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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Modeling Shock Waves Using Exponential Interpolation Functions With The Least-Squares Finite Element Method, Bradford Scott Smith Jr.
Modeling Shock Waves Using Exponential Interpolation Functions With The Least-Squares Finite Element Method, Bradford Scott Smith Jr.
Mechanical & Aerospace Engineering Theses & Dissertations
The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation …
Heuristic And Exact Algorithms For The Two-Machine Just In Time Job Shop Scheduling Problem, Mohammed Al Salem, Leonardo Bedoya-Valencia, Ghaith Rabadi
Heuristic And Exact Algorithms For The Two-Machine Just In Time Job Shop Scheduling Problem, Mohammed Al Salem, Leonardo Bedoya-Valencia, Ghaith Rabadi
Engineering Management & Systems Engineering Faculty Publications
The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much …
Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu
Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu
Mathematics & Statistics Faculty Publications
We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter ξ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate. © 2016 …
Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo
Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo
Mathematics & Statistics Faculty Publications
We study the de Gennes free energy for smectic A liquid crystals over S2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter a, and investigate the behaviors of the minimizers when the field strength is of order O (ε-1). In this regime, we show via Γ-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. We also analyze the Chen-Lubensky free energy, which includes the second order gradient of the smectic order parameter, and …
Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak
Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak
Mathematics & Statistics Faculty Publications
A brief summary of the physical context to this paper is provided, and the deviation angle undergone by an incident ray after k internal reflections inside a transparent unit sphere is formulated. For radially inhomogeneous spheres (in particular) this angle is related to a ray-path integral; an improper integral for which there are relatively few known exact analytical forms, even for simple refractive index profiles n(r). Thus for a linear profile the integral is a combination of incomplete elliptic integrals of the first and third kinds (though not all are as complicated as this). The ray-path integral is evaluated …