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The nonlinear forcing terms for the wave equation in general curvilinear coordinates are derived based on an isotropic homogeneous weakly nonlinear elastic material. The expressions for the nonlinear part of the first Piola-Kirchhoff stress are specialized for axisymmetric torsional and longitudinal fundamental waves in a circular cylinder. The matrix characteristics of the nonlinear forcing terms and secondary mode wave structures are manipulated to analyze the higher harmonic generation due to the guided wave mode self-interactions and mutual interactions. It is proved that both torsional and longitudinal secondary wave fields can be cumulative by a specific type of guided wave mode interactions. A method for the selection of preferred fundamental excitations that generate strong cumulative higher harmonics is formulated, and described in detail for second harmonic generation. Nonlinear finite element simulations demonstrate second harmonic generation by T(0,3) and L(0,4) modes at the internal resonance points. A linear increase of the normalized modal amplitude ratio A2/A1(2) over the propagation distance is observed for both cases, which indicates that mode L(0,5) is effectively generated as a cumulative second harmonic. Counter numerical examples demonstrate that synchronism and sufficient power flux from the fundamental mode to the secondary mode must occur for the secondary wave field to be strongly cumulative.

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A plate ray perspective for elastic wave propagation in hollow circular cylinders is presented in order to excite a predominant flexural mode, which in turn generates higher order harmonics due to nonlinear material behavior. The scattering angles are determined for the internally resonant higher order harmonics due to the interactions of two collimated waves. Primary waves that can generate strongly cumulative higher order harmonics are identified for mode self interactions and mutual interactions. A helical inter-digital transducer has been designed for the excitation of a single dominant flexural mode. Numerical evaluations that demonstrate cumulative second harmonic generation are undertaken for both torsional and longitudinal flexural waves. Quadratic sum and difference harmonic generation is observed for the mutual interaction between two primary torsional flexural wave modes.

In recent years, the effects of Lorentz symmetry breaking in cosmology has attracted considerable amount of attention. In cosmological context several topics can be affected by Lorentz violation,e.g., inflationary scenario, CMB, dark energy problem and barryogenesis. In this paper we consider the cosmological particle creation due to Lorentz violation (LV). We consider an exactly solvable model for finding the spectral properties of particle creation in an expanding space-time exhibiting Lorentz violation. In this model we calculate the spectrum and its variations with respect to the rate and the amount of space-time expansion.

In the present study, the permeabilities of Al–15·5 wt-%Cu and Al–19·5 wt-%Cu have been determined numerically by solving the full Navier–Stokes equations on 3D geometries of interdendritic channels obtained by X-ray microtomography. The samples for X-ray microtomography imaging were sectioned from different heights in directionally solidified cylinders in order to obtain a variety of microstructures for each composition. The flow has been solved using a second order accurate finite volume method approach. The effect of employing uniform or unstructured mesh on the calculated permeability has been studied. The Marching–Cube triangulation method was used to extract accurate surfaces for unstructured volume meshing. Calculated values of permeability for this range of solid fractions show partial agreement with previous experiments. Observed deviations are analysed and ultimately attributed to experimental error associated with the difficulties of measuring permeability.

The nucleation and growth kinetics of equiaxed eutectic grains in hypoeutectic Al-Cu alloys has been investigated numerically and experimentally. Three-dimensional geometries of eutectic/ primary phases obtained by X-ray microtomography (XMT) have been used to generate computational domains for use with a eutectic transformation model. The samples for XMT analysis were extracted from a series of small-scale castings of Al-20 wt pct Cu solidified with different cooling rates to obtain a variety of microstructures. The stochastic nucleation technique has been coupled with a deterministic cellular automaton (CA) model to simulate the nucleation and growth of eutectic grains within the interdendritic network characterized by the XMT analysis. An inverse analysis approach has been employed to quantify the deterministic nucleation and growth relationships in the eutectic solidification model. Metallographic measurements of eutectic size and density made on cast samples solidified with a variety of cooling rates and quenched at different times after the start of the eutectic transformation were used in the inverse analysis. The current approach provides a realistic description of eutectic grain evolution in multicomponent alloys.

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