Browsing Faculty Works, Department of Mathematics by Title
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The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia
(American Institute of Physics, 200401)Direct numerical simulations are conducted with a volumeoffluid continuous surface stress algorithm. The linear equation of state is used to characterize the effects of an insoluble surfactant at low concentration on a ... 
The effect of negative feedback loops on the dynamics of Boolean networks
(CELL PRESS, 200807)Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, ... 
the effect of nonzero viscosity ratio on the stability of fingers and bubbles in a HeleShaw cell
(AIP Publishing, 198811)The linear stability of a steadily moving bubble or a finger in a Hele–Shaw cell is considered in the case when gravity and the ratio between the viscosities of the less and more viscous fluids are nonzero. The effect of ... 
the effect of surface tension on the shape of a HeleShaw cell bubble
(AIP Publishing, 198611)Numerical and asymptotic solutions are found for the steady motion of a symmetrical bubble through a parallel‐sided channel in a Hele–Shaw cell containing a viscous liquid. The degeneracy of the Taylor–Saffman zero ... 
The PMU placement problem
(Siam Publications, 2005)PMU placement problem is an optimization problem abstracted from an approach to supervising an electrical power system. The power system is modeled as a graph, and adequate supervision of the system requires that the voltage ... 
the RiemannHilbert problem for nonsymmetric systems
(AIP Publishing, 199112)A comparison of the RiemannHilbert problem and the WienerHopf factorization problem arising in the solution of halfspace singular integral equations is presented. Emphasis is on the factorization of functions lacking ... 
the semiclassical limit of quantum dynamics. I. time evolution
(AIP Publishing, 198802)The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) =−(ℏ2/2m)Δ+V on L 2(R n ) is studied for a large class of potentials. By convolving with certain Gaussian states, classically determined asymptotic ... 
The thinlayer effect and interfacial stability in a twolayer Couette flow with similar liquids
(AIP Publishing, 198706)The linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties. The interfacial ... 
Topologies between compact and uniform convergence on function spaces
(Hindawi, 19930101)This paper studies two topologies on the set of all continuous realvalued functionson a Tychonoff space which lie between the topologies of compact convergence and uniformconvergence. 
Transfer function approach to output specification in certain linear distributed parameter systems
(American Institute of Mathematical Sciences, 2003)We carry out error estimation of a class of immersed finite element (IFE) methods for elliptic interface problems with both perfect and imperfect interface jump conditions. A key feature of these methods is that their ... 
transverse plasma oscillations
(AIP Publishing, 1979)An operator theoretic approach is used to solve the linearized Vlasov–Maxwell equations for transverse plasma oscillations. In particular, the special cases of simple and second‐order real zeros of the plasma dispersion ... 
Understanding the complex patterns observed during hepatitis B Virus therapy
(MDPI, 20170519)Data from human clinical trials have shown that the hepatitis B virus (HBV) follows complex profiles, such as biphasic, triphasic, stepwise decay and rebound. We utilized a deterministic model of HBV kinetics following ... 
uniqueness of solutions to linearized Boltzmann equation
(AIP Publishing, 197801)Uniqueness theorems are proved for the linearized Boltzmann equation for both the ’’exterior’’ and ’’interior’’ problems under generalized Maxwellboundary conditions. The solution space is a weighted L p space, and agrees ... 
Using startup of steady shear flow in a sliding plate rheometer to determine material parameters for the purpose of predicting long fiber orientation
(AIP Publishing, 20120701)The properties of long glass fiber reinforced parts, such as those manufactured by means of injection molding and compression molding, are highly dependent on the fiber orientation generated during processing. A sliding ... 
Using transient shear rheology to determine material parameters in fiber suspension theory
(AIP Publishing, 20090501)Fiber suspension theory model parameters for use in the simulation of fiber orientation in complex flows are, in general, either calculated from theory or fit to experimentally determined fiber orientation generated in ... 
viscosity and density stratification in vertical Poiseuille flow
(AIP Publishing, 198706)The linear stability of plane three_layer vertical Poiseuille flow is considered. The layers are composed of two immiscible fluids, one next to the walls and one centrally located. The fluids have different viscosities and ... 
Vlasov theory of plasma oscillations: linearapproximation
(AIP Publishing, 1977)A functional analytic approach to the linearized collisionless Vlasov equation is presented utilizing a resolvent integration technique on the resolvent of the transport operator evaluated at a particular point. Formulae ... 
wall energy relaxation in the CahnHilliard model for moving contact lines
(AIP Publishing, 201101)The CahnHilliard model uses diffusion between fluid components to regularize the stress singularity at a moving contact line. In addition, it represents the dynamics of the nearwall layer by the relaxation of a wall ... 
wave operators for the matrix ZakharovShabat system
(AIP Publishing, 201005)In this article, we prove the similarity (and, in the focusing case, the Junitary equivalence) of the free Hamiltonian and the restriction of the full Hamiltonian to the maximal invariant subspace on which its spectrum ...