D'Alembert sums for vibrating bar with viscous ends

We describe a new method for finding analytic solutions to some initial-boundary problems for partial differential equations with constant coefficients. The method is based on expanding the denominator of the Laplace transformed Green's function of the problem into a convergent geometric series. If the denominator is a linear combination of exponents with real powers one obtains a closed form solution as a sum with finite but time dependent number of terms. We call it a d'Alembert sum. This representation is computationally most effective for small evolution times, but it remains valid even when the system of eigenmodes is incomplete and the eigenmode expansion is unavailable. Moreover, it simplifies in such cases. In vibratory problems d'Alembert sums represent superpositions of original and partially reflected traveling waves. They generalize the d'Alembert type formulas for the wave equation, and reduce to them when original waves can undergo only finitely many reflections in the entire course of evolution. The method is applied to vibrations of a bar with dampers at each end and at some internal point. The results are illustrated by computer simulations and comparisons to modal and FEM solutions.Comment: 18 pages, 8 figure

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.Comment: 4 pages with 4 postscript figures (uses Revtex 3.1, Latex2e, multicol.sty, epsf.sty and rotate.sty). Submitted to PR

Integrable Euler top and nonholonomic Chaplygin ball

We discuss the Poisson structures, Lax matrices, $r$-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio

Characterization of carbon fibrous material from platanus achenes as platinum catalysts support

Carbon materials with developed porosity are usually used as supports for platinum catalysts. Physico-chemical characteristics of the support influence the properties of platinum deposited and its catalytic activity. In our studies, we deposited platinum on carbon fibrous like materials obtained from platanus seeds - achenes. The precursor was chemically activated with different reagents: NaOH, pyrogallol, and H2O2, before the carbonization process. Platinum was deposited on all substrates to study the influence of the substrate properties on the activity of the catalyst. Carbon materials were characterized by nitrogen adsorption/desorption isotherms measurements, X-ray diffraction, and scanning electron microscopy. It was noticed that the adsorption characteristics of carbon support affected the structure of platinum deposits and thus their activity

Aportes desde la gestión integral del recurso hídrico para la determinación de la capacidad de carga turística en destinos insulares. caso de estudio Islas de Providencia y Santa Catalina

Los procesos turísticos que no son adecuadamente planificados generan presión sobre los sistemas ambientales, generando conflictos, problemas y decisiones difíciles de abordar por su complejidad enmarcada en la relación sociedad-naturaleza. Es evidente que estos procesos además de atentar contra el patrimonio natural, representan una gran amenaza para el patrimonio social y cultural. De acuerdo con la Organización Mundial del Turismo, este sector presenta un crecimiento importante en los últimos años y se prevé, que siga creciendo en los próximos. Es necesario entonces, estudiar de qué manera se pueden gestionar los destinos turísticos para ofrecer servicios de calidad garantizando la sostenibilidad. Los Estudios de Capacidad de Carga Turística representan uno de los instrumentos de mayor importancia para lograr estos propósitos, donde a través de un proceso sistemático se analizan variables que tienen influencia directa sobre el territorio y la prestación de servicios turísticos, con el fin de determinar la cantidad de visitantes que puede recibir y/o atender un destino sin alterar de manera significativa sus dinámicas naturales, sociales y culturales

An Approach of Integrating Communication Services in Applications for Android-Based Digital TV Receivers

Digital TV receivers are becoming increasingly powerful devices allowing consumers to not only watch television broadcasts but also to access the Internet or communicate to other devices in the same local area network through either an Ethernet connection or by using a wireless connection. As the living room represents a meeting place for family and friends to gather and socialize in, the possibility of playing informal games using the television set as the interaction device is very attractive. This paper presents a developed application that integrates new communication capabilities of digital TV receivers running the Android OS. The application is a game showing its content overlaid on top of a television program whereas Android mobile devices are used as controllers. The performance of the application is tested by measuring the response times of the various communication services and by analyzing feedback from a selected group of users