system N\rw\infty, i/N\rw x\in[0,1] has a unique
density profile \p_\a(x) except for some special values of the r_\a for
which the system undergoes a second order phase transition from a uniform to a
nonuniform periodic profile at a critical temperature .Comment: 25 pages, 6 figure
Phase fluctuations in the ABC model
We analyze the fluctuations of the steady state profiles in the modulated
phase of the ABC model. For a system of sites, the steady state profiles
move on a microscopic time scale of order . The variance of their
displacement is computed in terms of the macroscopic steady state profiles by
using fluctuating hydrodynamics and large deviations. Our analytical prediction
for this variance is confirmed by the results of numerical simulations
On the dynamical behavior of the ABC model
We consider the ABC dynamics, with equal density of the three species, on the
discrete ring with sites. In this case, the process is reversible with
respect to a Gibbs measure with a mean field interaction that undergoes a
second order phase transition. We analyze the relaxation time of the dynamics
and show that at high temperature it grows at most as while it grows at
least as at low temperature
Phase diagram of the ABC model on an interval
The three species asymmetric ABC model was initially defined on a ring by
Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was
later studied by Clincy, Derrida, and Evans. Here the latter model is studied
on a one-dimensional lattice of N sites with closed (zero flux) boundaries. In
this geometry the local particle conserving dynamics satisfies detailed balance
with respect to a canonical Gibbs measure with long range asymmetric pair
interactions. This generalizes results for the ring case, where detailed
balance holds, and in fact the steady state measure is known only for the case
of equal densities of the different species: in the latter case the stationary
states of the system on a ring and on an interval are the same. We prove that
in the N to infinity limit the scaled density profiles are given by (pieces of)
the periodic trajectory of a particle moving in a quartic confining potential.
We further prove uniqueness of the profiles, i.e., the existence of a single
phase, in all regions of the parameter space (of average densities and
temperature) except at low temperature with all densities equal; in this case a
continuum of phases, differing by translation, coexist. The results for the
equal density case apply also to the system on the ring, and there extend
results of Clincy et al.Comment: 52 pages, AMS-LaTeX, 8 figures from 10 eps figure files. Revision:
minor changes in response to referee reports; paper to appear in J. Stat.
Phy
Entrepreneurial intention studies: A hybrid bibliometric method to identify new directions for theory and research
Fragmentation is the main obstacle to scientific progress on entrepreneurial intention. To address this issue, we systematise the current literature with a hybrid bibliometric method that combines co-citation and bibliographic coupling analysis for the first time in entrepreneurial intention studies to show the field's knowledge base and research fronts and to examine how divergent perspectives have challenged the core knowledge of the field. We highlight three recurring dimensions of entrepreneurial intention studies: (1) personal factors, (2) social factors and (3) investigational settings. In addition to introducing new constructs, divergent perspectives have emphasised the interplay between these components and challenged the mechanisms connecting them. Based on these findings, we extend previous classifications in the literature by providing a framework that integrates divergent perspectives with the field's knowledge base, helping establish future research avenues and improving the theorising process of entrepreneurial intention
Spacecraft VLBI tracking to enhance stellar occultations astrometry of planetary satellites
Stellar occultations currently provide the most accurate ground-based
measurements of the positions of natural satellites (down to a few kilometres
for the Galilean moons). However, when using these observations in the
calculation of satellite ephemerides, the uncertainty in the planetary
ephemerides dominates the error budget of the occultation. We quantify the
local refinement in the central planet's position achievable by performing Very
Long Baseline Interferometry (VLBI) tracking of an in-system spacecraft
temporally close to an occultation. We demonstrate the potential of using VLBI
to enhance the science return of stellar occultations for satellite
ephemerides. We identified the most promising observation and tracking
opportunities offered by the Juno spacecraft around Jupiter as perfect test
cases, for which we ran simulations of our VLBI experiment. VLBI tracking at
Juno's perijove close to a stellar occultation locally (in time) reduces the
uncertainty in Jupiter's angular position in the sky to 250-400 m. This
represents up to an order of magnitude improvement with respect to current
solutions and is lower than the stellar occultation error, thus allowing the
moon ephemeris solution to fully benefit from the observation. Our simulations
showed that the proposed tracking and observation experiment can efficiently
use synergies between ground- and space-based observations to enhance the
science return on both ends. The reduced error budget for stellar occultations
indeed helps to improve the moons' ephemerides, which in turn benefit planetary
missions and their science products, such as the recently launched JUICE and
upcoming Europa Clipper missions
- …