Browsing Scholarly Works, Department of Mathematics by Title
Now showing items 1-20 of 243
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A comparison of viscoelastic stress wakes for two-dimensional and three-dimensional Newtonian drop deformations in a viscoelastic matrix under shear
(American Institute of Physics, 2009-07)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 two-dimensional (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 Newton-type 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 ill-posed 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 round-off error problems due to its use of extremely nonuniform partitions and the sensitivity ... -
A Linear Algorithm for Ambient Seismic Noise Double Beamforming Without Crosscorrelations
(2020-01-02)Geoscientists and engineers are increasingly using denser arrays for continuous seismic monitoring, and often turning to ambient seismic noise interferometry for low-cost near-surface imaging. While ambient noise interferometry ... -
A multiple-scales space-time analysis of a randomly perturbed one-dimensional wave equation
(AIP Publishing, 1977-10)An initial value problem for one_dimensional wave propagation is considered; the medium is assumed to be randomly perturbed as a function of both space and time. The stochastic perturbation theory of Papanicolaou and Keller ... -
A note on the switching adiabatic theorem
(AIP Publishing, 2012-10)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 two-layer Couette flaw
(AIP Publishing, 1998-12)The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity ... -
A regularized Gauss-Newton 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 pod-deim 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 p-Monotone viscosity solutions of Hamilton-Jacobi equations in bounded domains
(Siam Publications, 2009)We consider a class of Hamilton-Jacobi equations H(x, Du(x)) - 0 with no u-dependence and with continuity properties consistent with recent applications in queueing theory. Continuous viscosity solutions are considered in ... -
A volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equations
(American Institute of Physics, 2013-08)We present a computational framework to address the flow of two immiscible viscous liquids which co-flow 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 Littlewood-Richardson rule, the ... -
Acceleration of tensor-product operations for high-order finite element methods
This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background to these operations and implementation ... -
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
(2011-07-20)Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based 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 ... -
Algebras and Varieties
(2020-03)In this paper we introduce new affine algebraic varieties whose points correspond to associative algebras. We show that the algebras within a variety share many important homological properties. In particular, any two ... -
An effective method for parameter estimation with pde constraints with multiple right-hand sides
(Siam Publications, 2012)Often, parameter estimation problems of parameter-dependent PDEs involve multiple right-hand sides. The computational cost and memory requirements of such problems increase linearly with the number of right-hand sides. For ... -
An elementary nonlinear beam theory with finite buckling deformation properties
(Siam Publications, 2002-04)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 Navier-Stokes flows with distributed control
(Siam Publications, 2000-05)We consider the mathematical formulation, analysis, and the numerical solution of a time-dependent optimal control problem associated with the tracking of the velocity of a Navier-Stokes ow in a bounded two-dimensional ...
