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Articles 31 - 60 of 117
Full-Text Articles in Applied Mathematics
A New Formulation Of Time Boundary Integral Equation For Acoustic Wave Scattering In The Presence Of A Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark
A New Formulation Of Time Boundary Integral Equation For Acoustic Wave Scattering In The Presence Of A Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark
Mathematics & Statistics Faculty Publications
It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In …
Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu
Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu
Mathematics & Statistics Faculty Publications
We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter ξ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate. © 2016 …
Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo
Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo
Mathematics & Statistics Faculty Publications
We study the de Gennes free energy for smectic A liquid crystals over S2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter a, and investigate the behaviors of the minimizers when the field strength is of order O (ε-1). In this regime, we show via Γ-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. We also analyze the Chen-Lubensky free energy, which includes the second order gradient of the smectic order parameter, and …
Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak
Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak
Mathematics & Statistics Faculty Publications
A brief summary of the physical context to this paper is provided, and the deviation angle undergone by an incident ray after k internal reflections inside a transparent unit sphere is formulated. For radially inhomogeneous spheres (in particular) this angle is related to a ray-path integral; an improper integral for which there are relatively few known exact analytical forms, even for simple refractive index profiles n(r). Thus for a linear profile the integral is a combination of incomplete elliptic integrals of the first and third kinds (though not all are as complicated as this). The ray-path integral is evaluated …
Lattice-Boltzmann Simulations Of The Thermally Driven 2d Square Cavity At High Rayleigh Numbers, Dario Contrino, Pierre Lallemand, Pietro Asinari, Li-Shi Luo
Lattice-Boltzmann Simulations Of The Thermally Driven 2d Square Cavity At High Rayleigh Numbers, Dario Contrino, Pierre Lallemand, Pietro Asinari, Li-Shi Luo
Mathematics & Statistics Faculty Publications
The thermal lattice Boltzmann equation (TLBE) with multiple-relaxation-times (MRT) collision model is used to simulate the steady thermal convective flows in the two-dimensional square cavity with differentially heated vertical walls at high Rayleigh numbers. The MRT-TLBE consists of two sets of distribution functions, i.e., a D2Q9 model for the mass-momentum equations and a D2Q5 model for the temperature equation. The dimensionless flow parameters are the following: the Prandtl number Pr = 0.71 and the Rayleigh number Ra = 106, 107, and 108. The D2Q9 + D2Q5 MRT-TLBE is shown to be second-order accurate and …
Lattice Boltzmann Simulations Of Thermal Convective Flows In Two Dimensions, Jia Wang, Donghai Wang, Pierre Lallemand, Li-Shi Luo
Lattice Boltzmann Simulations Of Thermal Convective Flows In Two Dimensions, Jia Wang, Donghai Wang, Pierre Lallemand, Li-Shi Luo
Mathematics & Statistics Faculty Publications
In this paper we study the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model for incompressible thermo-hydrodynamics with the Boussinesq approximation. We use the MRT thermal LBE (TLBE) to simulate the following two flows in two dimensions: the square cavity with differentially heated vertical walls and the Rayleigh-Benard convection in a rectangle heated from below. For the square cavity, the flow parameters in this study are the Rayleigh number Ra = 103-106, and the Prandtl number Pr = 0.71; and for the Rayleigh-Benard convection in a rectangle, Ra = 2 . 103, 10 …
Duality Of The Weak Parallelogram Laws On Banach Spaces, Raymond Cheng, Charles B. Harris
Duality Of The Weak Parallelogram Laws On Banach Spaces, Raymond Cheng, Charles B. Harris
Mathematics & Statistics Faculty Publications
This paper explores a family of weak parallelogram laws for Banach spaces. Some basic properties of such spaces are obtained. The main result is that a Banach space satisfies a lower weak parallelogram law if and only if its dual satisfies an upper weak parallelogram law, and vice versa. Connections are established between the weak parallelogram laws and the following: subspaces, quotient spaces, Cartesian products, and the Rademacher type and co-type properties.
Mesoscopic Methods In Engineering And Science, Jos Derksen, Dmitry Eskin, Li-Shi Luo, Manfred Krafczyk
Mesoscopic Methods In Engineering And Science, Jos Derksen, Dmitry Eskin, Li-Shi Luo, Manfred Krafczyk
Mathematics & Statistics Faculty Publications
(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the …
Wavelet Collocation Method And Multilevel Augmentation Method For Hammerstein Equations, Hideaki Kaneko, Khomsan Neamprem, Boriboon Novaprateep
Wavelet Collocation Method And Multilevel Augmentation Method For Hammerstein Equations, Hideaki Kaneko, Khomsan Neamprem, Boriboon Novaprateep
Mathematics & Statistics Faculty Publications
No abstract provided.
