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

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

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

Energy radiation of moving cracks

The energy radiated by moving cracks in a discrete background is analyzed. The energy flow through a given surface is expressed in terms of a generalized Poynting vector. The velocity of the crack is determined by the radiation by the crack tip. The radiation becomes more isotropic as the crack velocity approaches the instability threshold.Comment: 7 pages, embedded figure

Optical response of finite-length carbon nanotubes

Optical response of finite-length metallic carbon nanotubes is calculated including effects of induced edge charges in a self-consistent manner. The results show that the main resonance corresponding to excitation of the fundamental plasmon mode with wave vector $\pi/l$ with $l$ being the tube length is quite robust and unaffected. This arises because the strong electric field associated with edge charges is screened and decays rapidly inside the nanotube. For higher-frequency resonances, the field starts to be mixed and tends to shift resonances to higher frequencies.Comment: 10 pages, 9 figures, to be published in J. Phys. Soc. Jp

Relativistic treatment of harmonics from impurity systems in quantum wires

Within a one particle approximation of the Dirac equation we investigate a defect system in a quantum wire. We demonstrate that by minimally coupling a laser field of frequency omega to such an impurity system, one may generate harmonics of multiples of the driving frequency. In a multiple defect system one may employ the distance between the defects in order to tune the cut-off frequency.Comment: 9 pages Latex, 8 eps figures, section added, numerics improve

Bragg diffraction of waves in one-dimensional doubly periodic media

The Bragg diffraction of waves in one-dimensional doubly periodic media is analyzed by means of Kogelnik’s coupled-waves technique. The spectrum problem and the problem of reflection from a half-space and from a layer are considered. It is shown that a devil’s-staircase type of spectrum causes characteristic peaks and valleys in the frequency dependence of the reflection coefficient