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

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 $\phi^4$ 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

Generalized stacking fault energetics and dislocation properties: compact vs. spread unit dislocation structures in TiAl and CuAu

We present a general scheme for analyzing the structure and mobility of dislocations based on solutions of the Peierls-Nabarro model with a two component displacement field and restoring forces determined from the ab-initio generalized stacking fault energetics (ie., the so-called $\gamma$-surface). The approach is used to investigate dislocations in L1$_{0}$ TiAl and CuAu; predicted differences in the unit dislocation properties are explicitly related with features of the $\gamma$-surface geometry. A unified description of compact, spread and split dislocation cores is provided with an important characteristic "dissociation path" revealed by this highly tractable scheme.Comment: 7 two columns pages, 2 eps figures. Phys. Rev. B. accepted November 199

Numerical study of domain coarsening in anisotropic stripe patterns

We study the coarsening of two-dimensional smectic polycrystals characterized by grains of oblique stripes with only two possible orientations. For this purpose, an anisotropic Swift-Hohenberg equation is solved. For quenches close enough to the onset of stripe formation, the average domain size increases with time as $t^{1/2}$. Further from onset, anisotropic pinning forces similar to Peierls stresses in solid crystals slow down defects, and growth becomes anisotropic. In a wide range of quench depths, dislocation arrays remain mobile and dislocation density roughly decays as $t^{-1/3}$, while chevron boundaries are totally pinned. We discuss some agreements and disagreements found with recent experimental results on the coarsening of anisotropic electroconvection patterns.Comment: 8 pages, 11 figures. Phys. Rev E, to appea

Evolution of a Network of Vortex Loops in HeII. Exact Solution of the "Rate Equation"

Evolution of a network of vortex loops in HeII due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function $n(l)$ of number of loops of length $l$ proposed by Copeland with coauthors. By using the special ansatz in the ''collision'' integral we have found the exact power-like solution of ''kinetic equation'' in stationary case. That solution is the famous equilibrium distribution $n(l)\varpropto l^{-5/2}$ obtained earlier in numerical calculations. Our result, however, is not equilibrium, but on the contrary, it describes the state with two mutual fluxes of the length (or energy) in space of the vortex loop sizes. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of order of interline space. We also obtain that the decay of the vortex tangle obeys the Vinen equation, obtained earlier phenomenologically. We evaluate also the full rate of reconnection events. PACS-number 67.40Comment: 4 pages, submitted to PR

Shear-melting of a hexagonal columnar crystal by proliferation of dislocations

A hexagonal columnar crystal undergoes a shear-melting transition above a critical shear rate or stress. We combine the analysis of the shear-thinning regime below the melting with that of synchrotron X-ray scattering data under shear and propose the melting to be due to a proliferation of dislocations, whose density is determined by both techniques to vary as a power law of the shear rate with a 2/3 exponent, as expected for a creep model of crystalline solids. Moreover, our data suggest the existence under shear of a line hexatic phase, between the columnar crystal and the liquid phase

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)]

The quantum smectic as a dislocation Higgs phase

The theory describing quantum-smectics in 2+1 dimensions, based on topological quantum melting is presented. This is governed by a dislocation condensate characterized by an ordering of Burger's vector and this `dual shear superconductor' manifests itself in the form of a novel spectrum of phonon-like modes.Comment: 5 pages, 3 figures; minor changes in the tex

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 $\epsilon_t \sim t^{-\theta}$, with $\theta \approx 0.7$, the fluctuations obey $\Delta \epsilon_t \sim t^{-\gamma}$, with $\gamma \approx 0.5$. 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