SOME REMARKS ON AFFINE EVOLUTION EQUATIONS WITH APPLICATIONS TO PARTICLE TRANSPORT THEORY

2000 ◽  
Vol 10 (06) ◽  
pp. 877-893 ◽  
Author(s):  
LUIGI BARLETTI
Keyword(s):  
Boundary Conditions ◽  
Banach Spaces ◽  
Particle Transport ◽  
Evolution Equations ◽  
Transport Theory ◽  
Time Dependent ◽  
Source Terms ◽  
Evolution Problems ◽  
Boundary Source ◽  
Transport Problems

We consider evolution problems with time-dependent inhomogeneous boundary conditions and discuss their relations with the theory of inhomogeneous evolution equations in Banach spaces. In the second part of the paper the attention is focused on particle transport problems with time-dependent boundary source terms.

Behavior of a Sequence of Geometric Transformations for a Truncated Ellipsoid Geometry in Transport Theory

2009 ◽  
Author(s):  
Rube´n Panta Pazos
Keyword(s):  
Boundary Conditions ◽  
Symmetry Axis ◽  
Transport Theory ◽  
Neutron Transport ◽  
Complex Function ◽  
Computational Techniques ◽  
Neutron Transport Equation ◽  
Geometric Transformations ◽  
The Right ◽  
Transport Problems

The neutron transport equation has been studied from different approaches, in order to solve different situations. The number of methods and computational techniques has increased recently. In this work we present the behavior of a sequence of geometric transformations evolving different transport problems in order to obtain solve a transport problem in a truncated ellipsoid geometry and subject to known boundary conditions. This scheme was depicted in 8, but now is solved for the different steps. First, it is considered a rectangle domain that consists of three regions, source, void and shield regions 5. Horseshoe domain: for that it is used the complex function: f:D→C,definedasf(z)=12ez+1ezwhereD=z∈C−0.5≤Re(z)≤0.5,−12π≤Im(z)≤12π(0.1) The geometry obtained is such that the source is at the focus of an ellipse, and the target coincides with the other focus. The boundary conditions are reflective in the left boundary and vacuum in the right boundary. Indeed, if the eccentricity is a number between 0,95 and 0,99, the distance between the source and the target ranges from 20 to 100 length units. The rotation around the symmetry axis of the horseshoe domain generates a truncated ellipsoid, such that a focus coincides with the source. In this work it is analyzed the flux in each step, giving numerical results obtained in a computer algebraic system. Applications: in nuclear medicine and others.

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