420,588 research outputs found
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.
Gauge Theory of Gravity and Supergravity
We present a formulation of gravity in terms of a theory based on complex
SU(2) gauge fields with a general coordinate invariant action functional
quadratic in the field strength. Self-duality or anti-self-duality of the field
strength emerges as a constraint from the equations of motion of this theory.
This in turn leads to Einstein gravity equations for a dilaton and an axion
conformally coupled to gravity for the self-dual constraint. The analysis has
also been extended to N=1 and 2 super Yang-Mills theory of complex SU(2) gauge
fields. This leads, besides other equations of motion, to
self-duality/anti-self-duality of generalized supercovariant field-strengths.
The self-dual case is then shown to yield as its solutions
supergravity equations respectively.Comment: 27 page
Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term
Since there are quantization ambiguities in constructing the Hamiltonian
constraint operator in isotropic loop quantum cosmology, it is crucial to check
whether the key features of loop quantum cosmology are robust against the
ambiguities. In this paper, we quantize the Lorentz term of the gravitational
Hamiltonian constraint in the spatially flat FRW model by two approaches
different from that of the Euclidean term. One of the approaches is very
similar to the treatment of the Lorentz part of Hamiltonian in loop quantum
gravity and hence inherits more features from the full theory. Two symmetric
Hamiltonian constraint operators are constructed respectively in the improved
scheme. Both of them are shown to have the correct classical limit by the
semiclassical analysis. In the loop quantum cosmological model with a massless
scalar field, the effective Hamiltonians and Friedmann equations are derived.
It turns out that the classical big bang is again replaced by a quantum bounce
in both cases. Moreover, there are still great possibilities for the expanding
universe to recollapse due to the quantum gravity effect.Comment: 8 pages, 2 figure
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