215 research outputs found
Cracks Cleave Crystals
The problem of finding what direction cracks should move is not completely
solved. A commonly accepted way to predict crack directions is by computing the
density of elastic potential energy stored well away from the crack tip, and
finding a direction of crack motion to maximize the consumption of this energy.
I provide here a specific case where this rule fails. The example is of a crack
in a crystal. It fractures along a crystal plane, rather than in the direction
normally predicted to release the most energy. Thus, a correct equation of
motion for brittle cracks must take into account both energy flows that are
described in conventional continuum theories and details of the environment
near the tip that are not.Comment: 6 page
Some exact results for the velocity of cracks propagating in non-linear elastic models
We analyze a piece-wise linear elastic model for the propagation of a crack
in a stripe geometry under mode III conditions, in the absence of dissipation.
The model is continuous in the propagation direction and discrete in the
perpendicular direction. The velocity of the crack is a function of the value
of the applied strain. We find analytically the value of the propagation
velocity close to the Griffith threshold, and close to the strain of uniform
breakdown. Contrary to the case of perfectly harmonic behavior up to the
fracture point, in the piece-wise linear elastic model the crack velocity is
lower than the sound velocity, reaching this limiting value at the strain of
uniform breakdown. We complement the analytical results with numerical
simulations and find excellent agreement.Comment: 9 pages, 13 figure
Supersonic crack propagation in a class of lattice models of Mode III brittle fracture
We study a lattice model for mode III crack propagation in brittle materials
in a stripe geometry at constant applied stretching. Stiffening of the material
at large deformation produces supersonic crack propagation. For large
stretching the propagation is guided by well developed soliton waves. For low
stretching, the crack-tip velocity has a universal dependence on stretching
that can be obtained using a simple geometrical argument.Comment: 4 pages, 3 figure
Spontaneous decay of excited atomic states near a carbon nanotube
Spontaneous decay process of an excited atom placed inside or outside (near
the surface) a carbon nanotube is analyzed. Calculations have been performed
for various achiral nanotubes. The effect of the nanotube surface has been
demonstrated to dramatically increase the atomic spontaneous decay rate -- by 6
to 7 orders of magnitude compared with that of the same atom in vacuum. Such an
increase is associated with the nonradiative decay via surface excitations in
the nanotube.Comment: 8 pages, 3 figure
Front Propagation up a Reaction Rate Gradient
We expand on a previous study of fronts in finite particle number
reaction-diffusion systems in the presence of a reaction rate gradient in the
direction of the front motion. We study the system via reaction-diffusion
equations, using the expedient of a cutoff in the reaction rate below some
critical density to capture the essential role of fl uctuations in the system.
For large density, the velocity is large, which allows for an approximate
analytic treatment. We derive an analytic approximation for the front velocity
depe ndence on bulk particle density, showing that the velocity indeed diverge
s in the infinite density limit. The form in which diffusion is impleme nted,
namely nearest-neighbor hopping on a lattice, is seen to have an essential
impact on the nature of the divergence
On selection criteria for problems with moving inhomogeneities
We study mechanical problems with multiple solutions and introduce a
thermodynamic framework to formulate two different selection criteria in terms
of macroscopic energy productions and fluxes. Studying simple examples for
lattice motion we then compare the implications for both resting and moving
inhomogeneities.Comment: revised version contains new introduction, numerical simulations of
Riemann problems, and a more detailed discussion of the causality principle;
18 pages, several figure
Propagating mode-I fracture in amorphous materials using the continuous random network (CRN) model
We study propagating mode-I fracture in two dimensional amorphous materials
using atomistic simulations. We used the continuous random network (CRN) model
of an amorphous material, creating samples using a two dimensional analogue of
the WWW (Wooten, Winer & Weaire) Monte-Carlo algorithm. For modeling fracture,
molecular-dynamics simulations were run on the resulting samples. The results
of our simulations reproduce the main experimental features. In addition to
achieving a steady-state crack under a constant driving displacement (which had
not yet been achieved by other atomistic models for amorphous materials), the
runs show micro-branching, which increases with driving, transitioning to
macro-branching for the largest drivings. Beside the qualitative visual
similarity of the simulated cracks to experiment, the simulation also succeeds
in explaining the experimentally observed oscillations of the crack velocity
Vortex-type elastic structured media and dynamic shielding
The paper addresses a novel model of metamaterial structure. A system of
spinners has been embedded into a two-dimensional periodic lattice system. The
equations of motion of spinners are used to derive the expression for the
chiral term in the equations describing the dynamics of the lattice. Dispersion
of elastic waves is shown to possess innovative filtering and polarization
properties induced by the vortextype nature of the structured media. The
related homogenised effective behavior is obtained analytically and it has been
implemented to build a shielding cloak around an obstacle. Analytical work is
accompanied by numerical illustrations.Comment: 24 pages, 13 figure
Discrete models of dislocations and their motion in cubic crystals
A discrete model describing defects in crystal lattices and having the
standard linear anisotropic elasticity as its continuum limit is proposed. The
main ingredients entering the model are the elastic stiffness constants of the
material and a dimensionless periodic function that restores the translation
invariance of the crystal and influences the Peierls stress. Explicit
expressions are given for crystals with cubic symmetry: sc, fcc and bcc.
Numerical simulations of this model with conservative or damped dynamics
illustrate static and moving edge and screw dislocations and describe their
cores and profiles. Dislocation loops and dipoles are also numerically
observed. Cracks can be created and propagated by applying a sufficient load to
a dipole formed by two edge dislocations.Comment: 23 pages, 15 figures, to appear in Phys. Rev.
Thermal Radiation From Carbon Nanotube in Terahertz Range
The thermal radiation from an isolated finite-length carbon nanotube (CNT) is
theoretically investigated both in near- and far-field zones. The formation of
the discrete spectrum in metallic CNTs in the terahertz range is demonstrated
due to the reflection of strongly slowed-down surface-plasmon modes from CNT
ends. The effect does not appear in semiconductor CNTs. The concept of CNT as a
thermal nanoantenna is proposed.Comment: 5 pages, 3 figure
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