Multiple buoyancy driven flows in a vertical cylinder heated from below

The structure of axisymmetric buoyancy-driven convection in a vertical cylinder heated from below is probed by finite element solution of the Boussinesq equations coupled with computed-implemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with Prandtl number of one and for cylinders with aspect ratio (Lambda) (defined as the height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curve for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous evolution of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shear-free sidewalls. The smooth transitions in flow structure with Rayleigh number and lambda are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Lambda or = Lambda * approximately 0.80 or by a limit point for Lambda Lambda *. The transition between these two modes may be described by the theory of multiple limit point bifurcation

Acoustic fatigue and sound transmission characteristics of a ram composite panel design

An experimental study to determine the acoustic fatigue characteristics of a flat multi-layered structural panel is described. The test panel represented a proposed design for the outer skin of a research application module to be housed within the space shuttle orbiter vehicle. The test specimen was mounted in one wall of the Wyle 100,000 cu ft reverberation room and exposed to a broadband acoustic environment having an overall level of 145 db. The test panel was exposed to nine separate applications of the acoustic environment, each application consisting of 250 seconds duration. Upon completion of the ninth test run, the specimen was exposed to a simulated micrometeoroid impact near the panel center. One additional test run of 250 seconds duration was then performed to complete the overall simulation of 50 flight missions. The experimental results show that no significant fatigue damage occurred until the test specimen was exposed to a simulated micrometeoroid impact. The intermediate foam layer forming the core of the test specimen suffered considerable damage due to this impact, causing a marked variation in the dynamic characteristics of the overall test panel. During the final application of the acoustic environment, the strain and acceleration response spectra showed considerable variation from those spectra obtained prior to impact of the panel. Fatigue damage from acoustic loading however, was limited to partial de-bonding around the edges of the composite panel

Quantum Thetas on Noncommutative T^4 from Embeddings into Lattice

In this paper we investigate the theta vector and quantum theta function over noncommutative T^4 from the embedding of R x Z^2. Manin has constructed the quantum theta functions from the lattice embedding into vector space (x finite group). We extend Manin's construction of the quantum theta function to the embedding of vector space x lattice case. We find that the holomorphic theta vector exists only over the vector space part of the embedding, and over the lattice part we can only impose the condition for Schwartz function. The quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function. However, two subsequent quantum translations from the embedding into the lattice part are non-additive, contrary to the additivity of those from the vector space part.Comment: 20 pages, LaTeX, version to appear in J. Phys.

Self-compensation in manganese-doped ferromagnetic semiconductors

We present a theory of interstitial Mn in Mn-doped ferromagnetic semiconductors. Using density-functional theory, we show that under the non-equilibrium conditions of growth, interstitial Mn is easily formed near the surface by a simple low-energy adsorption pathway. In GaAs, isolated interstitial Mn is an electron donor, each compensating two substitutional Mn acceptors. Within an impurity-band model, partial compensation promotes ferromagnetic order below the metal-insulator transition, with the highest Curie temperature occurring for 0.5 holes per substitutional Mn.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

A current disruption mechanism in the neutral sheet for triggering substorm expansions

Two main areas were addressed in support of an effort to understand mechanism responsible for the broadband electrostatic noise (BEN) observed in the magnetotail. The first area concerns the generation of BEN in the boundary layer region of the magnetotail whereas the second area concerns the occassional presence of BEN in the neutral sheet region. For the generation of BEN in the boundary layer region, a hybrid simulation code was developed to perform reliable longtime, quiet, highly resolved simulations of field aligned electron and ion beam flow. The result of the simulation shows that broadband emissions cannot be generated by beam-plasma instability if realistic values of the ion beam parameters are used. The waves generated from beam-plasma instability are highly discrete and are of high frequencies. For the plasma sheet boundary layer condition, the wave frequencies are in the kHz range, which is incompatible with the observation that the peak power in BEN occur in the 10's of Hz range. It was found that the BEN characteristics are more consistent with lower hybrid drift instability. For the occasional presence of BEN in the neutral sheet region, a linear analysis of the kinetic cross-field streaming instability appropriate to the neutral sheet condition just prior to onset of substorm expansion was performed. By solving numerically the dispersion relation, it was found that the instability has a growth time comparable to the onset time scale of substorm onset. The excited waves have a mixed polarization in the lower hybrid frequency range. The imposed drift driving the instability corresponds to unmagnetized ions undergoing current sheet acceleration in the presence of a cross-tail electric field. The required electric field strength is in the 10 mV/m range which is well within the observed electric field values detected in the neutral sheet during substorms. This finding can potentially account for the disruption of cross-tail current and its diversion to the ionosphere to form the substorm current wedge. Furthermore, a number of features associated with substorm expansion onset can be understood based on this substorm onset scenario

