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Articles 781 - 810 of 817
Full-Text Articles in Mathematics
Soliton Solutions To Integrable Equations, Haiqi Wang
Soliton Solutions To Integrable Equations, Haiqi Wang
Theses and Dissertations - UTB/UTPA
In recent years, integrable systems and soliton theory play an important role in the study of nonlinear water wave equations. In this thesis, we will focus on the procedure of how to get soliton solutions for integrable equations. The fundamental idea is to use the traveling wave setting to convert a partial differential equation to an ordinary differential equation and to solve ordinary differential equations yields soliton solutions for the integrable equations under certain boundary conditions at both negative and positive infinities. In our work, we will consider five integrable equations and present their solitons solutions, one of which will …
Modeling Instabilities Of Electrically Driven Jets With Finite Conductivity Under Constant Or Variable Applied Field, Saulo I. Orizaga
Modeling Instabilities Of Electrically Driven Jets With Finite Conductivity Under Constant Or Variable Applied Field, Saulo I. Orizaga
Theses and Dissertations - UTB/UTPA
We investigate the problem of spatial (S), combined spatial and temporal (CST), and non-linear temporal instability (NLT) of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton‟s Method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One …
Duffing-Van Der Pol Type Oscillator, Guangyue Gao
Duffing-Van Der Pol Type Oscillator, Guangyue Gao
Theses and Dissertations - UTB/UTPA
The nonlinear Duffing-van der Pol oscillator system is studied by means of the Lie symmetry reduction method and the Preller-Singer method. With the particular case of coefficients, this system has physical relevance as a simple model in certain flow-induced structural vibration problems. Under certain parametric conditions, we are concerned with the first integrals of the Duffing-van der Pol oscillator system. After making a series of variable transformations, we apply the Preller-Singer method and the Lie symmetry reduction method to obtain the first integrals of the simplified equations without complicated calculations.
Bifurcations Of Traveling Wave Solutions For An Integrable Equation, Jibin Li, Zhijun Qiao
Bifurcations Of Traveling Wave Solutions For An Integrable Equation, Jibin Li, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
This paper deals with the following equation mt= 1/2 1/mk xxx− 1/2 1/mk x, which is proposed by Z. J. Qiao J. Math. Phys. 48, 082701 2007 and Qiao and Liu Chaos, Solitons Fractals 41, 587 2009. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the …
Spatial Instability Of Electrically Driven Jets With Finite Conductivity And Under Constant Or Variable Applied Field, Saulo Orizaga, Daniel N. Riahi
Spatial Instability Of Electrically Driven Jets With Finite Conductivity And Under Constant Or Variable Applied Field, Saulo Orizaga, Daniel N. Riahi
School of Mathematical & Statistical Sciences Faculty Publications
We investigate the problem of spatial instability of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton’s method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One of these modes is enhanced by the strength Ω of …
A Dna Approach To The Road-Coloring Problem, Arindam Roy
A Dna Approach To The Road-Coloring Problem, Arindam Roy
Theses and Dissertations - UTB/UTPA
The Road-Coloring Problem in graph theory can be stated as follows: Is any irreducible aperiodic directed graph with constant outdegree 2 road-colorable? In other words, does such a graph have a synchronizing instruction? That is to say: can we label (or color) the two outgoing edges at each vertex, one with “b” or blue color and the other with “r” or red color, in such a manner that there will be an instruction in the form of a finite sequence in “b”s and “r”s (example: rrbrbbbr) such that this instruction will lead each vertex to the same “target” vertex? This …
Analytical And Computational Studies Of Magneto-Convection In Solidifying Mushy Layer, Mallikarjunaiah Siddapura Muddamallappa
Analytical And Computational Studies Of Magneto-Convection In Solidifying Mushy Layer, Mallikarjunaiah Siddapura Muddamallappa
Theses and Dissertations - UTB/UTPA
Natural convection in solidifying binary media is of great interest due to it's applications in material processing and crystal growth industries. Convective flows between the layers of melt during alloy solidification is known to produce mechanical imperfections such as freckle's. Hence it is important to investigate the criterion for freckling and discover the means of suppressing it. A mushy layer, which has both solid and fluid components and is formed between underlying solid and overlying liquid, is known to produce chimneys, which are narrow, vertical vents, devoid of solid. We consider the problem of magneto-convection in a horizontal mushy layer …
Two-Dimensional Wigner-Ville Transforms And Their Basic Properties, Bheemaiah Veena Shankara Narayana Rao
Two-Dimensional Wigner-Ville Transforms And Their Basic Properties, Bheemaiah Veena Shankara Narayana Rao
Theses and Dissertations - UTB/UTPA
This thesis deals with Wigner-Ville transforms and their basic properties. The Wigner-Ville transforms are a non-linear transform which constitute an important tool in nonstationary signal analysis. Wigner-Ville transforms in one dimension and their basic properties are discussed here. Special attention is given to formulation of two dimensional Wigner-Ville transform, its inversion formula and some of their basic properties. Some applications of Wigner-Ville transforms are also briefly discussed.
