Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a

Electromagnetic wave diffraction from an infinite array of complex-shaped microstrip reflectors

A numerical-analytical method is developed for solving surface integral equations (IEs) describing electromagnetic wave diffraction from arrays of complex-shaped planar reflectors. Solutions to these equations are regularized via analytical transformation of the separated singular part of the matrix kernel. Basis functions satisfying the metal-edge condition are determined on the entire surface of the complex region. The amplitude and phase responses of arrays consisting of polygonal reflectors are numerically investigated.

Modulational instability in asymmetric coupled wave functions

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schrödinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.

Numerical Study of Wave Slamming on an Oscillating Flap

Bottom hinged Oscillating Wave Surge Converters (OWSCs) are efficient devices for extracting power from ocean waves. There is limited knowledge about wave slamming on such devices. This paper deals with numerical studies of wave slamming on an oscillating flap to investigate the mechanism of slamming events. In our model, the Navier–Stokes equations are discretized using the Finite Volume method with the Volume of Fluid (VOF) approach for interface capturing. Waves are generated by a flaptype wave maker in the numerical wave tank, and the dynamic mesh method is applied to model the motion of the oscillating flap. Basic mesh and time step refinement studies are performed. The flow characteristics in a slamming event are analysed based on numerical results. Various simulations with different flap densities, water depths and wave amplitudes are performed for a better understanding of the slamming.

On the use of OpenFOAM to model Oscillating wave surge converters

The Computational Fluid Dynamic (CFD) toolbox OpenFOAM is used to assess the applicability of Reynolds-Averaged Navier-Stokes (RANS) solvers to the simulation of Oscillating Wave Surge Converters (OWSC) in significant waves. Simulation of these flap type devices requires the solution of the equations of motion and the representation of the OWSC’s motion in a moving mesh. A new way to simulate the sea floor inside a section of the moving mesh with a moving dissipation zone is presented. To assess the accuracy of the new solver, experiments are conducted in regular and irregular wave traces for a full three dimensional model. Results of acceleration and flow features are presented for numerical and experimental data. It is found that the new numerical model reproduces experimental results within the bounds of experimental accuracy.

A Review of Numerical Modelling of Wave Energy Converter Arrays

Large-scale commercial exploitation of wave energy is certain to require the deployment of wave energy converters (WECs) in arrays, creating ‘WEC farms’. An understanding of the hydrodynamic interactions in such arrays is essential for determining optimum layouts of WECs, as well as calculating the area of ocean that the farms will require. It is equally important to consider the potential impact of wave farms on the local and distal wave climates and coastal processes; a poor understanding of the resulting environmental impact may hamper progress, as it would make planning consents more difficult to obtain. It is therefore clear that an understanding the interactions between WECs within a farm is vital for the continued development of the wave energy industry.To support WEC farm design, a range of different numerical models have been developed, with both wave phase-resolving and wave phase-averaging models now available. Phase-resolving methods are primarily based on potential flow models and include semi-analytical techniques, boundary element methods and methods involving the mild-slope equations. Phase-averaging methods are all based around spectral wave models, with supra-grid and sub-grid wave farm models available as alternative implementations.The aims, underlying principles, strengths, weaknesses and obtained results of the main numerical methods currently used for modelling wave energy converter arrays are described in this paper, using a common framework. This allows a qualitative comparative analysis of the different methods to be performed at the end of the paper. This includes consideration of the conditions under which the models may be applied, the output of the models and the relationship between array size and computational effort. Guidance for developers is also presented on the most suitable numerical method to use for given aspects of WEC farm design. For instance, certain models are more suitable for studying near-field effects, whilst others are preferable for investigating far-field effects of the WEC farms. Furthermore, the analysis presented in this paper identifies areas in which the numerical modelling of WEC arrays is relatively weak and thus highlights those in which future developments are required.

Projected equations of motion approach to hybrid quantum/classical dynamics in dielectric-metal composites

We introduce a hybrid method for dielectric-metal composites that describes the dynamics of the metallic system classically whilst retaining a quantum description of the dielectric. The time-dependent dipole moment of the classical system is mimicked by the introduction of projected equations of motion (PEOM) and the coupling between the two systems is achieved through an effective dipole-dipole interaction. To benchmark this method, we model a test system (semiconducting quantum dot-metal nanoparticle hybrid). We begin by examining the energy absorption rate, showing agreement between the PEOM method and the analytical rotating wave approximation (RWA) solution. We then investigate population inversion and show that the PEOM method provides an accurate model for the interaction under ultrashort pulse excitation where the traditional RWA breaks down.