On The Global Stability Of A Generalized Cholera Epidemiological Model, Yuanji Cheng, Jin Wang, Xiuxiang Yang
On The Global Stability Of A Generalized Cholera Epidemiological Model, Yuanji Cheng, Jin Wang, Xiuxiang Yang
Mathematics & Statistics Faculty Publications
In this paper, we conduct a careful global stability analysis for a generalized cholera epidemiological model originally proposed in [J. Wang and S. Liao, A generalized cholera model and epidemic/endemic analysis, J. Biol. Dyn. 6 (2012), pp. 568-589]. Cholera is a water-and food-borne infectious disease whose dynamics are complicated by the multiple interactions between the human host, the pathogen, and the environment. Using the geometric approach, we rigorously prove the endemic global stability for the cholera model in three-dimensional (when the pathogen component is a scalar) and four-dimensional (when the pathogen component is a vector) systems. This work unifies the …
Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang
Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang
Mathematics & Statistics Faculty Publications
In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.
Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko
Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko
Mathematics & Statistics Faculty Publications
No abstract provided.
Mesoscopic Methods In Engineering And Science, Chuguang Zheng, Jiding Lu, Zhaoli Guo, Li-Shi Luo, Manfred Krafczyk
Mesoscopic Methods In Engineering And Science, Chuguang Zheng, Jiding Lu, Zhaoli Guo, Li-Shi Luo, Manfred Krafczyk
Mathematics & Statistics Faculty Publications
Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics …
Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Stability, Charles B. Harris, Richard D. Noren
Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Stability, Charles B. Harris, Richard D. Noren
Mathematics & Statistics Faculty Publications
We study stability of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation u'(t) + ∫0 β (t - s)Au(s) ds = 0, t ≥ 0, u(0) = u0, which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real Hilbert space, and β (t) is locally integrable, nonnegative, nonincreasing, convex, and -β'(t) is convex. We establish stability of the method under these hypotheses on β(t). Thus, …
Probability Models For Blackjack Poker, Charlie H. Cooke
Probability Models For Blackjack Poker, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. in order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer's seven. Theoretical and experimental methods are used in order …
Mesoscopic Methods In Engineering And Science, Alfons Hoekstra, Li-Shi Luo, Manfred Krafczyk
Mesoscopic Methods In Engineering And Science, Alfons Hoekstra, Li-Shi Luo, Manfred Krafczyk
Mathematics & Statistics Faculty Publications
(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the …
A Two-Population Insurgency In Colombia: Quasi-Predator-Prey Models - A Trend Towards Simplicity, John A. Adam, John A. Sokolowski, Catherine M. Banks
A Two-Population Insurgency In Colombia: Quasi-Predator-Prey Models - A Trend Towards Simplicity, John A. Adam, John A. Sokolowski, Catherine M. Banks
Mathematics & Statistics Faculty Publications
A sequence of analytic mathematical models has been developed in the context of the "low-level insurgency" in Colombia, from 1993 to the present. They are based on generalizations of the two-population "predator-prey" model commonly applied in ecological modeling, and interestingly, the less sophisticated models yield more insight into the problem than the more complicated ones, but the formalism is available to adapt the model "upwards" in the event that more data becomes available, or as the situation increases in complexity. Specifically, so-called "forcing terms" were included initially in the coupled differential equations to represent the effects of government policies towards …
A Simplified Model For Growth Factor Induced Healing Of Wounds, F. J. Vermolen, E. Van Baaren, J. A. Adam
A Simplified Model For Growth Factor Induced Healing Of Wounds, F. J. Vermolen, E. Van Baaren, J. A. Adam
Mathematics & Statistics Faculty Publications
A mathematical model is developed for the rate of healing of a circular or elliptic wound. In this paper the regeneration, decay and transport of a generic 'growth factor', which induces the healing of the wound, is taken into account. Further, an equation of motion is derived for radial healing of a circular wound. The expressions for the equation of motion and the distribution of the growth factor are related in such a way that no healing occurs if the growth factor concentration at the wound edge is below a threshold value. In this paper we investigate the influence of …
On The Existence Of Strong Solutions To Autonomous Differential Equations With Minimal Regularity, Charlie H. Cooke
On The Existence Of Strong Solutions To Autonomous Differential Equations With Minimal Regularity, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
For proving the existence and uniqueness of strong solutions to
dY/dt = F(Y), Y(0) = C,
the most quoted condition seen in elementary differential equations texts is that F(Y) and its first derivative be continuous. One wonders about the existence of a minimal regularity condition which allows unique strong solutions. In this note, a bizarre example is seen where F(Y) is not differentiable at an equilibrium solution; yet unique non-global strong solutions exist at each point, whereas global non-unique weak solutions are allowed. A characterizing theorem is obtained.
