Hemphill, Amanda J. Ph.D. Purdue University, May 2015. Development of Experimental and Instrumental Systems to Study Biological Systems. Major Professor: Brian A. Todd. Chapters 1-4 of this thesis describes the development of an experimental system to measure diffusion-limited reaction kinetics in a biological environment. About 100 years ago, the relationship between reaction rate and diffusio...

the effect of mechanical activation on structural changes and kinetics of carbothermic reduction of hematite with graphite was studied in this research. hematite powder mixture with graphite (with stoichiometry ratio c/o=1) was milled for the time periods of zero to 50 hours, and the structural changes were studied using x ray diffraction (xrd). the effect of mechanical activation on the kineti...

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by ...

In the past decade, advances in molecular biology such as the development of non-invasive single molecule imaging techniques have given us a window into the intricate biochemical activities that occur inside cells. In this chapter we review four distinct theoretical and simulation frameworks: (i) non-spatial and deterministic, (ii) spatial and deterministic, (iii) non-spatial and stochastic and...

Mathematical modeling and simulation of biochemical reaction networks facilitates our understanding of metabolic and signaling processes. For closed, well-mixed reaction systems, it is straightforward to derive kinetic equations that govern the concentrations of the reactants and products. The usual way of deriving kinetic equations involves application of the principle of conservation of mass ...

Reactions in restricted spaces rarely get stirred vigorously by convection and are thus controlled by diffusion. Furthermore, the compactness of the Brownian motion leads to both anomalous diffusion and anomalous reaction kinetics. Elementary binary reactions of the type A + A + Products, A + B + Products, and A + C + C + Products are discussed theoretically for both batch and steady-state cond...

dimension di, while the rest of the d-dimensional space is occupied by identical mobile particles. The Smoluchowski rate theory suggests that the immobile reactants concentration, s(t), exhibits interesting behavior as a function of the codimension, d̄ ≡ d− di. This survival probability undergoes a survival-to-extinction transition at d̄c = 2. For d̄ < d̄c, a finite fraction of the immobile reactan...

In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A grid-based version of MIM is developed. Generalizations to open systems are suggested. ...

We study the kinetics of a diffusion-controlled reaction in which perfect traps (scavengers) diffuse and consume randomly distributed particles. We find that the number of particles remaining after time t decays as exp(-actd”), for spatial dimensions d 1 2 , and as exp(-act) for d 3 2 , where U is a constant, and c is the trap concentration. These predictions are supported by Monte Carlo data i...