Reaction-Diffusion Systems With A Nonlinear Rate Of Growth, Yubing Wan
Reaction-Diffusion Systems With A Nonlinear Rate Of Growth, Yubing Wan
Theses and Dissertations - UTB/UTPA
In the literature there are quite a few elegant approaches which have been proposed to find (he first integrals of nonlinear differential equations. Recently, the modified Prelle-Singer method for finding the first integrals of second-order nonlinear ordinary differential equations (ODEs) has attracted considerable attention. Many researchers used this method to derive the first integrals to various systems. In this thesis, we are concerned with the first integrals for reaction-diffusion systems with a nonlinear rate of growth. Under certain parametric conditions we express the first integrals explicitly by applying an analytical method as well as the modified Prelle-Singer method.
Integrable Equations With Non-Smooth Solitons, Xianqi Li
Integrable Equations With Non-Smooth Solitons, Xianqi Li
Theses and Dissertations - UTB/UTPA
In this thesis, we present a class of integrable equations with non-smooth soliton solutions. In particular, we derive the bi-Hamiltonian structure and Lax pair of the equation pt = bux + \[{u2 — u1)p]x,p = u — uxx, which guarantee its integrability. Another interesting integrable equation we study is (=Jff!i)t = 2uux, which is exactly the first member of the negative KdV hierarchy. Through traveling wave setting arid phase step analysis, we obtain non-smooth soliton solutions of these integrable equations under different boundary condition at infinities. These equations were shown to have peaked soliton (peakon), "W/M-shape" peakon or cusped soliton …
Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare
Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare
School of Mathematical & Statistical Sciences Faculty Publications
We consider the problem of steady flow around a growing protein crystal in a medium of its solution in a normal gravity environment. The whole flow system is assumed to be rotating with a constant angular velocity about a vertical axis which is anti-parallel to the gravity vector. Convective flow takes place due to the solute depletion around the growing crystal which leads to a buoyancy driven flow. Such convective flow can produce inhomogeneous solute concentration, which subsequently generate non-uniformities in the crystal’s structure finalizing lower quality protein crystal. Using scaling analysis within a diffusion boundary layer around the crystal, …
A Comparative Study Of Risk Factors Involved In Diabetes Between Texas And Other States, Andres Padilla Oviedo
A Comparative Study Of Risk Factors Involved In Diabetes Between Texas And Other States, Andres Padilla Oviedo
Theses and Dissertations - UTB/UTPA
Diabetes is a serious concern in the United States and Texas is a state with high percentage of diabetes. The risk factors contributing to diabetes are current smoking, high blood cholesterol, hypertension, physical inactivity etc. In this thesis, we would like to identify the crucial risk factors for Texas. This motivates us to use the online data resources for a comparative study between Texas and other states. Looking at the data, we decide to use independent sample t-tests and independent sample non parametric tests [Wilcoxon Mann Whitney] for such comparative studies. This analysis has two parts – in the first …
Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas
Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas
School of Mathematical & Statistical Sciences Faculty Publications
We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L’vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of nonperturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that …
Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty
Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we discuss some interesting applications of Dirac's delta function in Statistics. We have tried to extend some of the existing results to the more than one variable case. While doing that, we particularly concentrate on the bivariate case.
Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas
Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas
School of Mathematical & Statistical Sciences Faculty Publications
We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. …
A Fragment On Euler's Constant In Ramanujan's Lost Notebook, Bruce C. Berndt, Timothy Huber
A Fragment On Euler's Constant In Ramanujan's Lost Notebook, Bruce C. Berndt, Timothy Huber
School of Mathematical & Statistical Sciences Faculty Publications
A formula for Euler’s constant found in Ramanujan’s lost notebook and also in a problem he submitted to the Journal of the Indian Mathematical Society is proved and discussed.
An Action For A Classical String, The Equation Of Motion And Group Invariant Classical Solutions, Paul Bracken
An Action For A Classical String, The Equation Of Motion And Group Invariant Classical Solutions, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.
Quantum Phases For A Generalized Harmonic Oscillator, Paul Bracken
Quantum Phases For A Generalized Harmonic Oscillator, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.
