We use a rapidly rotating tank lled with water to study the random walks of tracer particles in two di erent ows: one with coherent structures (vortices and jets), and one without (weakly turbulent). Most random walks, such as those taken by dye molecules di using by Brownian motion, obey the Central Limit Theorem; their motion can be characterized by a di usion constant. The random walks in ou...

‎The ‎method ‎of ‎quasilinearization ‎is ‎an ‎effective ‎tool ‎to ‎solve nonlinear ‎equations ‎when ‎some ‎conditions‎ on ‎the ‎nonlinear term ‎of ‎the ‎problem ‎are ‎satisfi‎‎ed. ‎W‎hen ‎the ‎conditions ‎hold, ‎applying ‎this ‎techniqu‎e ‎gives ‎two ‎sequences of ‎coupled ‎linear ‎equations‎ and ‎the ‎solutions ‎of ‎th‎ese ‎linear ‎equations ‎are quadratically ‎convergent ‎to ‎the ‎solution ‎o...

Photothermal depth pro lometry is formulated as a non-linear inverse scattering problem. Starting with the one dimensional heat di usion equation, we derive a mathematical model relating arbitrary variation in the depth-dependent thermal conductivity to observed thermal wave elds at the surface of a material sample. The form of the model is particularly convenient for incorporation into a non-l...

In this paper, we consider an inverse problem of linear heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation tern from an overspecified condition on the boundary

in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...

Radiotherapy plays an increasingly important role in cancer treatment, and medical imaging plays an increasingly important role in radiotherapy. Magnetic resonance imaging (MRI) is poised to be a major component in the development towards more e ective radiotherapy treatments with fewer side e ects. This thesis attempts to contribute in realizing this potential. Radiotherapy planning requires s...

Synopsis We compute the higher-order statistics of the 3D spin displacement probability distributions measured with mean apparent propagator (MAP) MRI and quantify microstructural tissue parameters such as the mean kurtosis (MK), axial kurtosis (K ), radial kurtosis (K ) and kurtosis fractional anisotropy (FA ). This extension of the family of MAP tissue parameters provides a direct link betwee...

We present a study of the local discontinuous Galerkin method for transient convection-di usion problems in one dimension. We show that p degree piecewise polynomial discontinuous nite element solutions of convection-dominated problems are O( xp+2) superconvergent at Radau points. For di usion-dominated problems, the solution's derivative is O( xp+2) superconvergent at the roots of the derivati...

Oxygen delivery to the tissues is crucial to survival but our understanding of the processes involved in the transport of oxygen from blood to tissue is incomplete. The aim of the present work is to illustrate a long-standing paradox regarding such transport by reporting new state-of-the-art measurements and by analyzing the results in several ways, thereby exploring possible resolutions of the...

GIS managers traditionally consider three perspectives of the nature of GIS when introducing GIS into an organization. When the GIS is developed to address focused and well de® ned problems of the organization, these perspectives adequately describe the changing identities of GIS in the study of its di€ usion. However when the GIS is developed to address strategic, but vaguely de® ned problems,...