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UTILIZATION OF TOTAL MASS AS A CONTROL IN DIFFUSION PROCESSES

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Date Issued:
2005
Abstract/Description:
As motivation for the mathematical problems considered in this work, consider a chamber in the form of a long linear transparent tube. We allow for the introduction or removal of material in a gaseous state at the ends of the tube. The material diffuses throughout the tube with or without reaction with other materials. By illuminating the tube on one side with a light source with a frequency range spanning the absorption range for the material and collecting the residual light that passes through the tube with photo-reception equipment, we can obtain a measurement of the total mass of material contained in the tube as a function of time. Using the total mass as switch points for changing the boundary conditions for introduction or removal of material. The objective is to keep the total mass of material in the tube oscillating between two set values such as $m0; \ u(x,0)=0,$ and $u(0,t)=u(1,t)=\psi(t),$ where $\psi(t)=u_0$ for $t_{2k} < t0; \ u(x,0)=0,$ and $u(0,t)=u(1,t)=\psi(t),$ where $\psi(t)=u_0$ for $t_{2k} < t0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\psi(t),$ where $\psi(t)=1$ for $t_{2k} < t0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\phi(t),$ where $a=a(x,t,u)$, and $\phi(t)=1$ for $t_{2k} < t
Title: UTILIZATION OF TOTAL MASS AS A CONTROL IN DIFFUSION PROCESSES.
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Name(s): Salman, Mohamed, Author
Cannon, John, Committee Chair
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2005
Publisher: University of Central Florida
Language(s): English
Abstract/Description: As motivation for the mathematical problems considered in this work, consider a chamber in the form of a long linear transparent tube. We allow for the introduction or removal of material in a gaseous state at the ends of the tube. The material diffuses throughout the tube with or without reaction with other materials. By illuminating the tube on one side with a light source with a frequency range spanning the absorption range for the material and collecting the residual light that passes through the tube with photo-reception equipment, we can obtain a measurement of the total mass of material contained in the tube as a function of time. Using the total mass as switch points for changing the boundary conditions for introduction or removal of material. The objective is to keep the total mass of material in the tube oscillating between two set values such as $m0; \ u(x,0)=0,$ and $u(0,t)=u(1,t)=\psi(t),$ where $\psi(t)=u_0$ for $t_{2k} < t0; \ u(x,0)=0,$ and $u(0,t)=u(1,t)=\psi(t),$ where $\psi(t)=u_0$ for $t_{2k} < t0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\psi(t),$ where $\psi(t)=1$ for $t_{2k} < t0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\phi(t),$ where $a=a(x,t,u)$, and $\phi(t)=1$ for $t_{2k} < t
Identifier: CFE0000551 (IID), ucf:46437 (fedora)
Note(s): 2005-05-01
Ph.D.
Arts and Sciences, Department of Mathematics
Doctorate
This record was generated from author submitted information.
Subject(s): Diffusion
Control
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0000551
Restrictions on Access: public
Host Institution: UCF

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