The problem under investigation is the heat equation in the upper half-plane, to which the di usion in the longitudinal direction has been suppressed, and augmented with a nonlinear oblique derivative condition. This paper proves global existence and qualitative properties to the Cauchy Problem for this model, furthering the study [18] of the self-similar solutions. The qualitative behaviour of...

Computational methods for a jump-di usion portfolio optimization application using a loguniform jump distribution are considered. In contrast to the usual geometric Brownian motion problem based upon two parameters, mean appreciation and di usive volatility, the jumpdi usion model will have at least ve, since jump process needs at least a rate, a mean and a variance, depending on the jump-ampli...

Abstract We study a queueing model with ordered arrivals, which can be called the (i)/GI/1 queue. Here, customers from a fixed, finite, population independently sample a time to arrive from some given distribution F , and enter the queue in order of the sampled arrival times. Thus, the arrival times are order statistics, and the inter-arrival times are di↵erences of consecutive ordered statisti...

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...

Conventional grayscale error di usion halftoning produces worms and other objectionable artifacts. Tone dependent error di usion (Li and Allebach) reduces these artifacts by controlling the di usion of quantization errors based on the input graylevel. Li and Allebach optimize error lter weights and thresholds for each (input) graylevel based on a human visual system model. This paper extends to...

Traditional error di usion halftoning is a high quality method for producing binary images from digital grayscale images. Error di usion shapes the quantization noise power into the high frequency regions where the human eye is the least sensitive. Error di usion may be extended to color images by using error lters with matrix-valued coe cients to take into account the correlation among color p...

The aim of this paper is to discuss di erent couplings between di usion, recrystallisation/grain growth, strain/stress, heat transfer and thermo-mechanical behaviour of metallic materials. The understanding of these di erent physical phenomena is needed to predict the long-term life of mechanical parts in components. Some results are presented and further studies are suggested to improve the ev...

This paper proposes a new class of nonlinear PDEs called the Gibbs Reaction And Di usion Equation GRADE for a variety of applications in computer vision image processing and graphics In two previous papers the authors have been studying a minimax entropy theory based on which a new class of Gibbs distributions are learned in a fully non parametric form from a set of observed images such as text...

A new nonlinear solution method is developed and applied to a non-equilibrium radiation di!usion problem. With this new method, Newton-like super-linear convergence is achieved in the nonlinear iteration, without the complexity of forming or inverting the Jacobian from a standard Newton method. The method is a unique combination of an outer Newton-based iteration and and inner conjugate gradien...

The production of modern microchips requires a large number of fabrication steps. One important step is the creation of semiconducting areas, where charged dopants are implanted into a semiconducting material and under the in uence of high temperatures the dopants penetrate into the layer. This redistribution of dopants and point defects can be described in terms of pair di usion mechanisms. Th...