Applied Math Seminar
                   Oct. 23, 3:30-4:30pm
                Mathematics Conference Room
                    16 Colchester Avenue



    Application of the Fokker-Planck Equation in Fiber Optics
    
    		      Prof. Taras Lakoba
    	 Department of Mathematics and Statistics, UVM
    

Abstract:

The main goal of fiber optics communication system is to transmit
information between points A and B with minimal distortions. The
transmitted information is recorded as a sequence of logical bits,
ONEs and ZEROs. The physical object that represents a ONE is a pulse
of electromagnetic field (e.g., in the  visible or infra-red range).

Pulses in optical fibers are corrupted during their propagation by 
a number of random and non-random factors. It is required to know
the probability with which a pulse is corrupted by a given amount, 
because it is this corruption that leads to errors in transmission
(e.g., "snow" on a TV screen, echoes in phone lines, etc.).
A model characterizing such corrupted pulses is a set of ordinary
stochastic differential equations (SDEs) for the pulse parameters
(e.g., amplitude, width, arrival time, etc.).  

In this talk, which I plan to make understandable for graduate students,
I will first describe how one can start with SDEs for the pulse parameters
and derive an evolution equation, called the Fokker-Planck equation (FPE),
for the probability density of these parameters. Next, I will discuss the
issue of numerical modeling of the SDEs and the relation between this issue
and the Stratanovich and Ito versions of the stochastic calculus. Finally,
I will consider a simple yet non-trivial example of the derivation of an
SDE for a quantity relevant to physical applications.