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Articles 1 - 30 of 63
Full-Text Articles in Applied Mathematics
Low Reynolds Number Locomotion Near Interfaces In Two-Fluid Media, Avriel Rowena Mae Cartwright
Low Reynolds Number Locomotion Near Interfaces In Two-Fluid Media, Avriel Rowena Mae Cartwright
Theses and Dissertations
Microorganisms often swim within complex fluid environments composed of multiple materials with very different properties. Biological locomotion, including swimming speed, is significantly impacted by the physical composition and rheology of the surrounding fluid environment, as well as the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary greatly. Through computational simulations, we first investigate the classical Taylor’s swimming sheet problem near interfaces within multi-fluid environments using a two-fluid immersed boundary method. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and …
Modeling And Simulation Of Ion-Induced Volume Phase Transitions In Chemically-Active Polyelectrolyte Gels, Bindi Mahesh Nagda
Modeling And Simulation Of Ion-Induced Volume Phase Transitions In Chemically-Active Polyelectrolyte Gels, Bindi Mahesh Nagda
Theses and Dissertations
Ion-induced volume phase transitions in polyelectrolyte gels play an important role in physiological processes such as mucus storage and secretion in the gut, nerve tissue excitation, and DNA packaging. Biological experiments show that polyelectrolyte gels may swell or collapse rapidly due to changes in external conditions such as ionic composition. The volume phase transition is accompanied by a monovalent/ divalent ion exchange between the polymer network and the solvent that make up the gel. We propose a 2D computational method for simulating mucus swelling and deswelling with a two-fluid mixture model. The model includes electro-diffusive transport of ionic species, the …
Global Upper Bounds For The Landau Equation Of Plasma Physics In The Very Soft Potentials Case, Caleb Solomon
Global Upper Bounds For The Landau Equation Of Plasma Physics In The Very Soft Potentials Case, Caleb Solomon
Theses and Dissertations
This paper explores global upper bounds for solutions of the Landau equation in the soft potentials case (γ < −2). In particular, this paper explores the case of γ ∈ [−3,−2). Working with a classical solution to the Landau equation weighted by a cut-off function χ and using the Moser iteration, an upper bound for the L∞v norm of the solution to the Landau equation f is obtained proportianally to the L2 v norm of f with the assumptions of positive, essentially bounded coefficients. The supremum of f for t ∈ [0, T], x ∈ R3, v ∈ BR for some large radius R is shown to be bounded polynomially in R.
On Clinical Use Of Infrared Cameras For Video-Based Estimation Of 3d Facial Kinematics, William Mackenzie Harrington
On Clinical Use Of Infrared Cameras For Video-Based Estimation Of 3d Facial Kinematics, William Mackenzie Harrington
Theses and Dissertations
Neurological and neurodegenerative disorders such as Parkinson’s disease (PD), amyotrophic lateral sclerosis (ALS), and stroke can cause speech and orofacial motor impairments with devastating effects on quality of life. Analysis of orofacial movement provides vital information for early diagnosis and tracking disease progression, but current clinical practice relies on perceptual assessments performed by clinicians, which are unreliable and insensitive to early symptoms. New methods in machine learning have enabled automatic and objective assessment of orofacial kinematics from color and depth videos, hence we introduce MEADepthCamera, a mobile application for RGB-D video and audio recording and automatic estimation of 3D facial …
Relaxation Of Variational Principles For Z-Problems In Effective Media Theory, Kenneth Beard
Relaxation Of Variational Principles For Z-Problems In Effective Media Theory, Kenneth Beard
Theses and Dissertations
In this thesis, we consider a class of Z-problems and their associated effective operators on Hilbert spaces which arise in effective media theory, especially within the theory of composites. We provide a unified approach to obtaining solutions of the Z-problem, formulas for the effective operator in terms of generalized Schur complements, and their associated variational principles (e.g., the Dirichlet minimization principle), while allowing for relaxation of the standard hypotheses on positivity and invertibility for the classes of operators usually considered in such problems. The Hilbert space framework developed here is inspired by the methods of orthogonal projections and Hodge decompositions. …
On A Class Of Critical N-Laplacian Problems, Tsz Chung Ho
On A Class Of Critical N-Laplacian Problems, Tsz Chung Ho
Theses and Dissertations
We establish some existence results for a class of critical N-Laplacian problems in a bounded domain in RN. In the absence of a suitable direct sum decomposition, we use an abstract linking theorem based on the Z2-cohomological index to obtain a nontrivial critical point.
