341 research outputs found
New light on the ‘Drummer of Tedworth’: conflicting narratives of witchcraft in Restoration England
This paper presents a definitive text of hitherto little-known early documents concerning ‘The Drummer of Tedworth’, a poltergeist case that occurred in 1662-3 and became famous not least due to its promotion by Joseph Glanvill in his demonological work, Saducismus Triumphatus. On the basis of these and other sources, it is shown how responses to the events at Tedworth evolved from anxious piety on the part of their victim, John Mompesson, to confident apologetic by Glanvill, before they were further affected by the emergence of articulate scepticism about the case
Disclination vortices in elastic media
The vortex-like solutions are studied in the framework of the gauge model of
disclinations in elastic continuum. A complete set of model equations with
disclination driven dislocations taken into account is considered. Within the
linear approximation an exact solution for a low-angle wedge disclination is
found to be independent from the coupling constants of the theory. As a result,
no additional dimensional characteristics (like the core radius of the defect)
are involved. The situation changes drastically for 2\pi vortices where two
characteristic lengths, l_\phi and l_W, become of importance. The asymptotical
behaviour of the solutions for both singular and nonsingular 2\pi vortices is
studied. Forces between pairs of vortices are calculated.Comment: 13 pages, published versio
Spacetime Defects: von K\'arm\'an vortex street like configurations
A special arrangement of spinning strings with dislocations similar to a von
K\'arm\'an vortex street is studied. We numerically solve the geodesic
equations for the special case of a test particle moving along twoinfinite rows
of pure dislocations and also discuss the case of pure spinning defects.Comment: 9 pages, 2figures, CQG in pres
An elastoplastic theory of dislocations as a physical field theory with torsion
We consider a static theory of dislocations with moment stress in an
anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We
obtain Yang-Mills type field equations which express the force and the moment
equilibrium. Additionally, we discuss several constitutive laws between the
dislocation density and the moment stress. For a straight screw dislocation, we
find the stress field which is modified near the dislocation core due to the
appearance of moment stress. For the first time, we calculate the localized
moment stress, the Nye tensor, the elastoplastic energy and the modified
Peach-Koehler force of a screw dislocation in this framework. Moreover, we
discuss the straightforward analogy between a screw dislocation and a magnetic
vortex. The dislocation theory in solids is also considered as a
three-dimensional effective theory of gravity.Comment: 38 pages, 6 figures, RevTe
Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation
The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a
single-particle relativistic quantum mechanical equation that defines unique
time-like particle trajectories. The particle trajectories are determined by
the conserved flow of the intrinsic energy density which can be derived from
the specification of the Klein-Gordon energy-momentum tensor in an
Einstein-Riemann space. The approach is illustrated by application to the
simple single-particle phenomena associated with square potentials.Comment: 14 pages, 11 figure
Mappings of least Dirichlet energy and their Hopf differentials
The paper is concerned with mappings between planar domains having least
Dirichlet energy. The existence and uniqueness (up to a conformal change of
variables in the domain) of the energy-minimal mappings is established within
the class of strong limits of homeomorphisms in the
Sobolev space , a result of considerable interest in the
mathematical models of Nonlinear Elasticity. The inner variation leads to the
Hopf differential and its trajectories.
For a pair of doubly connected domains, in which has finite conformal
modulus, we establish the following principle:
A mapping is energy-minimal if and only if
its Hopf-differential is analytic in and real along the boundary of .
In general, the energy-minimal mappings may not be injective, in which case
one observes the occurrence of cracks in . Nevertheless, cracks are
triggered only by the points in the boundary of where fails to be
convex. The general law of formation of cracks reads as follows:
Cracks propagate along vertical trajectories of the Hopf differential from
the boundary of toward the interior of where they eventually terminate
before making a crosscut.Comment: 51 pages, 4 figure
Volterra Distortions, Spinning Strings, and Cosmic Defects
Cosmic strings, as topological spacetime defects, show striking resemblance
to defects in solid continua: distortions, which can be classified into
disclinations and dislocations, are line-like defects characterized by a delta
function-valued curvature and torsion distribution giving rise to rotational
and translational holonomy. We exploit this analogy and investigate how
distortions can be adapted in a systematic manner from solid state systems to
Einstein-Cartan gravity. As distortions are efficiently described within the
framework of a SO(3) {\rlap{\supset}\times}} T(3) gauge theory of solid
continua with line defects, we are led in a straightforward way to a Poincar\'e
gauge approach to gravity which is a natural framework for introducing the
notion of distorted spacetimes. Constructing all ten possible distorted
spacetimes, we recover, inter alia, the well-known exterior spacetime of a
spin-polarized cosmic string as a special case of such a geometry. In a second
step, we search for matter distributions which, in Einstein-Cartan gravity, act
as sources of distorted spacetimes. The resulting solutions, appropriately
matched to the distorted vacua, are cylindrically symmetric and are interpreted
as spin-polarized cosmic strings and cosmic dislocations.Comment: 24 pages, LaTeX, 9 eps figures; remarks on energy conditions added,
discussion extended, version to be published in Class. Quantum Gra
Progress in Classical and Quantum Variational Principles
We review the development and practical uses of a generalized Maupertuis
least action principle in classical mechanics, in which the action is varied
under the constraint of fixed mean energy for the trial trajectory. The
original Maupertuis (Euler-Lagrange) principle constrains the energy at every
point along the trajectory. The generalized Maupertuis principle is equivalent
to Hamilton's principle. Reciprocal principles are also derived for both the
generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis
Principle is the classical limit of Schr\"{o}dinger's variational principle of
wave mechanics, and is also very useful to solve practical problems in both
classical and semiclassical mechanics, in complete analogy with the quantum
Rayleigh-Ritz method. Classical, semiclassical and quantum variational
calculations are carried out for a number of systems, and the results are
compared. Pedagogical as well as research problems are used as examples, which
include nonconservative as well as relativistic systems
The gauge theory of dislocations: static solutions of screw and edge dislocations
We investigate the T(3)-gauge theory of static dislocations in continuous
solids. We use the most general linear constitutive relations bilinear in the
elastic distortion tensor and dislocation density tensor for the force and
pseudomoment stresses of an isotropic solid. The constitutive relations contain
six material parameters. In this theory both the force and pseudomoment
stresses are asymmetric. The theory possesses four characteristic lengths l1,
l2, l3 and l4 which are given explicitely. We first derive the
three-dimensional Green tensor of the master equation for the force stresses in
the translational gauge theory of dislocations. We then investigate the
situation of generalized plane strain (anti-plane strain and plane strain).
Using the stress function method, we find modified stress functions for screw
and edge dislocations. The solution of the screw dislocation is given in terms
of one independent length l1=l4. For the problem of an edge dislocation, only
two characteristic lengths l2 and l3 arise with one of them being the same
l2=l1 as for the screw dislocation. Thus, this theory possesses only two
independent lengths for generalized plane strain. If the two lengths l2 and l3
of an edge dislocation are equal, we obtain an edge dislocation which is the
gauge theoretical version of a modified Volterra edge dislocation. In the case
of symmetric stresses we recover well known results obtained earlier.Comment: 33 pages, 17 figure
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