Optimizing the fractional power in a model with stochastic PDE constraints

We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation. Well-posedness of the state equation and differentiability properties with respect to the fractional parameter s are established. We show that under certain conditions on the noise, optimality conditions for the control problem can be established

The point vortex model for the Euler equation

In this article we describe the system of point vortices, derived by Helmholtz from the Euler equation, and their associated Gibbs measures. We discuss solution concepts and available results for systems of point vortices with deterministic and random circulations, and further generalizations of the point vortex model

Limit theorems and fluctuations for point vortices of generalized Euler equations

We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations

A simulated annealing approach to optimal storing in a multi-level warehouse

We propose a simulated annealing algorithm specifically tailored to optimise total retrieval times in a multi-level warehouse under complex pre-batched picking constraints. Experiments on real data from a picker-to-parts order picking process in the warehouse of a European manufacturer show that optimal storage assignments do not necessarily display features presumed in heuristics, such as clustering of positively correlated items or ordering of items by picking frequency. In an experiment run on more than 4000 batched orders with 1 to 150 items per batch, the storage assignment suggested by the algorithm produces a 21\% reduction in the total retrieval time with respect to a frequency-based storage assignment

Point vortices for inviscid generalized surface quasi-geostrophic models

We give a rigorous proof of the validity of the point vortex description for a class of inviscid generalized surface quasi-geostrophic models on the whole plane

The scaling limit of a particle system with long-range interaction

We describe the behaviour of a particle system with long-range interactions, in which the range of interactions is allowed to depend on the size of the system. We give conditions on the interaction strength under which the scaling limit of the particle system is a well-posed stochastic PDE. As a corollary we obtain that the metastable behaviour of the system is described by the Stochastic Allen\tire Cahn equation, which has been analyzed by Barret, Bovier and Meleard, Barret and Berglund and Gentz

CONVERGENCE OF A SEMIDISCRETE SCHEME FOR A FORWARD-BACKWARD PARABOLIC EQUATION

We study the convergence of a semidiscrete scheme for: the forward-backward parabolic equation u(t) = (W '(u(x)))(x) with periodic boundary conditions in one space dimension, where W is a standard double-well potential. We characterize the equation satisfied by the limit of the discretized solutions as the grid size goes to zero. Using an approximation argument, we show that it is possible to flow initial data (u) over bar having regions where (u) over barx falls within the concave region {W '' in its unstable region. Our result can be viewed as a characterization, among all Young measure solutions of the equation, of the much smaller subset of those solutions which can be obtained as limit of the semidiscrete scheme

Terahertz-driven polymerization of resists in nanoantennas

Plasmon-mediated polymerization has been intensively studied for various applications including nanolithography, near-field mapping, and selective functionalization. However, these studies have been limited from the near-infrared to the ultraviolet regime. Here, we report a resist polymerization using intense terahertz pulses and various nanoantennas. The resist is polymerized near the nanoantennas, where giant field enhancement occurs. We experimentally show that the physical origin of the cross-linking is a terahertz electron emission from the nanoantenna, rather than multiphoton absorption. Our work extends nano-photochemistry into the terahertz frequencies