COSMIC STRINGS IN THE WIRE APPROXIMATION

This free book is a comprehensive survey of the current state of knowledge about the
dynamics and gravitational properties of cosmic strings treated in the idealized
classical approximation as line singularities described by the Nambu-Goto
action. The author’s purpose is to provide a standard reference to all work that
has been published since the mid-1970s and to link this work together in a
single conceptual framework and a single notational formalism. A working
knowledge of basic general relativity is assumed. The ebook will be essential
reading for researchers and postgraduate students in mathematics, theoretical
physics, and astronomy interested in cosmic strings.

One of the most striking successes of modern science has been to reduce the
complex panoply of dynamical phenomena we observe in the world around usfrom
the build-up of rust on a car bumper to the destructive effects of cyclonic
winds-to the action of only four fundamental forces: gravity, electromagnetism,
and the strong and weak nuclear forces. This simple picture of four fundamental
forces, which became evident only after the isolation of the strong and weak
nuclear forces in the 1930s, was simplified even further when Steven Weinberg in
1967 and Abdus Salam in 1968 independently predicted that the electromagnetic
and weak forces would merge at high temperatures to form a single electroweak
force.
The Weinberg-Salam model of electroweak unification was the first practical
realization of the Higgs mechanism, a theoretical device whereby a system of
initially massless particles and fields can be given a spectrum of masses by
coupling it to a massive scalar field. The model has been extremely successful
not only in describing the known weak reactions to high accuracy, but also in
predicting the masses of the carriers of the weak force, the W± and ZO bosons,
which were experimentally confirmed on their discovery in 1982-83.

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Over the years, the “Red Book” has become the authoritative reference for
each new version of the OpenGL API. Now we have the “Gold Book” for
OpenGL ES 2.0—a cross-platform open standard ushering in a new era of
shader programmability and visual sophistication for a wide variety of
embedded and mobile devices, from game consoles to automobiles, from
set top boxes to mobile phones.

OpenGL ES 2.0 is a software interface for rendering sophisticated 3D graphics
on handheld and embedded devices. OpenGL ES 2.0 is the primary
graphics library for handheld and embedded devices with programmable
3D hardware including cell phones, PDAs, consoles, appliances, vehicles,
and avionics. With OpenGL ES 2.0, the full programmability of shaders has
made its way onto small and portable devices. This book details the entire
OpenGL ES 2.0 API and pipeline with detailed examples in order to provide
a guide for developing a wide range of high-performance 3D applications
for handheld devices.

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This free ebook is about one big idea: You can synthesize a variety of complicated
functions from pure sinusoids in much the same way that you produce a major chord
by striking nearby C, E, G keys on a piano. A geometric version of this idea forms
the basis for the ancient Hipparchus-Ptolemy model of planetary motion (Almagest,
2nd century see Fig. 1.2). It was Joseph Fourier (Analytical Theory of Heat, 1815),
however, who developed modern methods for using trigonometric series and integrals
as he studied the flow of heat in solids. Today, Fourier analysis is a highly
evolved branch of mathematics with an incomparable range of applications and with
an impact that is second to none (see Appendix 1). If you are a student in one of
the mathematical, physical, or engineering sciences, you will almost certainly find
it necessary to learn the elements of this subject. My goal in writing this book is
to help you acquire a working knowledge of Fourier analysis early in your career.
If you have mastered the usual core courses in calculus and linear algebra, you
have the maturity to follow the presentation without undue difficulty. A few of the
proofs and more theoretical exercises require concepts (uniform continuity, uniform
convergence, . . . ) from an analysis or advanced calculus course. You may choose to
skip over the difficult steps in such arguments and simply accept the stated results.
The text has been designed so that you can do this without severely impacting
your ability to learn the important ideas in the subsequent chapters. In addition, I
will use a potpourri of notions from undergraduate courses in differential equations
[solve y
(x) + ?y(x) = 0, y
(x) = xy(x), y

