744 research outputs found
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
Remarkable Objects: Supporting Collaboration in a Creative Environment
In this paper, we report the results of a field trial of a Ubicomp system called CAM that is aimed at supporting and enhancing collaboration in a design studio environment. CAM uses a mobile-tagging application which allows designers to collaboratively store relevant information onto their physical design objects in the form of messages, annotations and external web links. The purpose of our field trial was to explore the role of augmented objects in supporting and enhancing creative work. Our results show that CAM was used not only used to support participantsâ mutual awareness and coordination but also to facilitate designers in appropriating their augmented design objects to be explorative, extendable and playful supporting creative aspects of design work. In general, our results show how CAM transformed static design objects into âremarkableâ objects that made the creative and playful side of cooperative design visible
Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter
Torsional degrees of freedom play an important role in modern gravity
theories as well as in condensed matter systems where they can be modeled by
defects in solids. Here we isolate a class of torsion models that support
torsion configurations with a localized, conserved charge that adopts integer
values. The charge is topological in nature and the torsional configurations
can be thought of as torsional `monopole' solutions. We explore some of the
properties of these configurations in gravity models with non-vanishing
curvature, and discuss the possible existence of such monopoles in condensed
matter systems. To conclude, we show how the monopoles can be thought of as a
natural generalization of the Cartan spiral staircase.Comment: 4+epsilon, 1 figur
Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor
We derive general relations between grain boundaries, rotational
deformations, and stress-free states for the mesoscale continuum Nye
dislocation density tensor. Dislocations generally are associated with
long-range stress fields. We provide the general form for dislocation density
fields whose stress fields vanish. We explain that a grain boundary (a
dislocation wall satisfying Frank's formula) has vanishing stress in the
continuum limit. We show that the general stress-free state can be written
explicitly as a (perhaps continuous) superposition of flat Frank walls. We show
that the stress-free states are also naturally interpreted as configurations
generated by a general spatially-dependent rotational deformation. Finally, we
propose a least-squares definition for the spatially-dependent rotation field
of a general (stressful) dislocation density field.Comment: 9 pages, 3 figure
The Dislocation Stress Functions From the Double Curl T(3)-Gauge Equation: Linearity and a Look Beyond
T(3)-gauge model of defects based on the gauge Lagrangian quadratic in the
gauge field strength is considered. The equilibrium equation of the medium is
fulfilled by the double curl Kroner's ansatz for stresses. The problem of
replication of the static edge dislocation along third axis is analysed under a
special, though conventional, choice of this ansatz. The translational gauge
equation is shown to constraint the functions parametrizing the ansatz (the
stress functions) so that the resulting stress component is not
that of the edge defect. Another translational gauge equation with the double
curl differential operator is shown to reproduce both the stress functions, as
well as the stress tensors, of the standard edge and screw dislocations.
Non-linear extension of the newly proposed translational gauge equation is
given to correct the linear defect solutions in next orders. New gauge
Lagrangian is suggested in the Hilbert-Einstein form.Comment: 21 pages, LaTeX, no figure
Volume elements and torsion
We reexamine here the issue of consistency of minimal action formulation with
the minimal coupling procedure (MCP) in spaces with torsion. In Riemann-Cartan
spaces, it is known that a proper use of the MCP requires that the trace of the
torsion tensor be a gradient, , and that the modified
volume element be
used in the action formulation of a physical model. We rederive this result
here under considerably weaker assumptions, reinforcing some recent results
about the inadequacy of propagating torsion theories of gravity to explain the
available observational data. The results presented here also open the door to
possible applications of the modified volume element in the geometric theory of
crystalline defects.Comment: Revtex, 8 pages, 1 figure. v2 includes a discussion on
-symmetr
Aharonov-Bohm Effect and Disclinations in an Elastic Medium
In this work we investigate quasiparticles in the background of defects in
solids using the geometric theory of defects. We use the parallel transport
matrix to study the Aharonov-Bohm effect in this background. For quasiparticles
moving in this effective medium we demonstrate an effect similar to the
gravitational Aharonov- Bohm effect. We analyze this effect in an elastic
medium with one and defects.Comment: 6 pages, Revtex
A gauge theoretic approach to elasticity with microrotations
We formulate elasticity theory with microrotations using the framework of
gauge theories, which has been developed and successfully applied in various
areas of gravitation and cosmology. Following this approach, we demonstrate the
existence of particle-like solutions. Mathematically this is due to the fact
that our equations of motion are of Sine-Gordon type and thus have soliton type
solutions. Similar to Skyrmions and Kinks in classical field theory, we can
show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page;
revised and extended versio
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
On the incompatibility of strains and its application to mesoscopic studies of plasticity
Structural transitions are invariably affected by lattice distortions. If the
body is to remain crack-free, the strain field cannot be arbitrary but has to
satisfy the Saint-Venant compatibility constraint. Equivalently, an
incompatibility constraint consistent with the actual dislocation network has
to be satisfied in media with dislocations. This constraint can be incorporated
into strain-based free energy functionals to study the influence of
dislocations on phase stability. We provide a systematic analysis of this
constraint in three dimensions and show how three incompatibility equations
accommodate an arbitrary dislocation density. This approach allows the internal
stress field to be calculated for an anisotropic material with spatially
inhomogeneous microstructure and distribution of dislocations by minimizing the
free energy. This is illustrated by calculating the stress field of an edge
dislocation and comparing it with that of an edge dislocation in an infinite
isotropic medium. We outline how this procedure can be utilized to study the
interaction of plasticity with polarization and magnetization.Comment: 6 pages, 2 figures; will appear in Phys. Rev.
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