Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...

We have reached our goal of implementing a computationally cheap algorithm for realtime rendering of realistic two-dimensional fire. The fire is simulated using computational fluid dynamics, vorticity confinement, and combustion modelling and visualized using black-body radiation. Small rotationally homogenous fires like torches and candles viewed in front are the best candidates when using thi...

LLE Review, Volume 66 57 One metric commonly used to evaluate the performance of inertial confinement fusion (ICF) targets is the ratio of the measured neutron yield to that predicted by a one-dimensional hydrodynamic simulation. When plotted versus the calculated convergence ratio of the implosion, this ratio [referred to as the YOC (yield-over-clean)] provides an indication of the nonuniformi...

In this Chapter QCD interactions between a quark and an anti-quark are discussed. In the heavy quark limit these potentials can be related to quarkonia and 1/m corrections can be systematically determined. Ex-citations of the ground state potential provide an entry point into the phenomenology of quark-gluon hybrids. The short-distance behaviour of non-perturbative potentials can serve as a tes...

The penalization method is used to take account of obstacles, such as the limiter, in a tokamak. Because of the magnetic confinement of the plasma in a tokamak, the transport occurs essentially in the direction parallel to the magnetic field lines. We study a 1D nonlinear hyperbolic system as a simplified model of the plasma transport in the area close to the wall. A penalization which cuts the...

In some practical Neural Network (NN) applications, fast response to external events within enormously short time is highly demanded. However, by using back propagation (BP) based on gradient descent optimisation method obviously not satisfy in several application due to serious problems associated with BP which are slow learning convergence velocity and confinement to shallow minima. Over the ...

We study the problem of dimension reduction for the three dimensional Gross– Pitaevskii equation (GPE) describing a Bose–Einstein condensate confined in a strongly anisotropic harmonic trap. Since the gas is assumed to be in a strong interaction regime, we have to analyse two combined singular limits: a semiclassical limit in the transport direction and the strong partial confinement limit in t...

In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic states for half-plane vortex dynamics decompose naturally into a nonlinear superposition of soliton-like states. Our approach is to combine techniques developed in the study of vortex confinement with weak convergenc...

The mixing of cold, high-density shell plasma with the low-density, hot spot plasma by the Rayleigh-Taylor instability in inertial confinement fusion is experimentally shown to correlate with the calculated perturbation feedthrough from the ablation surface to the inner shell surface. A fourfold decrease in the density of shell material in the mix region of direct drive implosions of gas filled...

This paper is devoted to the linearized Vlasov–Poisson–Fokker–Planck system in presence of an external potential confinement. We investigate large time behaviour solutions using hypocoercivity methods and a notion scalar product adapted Poisson coupling. Our framework provides estimates which are uniform diffusion limit. As application simple case, we study one-dimensional case prove exponentia...