10,511 research outputs found
Dynamic Crack Tip Equation of Motion: High-speed Oscillatory Instability
A dynamic crack tip equation of motion is proposed based on the autonomy of
the near-tip nonlinear zone of scale , symmetry principles,
causality and scaling arguments. Causality implies that the asymptotic
linear-elastic fields at time are determined by the crack path at a {\bf
retarded time} , where the delay time scales with the ratio
of and the typical wave speed within the nonlinear zone.
The resulting equation is shown to agree with known results in the quasi-static
regime. As a first application in the fully dynamic regime, an approximate
analysis predicts a high-speed oscillatory instability whose characteristic
scale is determined by . This prediction is corroborated by
experimental results, demonstrating the emergence of crack tip inertia-like
effects.Comment: 4 pages, 2 figures; minor change
Equilibrium orbit analysis in a free-electron laser with a coaxial wiggler
An analysis of single-electron orbits in combined coaxial wiggler and axial
guide magnetic fields is presented. Solutions of the equations of motion are
developed in a form convenient for computing orbital velocity components and
trajectories in the radially dependent wiggler. Simple analytical solutions are
obtained in the radially-uniform-wiggler approximation and a formula for the
derivative of the axial velocity with respect to Lorentz factor
is derived. Results of numerical computations are presented and the
characteristics of the equilibrium orbits are discussed. The third spatial
harmonic of the coaxial wiggler field gives rise to group orbits which
are characterized by a strong negative mass regime.Comment: 13 pages, 9 figures, to appear in phys. rev.
Reconstruction of potential energy profiles from multiple rupture time distributions
We explore the mathematical and numerical aspects of reconstructing a
potential energy profile of a molecular bond from its rupture time
distribution. While reliable reconstruction of gross attributes, such as the
height and the width of an energy barrier, can be easily extracted from a
single first passage time (FPT) distribution, the reconstruction of finer
structure is ill-conditioned. More careful analysis shows the existence of
optimal bond potential amplitudes (represented by an effective Peclet number)
and initial bond configurations that yield the most efficient numerical
reconstruction of simple potentials. Furthermore, we show that reconstruction
of more complex potentials containing multiple minima can be achieved by
simultaneously using two or more measured FPT distributions, obtained under
different physical conditions. For example, by changing the effective potential
energy surface by known amounts, additional measured FPT distributions improve
the reconstruction. We demonstrate the possibility of reconstructing potentials
with multiple minima, motivate heuristic rules-of-thumb for optimizing the
reconstruction, and discuss further applications and extensions.Comment: 20 pages, 9 figure
Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations
This article describes coherent gradient sensing (CGS) as an optical, full-field, real-time, nonintrusive, and noncontact technique for the measurement of curvatures and nonuniform curvature changes in film-substrate systems. The technique is applied to the study of curvature fields in thin Al films (6 mum) deposited on thin circular silicon wafers (105 mum) of "large" in-plane dimensions (50.8 mm in diameter) subjected to thermal loading histories. The loading and geometry is such that the system experiences deformations that are clearly within the nonlinear range. The discussion is focused on investigating the limits of the range of the linear relationship between the thermally induced mismatch strain and the substrate curvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and finally, on the bifurcation of deformation mode from axial symmetry to asymmetry with increasing mismatch strain. Results obtained on the basis of both simple models and more-detailed finite-element simulations are compared with the full-field CGS measurements with the purpose of validating the analytical and numerical models
Autonomy and Singularity in Dynamic Fracture
The recently developed weakly nonlinear theory of dynamic fracture predicts
corrections to the standard asymptotic linear elastic
displacement-gradients, where is measured from the tip of a tensile crack.
We show that the singularity does not automatically conform with the
notion of autonomy (autonomy means that any crack tip nonlinear solution is
uniquely determined by the surrounding linear elastic fields) and
that it does not automatically satisfy the resultant Newton's equation in the
crack parallel direction. We show that these two properties are interrelated
and that by requiring that the resultant Newton's equation is satisfied,
autonomy of the singular solution is retained. We further show that the
resultant linear momentum carried by the singular fields vanishes
identically. Our results, which reveal the physical and mathematical nature of
the new solution, are in favorable agreement with recent near tip measurements.Comment: 4 pages, 2 figures, related papers: arXiv:0902.2121 and
arXiv:0807.486
Defending capitalism: a review of Merle Lipton's Capitalism and apartheid
Paper presented at the Wits History Workshop: The Making of Class, 9-14 February, 198
Non-universality in Micro-branching Instabilities in Rapid Fracture: the Role of Material Properties
In spite of the apparent similarity of micro-branching instabilities in
different brittle materials, we propose that the physics determining the
typical length- and time-scales characterizing the post-instability patterns
differ greatly from material to material. We offer a scaling theory connecting
the pattern characteristics to material properties (like molecular weight) in
brittle plastics like PMMA, and stress the fundamental differences with
patterns in glass which are crucially influenced by 3-dimensional dynamics. In
both cases the present ab-initio theoretical models are still too far from
reality, disregarding some fundamental physics of the phenomena.Comment: 4 pages, 6 figures, PRL submitte
The rise and fall of the Indian peasantry in Natal
Paper presented at the Wits History Workshop: Structure and Experience in the Making of Apartheid, 6-10 February, 1990
Strain induced stabilization of stepped Si and Ge surfaces near (001)
We report on calculations of the formation energies of several [100] and
[110] oriented step structures on biaxially stressed Si and Ge (001) surfaces.
It is shown that a novel rebonded [100] oriented single-height step is strongly
stabilized by compressive strain compared to most well-known step structures.
We propose that the side walls of ``hut''-shaped quantum dots observed in
recent experiments on SiGe/Si films are made up of these steps. Our
calculations provide an explanation for the nucleationless growth of shallow
mounds, with steps along the [100] and [110] directions in low- and high-misfit
films, respectively, and for the stability of the (105) facets under
compressive strain.Comment: to appear in Appl. Phys. Lett.; v2=minor corrections,figs resize
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