Inclusion of spin-orbit coupling into tight binding bandstructure calculations for bulk and superlattice semiconductors

Recent interest in superlattice based semiconductor devices has led to the need for the ability to make accurate superlattice bandstructure calculations. The tight binding model formalism has already been applied to this problem. In this paper, a technique is presented for the inclusion of spin-orbit coupling into the tight binding formalism. The most attractive feature of the technique presented is that it does not increase the size of the basis which may already be very large for superlattices. This allows a more accurate calculation of the superlattice bandstructure at no additional cost.     

A PENNY-SHAPED CRACK IN A MAGNETOELECTROELASTIC LAYER UNDER RADIAL SHEAR IMPACT LOADING

This paper analyzes the dynamic magnetoelectroelastic behavior induced by a penny- shaped crack in a magnetoelectroelastic layer.The crack surfaces are subjected to only radial shear impact loading.The Laplace and Hankel transform techniques are employed to reduce the prob- lem to solving a Fredholm integral equation.The dynamic stress intensity factor is obtained and numerically calculated for different layer heights.And the corresponding static solution is given by simple analysis.It is seen that the dynamic stress intensity factor for cracks in a magnetoelec- troelastic layer has the same expression as that in a purely elastic material.And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a>2.     

Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry

We analyze unfoldings of a codimension two, steady-state/steady-state modal interaction possessing O(2) symmetry. At the degenerate bifurcation point there are two zero eigenvalues, each of multiplicity two. The spatial wavenumbers of the critical modes k_i are assumed to satisfy k₂ = 2k₁. We base our analysis on a detailed study of the third order truncation of the resulting equivariant normal form, which is a four-dimensional vector field. We find that heteroclinic cycles and modulated travelling waves exist for open sets of parameter values near the codimension two bifurcation point. We provide conditions on parameters which guarantee existence and uniqueness of such solutions and we investigate their stability types. We argue that such motions will be prevalent in continuum systems having the symmetry of translation and reflection with respect to one (or more) spatial directions.     

The long-wavelength approximation and the theory of Davydov solitons

We indicate some inconsistencies in the application of the long-wavelength approximation in the standard derivation of Davydov solitons. Consistent approach indicates that the scope of applicability of the theory is much smaller than previously thought.     

Measurement of the dimension spectrum ƒ(α): Fixed-mass approach

We apply the fixed-mass method to the measurement of the dimension spectrum ƒ(α), through the scaling behaviour of the nearest-neighbour distances distribution P(δ, n, k), avoiding the direct evaluation of pointwise dimensions α(x). The method shows good convergence properties also for high-dimensional attractors and embedded experimental signals, due to the small statistical fluctuations of nearest-neighbour distances in high dimensions.     

Fibre spinning of a weakly elastic liquid

This paper presents a study of a silicone oil (poly(dimethyl siloxane)) in extensional deformation using an instrument developed recently by the authors. Data from steady shear and low amplitude sinusoidal deformation of this liquid clearly establish that it is weakly elastic. The viscometric data, for shear rates less than 100 s ⁻¹, are best represented by either the Maxwell model or the Jeffrey's model, the latter being marginally superior. The extensional data show that at low deformation rates, this fluid exhibits a Newtonian behavior with an apparent extensional viscosity equal to three times the shear viscosity. Under these conditions the velocity profiles along the spinline are also well represented by the Newtonian model. However, at higher deformation rates better predictions of the velocity profiles are obtained from the Jeffrey's and Maxwell models. At deformation rates above 100 s ⁻¹ none of these simple models is adequate. Under the conditions used in these experiments, the fractional increase in tensile stress along the fiber is shown both theoretically and experimentally to be a unique function of the total strain. Furthermore, the apparent extensional viscosity at any point on the spinline can be calculated from steady state expressions if allowance is made for the variation of stretch rates by defining a time averaged stretch rate.The results obtained here show that elasticity must be considered if these model liquids are used to conduct rheological experiments at high deformation rates. Additionally, it is found that elastic effects in extension can be predicted using simple constitutive equations provided viscometric data can be represented properly in the deformation rate range of interest. Finally, the present research further substantiates the utility of the extensional viscometer developed by the authors.     

Elliptic solution for two nonlinear interacting oscillators

Bykovskij and Inozemtsev have obtained the exact solution for two nonlinear oscillators with a certain type of interaction. Here more general cases are considered, and exact solutions have been obtained.