Leaky surface-elastic-waves on flat and highly corrugated surfaces for isotropic non-dissipative media

The dispersion relation for Rayleigh waves on a grating-surface of a semi-infinite, isotropic, nondissipative, elastic medium is solved numerically, with complex wave vector k or complex frequency, in the radiative region (above the bulk transverse sound-line) and within the first frequency-gap on the Brillouin zone boundary created by the grating periodicity. The acoustic attenuation, found from the imaginary part of k, agrees well with experiment. A dispersive branch, with corresponding complex-solutions for the flat surface, between the bulk transverse and longitudinal sound-lines, representing a new leaky mode or surface resonance, accounts for the principal peak in the attenuation.     

Crystal chirality and optical rotation sense in isomorphous NaClO3 and NaBrO3

Combined optical and anomalous x-ray diffraction measurements confirm an earlier report that crystals of isomorphous NaClO₃ and NaBrO₃ with identical chirality (handedness of atomic arrangement) rotate plane polarized light in opposite senses.     

Thermal blooming in gases

The absorption of light and subsequent thermalisation of the absorbed energy can be significantly affected by the presence of non-equilibrium population distributions in gases. The phenomenon of thermal blooming in gases is discussed from this standpoint. It is shown that a transient phenomenon of absorption cooling can occur, leading to a focusing rather than defocusing of an incident laser beam. Flux densities causing saturation in air and pure CO₂ are calculated. For vibrational saturation in air, I > 3.66 kw/cm², for pure CO₂, I > 4.58 kw/cm². For rotational saturation, in either gas, I > 840 kw/cm².     

Dynamics of Parkinsonian tremor during deep brain stimulation

The mechanism by which chronic, high frequency, electrical deep brain stimulation (HF-DBS) suppresses tremor in Parkinson's disease is unknown. Rest tremor in subjects with Parkinson's disease receiving HF-DBS was recorded continuously throughout switching the deep brain stimulator on (at an effective frequency) and off. These data suggest that the stimulation induces a qualitative change in the dynamics, called a Hopf bifurcation, so that the stable oscillations are destabilized. We hypothesize that the periodic stimulation modifies a parameter affecting the oscillation in a time dependent way and thereby induces a Hopf bifurcation. We explore this hypothesis using a schematic network model of an oscillator interacting with periodic stimulation. The mechanism of time-dependent change of a control parameter in the model captures two aspects of the dynamics observed in the data: (1) a gradual increase in tremor amplitude when the stimulation is switched off and a gradual decrease in tremor amplitude when the stimulation is switched on and (2) a time delay in the onset and offset of the oscillations. This mechanism is consistent with these rest tremor transition data and with the idea that HF-DBS acts via the gradual change of a network property. (c) 2001 American Institute of Physics.     

Scroll waves in spherical shell geometries

The evolution of scroll waves in excitable media with spherical shell geometries is studied as a function of shell thickness and outer radius. The motion of scroll wave filaments that are the locii of phaseless points in the medium and organize the wave pattern is investigated. When the inner radius is sufficiently large the filaments remain attached to both the inner and outer surfaces. The minimum size of the sphere that supports spiral waves and the maximum number of spiral waves that can be sustained on a sphere of given size are determined for both regular and random initial distributions. When the inner radius is too small to support spiral waves the filaments detach from the inner surface and form a curved filament connecting the two spiral tips in the surface. In certain parameter domains the filament is an arc of a circle that shrinks with constant shape. For parameter values close to the meandering border, the filament grows and collisions with the sphere walls lead to turbulent filament dynamics. (c) 2001 American Institute of Physics.     

Inverse vulcanization of elemental sulfur and styrene for polymeric cathodes in Li‐S batteries

High sulfur content copolymers were prepared via the inverse vulcanization of elemental sulfur with styrene. This reaction was carried out at a relatively low temperature and invokes a new chain transfer mechanism of abstraction of benzylic protons to form stable copolymers. The use of styrene as a comonomer for inverse vulcanization was attractive due to the low cost and wide spread industrial use of styrenics in free radical processes. The copolymers were used as the active cathode material in Li‐S batteries that exhibited outstanding device performance, maintaining 489 mAh/g capacity after 1000 cycles. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 107–116     

Nonlinear Hyperbolic Systems: Nondegenerate Flux,Inner Speed Variation,and Graph Solutions

We study the Cauchy problem for general nonlinear strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time regularity of the graph solutions (X,U) introduced by LeFloch, and propose a geometric version of our scheme; in turn, the spatial component X of a graph solution can be chosen to be continuous in both time and space, while its component U is continuous in space and has bounded variation in time.     

Wetting front instability in unsaturated porous media: A three-dimensional study in initially dry sand

Three-dimensional fingers caused by gravity driven, wetting front instability in unsaturated porous media were explored through laboratory experimentation. Two sets of experiments were conducted using initially dry sand in large 30 cm diameter columns to guide analytical development for finger velocity and diameter. The first set consisted of ponding water on a two-layer sand system with a fine sand overlying a coarse sand. Here, a complicated pattern of interaction among fingers was found to occur. In the second set, water was applied directly to the coarse layer as 2 cm diameter area sources, enabling systematic study of individual finger structure. Based on dimensional analysis and the experimental results, general relationships were found for finger velocity and cross-sectional area as a function of both the flux through the finger and hydraulic properties of the coarse layer represented by the sorptivity, saturated conductivity, and initial and saturated moisture contents. Unlike the two-dimensional case, air entrapment was an important factor in explaining the experimental results.