A System Equivalence Related To Dulac's Extension Of Bendixson's Negative Theorem For Planar Dynamical Systems, Charlie H. Cooke
A System Equivalence Related To Dulac's Extension Of Bendixson's Negative Theorem For Planar Dynamical Systems, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
Bendixson's Theorem [H. Ricardo, A Modem Introduction to Differential Equations, Houghton-Mifflin, New York, Boston, 2003] is useful in proving the non-existence of periodic orbits for planar systems
dx/dt = F(x, y), dy/dt = G (x, y)
in a simply connected domain D, where F, G are continuously differentiable. From the work of Dulac [M. Kot, Elements of Mathematical Ecology, 2nd printing, University Press, Cambridge, 2003] one suspects that system (1) has periodic solutions if and only if the more general system
dx/d tau = B(x, y)F(x, y), dy/d tau = B(x, y)G(x, y)
does, which makes the subcase (1) more …
Bounds On Element Order In Rings Z(M) With Divisors Of Zero, C. H. Cooke
Bounds On Element Order In Rings Z(M) With Divisors Of Zero, C. H. Cooke
Mathematics & Statistics Faculty Publications
If p is a prime, integer ring Zp has exactly ¢¢(p) generating elements ω, each of which has maximal index Ip(ω) = (p) = p − 1. But, if m = ΠRJ = 1pαJJ is composite, it is possible that Zm does not possess a generating element, and the maximal index of an element is not easily discernible. Here, it is determined when, in the absence of a generating element, one can still with confidence place bounds on the maximal index. Such a bound is usually less than ¢(m …
Computational Protein Biomarker Prediction: A Case Study For Prostate Cancer, Michael Wagner, Dayanand N. Naik, Alex Pothen, Srinivas Kasukurti, Raghu Ram Devineni, Bao-Ling Adam, O. John Semmes, George L. Wright Jr.
Computational Protein Biomarker Prediction: A Case Study For Prostate Cancer, Michael Wagner, Dayanand N. Naik, Alex Pothen, Srinivas Kasukurti, Raghu Ram Devineni, Bao-Ling Adam, O. John Semmes, George L. Wright Jr.
Mathematics & Statistics Faculty Publications
Background: Recent technological advances in mass spectrometry pose challenges in computational mathematics and statistics to process the mass spectral data into predictive models with clinical and biological significance. We discuss several classification-based approaches to finding protein biomarker candidates using protein profiles obtained via mass spectrometry, and we assess their statistical significance. Our overall goal is to implicate peaks that have a high likelihood of being biologically linked to a given disease state, and thus to narrow the search for biomarker candidates.
Results: Thorough cross-validation studies and randomization tests are performed on a prostate cancer dataset with over 300 patients, obtained …
Healing Times For Circular Wounds On Plane And Spherical Bone Surfaces, J. A. Adam
Healing Times For Circular Wounds On Plane And Spherical Bone Surfaces, J. A. Adam
Mathematics & Statistics Faculty Publications
A mathematical model is developed for the rate of healing of a circular wound in a spherical "skull". The motivation for this model is based on experimental studies of the "'critical size defect" (CSD) in animal models; this has been defined as the smallest intraosseous wound that does not heal by bone formation during the lifetime of the animal [1]. For practical purposes, this timescale can usually be taken as one year. In [2], the definition was further extended to a defect which has less than ton percent bony regeneration during the lifetime of the animal. CSDS can "heal" by …
The Effect Of Surface Curvature On Wound Healing In Bone, J. A. Adam
The Effect Of Surface Curvature On Wound Healing In Bone, J. A. Adam
Mathematics & Statistics Faculty Publications
The time-independent nonhomogeneous diffusion equation is solved for the equilibrium distribution of wound-induced growth factor over a hemispherical surface. The growth factor is produced at the inner edge of a circular wound and stimulates healing in regions where the concentration exceeds a certain threshold value. An implicit analytic criterion is derived for complete healing of the wound. (C) 2001 Elsevier Science Ltd. All rights reserved.
