18,426 research outputs found
Transient Random Walks in Random Environment on a Galton-Watson Tree
We consider a transient random walk in random environment on a
Galton--Watson tree. Under fairly general assumptions, we give a sharp and
explicit criterion for the asymptotic speed to be positive. As a consequence,
situations with zero speed are revealed to occur. In such cases, we prove that
is of order of magnitude , with . We also
show that the linearly edge reinforced random walk on a regular tree always has
a positive asymptotic speed, which improves a recent result of Collevecchio
\cite{Col06}
Classification of n-qubit states with minimum orbit dimension
The group of local unitary transformations acts on the space of n-qubit pure
states, decomposing it into orbits. In a previous paper we proved that a
product of singlet states (together with an unentangled qubit for a system with
an odd number of qubits) achieves the smallest possible orbit dimension, equal
to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits.
In this paper we show that any state with minimum orbit dimension must be of
this form, and furthermore, such states are classified up to local unitary
equivalence by the sets of pairs of qubits entangled in singlets.Comment: 15 pages, latex, revision 2, conclusion added, some proofs shortene
Upgrades of beam diagnostics in support of emittance-exchange experiments at the Fermilab A0 photoinjector
The possibility of using electron beam phase space manipulations to support a
free-electron laser accelerator design optimization has motivated our research.
An on-going program demonstrating the exchange of transverse horizontal and
longitudinal emittances at the Fermilab A0 photoinjector has benefited recently
from the upgrade of several of the key diagnostics stations. Accurate
measurements of these properties upstream and downstream of the exchanger
beamline are needed. Improvements in the screen resolution term and reduced
impact of the optical system's depth-of-focus by using YAG:Ce single crystals
normal to the beam direction will be described. The requirement to measure
small energy spreads (<10 keV) in the spectrometer and the exchange process
which resulted in bunch lengths less than 500 fs led to other diagnostics
performance adjustments and upgrades as well. A longitudinal to transverse
exchange example is also reported.Comment: 16 p
Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II
The strong convergence of Wong-Zakai approximations of the solution to the
reflecting stochastic differential equations was studied in [2]. We continue
the study and prove the strong convergence under weaker assumptions on the
domain.Comment: To appear in "Stochastic Analysis and Applications 2014-In Honour of
Terry Lyons", Springer Proceedings in Mathematics and Statistic
Understanding the dynamics of cellular responsiveness to modifications of metabolic substrates in perifusion
A novel microperifusion system with capabilities for continuous, real-time, potentiometric monitoring of extracellular hydrogen ion concentration has been used to define the response of HeLa cells to abrupt changes in extracellular energy sources or introduction of an inhibitor of glycolysis. Glycolytic inhibition, induced by removal of glucose or introduction of iodoacetate, each led to a rapid, continuous decrease in acid release. The response to iodoacetate took longer than removal of glucose, perhaps due to the time required for binding and activation. Once inhibition began, however, the rate of change was greater than following glucose removal. Conversely, recovery time following iodoacetate inhibition was much slower than with glucose removal. Unlike the response to short-term glucose depletion, a second pulse of iodoacetate resulted in a faster response followed by an even longer recovery time. The response to switching between glucose and glutamine began almost without evident delay. The response patterns revealed that HeLa cells prefer glutamine to glucose, but, in the presence of both energy sources, some glucose continues to be used. In summary, these results indicate that continuous, real-time monitoring of the kinetics of hydrogen-ion release can be used to gain new insights into the dynamics of cellular response to perturbations of extracellular energy sources. © 1994 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49889/1/1041600103_ftp.pd
Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
Monte Carlo simulations and finite-size scaling analysis have been carried
out to study the critical behavior in a two-dimensional system of particles
with two bonding sites that, by decreasing temperature or increasing density,
polymerize reversibly into chains with discrete orientational degrees of
freedom and, at the same time, undergo a continuous isotropic-nematic (IN)
transition. A complete phase diagram was obtained as a function of temperature
and density. The numerical results were compared with mean field (MF) and real
space renormalization group (RSRG) analytical predictions about the IN
transformation. While the RSRG approach supports the continuous nature of the
transition, the MF solution predicts a first-order transition line and a
tricritical point, at variance with the simulation results.Comment: 12 pages, 10 figures, supplementary informatio
Slow movement of a random walk on the range of a random walk in the presence of an external field
In this article, a localisation result is proved for the biased random walk
on the range of a simple random walk in high dimensions (d \geq 5). This
demonstrates that, unlike in the supercritical percolation setting, a slowdown
effect occurs as soon a non-trivial bias is introduced. The proof applies a
decomposition of the underlying simple random walk path at its cut-times to
relate the associated biased random walk to a one-dimensional random walk in a
random environment in Sinai's regime
Cosmological solutions, p-branes and the Wheeler-DeWitt equation
The low energy effective actions which arise from string theory or M-theory
are considered in the cosmological context, where the graviton, dilaton and
antisymmetric tensor field strengths depend only on time. We show that previous
results can be extended to include cosmological solutions that are related to
the E_N Toda equations. The solutions of the Wheeler-DeWitt equation in
minisuperspace are obtained for some of the simpler cosmological models by
introducing intertwining operators that generate canonical transformations
which map the theories into free theories. We study the cosmological properties
of these solutions, and also briefly discuss generalised Brans-Dicke models in
our framework. The cosmological models are closely related to p-brane solitons,
which we discuss in the context of the E_N Toda equations. We give the explicit
solutions for extremal multi-charge (D-3)-branes in the truncated system
described by the D_4 =O(4,4) Toda equations.Comment: 11 pages (2-column), Revte
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