Mathematical Models And Stability Analysis Of Cholera Dynamics, 2010 Old Dominion University

#### Mathematical Models And Stability Analysis Of Cholera Dynamics, Shu Liao

*Mathematics & Statistics Theses & Dissertations*

In this dissertation, we present a careful mathematical study of several epidemic cholera models, including the model of Codeco [11] in 2001, that of Hartley, Morris and Smith [22] in 2006, and that of Mukandavire, Liao, Wang and Gaff *et al.* [60] in 2010. We formally derive the basic reproduction number *R*0 for each model by computing the spectral radius of the next generation matrix. We focus our attention on the stability analysis at the disease-free equilibrium which determines the short-term epidemic behavior, and the endemic equilibrium which determines the long-term disease dynamics. Particularly, we incorporate the Volterra-Lyapunov matrix ...

Evolution Of Solitary Waves For A Perturbed Nonlinear Schrodinger Equation, 2009 University of Wollongong

#### Evolution Of Solitary Waves For A Perturbed Nonlinear Schrodinger Equation, Tim Marchant

*Tim Marchant*

Soliton perturbation theory is used to determine the evolution of a solitary wave described by a perturbed nonlinear Schrödinger equation. Perturbation terms, which model wide classes of physically relevant perturbations, are considered. An analytical solution is found for the first-order correction of the evolving solitary wave. This solution for the solitary wave tail is in integral form and an explicit expression is found, for large time. Singularity theory, usually used for combustion problems, is applied to the large time expression for the solitary wave tail. Analytical results are obtained, such as the parameter regions in which qualitatively different types of ...

Multiple Decrement Modeling In The Presence Of Interval Censoring And Masking, 2009 Laurentian University

#### Multiple Decrement Modeling In The Presence Of Interval Censoring And Masking, Peter Adamic, Stephanie Dixon, Daniel Gillis

*Stephanie Dixon*

A self-consistent algorithm will be proposed to non-parametrically estimate the cause-specific cumulative incidence functions (CIFs) in an interval censored, multiple decrement context. More specifically, the censoring mechanism will be assumed to be a mixture of case 2 interval-censored data with the additional possibility of exact observations. The proposed algorithm is a generalization of the classical univariate algorithms of Efron and Turnbull. However, unlike any previous non-parametric models proposed in the literature to date, the algorithm will explicitly allow for the possibility of any combination of masked modes of failure, where failure is known only to occur due to a subset ...

A Tangent-Plane, Marker-Particle Method For The Computation Of Three-Dimensional Solid Surfaces Evolving By Surface Diffusion On A Substrate, 2009 Western Kentucky University

#### A Tangent-Plane, Marker-Particle Method For The Computation Of Three-Dimensional Solid Surfaces Evolving By Surface Diffusion On A Substrate, Ping Du, Mikhail Khenner, Harris Wong

*Mikhail Khenner*

We introduce a marker-particle method for the computation of three-dimensional solid surface morphologies evolving by surface diffusion. The method does not use gridding of surfaces or numerical differentiation, and applies to surfaces with finite slopes and overhangs. We demonstrate the method by computing the evolution of perturbed cylindrical wires on a substrate. We show that computed growth rates at early times agree with those predicted by the linear stability analysis. Furthermore, when the marker particles are redistributed periodically to maintain even spacing, the method can follow breakup of the wire.

Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, 2009 Western Kentucky University

#### Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

*Mikhail Khenner*

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O#1;#3;Bi#2;, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.

Thickness-Dependent Spontaneous Dewetting Morphology Of Ultrathin Ag Films, 2009 Washington University in St Louis

#### Thickness-Dependent Spontaneous Dewetting Morphology Of Ultrathin Ag Films, H Krishna, R Sachan, J Strader, C Favazza, Mikhail Khenner, Ramki Kalyanaraman

*Mikhail Khenner*

We show here that the morphological pathway of spontaneous dewetting of ultrathin Ag films on SiO2 under nanosecond laser melting is found to be film thickness dependent. For films with thickness h between 2<=h<=9.5 nm, the intermediate stages of the morphology consisted of bicontinuous structures. For films 11.5<=h<=20 nm, the intermediate stages consisted of regularly-sized holes. Measurement of the characteristic length scales for different stages of dewetting as a function of film thickness showed a systematic increase, which is consistent with the spinodal dewetting instability over the entire thickness range investigated. This change in morphology with thickness is consistent with observations made previously for polymer films [A. Shama et al, Phys. Rev. Lett., v81, pp3463 (1998); R. Seemann et al, J. Phys. Cond. Matt., v13, pp4925, (2001)]. Based on the behavior of free energy curvature that incorporates intermolecular forces, we have estimated the morphological transition thickness for Ag on SiO2. The theory predictions agree well with observations for Ag. These results show that it is possible to form a variety of complex Ag nanomorphologies in a consistent manner, which could be useful in optical applications of Ag surfaces, such as in surface enhanced Raman sensing.

Symmetries Of The Central Vestibular System: Forming Movements For Gravity And A Three-Dimensional World, 2009 Portland State University

#### Symmetries Of The Central Vestibular System: Forming Movements For Gravity And A Three-Dimensional World, Gin Mccollum, Douglas A. Hanes

*Gin McCollum*

Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified by geometric conditions. Symmetry groups have been found to structure experimentally-recorded pathways of the central vestibular system. When related to geometric conditions in three-dimensional physical space, these symmetry groups make sense as a logical foundation for sensorimotor coordination.

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, 2009 DePaul University and Columbia College Chicago

#### The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

*Byron E. Bell*

No abstract provided.

Cyclohexane Oxidation And Cyclohexyl Hydroperoxide Decomposition By Poly(4-Vinylpyridine-Co-Divinylbenzene) Supported Cobalt And Chromium Complexes, 2009 Institute of Chemistry, Technology and Metallurgy

#### Cyclohexane Oxidation And Cyclohexyl Hydroperoxide Decomposition By Poly(4-Vinylpyridine-Co-Divinylbenzene) Supported Cobalt And Chromium Complexes, Zeljko D. Cupic

*Zeljko D Cupic*

No abstract provided.

Heteroclinic Solutions To An Asymptotically Autonomous Second-Order Equation, 2009 Embry-Riddle Aeronautical University

#### Heteroclinic Solutions To An Asymptotically Autonomous Second-Order Equation, Gregory S. Spradlin

*Gregory S. Spradlin*

The Tangled Tale Of Phase Space, 2009 Purdue University

#### The Tangled Tale Of Phase Space, David D. Nolte

*David D Nolte*

Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, 2009 Wright State University - Main Campus

#### Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

*Yi Li*

Canonical Representation For Approximating Solution Of Fuzzy Polynomial Equations, 2009 Imam Khomeini International University

#### Canonical Representation For Approximating Solution Of Fuzzy Polynomial Equations, M. Salehnegad, Saeid Abbasbandy, M. Mosleh, M. Otadi

*Saeid Abbasbandy*

No abstract provided.