99 research outputs found
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
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
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
Microscopic theory of quantum dot interactions with quantum light: local field effect
A theory of both linear and nonlinear electromagnetic response of a single QD
exposed to quantum light, accounting the depolarization induced local--field
has been developed. Based on the microscopic Hamiltonian accounting for the
electron--hole exchange interaction, an effective two--body Hamiltonian has
been derived and expressed in terms of the incident electric field, with a
separate term describing the QD depolarization. The quantum equations of motion
have been formulated and solved with the Hamiltonian for various types of the
QD excitation, such as Fock qubit, coherent fields, vacuum state of
electromagnetic field and light with arbitrary photonic state distribution. For
a QD exposed to coherent light, we predict the appearance of two oscillatory
regimes in the Rabi effect separated by the bifurcation. In the first regime,
the standard collapse--revivals phenomenon do not reveal itself and the QD
population inversion is found to be negative, while in the second one, the
collapse--revivals picture is found to be strongly distorted as compared with
that predicted by the standard Jaynes-Cummings model. %The model developed can
easily be extended to %%electromagnetic excitation. For the case of QD
interaction with arbitrary quantum light state in the linear regime, it has
been shown that the local field induce a fine structure of the absorbtion
spectrum. Instead of a single line with frequency corresponding to which the
exciton transition frequency, a duplet is appeared with one component shifted
by the amount of the local field coupling parameter. It has been demonstrated
the strong light--mater coupling regime arises in the weak-field limit. A
physical interpretation of the predicted effects has been proposed.Comment: 14 pages, 7 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.
Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture
We generalize lattice models of brittle fracture to arbitrary nonlinear force
laws and study the existence of arrested semi-infinite cracks. Unlike what is
seen in the discontinuous case studied to date, the range in driving
displacement for which these arrested cracks exist is very small. Also, our
results indicate that small changes in the vicinity of the crack tip can have
an extremely large effect on arrested cracks. Finally, we briefly discuss the
possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication
Velocity Fluctuations in Dynamical Fracture: the Role of Microcracks
We address the velocity fluctuations of fastly moving cracks in stressed
materials. One possible mechanism for such fluctuations is the interaction of
the main crack with micro cracks (irrespective whether these are existing
material defects or they form during the crack evolution). We analyze carefully
the dynamics (in 2 space dimensions) of one macro and one micro crack, and
demonstrate that their interaction results in a {\em large} and {\em rapid}
velocity fluctuation, in qualitative correspondence with typical velocity
fluctuations observed in experiments. In developing the theory of the dynamical
interaction we invoke an approximation that affords a reduction in mathematical
complexity to a simple set of ordinary differential equations for the positions
of the cracks tips; we propose that this kind of approximation has a range of
usefulness that exceeds the present context.Comment: 7 pages, 7 figure
Phase-Field Model of Mode III Dynamic Fracture
We introduce a phenomenological continuum model for mode III dynamic fracture
that is based on the phase-field methodology used extensively to model
interfacial pattern formation. We couple a scalar field, which distinguishes
between ``broken'' and ``unbroken'' states of the system, to the displacement
field in a way that consistently includes both macroscopic elasticity and a
simple rotationally invariant short scale description of breaking. We report
two-dimensional simulations that yield steady-state crack motion in a strip
geometry above the Griffith threshold.Comment: submitted to PR
van der Waals coupling in atomically doped carbon nanotubes
We have investigated atom-nanotube van der Waals (vdW) coupling in atomically
doped carbon nanotubes (CNs). Our approach is based on the perturbation theory
for degenerated atomic levels, thus accounting for both weak and strong
atom-vacuum-field coupling. The vdW energy is described by an integral equation
represented in terms of the local photonic density of states (DOS). By solving
it numerically, we demonstrate the inapplicability of standard
weak-coupling-based vdW interaction models in a close vicinity of the CN
surface where the local photonic DOS effectively increases, giving rise to an
atom-field coupling enhancement. An inside encapsulation of atoms into the CN
has been shown to be energetically more favorable than their outside adsorption
by the CN surface. If the atom is fixed outside the CN, the modulus of the vdW
energy increases with the CN radius provided that the weak atom-field coupling
regime is realized (i.e., far enough from the CN). For inside atomic position,
the modulus of the vdW energy decreases with the CN radius, representing a
general effect of the effective interaction area reduction with lowering the CN
curvature.Comment: 15 pages, 5 figure
Spontaneous decay dynamics in atomically doped carbon nanotubes
We report a strictly non-exponential spontaneous decay dynamics of an excited
two-level atom placed inside or at different distances outside a carbon
nanotube (CN). This is the result of strong non-Markovian memory effects
arising from the rapid variation of the photonic density of states with
frequency near the CN. The system exhibits vacuum-field Rabi oscillations, a
principal signature of strong atom-vacuum-field coupling, when the atom is
close enough to the nanotube surface and the atomic transition frequency is in
the vicinity of the resonance of the photonic density of states. Caused by
decreasing the atom-field coupling strength, the non-exponential decay dynamics
gives place to the exponential one if the atom moves away from the CN surface.
Thus, atom-field coupling and the character of the spontaneous decay dynamics,
respectively, may be controlled by changing the distance between the atom and
CN surface by means of a proper preparation of atomically doped CNs. This opens
routes for new challenging nanophotonics applications of atomically doped CN
systems as various sources of coherent light emitted by dopant atoms.Comment: 10 pages, 4 figure
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