الصفحة 1
الصفحة 1
Once upon a time : illustrations from fairytales, fables, primers, pop-ups, and other children's books
The 1905 obituary of John McLoughlin, Jr., in Publisher's Weekly declared,?Every child in the land knows the McLoughlin books. ... In fact, the history in the last decade of colored toy books for youngsters is the history of Mr. McLoughlin and his firm.?
Nonlinear Waves : Classical and Quantum Aspects
Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Nonlinear Oscillations of Hamiltonian PDEs
After introducing the reader to classical finite-dimensional dynamical system theory, including the Weinstein–Moser and Fadell–Rabinowitz resonant center theorems,the author develops the analogous theory for completely resonant nonlinear wave equations. Within this theory, both problems of small divisors and infinite bifurcation phenomena occur, requiring the use of Nash–Moser theory as well as minimax variational methods. These techniques are presented in a self-contained manner together with other basic notions of Hamiltonian PDEs and number theory.
Mathematical Physics of Quantum Mechanics : Selected and Refereed Lectures from QMath9
At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.
Hans Christian Ørsted and the Romantic Legacy in Science : Ideas, Disciplines, Practices
This volume owes its origin to the perception of a puzzling paradox. Hans Christian Ørsted, the great Danish scientist and philosopher, was one of the founders of modern physics through his experimental discovery in 1820 of the interaction of electricity and magnetism—a key step and model for the further unification of the forces of nature. Followers such as Maxwell and Einstein were, and today searchers worldwide are, enchanted by the hope for a completion of that grand program. In addition to Ørsted’s discovery of electromagnetism, his work in science included other fields, chiefly high-pressure physics and acoustics.
Gravity, Black Holes, and the Very Early Universe : An Introduction to General Relativity and Cosmology
In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. By 1925, quantum mechanics had been born out of the dissection of these two theories, and shortly after that, relativistic quantum field theory. We now had in place some important ties between the laws of physics and the types of particle interactions the new physics was uncovering. Gravity is one of the four types of forces that are found throughout the universe. In fact, although it is a relatively weak force, it operates at huge distances, and so must be accounted for in any cosmological system. Unfortunately, gravity continues to defy our neat categorization of how all the forces in nature work together.
Geometric mechanics on riemannian manifolds : Applications to partial differential equations
This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the Euler–Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible. It includes : Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton–Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves.
General Relativity
this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle.
Fuchsian Reduction : Applications to Geometry, Cosmology, and Mathematical Physics
Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the 1990s for semilinear wave equations, Fuchsian reduction research has grown in response to those problems in pure and applied mathematics where numerical computations fail.
Fluctuations, Information, Gravity and the Quantum Potential
A main theme of the book outlines the role of the quantum potential in quantum mechanics and general relativity and one of its origins via fluctuations formulated in terms of Fisher information. Another theme is the description of various approaches to Bohmian mechanics and their role in quantum mechanics and general relativity. Along the way various approaches to, for instance, the Dirac equation, the Einstein equations, the Klein-Gordon equation, the Maxwell equations and the Schr?dinger equations are described. Statistics and geometry are intertwined in various ways and, among other matters, the aether, cosmology, entropy, fractals, quantum Kaehler geometry, the vacuum and the zero point field are discussed. There is also some speculative material and some original work along with material extracted from over 1000 references and the work is current up to April 2005.
Ernst Equation and Riemann Surfaces : Analytical and Numerical Methods
Exact solutions to Einstein`s equations have been useful for the understanding of general relativity in many respects. They have led to physical concepts as black holes and event horizons and helped to visualize interesting features of the theory. In addition they have been used to test the quality of various approximation methods and numerical codes. The most powerful solution generation methods are due to the theory of Integrable Systems. In the case of axisymmetric stationary spacetimes the Einstein equations are equivalent to the completely integrable Ernst equation. In this volume the solutions to the Ernst equation associated to Riemann surfaces are studied in detail and physical and mathematical aspects of this class are discussed both analytically and numerically.
Emergent Nonlinear Phenomena in Bose-Einstein Condensates : Theory and Experiment
This book, written by experts in the fields of atomic physics and nonlinear science, consists of reviews of the current state of the art at the interface of these fields, as is exemplified by the modern theme of Bose-Einstein condensates. Topics covered include bright, dark, gap and multidimensional solitons; vortices; vortex lattices; optical lattices; multicomponent condensates; manipulation of condensates; mathematical methods/rigorous results; and aspects beyond the mean field approach. A distinguishing feature of the contents is the detailed incorporation of both the experimental and theoretical viewpoints through subsections of the relevant chapters.
