Center manifolds in equations from hydrodynamics

Elliptic partial differential equations on tubular domains arise in hydrodynamics and in other applied settings. The center manifold approach to the analysis of small solutions has as one of its steps the study of a reduced equation of differential-integral type leading to a system of ordinary differential equations, generally of finite order. Here we give existence and regularity results for reduced equations which are adapted to the Hölder space setting and which are suitable for application to quasi-linear problems. Applications to flow problems are given.deceasedThis research has been supported by the National Science Foundation and the Sloan Foundation     

Demonstration of ignition radiation temperatures in indirect-drive inertial confinement fusion hohlraums

We demonstrate the hohlraum radiation temperature and symmetry required for ignition-scale inertial confinement fusion capsule implosions. Cryogenic gas-filled hohlraums with 2.2 mm-diameter capsules are heated with unprecedented laser energies of 1.2 MJ delivered by 192 ultraviolet laser beams on the National Ignition Facility. Laser backscatter measurements show that these hohlraums absorb 87% to 91% of the incident laser power resulting in peak radiation temperatures of T(RAD)=300 eV and a symmetric implosion to a 100 μm diameter hot core.     

Dispersive power and crossover temperature,TCO, of two polar nematic liquid crystals in the visible spectral region

Refractive index studies are carried out on two highly polar liquid crystals: 1. N-(p-n-methoxy benzylidene)-p-amino benzonitrile, PmBAB, 2. N-(p-n-ethoxy benzylidene)-p-amino benzonitrile, PeBAB. The experimental investigations are carried out in the visible region at four different wavelengths, namely, 633, 589, 546 and 436 nm. The two compounds exhibit only the nematic liquid crystalline phase in between the isotropic and crystalline solid. The dispersive power ω is estimated for two consecutive wavelengths for the case of <n>, n_e and n_o for different wavelengths and found to be constant with temperature. Further the temperature gradients of n_e and n_o are estimated, and the crossover temperature is obtained using dn_o/dT for all the wavelengths.     

Steering in computational science: Mesoscale modelling and simulation

This paper outlines the benefits of computational steering for high performance computing applications. Lattice-Boltzmann mesoscale fluid simulations of binary and ternary amphiphilic fluids in two and three dimensions are used to illustrate the substantial improvements which computational steering offers in terms of resource efficiency and time to discover new physics. We discuss details of our current steering implementations and describe their future outlook with the advent of computational grids.     

Small internal waves in two-fluid systems

This paper treats travelling waves in a heterogeneous, inviscid, non-diffusive fluid bounded between two horizontal boundaries. The fluid has two incompressible components of different, but constant density and is acted on by gravity. The flow is steady when viewed in a moving reference frame and gives rise to a quasilinear elliptic problem with an eigenvalue parameter related to the wave speed. The small amplitude solutions are analyzed using a dynamical systems approach. A center manifold reduction in combination with a conserved quantity for the flow is used to parametrise all small solutions of the full elliptic system in terms of solutions of an autonomous first order ordinary differential equation for a principal component of the wave amplitude. The result is a characterization of all small waves, irrotational in each fluid, near the critical speed for the system. They are: solitary waves; surges connecting distinct conjugate flows at extreme ends of the channel; conjugate flows; and periodic waves.