scholarly journals Lattice dynamics in the half-space. Energy transport equation

2010 ◽  
Vol 51 (8) ◽  
pp. 083301 ◽  
Author(s):  
T. V. Dudnikova
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Lattice Dynamics ◽  
Energy Transport

Approximate solutions to the half-space integral transport equation near a plane boundary

1980 ◽  
Vol 58 (9) ◽  
pp. 1291-1310 ◽  
Author(s):  
Michael S. Milgram
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Matrix Multiplication ◽  
Solution Space ◽  
Plane Geometry ◽  
Plane Boundary ◽  
Infinite Plane ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Integral Transport

A set of functions spanning the solution space of the integral transport equation near a boundary in semi-infinite plane geometry is obtained and used to reduce the problem to that of a system of linear algebraic equations. Expressions for the boundary angular flux are obtained by matrix multiplication, and the theory is extended to adjacent half-space problems by matching the angular flux at the boundary. Thus a unified theory is obtained for well-behaved arbitrary sources in semi-infinite plane geometry. Numerical results are given for both Milne's problem and the problem of constant production in adjacent half-spaces, and albedo problems in semi-infinite geometry. The solutions for the flux density are best near the boundary, and for the angular flux are best for angles near the plane of the boundary; it is conjectured that the theory will prove most useful when extended to arrays of finite slabs.

scholarly journals Numerical Simulations of Optical Knots in YSO Outflows

1997 ◽  
Vol 182 ◽  
pp. 313-322
Author(s):  
F. Rubini ◽  
S. Lorusso ◽  
C. Giovanardi ◽  
F. Leeuwin
Keyword(s):  
Numerical Simulations ◽  
Transport Equation ◽  
Energy Transport ◽  
Optical Emission ◽  
Chemical Parameters ◽  
Physical And Chemical Parameters ◽  
3D Effects ◽  
Physical And Chemical ◽  
Oblique Shocks ◽  
Good Agreement

The aim of this work is to show that, though 3D effects should be invoked to explain the less regular arc-like regions, the internal knotty emissions may be explained through a roughly axisymmetric pattern of oblique shocks.To this purpose, numerical simulations of non-equilibrium, radiative, hydrodynamical jets in axisymmetric geometry have been performed. After showing that the internal reflecting waves, travelling in the beam of a stellar jet, steepen into oblique shocks, we verify that the optical emission arising from the shocked regions is in good agreement with observations.Since the optical emission strongly depends on the physical and chemical parameters, (namely temperature and electron densities inside the emitting regions), special care is devoted to solving the energy transport equation.

A transport-equation description of nonlinear ocean surface wave interactions

1975 ◽  
Vol 70 (4) ◽  
pp. 815-826 ◽  
Author(s):  
Kenneth M. Watson ◽  
Bruce J. West
Keyword(s):  
Surface Wave ◽  
Transport Equation ◽  
Energy Transport ◽  
Wave Spectrum ◽  
Interaction Mechanism ◽  
Wave Interaction ◽  
Ocean Current ◽  
Wave Interactions ◽  
Ocean Surface Wave ◽  
Wind Source

The evolution of the power spectrum of surface gravity waves is described by means of an energy transport equation. A slowly varying, prescribed ocean current and wind source are assumed to account for spatial inhomogeneities in the surface wave spectrum. These inhomogeneities lead to a new nonlinear wave-wave interaction mechanism.

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