Date: Jan 22nd, Tuesday
Time: 11:45 am
Place: Little 339 (the Atrium)
Speaker: Dr. Shabanov

Title:
 Mathematical modeling of plasma plumes expanding into vacuum
and remote chemical analysis
　

Abstract:
I will present a dynamical model that is used in data
processing for remote chemical analysis. The model consists of there
second-order nonlinear ODE's. I will also formulate an unsolved
problem for this dynamical model which is important
for applications. This is a good PhD project in applied mathematics.
A more detailed description is below.

Detailed abstract: Imagine that you have a portable device that is able
to tell you chemical compounds of material that is 50-100 yards
away from you, e.g., on a bamper of a car, on a wall, smoke
coming out of chimney, etc. One might think about a lot of good
things one can do with such a device.

One of the approaches to develop the device is based on the spectral
analysis of laser-induced plasmas. A laser pulse evaporates a tiny piece
of material turning it into a plume of hot plasma. The plume expands,
cools, and emit light. The light is observed by a device, called a
spectrograph, that produces the light intensity as a function of frequency
(wave length). Each chemical element is uniquely characterized
by positions of sharp maxima, called spectral lines, of the intensity
function. Values of the intensity function at its local maxima depend on
concentrations of corresponding chemical elements. There is a data
processing that allows one to calculate concentrations of chemical
compounds using the intensity function. The key element of the algorithm
is a mathematical model of plasma plume evoluton which tells how much
light is emited by the expanding plume at every moment of time given the
concentrations.

In general, plasma dynamics can be described by Navier-Stokes equations
supplemented by the equation of state and, hence, any such model must be
derived from them. One of the characteristic features of plasma plume
evolution is the flip-over effect, recently studied by my collegues from
the UF chemistry department.
If the plasma plume has initially a cigar-like shape,
then it evolves into a pancake-like shape (the converse is also true).

I will present a simple dynamical model, obtained from the Navier-Stokes
equations, which has been shown to provide an excellent agreement with
numerical and exparimental data on the laser-induced plasma plume
evolution. There is one unsolved problem though. One should prove that the
flip-over effect occurs exactly once in due course as seen in experiments
and, thereby, to confirm the validity of the model for large times.
>From the technical point of view, the problem is to prove a certain
property of solutions of a system of three second-order nonlinear ODE's.
This is a good PhD project in applied mathematics.

The pizza and drinks will be provided after the talk.