Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations

In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential and Weierstrass functionsComment: 4 pages, some changes in the text according to referees' suggestions, added one reference, accepted at Central Europ. J. Phy

Nonlinear second order ODE's: Factorizations and particular solutions

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we developed in Phys. Rev. E 71 (2005) 046607Comment: 6 pages, v3=published versio

Supersymmetric methods in the traveling variable: inside neurons and at the brain scale

We apply the mathematical technique of factorization of differential operators to two different problems. First we review our results related to the supersymmetry of the Montroll kinks moving onto the microtubule walls as well as mentioning the sine-Gordon model for the microtubule nonlinear excitations. Second, we find analytic expressions for a class of one-parameter solutions of a sort of diffusion equation of Bessel type that is obtained by supersymmetry from the homogeneous form of a simple damped wave equations derived in the works of P.A. Robinson and collaborators for the corticothalamic system. We also present a possible interpretation of the diffusion equation in the brain contextComment: 14 pages, 1 figur

Mathematical methods of factorization and a feedback approach for biological systems

The first part of the thesis is devoted to factorizations of linear and nonlinear differential equations leading to solutions of the kink type. The second part contains a study of the synchronization of the chaotic dynamics of two Hodgkin-Huxley neurons by means of the mathematical tools belonging to the geometrical control theory.Comment: Ph. D. Thesis at IPICyT, San Luis Potosi, Mexico, 102 pp, 40 figs. Supervisors: Dr. H.C. Rosu and Dr. R. Fema

Riccati nonhermiticity with application to the Morse potential

A supersymmetric one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrodinger equations in particle physics is described at the general level. By this means we are able to introduce a nonhermitic Hamiltonian having the imaginary part proportional to the solution of a Riccati equation of the Witten type. The procedure is applied to the exactly solvable Morse potential introducing in this way the corresponding nonhermitic Morse problem. A possible application is to molecular diffraction in evanescent waves over nanostructured surfacesComment: 8 pages, 4 figure

Classical harmonic oscillator with Dirac-like parameters and possible applications

We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schroedinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of these modes. Generalizations to several K parameters are also possible and lead to analytical results. If the problem is passed to the physical optics (and/or acoustics) context by switching from the oscillator equation to the corresponding Helmholtz equation, one may hope to detect the K-modes as waveguide modes of specially designed waveguides and/or cavitiesComment: 14 pages, 9 figures, revised, accepted at J. Phys.

Plan de Negocios para una planta dedicada al tratamiento cuarentenario de la fruticultura de exportacion en base a un acelerador de electrones

195 p.El plan de negocios para una planta dedicada al tratamiento cuarentenario de la fruticultura de exportación en base a un acelerador de electrones. El negocio de la exportación de productos hortofrutícola está siendo cada vez más regulado desde los países importadores. Dentro de estas regulaciones esta el Protocolo de Montreal, firmado y ratificado por Chile. Esto implica un calendario para la congelación, reducción y eliminación del uso del bromuro de metilo, gas considerado dañino para la salud humana e inhibidor de la capa de ozono. Este estudio toma irradiación de la fruta con energía ionizante producida con acelerador de electrones como alternativa al bromuro de metilo, centrándose en el tratamiento de la Uva de Mesa exportada a Estados Unidos y proyectando la construcción de dos plantas. Se realiza un estudio de mercado para determinar la demanda potencial por este servicio, que se calcula en 260 millones de kilogramos de Uva de Mesa y 350 millones de kilogramos de Otros productos. Estos últimos se incluyen en el proyecto básicamente para reducir la estacionalidad que implica la exportación de Uva de Mesa. El estudio continúa con la localización óptima para las instalaciones de irradiación. Estas son ubicadas en las cercanías de los puertos de Valparaíso y San Antonio para captar los envíos que salgan por barco hacia Estados Unidos. Luego, en este estudio, se proyecta la construcción de las plantas de irradiación. Estas plantas tienen una capacidad inicial de producción, en conjunto, de 288 mil pallets, unos 200 millones de kilogramos, en forma anual. Luego de dos años se propone una reinversión para aumentar esta capacidad al doble. La evaluación económica se realiza considerando distintos escenarios de financiamiento bancario y criterios de decisión como el valor actual neto (VAN), y la tasa interna de retorno (TIR). Además, se analiza la sensibilidad de estos criterios de acuerdo a la variación del precio del servicio. En todos los casos, el proyecto resulta ser rentable, con una TIR que varía entre 29% y 54% y un VAN entre $6.200 millones y$7200 millones. Las aplicaciones de la irradiación con energía ionizante no sólo se remiten al ámbito alimenticio. Sus usos van desde la esterilización de materiales quirúrgicos hasta la modificación de las propiedades físicas de los polímeros, abriendo un abanico de posibilidades para su uso

An Approach to Comprehensively Evaluate Potential Park and Ride Facilities

ABSTRACTA park and ride facility provides an option to car drivers to park their cars and switch to public transportation for the remaining portions of their trips. Although park and ride has been implemented in many cities in the United States and integrated with different modes of transportation, no comprehensive approach has been developed in published literature to assess the feasibility of a potential park and ride site. This research proposes a comprehensive approach, which consists of the following tasks, to evaluate potential park and ride facilities: 1Site location analysis2Bus system reliability analysis3Parking supply and usage analysis4Mode choice model5User demand and ridership estimation6Cost estimation and economic impacts analysisThe application of the proposed tasks was demonstrated through a case study of a site in the City of El Paso, Texas

Traveling kinks in cubic nonlinear Ginzburg-Landau equations

Nonlinear cubic Euler-Lagrange equations of motion in the traveling variable are usually derived from Ginzburg-Landau free energy functionals frequently encountered in several fields of physics. Many authors considered in the past damped versions of such equations with the damping term added by hand simulating the friction due to the environment. It is known that even in this damped case kink solutions can exist. By means of a factorization method, we provide analytic formulas for several possible kink solutions of such equations of motion in the undriven and constant field driven cases, including the recently introduced Riccati parameter kinks which were not considered previously in such a context. The latter parameter controls the delay of the switching stage of the kinksComment: 11 pages, 4 figures, final versio