Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential

We prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen'ev-Peskov (1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked

Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions

We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some uniform bounds on some hydrodynamic quantities. This lower bound is independent of time and space. When the collision kernel satisfies Grad's cutoff assumption, the lower bound is a global Maxwellian and its asymptotic behavior in velocity is optimal, whereas for non-cutoff collision kernels the lower bound we obtain decreases exponentially but faster than the Maxwellian. Our results cover solutions constructed in a spatially homogeneous setting, as well as small-time or close-to-equilibrium solutions to the full Boltzmann equation in the torus. The constants are explicit and depend on the a priori bounds on the solution.Comment: 37 page

Aerodynamic characteristics of a supersonic cruise airplane configuration at Mach numbers of 2.30, 2.96, and 3.30

An investigation was made in the Langley Unitary Plan wind tunnel at Mach numbers of 2.30, 2.96, and 3.30 to determine the static longitudinal and lateral aerodynamic characteristics of a model of a supersonic cruise airplane. The configuration, with a design Mach number of 3.0, has a highly swept arrow wing with tip panels of lesser sweep, a fuselage chine, outboard vertical tails, and outboard engines mounted in nacelles beneath the wings. For wind tunnel test conditions, a trimmed value above 6.0 of the maximum lift-drag ratio was obtained at the design Mach number. The configuration was statically stable, both longitudinally and laterally. Data are presented for variations of vertical-tail roll-out and toe-in and for various combinations of components. Some roll control data are shown as are data for the various sand grit sizes used in fixing the boundary layer transition location

Pinsker estimators for local helioseismology

A major goal of helioseismology is the three-dimensional reconstruction of the three velocity components of convective flows in the solar interior from sets of wave travel-time measurements. For small amplitude flows, the forward problem is described in good approximation by a large system of convolution equations. The input observations are highly noisy random vectors with a known dense covariance matrix. This leads to a large statistical linear inverse problem. Whereas for deterministic linear inverse problems several computationally efficient minimax optimal regularization methods exist, only one minimax-optimal linear estimator exists for statistical linear inverse problems: the Pinsker estimator. However, it is often computationally inefficient because it requires a singular value decomposition of the forward operator or it is not applicable because of an unknown noise covariance matrix, so it is rarely used for real-world problems. These limitations do not apply in helioseismology. We present a simplified proof of the optimality properties of the Pinsker estimator and show that it yields significantly better reconstructions than traditional inversion methods used in helioseismology, i.e.\ Regularized Least Squares (Tikhonov regularization) and SOLA (approximate inverse) methods. Moreover, we discuss the incorporation of the mass conservation constraint in the Pinsker scheme using staggered grids. With this improvement we can reconstruct not only horizontal, but also vertical velocity components that are much smaller in amplitude

Field-dependent diamagnetic transition in magnetic superconductor Sm1.85Ce0.15CuO4−ySm_{1.85} Ce_{0.15} Cu O_{4-y}

The magnetic penetration depth of single crystal $\rm{Sm_{1.85}Ce_{0.15}CuO_{4-y}}$ was measured down to 0.4 K in dc fields up to 7 kOe. For insulating $\rm{Sm_2CuO_4}$, Sm$^{3+}$ spins order at the N\'{e}el temperature, $T_N = 6$ K, independent of the applied field. Superconducting $\rm{Sm_{1.85}Ce_{0.15}CuO_{4-y}}$ ($T_c \approx 23$ K) shows a sharp increase in diamagnetic screening below $T^{\ast}(H)$ which varied from 4.0 K ($H = 0$) to 0.5 K ($H =$ 7 kOe) for a field along the c-axis. If the field was aligned parallel to the conducting planes, $T^{\ast}$ remained unchanged. The unusual field dependence of $T^{\ast}$ indicates a spin freezing transition that dramatically increases the superfluid density.Comment: 4 pages, RevTex

Distributed upper-surface blowing concept

A low speed investigation was conducted in the Langley V/STOL tunnel to determine the powered lift aerodynamic performance of a distributed upper surface blown propulsive lift transport model. The model used blowing slots across the span of the wing to produce a thin jet efflux near the leading edge and at the knee of the trailing edge flap (internally blown jet flap). Results indicate that these concepts have both good propulsive related lift and low drag due to lift characteristics because of uniform spanwise propulsive thrust. The leading edge blowing concept provides low speed lift characteristics which are competitive with the flap-hinge-line blowing concept and does not require additional leading edge treatment for prevention of abrupt stall