Expansions of the real field by open sets: definability versus interpretability

An open set U of the real numbers R is produced such that the expansion (R,+,x,U) of the real field by U defines a Borel isomorph of (R,+,x,N) but does not define N. It follows that (R,+,x,U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (R,+,x). In particular, there is a Cantor subset K of R such that for every exponentially bounded o-minimal expansion M of (R,+,x), every subset of R definable in (M,K) either has interior or is Hausdorff null.Comment: 14 page

Extended Feynman Formula for the Harmonic Oscillator by the Discrete Time Method

We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the most reliable regularization of path integral. It is shown that this method leads to the result with, especially at caustics, more rigorous derivation than previous.Comment: 9 page

An investigation into the fertilizer particle dynamics off-the-disc

The particle size range specifications for two biosolids-derived organomineral fertilizers (OMF) known as OMF10 (10:4:4) and OMF15 (15:4:4) were established. Such specifications will enable field application of OMF with spinning disc systems using conventional tramlines spacing. A theoretical model was developed, which predicts the trajectory of individual fertilizer particles off-the-disc. The drag coefficient (Cd) was estimated for small time steps (10-6 s) in the trajectory of the particle as a function of the Reynolds number. For the range of initial velocities (20 to 40 m s-1), release angles (0° to 10°) and particle densities (1000 to 2000 kg m-3) investigated, the analysis showed that OMF10 and OMF15 need to have particle diameters between 1.10 and 5.80 mm, and between 1.05 and 5.50 mm, respectively, to provide similar spreading performance to urea with particle size range of 1.00 to 5.25 mm in diameter. OMF10 and OMF15 should have 80% (by weight) of particles between 2.65 and 4.30 mm, and between 2.55 and 4.10 mm, respectively. Due to the physical properties of the material, disc designs and settings that enable working at a specified bout width by providing a small upward particle trajectory angle (e.g., 10°) are preferred to high rotational velocities. However, field application of OMF with spinning discs applicators may be restricted to tramlines spaced at a maximum of 24 m; particularly, when some degree of overlapping is required between two adjacent bouts. The performance of granular fertilizers can be predicted based on properties of the material, such as particle density and size range, using the contour plots developed in this study

Numerical framework for transcritical real-fluid reacting flow simulations using the flamelet progress variable approach

An extension to the classical FPV model is developed for transcritical real-fluid combustion simulations in the context of finite volume, fully compressible, explicit solvers. A double-flux model is developed for transcritical flows to eliminate the spurious pressure oscillations. A hybrid scheme with entropy-stable flux correction is formulated to robustly represent large density ratios. The thermodynamics for ideal-gas values is modeled by a linearized specific heat ratio model. Parameters needed for the cubic EoS are pre-tabulated for the evaluation of departure functions and a quadratic expression is used to recover the attraction parameter. The novelty of the proposed approach lies in the ability to account for pressure and temperature variations from the baseline table. Cryogenic LOX/GH2 mixing and reacting cases are performed to demonstrate the capability of the proposed approach in multidimensional simulations. The proposed combustion model and numerical schemes are directly applicable for LES simulations of real applications under transcritical conditions.Comment: 55th AIAA Aerospace Sciences Meeting, Dallas, T

Quantum wires from coupled InAs/GaAs strained quantum dots

The electronic structure of an infinite 1D array of vertically coupled InAs/GaAs strained quantum dots is calculated using an eight-band strain-dependent k-dot-p Hamiltonian. The coupled dots form a unique quantum wire structure in which the miniband widths and effective masses are controlled by the distance between the islands, d. The miniband structure is calculated as a function of d, and it is shown that for d>4 nm the miniband is narrower than the optical phonon energy, while the gap between the first and second minibands is greater than the optical phonon energy. This leads to decreased optical phonon scattering, providing improved quantum wire behavior at high temperatures. These miniband properties are also ideal for Bloch oscillation.Comment: 5 pages revtex, epsf, 8 postscript figure

Directed percolation with a single defect site

In a recent study [arXiv:1011.3254] the contact process with a modified creation rate at a single site was shown to exhibit a non-universal scaling behavior with exponents varying with the creation rate at the special site. In the present work we argue that the survival probability decays according to a stretched exponential rather than a power law, explaining previous observations.Comment: 8 pages, 3 figure

Bias Analysis in Entropy Estimation

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analyzed.Comment: 5 pages, 3 figure

High resolution nighttime cloud-cover radiometer Quarterly report XVII, 1 Oct. 1965 - 1 Jan. 1966

Electronic, optical, mechanical, and electron packaging component and system design reviews for high resolution cloud cover infrared radiomete