606 research outputs found
Critical examination of cohesive-zone models in the theory of dynamic fracture
We have examined a class of cohesive-zone models of dynamic mode-I fracture,
looking both at steady-state crack propagation and its stability against
out-of-plane perturbations. Our work is an extension of that of Ching, Langer,
and Nakanishi (CLN) (Phys. Rev. E, vol. 53, no. 3, p. 2864 (1996)), who studied
a non-dissipative version of this model and reported strong instability at all
non-zero crack speeds. We have reformulated the CLN theory and have discovered,
surprisingly, that their model is mathematically ill-posed. In an attempt to
correct this difficulty and to construct models that might exhibit realistic
behavior, we have extended the CLN analysis to include dissipative mechanisms
within the cohesive zone. We have succeeded to some extent in finding
mathematically well posed systems; and we even have found a class of models for
which a transition from stability to instability may occur at a nonzero crack
speed via a Hopf bifurcation at a finite wavelength of the applied
perturbation. However, our general conclusion is that these cohesive-zone
models are inherently unsatisfactory for use in dynamical studies. They are
extremely difficult mathematically, and they seem to be highly sensitive to
details that ought to be physically unimportant.Comment: 19 pages, REVTeX 3.1, epsf.sty, also available at
http://itp.ucsb.edu/~lobkovs
Microstructural Shear Localization in Plastic Deformation of Amorphous Solids
The shear-transformation-zone (STZ) theory of plastic deformation predicts
that sufficiently soft, non-crystalline solids are linearly unstable against
forming periodic arrays of microstructural shear bands. A limited nonlinear
analysis indicates that this instability may be the mechanism responsible for
strain softening in both constant-stress and constant-strain-rate experiments.
The analysis presented here pertains only to one-dimensional banding patterns
in two-dimensional systems, and only to very low temperatures. It uses the
rudimentary form of the STZ theory in which there is only a single kind of zone
rather than a distribution of them with a range of transformation rates.
Nevertheless, the results are in qualitative agreement with essential features
of the available experimental data. The nonlinear theory also implies that
harder materials, which do not undergo a microstructural instability, may form
isolated shear bands in weak regions or, perhaps, at points of concentrated
stress.Comment: 32 pages, 6 figure
Steady-State Cracks in Viscoelastic Lattice Models II
We present the analytic solution of the Mode III steady-state crack in a
square lattice with piecewise linear springs and Kelvin viscosity. We show how
the results simplify in the limit of large width. We relate our results to a
model where the continuum limit is taken only along the crack direction. We
present results for small velocity, and for large viscosity, and discuss the
structure of the critical bifurcation for small velocity. We compute the size
of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure
Aharonov-Bohm oscillations in a mesoscopic ring with a quantum dot
We present an analysis of the Aharonov-Bohm oscillations for a mesoscopic
ring with a quantum dot inserted in one of its arms. It is shown that
microreversibility demands that the phase of the Aharonov-Bohm oscillations
changes {\it abruptly} when a resonant level crosses the Fermi energy. We use
the Friedel sum rule to discuss the conservation of the parity of the
oscillations at different conductance peaks. Our predictions are illustrated
with the help of a simple one channel model that permits the variation of the
potential landscape along the ring.Comment: 11 pages, Revtex style, 3 figures under request. Submitted to Phys.
Rev. B (rapid communications
Growth Kinetics in a Phase Field Model with Continuous Symmetry
We discuss the static and kinetic properties of a Ginzburg-Landau spherically
symmetric model recently introduced (Phys. Rev. Lett. {\bf 75}, 2176,
(1995)) in order to generalize the so called Phase field model of Langer. The
Hamiltonian contains two invariant fields and bilinearly
coupled. The order parameter field evolves according to a non conserved
dynamics, whereas the diffusive field follows a conserved dynamics. In the
limit we obtain an exact solution, which displays an interesting
kinetic behavior characterized by three different growth regimes. In the early
regime the system displays normal scaling and the average domain size grows as
, in the intermediate regime one observes a finite wavevector
instability, which is related to the Mullins-Sekerka instability; finally, in
the late stage the structure function has a multiscaling behavior, while the
domain size grows as .Comment: 9 pages RevTeX, 9 figures included, files packed with uufiles to
appear on Phy. Rev.
Numerical study of the shape and integral parameters of a dendrite
We present a numerical study of sidebranching of a solidifying dendrite by
means of a phase--field model. Special attention is paid to the regions far
from the tip of the dendrite, where linear theories are no longer valid. Two
regions have been distinguished outside the linear region: a first one in which
sidebranching is in a competition process and a second one further down where
branches behave as independent of each other. The shape of the dendrite and
integral parameters characterizing the whole dendrite (contour length and area
of the dendrite) have been computed and related to the characteristic tip
radius for both surface tension and kinetic dominated dendrites. Conclusions
about the different behaviors observed and comparison with available
experiments and theoretical predictions are presented.Comment: 10 pages, 7 figures, Accepted for publication in Phys. Rev.
Statistical Mechanics of Nonuniform Magnetization Reversal
The magnetization reversal rate via thermal creation of soliton pairs in
quasi-1D ferromagnetic systems is calculated. Such a model describes e.g. the
time dependent coercivity of elongated particles as used in magnetic recording
media. The energy barrier that has to be overcome by thermal fluctuations
corresponds to a soliton-antisoliton pair whose size depends on the external
field. In contrast to other models of first order phase transitions such as the
phi^4 model, an analytical expression for this energy barrier is found for all
values of the external field. The magnetization reversal rate is calculated
using a functional Fokker-Planck description of the stochastic magnetization
dynamics. Analytical results are obtained in the limits of small fields and
fields close to the anisotropy field. In the former case the hard-axis
anisotropy becomes effectively strong and the magnetization reversal rate is
shown to reduce to the nucleation rate of soliton-antisoliton pairs in the
overdamped double sine-Gordon model. The present theory therefore includes the
nucleation rate of soliton-antisoliton pairs in the double sine-Gordon chain as
a special case. These results demonstrate that for elongated particles, the
experimentally observed coercivity is significantly lower than the value
predicted by the standard theories of N\'eel and Brown.Comment: 21 pages RevTex 3.0 (twocolumn), 6 figures available on request, to
appear in Phys Rev B, Dec (1994
Phase separation and pattern formation
Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe
Ordering and finite-size effects in the dynamics of one-dimensional transient patterns
We introduce and analyze a general one-dimensional model for the description
of transient patterns which occur in the evolution between two spatially
homogeneous states. This phenomenon occurs, for example, during the
Freedericksz transition in nematic liquid crystals.The dynamics leads to the
emergence of finite domains which are locally periodic and independent of each
other. This picture is substantiated by a finite-size scaling law for the
structure factor. The mechanism of evolution towards the final homogeneous
state is by local roll destruction and associated reduction of local
wavenumber. The scaling law breaks down for systems of size comparable to the
size of the locally periodic domains. For systems of this size or smaller, an
apparent nonlinear selection of a global wavelength holds, giving rise to long
lived periodic configurations which do not occur for large systems. We also
make explicit the unsuitability of a description of transient pattern dynamics
in terms of a few Fourier mode amplitudes, even for small systems with a few
linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende
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