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Unique Quantum Stress Fields
We have recently developed a geometric formulation of the stress field for an
interacting quantum system within the local density approximation (LDA) of
density functional theory (DFT). We obtain a stress field which is invariant
with respect to choice of energy density. In this paper, we explicitly
demonstrate this uniqueness by deriving the stress field for different energy
densities. We also explain why particular energy densities give expressions for
the stress field that are more tractable than others, thereby lending
themselves more easily to first-principles calculations.Comment: To appear in Proceedings for Fundamental Physics of Ferroelectrics
(2001
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
Internal stresses in steel plate generated by shape memory alloy inserts
Neutron strain scanning was employed to investigate the internal stress fields in steel plate coupons with embedded prestrained superelastic NiTi shape memory alloy inserts. Strain fields in steel were evaluated at T = 21 °C and 130 °C on virgin coupons as well as on mechanically and thermally fatigued coupons. Internal stress fields were evaluated by direct calculation of principal stress components from the experimentally measured lattice strains as well as by employing an inverse finite element modeling approach. It is shown that if the NiTi inserts are embedded into the elastic steel matrix following a carefully designed technological procedure, the internal stress fields vary with temperature in a reproducible and predictable way. It is estimated that this mechanism of internal stress generation can be safely applied in the temperature range from −20 °C to 150 °C and is relatively resistant to thermal and mechanical fatigue. The predictability and fatigue endurance of the mechanism are of essential importance for the development of future smart metal matrix composites or smart structures with embedded shape memory alloy components
A Geometric Formulation of Quantum Stress Fields
We present a derivation of the stress field for an interacting quantum system
within the framework of local density functional theory. The formulation is
geometric in nature and exploits the relationship between the strain tensor
field and Riemannian metric tensor field. Within this formulation, we
demonstrate that the stress field is unique up to a single ambiguous parameter.
The ambiguity is due to the non-unique dependence of the kinetic energy on the
metric tensor. To illustrate this formalism, we compute the pressure field for
two phases of solid molecular hydrogen. Furthermore, we demonstrate that
qualitative results obtained by interpreting the hydrogen pressure field are
not influenced by the presence of the kinetic ambiguity.Comment: 22 pages, 2 figures. Submitted to Physical Review B. This paper
supersedes cond-mat/000627
Analytic approximation and an improved method for computing the stress-energy of quantized scalar fields in Robertson-Walker spacetimes
An improved method is given for the computation of the stress-energy tensor
of a quantized scalar field using adiabatic regularization. The method works
for fields with arbitrary mass and curvature coupling in Robertson-Walker
spacetimes and is particularly useful for spacetimes with compact spatial
sections. For massless fields it yields an analytic approximation for the
stress-energy tensor that is similar in nature to those obtained previously for
massless fields in static spacetimes.Comment: RevTeX, 8 pages, no figure
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