Biodiesel: Tomorrow\u27s Fuel, Today\u27s Solution

Study of physical and chemical properties of biodiesel fuels derived from poultry and plant fats

Adaptive feed array compensation system for reflector antenna surface distortion

The feasibility of a closed loop adaptive feed array system for compensating reflector surface deformations has been investigated. The performance characteristics (gain, sidelobe level, pointing, etc.) of large communication antenna systems degrade as the reflector surface distorts mainly due to thermal effects from a varying solar flux. The compensating systems described in this report can be used to maintain the design performance characteristics independent of thermal effects on the reflector surface. The proposed compensating system employs the concept of conjugate field matching to adjust the feed array complex excitation coefficients

Calculation of Superdiffusion for the Chirikov-Taylor Model

It is widely known that the paradigmatic Chirikov-Taylor model presents enhanced diffusion for specific intervals of its stochasticity parameter due to islands of stability, which are elliptic orbits surrounding accelerator mode fixed points. In contrast with normal diffusion, its effect has never been analytically calculated. Here, we introduce a differential form for the Perron-Frobenius evolution operator in which normal diffusion and superdiffusion are treated separately through phases formed by angular wave numbers. The superdiffusion coefficient is then calculated analytically resulting in a Schloemilch series with an exponent $\beta=3/2$ for the divergences. Numerical simulations support our results.Comment: 4 pages, 2 figures (revised version

Analytical approximation of a distorted reflector surface defined by a discrete set of points

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern

Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection

Results from direct numerical simulations for three dimensional Rayleigh-Benard convection in a cylindrical cell of aspect ratio 1/2 and Pr=0.7 are presented. They span five decades of Ra from $2\times 10^6$ to $2 \times10^{11}$. Good numerical resolution with grid spacing $\sim$ Kolmogorov scale turns out to be crucial to accurately calculate the Nusselt number, which is in good agreement with the experimental data by Niemela et al., Nature, 404, 837 (2000). In underresolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the fully resolved case, because the thermal dissipation close to the sidewall (where the grid cells are largest) is insufficient. We compared the fully resolved thermal boundary layer profile with the Prandtl-Blasius profile. We find that the boundary layer profile is closer to the Prandtl Blasius profile at the cylinder axis than close to the sidewall, due to rising plumes in that region.Comment: 10 pages, 6 figure

Spectra of lens spaces from 1-norm spectra of congruence lattices

To every $n$-dimensional lens space $L$, we associate a congruence lattice $\mathcal L$ in $\mathbb Z^m$, with $n=2m-1$ and we prove a formula relating the multiplicities of Hodge-Laplace eigenvalues on $L$ with the number of lattice elements of a given $\|\cdot\|_1$-length in $\mathcal L$. As a consequence, we show that two lens spaces are isospectral on functions (resp.\ isospectral on $p$-forms for every $p$) if and only if the associated congruence lattices are $\|\cdot\|_1$-isospectral (resp.\ $\|\cdot\|_1$-isospectral plus a geometric condition). Using this fact, we give, for every dimension $n\ge 5$, infinitely many examples of Riemannian manifolds that are isospectral on every level $p$ and are not strongly isospectral.Comment: Accepted for publication in IMR

Strongly isospectral manifolds with nonisomorphic cohomology rings

For any $n\geq 7$, $k\geq 3$, we give pairs of compact flat $n$-manifolds $M, M'$ with holonomy groups $\mathbb Z_2^k$, that are strongly isospectral, hence isospectral on $p$-forms for all values of $p$, having nonisomorphic cohomology rings. Moreover, if $n$ is even, $M$ is K\"ahler while $M'$ is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for $n=24$ and $k=3$ there is a family of eight compact flat manifolds (four of them K\"ahler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds.Comment: 25 pages, to appear in Revista Matem\'atica Iberoamerican