Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Fragile-glass behavior of a short-range p-spin model

We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.

Influence of personality factors on the consumption of personal care products

The study is significant from both an application perspective of marketing management as well as from an academic angle. The market for personal care products is a highly fragmented one, with intense competition for specific niche segments. It is well known in marketing literature that the bulk of the volume of sale is accounted for by the minority who are the heavy users. This study will help the marketers to identify the personality profile of such a group and understand how the interaction of personality factors at least partially explains differences in consumption. This knowledge might be useful for better segmentation using psychographic variables as well as for designing specific advertisement campaigns to target the vulnerable groups of customers. From a theoretical perspective, the research may contribute to understanding how specific personality variables and their interaction lead to differences in consumption. The knowledge corresponding to self theory, social comparison theory, persuasibility, evidence from psychology of eating disorders: these all may be integrated into a common frame work for explaining consumption of products having a social function.

Studies on gaussian effective potentials in some models

In classical field theory, the ordinary potential V is an energy density for that state in which the field assumes the value ¢. In quantum field theory, the effective potential is the expectation value of the energy density for which the expectation value of the field is ¢o. As a result, if V has several local minima, it is only the absolute minimum that corresponds to the true ground state of the theory. Perturbation theory remains to this day the main analytical tool in the study of Quantum Field Theory. However, since perturbation theory is unable to uncover the whole rich structure of Quantum Field Theory, it is desirable to have some method which, on one hand, must go beyond both perturbation theory and classical approximation in the points where these fail, and at that time, be sufficiently simple that analytical calculations could be performed in its framework During the last decade a nonperturbative variational method called Gaussian effective potential, has been discussed widely together with several applications. This concept was described as a means of formalizing our intuitive understanding of zero-point fluctuation effects in quantum mechanics in a way that carries over directly to field theory.

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.

Re-Framing Trade

Given the substantial and increasing encroachment of trade agreements into almost every aspect of economic and social life, there is a pressing need for research that provides a more coherent framework for understanding the source and effectiveness of organised labour ’s power and capacity to influence international trade policy. Taking the union protests against the General Agreement on Trade in Services (GATS) as a case study, this research uses core concepts derived from social movement theory to analyse the opportunities that existed for unions to influence these trade negotiations and their capacity to identify and take advantage of such opportunities. Importantly, it adds a power analysis designed to reveal the sources of power that unions draw on to take action. The research demonstrates that even where unions faced considerable constraints they were able to re-frame trade issues in a way that built broad support for their position and to utilise opportunities in the trade negotiation process to mobilise resistance against the GATS and further liberalisation of services. The theoretical framework developed for the research provides conceptual tools that can be developed for improving strategic campaign planning and for analytical assessment of past campaigns. The theoretical framework developed for this research has potential for further application as an analytical and strategic planning tool for unions.

Factorial Hidden Markov Models

We present a framework for learning in hidden Markov models with distributed state representations. Within this framework, we derive a learning algorithm based on the Expectation--Maximization (EM) procedure for maximum likelihood estimation. Analogous to the standard Baum-Welch update rules, the M-step of our algorithm is exact and can be solved analytically. However, due to the combinatorial nature of the hidden state representation, the exact E-step is intractable. A simple and tractable mean field approximation is derived. Empirical results on a set of problems suggest that both the mean field approximation and Gibbs sampling are viable alternatives to the computationally expensive exact algorithm.

Militancia en el movimiento ambientalista del sur de Bogotá: el caso de Casa Useme

Las redes sociales son una de tantas posibles explicaciones al por qué la gente se adhiere a los movimientos sociales y participa de sus luchas. Sin embargo, los acercamientos que se han hecho a la militancia desde las redes sociales tienden a ser rígidos, debido a que sólo diferencian entre los que militan y los que no militan, dejando fuera del espectro una gran cantidad de matices que existen entre las personas que pertenecen a un movimiento social determinado. Este estudio de caso trata de responder a este interrogante con el concepto de compromiso, el cual es un intento de matizar la militancia en un movimiento social desde la teoría de las redes sociales. Adicionalmente, esta investigación trata de acercarse al fenómeno poco conocido del ambientalismo al sur de Bogotá. El cual es un movimiento social joven, en pleno proceso de expansión, con muchos simpatizantes y militantes, pero poco conocido por la academia y por la gente que no habita este espacio.

Análisis del proceso de negociación del Tratado de Libre Comercio Colombo Canadiense, para el sector agrícola. Periodo 2007 – 2008

En el mundo se está evidenciando un proceso de globalización, que ha impulsado a los Estados a una interacción, generando cambios significativos a nivel económico, cultural, político y social. Un reflejo de lo anterior, es la iniciativa de negociación del Tratado de Libre Comercio Colombo Canadiense, que además refleja una nueva etapa del Proceso de Apertura Económica iniciada en Colombia hace más de una década. El TLC Colombo Canadiense materializa la primera iniciativa bilateral entre estos dos países, enfocada a una negociación de Libre Comercio, sin embargo, los dos Estados ya habían tenido antecedentes de negociaciones comerciales multilaterales. Las negociaciones de Libre Comercio entre estos dos países, se desarrollaron en cinco rondas de negociación celebradas desde junio de 2007 hasta julio de 2008. Para el Sector Agrícola específicamente, las negociaciones fueron muy productivas, obteniendo los mejores resultados frente a las propuestas ofensivas tanto de Canadá como de Colombia. Frente a la entrada en vigor del TLC Colombo Canadiense, se evidenciaron distintas posiciones tanto de algunos representantes de la sociedad civil, como de organizaciones no gubernamentales, la academia, entre otros, que rechazaban completamente el acuerdo, alegando especialmente el tema del conflicto armado interno en Colombia, la violación a los Derechos Humanos, la falta de garantías a los derechos de los trabajadores y a los sindicatos, entre otros temas sociales.

Exercise sheet 3 pdf

Exercises and solutions in PDF

Exercise sheet 3

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