(x) + ?2y(x) = 0, . . . ], complex analysis
(Euler’s formula: ei? = cos ?+i sin ?, arithmetic for complex numbers, . . . ), number
theory (integer addition and multiplication modulo N, Euclid’s gcd algorithm, . . . ),
probability (random variable, mean, variance, . . . ), physics (F = ma, conservation
of energy, Huygens’ principle, . . . ), signals and systems (LTI systems, low-pass
filters, the Nyquist rate, . . . ), etc. You will have no trouble picking up these
concepts as they are introduced in the text and exercises.
If you wish, you can find additional information about almost any topic in
this book by consulting the annotated references at the end of the corresponding
chapter. You will often discover that I have abandoned a traditional presentation
in favor of one that is in keeping with my goal of making these ideas accessible
to undergraduates. For example, the usual presentation of the Schwartz theory
of distributions assumes some familiarity with the Lebesgue integral and with
a graduate-level functional analysis course. In contrast, my development of ?,
X, . . . in Chapter 7 uses only notions from elementary calculus. Once you master
this theory, you can use generalized functions to study sampling, PDEs, wavelets,
probability, diffraction, . . . .
The exercises (541 of them) are my greatest gift to you! Read each chapter
carefully to acquire the basic concepts, and then solve as many problems as you
can. You may find it beneficial to organize an interdisciplinary study group, e.g.,
mathematician + physicist + electrical engineer. Some of the exercises provide
routine drill: You must learn to find convolution products, to use the FT calculus,
to do routine computations with generalized functions, etc. Some supply historical
perspective: You can play Gauss and discover the FFT, analyze Michelson and
Stratton’s analog supercomputer for summing Fourier series, etc. Some ask for
mathematical details: Give a sufficient condition for . . . , given an example of . . . ,
show that, . . . . Some involve your personal harmonic analyzers: Experimentally
determine the bandwidth of your eye, describe what would you hear if you replace
notes with frequencies f1, f2, . . . by notes with frequencies C/f1, C/f2, . . . . Some
prepare you for computer projects: Compute ? to 1000 digits, prepare a movie for
a vibrating string, generate the sound file for Risset’s endless glissando, etc. Some
will set you up to discover a pattern, formulate a conjecture, and prove a theorem.
(It’s quite a thrill when you get the hang of it!) I expect you to spend a lot of time
working exercises, but I want to help you work efficiently. Complicated results are
broken into simple steps so you can do (a), then (b), then (c), . . . until you reach
the goal. I frequently supply hints that will lead you to a productive line of inquiry.
You will sharpen your problem-solving skills as you take this course.

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Addressing both experimental as well as theoretical aspects, the free ebook covers the
thermochemical and combustion characteristics of all important types of
energetic materials, such as explosives, propellants, and the new class of
pyrolants, as well as related phenomena. It presents the fundamental bases of
the energetics of materials, deflagration and detonation, thermochemical process
of decomposition and combustion, plus combustion wave structures. The book also
goes on to discuss the combustion mechanisms of various types of energetic
materials, propellants, and explosives, based on the heat transfer process in
the combustion waves. The burning rate models are also presented as an aid to
understanding the rate-controlling steps of combustion processes, thus
demonstrating the relationships of burning rate versus pressure and initial
temperature. As a major topic new to this edition, new propulsion methods such
as duct rockets, ramjets, pulse motors and thrusters are described in detail,
while appendices on flow field dynamics and shock wave propagation have been
added.

Pyrodynamics describes the process of energy conversion from chemical energy to
mechanical energy through combustion phenomena, including thermodynamic
and fluid dynamic changes. Propellants and explosives are energetic condensed
materials composed of oxidizer-fuel components that produce high-temperature
molecules. Propellants are used to generate high-temperature and low-molecular
combustion products that are converted into propulsive forces. Explosives are used
to generate high-pressure combustion products accompanied by a shock wave that
yield destructive forces. This chapter presents the fundamentals of thermodynamics
and fluid dynamics needed to understand the pyrodynamics of propellants and
explosives.

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This free ebook differs from others in the field in that it has been prepared very
much with students and their needs in mind, having been classroom tested over
many years.  It is a true “learner’s book” made for students who require a
deeper understanding of probability and statistics. It presents the fundamentals
of the subject along with concepts of probabilistic modelling, and the process
of model selection, verification and analysis.  Furthermore, the inclusion of
more than 100 examples and 200 exercises (carefully selected from a wide range
of topics), along with a solutions manual for instructors, means that this text
is of real value to students and lecturers across a range of engineering
disciplines.

This free ebook was written for an introductory one-semester or two-quarter course
in probability and statistics for students in engineering and applied sciences. No
previous knowledge of probability or statistics is presumed but a good understanding
of calculus is a prerequisite for the material.
The development of this book was guided by a number of considerations
observed over many years of teaching courses in this subject area, including the
following:

*As an introductory course, a sound and rigorous treatment of the basic
principles is imperative for a proper understanding of the subject matter
and for confidence in applying these principles to practical problem solving.
A student, depending upon his or her major field of study, will no doubt
pursue advanced work in this area in one or more of the many possible
directions. How well is he or she prepared to do this strongly depends on
his or her mastery of the fundamentals.

*It is important that the student develop an early appreciation for applications.
Demonstrations of the utility of this material in nonsuperficial applications
not only sustain student interest but also provide the student with
stimulation to delve more deeply into the fundamentals.

*Most of the students in engineering and applied sciences can only devote one
semester or two quarters to a course of this nature in their programs.
Recognizing that the coverage is time limited, it is important that the material
be self-contained, representing a reasonably complete and applicable body of
knowledge.

The choice of the contents for this free ebook is in line with the foregoing
observations. The major objective is to give a careful presentation of the
fundamentals in probability and statistics, the concept of probabilistic modeling,
and the process of model selection, verification, and analysis. In this text,
definitions and theorems are carefully stated and topics rigorously treated
but care is taken not to become entangled in excessive mathematical details.

Practical examples are emphasized; they are purposely selected from many
different fields and not slanted toward any particular applied area. The same
objective is observed in making up the exercises at the back of each chapter.

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