46 research outputs found
On a Class of Martingale Problems on Banach Spaces
We introduce the local martingale problem associated to semilinear stochastic
evolution equations driven by a cylindrical Wiener process and establish a
one-to-one correspondence between solutions of the martingale problem and
(analytically) weak solutions of the stochastic equation. We also prove that
the solutions of well-posed equations are strong Markov processes. We apply our
results to semilinear stochastic equations with additive noise where the
semilinear term is merely measurable and to stochastic reaction-diffusion
equations with H\"older continuous multiplicative noise.Comment: Incorporated referee's comments; final versio
Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces
We prove a Miyadera-Voigt type perturbation theorem for strong Feller
semigroups. Using this result, we prove well-posedness of the semilinear
stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdW_H(t) on a separable
Banach space E, assuming that F is bounded and measurable and that the
associated linear equation, i.e. the equation with F = 0, is well-posed and its
transition semigroup is strongly Feller and satisfies an appropriate gradient
estimate. We also study existence and uniqueness of invariant measures for the
associated transition semigroup.Comment: Revision based on the referee's comment
Simplified models of electromagnetic and gravitational radiation damping
In previous work the authors analysed the global properties of an approximate
model of radiation damping for charged particles. This work is put into context
and related to the original motivation of understanding approximations used in
the study of gravitational radiation damping. It is examined to what extent the
results obtained previously depend on the particular model chosen. Comparisons
are made with other models for gravitational and electromagnetic fields. The
relation of the kinetic model for which theorems were proved to certain
many-particle models with radiation damping is exhibited
Existence of axially symmetric static solutions of the Einstein-Vlasov system
We prove the existence of static, asymptotically flat non-vacuum spacetimes
with axial symmetry where the matter is modeled as a collisionless gas. The
axially symmetric solutions of the resulting Einstein-Vlasov system are
obtained via the implicit function theorem by perturbing off a suitable
spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page
Approximating the coefficients in semilinear stochastic partial differential equations
We investigate, in the setting of UMD Banach spaces E, the continuous
dependence on the data A, F, G and X_0 of mild solutions of semilinear
stochastic evolution equations with multiplicative noise of the form dX(t) =
[AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical
Brownian motion on a Hilbert space H. We prove continuous dependence of the
compensated solutions X(t)-e^{tA}X_0 in the norms
L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n
are uniformly sectorial and converge to A in the strong resolvent sense, and
that the approximating nonlinearities F_n and G_n are uniformly Lipschitz
continuous in suitable norms and converge to F and G pointwise. Our results are
applied to a class of semilinear parabolic SPDEs with finite-dimensional
multiplicative noise.Comment: Referee's comments have been incorporate
Diffraction of complex molecules by structures made of light
We demonstrate that structures made of light can be used to coherently
control the motion of complex molecules. In particular, we show diffraction of
the fullerenes C60 and C70 at a thin grating based on a standing light wave. We
prove experimentally that the principles of this effect, well known from atom
optics, can be successfully extended to massive and large molecules which are
internally in a thermodynamic mixed state and which do not exhibit narrow
optical resonances. Our results will be important for the observation of
quantum interference with even larger and more complex objects.Comment: 4 pages, 3 figure
Resonances in a two-dimensional electron waveguide with a single delta-function scatterer
We study the conductance properties of a straight two-dimensional electron
waveguide with an s-like scatterer modeled by a single delta-function potential
with a finite number of modes. Even such a simple system exhibits interesting
resonance phenomena. These resonances are explained in terms of quasi-bound
states both by using a direct solution of the Schroedinger equation and by
studying the Green's function of the system. Using the Green's function we
calculate the survival probability as well as the power absorption and show the
influence of the quasi-bound states on these two quantities.Comment: 5 pages, 6 figures, to be published in Physical Review
The STRANDS project: long-term autonomy in everyday environments
Thanks to the efforts of the robotics and autonomous systems community, the myriad applications and capacities of robots are ever increasing. There is increasing demand from end users for autonomous service robots that can operate in real environments for extended periods. In the Spatiotemporal Representations and Activities for Cognitive Control in Long-Term Scenarios (STRANDS) project (http://strandsproject.eu), we are tackling this demand head-on by integrating state-of-the-art artificial intelligence and robotics research into mobile service robots and deploying these systems for long-term installations in security and care environments. Our robots have been operational for a combined duration of 104 days over four deployments, autonomously performing end-user-defined tasks and traversing 116 km in the process. In this article, we describe the approach we used to enable long-term autonomous operation in everyday environments and how our robots are able to use their long run times to improve their own performance