Non-affine geometrization can lead to nonphysical instabilities

Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out within geometrical frameworks, by measuring the broadening rate of a bundle of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We find that this geometrical analysis measures the actual stability when the length of any geodesic is proportional to the corresponding time interval. We prove that the Jacobi metric is not always an appropriate parametrization by showing that it predicts chaotic behavior for a system of harmonic oscillators. Furthermore, we show, by explicit calculation, that the correspondence between dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find that the Eisenhart dynamics corresponds to the actual tangent dynamics and is therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures: http://iopscience.iop.org/1751-8121/48/7/07510

Measurement of opaque film thickness

The theoretical and experimental framework for thickness measurements of thin metal films by low frequency thermal waves is described. Although it is assumed that the films are opaque and the substrates are comparatively poor thermal conductors, the theory is easily extended to other cases of technological interest. A brief description is given of the thermal waves and the experimental arrangement and parameters. The usefulness of the technique is illustrated for making absolute measurements of the thermal diffusivities of isotropic substrate materials. This measurement on pure elemental solids provides a check on the three dimensional theory in the limiting case of zero film thickness. The theoretical framework is then presented, along with numerical calculations and corresponding experimental results for the case of copper films on a glass substrate

Computer simulations of an impurity in a granular gas under planar Couette flow

We present in this work results from numerical solutions, obtained by means of the direct simulation Monte Carlo (DSMC) method, of the Boltzmann and Boltzmann--Lorentz equations for an impurity immersed in a granular gas under planar Couette flow. The DSMC results are compared with the exact solution of a recent kinetic model for the same problem. The results confirm that, in steady states and over a wide range of parameter values, the state of the impurity is enslaved to that of the host gas: it follows the same flow velocity profile, its concentration (relative to that of the granular gas) is constant in the bulk region, and the impurity/gas temperature ratio is also constant. We determine also the rheological properties and nonlinear hydrodynamic transport coefficients for the impurity, finding a good semi-quantitative agreement between the DSMC results and the theoretical predictions.Comment: 23 pages, 11 figures; v2: minor change

A one-sided Prime Ideal Principle for noncommutative rings

Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals and their commutative counterparts. We prove the Completely Prime Ideal Principle, a theorem stating that right ideals that are maximal in a specific sense must be completely prime. We offer a number of applications of the Completely Prime Ideal Principle arising from many diverse concepts in rings and modules. These applications show how completely prime right ideals control the one-sided structure of a ring, and they recover earlier theorems stating that certain noncommutative rings are domains (namely, proper right PCI rings and rings with the right restricted minimum condition that are not right artinian). In order to provide a deeper understanding of the set of completely prime right ideals in a general ring, we study the special subset of comonoform right ideals.Comment: 38 page

Effective Dielectric Constants of Photonic Crystal of Aligned Anisotropic Cylinders: Application to the Optical Response of Periodic Array of Carbon Nanotubes

We calculate the static dielectric tensor of a periodic system of aligned anisotropic dielectric cylinders. Exact analytical formulas for the effective dielectric constants for the E- and H- eigenmodes are obtained for arbitrary 2D Bravais lattice and arbitrary cross-section of anisotropic cylinders. It is shown that depending on the symmetry of the unit cell photonic crystal of anisotropic cylinders behaves in the low-frequency limit like uniaxial or biaxial natural crystal. The developed theory of homogenization of anisotropic cylinders is applied for calculations of the dielectric properties of photonic crystals of carbon nanotubes

Evaluating the impact of an environmental education programme; an empirical study in Mexico.

This study draws on information from 11 in-depth interviews, two focus groups and 72 written questionnaires to evaluate an extra-curricular environmental education programme on forestry designed for preparatory school students from a small rural community in Mexico. Specifically, the study assessed the impact of the programme on the ecological knowledge of 72 students. Qualitative feedback suggests that students learnt about forestry, acquired greater awareness of the importance of conservation for the local environment and enjoyed the participatory teaching methods used in the programme. Quantitative results show a positive and significant association between the number of times a student participated in the programme and the student&rsquo;s ecological knowledge. Students who participated in the programme once had a 16.3% higher knowledge on ecological concepts and knew, on average, 1.5 more local forest plants than students who never attended it (p&lt;.001). Findings suggest that the inclusion of participatory environmental education programmes in preparatory schools would improve the acquisition of ecological knowledge. Further research could consider the consistency of the findings by replicating participatory methods presented here and by using an experimental research design.<br /