Stability of one-dimensional boundary layers by using Green's functions

2001 ◽  
Vol 54 (11) ◽  
pp. 1343-1385 ◽  
Author(s):  
Emmanuel Grenier ◽  
Fr�d�ric Rousset
Keyword(s):  
Boundary Layers ◽  
Green's Functions ◽  
Green’S Functions ◽  
One Dimensional ◽  
Dimensional Boundary

scholarly journals Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

2019 ◽  
Vol 24 (1) ◽  
pp. 26 ◽  
Author(s):  
Sergey Davydov ◽  
Andrei Zemskov ◽  
Elena Akhmetova
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Equilibrium ◽  
Linear Equations ◽  
Integral Form ◽  
External Effects ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
The Laplace Transform

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes.

Time-Dependent Green’s Functions Description of One-Dimensional Nuclear Mean-Field Dynamics

2009 ◽  
Author(s):  
Arnau Rios ◽  
Pawel Danielewicz ◽  
Brent Barker ◽  
Pawel Danielewicz
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Mean Field ◽  
Time Dependent ◽  
One Dimensional

Green's functions of one-dimensional quasicrystal bi-material with piezoelectric effect

2016 ◽  
Vol 380 (39) ◽  
pp. 3222-3228 ◽  
Author(s):  
Liangliang Zhang ◽  
Di Wu ◽  
Wenshuai Xu ◽  
Lianzhi Yang ◽  
Andreas Ricoeur ◽  
...  
Keyword(s):  
Green's Functions ◽  
Piezoelectric Effect ◽  
Green’S Functions ◽  
One Dimensional

A Two-Dimensional Cylindrical Transient Conduction Solution Using Green’s Functions

2013 ◽  
Author(s):  
Robert L. McMasters ◽  
James V. Beck
Keyword(s):  
Parameter Estimation ◽  
Green's Functions ◽  
Bessel Functions ◽  
Numerical Solutions ◽  
Green’S Functions ◽  
Two Dimensional ◽  
Trigonometric Functions ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
One Dimensional

There are many applications for problems involving thermal conduction in two-dimensional cylindrical objects. Experiments involving thermal parameter estimation are a prime example, including cylindrical objects suddenly placed in hot or cold environments. In a parameter estimation application, the direct solution must be run iteratively in order to obtain convergence with the measured temperature history by changing the thermal parameters. For this reason, commercial conduction codes are often inconvenient to use. It is often practical to generate numerical solutions for such a test, but verification of custom-made numerical solutions is important in order to assure accuracy. The present work involves the generation of an exact solution using Green’s functions where the principle of superposition is employed in combining a one-dimensional cylindrical case with a one-dimensional Cartesian case to provide a temperature solution for a two-dimensional cylindrical. Green’s functions are employed in this solution in order to simplify the process, taking advantage of the modular nature of these superimposed components. The exact solutions involve infinite series of Bessel functions and trigonometric functions but these series sometimes converge using only a few terms. Eigenvalues must be determined using Bessel functions and trigonometric functions. The accuracy of the solutions generated using these series is extremely high, being verifiable to eight or ten significant digits. Two examples of the solutions are shown as part of this work for a family of thermal parameters. The first case involves a uniform initial condition and homogeneous convective boundary conditions on all of the surfaces of the cylinder. The second case involves a nonhomogeneous convective boundary condition on a part of one of the planar faces of the cylinder and homogeneous convective boundary conditions elsewhere with zero initial conditions.

Exact Phonon Green's Functions of One-Dimensional Quasiperiodic Lattices

1992 ◽  
Vol 170 (2) ◽  
pp. 435-441
Author(s):  
J. X. Zhong ◽  
J. R. Yan ◽  
J. Q. You
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
One Dimensional
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