Application of finite element approach to transonic flow problems

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed

Analysis of an Inverse Problem Arising in Photolithography

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur

Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution

We present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead. This solution is derived by treating the nonlinearity in bending elasticity through the (topological) Bogomol'nyi decomposition technique and elastic compatibility. We recover the ``hat-model'' approximation in the limit of a small latex bead and find that the region antipodal to the grafted latex bead flattens. We also derive the appropriate shape equation using the variational principle and relevant constraints.Comment: 12 pages, 2 figures, LaTeX2e+REVTeX+AmSLaTe

Study of a degenerate dipolar Fermi gas of 161Dy atoms

We study properties of a single-component (spin polarized) degenerate dipolar Fermi gas of 161Dy atoms using a hydrodynamic description. Under axially-symmetric trapping we suggest reduced one- (1D) and two-dimensional (2D) description of the same for cigar and disk shapes, respectively. In addition to a complete numerical solution of the hydrodynamic model we also consider a variational approximation of the same. For a trapped system under appropriate conditions, the variational approximation as well as the reduced 1D and 2D models are found to yield results for shape, size and chemical potential of the system in agreement with the full numerical solution of the three-dimensional (3D) model. For the uniform system we consider anisotropic sound propagation in 3D. An analytical result for anisotropic sound propagation in uniform dipolar degenerate Fermi gas is found to be in agreement with results of numerical simulation in 3D

Quantum Monte Carlo Analysis of Exchange and Correlation in the Strongly Inhomogeneous Electron Gas

We use variational quantum Monte Carlo to calculate the density-functional exchange-correlation hole n_{xc}, the exchange-correlation energy density e_{xc}, and the total exchange-correlation energy E_{xc}, of several electron gas systems in which strong density inhomogeneities are induced by a cosine-wave potential. We compare our results with the local density approximation and the generalized gradient approximation. It is found that the nonlocal contributions to e_{xc} contain an energetically significant component, the magnitude, shape, and sign of which are controlled by the Laplacian of the electron density.Comment: 4 pages, 3 figure