Continuous Centrifuge Decelerator for Polar Molecules

Producing large samples of slow molecules from thermal-velocity ensembles is a formidable challenge. Here we employ a centrifugal force to produce a continuous molecular beam with a high flux at near-zero velocities. We demonstrate deceleration of three electrically guided molecular species, CH$_3$F, CF$_3$H, and CF$_3$CCH, with input velocities of up to $200\,\rm{m\,s^{-1}}$ to obtain beams with velocities below $15\,\rm{m\,s^{-1}}$ and intensities of several $10^9\,\rm{mm^{-2}\,s^{-1}}$. The centrifuge decelerator is easy to operate and can, in principle, slow down any guidable particle. It has the potential to become a standard technique for continuous deceleration of molecules.Comment: 5 pages, 4 figures; version accepted for publication in PR

Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial

This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.Comment: arXiv admin note: text overlap with arXiv:1606.0661

Efficient numerical approximation of a non-regular Fokker–Planck equation associated with first-passage time distributions

In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker–Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation is required, e.g., for model evaluation and parameter fitting. However, the prescribed boundary conditions lead to a strong singularity and thus to slow convergence of numerical approximations. In this article we demonstrate that the solution can be related to the solution of a parabolic PDE on a rectangular space-time domain with homogeneous initial and boundary conditions by transformation and subtraction of a known function. We verify that the solution of the new PDE is indeed more regular than the solution of the original PDE and proceed to discretize the new PDE using a space-time minimal residual method. We also demonstrate that the solution depends analytically on the parameters determining the boundaries as well as the drift. This justifies the use of a sparse tensor product interpolation method to approximate the PDE solution for various parameter ranges. The predicted convergence rates of the minimal residual method and that of the interpolation method are supported by numerical simulations