A Computational Model Of Arterial Thrombus Mechanics In Stenotic Channels, Elise Kole Aspray
A Computational Model Of Arterial Thrombus Mechanics In Stenotic Channels, Elise Kole Aspray
Theses and Dissertations
Platelet aggregation is one of the major components of blood clotting. The proximal cause of most heart attacks and many strokes is the rapid formation of a blood clot (thrombus) in response to the rupture or erosion of an arterial atherosclerotic plaque. In the context of a stenotic artery (i.e., an artery whose lumen is partially blocked by the plaque) understanding how the thrombus forms presents additional challenges because of the extremely high shear rates and stresses present as a consequence of the constriction. In this dissertation, we use a two-phase continuum model to investigate the stability of an existing …
Stability Results For Special Solutions Of Scalar-Field Equations With Variable Coeffcients, Mashael Ibrahiem Alammari
Stability Results For Special Solutions Of Scalar-Field Equations With Variable Coeffcients, Mashael Ibrahiem Alammari
Theses and Dissertations
We study the long-time behavior of general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. In the first part of the dissertation, we take the coefficients to be uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are motivated by the question of how these perturbations of the equation may change the stability properties of kink solutions (one-dimensional topological solitons). We prove existence of a stationary kink solution in our setting, and perform a detailed spectral analysis of the corresponding linearized operator, based on perturbing the linearized operator around the constant-coefficient kink. …
The Brezis-Nirenberg Problem For The Generalized Kirchhoff Equation, Erisa Hasani
The Brezis-Nirenberg Problem For The Generalized Kirchhoff Equation, Erisa Hasani
Theses and Dissertations
We study a class of critical Kirchhoff problems with a general nonlocal term. The main difficulty here is the absence of a closed-form formula for the compactness threshold. First we obtain a variational characterization of this threshold level. Then we prove a series of existence and multiplicity results based on this variational characterization.
Schur Complement Algebra And Operations With Applications In Multivariate Functions, Realizations, And Representations, Anthony Dean Stefan
Schur Complement Algebra And Operations With Applications In Multivariate Functions, Realizations, And Representations, Anthony Dean Stefan
Theses and Dissertations
We provide a new approach to the following multidimensional realizability problem: Can an arbitrary square matrix, whose entries are from the field of multivariate rational functions over the complex numbers, be realized as a Schur complement of a linear matrix pencil with symmetries? To answer this problem, we prove the main theorem of M. Bessmertny˘ı,“On realizations of rational matrix functions of several complex variables,” in Vol. 134 of Oper. Theory Adv. Appl., pp. 157-185, Birkh¨auser Verlag, Basel, 2002 and have included additional symmetries as an extension to his results. Furthermore, we were so thorough in our constructive approach that we …
Optimal Control Of Multiphase Free Boundary Problems For Nonlinear Parabolic Equations, Evan Cosgrove
Optimal Control Of Multiphase Free Boundary Problems For Nonlinear Parabolic Equations, Evan Cosgrove
Theses and Dissertations
Dissertation research is on the optimal control of systems with distributed parameters described by singular nonlinear partial differential equations (PDE) modeling multi-phase Stefan type second order parabolic free boundary problems. This type of free boundary problems arise in various applications, such as biomedical engineering problem on the laser ablation of biological tissues, aerospace engineering problem on the ice accretion in aircrafts mid-flight, biomedical problem on the growth of cancerous tumor, and many other phase transition processes in thermophysics and fluid mechanics. The aim of the optimal control of distributed free boundary systems is two fold: identification of functional parameters of …
Numerical Simulation Of Low Reynolds Number Locomotion In Viscoelastic Media, Nesreen Abdulrahim Althobaiti
