An observation on the experimental measurement of dislocation density

The common practice of ignoring the elastic strain gradient in measurements of geometrically necessary dislocation (GND) density is critically examined. It is concluded that the practice may result in substantial errors. Our analysis points to the importance of spatial variations of the elastic strain field in relation to its magnitude in inferring estimates of dislocation density from measurements

Roughening and preroughening in the six vertex model with an extended range of interaction

We study the phase diagram of the BCSOS model with an extended interaction range using transfer matrix techniques, pertaining to the (100) surface of single component fcc and bcc crystals. The model shows a 2x2 reconstructed phase and a disordered flat phase. The deconstruction transition between these phases merges with a Kosterlitz-Thouless line, showing an interplay of Ising and Gaussian degrees of freedom. As in studies of the fully frustrated XY model, exponents deviating from Ising are found. We conjecture that tri-critical Ising behavior may be a possible explanation for the non-Ising exponents found in those models.Comment: 25 pages in RevTeX 3.0, seven uuencoded postscript figures, REPLACED because of submission error (figures were not included

Is surface melting a surface phase transition?

Monte Carlo or Molecular Dynamics calculations of surfaces of Lennard-Jones systems often indicate, apart from a gradual disordering of the surface called surface melting, the presence of a phase transition at the surface, but cannot determine the nature of the transition. In the present paper, we provide for a link between the continuous Lennard-Jones system and a lattice model. We apply the method for the (001) surface of a Lennard-Jones fcc structure pertaining to Argon. The corresponding lattice model is a Body Centered Solid on Solid model with an extended range of interaction, showing in principle rough, flat and disordered flat phases. We observe that entropy effects considerably lower the strength of the effective couplings between the atoms. The Argon (001) face is shown to exhibit a phase transition at T=70.5 +- 0.5 K, and we identify this transition as roughening. The roughening temperature is in good correspondence with experimental results for Argon.Comment: 17 pages REVTeX, 14 uuencoded postscript figures appende

Spatial and structural stability in thermoelasto-dynamics on a half-cylinder

EnThe linear nonhomogeneous thermoelastodynamic problem in a half-cylinder is considered subject to assigned initial conditions, and to the displacement and temperature being specified over the base, and vanishing on the lateral boundary. Spatial stability, derived from a differential inequality, establishes that the mean-square volume integrals of displacement and temperature are bounded above by a decaying function of axial distance for each finite positive time instant. Structural stability, which here relates to continuous dependence of the displacement on the thermal coupling, depends upon the construction of further differential inequalities

Spatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section

The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-015-9523-8Alternative growth and decay estimates, reminiscent of the classical Phragmén-Lindelöf principle, are derived for a linearised thermoelastic body whose plane crosssections increase unboundedly with respect to a given direction. The proof uses a modified Poincaré inequality to construct a differential inequality for a weighted linear combination of the cross-sectional mechanical and thermal energy fluxes. Decay estimates are deduced also for the cross-sectional mean square measures of the displacement and temperature. An explicit upper bound in terms of base data is established for the amplitude occurring in the decay estimates.Peer ReviewedPostprint (author’s final draft

Spatial decay in transient heat conduction for general elongated regions

Zanaboni's procedure for establishing Saint-Venant's principle is ex- tended to anisotropic homogeneous transient heat conduction on regions that are successively embedded in each other to become indefinitely elon- gated. No further geometrical restrictions are imposed. The boundary of each region is maintained at zero temperature apart from the common surface of intersection which is heated to the same temperature assumed to be of bounded time variation. Heat sources are absent. Subject to these conditions, the thermal energy, supposed bounded in each region, becomes vanishingly small in those parts of the regions suficiently remote from the heated common surface. As with the original treatment, the proof involves certain monotone bounded sequences, and does not depend upon differential inequalities or the maximum principle. A definition is presented of an elongated region.Peer ReviewedPostprint (author's final draft

On quasi-static approximations in linear thermoelastodynamics

The validity of the coupled and uncoupled quasi-static approximations is considered for the initial boundary value problem of linear thermoelasticity subject to homoge-neous Dirichlet boundary conditions, and for solutions and their derivatives that are mean-square integrable. Essential components in the proof, of independent interest, are conservation laws and associated estimates for the exact and approximate systemsPeer ReviewedPostprint (author's final draft

Non-Uniqueness in Plane Fluid Flows

Examples of dynamical systems proposed by Artstein and Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point produces an infinite number of solutions with the same initial data. Dafermos appeals to a maximal entropy rate criterion to recover uniqueness. These results are here interpreted as non-unique Lagrange trajectories on a particular spatial region. The corresponding velocity is proved consistent with plane steady compressible fluid flows that for specified pressure and mass density satisfy not only the Euler equations but also the Navier-Stokes equations for specially chosen volume and (positive) shear viscosities. The maximal entropy rate criterion recovers uniqueness.Comment: 25 pages, 10 figure

Breakdown of a conservation law in incommensurate systems

We show that invariance properties of the Lagrangian of an incommensurate system, as described by the Frenkel Kontorova model, imply the existence of a generalized angular momentum which is an integral of motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the system as floating (when it is conserved) or locked (when it is not). We find that, during the dynamics, the non-linear couplings of our model cause parametric phonon excitations which lead to the appearance of Umklapp terms and to a sudden deviation of the generalized momentum from a constant value, signalling a dynamical transition from a floating to a pinned state. We point out that this transition is related but does not coincide with the onset of sliding friction which can take place when the system is still floating.Comment: 7 pages, 6 figures, typed with RevTex, submitted to Phys. Rev. E Replaced 27-03-2001: changes to text, minor revision of figure