An alternative method for deriving water wave dispersion relations and evolution equations is to use a weak formulation. The free-surface displacement η is written as an eigenfunction expansion,

Displacement mapping was originally created as a rendering tool to provide small-scale modulation of an underlying smooth surface. However, it has now emerged as a sculpting tool, to the extent that complex geometry can effectively be added to a scene at rendering time. The attendant complexity of displacement maps is placing increased demands on rendering systems, from quality, performance, an...

The bending behavior of composites sandwich plates with multi-layered laminated face sheets has been investigated, using a new four-nodded rectangular finite element formulation based on a layer-wise theory. Both, first order and higher-order shear deformation; theories are used in order to model the face sheets and the core, respectively. Unlike any other layer-wise theory, the number of degre...

A stabilised low-order finite element methodology is presented for the numerical simulation of a mixed conservation law formulation in fast solid dynamics. The mixed formulation, where the unknowns are linear momentum, deformation gradient and total energy, can be cast in the form of a system of first order hyperbolic equations. The difficulty associated with locking effects commonly encountere...

The difficult challenge of simulating diffuse and complex fracture patterns in tough structural composites is at last beginning to yield to conceptual and computational advances in fracture modeling. Contributing successes include the refinement of cohesive models of fracture and the formulation of hybrid stress-strain and traction-displacement models that combine continuum (spatially averaged)...

A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance. A new unitary formulation of Einstein’s tensor illuminates long-standing problems with energy-momentum conservation i...

This presentation describes the contribution of the group at KUN to Work-packages 2 and 3 in the following directions: (1) study of the properties and the behavior of variable versus fixed preconditioners, based on the so-called separate displacement component (SDC) formulation of the linear elasticity problem; (2) solution of problems with nearly incompressible material properties, based on a ...

This report presents a literature review on the modeling of dielectric polymer actuators (DPA). The principle of actuation of these actuators and the underlying physics of dielectrics is exposed in order to introduce all the sources of difficulty responsible for the complex behaviour of DPAs. A variational formulation is proposed to model the behaviour of DPA, based on the variation of the diel...

We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavi...