The measured mass distributions of fragments from 26 fractured objects of gypsum, soap, stearic paraffin, and potato show evidence of obeying scaling laws; this suggests the possibility of self-organized criticality in fragmenting. The probability of finding a fragment scales inversely to a power of the mass; the power, or scaling exponent, was found to depend on the shape of the object rather than on the material. For objects of different shapes (balls, cubes, half cubes, plates, and bars) scaling was found for fragment sizes smaller than the smallest dimension of the object undergoing fragmentation.

Nonlinear mode interactions and pattern formation occurring along the primary stability boundary for counterrotating eccentric cylinders have been studied experimentally. Counterrotating concentric cylinders produce either Taylor vortex flow or spiral vortices with various azimuthal wave numbers. Eccentric cylinders break the rotational symmetry of the base flow, introducing a delay of the onset of the primary instability and changes in the locations of the bicritical points separating patterns with differing azimuthal wave number. A theoretical model for this system is in qualitative agreement with the observations.

I develop a general approach for computing random-function solutions of the periodic Korteweg–de Vries (KdV) equation using the inverse scattering transform (IST) in the hyperelliptic function representation. I exploit IST to construct realizations of KdV random processes which have power-law spectra, ${\mathit{k}}^{\mathrm{-}\gamma }$ (k the wave number, γ a constant), and uniformly distributed random IST phases on (-π,π). IST characterizes these realizations in terms of solitons moving in a sea of background radiation and is thus able to extract solitons, by nonlinear filtering techniques, from complex, random motions described by the KdV equation.

Based on statistical theormodynamic fluctuation arguments, it is shown here for the first time that thermally excited spin-flip laser emission from the fusion product protons can occur in large tokamak devices that are entering the reactor regime of operation. Existing experimental data from TFTR support this conjecture, in the sense that these measurements are in complete agreement with the predictions of the quasilinear theory of the spin-flip laser.

In order to test the validity of the fluid drift approximation when ion dynamics are stochastic, the time-dependent ion-fluid velocity field in a coherent, drift-Alfvén wave has been measured in Caltech’s Encore tokamak using plasma planar laser induced fluorescence. Many measured parameters of the wave are well described by the drift approximation above a threshold for stochastic ion dynamics, including the flow pattern in the single measured component of the ion-fluid velocity field. Surprisingly, the theory fails at a fundamental level by predicting flow speeds 10 times larger than those measured (‖${\mathit{u}}_{\max }$‖≊${10}^5$ cm/s).

Experimental evidence of the nonlinear nature of the broadband edge fluctuations has been obtained in edge turbulence in the Advanced Toroidal Facility torsatron. Whereas little nonlinear wave interaction is found in the scrape-off layer region, three-wave coupling is enhanced in the plasma edge region (r<${\mathit{a}}_{\mathrm{shear}}$). The degree of three-wave coupling strongly depends on the plasma conditions; it decreases in the temperature range (${\mathit{T}}_{\mathit{e}}$≊10 eV) where the ionization rates depend strongly on ${\mathit{T}}_{\mathit{e}}$ suggesting a link between ionization source and turbulence.

The linear stability analysis of unsteady ablation fronts is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code orchid.

A localized transition zone is observed between turbulent, long-wavelength density fluctuations (${\mathit{k}}_{\mathrm{\perp }}$<2 ${\mathrm{cm}}^{\mathrm{-}1}$) in the core and edge of beam-heated discharges in TFTR. The core turbulence is unimodal while the edge has two counterpropagating modes, both of which are spectrally distinct from the core fluctuations. The fluctuation amplitude in the core scales with the global energy confinement time while in the edge it does not. These observations suggest that distinct modes are responsible for turbulence in the two regions and that only the core mode is directly related to global confinement.

We present scanning tunneling microscope images of benzene adsorbed on the Pt{111} surface. We find three distinct types of images for isolated benzene molecules, depending upon the benzene adsorption site. This site dependence is in agreement with recent theoretical calculations, and may limit the usefulness of the scanning tunneling microscope in elucidating the structures of adsorpted molecules.

A Brillouin scattering study of the pressure dependence of the elastic properties of ${\mathrm{AlPO}}_4$ single crystals is presented. On increasing the pressure there is clear evidence of a phase transformation at 15 GPa; this is consistent with previous Raman and x-ray measurements which report an amorphous phase at high pressures. On decreasing the pressure the sample not only recrystallizes at ≊7 GPa but it reverts to a single crystal with the initial crystallographic orientation. This surprising behavior confirms the claims, based on birefringence measurements, of Kruger and Jeanloz [Science 249, 647 (1990)]. Our results also indicate that, even in the amorphous phase, ${\mathrm{AlPO}}_4$ remains elastically anisotropic.

Pressure-induced structural transformation in ${\mathrm{SiO}}_2$ glass is investigated with molecular dynamics. At high densities, the height of the first sharp diffraction peak is considerably diminished, its position changes from 1.6 to 2.2 A${\mathrm{̊}}^{\mathrm{-}1}$, and a new peak appears at 2.85 A${\mathrm{̊}}^{\mathrm{-}1}$. At twice the normal density, the Si-O bond length increases, the Si-O coordination changes from 4 to 6, and the O-Si-O band angle changes from 109° to 90°. This is a tetrahedral to octahedral transformation, which was reported recently by Meade, Hemley, and Mao [Phys. Rev. Lett. 69, 1387 (1992)]. Results for phonon density of states also reveal significant changes at high pressures.