Numerical Simulation Of Low Reynolds Number Locomotion In Viscoelastic Media, Nesreen Abdulrahim Althobaiti
Theses and Dissertations
We use computational models to investigate 2D swimmers within various fluid media with low Reynolds Number. Extensions of the standard Immersed Boundary (IB) Method are proposed so that the fluid media may satisfy no slip, partial slip or free-slip conditions on the moving boundary. The fluid equations are solved through a Multigrid preconditioned GMRES solver. Our numerical results indicate that slip may lead to substantial speed enhancement for swimmers in a viscoelastic fluid, as well as in a viscoelastic two-fluid mixture. Under the slip conditions, the speed of locomotion is dependent in a nontrivial way on both the viscosity and …
A Computational Investigation Of The Biomechanics For Platelets Aggregation, Ghadah Mohammed Alhawael
A Computational Investigation Of The Biomechanics For Platelets Aggregation, Ghadah Mohammed Alhawael
Theses and Dissertations
The proximal cause of most heart attacks and many strokes is the rapid formation of a blood clot (thrombus) in response to the rupture or erosion of an arterial atherosclerotic plaque. The formation of a thrombus in arteries is a very complex process whose workings are subjects of intense research. In this dissertation, we investigate the biomechanics of platelet aggregation in large arteries using a two-phase continuum computational model. The model tracks the number densities of various platelet populations, the concentration of one platelet-activating chemical, as well as the number densities of inter-platelet bonds. Through the formation of elastic bonds, …
Critical Elliptic Boundary Value Problems With Singular Trudinger-Moser Nonlinearities, Shiqiu Fu
Critical Elliptic Boundary Value Problems With Singular Trudinger-Moser Nonlinearities, Shiqiu Fu
Theses and Dissertations
In this dissertation, we prove the existence of solutions for two classes of eliptic problems that are critical with respect to singular Trudinger-Moser embedding. The proofs are based on compactness and regularity arguments.
Optimal Control Of Coefficients For The Second Order Parabolic Free Boundary Problems, Ali Hagverdiyev
Optimal Control Of Coefficients For The Second Order Parabolic Free Boundary Problems, Ali Hagverdiyev
Theses and Dissertations
Dissertation aims to analyze inverse Stefan type free boundary problem for the second order parabolic PDE with unknown parameters based on the additional information given in the form of the distribution of the solution of the PDE and the position of the free boundary at the final moment. This type of ill-posed inverse free boundary problems arise in many applications such as biomedical engineering problem about the laser ablation of biomedical tissues, in-flight ice accretion modeling in aerospace industry, and various phase transition processes in thermophysics and fluid mechanics. The set of unknown parameters include a space-time dependent diffusion, convection …
Some Free Boundary Problems For The Nonlinear Degenerate Multidimensional Parabolic Equations Modeling Reaction-Diffusion Processes, Amna Abu Weden
Some Free Boundary Problems For The Nonlinear Degenerate Multidimensional Parabolic Equations Modeling Reaction-Diffusion Processes, Amna Abu Weden
Theses and Dissertations
This dissertation presents a full classification of the short-time behavior of the interfaces or free boundaries for the nonlinear second order degenerate multidimensional parabolic partial differential equation (PDE) ut −∆u m +buβ = 0, x ∈ R N ,0 < t < T (1) with m > 0, β > 0,b ∈ R, arising in various applications in fluid mechanics, filtration of oil or gas in a porous media, plasma physics, reaction-diffusion equations in chemical kinetics, population dynamics in mathematical biology etc. as a mathematical model of nonlinear diffusion phenomena in the presence of the absorption or release of energy. Cauchy problem with compactly supported and nonnegative initial function …
Computational Models For Biological Locomotion In Gels, Hashim Mohammed Alshehri
Computational Models For Biological Locomotion In Gels, Hashim Mohammed Alshehri
Theses and Dissertations
