Mathematical Sciences

School of Natural Sciences & Mathematics

Computational Science Seminar F15

Nov 20Alexey Sukhinin Mathematics, SMU From single to multi-color filamentation of high energy pulses in atmosphere Light filamentation is a rapidly growing area of research due to many possible applications including remote sensing, lightning control, lidar, and directed energy. Most of the studies in the past had been around femtosecond filamentation. However, use of longer pulses could lead to longer and more energetic filament propagation. In this talk I will discuss modeling aspects of laser filamentation including self-focusing, plasma formation due to multiphoton ionization, spatial stability of fundamental and vortex filaments and other effects.
Nov 13 Jianzhong Su Mathematics, UT Arlington Globally Convergent methods for inverse problems in Diffuse Optical Tomography and its applications
In this talk, we give an overview of both theory and experimental applications of a numerical Globally Convergent Method (GCM) for an inverse problem in Diffuse Optical Tomography. The method is for an inverse problem for an elliptic partial differential equation with an unknown potential, an important mathematical problem at the core of Near-Infrared laser imaging technology. The GCM reconstruction method fundamentally differs from other current methods based on the Newton’s method or optimization scheme. GCM does not require a relative precise first guess and hence it is capable in dealing with complex media and realistic geometry for biomedical applications. Several sets of boundary data measurements are
generated by placing the light source at several designated locations. Mathematically, a global convergence theorem assures the success of the numerical reconstruction method. Then we use this method in experiments of an optical phantom emulating rat brain suffering a stroke. We present the experimental setup of optical measurements and report accurate images and their physical parameters of hidden interior objects inside an optical phantom, which are reconstructed based on light intensity data collected on the object’s surface. Finally we test the method in animal experiments. The examples illustrate how the mathematical theory of GCM be used in tomographic reconstruction of experimental data.
Oct 23Gaik Ambartsoumian Mathematics, UT Arlington Broken-ray and conical Radon transforms in imaging Broken-ray and conical Radon transforms appear in mathematical models of various novel imaging modalities, including single scattering optical tomography and some imaging techniques based on Compton scattering effect. The talk will discuss the known results and recent developments in the study of these integrals transforms, their applications and the open problems.
Oct 9 William Anderson Mechanical Engineering, UTD Large-eddy simulation of rough wall turbulence: effects of complex topography, evidence of inner-outer effects, and the role of turbulence in aeolian systems
Sep 4 John Zweck Math, UTD Spectra of Short Pulse Solutions of the Cubic-Quintic Complex Ginzburg Landau Equation near Zero Dispersion Mode-locked femtosecond lasers are high performance optical systems for ultra-precise measurement of time, frequency, and distance. The cubic-quintic complex Ginzburg-Landau equation provides a qualitative model for the generation of short-pulses in mode-locked lasers. We describe a computational method to compute spectra and slowly-decaying eigenfunctions of linearizations of the cubic-quintic complex Ginzburg-Landau equation about numerically-determined stationary solutions. In the presence of large dissipative effects, we discover variations in the structure of the spectrum as the dispersion crosses zero that are not predicted by the small dissipation theory of Kapitula and Sandstede. In particular, in the normal dispersion regime we observe a jump in the number of discrete eigenvalues when a pair of real eigenvalues merges with the intersection point of the two branches of the continuous spectrum. Finally, we will describe applications to the modeling of noise effects in short pulse lasers.

These results were obtained in joint work with Yannan Shen, Shaokang Wang, and Curtis Menyuk.
Aug 28SIAM Student Chapter