59,760 research outputs found
Superposition Formulas for Darboux Integrable Exterior Differential Systems
In this paper we present a far-reaching generalization of E. Vessiot's
analysis of the Darboux integrable partial differential equations in one
dependent and two independent variables. Our approach provides new insights
into this classical method, uncovers the fundamental geometric invariants of
Darboux integrable systems, and provides for systematic, algorithmic
integration of such systems. This work is formulated within the general
framework of Pfaffian exterior differential systems and, as such, has
applications well beyond those currently found in the literature. In
particular, our integration method is applicable to systems of hyperbolic PDE
such as the Toda lattice equations, 2 dimensional wave maps and systems of
overdetermined PDE.Comment: 80 page report. Updated version with some new sections, and major
improvements to other
From an axiological standpoint
I maintain that intrinsic value is the fundamental concept of axiology. Many contemporary philosophers disagree; they say the proper object of value theory is final value. I examine three accounts of the nature of final value: the first claims that final value is non‐instrumental value; the second claims that final value is the value a thing has as an end; the third claims that final value is ultimate or non‐derivative value. In each case, I argue that the concept of final value described is either identical with the classical notion of intrinsic value or is not a plausible candidate for the primary concept of axiology
Bulk Spin-Hall Effect
We show that a two-dimensional spin-orbit-coupled system in the presence of a
charge/spin-density wave with a wave-vector perpendicular to an applied
electric field supports bulk manifestations of the direct/inverse spin-Hall
effect. We develop a theory of this phenomenon in the framework of the spin
diffusion equation formalism and show that, due to the inhomogeneity created by
a spin-grating, an anomalous bulk charge-density wave is induced away from
sample boundaries. The optimal conditions for the observation of the effect are
determined. The main experimental manifestation of the bulk spin-Hall effect,
the induced charge/spin-density-wave, is characterized by a pi/2-phase shift
relative to the initial non-homogeneous spin/charge-polarization profile and
has a non-monotonic time-varying amplitude.Comment: 4 pages, 4 figure
Data compressor Patent
Description of system for recording and reading out data related to distribution of occurrence of plurality of event
Triangleland. I. Classical dynamics with exchange of relative angular momentum
In Euclidean relational particle mechanics, only relative times, relative
angles and relative separations are meaningful. Barbour--Bertotti (1982) theory
is of this form and can be viewed as a recovery of (a portion of) Newtonian
mechanics from relational premises. This is of interest in the absolute versus
relative motion debate and also shares a number of features with the
geometrodynamical formulation of general relativity, making it suitable for
some modelling of the problem of time in quantum gravity. I also study
similarity relational particle mechanics (`dynamics of pure shape'), in which
only relative times, relative angles and {\sl ratios of} relative separations
are meaningful. This I consider firstly as it is simpler, particularly in 1 and
2 d, for which the configuration space geometry turns out to be well-known,
e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail.
Secondly, the similarity model occurs as a sub-model within the Euclidean
model: that admits a shape--scale split. For harmonic oscillator like
potentials, similarity triangleland model turns out to have the same
mathematics as a family of rigid rotor problems, while the Euclidean case turns
out to have parallels with the Kepler--Coulomb problem in spherical and
parabolic coordinates. Previous work on relational mechanics covered cases
where the constituent subsystems do not exchange relative angular momentum,
which is a simplifying (but in some ways undesirable) feature paralleling
centrality in ordinary mechanics. In this paper I lift this restriction. In
each case I reduce the relational problem to a standard one, thus obtain
various exact, asymptotic and numerical solutions, and then recast these into
the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure
Quantum Cosmological Relational Model of Shape and Scale in 1-d
Relational particle models are useful toy models for quantum cosmology and
the problem of time in quantum general relativity. This paper shows how to
extend existing work on concrete examples of relational particle models in 1-d
to include a notion of scale. This is useful as regards forming a tight analogy
with quantum cosmology and the emergent semiclassical time and hidden time
approaches to the problem of time. This paper shows furthermore that the
correspondence between relational particle models and classical and quantum
cosmology can be strengthened using judicious choices of the mechanical
potential. This gives relational particle mechanics models with analogues of
spatial curvature, cosmological constant, dust and radiation terms. A number of
these models are then tractable at the quantum level. These models can be used
to study important issues 1) in canonical quantum gravity: the problem of time,
the semiclassical approach to it and timeless approaches to it (such as the
naive Schrodinger interpretation and records theory). 2) In quantum cosmology,
such as in the investigation of uniform states, robustness, and the qualitative
understanding of the origin of structure formation.Comment: References and some more motivation adde
Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
I approach the Problem of Time and other foundations of Quantum Cosmology
using a combined histories, timeless and semiclassical approach. This approach
is along the lines pursued by Halliwell. It involves the timeless probabilities
for dynamical trajectories entering regions of configuration space, which are
computed within the semiclassical regime. Moreover, the objects that Halliwell
uses in this approach commute with the Hamiltonian constraint, H. This approach
has not hitherto been considered for models that also possess nontrivial linear
constraints, Lin. This paper carries this out for some concrete relational
particle models (RPM's). If there is also commutation with Lin - the Kuchar
observables condition - the constructed objects are Dirac observables.
Moreover, this paper shows that the problem of Kuchar observables is explicitly
resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach
for nontrivial linear constraints that is also a construction of Dirac
observables, I consider theories for which Kuchar observables are formally
known, giving the relational triangle as an example. As a second route, I apply
an indirect method that generalizes both group-averaging and Barbour's best
matching. For conceptual clarity, my study involves the simpler case of
Halliwell 2003 sharp-edged window function. I leave the elsewise-improved
softened case of Halliwell 2009 for a subsequent Paper II. Finally, I provide
comments on Halliwell's approach and how well it fares as regards the various
facets of the Problem of Time and as an implementation of QM propositions.Comment: An improved version of the text, and with various further references.
25 pages, 4 figure
Children's Databases - Safety and Privacy
This report describes in detail the policy background, the systems that are being built, the problems with them, and the legal situation in the UK. An appendix looks at Europe, and examines in particular detail how France and Germany have dealt with these issues. Our report concludes with three suggested regulatory action strategies for the Commissioner: one minimal strategy in which he tackles only the clear breaches of the law, one moderate strategy in which he seeks to educate departments and agencies and guide them towards best practice, and finally a vigorous option in which he would seek to bring UK data protection practice in these areas more in line with normal practice in Europe, and indeed with our obligations under European law
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