We investigated Low Reynold’s Number Locomotion in two-phase biological gels. The gel is composed of two materials: a viscous fluid solvent phase and a viscoelastic polymer network phase. A novel Two-phase Immersed Boundary Method (IBM) is developed to simulate the complicated interactions between an elastic boundary and a mixture of two fluids with very different physical properties. A further extension of the method is developed for the case where fluids satisfy partial-slip and free-slip conditions on the elastic boundary. Our major conclusions are summarized as following: (i) Our numerical scheme is proved to be robust and efficient. It can successfully …
Analysis Of Interfaces For The Nonlinear Degenerate Second Order Parabolic Equations Modeling Diffusion-Convection Processes, Lamees Kadhim Ali Alzaki
Analysis Of Interfaces For The Nonlinear Degenerate Second Order Parabolic Equations Modeling Diffusion-Convection Processes, Lamees Kadhim Ali Alzaki
Theses and Dissertations
Dissertation pursues analysis of the short-time evolution of interfaces or free boundaries for the non-negative solutions of the nonlinear degenerate second order parabolic partial differential equation (PDE) ut = ( u m ) xx +b ( u γ ) x , x ∈ R,t > 0; m > 1, γ > 0,b ∈ R (1) modeling diffusion-convection processes arising in fluid or gas flow in a porous media, plasma physics, population dynamics in mathematical biology and other applications. Due to the implicit degeneration (m > 1), PDE (1) it possesses a property of the finite speed of propagation and develops interfaces or free boundaries …
Nonlocal Boundary Value Problems For Linear Hyperbolic Systems With Two Independent Variables, Afrah Almutairi
Nonlocal Boundary Value Problems For Linear Hyperbolic Systems With Two Independent Variables, Afrah Almutairi
Theses and Dissertations
Nonlocal boundary value problems in a characteristic rectangle for second order linear hyperbolic systems are considered. There are established: (i) Unimprovable sufficient conditions for general boundary value problems to possess the Fredholm property; (ii) Optimal sufficient conditions of unique solvability of general boundary value problems; (iii) Effective sufficient conditions for doubly periodic problems to possess the Fredholm property; (iv) Unimprovable sufficient conditions of unique solvability of doubly periodic problems; (v) Effective sufficient conditions for boundary value problems of periodic type to possess the Fredholm property; (vi) Unimprovable sufficient conditions of unique solvability of boundary value problems of periodic type; (vii) …
Stability Analysis Of Neutral Functional Differential Equations Arising In Partial Element Equivalent Circuit Models, Howard Michael Allison
Stability Analysis Of Neutral Functional Differential Equations Arising In Partial Element Equivalent Circuit Models, Howard Michael Allison
Theses and Dissertations
Neutral Functional Differential Equations (NFDEs) arise in the study of the Partial Element Equivalent Circuit (PEEC) model with time delays. We present sufficient conditions for asymptotic stability and global stability in the delays of the PEEC NFDE’s, using Lyapunov-Razumikhin function methods.. We develop, for the first time, a standard mixing-type nonlinearity for the PEEC NFDEs. Introducing time invariant and time varying nonlinear perturbation to the PEEC NFDEs, we develop sufficient conditions for stability of the nonlinear perturbed PEEC NFDEs and convergence of the nonlinear system to the original stable linear autonomous system. We also develop sufficient conditions for stability and …
Two-Point Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations, Audison Beaubrun
Two-Point Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations, Audison Beaubrun
Theses and Dissertations
Two–point boundary value problems in a multidimensional box for higher order nonlinear hyperbolic equations are considered. The concepts of a strongly isolated solution, and locally and globally strong well–posedness of a nonlinear boundary value problem are introduced. For general two–point boundary value problems and periodic problems there are established: (i) Necessary and sufficient conditions of locally and globally strong well–posedness; (ii) Unimprovable Sufficient conditions of solvability. For the Dirichlet and Periodic type problems for equations of even order there are established: (i) Effective sufficient conditions of solvability and locally strong well–posedness; (ii) Unimprovable sufficient conditions of solvability for the case, …
Qualitative Analysis Of The Nonlinear Double Degenerate Parabolic Equation Of Turbulent Filtration With Absorption, Adam Prinkey
Qualitative Analysis Of The Nonlinear Double Degenerate Parabolic Equation Of Turbulent Filtration With Absorption, Adam Prinkey
Theses and Dissertations
The goal of the dissertation is to pursue qualitative analysis of the mathematical model of turbulent polytropic filtration of a gas in a porous media with reaction or absorption described by the second order nonlinear double degenerate parabolic equation ∂u ∂t − ∂ ∂x F [ ∂u m ∂x ] + Q(u) = 0, (1) where F(y) = |y| p−1 y, Q(u) = buβ , m, p, β > 0, b ∈ R. In the absence of the reaction term there is a finite speed of propagation with an expanding interface in the case of slow diffusion (mp > 1), and infinite …
Generalized Random Measures On Topological Spaces, Ali Hussein Mahmood Al-Obaidi
Generalized Random Measures On Topological Spaces, Ali Hussein Mahmood Al-Obaidi
Theses and Dissertations
Our work deals with classes of random measures on -compact Hausdorff spaces perturbed by stochastic processes. We render a rigorous construction of the stochastic integral of functions of two variables and show that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. We further introduce and study a marked Poisson random measure on a - compact Hausdorff space. The underlying parameters of this measure are changing in accordance with the evolution of a stochastic process. This generalized random measure …
On The Qualitative Theory Of The Nonlinear Parabolic P-Laplacian Type Reaction-Diffusion Equations, Roqia Abdullah Jeli
On The Qualitative Theory Of The Nonlinear Parabolic P-Laplacian Type Reaction-Diffusion Equations, Roqia Abdullah Jeli
Theses and Dissertations
This dissertation presents full classification of the evolution of the interfaces and asymptotics of the local solution near the interfaces and at infinity for the nonlinear second order parabolic p-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration ut − ( |ux| p−2 ux ) x +buβ = 0, p > 1, β > 0. (1) Nonlinear partial differential equation (1) is a key model example expressing competition between nonlinear diffusion with gradient dependent diffusivity in either slow (p > 2) or fast (1 < p < 2) regime and nonlinear state dependent reaction (b > 0) or absorption (b < 0) forces. If interface is finite, it may expand, shrink, or remain stationary as a result of the competition of the diffusion and reaction terms near the interface, expressed in terms of the parameters p, β,sign b, and asymptotics of the initial function near its support. In the fast diffusion regime strong domination of the diffusion causes infinite speed of propagation and interfaces are absent. In all cases with finite interfaces we prove the explicit formula for the interface and the local solution with accuracy up to constant coefficients. We prove explicit asymptotics of the local solution at infinity in all cases with infinite speed of propagation. The methods of the proof are generaliii ization of the methods developed in U.G. Abdulla & J. King, SIAM J. Math. Anal., 32, 2(2000), 235-260; U.G. Abdulla, Nonlinear Analysis, 50, 4(2002), 541-560 and based on rescaling laws for the nonlinear PDE and blow-up techniques for the identification of the asymptotics of the solution near the interfaces, construction of barriers using special comparison theorems in irregular domains with characteristic boundary curves.
Lower Order Perturbations Of Critical Fractional Laplacian Equations, Khalid Fanoukh Al Oweidi
Lower Order Perturbations Of Critical Fractional Laplacian Equations, Khalid Fanoukh Al Oweidi
Theses and Dissertations
We give sufficient conditions for the existence of nontrivial solutions to a class of critical nonlocal problems of the Brezis-Nirenberg type. Our result extends some results in the literature for the local case to the nonlocal setting. It also complements the known results for the nonlocal case.