Elements of Numerical Relativity : From Einstein`s Equations to Black Hole Simulations
Spurred by the current development of numerous large-scale projects for detecting gravitational radiation, with the aim to open a completely new window to the observable Universe, numerical relativity has become a major field of research over the past years. Indeed, numerical relativity is the standard approach when studying potential sources of gravitational waves, where strong fields and relativistic velocities are part of any physical scenario. This book can be considered a primer for both graduate students and non-specialist researchers wishing to enter the field. Starting from the most basic insights and aspects of numerical relativity, Elements of Numerical Relativity develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism, gauge, initial and boundary conditions as well as various numerical algorithms. The tests and applications proposed in this book can be performed on a standard PC.
Einsteins Spacetime : An Introduction to Special and General Relativity
Einstein's Space-Time: An Introduction to Special and General Relativity is a textbook addressed to students in physics and other people interested in Relativity and a history of physics. The book contains a complete account of Special Relativity that begins with the historical analysis of the reasons that led to a change in our manner of regarding the space and time.
Einsteins General Theory of Relativity : With Modern Applications in Cosmology
Einstein’s General Theory of Relativity: With Modern Applications in Cosmology by Oyvind Gron and Sigbjorn Hervik is about gravity and the concept of gravity as Albert Einstein saw it- curved spaces, four-dimensional manifolds and geodesics. The book starts with the 1st principals of relativity and an introduction to Einstein’s field equations. Next up are the three classical tests of the relativity theory and an introduction to black holes.
Einsteins Enigma or Black Holes in My Bubble Bath
Einstein's Enigma or Black Holes in My Bubble Bath tells the story of gravitation theory from the early historic origins to the latest developments in astrophysics, focusing on Albert Einstein's theory of general relativity and black-hole physics. Through engaging conversations and napkin-scribbled diagrams come tumbling the rudiments of relativity, spacetime and much of modern physics, narrated with high didactic and literary talent, and each embedded in casual lessons given by a worldly astrophysicist to his friend Alfie, a freelance organiser of proposals. Join the intellectual fun and exalt in the frothy ideas while vicariously taking relaxing baths in this magical bathtub.
Einstein’s Struggles with Quantum Theory : A Reappraisal
This unique book presents a mathematical as well as a non-mathematical route through the theories, controversies, and investigations, making the discourse both readable and understandable to anyone interested in Einstein and quantum theory. The authors also examine recent developments in quantum theory and reveal the influence Einstein has had, and will continue to have, in this important field.
Einstein, 1905-2005 : Poincaré Seminar 2005
This volume is devoted to Einstein's 1905 papers and their legacy. After a presentation of Einstein's epistemological approach to physics, and the genesis of special relativity, a centenary perspective is offered. The geometry of relativistic spacetime is explained in detail. Single photon experiments are presented, as a spectacular realization of Einstein's light quanta hypothesis. A previously unpublished lecture by Einstein, which presents an illuminating point of view on statistical physics in 1910, at the dawn of quantum mechanics, is reproduced. The volume ends with an essay on the historical, physical and mathematical aspects of Brownian motion.
Einstein Manifolds
"[...] an efficient reference book for many fundamental techniques of Riemannian geometry. [...] despite its length, the reader will have no difficulty in getting the feel of its contents and discovering excellent examples of all interaction of geometry with partial differential equations, topology, and Lie groups. Above all, the book provides a clear insight into the scope and diversity of problems posed by its title."
Earthquakes : Simulations, Sources and Tsunamis
This book includes a variety of studies that focus on the modeling of tsunamis and earthquakes, both large-scale simulation and visualization programs, as well as detailed models of small-scale features. Particular attention is paid to computational techniques, languages, and hardware that can be used to facilitate data analysis, visualization, and modeling. Also included are studies of several earthquake forecasting techniques and associated comparisons of their results with historic earthquake data. Finally, the volume ends with theoretical analyses of statistical properties of seismicity by internationally recognized experts in the field. This volume will be of particular interest to researchers interested in the multiscale simulation and visualization of large earthquakes and tsunamis.
