330 research outputs found
Ab initio parametrised model of strain-dependent solubility of H in alpha-iron
The calculated effects of interstitial hydrogen on the elastic properties of
alpha-iron from our earlier work are used to describe the H interactions with
homogeneous strain fields using ab initio methods. In particular we calculate
the H solublility in Fe subject to hydrostatic, uniaxial, and shear strain. For
comparison, these interactions are parametrised successfully using a simple
model with parameters entirely derived from ab initio methods. The results are
used to predict the solubility of H in spatially-varying elastic strain fields,
representative of realistic dislocations outside their core. We find a strong
directional dependence of the H-dislocation interaction, leading to strong
attraction of H by the axial strain components of edge dislocations and by
screw dislocations oriented along the critical slip direction. We
further find a H concentration enhancement around dislocation cores, consistent
with experimental observations.Comment: part 2/2 from splitting of 1009.3784 (first part was 1102.0187),
minor changes from previous version
Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects
We develop a theory of Brownian motion of a massive particle, including the
effects of inertia (Kramers' problem), in spaces with curvature and torsion.
This is done by invoking the recently discovered generalized equivalence
principle, according to which the equations of motion of a point particle in
such spaces can be obtained from the Newton equation in euclidean space by
means of a nonholonomic mapping. By this principle, the known Langevin equation
in euclidean space goes over into the correct Langevin equation in the Cartan
space. This, in turn, serves to derive the Kubo and Fokker-Planck equations
satisfied by the particle distribution as a function of time in such a space.
The theory can be applied to classical diffusion processes in crystals with
defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm
Gauge theory of disclinations on fluctuating elastic surfaces
A variant of a gauge theory is formulated to describe disclinations on
Riemannian surfaces that may change both the Gaussian (intrinsic) and mean
(extrinsic) curvatures, which implies that both internal strains and a location
of the surface in R^3 may vary. Besides, originally distributed disclinations
are taken into account. For the flat surface, an extended variant of the
Edelen-Kadic gauge theory is obtained. Within the linear scheme our model
recovers the von Karman equations for membranes, with a disclination-induced
source being generated by gauge fields. For a single disclination on an
arbitrary elastic surface a covariant generalization of the von Karman
equations is derived.Comment: 13 page
Autoparallels From a New Action Principle
We present a simpler and more powerful version of the recently-discovered
action principle for the motion of a spinless point particle in spacetimes with
curvature and torsion. The surprising feature of the new principle is that an
action involving only the metric can produce an equation of motion with a
torsion force, thus changing geodesics to autoparallels. This additional
torsion force arises from a noncommutativity of variations with parameter
derivatives of the paths due to the closure failure of parallelograms in the
presence of torsionComment: Paper in src. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Read paper directly
with Netscape under
http://www.physik.fu-berlin.de/~kleinert/kleiner_re243/preprint.htm
Regge Calculus in Teleparallel Gravity
In the context of the teleparallel equivalent of general relativity, the
Weitzenbock manifold is considered as the limit of a suitable sequence of
discrete lattices composed of an increasing number of smaller an smaller
simplices, where the interior of each simplex (Delaunay lattice) is assumed to
be flat. The link lengths between any pair of vertices serve as independent
variables, so that torsion turns out to be localized in the two dimensional
hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a
vector undergoes a dislocation in relation to its initial position as it is
parallel transported along the perimeter of the dual lattice (Voronoi polygon),
we obtain the discrete analogue of the teleparallel action, as well as the
corresponding simplicial vacuum field equations.Comment: Latex, 10 pages, 2 eps figures, to appear in Class. Quant. Gra
Torsion Degrees of Freedom in the Regge Calculus as Dislocations on the Simplicial Lattice
Using the notion of a general conical defect, the Regge Calculus is
generalized by allowing for dislocations on the simplicial lattice in addition
to the usual disclinations. Since disclinations and dislocations correspond to
curvature and torsion singularities, respectively, the method we propose
provides a natural way of discretizing gravitational theories with torsion
degrees of freedom like the Einstein-Cartan theory. A discrete version of the
Einstein-Cartan action is given and field equations are derived, demanding
stationarity of the action with respect to the discrete variables of the
theory
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
Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor
The lecture explains the geometric basis for the recently-discovered
nonholonomic mapping principle which specifies certain laws of nature in
spacetimes with curvature and torsion from those in flat spacetime, thus
replacing and extending Einstein's equivalence principle. An important
consequence is a new action principle for determining the equation of motion of
a free spinless point particle in such spacetimes. Surprisingly, this equation
contains a torsion force, although the action involves only the metric. This
force changes geodesic into autoparallel trajectories, which are a direct
manifestation of inertia. The geometric origin of the torsion force is a
closure failure of parallelograms. The torsion force changes the covariant
conservation law of the energy-momentum tensor whose new form is derived.Comment: Corrected typos. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re261/preprint.htm
The Inverse Variational Problem for Autoparallels
We study the problem of the existence of a local quantum scalar field theory
in a general affine metric space that in the semiclassical approximation would
lead to the autoparallel motion of wave packets, thus providing a deviation of
the spinless particle trajectory from the geodesics in the presence of torsion.
The problem is shown to be equivalent to the inverse problem of the calculus of
variations for the autoparallel motion with additional conditions that the
action (if it exists) has to be invariant under time reparametrizations and
general coordinate transformations, while depending analytically on the torsion
tensor. The problem is proved to have no solution for a generic torsion in
four-dimensional spacetime. A solution exists only if the contracted torsion
tensor is a gradient of a scalar field. The corresponding field theory
describes coupling of matter to the dilaton field.Comment: 13 pages, plain Latex, no figure
Gravitational Geometric Phase in the Presence of Torsion
We investigate the relativistic and non-relativistic quantum dynamics of a
neutral spin-1/2 particle submitted an external electromagnetic field in the
presence of a cosmic dislocation. We analyze the explicit contribution of the
torsion in the geometric phase acquired in the dynamic of this neutral
spinorial particle. We discuss the influence of the torsion in the relativistic
geometric phase. Using the Foldy-Wouthuysen approximation, the non-relativistic
quantum dynamics are studied and the influence of the torsion in the
Aharonov-Casher and He-McKellar-Wilkens effects are discussed.Comment: 14 pages, no figur
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