Generating Functions for the Exact Solution of the Transport Equation. I

1968 ◽  
Vol 9 (10) ◽  
pp. 1722-1731 ◽  
Author(s):  
I. K. Abu‐Shumays ◽  
E. H. Bareiss
Keyword(s):  
Exact Solution ◽  
Transport Equation ◽  
Generating Functions

scholarly journals ACCURATE MODELLING OP TWO-DIMENSIONAL MASS TRANSPORT

1984 ◽  
Vol 1 (19) ◽  
pp. 163
Author(s):  
Lance Bode ◽  
Rodney J. Sobey
Keyword(s):  
Exact Solution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Transport Equation ◽  
Spatial Dimension ◽  
Convective Transport ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Numerical Errors ◽  
Moving Coordinate

Any numerical solution of the convective transport equation in an Eulerian framework will exhibit inherent numerical dispersion and solution oscillations. The magnitude of such numerical errors is often so severe as to destroy the value of many computed solutions. A successful and economical algorithm for the convective transport equation in one spatial dimension has been published recently by one of the authors (RJS), in which an exact solution is achieved by means of a moving coordinate system. The present study describes the extension of this work to the more important and challenging two-dimensional case.

scholarly journals Exact Solution of Some Quarter Plane Walks with Interacting Boundaries

10.37236/8024 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
N. R. Beaton ◽  
A. L. Owczarek ◽  
A. Rechnitzer
Keyword(s):  
Exact Solution ◽  
Random Walks ◽  
Generating Function ◽  
Generating Functions ◽  
Quarter Plane ◽  
Statistical Mechanical

The set of random walks with different step sets (of short steps) in the quarter plane has provided a rich set of models that have profoundly different integrability properties. In particular, 23 of the 79 effectively different models can be shown to have generating functions that are algebraic or differentiably finite. Here we investigate how this integrability may change in those 23 models where in addition to length one also counts the number of sites of the walk touching either the horizontal and/or vertical boundaries of the quarter plane. This is equivalent to introducing interactions with those boundaries in a statistical mechanical context. We are able to solve for the generating function in a number of cases. For example, when counting the total number of boundary sites without differentiating whether they are horizontal or vertical, we can solve the generating function of a generalised Kreweras model. However, in many instances we are not able to solve as the kernel methodology seems to break down when including counts with the boundaries.

Exact solution of the neutron transport equation in spherical geometry

Kerntechnik ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. 132-135
Author(s):  
F. Anlı ◽  
A. Akkurt ◽  
H. Yıldırım ◽  
K. Ateş
Keyword(s):  
Exact Solution ◽  
Transport Equation ◽  
Neutron Transport ◽  
Spherical Geometry ◽  
Neutron Transport Equation
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