1,998 research outputs found
Maximal -regularity for stochastic evolution equations
We prove maximal -regularity for the stochastic evolution equation
\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t),
\qquad t\in [0,T],
U(0) & = u_0, {aligned}. under the assumption that is a sectorial
operator with a bounded -calculus of angle less than on
a space . The driving process is a cylindrical
Brownian motion in an abstract Hilbert space . For and
and initial conditions in the real interpolation space
\XAp we prove existence of unique strong solution with trajectories in
L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities
F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to
\g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their
second variables with small enough Lipschitz constants. Extensions to the case
where is an adapted operator-valued process are considered as well.
Various applications to stochastic partial differential equations are worked
out in detail. These include higher-order and time-dependent parabolic
equations and the Navier-Stokes equation on a smooth bounded domain
\OO\subseteq \R^d with . For the latter, the existence of a unique
strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi
Multi-objective improvement of software using co-evolution and smart seeding
Optimising non-functional properties of software is an important part of the implementation process. One such property is execution time, and compilers target a reduction in execution time using a variety of optimisation techniques. Compiler optimisation is not always able to produce semantically equivalent alternatives that improve execution times, even if such alternatives are known to exist. Often, this is due to the local nature of such optimisations. In this paper we present a novel framework for optimising existing software using a hybrid of evolutionary optimisation techniques. Given as input the implementation of a program or function, we use Genetic Programming to evolve a new semantically equivalent version, optimised to reduce execution time subject to a given probability distribution of inputs. We employ a co-evolved population of test cases to encourage the preservation of the programâs semantics, and exploit the original program through seeding of the population in order to focus the search. We carry out experiments to identify the important factors in maximising efficiency gains. Although in this work we have optimised execution time, other non-functional criteria could be optimised in a similar manner
Racetrack inflation and assisted moduli stabilisation
We present a model of inflation based on a racetrack model without flux
stabilization. The initial conditions are set automatically through topological
inflation. This ensures that the dilaton is not swept to weak coupling through
either thermal effects or fast roll. Including the effect of non-dilaton fields
we find that moduli provide natural candidates for the inflaton. The resulting
potential generates slow-roll inflation without the need to fine tune
parameters. The energy scale of inflation must be near the GUT scale and the
scalar density perturbation generated has a spectrum consistent with WMAP data.Comment: 17 pages, 6 figures (Latex); Error in v.1 eliminated and improved
example of modular inflation presente
The Price of WMAP Inflation in Supergravity
The three-year data from WMAP are in stunning agreement with the simplest
possible quadratic potential for chaotic inflation, as well as with new or
symmetry-breaking inflation. We investigate the possibilities for incorporating
these potentials within supergravity, particularly of the no-scale type that is
motivated by string theory. Models with inflation driven by the matter sector
may be constructed in no-scale supergravity, if the moduli are assumed to be
stabilised by some higher-scale dynamics and at the expense of some
fine-tuning. We discuss specific scenarios for stabilising the moduli via
either D- or F-terms in the effective potential, and survey possible
inflationary models in the presence of D-term stabilisation.Comment: 15 pages, 6 figures, plain Late
On inversions and Doob -transforms of linear diffusions
Let be a regular linear diffusion whose state space is an open interval
. We consider a diffusion which probability law is
obtained as a Doob -transform of the law of , where is a positive
harmonic function for the infinitesimal generator of on . This is the
dual of with respect to where is the speed measure of
. Examples include the case where is conditioned to stay above
some fixed level. We provide a construction of as a deterministic
inversion of , time changed with some random clock. The study involves the
construction of some inversions which generalize the Euclidean inversions.
Brownian motion with drift and Bessel processes are considered in details.Comment: 19 page
Random walk on the range of random walk
We study the random walk X on the range of a simple random walk on †d in dimensions dâ„4. When dâ„5 we establish quenched and annealed scaling limits for the process X, which show that the intersections of the original simple random walk path are essentially unimportant. For d=4 our results are less precise, but we are able to show that any scaling limit for X will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions. Furthermore, we demonstrate that when d=4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of X to the origin
Anomalous U(1) D-term Contribution in Type I String Models
We study the -term contribution for anomalous U(1) symmetries in type I
string models and derive general formula for the -term contribution,
assuming that the dominant source of SUSY breaking is given by -terms of the
dilaton, (overall) moduli or twisted moduli fields. On the basis of the
formula, we also point out that there are several different features from the
case in heterotic string models. The differences originate from the different
forms of K\"ahler potential between twisted moduli fields in type I string
models and the dilaton field in heterotic string models.Comment: 16 pages, latex, no figur
Graphene Oxide Hybrid with SulfurâNitrogen Polymer for High-Performance Pseudocapacitors
Toward the introduction of fast faradaic pseudocapacitive behavior and the increase of the specific capacitance of carbon-based electrodes, we covalently functionalized graphene oxide with a redox active thiourea-formaldehyde polymer, yielding a multifunctional hybrid system. The multiscale physical and chemical characterization of the novel 3-dimensional hybrid revealed high material porosity with high specific surface area (402 m2 gâ1) and homogeneous element distribution. The presence of multiple functional groups comprising sulfur, nitrogen, and oxygen provide additional contribution of Faradaic redox reaction in supercapacity performance, leading to a high effective electrochemical pseudocapacitance. Significantly, our graphene-based 3-dimensional thiourea-formaldehyde hybrid exhibited specific capacitance as high as 400 F gâ1, areal capacitance of 160 mF cmâ2, and an energy density of 11.1 mWh cmâ3 at scan rate of 1 mV sâ1 with great capacitance retention (100%) after 5000 cycles at scan rate of 100 mV sâ1
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