824 research outputs found
Local asymptotics for controlled martingales
We consider controlled martingales with bounded steps where the controller is
allowed at each step to choose the distribution of the next step, and where the
goal is to hit a fixed ball at the origin at time . We show that the
algebraic rate of decay (as increases to infinity) of the value function in
the discrete setup coincides with its continuous counterpart, provided a
reachability assumption is satisfied. We also study in some detail the
uniformly elliptic case and obtain explicit bounds on the rate of decay. This
generalizes and improves upon several recent studies of the one dimensional
case, and is a discrete analogue of a stochastic control problem recently
investigated in Armstrong and Trokhimtchouck [Calc. Var. Partial Differential
Equations 38 (2010) 521-540].Comment: Published at http://dx.doi.org/10.1214/15-AAP1123 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the Composition of Gauge Structures
A formulation for a non-trivial composition of two classical gauge structures
is given: Two parent gauge structures of a common base space are synthesized so
as to obtain a daughter structure which is fundamental by itself. The model is
based on a pair of related connections that take their values in the product
space of the corresponding Lie algebras. The curvature, the covariant exterior
derivatives and the associated structural identities, all get contributions
from both gauge groups. The various induced structures are classified into
those whose composition is given just by trivial means, and those which possess
an irreducible nature. The pure irreducible piece, in particular, generates a
complete super-space of ghosts with an attendant set of super-BRST variation
laws, both of which are purely of a geometrical origin.Comment: Few elaborations are added to section 4 and section 5. To be
published in Journal of Physics A: Mathematical and General. 21 page
Limited Range Fractality of Randomly Adsorbed Rods
Multiple resolution analysis of two dimensional structures composed of
randomly adsorbed penetrable rods, for densities below the percolation
threshold, has been carried out using box-counting functions. It is found that
at relevant resolutions, for box-sizes, , between cutoffs given by the
average rod length and the average inter-rod distance $r_1$, these
systems exhibit apparent fractal behavior. It is shown that unlike the case of
randomly distributed isotropic objects, the upper cutoff $r_1$ is not only a
function of the coverage but also depends on the excluded volume, averaged over
the orientational distribution. Moreover, the apparent fractal dimension also
depends on the orientational distributions of the rods and decreases as it
becomes more anisotropic. For box sizes smaller than the box counting
function is determined by the internal structure of the rods, whether simple or
itself fractal. Two examples are considered - one of regular rods of one
dimensional structure and rods which are trimmed into a Cantor set structure
which are fractals themselves. The models examined are relevant to adsorption
of linear molecules and fibers, liquid crystals, stress induced fractures and
edge imperfections in metal catalysts. We thus obtain a distinction between two
ranges of length scales: where the internal structure of the
adsorbed objects is probed, and where their distribution is
probed, both of which may exhibit fractal behavior. This distinction is
relevant to the large class of systems which exhibit aggregation of a finite
density of fractal-like clusters, which includes surface growth in molecular
beam epitaxy and diffusion-limited-cluster-cluster-aggregation models.Comment: 10 pages, 7 figures. More info available at
http://www.fh.huji.ac.il/~dani/ or
http://www.fiz.huji.ac.il/staff/acc/faculty/biham or
http://chem.ch.huji.ac.il/employee/avnir/iavnir.htm . Accepted for
publication in J. Chem. Phy
Remarks on a constrained optimization problem for the Ginibre ensemble
We study the limiting distribution of the eigenvalues of the Ginibre ensemble
conditioned on the event that a certain proportion lie in a given region of the
complex plane. Using an equivalent formulation as an obstacle problem, we
describe the optimal distribution and some of its monotonicity properties
Exactly Marginal Deformations of N=4 SYM and of its Supersymmetric Orbifold Descendants
In this paper we study exactly marginal deformations of field theories living
on D3-branes at low energies. These theories include N=4 supersymmetric
Yang-Mills theory and theories obtained from it via the orbifolding procedure.
We restrict ourselves only to orbifolds and deformations which leave some
supersymmetry unbroken. A number of new families of N=1 superconformal field
theories are found. We analyze the deformations perturbatively, and also by
using general arguments for the dimension of the space of exactly marginal
deformations. We find some cases where the space of perturbative exactly
marginal deformations is smaller than the prediction of the general analysis at
least up to three-loop order), and other cases where the perturbative result
(at low orders) has a non-generic form.Comment: 25 pages, 1 figure. v2: added preprint number, references adde
Stochastic Simulations of the Repressilator Circuit
The genetic repressilator circuit consists of three transcription factors, or
repressors, which negatively regulate each other in a cyclic manner. This
circuit was synthetically constructed on plasmids in {\it Escherichia coli} and
was found to exhibit oscillations in the concentrations of the three
repressors. Since the repressors and their binding sites often appear in low
copy numbers, the oscillations are noisy and irregular. Therefore, the
repressilator circuit cannot be fully analyzed using deterministic methods such
as rate-equations. Here we perform stochastic analysis of the repressilator
circuit using the master equation and Monte Carlo simulations. It is found that
fluctuations modify the range of conditions in which oscillations appear as
well as their amplitude and period, compared to the deterministic equations.
The deterministic and stochastic approaches coincide only in the limit in which
all the relevant components, including free proteins, plasmids and bound
proteins, appear in high copy numbers. We also find that subtle features such
as cooperative binding and bound-repressor degradation strongly affect the
existence and properties of the oscillations.Comment: Accepted to PR
Diffusion-limited reactions on disordered surfaces with continuous distributions of binding energies
We study the steady state of a stochastic particle system on a
two-dimensional lattice, with particle influx, diffusion and desorption, and
the formation of a dimer when particles meet. Surface processes are thermally
activated, with (quenched) binding energies drawn from a \emph{continuous}
distribution. We show that sites in this model provide either coverage or
mobility, depending on their energy. We use this to analytically map the system
to an effective \emph{binary} model in a temperature-dependent way. The
behavior of the effective model is well-understood and accurately describes key
quantities of the system: Compared with discrete distributions, the temperature
window of efficient reaction is broadened, and the efficiency decays more
slowly at its ends. The mapping also explains in what parameter regimes the
system exhibits realization dependence.Comment: 23 pages, 8 figures. Submitted to: Journal of Statistical Mechanics:
Theory and Experimen
Surface potential at a ferroelectric grain due to asymmetric screening of depolarization fields
Nonlinear screening of electric depolarization fields, generated by a stripe
domain structure in a ferroelectric grain of a polycrystalline material, is
studied within a semiconductor model of ferroelectrics. It is shown that the
maximum strength of local depolarization fields is rather determined by the
electronic band gap than by the spontaneous polarization magnitude.
Furthermore, field screening due to electronic band bending and due to presence
of intrinsic defects leads to asymmetric space charge regions near the grain
boundary, which produce an effective dipole layer at the surface of the grain.
This results in the formation of a potential difference between the grain
surface and its interior of the order of 1 V, which can be of either sign
depending on defect transition levels and concentrations. Exemplary acceptor
doping of BaTiO3 is shown to allow tuning of the said surface potential in the
region between 0.1 and 1.3 V.Comment: 14 pages, 11 figures, submitted to J. Appl. Phy
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