Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System

We study the Hilbert expansion for small Knudsen number $\varepsilon$ for the Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi \theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\theta_{0}(t,x)},\text{\ }\theta_{0}(t,x)=K\rho_{0}^{2/3}(t,x).$Our main result states that if the Hilbert expansion is valid at$t=0$for well-prepared small initial data with irrotational velocity$u_0$, then it is valid for$0\leq t\leq \varepsilon ^{-{1/2}\frac{2k-3}{2k-2}},$where$\rho_{0}(t,x)$and$ u_{0}(t,x)$satisfy the Euler-Poisson system for monatomic gas$\gamma=5/3$

Conductance spectra of metallic nanotube bundles

We report a first principles analysis of electronic transport characteristics for (n,n) carbon nanotube bundles. When n is not a multiple of 3, inter-tube coupling causes universal conductance suppression near Fermi level regardless of the rotational arrangement of individual tubes. However, when n is a multiple of 3, the bundles exhibit a diversified conductance dependence on the orientation details of the constituent tubes. The total energy of the bundle is also sensitive to the orientation arrangement only when n is a multiple of 3. All the transport properties and band structures can be well understood from the symmetry consideration of whether the rotational symmetry of the individual tubes is commensurate with that of the bundle

Spin singlet pairing in the superconducting state of NaxCoO2\cdot1.3H2O: evidence from a ^{59}Co Knight shift in a single crystal

We report a ^{59}Co Knight shift measurement in a single crystal of the cobalt oxide superconductor Na_{x}CoO_2\cdot1.3H_2O (T_c=4.25 K). We find that the shift due to the spin susceptibility, K^s, is substantially large and anisotropic, with the spin shift along the a-axis K^s_a being two times that along the c-axis K^s_c. The shift decreases with decreasing temperature (T) down to T\sim100 K, then becomes a constant until superconductivity sets in. Both K^s_a and K^s_c decrease below T_c. Our results indicate unambiguously that the electron pairing in the superconducting state is in the spin singlet form.Comment: 4 pages, 5 figure

Integrated health monitoring and controls for rocket engines

Current research in intelligent control systems at the Lewis Research Center is described in the context of a functional framework. The framework is applicable to a variety of reusable space propulsion systems for existing and future launch vehicles. It provides a 'road map' technology development to enable enhanced engine performance with increased reliability, durability, and maintainability. The framework hierarchy consists of a mission coordination level, a propulsion system coordination level, and an engine control level. Each level is described in the context of the Space Shuttle Main Engine. The concept of integrating diagnostics with control is discussed within the context of the functional framework. A distributed real time simulation testbed is used to realize and evaluate the functionalities in closed loop

Observation of an in-plane magnetic-field-driven phase transition in a quantum Hall system with SU(4) symmetry

In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving rise to a novel ground state. For example, pseudospin quantum Hall ferromagnet of broken SU(2) symmetry has been realized by bringing two Landau levels close to degeneracy in a bilayer quantum Hall system. In the past several years, the exploration of collective states in other multi-component quantum Hall systems has emerged. Here we show the conventional pseudospin quantum Hall ferromagnetic states with broken SU(2) symmetry collapsed rapidly into an unexpected state with broken SU(4) symmetry, by in-plane magnetic field in a two-subband GaAs/AlGaAs two-dimensional electron system at filling factor around $\nu=4$. Within a narrow tilting range angle of 0.5 degrees, the activation energy increases as much as 12 K. While the origin of this puzzling observation remains to be exploited, we discuss the possibility of a long-sought pairing state of electrons with a four-fold degeneracy.Comment: 13 pages, 4 figure

Decay and Continuity of Boltzmann Equation in Bounded Domains

Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: inflow, bounce-back reflection, specular reflection, and diffuse reflection. We establish exponential decay in $L^{\infty}$ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set of the velocity at the boundary. Our contribution is based on a new $L^{2}$ decay theory and its interplay with delicate $$ decay analysis for the linearized Boltzmann equation, in the presence of many repeated interactions with the boundary.Comment: 89 pages

The private capacity of quantum channels is not additive

Recently there has been considerable activity on the subject of additivity of various quantum channel capacities. Here, we construct a family of channels with sharply bounded classical, hence private capacity. On the other hand, their quantum capacity when combined with a zero private (and zero quantum) capacity erasure channel, becomes larger than the previous classical capacity. As a consequence, we can conclude for the first time that the classical private capacity is non-additive. In fact, in our construction even the quantum capacity of the tensor product of two channels can be greater than the sum of their individual classical private capacities. We show that this violation occurs quite generically: every channel can be embedded into our construction, and a violation occurs whenever the given channel has larger entanglement assisted quantum capacity than (unassisted) classical capacity.Comment: 4+4 pages, 2 eps figures. V2 has title and abstract changed; its new structure reflects the final version of a main paper plus appendices containing mathematical detail

Hilbert Expansion from the Boltzmann equation to relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.Comment: 50 page