Browsing Faculty Works, Department of Mathematics by Title
Now showing items 176195 of 226

resolvent integration techniques for generalized transport equations
(AIP Publishing, 197906)A generalized class of ’’transport type’’ equations is studied, including most of the known exactly solvable models; in particular, the transport operator K is a scalar type spectral operator. A spectral resolution for K ... 
resonances in a box
(AIP Publishing, 200001)We investigate a numerical method for studying resonances in quantum mechanics. We prove rigorously that this method yields accurate approximations to resonance energies and widths for shape resonances in the semiclassical ... 
Riesz bases and positive operators on Hilbert space
(Hindawi, 20030101)It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product onH in which it is an orthonormal ... 
Robust optimal switching control for nonlinear systems
(Siam Publications, 200209)We formulate a robust optimal control problem for a general nonlinear system with finitely many admissible control settings and with costs assigned to switching of controls. e formulate the problem both in an L2gain/dissipative ... 
Scalings for fragments produced from drop breakup in shear flow with inertia
(American Institute of Physics, 200108)When a drop is sheared in a matrix liquid, the largest daughter drops are produced by elongative end pinching. The daughter drop size is found to scale with the critical drop size that would occur under the same flow ... 
scattering and inverse scattering in onedimensional nonhomogeneous media
(AIP Publishing, 199205)The wave propagation in a onedimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrodinger equation d2psi/dx2 ... 
semiclassical wavepacket scattering in one and two dimensions
(AIP Publishing, 200411)We prove that under short range potentials a semiclassical wave packet's propagation is accurate for infinite times in the (h) over bar >0 limit. (C) 2004 American Institute of Physics. 
Short wave stability for inviscid shear flow
(Siam Publications, 2008)We consider the linear stability of inviscid shear flows. While it is well known that discontinuous velocity profiles lead to short wave instabilities and illposedness, known examples of instability for smooth profiles ... 
Simulating WithinVector Generation of Malaria Parasite Diversity
(PLOS, 20170522)Plasmodium falciparum, the most virulent human malaria parasite, undergoes asexual reproduction within the human host, but reproduces sexually within its vector host, the Anopheles mosquito. Consequently, the mosquito stage ... 
A singular perturbation study of the RoliePoly model
(20170615) 
Smallenergy analysis for the selfadjoint matrix Schrodinger operator on the half line
(AIP Publishing, 201110)The matrix Schrodinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a ... 
Smallenergy asymptotics of the scattering matrix for the matrix Schrodinger equation on the line
(AIP Publishing, 200110)The onedimensional matrix Schrodinger equation is considered when the matrix potential is selfadjoint with entries that are integrable and have finite first moments. The smallenergy asymptotics of the scattering ... 
solution of multigroup transport equation in Lp spaces
(AIP Publishing, 197611)The isotropic multigroup transport equation is solved in L p , p_1, for both half range and full range problems, using resolvent integration techniques. The connection between these techniques and a spectral decomposition ... 
Solutions and optimality criteria to box constrained nonconvex minimization problems
(American Institute of Mathematical Sciences, 20070501)The design of elastic structures to optimize strength and economy of materials is a fundamental problem in structural engineering and related areas of applied mathematics. In this article we explore a finite dimensional ... 
Solving the GinzburgLandau equations by finiteelement methods
(American Physical Society, 199210)We consider finiteelement methods for the approximation of solutions of the GinzburgLandau equations of superconductivity. The methods are based on a discretization of the EulerLagrange equations resulting from the ... 
Soundultrasound interaction in bubbly fluids: Theory and possible applications
(American Institute of Physics, 200112)The interaction between sound and ultrasound waves in a weakly compressible viscous liquid with gas bubbles is considered. Using the method of multiple scales one and twodimensional nonlinear interaction equations are ... 
spectral properties of the KronigPenney Hamiltonian with a localized impurity
(AIP Publishing, 198906)It is shown that there exist bound states of the operator H ±λ=−(d 2/d x 2) +∑ m∈Z δ(⋅−(2m+1)π)±λW, W being an L 1(−∞,+∞) non‐negative function, in every sufficiently far gap of the spectrum of H 0=−d 2/d x 2 +∑ m∈Z ... 
Spontaneous penetration of a nonwetting drop into an exposed pore
(American Institute of Physics, 201305)We consider the penetration process of a liquid drop approaching an exposed pore along the axis of symmetry, which is intended to model the penetration of nonwetting drops into a porous medium. Inertia and gravity are ...