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A model, combining acoustical radiosity and the image source method, including phase shifts on reflection, has been developed. The model is denoted Phased Acoustical Radiosity and Image Source Method (PARISM), and it has been developed in order to be able to model both specular and diffuse reflections with complex-valued and angle-dependent boundary conditions. This paper mainly describes the combination of the two models and the implementation of the angle-dependent boundary conditions. It furthermore describes how a pressure impulse response is obtained from the energy-based acoustical radiosity by regarding the model as being stochastic. Three methods of implementation are proposed and investigated, and finally, recommendations are made for their use. Validation of the image source method is done by comparison with finite element simulations of a rectangular room with a porous absorber ceiling. Results from the full model are compared with results from other simulation tools and with measurements. The comparisons of the full model are done for real-valued and angle-independent surface properties. The proposed model agrees well with both the measured results and the alternative theories, and furthermore shows a more realistic spatial variation than energy-based methods due to the fact that interference is considered. [ABSTRACT FROM AUTHOR]

We introduce a two-dimensional lattice model of granular matter. Using a combination of proof and simulation we demonstrate an order/disorder phase transition in the model, to which we associate the granular phenomenon of random close packing. We use Peierls contours to prove that the model is sensitive to boundary conditions at high density and Markov chain Monte Carlo simulation to show it is insensitive at low density. [ABSTRACT FROM AUTHOR]

Numerical continuation is used to compute a multiplicity of stable spatially localized steady states in doubly diffusive convection in a vertical slot driven by imposed horizontal temperature and concentration gradients. The calculations focus on the so-called opposing case, in which the imposed horizontal thermal and solutal gradients are in balance. No-slip boundary conditions are used at the sides; periodic boundary conditions with large spatial period are used in the vertical direction. The results demonstrate the presence of homoclinic snaking in this system, and can be interpreted in terms of a pinning region in parameter space. The dynamics outside of this region are studied using direct numerical simulation. [ABSTRACT FROM AUTHOR]