On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi
On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi
School of Mathematical & Statistical Sciences Faculty Publications
This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, …
Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung
Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung
School of Mathematical & Statistical Sciences Faculty Publications
In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally $\alpha$-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one "energy''-like and one "enstrophy''-like. In a finite inertial range there are in general two spectral fluxes, one associated with each conserved quantity. We derive here an inequality comparing the relative magnitudes of the "energy'' and "enstrophy'' fluxes for finite or infinitesimal dissipations, and for hyper or hypo viscosities. When this inequality is satisfied, as is the case of 2D turbulence,where the energy flux contribution to the energy spectrum is small, the subdominant part will be effectively hidden. …
New Integrable Hierarchy, Its Parametric Solutions, Cuspons, One-Peak Solitons, And M/W-Shape Peak Solitons, Zhijun Qiao
New Integrable Hierarchy, Its Parametric Solutions, Cuspons, One-Peak Solitons, And M/W-Shape Peak Solitons, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we propose a new completely integrable hierarchy. Particularly in the hierarchy we draw two new soliton equations: 1 mt= 1 2 1/m2xxx− 1 2 1/m2 x; 2 mt+mx u2−ux 2+2m2ux=0, m=u−uxx. The first one is the second positive member in the hierarchy while the second one is the second negative member in the hierarchy. Both equations can be derived from the two-dimensional Euler equation by using the approximation procedure. All equations in the hierarchy are proven to have bi-Hamiltonian operators and Lax pairs through solving a crucial matrix equation. Moreover, we develop parametric solutions of the entire …
On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas
On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity. The quasi-Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather …
Solving Ramanujan's Differential Equations For Eisenstein Series Via A First Order Riccati Equation, James M. Hill, Bruce C. Berndt, Timothy Huber
Solving Ramanujan's Differential Equations For Eisenstein Series Via A First Order Riccati Equation, James M. Hill, Bruce C. Berndt, Timothy Huber
School of Mathematical & Statistical Sciences Faculty Publications
In this paper we prove that Ramanujan's differential equations for the Eisenstein series P, Q, and R are invariant under a simple one-parameter stretching group of transformations. Using this, we show that the three differential equations may be reduced to a first order Riccati differential equation, the solution of which may be represented in terms of hypergeometric functions. The resulting formulas allow for the derivation of parametric representations of P, Q, and R, analogous to representations in Ramanujan's second notebook. In contrast, in the classical approach, one first needs to derive the fundamental formula connecting theta functions with elliptic integrals. …
A New Integrable Equation With Cuspons And W/M-Shape-Peaks Solitons, Zhijun Qiao
A New Integrable Equation With Cuspons And W/M-Shape-Peaks Solitons, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we propose a new completely integrable wave equation: mt+mx u2 −ux 2 +2m2ux=0, m=u−uxx. The equation is derived from the two dimensional Euler equation and is proven to have Lax pair and bi-Hamiltonian structures. This equation possesses new cusp solitons—cuspons, instead of regular peakons ce− −ct with speed c. Through investigating the equation, we develop a new kind of soliton solutions—“W/M”-shape-peaks solitons. There exist no smooth solitons for this integrable water wave equation.
Jointly Hyponormal Pairs Of Commuting Subnormal Operators Need Not Be Jointly Subnormal, Raúl E. Curto, Jasang Yoon
Jointly Hyponormal Pairs Of Commuting Subnormal Operators Need Not Be Jointly Subnormal, Raúl E. Curto, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of R. Curto, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality.
Recent Developments In Understanding Two-Dimensional Turbulence And The Nastrom-Gage Spectrum, Eleftherios Gkioulekas, Ka Kit Tung
Recent Developments In Understanding Two-Dimensional Turbulence And The Nastrom-Gage Spectrum, Eleftherios Gkioulekas, Ka Kit Tung
School of Mathematical & Statistical Sciences Faculty Publications
Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasigeostrophic turbulence.
Disintegration-Of-Measure Techniques For Commuting Multivariable Weighted Shifts, Raúl E. Curto, Jasang Yoon
Disintegration-Of-Measure Techniques For Commuting Multivariable Weighted Shifts, Raúl E. Curto, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting $n$-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal $2$-variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights.
K-Hyponormality Of Multivariable Weighted Shifts, Raúl E. Curto, Sang Hoon Lee, Jasang Yoon
K-Hyponormality Of Multivariable Weighted Shifts, Raúl E. Curto, Sang Hoon Lee, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
We characterize joint k-hyponormality for 2-variable weighted shifts. Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k+1) -hyponormality for each k ≥ 1. As a consequence, we obtain an abstract solution to the Lifting Problem for Commuting Subnormals.
Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath
Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath
School of Mathematical & Statistical Sciences Faculty Publications
This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integrals.
Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp
Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp
School of Mathematical & Statistical Sciences Faculty Publications
In this paper we deal with the category of nonlinear evolution equations ~NLEEs! associated with the spectral problem and provide an approach for constructing their algebraic structure and r-matrix. First we introduce the category of NLEEs, which is composed of various positive order and negative order hierarchies of NLEEs both integrable and nonintegrable. The whole category of NLEEs possesses a generalized Lax representation. Next, we present two different Lie algebraic structures of the Lax operator: one of them is universal in the category, i.e., independent of the hierarchy, while the other one is nonuniversal in the hierarchy, i.e., dependent on …