2,929 research outputs found
Wall-thickness changes predicted in hollow-drawn tubing
Hollow-tube drawing or tube sinking theory is based on the concept of continuous distribution of dislocations. Material composition, parameter influence, and die-angle are determining factors in derivation of the theoretical model
Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region
Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities
Mesoscale theory of grains and cells: crystal plasticity and coarsening
Solids with spatial variations in the crystalline axes naturally evolve into
cells or grains separated by sharp walls. Such variations are mathematically
described using the Nye dislocation density tensor. At high temperatures,
polycrystalline grains form from the melt and coarsen with time: the
dislocations can both climb and glide. At low temperatures under shear the
dislocations (which allow only glide) form into cell structures. While both the
microscopic laws of dislocation motion and the macroscopic laws of coarsening
and plastic deformation are well studied, we hitherto have had no simple,
continuum explanation for the evolution of dislocations into sharp walls. We
present here a mesoscale theory of dislocation motion. It provides a
quantitative description of deformation and rotation, grounded in a microscopic
order parameter field exhibiting the topologically conserved quantities. The
topological current of the Nye dislocation density tensor is derived from a
microscopic theory of glide driven by Peach-Koehler forces between dislocations
using a simple closure approximation. The resulting theory is shown to form
sharp dislocation walls in finite time, both with and without dislocation
climb.Comment: 5 pages, 3 figure
Bending crystals: Emergence of fractal dislocation structures
We provide a minimal continuum model for mesoscale plasticity, explaining the
cellular dislocation structures observed in deformed crystals. Our dislocation
density tensor evolves from random, smooth initial conditions to form
self-similar structures strikingly similar to those seen experimentally -
reproducing both the fractal morphologies and some features of the scaling of
cell sizes and misorientations analyzed experimentally. Our model provides a
framework for understanding emergent dislocation structures on the mesoscale, a
bridge across a computationally demanding mesoscale gap in the multiscale
modeling program, and a new example of self-similar structure formation in
non-equilibrium systems.Comment: 4 pages, 4 figures, 5 movies (They can be found at
http://www.lassp.cornell.edu/sethna/Plasticity/SelfSimilarity.html .) In
press at Phys. Rev. Let
An atomic mechanism for the boson peak in metallic glasses
The boson peak in metallic glasses is modeled in terms of local structural
shear rearrangements. Using Eshelby's solution of the corresponding elasticity
theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can
calculate the saddle point energy of such a structural rearrangement. The
neighbourhood of the saddle point gives rise to soft resonant vibrational
modes. One can calculate their density, their kinetic energy, their fourth
order potential term and their coupling to longitudinal and transverse sound
waves.Comment: 9 pages, 7 figures, 31 references, contribution to 11th International
Workshop on Complex Systems, Andalo (Italy), March 200
Effective Elastic Moduli in Solids with High Crack Density
We investigate the weakening of elastic materials through randomly
distributed circles and cracks numerically and compare the results to
predictions from homogenization theories. We find a good agreement for the case
of randomly oriented cracks of equal length in an isotropic plane-strain medium
for lower crack densities; for higher densities the material is weaker than
predicted due to precursors of percolation. For a parallel alignment of cracks,
where percolation does not occur, we analytically predict a power law decay of
the effective elastic constants for high crack densities, and confirm this
result numerically.Comment: 8 page
Detailed Analysis of Balmer Lines in a Sloan Digital Sky Survey Sample of 90 Broad Line Active Galactic Nuclei
In order to contribute to the general effort aiming at the improvement of our
knowledge about the physical conditions within the Broad Line Region (BLR) of
Active Galactic Nuclei (AGN), here we present the results achieved by our
analysis of the spectral properties of a sample of 90 broad line emitting
sources, collected at the Sloan Digital Sky Survey (SDSS) database. By focusing
our attention mainly onto the Balmer series of hydrogen emission lines, which
is the dominant feature in the optical wavelength range of many BLR spectra, we
extracted several flux and profile measurements, which we related to other
source properties, such as optical continuum luminosities, inferred black hole
masses, and accretion rates. Using the Boltzmann Plot method to investigate the
Balmer line flux ratios as a function of the line profiles, we found that
broader line emitting AGN typically have larger H_alpha / H_beta and smaller
H_gamma / H_beta and H_delta / H_beta line ratios. With the help of some recent
investigations, we model the structure of the BLR and we study the influence of
the accretion process on the properties of the BLR plasma.Comment: 14 pages, 11 figures, fixes the wrong names of 4 objects; published
on Ap
Point defect in solids: Shear dominance of the far-field energy
It is shown that the elastic energy far from a point defect in an isotropic
solid is mainly shear elastic energy. The calculation, which is based on a
standard dipole expansion, shows that no matter how large or small the bulk
modulus is compared to the shear modulus, less than 10% of the distant point
defect energy is associated with volume changes.Comment: Brief not
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