The elimination of the FexAly type phases was considered the solution to low ductility presented in aluminum-steel welded joints. Recently, the researches do not seek the suppression but the control of the thickness of these compounds. In this work, Al-Fe joints were manufactured by solid state and fusion welding, looking for controlling the formation of intermetallic comp...

irradiation of &methyl; spiro [2.5] oct-7-en-4-one through its singlet excited state resulted in the formation of 4-methyl spiro [2.5] oct-4-en -6-one. we have used the cyclopropyl moiety in the molecule as a probe to study the operating mechanism in the photochemistry of ?, ?-unsaturated compounds. the results showed that this photoisomerization probably occurs through a concerted process.

This project studies the nonhomogeneous steady-state solutions of the Gray-Scott model, a system of nonlinear partial differential equations that has received attention in the past decade in the context of pattern formation and morphogenesis. Morphogenesis, or ‘birth of shape’, is the biological term for the initial formation of patterns that occur in development as cells begin to differentiate...

We examine sequential spatial pattern formation in a tissue interaction model for skin organ morphogenesis. Pattern formation occurs as a front sweeps across the domain leaving in its wake a steady state spatial pattern. Extensive numerical simulations show that these fronts travel with constant wave speed. By considering the envelope of the solution profile we present a novel method of calcula...

The intermediate state of a type-I superconductor is a classical example of energy-driven pattern-formation, first studied by Landau in 1937. Three of us recently derived five different rigorous upper bounds for the ground state energy, corresponding to different microstructural patterns, but only one of them was complemented by a lower bound with the same scaling [Choksi, Kohn, Otto, J. Nonlin...

Pattern formation is one of the important topics in biological study. The publication of the paper by Turing [8] gave us a big hint for how the biological patterns formed. Turing suggested that some reaction-diffusion systems with suitable range of parameters could give the spatial patterns in concentrations. In his study, the pattern formation is based on the conjunction of local selfenhanceme...

Abstract. This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the no...

This summer I worked on several projects unrelated to each other. The first project was an extension of what I researched last summer with Dr. Keshet and Dr. Ward. Our group looked at several models of nonlinear motor dynamics in the cell, including kinesins along microtubules, as well as myosins along actin filaments. These models were essentially a collection of nonlinear coupled PDEs describ...

In this paper, the pattern formation of the attraction-repulsion Keller-Segel (ARKS) system is studied analytically and numerically. By the Hopf bifurcation theorem as well as the local and global bifurcation theorem, we rigorously establish the existence of time-periodic patterns and steady state patterns for the ARKS model in the full parameter regimes, which are identified by a linear stabil...