Matching Items (399)
Filtering by

Clear all filters

149730-Thumbnail Image.png
Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears

Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
150182-Thumbnail Image.png
Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
150552-Thumbnail Image.png
Description
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity

This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2012
154866-Thumbnail Image.png
Description
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,

representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´

tivistic wave equations that will play an important role in the work to follow. In Chapter 2,

a complex covariant form of the classical

Chapter 1 introduces some key elements of important topics such as; quantum mechanics,

representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´

tivistic wave equations that will play an important role in the work to follow. In Chapter 2,

a complex covariant form of the classical Maxwell’s equations in a moving medium or at

rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum

tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its

connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´

netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.

Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s

equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell

and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´

operators of the Poincare group. A connection between the spin of a particle/field and ´

consistency of the corresponding overdetermined system is emphasized in the massless

case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which

is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨

evolution of exact wave functions of the generalized harmonic oscillators is determined

in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is

shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem

for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the

methods introduced in Chapter 5 a model for the quantization of an electromagnetic field

in a variable media is analyzed. The concept of quantization of an electromagnetic field

in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode

of radiation for this model is used to find time-dependent photon amplitudes in relation

to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the

uncertainty relation, are explicitly given in terms of the Ermakov-type system.
ContributorsLanfear, Nathan A (Author) / Suslov, Sergei (Thesis advisor) / Kotschwar, Brett (Thesis advisor) / Platte, Rodrigo (Committee member) / Matyushov, Dmitry (Committee member) / Kuiper, Hendrik (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2016
149547-Thumbnail Image.png
Description
In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has

In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrödinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrödinger equation in R^n with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrödinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
ContributorsCordero-Soto, Ricardo J (Author) / Suslov, Sergei (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Engman, Martin (Committee member) / Herrera-Valdez, Marco (Committee member) / Arizona State University (Publisher)
Created2011
128242-Thumbnail Image.png
Description

This study reports a preparation method of a new moisture swing sorbent for CO2 capture from air. The new sorbent components include ion exchange resin (IER) and polyvinyl chloride (PVC) as a binder. The IER can absorb CO2 when surrounding is dry and release CO2 when surrounding is wet. The

This study reports a preparation method of a new moisture swing sorbent for CO2 capture from air. The new sorbent components include ion exchange resin (IER) and polyvinyl chloride (PVC) as a binder. The IER can absorb CO2 when surrounding is dry and release CO2 when surrounding is wet. The manuscript presents the studies of membrane structure, kinetic model of absorption process, performance of desorption process and the diffusivity of water molecules in the CO2 absorbent. It has been proved that the kinetic performance of CO2 absorption/desorption can be improved by using thin binder and hot water treatment. The fast kinetics of P-100-90C absorbent is due to the thin PVC binder, and high diffusion rate of H[subscript 2]O molecules in the sample. The impressive is this new CO2 absorbent has the fastest CO2 absorption rate among all absorbents which have been reported by other up-to-date literatures.

ContributorsShi, Xiaoyang (Author) / Li, Qibin (Author) / Wang, Tao (Author) / Lackner, Klaus (Author) / Ira A. Fulton Schools of Engineering (Contributor)
Created2017-06-22
128252-Thumbnail Image.png
Description

The objective of this study was to find out the impact of environmental conditions on the survival of intestinal parasites on environmental surfaces commonly implicated in the transmission of these parasites. The study was performed by incubating Cryptosporidium and Giardia (oo)cysts on environmentally relevant surfaces such as brushed stainless steel,

The objective of this study was to find out the impact of environmental conditions on the survival of intestinal parasites on environmental surfaces commonly implicated in the transmission of these parasites. The study was performed by incubating Cryptosporidium and Giardia (oo)cysts on environmentally relevant surfaces such as brushed stainless steel, formica, ceramic, fabric, and skin. Parallel experiments were conducted using clean and soiled coupons incubated under three temperatures. The die-off coefficient rates (K) were calculated using first-order exponential formula. For both parasites, the fastest die-off was recorded on fabric, followed by ceramic, formica, skin, and steel. Die-off rates were directly correlated to the incubation temperatures and surface porosity. The presence of organic matter enhanced the survivability of the resting stages of test parasites. The decay rates calculated in this study can be used in models for public health decision-making process and highlights the mitigation role of hand hygiene agents in their prevention and control.