High-pressure optical and x-ray studies of ${\mathrm{H}}_2$-${\mathrm{H}}_2$O mixtures have revealed the formation of the first hydrogen clathrate hydrates. A rhombohedral hydrate with a ${\mathrm{H}}_2$O sublattice similar to ice II and a ${\mathrm{H}}_2$:${\mathrm{H}}_2$O ratio of 1:6 is stable between 0.75 and 3.1 GPa (295 K). Above 2.3 GPa, a novel hydrate forms with the ${\mathrm{H}}_2$O molecules in a cubic diamond structure and with a very high ${\mathrm{H}}_2$:${\mathrm{H}}_2$O stoichiometry of 1:1. The ${\mathrm{H}}_2$ molecules occupy voids in the ${\mathrm{H}}_2$O framework, thus improving the packing efficiency and stabilizing this hydrate to very high pressures of at least 30 GPa.

A vacancy defect is observed by positron annihilation in n-type Si- and Sn-doped ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As (x≥0.18). The vacancy is not observed after optical ionization of the DX center. The disappearance of the vacancy signal is persistent below a critical temperature. Thermal ionization of the DX center removes the vacancy signal above 300 K. We conclude that the deep ground state of the DX center contains the vacancy. The results are in perfect agreement with the theoretical predictions of the large displacements of the Si and Sn atoms from the substitutional configuration when the DX state is occupied.

Here we demonstrate the first evidence that phase separation in polymer solutions could be essentially different from that in binary liquid systems. This difference is likely to originate from the strong asymmetry in molecular dynamics between the two separated phases. When the rheological time of the polymer-rich phase is slower than the deformation time, the stress field can be strongly coupled with the concentration diffusion and the coarsening dynamics is dominated by the viscoelastic effect. This causes mechanically dominated pattern evolution. The dynamic symmetry should be considered in addition to the static, composition symmetry.

Linear elasticity is unable to predict completely the dynamics of a rapidly moving crack without the addition of a phenomenological fracture energy. Our measurements of acoustic emission, crack velocity, and surface structure demonstrate quantitatively similar dynamical fracture behavior in two very different materials, polymethylmethacrylate and soda-lime glass. This unexpected agreement suggests that there exist universal features of the fracture energy that result from dissipation of energy in a dynamical instability.

We describe x-ray scattering studies of the structure and morphology of a stepped Pt(001) surface between 300 and 1850 K. Two distinct faceting transformations are observed. Above 1820 K, we find an unreconstructed, stepped surface. Between 1820 and 1620 K, there is coexistence among hexagonally reconstructed, step-free domains and unreconstructed, stepped domains. The tilt angle of the unreconstructed domains exhibits a one-half power-law dependence on reduced temperature. At 1620 K, there is a second morphological transformation at which the unreconstructed domains are replaced by magic vicinals.

We have investigated the influence of a surfactant on the equilibrium surface morphology in the pseudomorphic regime of heteroepitaxial growth. At 700 °C, 8 monolayers of Ge on Si(001) using Sb as surfactant form strained islands with a size of ∼300 Å, allowing partial elastic relaxation. The surface morphology depends strongly on the Sb coverage and changes from islands with [117] facets at high Sb coverage via round, flat cones with an inclination angle of 12° to islands rotated by 45° with [105] facets formed during growth at low Sb coverage. The equilibrium conditions are verified by the reversible transition from [117] facets to 12° cones initiated by a change of the surfactant coverage.

We use the dynamic renormalization group technique to study a continuum model for molecular beam epitaxy for both one- and two-dimensional substrates. Relaxation of the growing film is due to surface tension and surface diffusion. In 1+1 dimensions we find a purely diffusive strong-coupling fixed point with a dynamic exponent z different from that given by the linear theory as well as the Edwards-Wilkinson fixed point and a fixed point corresponding to unstable growth. In 2+1 dimensions the purely diffusive fixed point is absent at the one loop order but the other two fixed points are still present.

We study the single-band Hubbard model via the functional-integral four-slave-boson formulation introduced by Kotliar and Ruckenstein, and show that a proper treatment of the continuum limit of the functional integral removes the inconsistencies due to an incorrect handling of this limit so far performed in the literature. It follows from our analysis that the Kotliar and Ruckenstein mean-field solution has to be abandoned in order to include fluctuation corrections in a systematic way. We show explicitly how to construct a suitable alternative solution which admits the inclusion of fluctuations.

An exciton crystal (EC) is predicted in a quasi-one-dimensional (1D) semiconductor quantum wire for the densities (1<${\mathit{r}}_{\mathit{s}}$≤5.5) due to the repulsive interaction between singlet excitons (x’s). Low-lying excitations, stability, and melting of the EC are determined within the Heitler-London approximation. The expected short condensation times (ps) will allow an EC formation in, e.g., GaAs quantum-well wires with relative short x lifetimes. For T≤10 K the EC is a pure quantum crystal which favors collective, coherent emission in the form of superradiance.