Predicting Flows of Rarefied Gases

DSMC Analysis Code (DAC) is a flexible, highly automated, easy-to-use computer program for predicting flows of rarefied gases -- especially flows of upper-atmospheric, propulsion, and vented gases impinging on spacecraft surfaces. DAC implements the direct simulation Monte Carlo (DSMC) method, which is widely recognized as standard for simulating flows at densities so low that the continuum-based equations of computational fluid dynamics are invalid. DAC enables users to model complex surface shapes and boundary conditions quickly and easily. The discretization of a flow field into computational grids is automated, thereby relieving the user of a traditionally time-consuming task while ensuring (1) appropriate refinement of grids throughout the computational domain, (2) determination of optimal settings for temporal discretization and other simulation parameters, and (3) satisfaction of the fundamental constraints of the method. In so doing, DAC ensures an accurate and efficient simulation. In addition, DAC can utilize parallel processing to reduce computation time. The domain decomposition needed for parallel processing is completely automated, and the software employs a dynamic load-balancing mechanism to ensure optimal parallel efficiency throughout the simulation

Analysis of Plume Impingement Effects from Orion Crew Service Module Dual Reaction Control System Engine Firings

Plume impingement effects on the Orion Crew Service Module (CSM) were analyzed for various dual Reaction Control System (RCS) engine firings and various configurations of the solar arrays. The study was performed using a decoupled computational fluid dynamics (CFD) and Direct Simulation Monte Carlo (DSMC) approach. This approach included a single jet plume solution for the R1E RCS engine computed with the General Aerodynamic Simulation Program (GASP) CFD code. The CFD solution was used to create an inflow surface for the DSMC solution based on the Bird continuum breakdown parameter. The DSMC solution was then used to model the dual RCS plume impingement effects on the entire CSM geometry with deployed solar arrays. However, because the continuum breakdown parameter of 0.5 could not be achieved due to geometrical constraints and because high resolution in the plume shock interaction region is desired, a focused DSMC simulation modeling only the plumes and the shock interaction region was performed. This high resolution intermediate solution was then used as the inflow to the larger DSMC solution to obtain plume impingement heating, forces, and moments on the CSM and the solar arrays for a total of 21 cases that were analyzed. The results of these simulations were used to populate the Orion CSM Aerothermal Database

Resonance-free Region in scattering by a strictly convex obstacle

We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonances lie below a cubic curve which is the same as in the case of the Neumann boundary condition. This generalizes earlier results on cubic poles free regions obtained for the Dirichlet boundary condition.Comment: 29 pages, 2 figure

Nucleation of Stable Superconductivity in YBCO-Films

By means of the linear dynamic conductivity, inductively measured on epitaxial films between 30mHz and 30 MHz, the transition line $T_g (B)$ to generic superconductivity is studied in fields between B=0 and 19T. It follows closely the melting line $T_m (B)$ described recently in terms of a blowout of thermal vortex loops in clean materials. The critical exponents of the correlation length and time near $T_g (B)$, however, seem to be dominated by some intrinsic disorder. Columnar defects produced by heavy-ion irradiation up to field-equivalent-doses of $B_{\phi} = 10T$ lead to a disappointing reduction of $T_g (B \to 0)$ while for $B>B_{\phi}$ the generic line of the pristine film is recovered. These novel results are also discussed in terms of a loop-driven destruction of generic superconductivity.Comment: 11 pages including 7 EPS figures, accepted for publication in the Proceedings of the Spring Meeting of the German Physical Society, Muenster 1999,Festkoerperprobleme/Advances in Solid State Physics 199

Limiting Carleman weights and anisotropic inverse problems

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic X-ray transform. Earlier results in dimension $n \geq 3$ were restricted to real-analytic metrics.Comment: 58 page

Axisymmetric Implementation for 3D-Based DSMC Codes

The primary objective in developing NASA s DSMC Analysis Code (DAC) was to provide a high fidelity modeling tool for 3D rarefied flows such as vacuum plume impingement and hypersonic re-entry flows [1]. The initial implementation has been expanded over time to offer other capabilities including a novel axisymmetric implementation. Because of the inherently 3D nature of DAC, this axisymmetric implementation uses a 3D Cartesian domain and 3D surfaces. Molecules are moved in all three dimensions but their movements are limited by physical walls to a small wedge centered on the plane of symmetry (Figure 1). Unfortunately, far from the axis of symmetry, the cell size in the direction perpendicular to the plane of symmetry (the Z-direction) may become large compared to the flow mean free path. This frequently results in inaccuracies in these regions of the domain. A new axisymmetric implementation is presented which aims to solve this issue by using Bird s approach for the molecular movement while preserving the 3D nature of the DAC software [2]. First, the computational domain is similar to that previously used such that a wedge must still be used to define the inflow surface and solid walls within the domain. As before molecules are created inside the inflow wedge triangles but they are now rotated back to the symmetry plane. During the move step, molecules are moved in 3D but instead of interacting with the wedge walls, the molecules are rotated back to the plane of symmetry at the end of the move step. This new implementation was tested for multiple flows over axisymmetric shapes, including a sphere, a cone, a double cone and a hollow cylinder. Comparisons to previous DSMC solutions and experiments, when available, are made

Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde

Nonlinear Seebeck Effect in a Model Granular Superconductor

The change of the Josephson supercurrent density of a weakly-connected granular superconductor in response to externally applied arbitrary thermal gradient dT/dx (nonlinear Seebeck effect) is considered within a model of 3D Josephson junction arrays. For dT/dx>(dT/dx)_c, where (dT/dx)_c is estimated to be of the order of 10^4 K/m for YBCO ceramics with an average grain's size of 10 microns, the weak-links-dominated thermopower S (Seebeck coefficient) is predicted to become strongly dT/dx-dependent.Comment: REVTEX, no figure

Scattering frequencies and Gervey 3 singularities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46619/1/222_2005_Article_BF01389032.pd

An inverse source problem for the heat equation and the enclosure method

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given.Comment: 23page