Numerical calculation of transonic boattail flow

A viscid-inviscid interaction procedure for the calculation of subsonic and transonic flow over a boattail was developed. This method couples a finite-difference inviscid analysis with an integral boundary-layer technique. Results indicate that the effect of the boundary layer is as important as an accurate inviscid method for this type of flow. Theoretical results from the solution of the full transonic-potential equation, including boundary layer effects, agree well with the experimental pressure distribution for a boattail. Use of the small disturbance transonic potential equation yielded results that did not agree well with the experimental results even when boundary-layer effects were included in the calculations

Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

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]

Giant Modal Gain, Amplified Surface Plasmon Polariton Propagation, and Slowing Down of Energy Velocity in a Metal-Semiconductor-Metal Structure

We investigated surface plasmon polariton (SPP) propagation in a metal-semiconductor-metal structure where semiconductor is highly excited to have optical gain. We show that near the SPP resonance, the imaginary part of the propagation wavevector changes from positive to hugely negative, corresponding to an amplified SPP propagation. The SPP experiences a giant gain that is 1000 times of material gain in the excited semiconductor. We show that such a giant gain is related to the slowing down of average energy propagation in the structur

Remarks on the extension of the Ricci flow

We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.Comment: 9 pages, to appear in Journal of Geometric Analysi

Positive Vibrational Entropy of Chemical Ordering in FeV

Inelastic neutron scattering and nuclear resonant inelastic x-ray scattering were used to measure phonon spectra of FeV as a B2 ordered compound and as a bcc solid solution. The two data sets were combined to give an accurate phonon density of states, and the phonon partial densities of states for V and Fe atoms. Contrary to the behavior of ordering alloys studied to date, the phonons in the B2 ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy by +0.22±0.03k_B/atom, which stabilizes the ordered phase to higher temperatures. First-principles calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites