1,150 research outputs found
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
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