Browsing Department of Mathematical Sciences by Title

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  • Naire, S.; Braun, Richard J.; Snow, S.A. (Department of Mathematical Sciences, 2002-05-09)
    A 2 + 1 dimensional mathematical model is constructed to study the evolution of a vertically-oriented thin, free liquid film draining under gravity when there is an insoluble surfactant, with finite surface viscosity, on ...
  • Tanoglu, G.B.; Braun, Richard J.; Cahn, J.W.; McFadden, G.B. (Department of Mathematical Sciences, 2003)
    The dependence of thermodynamic properties of planar interphase boundaries (IPBs) and antiphase boundaries (APBs) in a binary alloy on an FCC lattice is studied as a function of their orientation. Using a recently-developed ...
  • Monk, Peter B.; Vacus, O. (Department of Mathematical Sciences, 2000)
    In this paper we propose a finite element discretization of the Maxwell-Landau-Lifchitz-Gilbert equations governing the electromagnetic field in a ferromagnetic material. Our point of view is that it is desirable for the ...
  • Rossi, Louis F. (Department of Mathematical Sciences, 2003)
    This article studies the use of moving, deforming elliptical Gaussian basis functions to compute the evolution of passive scalar quantities in a two-dimensional, incompressible flow field. We compute an evolution equation ...
  • Pelesko, John A.; Driscoll, Tobin A. (Kluwer Academic Publishers (see: http://www.sherpa.ac.uk/romeo.php for publisher's conditions for archiving in an institutional repository), 2004-09-28)
    The mathematical modeling and analysis of electrostatically actuated micro- and nanoelectromechanical systems (MEMS and NEMS) has typically relied upon simplified electrostatic field approximations to facilitate the analysis. ...
  • Cirillo, Michelle (2015-05-04)
    This applet was designed to be used with the "Mathematics Discourse in Secondary Classrooms" professional development materials. The applet allows the user to explore questions about how the area and perimeter of a triangle ...
  • Zhang, Shangyou; Olagunju, David O. (Department of Mathematical Sciences, 2004-11-19)
    Steady non-isothermal parallel-plate flow of a Newtonian fluid with a temperature dependent viscosity is considered. The viscosity is modelled by a Nahme type law. We apply axisymmetric Q k finite elements to the coupled ...
  • Dallas, A.G. (Department of Mathematical Sciences, 2000)
    The classical solutions of the Heimholtz equation resulting from the separation-of-variables procedure in spherical coördinates are frequently used in one way or another to approximate other solutions. In particular, traces ...
  • Hsiao, George C. (Department of Mathematical Sciences, 2004)
    Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. This paper gives an overview ...
  • Hsiao, George C.; Wendland, W.L. (Department of Mathematical Sciences, 2000)
    This expository paper is concerned with the direct integral formulations for boundary value problems of the Helmholtz equation. We discuss unique solvability for the corresponding boundary integral equations and its ...
  • Debisschop, C.A.; Braun, Richard J.; Snow, S.A. (Department of Mathematical Sciences, 2001-09-12)
    We study the evolution of a Newtonian free surface of a thin film above a solid wall. We consider the case in which the horizontal solid is covered by a non-wetting fluid and an insoluble monolayer of surfactant is present ...
  • Cirillo, Michelle (The Department of Mathematics, National Taiwan Normal University Taipei, Taiwan, 2009)
    As pointed out by Stylianides (2007), a major reason that proof and proving have been given increased attention in recent years is because they are fundamental to doing and knowing mathematics and communicating mathematical ...
  • Rossi, Louis F. (Department of Mathematics, 2003)
    This paper presents results from a head-to-head comparison of two Lagrangian methods for solutions to the two-dimensional, incompressible convection-diffusion equations. The first Lagrangian method is an axisymmetric ...
  • Platte, Rodrigo B.; Driscoll, Tobin A. (Department of Mathematical Sciences, 2003-03-21)
    Radial basis function (RBF) approximations have been successfully used to solve boundary-value problems numerically. We show that RBFs can also be used to compute eigenmodes of elliptic operators. Special attention is ...
  • Cirillo, Michelle; Kosko, Karl W.; Newton, Jill; Staples, Megan; Weber, Keith (East Lansing, MI: Michigan State University, 2015)
    Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other ...
  • Chandler, D.B.; Xiang, Qing (Department of Mathematical Sciences, 2002)
    By modifying the constructions in [10] and [15], we construct a family of cyclic ((q 3k − 1)/(q − 1), q − 1, q 3k − 1 , q 3k − 2 ) relative difference sets, where q = 3 e . These relative difference sets are “liftings” ...
  • Cakoni, Fioralba; Colton, David; Monk, Peter B. (Department of Mathematical Sciences, 2002)
    We consider the direct and inverse scattering problems for partially coated obstacles. To this end, we first use the method of integral equations of the first kind to solve a scattering problem for the Helmholtz equation ...
  • Monk, Peter B. (Department of Mathematical Sciences, 2002)
    The time harmonic Maxwell's equations for a lossless medium are neither elliptic or definite. Hence the analysis of numerical schemes for these equations presents some unusual difficulties. In this paper we give a simple ...
  • Hsiao, George C.; Steinbach, O.; Wendland, W.L. (Department of Mathematical Sciences, 2000-12-21)
    Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain ...
  • Borwein, J. M.; Luke, D. Russell (Department of Mathematical Sciences, 2004-11-19)
    We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were ...

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