arXiv subjects

Emily Stone

Publications and source records attributed to Emily Stone.

3 recordsLinked to original sources

arXiv2016

The Dynamics of Vector-Borne Relapsing Diseases

In this paper we describe the dynamics of a vector-borne relapsing disease, such as tick-borne relapsing fever, using the methods of compartmental models. After some motivation, model description, and a brief overview of the theory of compartmental models, we compute a general form of the reproductive ratio $R_0$, which is the average number of new infections produced by a single infected individual. A disease free equilibrium undergoes a bifurcation at $R_0 =1$ and we show that for an arbitrary number of relapses it is a transcritical bifurcation with a single branch of endemic equilibria that is locally asymptotically stable for $R_0$ sufficiently close to 1. We close with some discussion and directions for future research.

math.DS↗

arXiv2006

A two stage model for quantitative PCR

PCR (Polymerase Chain Reaction), a method which replicates a selected sequence of DNA, has revolutionized the study of genomic material, but mathematical study of the process has been limited to simple deterministic models or descriptions relying on stochastic processes. In this paper we develop a suite of deterministic models for the reactions of quantitative PCR (Polymerase Chain Reaction) based on the law of mass action. Maps are created from DNA copy number in one cycle to the next, with ordinary differential equations describing the evolution of difference molecular species during each cycle. Qualitative analysis is preformed at each stage and parameters are estimated by fitting each model to data from Roche LightCycler (TM) runs.

q-bio.BM↗

arXiv2005

Investigations of Process Damping Forces in Metal Cutting

Using finite element software developed for metal cutting by Third Wave Systems we investigate the forces involved in chatter, a self-sustained oscillation of the cutting tool. The phenomena is decomposed into a vibrating tool cutting a flat surface work piece, and motionless tool cutting a work piece with a wavy surface. While cutting the wavy surface, the shearplane was seen to oscillate in advance of the oscillation of the depth of cut, as were the cutting, thrust, and shear plane forces. The vibrating tool was used to investigate process damping through the interaction of the relief face of the tool and the workpiece. Crushing forces are isolated and compared to the contact length between the tool and workpiece. We found that the wavelength dependence of the forces depended on the relative size of the wavelength to the length of the relief face of the tool. The results indicate that the damping force from crushing will be proportional to the cutting speed for short tools, and inversely proportional for long tools.

cs.CE↗