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Subgroups Of The Torelli Group, Leah R. Childers 2010 Louisiana State University and Agricultural and Mechanical College

Subgroups Of The Torelli Group, Leah R. Childers

LSU Doctoral Dissertations

Let Mod(Sg) be the mapping class group of an orientable surface of genus g, Sg. The action of Mod(Sg) on the homology of Sg induces the well-known symplectic representation:

Mod(Sg) ---> Sp(2g, Z).
The kernel of this representation is called the Torelli group, I(Sg).

We will study two subgroups of I(Sg). First we will look at the subgroup generated by all SIP-maps, SIP(Sg). We will show SIP(Sg) is not I(Sg) and is in fact an infinite index subgroup of I(Sg). We will also classify which SIP-maps are in the kernel of ...


Method Of Riemann Surfaces In Modelling Of Cavitating Flow, Anna Zemlyanova 2010 Louisiana State University and Agricultural and Mechanical College

Method Of Riemann Surfaces In Modelling Of Cavitating Flow, Anna Zemlyanova

LSU Doctoral Dissertations

This dissertation is concerned with the applications of the Riemann-Hilbert problem on a hyperelliptic Riemann surface to problems on supercavitating flows of a liquid around objects. For a two-dimensional steady irrotational flow of liquid it is possible to introduce a complex potential w(z) which allows to apply the powerful methods of complex analysis to the solution of fluid mechanics problems. In this work problems on supercavitating flows of a liquid around one or two wedges have been stated. The Tulin single-spiral-vortex model is employed as a cavity closure condition. The flow domain is transformed into an auxiliary domain with ...


Evolution Of Solitary Waves For A Perturbed Nonlinear Schrodinger Equation, Tim Marchant 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, Peter Adamic, Stephanie Dixon, Daniel Gillis 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, Ping Du, Mikhail Khenner, Harris Wong 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, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev 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, H Krishna, R Sachan, J Strader, C Favazza, Mikhail Khenner, Ramki Kalyanaraman 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, Gin McCollum, Douglas A. Hanes 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, Byron E. Bell 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, Zeljko D. Cupic 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, Gregory S. Spradlin 2009 Embry-Riddle Aeronautical University

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

Gregory S. Spradlin

We study the differential equation ¨x(t) = a(t)V' (x(t)), where V is a double-well potential with minima at x = ±1 and a(t) → l > 0 as |t| → ∞. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t) → −1 as t → −∞ and x(t) → 1 as t → ∞. The assumptions allow l − a(t) to change sign for arbitrarily large values of |t|, and do not restrict the decay rate of |l −a(t)| as |t| → ∞.


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


The Tangled Tale Of Phase Space, David D. Nolte 2009 Purdue University

The Tangled Tale Of Phase Space, David D. Nolte

David D Nolte

(Preview of Chapter 6: Galileo Unbound: Oxford 2018) Phase space has been called one of the most powerful inventions of modern science.  But its historical origins are clouded in a tangle of independent discovery and mis-attributions that persist today.  This Physics Today article unravels the twisted tale of the discovery and the naming of phase space that began with Liouville in 1838, but by no means ended there, culminating in an encyclopedia article of 1911 that had unintended and lasting etymological side effects never intended by its authors.


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

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.


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