Alfredo Macías - Böcker

Divided into four parts, this book covers developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part one is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part three is devoted to cosmological and inflationary scenarios.Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity.

The first part of this book is devoted to the topic of quantum gravity and string theories, mainly concerned with results in the study of discretizations in classical and quantum general relativity, non-commutative theories of gravity, supergravity and Berezin description of Kaehler quotients. The field to particle transition problem is also considered. The second part deals with cosmology and black holes. Here, cosmological, inflationary, and braneworld scenarios are investigated. Moreover, some scalar field models for the dark matter content of the universe as well as new models of protostellar collapse and fragmentation are presented. This part includes also a study of de Sitter/Anti-de Sitter phase transition for black holes, an understanding of hairy black holes and an improvement of the no-hair theorem proof for the Proca field. The third part is devoted to exact solutions, in particular classical and quantum cosmological solutions in scalar-tensor theories. Additionally, a discussion about conformally flat axisymmetric spacetimes and some considerations on accelerated expansion in scalar-tensor theories are presented.Experimental and some mixed topics are included in the final part. Among them is an experimental foundation of nonlocality and superluminal signal velocity in photonic tunneling, a proposal for testing the weak equivalence principle for charged particles in space. Moreover, a possible new type of skewon field linked to Maxwell theory is also presented, and an authoritative discussion at the interface of quantum and gravitational realms.

The first part is devoted to colloidal particles and stochastic dynamics, mainly concerned with recent authoritative results in the study of interactions between colloidal particles and transport properties in colloids and ferrocolloids. Recent advances in non-equilibrium statistical physics, such as stochastic resonance, Brownian motors, ratchets and noise-induced transport are also reported. The second part deals with biological systems and polymers. Here, standard simulation methodology to treat diffusional dynamics of multi-protein systems and proton transport in macromolecules is presented. Results of nervous system, spectroscopy of biological membrane models, and Monte Carlo simulations of polymers chains are also discussed. The third part is concerned with granular materials and quantum systems, in particular an effective-medium theory for a random system is reported. Additionally, a comprehensive treatment of spin and charge order in the vortex lattice of the cuprates, both theoretical and experimental, is included. Thermodynamics analogies between Bose-Einstein condensation and black-body radiation are also presented.The last part of the book contains recent developments of certain topics of liquid crystals and molecular fluids, including nonequilibrium thermal light scattering from nematic liquid crystals, relaxation in the kinetic Ising model on the periodic in homogeneous chain, models for thermotropic liquid-crystals, thermodynamic properties of fluids with discrete potentials as well as of fluids determined from the speed of sound effective potentials, and second viral coefficient for polar fluids.

This volume is divided into three parts and includes results, reviews, and developments of some special topics on hydrodynamics, dynamical systems, astrophysics, quantum mechanics, relativity, and DNA evolution. The first part deals with hydrodynamics including historical aspects, applications of recent theories to extend the Navier-Stokes regime, and new results on known methods for going beyond the Navier-Stokes equations. The second part is devoted to dynamical systems including new results on the problem of regularization of collisions and the Poincare continuation method. The second part also contains reviews of several aspects of the theory of dynamical systems. The third part deals with microquasars and astrophysics, fundamental aspects of quantum mechanics, superluminal propagation, and DNA evolution.

The first part is devoted to the topic of quantum gravity and string theories, mainly concerned with recent authoritative results in the study of discretizations in classical and quantum general relativity, non-commutative theories of gravity, (2+1)-dimensional supergravity, and Berezin description of Kaehler quotients. The field to particle transition problem is also considered. The second part deals with cosmology and black holes. Here, cosmological, inflationary, and braneworld scenarios are investigated. Moreover, some scalar field models for the dark matter content of the universe as well as new models of protostellar collapse and fragmentation are presented. This part includes also a study of de Sitter/Anti-de Sitter phase transition for black holes, an understanding of hairy black holes and an improvement of the no-hair theorem proof for the Proca field. The third part is devoted to exact solutions, in particular classical and quantum cosmological solutions in scalar-tensor theories. Additionally, a discussion about conformally flat axisymmetric spacetimes and some considerations on accelerated expansion in scalar-tensor theories are presented.Experimental and some mixed topics are included in the final part.Among them is an experimental foundation of nonlocality and superluminal signal velocity in photonic tunneling, a proposal for testing the weak equivalence principle for charged particles in space. Moreover, a possible new type of skewon field linked to Maxwell theory is also presented, and an authoritative discussion at the interface of quantum and gravitational realms.

The FIRST MEXICAN MEETING ON MATHEMATICAL AND EXPERI­ MENTAL PHYSICS was held at EL COLEGIO N ACIONAL in Mexico Cit­ y, Mexico, from September 10 to 14, 2001. This event consisted of the LEOPOLDO GARciA-COLiN SCHERER Medal Lecture, delivered by Prof. Nicholas G. van Kampen, a series of plenary talks by Leopoldo Garcia-Colin, Giinter Nimtz, Luis F. Rodriguez, Ruoon Barrera, and Donald Saari, and of three parallel symposia, namely, Cosmology and Gravitation, Statistical Physics and Beyond, and Hydrodynamics and Dynamical Systems. The response from the Physics community was enthusiastic, with over 200 participants and around 80 speakers, from allover the world: USA, Canada, Mexico, Germany, France, Holland, United Kingdom, Switzerland, Spain, and Hungary. The main aim of the conference is to provide a scenario to Mexican researchers on the topics of Mathematical and Experimental Physics in order to keep them in contact with work going on in other parts of the world and at the same time to motivate and support the young and mid­ career researchers from our country. To achieve this goal, we decided to the most distinguished experts in the subjects of the invite as lecturers conference and to give the opportunity to young scientist to communi­ cate the results of their work. The plan is to celebrate this international endeavor every three years.

The FIRST MEXICAN MEETING ON MATHEMATICAL AND EXPERI­ MENTAL PHYSICS was held at EL COLEGIO NACIONAL in Mexico City, Mexico, from September 10 to 14, 2001. This event consisted of the LEOPOLDO GARciA-COLIN SCHERER Medal Lecture, delivered by Prof. Nicholas G. van Kampen, a series of plenary talks by Leopoldo Garcia­ CoHn, GUnter Nimtz, Luis F. Rodriguez, Ruoon Barrera, and Donald Saari, and of three parallel symposia, namely, Cosmology and Gravita­ tion, Statistical Physics and Beyond, and Hydrodynamics and Dynam­ ical Systems. The response from the Physics community was enthusi­ astic, with over 200 participants and around 80 speakers, from all over the world: USA, Canada, Mexico, Germany, France, Holland, United Kingdom, Switzerland, Spain, and Hungary. The main aim of the conference is to provide a scenario to Mexican researchers on the topics of Mathematical and Experimental Physics in order to keep them in contact with work going on in other parts of the world and at the same time to motivate and support the young and mid­ career researchers from our country. To achieve this goal, we decided to invite as lecturers the most distinguished experts in the subjects of the conference and to give the opportunity to young scientist to communi­ cate the results of their work. The plan is to celebrate this international endeavor every three years.

Divided into four parts, this book covers recent developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part One is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part Two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part Three is devoted to cosmological and inflationary scenarios. Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity.Thus, this book is the most up-to-date, comprehensive collection of papers on the subject of exact solutions and scalar fields in gravity and is a valuable tool for researchers in the area.

These proceedings contain lecture notes on computer algebra, cosmological models, quantum cosmology, and black hole physics. Several research articles which cover different aspects of classical cosmology, exact solutions to Einstein's equations, and quantum field theory are also included.