ContributorsAlum, Absar (Author) / Absar, Isra M. (Author) / Asaad, Hamas (Author) / Rubino, Joseph R. (Author) / Ijaz, M. Khalid (Author) / Ira A. Fulton Schools of Engineering (Contributor)
Created2014-06-17
128263-Thumbnail Image.png
Description

Tree-like structures are ubiquitous in nature. In particular, neuronal axons and dendrites have tree-like geometries that mediate electrical signaling within and between cells. Electrical activity in neuronal trees is typically modeled using coupled cable equations on multi-compartment representations, where each compartment represents a small segment of the neuronal membrane. The

Tree-like structures are ubiquitous in nature. In particular, neuronal axons and dendrites have tree-like geometries that mediate electrical signaling within and between cells. Electrical activity in neuronal trees is typically modeled using coupled cable equations on multi-compartment representations, where each compartment represents a small segment of the neuronal membrane. The geometry of each compartment is usually defined as a cylinder or, at best, a surface of revolution based on a linear approximation of the radial change in the neurite. The resulting geometry of the model neuron is coarse, with non-smooth or even discontinuous jumps at the boundaries between compartments. We propose a hyperbolic approximation to model the geometry of neurite compartments, a branched, multi-compartment extension, and a simple graphical approach to calculate steady-state solutions of an associated system of coupled cable equations. A simple case of transient solutions is also briefly discussed.

Created2014-07-09
128269-Thumbnail Image.png
Description

Ferromagnetic Heusler Co2FeAl0.5Si0.5 epitaxial thin-films have been fabricated in the L21 structure with saturation magnetizations over 1200 emu/cm3. Andreev reflection measurements show that the spin polarization is as high as 80% in samples sputtered on unheated MgO (100) substrates and annealed at high temperatures. However, the spin polarization is considerably

Ferromagnetic Heusler Co2FeAl0.5Si0.5 epitaxial thin-films have been fabricated in the L21 structure with saturation magnetizations over 1200 emu/cm3. Andreev reflection measurements show that the spin polarization is as high as 80% in samples sputtered on unheated MgO (100) substrates and annealed at high temperatures. However, the spin polarization is considerably smaller in samples deposited on heated substrates.

ContributorsVahidi, Mahmoud (Author) / Gifford, Jessica (Author) / Zhang, Shengke (Author) / Krishnamurthy, S. (Author) / Yu, Z. G. (Author) / Lei, Yu (Author) / Huang, Mengchu (Author) / Youngbull, Cody (Author) / Chen, Tingyong (Author) / Newman, Nathan (Author) / Ira A. Fulton Schools of Engineering (Contributor)
Created2014-04-15
128272-Thumbnail Image.png
Description

Throughout history, various civilizations developed methodologies for the collection and disposal of human waste. The methodologies throughout the centuries have been characterized by technological peaks on the one hand, and by the disappearance of the technologies and their reappearance on the other. The purpose of this article is to trace

Throughout history, various civilizations developed methodologies for the collection and disposal of human waste. The methodologies throughout the centuries have been characterized by technological peaks on the one hand, and by the disappearance of the technologies and their reappearance on the other. The purpose of this article is to trace the development of sewage collection and transport with an emphasis on toilets in ancient civilizations. Evolution of the major achievements in the scientific fields of sanitation with emphasis on the lavatory (or toilets) technologies through the centuries up to the present are presented. Valuable insights into ancient wastewater technologies and management with their apparent characteristics of durability, adaptability to the environment, and sustainability are provided. Gradual steps improved the engineering results until the establishment of the contemporary toilet system, which provides a combined solution for flushing, odor control, and the sanitation of sewerage. Even though the lack of proper toilet facilities for a great percentage of the present day global population is an embarrassing fact, the worldwide efforts through millennia for the acquisition of a well-engineered toilet were connected to the cultural level of each period.

ContributorsAntoniou, Georgios P. (Author) / De Feo, Giovanni (Author) / Fardin, Franz (Author) / Tamburrino, Aldo (Author) / Khan, Saifullah (Author) / Tie, Fang (Author) / Reklaityte, Ieva (Author) / Kanetaki, Eleni (Author) / Zheng, Xiao Yun (Author) / Mays, Larry (Author) / Angelakis, Andreas N. (Author) / Ira A. Fulton Schools of Engineering (Contributor)
Created2016-08-13