Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

A feasibility study for advanced technology integration for general aviation

An investigation was conducted to identify candidate technologies and specific developments which offer greatest promise for improving safety, fuel efficiency, performance, and utility of general aviation airplanes. Interviews were conducted with general aviation airframe and systems manufacturers and NASA research centers. The following technologies were evaluated for use in airplane design tradeoff studies conducted during the study: avionics, aerodynamics, configurations, structures, flight controls, and propulsion. Based on industry interviews and design tradeoff studies, several recommendations were made for further high payoff research. The most attractive technologies for use by the general aviation industry appear to be advanced engines, composite materials, natural laminar flow airfoils, and advanced integrated avionics systems. The integration of these technologies in airplane design can yield significant increases in speeds, ranges, and payloads over present aircraft with 40 percent to 50 percent reductions in fuel used

On the induced gauge invariant mass

We derive a general expression for the gauge invariant mass (m_G) for an Abelian gauge field, as induced by vacuum polarization, in 1+1 dimensions. From its relation to the chiral anomaly, we show that m_G has to satisfy a certain quantization condition. This quantization can be, on the other hand, explicitly verified by using the exact general expression for the gauge invariant mass in terms of the fermion propagator. This result is applied to some explicit examples, exploring the possibility of having interesting physical situations where the value of $m_G$ departs from its canonical value. We also study the possibility of generalizing the results to the 2+1 dimensional case at finite temperature, showing that there are indeed situations where a finite and non-vanishing gauge invariant mass is induced.Comment: 18 pages, Latex, 3 figures (pstex

Coherent current transport in wide ballistic Josephson junctions

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances.Comment: 4 pages, 4 figure

Anyons as quon particles

The momentum operator representation of nonrelativistic anyons is developed in the Chern - Simons formulation of fractional statistics. The connection between anyons and the q-deformed bosonic algebra is established.Comment: 10 pages,Late

Operator Algebra in Chern-Simons Theory on a Torus

We consider Chern-Simons gauge theory on a torus with both nonrelativistic and relativistic matter. It is shown that the Hamiltonian and two total momenta commute among themselves only in the physical Hilbert space. We also discuss relations among degenerate physical states, degenerate vacua, and the existence of multicomponent Schrodinger wavefunctions.Comment: 12 pages, TPI-Minn-92/41-T, UMN-TH-1105/9

Spin transport of electrons through quantum wires with spatially-modulated strength of the Rashba spin-orbit interaction

We study ballistic transport of spin-polarized electrons through quantum wires in which the strength of the Rashba spin-orbit interaction (SOI) is spatially modulated. Subband mixing, due to SOI, between the two lowest subbands is taken into account. Simplified approximate expressions for the transmission are obtained for electron energies close to the bottom of the first subband and near the value for which anticrossing of the two lowest subbands occurs. In structures with periodically varied SOI strength, {\it square-wave} modulation on the spin transmission is found when only one subband is occupied and its possible application to the spin transistor is discussed. When two subbands are occupied the transmission is strongly affected by the existence of SOI interfaces as well as by the subband mixing

Medium Effects on Binary Collisions with the Delta Resonance

To facilitate the relativistic heavy-ion calculations based on transport equations, the binary collisions involving a $\Delta$ resonance in either the entrance channel or the exit channel are investigated within a Hamiltonian formulation of $\pi NN$ interactions. An averaging procedure is developed to define a quasi-particle $\Delta^*$ and to express the experimentally measured $NN\rightarrow \pi NN$ cross section in terms of an effective $NN\rightarrow N\Delta^\ast$ cross section. In contrast to previous works, the main feature of the present approach is that the mass and the momentum of the produced $\Delta^*$'s are calculated dynamically from the bare $\Delta \leftrightarrow \pi N$ vertex interaction of the model Hamiltonian and are constrained by the unitarity condition. The procedure is then extended to define the effective cross sections for the experimentally inaccessible $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions. The predicted cross sections are significantly different from what are commonly assumed in relativistic heavy-ion calculations. The $\Delta$ potential in nuclear matter has been calculated by using a Bruckner-Hartree-Fock approximation. By including the mean-field effects on the $\Delta$ propagation, the effective cross sections of the $NN\rightarrow N\Delta^\ast$, $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions in nuclear matter are predicted. It is demonstrated that the density dependence is most dramatic in the energy region close to the pion production threshold.Comment: 20 pages, RevTe

Ballistic spin-polarized transport and Rashba spin precession in semiconductor nanowires

We present numerical calculations of the ballistic spin-transport properties of quasi-one-dimensional wires in the presence of the spin-orbit (Rashba) interaction. A tight-binding analog of the Rashba Hamiltonian which models the Rashba effect is used. By varying the robustness of the Rashba coupling and the width of the wire, weak and strong coupling regimes are identified. Perfect electron spin-modulation is found for the former regime, regardless of the incident Fermi energy and mode number. In the latter however, the spin-conductance has a strong energy dependence due to a nontrivial subband intermixing induced by the strong Rashba coupling. This would imply a strong suppression of the spin-modulation at higher temperatures and source-drain voltages. The results may be of relevance for the implementation of quasi-one-dimensional spin transistor devices.Comment: 19 pages (incl. 9 figures). To be published in PR