Assessment of the validity of the one-dimensional approximation in the velocity Structure Modeling Based on the Spatial Correlation of Seismic Motions

2021 ◽  
Author(s):  
Daiki Torii ◽  
Hiroaki Sato ◽  
Shoma Yamamoto ◽  
Atsushi Okazaki
Keyword(s):  
Spatial Correlation ◽  
Velocity Structure ◽  
Structure Modeling ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One

A Stefan problem in a Bridgman crystal grower

1995 ◽  
Vol 6 (3) ◽  
pp. 191-199
Author(s):  
P. den Decker ◽  
R. van der Hout ◽  
C. J. Van Duijn ◽  
L. A. Peletier
Keyword(s):  
Critical Speed ◽  
Internal Heat ◽  
Mushy Region ◽  
Dimensional Model ◽  
Real Situation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One ◽  
Strong Curvature ◽  
Bridgman Crystal Grower

We discuss a one-dimensional model for a Bridgman crystal grower, where the removal of heat is described by an internal heat sink. A consequence is the apparent existence of mushy regions for relatively large velocities of the cooling machine; these mushy regions are an artefact of the one-dimensional approximation. We show that for some types of cooling profiles there exists a critical speed for the existence of mushy regions, whereas for different cooling profiles no such critical speed exists. The presence of a mushy region may indicate a strong curvature of the liquid/solid interface in the real situation.

Kinetic calculation of a turbulent flame in the one-dimensional approximation

1980 ◽  
Vol 16 (4) ◽  
pp. 365-369
Author(s):  
V. Ya. Basevich ◽  
V. P. Volodin ◽  
S. M. Kogarko ◽  
N. I. Peregudov
Keyword(s):  
Turbulent Flame ◽  
Kinetic Calculation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One

Thermochemical Response of Honeycomb Sandwich Panels

1983 ◽  
Vol 1 (5) ◽  
pp. 379-395
Author(s):  
Kumar Ramohalli
Keyword(s):  
Thermal Conductivity ◽  
Analytical Solution ◽  
Thermal Conductivity Coefficient ◽  
Sandwich Panels ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Honeycomb Sandwich ◽  
The One

A simple study aimed at predicting the Thermochemical Response of honey comb sandwich panels is presented. The overall thermal conductivity coefficient for the panel is obtained through a consideration of the convective gas move ment within the cell spaces. The earlier correlations of Catton and Edwards are used. The analytical solution for the one-dimensional approximation is quoted from an earlier study.

Amplification and attenuation of waves of finite duration by means of a bubble zone in the one-dimensional approximation

2012 ◽  
Vol 9 (2) ◽  
pp. 33-37
Author(s):  
M.N. Galimzyanov
Keyword(s):  
Solid Wall ◽  
Nonlinear Effects ◽  
Uneven Distribution ◽  
Pressure Waves ◽  
One Dimensional ◽  
Finite Duration ◽  
Dimensional Approximation ◽  
The One ◽  
Bubble Zone ◽  
As Effects

Some peculiarities of the dynamics of pressure waves in a fluid containing bubble zone of finite dimensions in the one-dimensional approximation are studied. The problem is considered taking into account nonlinear effects. The results of the action of wave pulses on a bubble area with an uneven distribution of bubbles are presented, as well as effects on a solid wall covered with a bubble area.

The one-dimensional approximation for infiltration in heterogeneous soils

1991 ◽  
Vol 27 (6) ◽  
pp. 1019-1027 ◽  
Author(s):  
Angelos L. Protopapas ◽  
Rafael L. Bras
Keyword(s):  
One Dimensional ◽  
Heterogeneous Soils ◽  
Dimensional Approximation ◽  
The One

Ocean Acoustics

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Mathematical Model ◽  
Velocity Structure ◽  
Potential Well ◽  
Ocean Acoustics ◽  
Underwater Sound ◽  
Acoustic Wave Propagation ◽  
One Dimensional ◽  
Acoustic Waveguides ◽  
Water Transmission ◽  
The One

This chapter deals with the mathematics of ocean acoustics. A number of environmental factors affect the transmission of sound in the ocean, including the depth and configuration of the bottom, the sound velocity structure within the ocean, and the shape of the ocean surface. The depths in the ocean are distributed in a peculiar manner, and the solution of underwater-sound problems may be grouped into two categories that differ mainly in terms of dimension: the average depths of water for deep-water transmission are 10,000 to 20,000 feet, whereas those for shallow-water transmission are less than 300 feet. The chapter first provides an overview of ocean acoustic waveguides before discussing one-dimensional waves in an inhomogeneous medium. It also considers a mathematical model of acoustic wave propagation in a stratified fluid and concludes with an analysis of the one-dimensional time-independent Schrödinger equation for solving the potential well problem.

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