We consider strong wave propagation in the generalized compressible Euler equations. Our results include pairwise interactions of nonlinear waves, smooth wave propagation, formation of gradient blowup and several exact examples. In particular, we directly generalize P.Lax’s gradient blowup results for conservation laws with two variables to the generalized compressible Euler equations.

The results of nuclear magnetic resonance (NMR) on thin $\sp3\rm{He}$-$\sp4$He mixture films at temperatures 24mK $\leq T \leq$ 650mK which are adsorbed to Nucleopore are reported. The nuclear magnetic susceptibility, the relaxation times T$\sb1$ and T$\sb2$, and the spin diffusion coefficient, D, were measured used pulsed NMR techniques in a 2 Tesla field. The $\sp4$He coverages investigated ranged from 0.137 $\leq n\sb4\leq$ 0.534 atoms A$\sp2$ with a fixed submonolayer $\sp3$He coverage of 0.00746 $\leq n\sb3 \leq$ 0.00749 atoms A$\sp2.$ At $n\sb4$ = 0.391 atoms/A$\sp2$ measurements were taken with the $\sp3$He coverage ranging 0.00749 $\leq n\sb3 \leq$ 0.0179 atoms/A$\sp2$. We present the $\sp3$He magnetization as a function of the $\sp4$He coverage. The magnetization is degenerate for temperatures below the Fermi temperature, T$\sb{F}$, and from the degenerate magnetization the hydrodynamic mass over a range of $\sp4$He coverages is obtained. Variational and density functional descriptions of the film are considered. The diffusion data are seen to rise rapidly, from 10$\sp{-8}$ to 10$\sp{-3}\ \rm{cm}\sp2$/sec, as the $\sp4$He coverage is increased from 0.19 to 0.39 atoms/A$\sp2$, a range of just 2.5 layers. For $T < T\sb{F}$ the temperature dependence of a degenerate Fermi gas is not seen; $D \not= T\sp{-2}$. For all coverages T$\sb1$ is two orders of magnitude larger than T$\sb2$. Two regimes are seen. For coverages $n\sb4 <$ 0.23 the temperature dependence of T$\sb1$ and T$\sb2$ are consistent with $\omega\tau\sb{c} \gg$ 1. A signature of the completion of the second layer of the $\sp4$He is seen in T$\sb{1}$. For coverages $n\sb4 >$ 0.23, $\omega\tau\sb{c} \ll$ 1 and the temperature dependence correlates with the superfluid areal density. Activated behavior is seen which probes higher bound states of the $\sp3$He in the $\sp4$He film.

Chaotic mixing of viscous fluids in slow flows is pervasive in the chemical and polymer industries but poorly understood. However, relatively simple experiments provide a wealth of information regarding mixing mechanisms and indicate the need for complementary theoretical developments in dynamical systems. In this thesis, we present a versatile cavity flow apparatus, capable of producing a variety of two-dimensional velocity fields, and use it to conduct a detailed experimental study of mixing of Newtonian and viscoelastic fluids in low Reynolds number flows. Since the goal is detailed understanding, only two time-periodic cavity flows induced by tangential wall motions are considered: one continuous and the other discontinuous. In the Newtonian case, the two flows produce exponential growth of intermaterial area, as expected from chaotic flows, and a mixture of islands and chaotic regions. A procedure for identifying periodic points and determining their movements is presented as well as how to make meaningful comparisons between periodic flows. We observe that periodic points move very much as a planetary system; planets (hyperbolic points) have moons (elliptic points) with twice the period of the planets; furthermore the spatial arrangement of periodic points becomes symmetric at regular time intervals. Detailed analyses reveal complex behavior: birth, bifurcation, and collapse of islands; formation and periodic motion of coherent structures, such as islands and large scale folds. Experimental results show that the viscoelastic systems also exhibit regular and chaotic regions, and the large scale structures--folds and symmetry--in the viscoelastic systems are remarkably similar to that of the Newtonian systems. But, the islands in the viscoelastic systems are significantly larger than the Newtonian's, and the size of those islands increases monotonically with increasing Deborah number.

No description available.

This dissertation details the nature of subnanosecond laser-induced microplasma dynamics, particularly concerning the evolution of the electron temperature and concentration. Central to this development is the advent of a femtosecond four-wave mixing (FWM) spectroscopic method. FWM (in the form of coherent anti-Stokes Raman scattering (CARS)) measurements are performed on the fundamental oxygen vibrational transition. An analytical expression is provided that accounts for the resonant and nonresonant contributions to the CARS signal generated from the interaction of broadband pump and Stokes pulses. The inherent phase mismatch is also accounted for, resulting in quantitative agreement between experiment and theory. FWM is then used to measure the early-time electron dynamics in the noble gas series from He to Xe following irradiation by an intense (10^14 Wcm-2) nonresonant 80 fs laser pulse. An electron impact ionization cooling model is presented to determine the evolution of electron kinetic energies following ionization. Kinetic energies are predicted to evolve from &gt; 20 eV to &lt; 1 eV in the first 1.5 ns. The initial degree of ionization is determined experimentally via measurement of the Bremsstrahlung background emission, and modeled with a modified ADK theory based on tunnel ionization. Combined, these two descriptions account for the evolution of both the electron temperature and concentration and provide quantitative agreement with the FWM measurements. The model is further tested with measurements of the gas pressure and pump laser intensity on the electron dynamics. The FWM experiments are concluded with a qualitative discussion of dissociative recombination dynamics occurring in molecular microplasmas. The microplasma environment is used as a source for the generation of two-level systems in the excited state manifold of atomic oxygen and argon. These two-level systems are coupled using moderately intense ~1 ps near-infrared (and near-resonant) pulses, resulting in Rabi sidebands with unprecedentedly large shifts in excess of 90 meV. A time-dependent generalized Rabi-cycling model is developed to account for the time-dependence of the laser electric field and subsequently the Rabi frequency. The Rabi radiation is determined to be coherent and tunable (up to 200 meV), providing a new method for ultrashort pulse generation. The dependence of the spectral positions of the Rabi sidebands on laser intensity affords the opportunity to simultaneously determine the ratios of transition dipole moments for the states accessed. / Chemistry

No description available.

No description available.

A dual photomultiplier system and a field probe has been used to study the optoelectrical phenomena is commercially pure SF6 and mixtures posºtºve of SF6 with oxygen free N2, underAimpulse voltages in a point plane gap. The luminous extension of the predischarge, the electric field at the cathode, and where possible the velocity of discharge propagation has been measured. An extrapolation technique has been used to estimate the critical pressure, and the results have been compared with those of other recently published work. An attempt has been made to establish the different regimes of operation with regard to leader formation both prior to and after streamers cross the gap. This has been done with particular emphasis on the d/r ratio and the field variation with increment in voltage. The cloud model has been shown to be inoperative under impulse voltage conditions such as in this thesis. Comparisons have been made of critical pressure determined under d. c. conditions with any available results obtained using impulse voltages. An attempt has been made to explain the large discrepancy particularly in SF6 between the calculated and experimentally determined values of Vi , the corona initiation voltage. The internal electric field and the electrostatic radius, -of the, discharge channel has been estimated. The analysis of the experimental results has been carried out for the stem and leader stages of the discharge development using an electrostatic model, prior to the streamers crossing the, gap and reaching the cathode, By comparing the , results with those of other authors, it has been shown that : the results of the leader internal electric field are in reasonable agreement with the work of others

No description available.

No description available.