Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions on the degree of the Forchheimer polynomial are imposed. We derive, for all time, the interior $L^\infty$-estimates for the pressure and its partial derivatives, and the interior $L^2$-estimates for its Hessian. The De Giorgi and Ladyzhenskaya-Uraltseva iteration techniques are used taking into account the special structures of the equations for both pressure and its gradient. These are combined with the uniform Gronwall-type bounds in establishing the asymptotic estimates when time tends to infinity

The Capillary Pumped Loop Flight Experiment (CAPL): A pathfinder for EOS

The CAPL shuttle flight experiment will provide microgravity verification of the prototype capillary pumped loop (CPL) thermal control system for EOS. The design of the experiment is discussed with particular emphasis on the new technology areas in ammonia two-phase reservior design and heat pipe heat exchanger development. The thermal and hydrodynamic analysis techniques and results are also presented, including pressure losses, fluid flow, and non-orbit heat rejection capability. CAPL experiment results will be presented after the flight, presently planned for 1993

A family of steady two-phase generalized Forchheimer flows and their linear stability analysis

We model multi-dimensional two-phase flows of incompressible fluids in porous media using generalized Forchheimer equations and the capillary pressure. Firstly, we find a family of steady state solutions whose saturation and pressure are radially symmetric and velocities are rotation-invariant. Their properties are investigated based on relations between the capillary pressure, each phase's relative permeability and Forchheimer polynomial. Secondly, we analyze the linear stability of those steady states. The linearized system is derived and reduced to a parabolic equation for the saturation. This equation has a special structure depending on the steady states which we exploit to prove two new forms of the lemma of growth of Landis-type in both bounded and unbounded domains. Using these lemmas, qualitative properties of the solution of the linearized equation are studied in details. In bounded domains, we show that the solution decays exponentially in time. In unbounded domains, in addition to their stability, the solution decays to zero as the spatial variables tend to infinity. The BernsteinComment: 33 page

Properties of Generalized Forchheimer Flows in Porous Media

The nonlinear Forchheimer equations are used to describe the dynamics of fluid flows in porous media when Darcy's law is not applicable. In this article, we consider the generalized Forchheimer flows for slightly compressible fluids and study the initial boundary value problem for the resulting degenerate parabolic equation for pressure with the time-dependent flux boundary condition. We estimate $L^\infty$-norm for pressure and its time derivative, as well as other Lebesgue norms for its gradient and second spatial derivatives. The asymptotic estimates as time tends to infinity are emphasized. We then show that the solution (in interior $L^\infty$-norms) and its gradient (in interior $L^{2-\delta}$-norms) depend continuously on the initial and boundary data, and coefficients of the Forchheimer polynomials. These are proved for both finite time intervals and time infinity. The De Giorgi and Ladyzhenskaya-Uraltseva iteration techniques are combined with uniform Gronwall-type estimates, specific monotonicity properties, suitable parabolic Sobolev embeddings and a new fast geometric convergence result.Comment: 63 page

Spinning Dust Emission: Effects of irregular grain shape, transient heating and comparison with WMAP results

Planck is expected to answer crucial questions on the early Universe, but it also provides further understanding on anomalous microwave emission. Electric dipole emission from spinning dust grains continues to be the favored interpretation of anomalous microwave emission. In this paper, we present a method to calculate the rotational emission from small grains of irregular shape with moments of inertia $I_{1}> I_{2}> I_{3}$. We show that a torque-free rotating irregular grain with a given angular momentum radiates at multiple frequency modes. The resulting spinning dust spectrum has peak frequency and emissivity increasing with the degree of grain shape irregularity, which is defined by $I_{1}:I_{2}:I_{3}$. We discuss how the orientation of dipole moment \bmu in body coordinates affects the spinning dust spectrum for different regimes of internal thermal fluctuations. We show that the spinning dust emissivity for the case of strong thermal fluctuations is less sensitive to the orientation of \bmu than in the case of weak thermal fluctuations. We calculate spinning dust spectra for a range of gas density and dipole moment. The effect of compressible turbulence on spinning dust emission intensity is investigated. We show that the emission intensity in a turbulent medium increases by a factor from 1.2-1.4 relative to that in a uniform medium, as sonic Mach number $M_{s}$ increases from 2-7. Finally, spinning dust parameters are constrained by fitting our improved model to five-year {\it Wilkinson Microwave Anisotropy Probe} cross-correlation foreground spectra, for both the H$\alpha$-correlated and 100 $\mu$m-correlated emission spectra.Comment: 24 pages, 17 figures, relation to molecular rotation spectra added, accepted by Astrophysical Journa