Averaging approximation to singularly perturbed nonlinear stochastic wave equations

An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq n\leq 3$\,. Here $\nu>0$ is a small parameter characterising the singular perturbation, and $\nu^\alpha$\,, $0\leq \alpha\leq 1/2$\,, parametrises the strength of the noise. Some scaling transformations and the martingale representation theorem yield the following effective approximation for small $\nu$, u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of \ord{\nu^\alpha}\,.Comment: 16 pages. Submitte

Installed performance of air-augmented nozzles based on analytical determination of internal ejector characteristics

Procedures for matching intake and ejector pumping characteristics of air-augmented nozzle

Micro-Raman Spectroscopy In The Undergraduate Research Laboratory

Modern materials science requires processing and characterization techniques for microscopic structures. Molecular probes such as Raman spectroscopy are some of the most viable tools, particularly if they are supplemented by imaging to obtain spatially resolved compositional information of inhomogeneous or low volume samples. In order to introduce these techniques and materials science experiments into the advanced undergraduate laboratory, we have constructed an inexpensive micro-Raman attachment, which consists of an off-the-shelf microscope and the coupling optics to an existing Raman spectrometer. The modification of the microscope, the optical coupling, and a low cost viewing system for positioning the laser excitation on the sample are described in detail. The students study molecular spectra of new materials such as diamond films, Fullerenes, and biological compounds with spatial resolution of several microns

Muonium as a shallow center in GaN

A paramagnetic muonium (Mu) state with an extremely small hyperfine parameter was observed for the first time in single-crystalline GaN below 25 K. It has a highly anisotropic hyperfine structure with axial symmetry along the [0001] direction, suggesting that it is located either at a nitrogen-antibonding or a bond-centered site oriented parallel to the c-axis. Its small ionization energy (=< 14 meV) and small hyperfine parameter (--10^{-4} times the vacuum value) indicate that muonium in one of its possible sites produces a shallow state, raising the possibility that the analogous hydrogen center could be a source of n-type conductivity in as-grown GaN.Comment: 4 figures, to be published in Phys. Rev. Letter

Comment on ``A new efficient method for calculating perturbative energies using functions which are not square integrable'': regularization and justification

The method recently proposed by Skala and Cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent. Even though this ratio comes out finite and gives the correct perturbation energies, the calculational process must be regularized to be justified. We examine one possible method of regularization and show that the proposed method gives traditional quantum mechanics results.Comment: 6 pages in REVTeX, no figure

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

Nanometric size effect on Ge diffusion in polycrystalline Si

The nanosize effect on Ge diffusion (850 \u3c = T \u3c = 1000 degrees C) in polycrystalline Si layers is investigated. The Ge diffusion coefficients in microcrystalline and nanocrystalline Si layers made of 30 mu m and 40 nm wide grains, respectively, are measured and compared. In the microcrystalline Si layer, the Ge diffusion coefficient in micrograin boundaries is measured using a conventional analytical solution of Fick\u27s equations corresponding to the Fisher model. In the nanocrystalline Si layer, the Ge diffusion coefficients in nanograins and in nanograin boundaries are measured via a method based on two-dimensional simulations using the Fisher model geometry. The diffusivities in nanograins and nanograin boundaries are one order of magnitude higher than in micrograins and micrograin boundaries, respectively. However, the nanosize effect appears to be different in grains and grain boundaries; despite that the activation energy for diffusion in 40 nm wide grains is at least 1 eV lower than in Si bulk. The activation energy in nanograin boundaries is about the same as in micrograin boundaries