Boundary Value Problems In A Multidimensional Box For Higher Order Linear And Quasi-Linear Hyperbolic Equations, Noha Aljaber
Boundary Value Problems In A Multidimensional Box For Higher Order Linear And Quasi-Linear Hyperbolic Equations, Noha Aljaber
Theses and Dissertations
Boundary value problems in a multidimensional box for higher order linear hyperbolic equations are considered. The concept of associated problems are introduced. For general boundary value problems there are established: (i) Necessary and sufficient conditions for a linear problem to have the Fredholm property in two–dimensional case; (ii) Necessary and sufficient conditions of well–posedness in two–dimensional case; (iii) Unimprovable sufficient conditions for a linear problem to have the Fredholm property; (iv) Unimprovable sufficient conditions of well–posedness and α–well–posedness; (v) Effective sufficient conditions of unqie solvability of two–point, periodic and Dirichlet type problems. (iv) Unimprovable conditions of unique solvability of two …
On The Qualitative Theory Of The Nonlinear Degenerate Second Order Parabolic Equations Modeling Reaction-Diffusion-Convection Processes, Habeeb Abed Kadhim Aal-Rkhais
On The Qualitative Theory Of The Nonlinear Degenerate Second Order Parabolic Equations Modeling Reaction-Diffusion-Convection Processes, Habeeb Abed Kadhim Aal-Rkhais
Theses and Dissertations
We consider nonlinear second order degenerate or singular parabolic equation ut − a(um)xx + buβ + c(up)x = 0, a, m, β, p > 0, b, c ∈ R describing reaction-diffusion-convection processes arising in many areas of science and engineering, such as filtration of oil or gas in porous media, transport of thermal energy in plasma physics, flow of chemically reacting fluid, evolution of populations in mathematical biology etc. We apply the methods developed in U.G. Abdulla, Journal of Differential Equations, 164, 2(2000), 321-354 for the reaction-diffusion equation (c = 0) and prove the existence, uniqueness, boundary regularity and comparison theorems …
Initial{Boundary And Nonlocal Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations With Two Independent Variables, Raja Ben-Rabha
Initial{Boundary And Nonlocal Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations With Two Independent Variables, Raja Ben-Rabha
Theses and Dissertations
Boundary value problems in a characteristic rectangle for nonlinear hyperbolic equations of higher order are considered. The concept of strong well–posedness of a boundary value problem is introduced. For initial–boundary value problems there are established: (i) Necessary and sufficient conditions of strong well–posedness; (ii) Unimprovable sufficient conditions of local and global solvability; (iii) Effective sufficient conditions of solvability of two–point, multi–point, periodic and Dirichlet type problems; (iv) Sharp a priori estimates of solutions of ill–posed initial–boundary value problems; (v) Unimprovable conditions guaranteeing unique solvability of ill–posed initial–boundary value problems. For nonlocal boundary value problems there are established: (i) Necessary and …
On The Classification Of The Second Minimal Orbits Of The Continuous Endomorphisms On The Real Line And Universality In Chaos, Naveed H. Iqbal
On The Classification Of The Second Minimal Orbits Of The Continuous Endomorphisms On The Real Line And Universality In Chaos, Naveed H. Iqbal
Theses and Dissertations
This dissertation presents full classification of second minimal odd periodic orbits of a continuous endomorphisms on the real line. A (2k + 1)-periodic orbit (k ≥ 3) is called second minimal for the map f , if 2k−1 is a minimal period of f in the Sharkovskii ordering. We prove that there are 4k−3 types of second minimal (2k+1)-orbits, each characterized with unique cyclic permutation and directed graph of transitions with accuracy up to inverses. The result is applied to the problem on the distribution of periodic windows within the chaotic regime of the bifurcation diagram of the one-parameter family …
On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos
On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos
Theses and Dissertations
We consider inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary heat flux is the control, and optimality criteria consists of the minimization of the L₂-norm declination of the trace of the solution to the Stefan problem from the temperature measurement on the fixed boundary. State vector solves multiphase Stefan problem in a weak formulation, which is equivalent to Neumann problem for the quasilinear parabolic PDE with discontinuous coefficient. Full discretization through finite differences is …