Longitudinal control effectiveness and entry dynamics of a single-stage-to-orbit vehicle

The classical theory of flight dynamics for airplane longitudinal stability and control analysis was extended to the case of a hypervelocity reentry vehicle. This includes the elements inherent in supersonic and hypersonic flight such as the influence of the Mach number on aerodynamic characteristics, and the effect of the reaction control system and aerodynamic controls on the trim condition through a wide range of speed. Phugoid motion and angle of attack oscillation for typical cases of cruising flight, ballistic entry, and glide entry are investigated. In each case, closed form solutions for the variations in altitude, flight path angle, speed and angle of attack are obtained. The solutions explicitly display the influence of different regions design parameters and trajectory variables on the stability of the motion

Twisted and Nontwisted Bifurcations Induced by Diffusion

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex files. Hard copy of figures available on request from [email protected]

Room-temperature lasing action in GaN quantum wells in the infrared 1.5 micron region

Large-scale optoelectronics integration is strongly limited by the lack of efficient light sources, which could be integrated with the silicon complementary metal-oxide-semiconductor (CMOS) technology. Persistent efforts continue to achieve efficient light emission from silicon in the extending the silicon technology into fully integrated optoelectronic circuits. Here, we report the realization of room-temperature stimulated emission in the technologically crucial 1.5 micron wavelength range from Er-doped GaN multiple-quantum wells on silicon and sapphire. Employing the well-acknowledged variable stripe technique, we have demonstrated an optical gain up to 170 cm-1 in the multiple-quantum well structures. The observation of the stimulated emission is accompanied by the characteristic threshold behavior of emission intensity as a function of pump fluence, spectral linewidth narrowing and excitation length. The demonstration of room-temperature lasing at the minimum loss window of optical fibers and in the eye-safe wavelength region of 1.5 micron are highly sought-after for use in many applications including defense, industrial processing, communication, medicine, spectroscopy and imaging. As the synthesis of Er-doped GaN epitaxial layers on silicon and sapphire has been successfully demonstrated, the results laid the foundation for achieving hybrid GaN-Si lasers providing a new pathway towards full photonic integration for silicon optoelectronics.Comment: 23 pages, 3 figure

Bose-Einstein supersolid phase for a novel type of momentum dependent interaction

A novel class of non-local interactions between bosons is found to favor a crystalline Bose-Einstein condensation ground state. By using both low energy effective field theory and variational wavefunction method, we compare this state not only with the homogeneous superfluid, as has been done previously, but also with the normal (non-superfluid) crystalline phase and obtain the phase diagram. The key characters are: the interaction potential displays a negative minimum at finite momentum which determines the wavevector of this supersolid phase; and the wavelength corresponding to the momentum minimum needs to be greater than the mean inter-boson distance.Comment: 4 pages 3 figures, fig 1 and fig 2 update

On the IMF in a Triggered Star Formation Context

The origin of the stellar initial mass function (IMF) is a fundamental issue in the theory of star formation. It is generally fit with a composite power law. Some clues on the progenitors can be found in dense starless cores that have a core mass function (CMF) with a similar shape. In the low-mass end, these mass functions increase with mass, albeit the sample may be somewhat incomplete; in the high-mass end, the mass functions decrease with mass. There is an offset in the turn-over mass between the two mass distributions. The stellar mass for the IMF peak is lower than the corresponding core mass for the CMF peak in the Pipe Nebula by about a factor of three. Smaller offsets are found between the IMF and the CMFs in other nebulae. We suggest that the offset is likely induced during a starburst episode of global star formation which is triggered by the formation of a few O/B stars in the multi-phase media, which naturally emerged through the onset of thermal instability in the cloud-core formation process. We consider the scenario that the ignition of a few massive stars photoionizes the warm medium between the cores, increases the external pressure, reduces their Bonnor?Ebert mass, and triggers the collapse of some previously stable cores. We quantitatively reproduce the IMF in the low-mass end with the assumption of additional rotational fragmentation.Comment: 3 figure

Numerical Simulation of Free-fountains in a Homogeneous Fluid

The behaviour of plane fountains, resulting from the injection of dense fluid upwards into a large container of homogeneous fluid of lower density, is investigated. The transient behaviour of fountains with parabolic inlet velocity profile and Reynolds numbers, 50 ≤ Re ≤ 150, Prandtl numbers, Pr=7, 300 and 700, and Froude numbers, Fr = 0.25 to 10.0 are studied numerically. The fountain behaviour falls into three distinct regimes; steady and symmetric; unsteady and periodic flapping; unsteady and aperiodic. The analytical scaling of nondimensional fountain height, zm, with Fr and Re is zm ∼ Fr4/3−2γ/3Re−γ. The constant γ is found empirically for each of the regimes. The fountain height decreases with increase in Reynolds number in the steady region but increases with Reynolds number in the unsteady regimes. However, the fountain height increases with Froude number in all regimes. Numerical results and the analytical scaling show that zm is independent of Prandtl number in the range considered. The fountain exhibits periodic lateral oscillations, i.e., periodic flapping for intermediate Froude numbers ranging from 1.25 ≤ Fr ≤ 2.25