Upper tails of self-intersection local times of random walks: survey of proof techniques

The asymptotics of the probability that the self-intersection local time of a random walk on $\Z^d$ exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some recently elaborated techniques and results. This is an extended summary of a talk held on the CIRM-conference on {\it Excess self-intersection local times, and related topics} in Luminy, 6-10 Dec., 2010.Comment: 11 page

The Parabolic Anderson Model with Acceleration and Deceleration

We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets stuck. On this scale, a new interesting variational problem arises in the description of the asymptotics. Furthermore, we find an upper critical scale above which the potential enters the asymptotics only via some average, but not via its extreme values. We make out altogether five phases, three of which can be described by results that are qualitatively similar to those from the constant-speed parabolic Anderson model in earlier work by various authors. Our proofs consist of adaptations and refinements of their methods, as well as a variational convergence method borrowed from finite elements theory.Comment: 19 page

Agile at home: tech startup lessons for making home working a success

Four distinctive elements will help stabilise and grow organisations during and after the Covid age, write Alexander König and Jonas Vette

Two-photon laser scanning fluorescence microscopy using photonic crystal fibre

We report the application of a simple yet powerful modular pulse compression system, based on photonic crystal fibres which improves upon incumbent twophoton laser scanning fluorescence microscopy techniques. This system provided more than a 7-fold increase in fluorescence yield when compared with a commercial two-photon microscopy system. From this, we infer pulses of infrared radiaton of less than 35 fs duration reaching the sample

ein Rückblick auf meine Mitarbeit im Gebiete der Sprach- und Religionswissenschaft

Digitalisat der Ausgabe von 1927, erschienen 201

Density measurements using coherence imaging spectroscopy based on Stark broadening

A coherence imaging camera has been set up at Pilot-PSI. The system is to be used for imaging the plasma density through the Stark effect broadening of the H(γ) line. Local density values are then obtained by the Abel inversion of the measured interferometric fringe contrast. This report will present the instrument setup and proof-of-principle demonstration. The inverted spatial electron density profiles obtained near the cascaded arc source of Pilot-PSI in discharges with axial magnetic field of B=0.4 T are compared with an independent measurement of electron density by Thomson scattering and good agreement is found.This work, supported by the European Communities under the contract of the Association EURATOM/FOM, was carried out within the framework of the European Fusion Programme with financial support from NWO

Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating

For many photonic applications, it is important to confine light of a specific wavelength at a certain volume of interest at low losses. So far, it is only possible to use the polarized light perpendicular to the solid grid lines to excite waveguide-plasmon polaritons in a waveguide-supported hybrid structure. In our work, we use a plasmonic grating fabricated by colloidal self-assembly and an ultrathin injection layer to guide the resonant modes selectively. We use gold nanoparticles self-assembled in a linear template on a titanium dioxide (TiO 2 ) layer to study the dispersion relation with conventional ultraviolet-visible-near-infrared spectroscopic methods. Supported with finite-difference in time-domain simulations, we identify the optical band gaps as hybridized modes: plasmonic and photonic resonances. Compared to metallic grids, the observation range of hybridized guided modes can now be extended to modes along the nanoparticle chain lines. With future applications in energy conversion and optical filters employing these cost-efficient and upscalable directed self-assembly methods, we discuss also the application in refractive index sensing of the particle-based hybridized guided modes. Copyright © 2019 American Chemical Society

Coherence-imaging approach to time-resolved charge-exchange recombination spectroscopy in high-temperature plasma

A coherence-based, or interferometric approach to spectral analysis of charge-exchange recombination (CXR) emission radiation from high-temperature plasma probed or heated using energetic neutral beams, offers a number of advantages over wavelength-domain instruments. The spectral-line shift and broadening are obtained from measurements of the spectralcoherence at a given fixed time delay. The coherence is monitored by first approximately isolating the spectral line of interest using an interference filter and subsequently imaging the spectral scene using a field-widened electro-optic path-delay-modulated polarization interferometer.Interferometers have the advantage of high-light throughput (no slit aperture). Moreover, because the spectral information is encoded at harmonics of the electro-optic modulation frequency, a single detector suffices to capture the spectral information, thereby opening the possibility for time-resolved two-dimensional spectralimaging. When unwanted spectral features are passed by the interference filter, the interpretation of the coherence phase and amplitude images can become ambiguous. By modulating the particle beam source, however, we show that coherence imaging using a single-delay modulatable interferometer can distinguish and characterize the Doppler-broadened CXR emission component against a significant background of continuum and intrinsic radiation, or pollution from nearby spectral features

Mechanotunable Surface Lattice Resonances in the Visible Optical Range by Soft Lithography Templates and Directed Self-Assembly

We demonstrate a novel colloidal self-assembly approach toward obtaining mechanically tunable, cost-efficient, and low-loss plasmonic nanostructures that show pronounced optical anisotropy upon mechanical deformation. Soft lithography and template-assisted colloidal self-assembly are used to fabricate a stretchable periodic square lattice of gold nanoparticles on macroscopic areas. We stress the impact of particle size distribution on the resulting optical properties. To this end, lattices of narrowly distributed particles (∼2% standard deviation in diameter) are compared with those composed of polydisperse ones (∼14% standard deviation). The enhanced particle quality sharpens the collective surface lattice resonances by 40% to achieve a full width at half-maximum as low as 16 nm. This high optical quality approaches the theoretical limit for this system, as revealed by electromagnetic simulations. One hundred stretching cycles demonstrate a reversible transformation from a square to a rectangular lattice, accompanied by polarization-dependent optical properties. On the basis of these findings we envisage the potential applications as strain sensors and mechanically tunable filters. © 2019 American Chemical Society