11,649 research outputs found
A microscopic model for solidification
We present a novel picture of a non isothermal solidification process
starting from a molecular level, where the microscopic origin of the basic
mechanisms and of the instabilities characterizing the approach to equilibrium
is rendered more apparent than in existing approaches based on coarse grained
free energy functionals \`a la Landau.
The system is composed by a lattice of Potts spins, which change their state
according to the stochastic dynamics proposed some time ago by Creutz. Such a
method is extended to include the presence of latent heat and thermal
conduction.
Not only the model agrees with previous continuum treatments, but it allows
to introduce in a consistent fashion the microscopic stochastic fluctuations.
These play an important role in nucleating the growing solid phase in the melt.
The approach is also very satisfactory from the quantitative point of view
since the relevant growth regimes are fully characterized in terms of scaling
exponents.Comment: 7 pages Latex +3 figures.p
Steady-state, effective-temperature dynamics in a glassy material
We present an STZ-based analysis of numerical simulations by Haxton and Liu
(HL). The extensive HL data sharply test the basic assumptions of the STZ
theory, especially the central role played by the effective disorder
temperature as a dynamical state variable. We find that the theory survives
these tests, and that the HL data provide important and interesting constraints
on some of its specific ingredients. Our most surprising conclusion is that,
when driven at various constant shear rates in the low-temperature glassy
state, the HL system exhibits a classic glass transition, including
super-Arrhenius behavior, as a function of the effective temperature.Comment: 9 pages, 6 figure
Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
We use the shear transformation zone (STZ) theory of dynamic plasticity to
study the necking instability in a two-dimensional strip of amorphous solid.
Our Eulerian description of large-scale deformation allows us to follow the
instability far into the nonlinear regime. We find a strong rate dependence;
the higher the applied strain rate, the further the strip extends before the
onset of instability. The material hardens outside the necking region, but the
description of plastic flow within the neck is distinctly different from that
of conventional time-independent theories of plasticity.Comment: 4 pages, 3 figures (eps), revtex4, added references, changed and
added content, resubmitted to PR
Rate dependent shear bands in a shear transformation zone model of amorphous solids
We use Shear Transformation Zone (STZ) theory to develop a deformation map
for amorphous solids as a function of the imposed shear rate and initial
material preparation. The STZ formulation incorporates recent simulation
results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state
effective temperature is rate dependent. The resulting model predicts a wide
range of deformation behavior as a function of the initial conditions,
including homogeneous deformation, broad shear bands, extremely thin shear
bands, and the onset of material failure. In particular, the STZ model predicts
homogeneous deformation for shorter quench times and lower strain rates, and
inhomogeneous deformation for longer quench times and higher strain rates. The
location of the transition between homogeneous and inhomogeneous flow on the
deformation map is determined in part by the steady state effective
temperature, which is likely material dependent. This model also suggests that
material failure occurs due to a runaway feedback between shear heating and the
local disorder, and provides an explanation for the thickness of shear bands
near the onset of material failure. We find that this model, which resolves
dynamics within a sheared material interface, predicts that the stress weakens
with strain much more rapidly than a similar model which uses a single state
variable to specify internal dynamics on the interface.Comment: 10 pages, 13 figures, corrected typos, added section on rate
strengthening vs. rate weakening material
Capillary-Wave Model for the Solidification of Dilute Binary Alloys
Starting from a phase-field description of the isothermal solidification of a
dilute binary alloy, we establish a model where capillary waves of the
solidification front interact with the diffusive concentration field of the
solute. The model does not rely on the sharp-interface assumption, and includes
non-equilibrium effects, relevant in the rapid-growth regime. In many
applications it can be evaluated analytically, culminating in the appearance of
an instability which, interfering with the Mullins-Sekerka instability, is
similar to that, found by Cahn in grain-boundary motion.Comment: 17 pages, 12 figure
Hamiltonians for curves
We examine the equilibrium conditions of a curve in space when a local energy
penalty is associated with its extrinsic geometrical state characterized by its
curvature and torsion. To do this we tailor the theory of deformations to the
Frenet-Serret frame of the curve. The Euler-Lagrange equations describing
equilibrium are obtained; Noether's theorem is exploited to identify the
constants of integration of these equations as the Casimirs of the euclidean
group in three dimensions. While this system appears not to be integrable in
general, it {\it is} in various limits of interest. Let the energy density be
given as some function of the curvature and torsion, . If
is a linear function of either of its arguments but otherwise arbitrary, we
claim that the first integral associated with rotational invariance permits the
torsion to be expressed as the solution of an algebraic equation in
terms of the bending curvature, . The first integral associated with
translational invariance can then be cast as a quadrature for or for
.Comment: 17 page
The Perils Of Authorship: Literary Propoerty And Nineteenth-Century American Fiction
This chapter examines the perils associated with American authorship during the early nineteenth century, with particular reference to issue of intellectual property and copyright. It begins with an analysis of the impact of intellectual property rights on publishing and the culture of reprinting, along with the influence of copyright on the American novel. It then considers the problem concerning the definition of “American authorship” and how the unstable nature of American authorship subjected writers who wished to promote it to charges of fraudulence. It also explores the question of originality among writers before concluding with a discussion of the radical expansion of publishing in the post-Civil War era and its effects on literary property and literary nationalism
Chemical composition and origin of nebulae around Luminous Blue Variables
We use the analysis of the heavy element abundances (C, N, O, S) in
circumstellar nebulae around Luminous Blue Variables to infer the evolutionary
phase in which the material has been ejected.
(1) We discuss the different effects that may have changed the gas
composition of the nebula since it was ejected
(2) We calculate the expected abundance changes at the stellar surface due to
envelope convection in the red supergiant phase. If the observed LBV nebulae
are ejected during the RSG phase, the abundances of the LBV nebulae require a
significantly smaller amount of mass to be lost than assumed in evolutionary
models.
(3) We calculate the changes in the surface composition during the main
sequence phase by rotation induced mixing. If the nebulae are ejected at the
end of the MS-phase, the abundances in LBV nebulae are compatible with mixing
times between 5 x 10^6 and 1 x 10^7 years. The existence of ON stars supports
this scenario.
(4) The predicted He/H ratio in the nebulae are significantly smaller than
the current observed photospheric values of their central stars.
Combining various arguments we show that the LBV nebulae are ejected during
the blue SG phase and that the stars have not gone through a RSG phase. The
chemical enhancements are due to rotation induced mixing, and the ejection is
possibly triggered by near-critical rotation. During the ejection, the outflow
was optically thick, which resulted in a large effective radius and a low
effective temperature. This also explains the observed properties of LBV dust.Comment: 18 pages, 4 figures, to be published in The Astrophysical Journal,
April 20, 200
Localized induction equation and pseudospherical surfaces
We describe a close connection between the localized induction equation
hierarchy of integrable evolution equations on space curves, and surfaces of
constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A:
Mathematical and Genera
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