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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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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Fundamentals of Biomechanics introduces the exciting
world of how human movement is created and how it can
be improved. Teachers, coaches and physical therapists
all use biomechanics to help people improve movement
and decrease the risk of injury. The free ebook presents a
comprehensive review of the major concepts of
biomechanics and summarizes them in nine principles
of biomechanics. Fundamentals of Biomechanics concludes
by showing how these principles can be used by movement
professionals to improve human movement. Specific case
studies are presented in physical education, coaching,
strength and conditioning, and sports medicine.

This free ebook is written for students taking
the introductory biomechanics course in
Kinesiology/HPERD. The book is designed
for majors preparing for all kinds of human
movement professions and therefore uses a
wide variety of movement examples to illustrate
the application of biomechanics.
While this approach to the application of
biomechanics is critical, it is also important
that students be introduced to the scientific
support or lack of support for these qualitative
judgments. Throughout the text extensive
citations are provided to support the
principles developed and give students references
for further study. Algebraic level
mathematics is used to teach mechanical
concepts. The focus of the mathematical examples
is to understand the mechanical
variables and to highlight the relationship
between various biomechanical variables,
rather than to solve quantitative biomechanical
word problems. It is obvious from
research in physics instruction that solving
quantitative word problems does not increase
the conceptual understanding of important
mechanical laws.

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One of the paradoxes of the physical sciences is that as our knowledge has
progressed, more and more diverse physical phenomena can be explained in terms
of fewer underlying laws, or principles. In Hidden Unity, eminent physicist John
Taylor puts many of these findings into historical perspective and documents how
progress is made when unexpected, hidden unities are uncovered between
apparently unrelated physical phenomena. Taylor cites examples from the ancient
Greeks to the present day, such as the unity of celestial and terrestrial
dynamics (17th century), the unity of heat within the rest of dynamics (18th
century), the unity of electricity, magnetism, and light (19th century), the
unity of space and time and the unification of nuclear forces with
electromagnetism (20th century). Without relying on mathematical detail,
Taylor’s emphasis is on fundamental physics, like particle physics and
cosmology. Balancing what is understood with the unestablished theories and
still unanswered questions, Taylor takes readers on a fascinating ongoing
journey.

As physics has progressed through the ages it has succeeded in
explaining more and more diverse phenomena with fewer and fewer
underlying principles. This lucid and wide-ranging book explains how
this understanding has developed by periodically uncovering unexpected
“hidden unities” in nature. The author deftly steers the reader on a
fascinating path that goes to the heart of physics – the search for and
discovery of elegant laws that unify and simplify our understanding of
the intricate universe in which we live.
Starting with the ancient Greeks, the author traces the development of
major concepts in physics right up to the present day. Throughout, the
presentation is crisp and informative, and only a minimum of
mathematics is used. Any reader with a background in mathematics or
physics will find this book provides fascinating insight into the
development of our fundamental understanding of the world, and the
apparent simplicity underlying it.
John C. Taylor is professor emeritus of mathematical physics at the
University of Cambridge. A pupil of the Nobel Prize–winner Abdus
Salam, Professor Taylor has had a long and distinguished career. In
particular, he was a discoverer of equations that play an important role
in the theory of the current “standard model” of particles and their
forces. In 1976, he published the first textbook on the subject, Gauge
Theories of Weak Interactions. He has taught theoretical physics at
Imperial College, London, and the Universities of Oxford and
Cambridge, and he has lectured around the world. In 1981 he was
elected a Fellow of the Royal Society.

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