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PAMIR (Parameterized Adaptive Multidimensional Integration
Routines) is a suite of Fortran programs for multidimensional
numerical integration over hypercubes, simplexes, and
hyper-rectangles in general dimension p, intended for use by
physicists, applied mathematicians, computer scientists, and
engineers. The programs, which are available on the internet at
www.pamir-integrate.com and are free for non-profit research use,
are capable of following localized peaks and valleys of the
integrand. Each program comes with a Message-Passing Interface
(MPI) parallel version for cluster use as well as serial
versions.The first chapter presents introductory material, similar
to that on the PAMIR website, and the next is a "manual" giving
much more detail on the use of the programs than is on the website.
They are followed by many examples of performance benchmarks and
comparisons with other programs, and a discussion of the
computational integration aspects of PAMIR, in comparison with
other methods in the literature. The final chapter provides details
of the construction of the algorithms, while the Appendices give
technical details and certain mathematical derivations.
PAMIR (Parameterized Adaptive Multidimensional Integration
Routines) is a suite of Fortran programs for multidimensional
numerical integration over hypercubes, simplexes, and
hyper-rectangles in general dimension p, intended for use by
physicists, applied mathematicians, computer scientists, and
engineers. The programs, which are available on the internet at
www.pamir-integrate.com and are free for non-profit research use,
are capable of following localized peaks and valleys of the
integrand. Each program comes with a Message-Passing Interface
(MPI) parallel version for cluster use as well as serial
versions.The first chapter presents introductory material, similar
to that on the PAMIR website, and the next is a "manual" giving
much more detail on the use of the programs than is on the website.
They are followed by many examples of performance benchmarks and
comparisons with other programs, and a discussion of the
computational integration aspects of PAMIR, in comparison with
other methods in the literature. The final chapter provides details
of the construction of the algorithms, while the Appendices give
technical details and certain mathematical derivations.
Foreword by Stephen L Adler (Institute for Advanced Study, USA)
Illustrations by Peggy Adler The term Phyllotaxis refers to the
patterns on plants formed by the arrangement of repeated biological
units. In nearly all cases, the Fibonacci Numbers and the Golden
Ratio occur in these arrangements. This topic has long fascinated
scientists. Over a period of more than two decades, Irving Adler
wrote a number of papers that construct a rigorously derived
mathematical model for Phyllotaxis, which are major and enduring
contributions to the field. These papers are collected in this
reprint volume to enable their access to a wider readership.
Quantum mechanics is our most successful physical theory. However,
it raises conceptual issues that have perplexed physicists and
philosophers of science for decades. This 2004 book develops an
approach, based on the proposal that quantum theory is not a
complete, final theory, but is in fact an emergent phenomenon
arising from a deeper level of dynamics. The dynamics at this
deeper level are taken to be an extension of classical dynamics to
non-commuting matrix variables, with cyclic permutation inside a
trace used as the basic calculational tool. With plausible
assumptions, quantum theory is shown to emerge as the statistical
thermodynamics of this underlying theory, with the canonical
commutation/anticommutation relations derived from a generalized
equipartition theorem. Brownian motion corrections to this
thermodynamics are argued to lead to state vector reduction and to
the probabilistic interpretation of quantum theory, making contact
with phenomenological proposals for stochastic modifications to
Schroedinger dynamics.
Quantum mechanics is our most successful physical theory. However,
it raises conceptual issues that have perplexed physicists and
philosophers of science for decades. This book develops a new
approach, based on the proposal that quantum theory is not a
complete, final theory, but is in fact an emergent phenomenon
arising from a deeper level of dynamics. The dynamics at this
deeper level are taken to be an extension of classical dynamics to
non-commuting matrix variables, with cyclic permutation inside a
trace used as the basic calculational tool. With plausible
assumptions, quantum theory is shown to emerge as the statistical
thermodynamics of this underlying theory, with the canonical
commutation/anticommutation relations derived from a generalized
equipartition theorem. Brownian motion corrections to this
thermodynamics are argued to lead to state vector reduction and to
the probabilistic interpretation of quantum theory, making contact
with recent phenomenological proposals for stochastic modifications
to Schrodinger dynamics.
This book presents a new formulation of quantum mechanics using quaternionic, rather than complex, numbers. The author is a highly respected theoretical physicist who has been working on quaternionic quantum mechanics for the last fourteen years. The author clearly explicates the relations between quaternionic, complex and real quantum mechanics, and the book is certain to be a major contribution to theoretical physics. Accessible to readers with a first-year graduate level quantum mechanics course.
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