The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor co. We show that, for the standard model problem of Poisson's equation on a rectangle, the optimal co and corresponding convergence rate can be obtained rigorously by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives new...

A two-dimensional numerical model was developed to determine the effect of the non-Newtonian behavior of blood on a pulsatile flow at the aortic bifurcation. The blood rheology was described by a weak-form Casson equation. The successive-over-relaxation (SOR) method was used to solve both the vorticity and Poisson equations numerically. It was disclosed that the non-Newtonian property of blood ...

Thermochemical relaxation behind a normal shock in Mars and Titan gas mixtures is simulated using a CFD solver, DPLR, for a hemisphere of 1 m radius; the thermochemical relaxation along the stagnation streamline is considered equivalent to the flow behind a normal shock. Flow simulations are performed for a Titan gas mixture (98% N2, 2% CH4 by volume) for shock speeds of 5.7 and 7.6 km/s and pr...

Cluster expansions have proven to be a valuable tool in alloy theory and other problems in materials science but the generation of cluster expansions can be a computationally expensive and time-consuming process. We present a Bayesian framework for developing cluster expansions that explicitly incorporates physical insight into the fitting procedure. We demonstrate how existing methods fit with...

We study the extension of total variation (TV), total deformation (TD), and (second-order) total generalised variation (TGV) to symmetric tensor fields. We show that for a suitable choice of finite-dimensional norm, these variational semi-norms are rotation-invariant in a sense natural and well-suited for application to diffusion tensor imaging (DTI). Combined with a positive definiteness const...

Lookback options are popular in OTC markets for currency hedging. The payoff of a lookback option depends on the minimum or maximum price of the underlying asset over the life of the contract. When the extreme values are continuously monitored, these options can be valued analytically (Conze and Viswanathan, 1991; Goldman et al., 1979a,b). On the other hand, when the maximum or the minimum is o...

The market pricing of OTC FX options displays both stochastic volatility and stochastic skewness in the risk-neutral distribution governing currency returns. To capture this unique phenomenon Carr and Wu developed a model (SSM) with three dynamical state variables. They then used Fourier methods to value simple European-style options. However pricing exotic options requires numerical solution o...

We consider networks of quadratic integrate-and-fire neurons coupled via both chemical synapses and gap junctions. After transforming to “theta neuron” coordinates, a network’s governing equations are of a form amenable to the use of the Ott/Antonsen ansatz. This ansatz allows us to derive an exact description of a network’s dynamics in the limit of an infinite number of neurons. For an all-to-...

In the midst of the digital revolution, the telecommunications industry is undergoing major changes. One of the changes affecting telcos is the increase in data sources from which to get customer feedback – big data, social media. Where this used to be fully controlled by companies through their call centres, websites and shops, today much feedback is expressed in social media, blogs, news site...