Browsing Faculty Works, Department of Mathematics by Title
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A Bistable Switch in Virus Dynamics Can Explain the Differences in Disease Outcome Following SIV Infections in Rhesus Macaques
(Frontiers, 20180606)Experimental studies have shown that the size and infectiousstage of viral inoculum influence disease outcomes in rhesus macaques infected with simian immunodeficiency virus. The possible contribution to disease outcome ... 
A comparison of viscoelastic stress wakes for twodimensional and threedimensional Newtonian drop deformations in a viscoelastic matrix under shear
(American Institute of Physics, 200907)A recent experimental study of a Newtonian drop suspended in a viscoelastic matrix undergoing simple shear displays a transient overshoot in drop deformation which is qualitatively similar to twodimensional (2D) numerical ... 
A finite element splitting extrapolation for second order hyperbolic equations
(Siam Publications, 2009)Splitting extrapolation is an efficient technique for solving large scale scientific and engineering problems in parallel. This article discusses a finite element splitting extrapolation for second order hyperbolic equations ... 
A general convergence analysis of some Newtontype methods for nonlinear inverse problems
(Siam Publications, 2011)We consider the methods x(n+1)(delta)  x(n)(delta)  g(alpha n) (F'(x(n)(delta))* F'(x(n)(delta)))F'(x(n)(delta))*(F(x(n)(delta))  y(delta)) for solving nonlinear illposed inverse problems F(x) = y using the only available ... 
A hybrid collocation method for volterra integral equations with weakly singular kernels
(Siam Publications, 2003)The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious roundoff error problems due to its use of extremely nonuniform partitions and the sensitivity ... 
A Network Biology Approach to Denitrification in Pseudomonas aeruginosa
(20150223)Pseudomonas aeruginosa is a metabolically flexible member of the Gammaproteobacteria. Under anaerobic conditions and the presence of nitrate, P. aeruginosa can perform (complete) denitrification, a respiratory process of ... 
A note on the switching adiabatic theorem
(AIP Publishing, 201210)We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class G(alpha) as a function of time, and we ... 
a numerical study of periodic disturbances on twolayer Couette flaw
(AIP Publishing, 199812)The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semiimplicit Stokes solver to enable computations at low Reynolds numbers, and a secondorder velocity ... 
A regularized GaussNewton trust region approach to imaging in diffuse optical tomography
(Siam Publications, 2011)We present a new algorithm for the solution of nonlinear least squares problems arising from parameterized imaging problems with diffuse optical tomographic data [D. Boas et al., IEEE Signal Process. Mag., 18 (2001), pp. ... 
A state space error estimate for poddeim nonlinear model reduction
(Siam Publications, 2012)This paper derives state space error bounds for the solutions of reduced systems constructed using proper orthogonal decomposition (POD) together with the discrete empirical interpolation method (DEIM) recently developed ... 
A uniqueness result for pMonotone viscosity solutions of HamiltonJacobi equations in bounded domains
(Siam Publications, 2009)We consider a class of HamiltonJacobi equations H(x, Du(x))  0 with no udependence and with continuity properties consistent with recent applications in queueing theory. Continuous viscosity solutions are considered in ... 
A volumeoffluid formulation for the study of coflowing fluids governed by the HeleShaw equations
(American Institute of Physics, 201308)We present a computational framework to address the flow of two immiscible viscous liquids which coflow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions ... 
Abacus proofs of Schur function identities
(Siam Publications, 2010)This article uses combinatorial objects called labeled abaci to give direct combinatorial proofs of many familiar facts about Schur polynomials. We use abaci to prove the Pieri rules, the LittlewoodRichardson rule, the ... 
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
(20110720)Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agentbased models, to gain a better understanding of them. The ... 
An affine deformation of the quantum cohomology ring of flag manifolds and periodic Toda lattice
Consider the generalized flag manifold $G/B$ and the corresponding affine flag manifold $\mathcal{Fl}_G$. In this paper we use curve neighborhoods for Schubert varieties in $\mathcal{Fl}_G$ to construct certain affine ... 
An effective method for parameter estimation with pde constraints with multiple righthand sides
(Siam Publications, 2012)Often, parameter estimation problems of parameterdependent PDEs involve multiple righthand sides. The computational cost and memory requirements of such problems increase linearly with the number of righthand sides. For ... 
An elementary nonlinear beam theory with finite buckling deformation properties
(Siam Publications, 200204)A simple nonlinear beam model is derived from basic principles. The assumption upon which the derivation is based is that axial motions are of second order compared with transverse motions of the beam. The existence of ... 
Analysis and approximation of the velocity tracking problem for NavierStokes flows with distributed control
(Siam Publications, 200005)We consider the mathematical formulation, analysis, and the numerical solution of a timedependent optimal control problem associated with the tracking of the velocity of a NavierStokes ow in a bounded twodimensional ... 
analytic theory for the selection of a twodimensional needle crystal at arbitrary Péclet number
(American Physical Society, 198910)An accurate analytic theory is presented for the velocity selection of a twodimensional needle crystal for arbitrary Péclet number for small values of the surfacetension parameter. The velocity selection is caused by the ... 
analytical solutions of model equations for two phase gas mixtures: Transverse velocity perturbations
(AIP Publishing, 1984)Model equations for a dilute binary gas system are derived, using a linear BGK scheme. Complete analytical solutions for the stationary half_space problem are obtained for transverse velocity perturbations. The method of ...