705 research outputs found
Domain Wall and Periodic Solutions of Coupled phi4 Models in an External Field
Coupled double well (phi4) one-dimensional potentials abound in both
condensed matter physics and field theory. Here we provide an exhaustive set of
exact periodic solutions of a coupled model in an external field in
terms of elliptic functions (domain wall arrays) and obtain single domain wall
solutions in specific limits. We also calculate the energy and interaction
between solitons for various solutions. Both topological and nontopological
(e.g. some pulse-like solutions in the presence of a conjugate field) domain
walls are obtained. We relate some of these solutions to the recently observed
magnetic domain walls in certain multiferroic materials and also in the field
theory context wherever possible. Discrete analogs of these coupled models,
relevant for structural transitions on a lattice, are also considered.Comment: 35 pages, no figures (J. Math. Phys. 2006
Oscillating elastic defects: competition and frustration
We consider a dynamical generalization of the Eshelby problem: the strain
profile due to an inclusion or "defect" in an isotropic elastic medium. We show
that the higher the oscillation frequency of the defect, the more localized is
the strain field around the defect. We then demonstrate that the qualitative
nature of the interaction between two defects is strongly dependent on
separation, frequency and direction, changing from "ferromagnetic" to
"antiferromagnetic" like behavior. We generalize to a finite density of defects
and show that the interactions in assemblies of defects can be mapped to XY
spin-like models, and describe implications for frustration and
frequency-driven pattern transitions.Comment: 4 pages, 5 figure
Modeling of Dislocation Structures in Materials
A phenomenological model of the evolution of an ensemble of interacting
dislocations in an isotropic elastic medium is formulated. The line-defect
microstructure is described in terms of a spatially coarse-grained order
parameter, the dislocation density tensor. The tensor field satisfies a
conservation law that derives from the conservation of Burgers vector.
Dislocation motion is entirely dissipative and is assumed to be locally driven
by the minimization of plastic free energy. We first outline the method and
resulting equations of motion to linear order in the dislocation density
tensor, obtain various stationary solutions, and give their geometric
interpretation. The coupling of the dislocation density to an externally
imposed stress field is also addressed, as well as the impact of the field on
the stationary solutions.Comment: RevTeX, 19 pages. Also at http://www.scri.fsu.edu/~vinals/jeff1.p
Predicting dislocation climb: Classical modeling versus atomistic simulations
The classical modeling of dislocation climb based on a continuous description
of vacancy diffusion is compared to recent atomistic simulations of dislocation
climb in body-centered cubic iron under vacancy supersaturation [Phys. Rev.
Lett. 105 095501 (2010)]. A quantitative agreement is obtained, showing the
ability of the classical approach to describe dislocation climb. The analytical
model is then used to extrapolate dislocation climb velocities to lower
dislocation densities, in the range corresponding to experiments. This allows
testing of the validity of the pure climb creep model proposed by Kabir et al.
[Phys. Rev. Lett. 105 095501 (2010)]
Fluctuations and scaling in creep deformation
The spatial fluctuations of deformation are studied in creep in the Andrade's
power-law and the logarithmic phases, using paper samples. Measurements by the
Digital Image Correlation technique show that the relative strength of the
strain rate fluctuations increases with time, in both creep regimes. In the
Andrade creep phase characterized by a power law decay of the strain rate
, with , the fluctuations obey
, with . The local
deformation follows a data collapse appropriate for an absorbing
state/depinning transition. Similar behavior is found in a crystal plasticity
model, with a jamming or yielding phase transition
Diffusion-controlled phase growth on dislocations
We treat the problem of diffusion of solute atoms around screw dislocations.
In particular, we express and solve the diffusion equation, in radial symmetry,
in an elastic field of a screw dislocation subject to the flux conservation
boundary condition at the interface of a new phase. We consider an incoherent
second-phase precipitate growing under the action of the stress field of a
screw dislocation. The second-phase growth rate as a function of the
supersaturation and a strain energy parameter is evaluated in spatial
dimensions d=2 and d=3. Our calculations show that an increase in the amplitude
of dislocation force, e.g. the magnitude of the Burgers vector, enhances the
second-phase growth in an alloy. Moreover, a relationship linking the
supersaturation to the precipitate size in the presence of the elastic field of
dislocation is calculated.Comment: 10 pages, 4 figures, a revised version of the paper presented in
MS&T'08, October 5-9, 2008, Pittsburg
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
Defects in Crystalline Packings of Twisted Filament Bundles: II. Dislocations and Grain Boundaries
Twisted and rope-like assemblies of filamentous molecules are common and
vital structural elements in cells and tissue of living organisms. We study the
intrinsic frustration occurring in these materials between the two-dimensional
organization of filaments in cross section and out-of-plane interfilament twist
in bundles. Using non-linear continuum elasticity theory of columnar materials,
we study the favorable coupling of twist-induced stresses to the presence of
edge dislocations in the lattice packing of bundles, which leads to a
restructuring of the ground-state order of these materials at intermediate
twist. The stability of dislocations increases as both the degree of twist and
lateral bundle size grow. We show that in ground states of large bundles,
multiple dislocations pile up into linear arrays, radial grain boundaries,
whose number and length grows with bundle twist, giving rise to a rich class of
"polycrystalline" packings.Comment: 10 pages, 7 figure
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