Advances In Space Radiation Shielding Codes, John W. Wilson, Ram K. Tripathi, Garry D. Qualls, Francis A. Cucinotta, Richard E. Prael, John W. Norbury, John H. Heinbockel, John Tweed, Giovanni De Angelis
Advances In Space Radiation Shielding Codes, John W. Wilson, Ram K. Tripathi, Garry D. Qualls, Francis A. Cucinotta, Richard E. Prael, John W. Norbury, John H. Heinbockel, John Tweed, Giovanni De Angelis
Mathematics & Statistics Faculty Publications
Early space radiation shield code development relied on Monte Carlo methods and made important contributions to the space program. Monte Carlo methods have resorted to restricted one-dimensional problems leading to imperfect representation of appropriate boundary conditions. Even so, intensive computational requirements resulted and shield evaluation was made near the end of the design process. Resolving shielding issues usually had a negative impact on the design. Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from …
The Range Of The Iterated Matrix Adjoint Operator, Tze-Jang Chen, Jenn-Tsann Lin, C. H. Cooke
The Range Of The Iterated Matrix Adjoint Operator, Tze-Jang Chen, Jenn-Tsann Lin, C. H. Cooke
Mathematics & Statistics Faculty Publications
The following inverse problem is considered: for a given n × n real matrix B, does there exist a real matrix A such that where the classical adjoint operation is intended? The rank of B and the number of applications of the adjoint operator determine the character of this general inverse problem for the iterated adjoint operator. Thus, for given B, the question of interest is whether or not B lies in the range of the iterated matrix adjoint operator. Maple V R5 is used as an aid to obtain results indicated here. (©) 2001 Elsevier Science Ltd. …
A Simplified Model Of Wound Healing - Ii: The Critical Size Defect In Two Dimensions, J. S. Arnold, John A. Adam
A Simplified Model Of Wound Healing - Ii: The Critical Size Defect In Two Dimensions, J. S. Arnold, John A. Adam
Mathematics & Statistics Faculty Publications
Recently, a one-dimensional model was developed which gives a reasonable explanation for the existence of a Critical Size Defect (CSD) in certain animals [1]. In this paper, we examine the more realistic two-dimensional model of a circular wound of uniform depth to see what modifications are to be found, as compared with the one-dimensional model, in studying the CSD phenomenon. It transpires that the range of CSD sizes for a reasonable estimate of parameter values is 1 mm-1 cm. More realistic estimates await the appropriate experimental data.
A Simplified Model Of Wound Healing (With Particular Reference To The Critical Size Defect), J. A. Adam
A Simplified Model Of Wound Healing (With Particular Reference To The Critical Size Defect), J. A. Adam
Mathematics & Statistics Faculty Publications
This paper is an attempt to construct a simple mathematical model of wound healing/tissue regeneration which reproduces some of the known qualitative features of those phenomena. It does not address the time development of the wound in any way, but does examine conditions (e.g., wound size) under which such healing may occur. Two related one-dimensional models are examined here. The first, and simpler of the two corresponds to a "swath" of tissue (or more realistically in this case, bone) removed from an infinite plane of tissue in which only a thin band of tissue at the wound edges takes part …
Algorithms For The Numerical Solution Of A Finite-Part Integral Equation, J. Tweed, R. St. John, M. H. Dunn
Algorithms For The Numerical Solution Of A Finite-Part Integral Equation, J. Tweed, R. St. John, M. H. Dunn
Mathematics & Statistics Faculty Publications
The authors investigate a hypersingular integral equation which arises in the study of acoustic wave scattering by moving objects. A Galerkin method and two collocation methods are presented for solving the problem numerically. These numerical techniques are compared and contrasted in three test problems.
Polynomial Construction Of Complex Hadamard Matrices With Cyclic Core, C. H. Cooke, I. Heng
Polynomial Construction Of Complex Hadamard Matrices With Cyclic Core, C. H. Cooke, I. Heng
Mathematics & Statistics Faculty Publications
Conditions are given which are necessary and sufficient to ensure invariance of an M-sequence under periodic rearrangement. In conjunction with a certain uniformity property of polynomial coefficients, these conditions yield a simple method by which complex Hadamard matrices with cyclic core can be constructed. In such cases, a real p-ary linear cyclic error correcting code may be associated with the complex Hadamard matrix.