The Maximal Invariance Group of Newtons's Equations for a Free Point Particle

The maximal invariance group of Newton's equations for a free nonrelativistic point particle is shown to be larger than the Galilei group. It is a semi-direct product of the static (nine-parameter) Galilei group and an $SL(2,R)$ group containing time-translations, dilations and a one-parameter group of time-dependent scalings called {\it expansions}. This group was first discovered by Niederer in the context of the free Schr\"odinger equation. We also provide a road map from the free nonrelativistic point particle to the equations of fluid mechanics to which the symmetry carries over. The hitherto unnoticed $SL(2, R)$ part of the symmetry group for fluid mechanics gives a theoretical explanation for an observed similarity between numerical simulations of supernova explosions and numerical simulations of experiments involving laser-induced implosions in inertial confinement plasmas. We also give examples of interacting many body systems of point particles which have this symmetry group.Comment: Plain TeX File: 15 Page

Computing reachable sets via barrier methods on SIMD architectures

Paper No. 1518, 20 pagesInternational audienceWe consider the problem of computing reachable sets of ODE-based control systems parallely on CUDA hardware. To this end, we modify an existing algorithm based on solving optimal control problems. The idea is to simplify the optimal control problems to pure feasibility problems instead of minimizing an objective function. We show that an interior point algorithm is well suited for solving the resulting feasibility problems and leads to a sequence of linear systems of equations with identical matrix layout. If the problem is defined properly, these matrices are sparse and can be transformed into a hierarchical lower arrow form which can be solved on CUDA hardware with sparse linear algebra and Cholesky's method. We demonstrate the performance of our new algorithm by computing the reachable sets of two test problems on a CPU implementation using several explicit and implicit Runge-Kutta methods of different order. The experiments reveal a significant speedup compared to the original optimal control algorithm

Cathodoluminescence spectroscopy of ambipolar diffusion in (Al,Ga)As barriers and capture of nonequilibrium carriers in GaAs quantum well

Ambipolar vertical diffusion of carriers generated in an Al0.3Ga0.7As barrier is investigated by cathodoluminescence CL spectroscopy in a system containing a sequence of GaAs-based quantum wells QWs . The intensity distribution of the CL line scan exhibits a single exponential decay for the first QW of the sequence, reflecting a pure diffusion-limited transport. However, the CL line scans of the second, third, and fourth QWs are governed by diffusion only for large separations between the electron beam and the corresponding QW. For smaller distances, the CL intensity distribution is significantly influenced by the carrier capture into the intervening QWs

Evolution of a magnetic flux tube in a sunspot penumbra

The motion of an individual magnetic flux tube inside the penumbra of a sunspot is studied numerically. Here, we present preliminary results. The thin flux tube approximation together with a simplified radiative heat exchange with the surroundings is used to study the evolution of a flux tube embedded into a background given by a global magneto-static sunspot model. The investigation is undertaken in order to verify the conjecture that convection in sunspot penumbrae occurs by an interchange of magnetic flux tubes. The code being developed can be used to study dynamic aspects of filamentary structure in the penumbra: the temporal and spatial fluctuations of the temperature and the magnetic field, the motion of bright penumbral grains, or the Evershed effect. Here we present the evolution of a wave formed by the tube whose fragment emerges in the penumbral photosphere and migrates towards the umbra. The properties of this wave show qualitative features of the observed bright penumbral grains with corresponding upward velocity and its correlation with brightness and the inclination of the magnetic field, and also of the Evershed effect

Field-dependent nonlinear luminescence response of (In,Ga)N/GaN quantum wells

We have investigated the electric-field- and excitation-density-induced variation of the optical transition energy and cathodoluminescence (CL) as well as photoluminescence intensity of a single (In,Ga)N/GaN quantum well deposited in the depletion region of a p-n junction. The electric-field dependence of the transition energy is significantly influenced by field screening in the depletion region due to the excited carriers and by filling of band tail states of localized excitons. The electric-field dependence of the CL intensity is characterized by an abrupt and strong quenching mainly due to drift of excited carriers in the depletion region. A gradual screening of the p-n junction field with increasing excitation density causes a strongly nonlinear CL response. We describe this nonlinear behavior theoretically by a rate equation model

Synthesis of atomically thin hexagonal boron nitride films on nickel foils by molecular beam epitaxy

Hexagonal boron nitride (h-BN) is a layered two-dimensional material with properties that make it promising as a dielectric in various applications. We report the growth of h-BN films on Ni foils from elemental B and N using molecular beam epitaxy. The presence of crystalline h-BN over the entire substrate is confirmed by Raman spectroscopy. Atomic force microscopy is used to examine the morphology and continuity of the synthesized films. A scanning electron microscopy study of films obtained using shorter depositions offers insight into the nucleation and growth behavior of h-BN on the Ni substrate. The morphology of h-BN was found to evolve from dendritic, star-shaped islands to larger, smooth triangular ones with increasing growth temperature

Selective area growth and characterization of InGaN nano-disks implemented in GaN nanocolumns with different top morphologies

This work reports on the morphology control of the selective area growth of GaN-based nanostructures on c-plane GaN templates. By decreasing the substrate temperature, the nanostructures morphology changes from pyramidal islands (no vertical m-planes), to GaN nanocolumns with top semipolar r-planes, and further to GaN nanocolumns with top polar c-planes. When growing InGaN nano-disks embedded into the GaN nanocolumns, the different morphologies mentioned lead to different optical properties, due to the semi-polar and polar nature of the r-planes and c-planes involved. These differences are assessed by photoluminescence measurements at low temperature and correlated to the specific nano-disk geometry