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Articles 1 - 2 of 2
Full-Text Articles in Non-linear Dynamics
Singularities And Global Solutions In The Schrodinger-Hartree Equation, Anudeep Kumar
Singularities And Global Solutions In The Schrodinger-Hartree Equation, Anudeep Kumar
FIU Electronic Theses and Dissertations
In 1922, Louis de Broglie proposed wave-particle duality and introduced the idea of matter waves. In 1925, Erwin Schrodinger, proposed a wave equation for de Broglie’s matter waves. The Schrodinger equation is described using the de Broglie’s matter wave, which takes the wave function, and describes its quantum state over time.
Herein, we study the generalized Hartree (gHartree) equation, which is a nonlinear Schrodinger type equation except now the nonlinearities are a nonlocal (convolution) type. In the gHartree equation, the influence on the behavior of the solutions is global as opposed to the case of local (power type) nonlinearities.
Our …
Theoretical Investigation Of Intra- And Inter-Cellular Spatiotemporal Calcium Patterns In Microcirculation, Jaimit B. Parikh
Theoretical Investigation Of Intra- And Inter-Cellular Spatiotemporal Calcium Patterns In Microcirculation, Jaimit B. Parikh
FIU Electronic Theses and Dissertations
Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC …