Three-dimensional wave propagation through single crystal solid–liquid interfaces

1998 ◽  
Vol 103 (3) ◽  
pp. 1353-1360 ◽  
Author(s):  
Yichi Lu ◽  
Haydn N. G. Wadley
Keyword(s):  
Wave Propagation ◽  
Single Crystal ◽  
Three Dimensional ◽  
Liquid Interfaces ◽  
Solid Liquid ◽  
Dimensional Wave

IS WAVE PROPAGATION COMPUTABLE OR CAN WAVE COMPUTERS BEAT THE TURING MACHINE?

2002 ◽  
Vol 85 (2) ◽  
pp. 312-332 ◽  
Author(s):  
KLAUS WEIHRAUCH ◽  
NING ZHONG
Keyword(s):  
Wave Propagation ◽  
Turing Machine ◽  
Sobolev Spaces ◽  
Three Dimensional ◽  
Subject Classification ◽  
Physical Machine ◽  
The Church ◽  
Dimensional Wave

According to the Church-Turing Thesis a number function is computable by the mathematically defined Turing machine if and only if it is computable by a physical machine. In 1983 Pour-El and Richards defined a three-dimensional wave $u(t,x)$ such that the amplitude $u(0,x)$ at time 0 is computable and the amplitude $u(1,x)$ at time 1 is continuous but not computable. Therefore, there might be some kind of wave computer beating the Turing machine. By applying the framework of Type 2 Theory of Effectivity (TTE), in this paper we analyze computability of wave propagation. In particular, we prove that the wave propagator is computable on continuously differentiable waves, where one derivative is lost, and on waves from Sobolev spaces. Finally, we explain why the Pour-El-Richards result probably does not help to design a wave computer which beats the Turing machine.2000 Mathematical Subject Classification: 03D80, 03F60, 35L05, 68Q05.

scholarly journals Direct observation of electric charges at solid/liquid interfaces with the pressure-wave-propagation method

2021 ◽  
Vol 109 ◽  
pp. 103527
Author(s):  
Assane Ndour ◽  
Stéphane Holé ◽  
Paul Leblanc ◽  
Thierry Paillat
Keyword(s):  
Wave Propagation ◽  
Direct Observation ◽  
Pressure Wave ◽  
Liquid Interfaces ◽  
Wave Propagation Method ◽  
Solid Liquid

For the Growth of 3 Inch D-Shaped GaAs Crystals by a Modified Horizontal Bridgman Process

1993 ◽  
Vol 207 (3) ◽  
pp. 185-195 ◽  
Author(s):  
M H Hsieh ◽  
C C Chieng ◽  
K H Lie ◽  
Y D Guo
Keyword(s):  
Dopant Concentration ◽  
Three Dimensional ◽  
Solidification Process ◽  
Temperature Fields ◽  
Liquid Interfaces ◽  
Axial Distribution ◽  
Mass Transfer Mechanism ◽  
Finite Volume Approach ◽  
Silicon Doped ◽  
Solid Liquid

Doped with silicon or zinc, 3 inch D-shaped GaAs crystals were grown by the modified two-temperature horizontal Bridgman (M2T-HB) technique. Then (1&10) wafers were sliced axially from the chunk of silicon-doped 3 inch GaAs crystals and chemically etched to reveal the growth striations of solid/liquid interfaces. Three-dimensional, numerical simulations of the solidification process for growing 3 inch crystals by the M2T-HB system were performed and compared with the etched (110) wafers from experiments. The heat- and mass-transfer mechanism through the melt is the combination of convection, conduction and radiation. The finite volume approach and the continuum model are employed to determine the position and shape of the interface of the solid/melt, dopant concentration and the temperature field in the crystal and melt. Two methods for computing the dopant concentration are (a) solving the transport equation of full mass concentration and (b) using the simplified model of equilibrium. The computed solidification fronts and the dopant distributions agree successfully with the experimental data, and the axial distribution of dopant concentration as well as flow and temperature fields are computed for information of the crystal quality.

scholarly journals A Formulation of Unified Three-Dimensional Wave Activity Flux of Inertia–Gravity Waves and Rossby Waves

2013 ◽  
Vol 70 (6) ◽  
pp. 1603-1615 ◽  
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato
Keyword(s):  
Wave Propagation ◽  
Gravity Waves ◽  
Rossby Waves ◽  
Three Dimensional ◽  
Wave Activity ◽  
Storm Tracks ◽  
Mean Flow ◽  
Wave Activity Flux ◽  
Inertia Gravity Waves ◽  
Dimensional Wave

Abstract A companion paper formulates the three-dimensional wave activity flux (3D-flux-M) whose divergence corresponds to the wave forcing on the primitive equations. However, unlike the two-dimensional wave activity flux, 3D-flux-M does not accurately describe the magnitude and direction of wave propagation. In this study, the authors formulate a modification of 3D-flux-M (3D-flux-W) to describe this propagation using small-amplitude theory for a slowly varying time-mean flow. A unified dispersion relation for inertia–gravity waves and Rossby waves is also derived and used to relate 3D-flux-W to the group velocity. It is shown that 3D-flux-W and the modified wave activity density agree with those for inertia–gravity waves under the constant Coriolis parameter assumption and those for Rossby waves under the small Rossby number assumption. To compare 3D-flux-M with 3D-flux-W, an analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim) data is performed focusing on wave disturbances in the storm tracks during April. While the divergence of 3D-flux-M is in good agreement with the meridional component of the 3D residual mean flow associated with disturbances, the 3D-flux-W divergence shows slight differences in the upstream and downstream regions of the storm tracks. Further, the 3D-flux-W magnitude and direction are in good agreement with those derived by R. A. Plumb, who describes Rossby wave propagation. However, 3D-flux-M is different from Plumb’s flux in the vicinity of the storm tracks. These results suggest that different fluxes (both 3D-flux-W and 3D-flux-M) are needed to describe wave propagation and wave–mean flow interaction in the 3D formulation.

Sign in / Sign up

Export Citation Format

Share Document