Vacuum Energy Density and Cosmological Constant in dS Brane World

We discuss the vacuum energy density and the cosmological constant of dS$_5$ brane world with a dilaton field. It is shown that a stable AdS$_4$ brane can be constructed and gravity localization can be realized. An explicit relation between the dS bulk cosmological constant and the brane cosmological constant is obtained. The discrete mass spectrum of the massive scalar field in the AdS$_4$ brane is used to acquire the relationship between the brane cosmological constant and the vacuum energy density. The vacuum energy density in the brane gotten by this method is in agreement with astronomical observations.Comment: 16 pages,4 figure

The effect of in-plane magnetic field on the spin Hall effect in Rashba-Dresselhaus system

In a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit couplings, there are two spin-split energy surfaces connected with a degenerate point. Both the energy surfaces and the topology of the Fermi surfaces can be varied by an in-plane magnetic field. We find that, if the chemical potential falls between the bottom of the upper band and the degenerate point, then simply by changing the direction of the magnetic field, the magnitude of the spin Hall conductivity can be varied by about 100 percent. Once the chemical potential is above the degenerate point, the spin Hall conductivity becomes the constant $e/8\pi$, independent of the magnitude and direction of the magnetic field. In addition, we find that the in-plane magnetic field exerts no influence on the charge Hall conductivity.Comment: 11 pages, 3 figures, to be published on Phys. Rev.

The magnetic dipole transitions in the (cbˉ)(c\bar{b}) binding system

The magnetic dipole transitions between the vector mesons $B_c^*$ and their relevant pseudoscalar mesons $B_c$ ($B_c$, $B_c^*$, $B_c(2S)$, $B_c^*(2S)$, $B_c(3S)$ and $B_c^*(3S)$ etc, the binding states of $(c\bar{b})$ system) of the $B_c$ family are interesting. To see the `hyperfine' splitting due to spin-spin interaction is an important topic for understanding the spin-spin interaction and the spectrum of the the $(c\bar{b})$ binding system. The knowledge about the magnetic dipole transitions is also very useful for identifying the vector boson $B_c^*$ mesons experimentally, whose masses are just slightly above the masses of their relevant pseudoscalar mesons $B_c$ accordingly. Considering the possibility to observe the vector mesons via the transitions at $Z^0$ factory and the potentially usages of the theoretical estimate on the transitions, we fucus our efforts on calculating the magnetic dipole transitions, i.e. precisely to calculate the rates for the transitions such as decays $B_c^*\to B_c\gamma$ and $B_c^*\to B_c e^+e^-$, and particularly work in the Behte-Salpeter framework. In the estimate, as a typical example, we carefully investigate the dependance of the rate $\Gamma(B_c^*\to B_c\gamma)$ on the mass difference $\Delta M=M_{B_c^*}-M_{B_c}$ as well.Comment: 10 pages, 2 figures, 1 tabl

Inclusive Decays of Bottom Hadrons in New Formulation of Heavy Quark Effective Field Theory

We apply the new formulation of heavy quark effective field theory (HQEFT) to the inclusive decays of bottom hadrons. The long-term ambiguity of using heavy quark mass or heavy hadron mass for inclusive decays is clarified within the framework of the new formulation of HQEFT. The $1/m_b$ order corrections are absent and contributions from $1/m_b^2$ terms are calculated in detail. This enables us to reliably extract the important CKM matrix element $|V_{cb}|$ from the inclusive semileptonic decay rates. The resulting lifetime ratios $\tau(B^0_s)/\tau(B^0)$ and $\tau(\Lambda_b)/\tau(B^0)$ are found to well agree with the experimental data. We also calculate in detail the inclusive semileptonic branching ratios and the ratios of the $\tau$ and $\beta$ decay rates as well as the charm countings in the $B^0$, $B^0_s$ and $\Lambda_b$ systems. For $B^0$ decays, all the observables are found to be consistent with the experimental data. More precise data for the $B^0$ decays and further experimental measurements for the $B^0_s$ and $\Lambda_b$ systems will be very useful for testing the framework of new formulation of HQEFT at the level of higher order corrections.Comment: 20 pages, RevTex, 8 figures, 3 tables, revised version with `dressed heavy quark' being addressed, to be published in Int. J. Mod. Phys.