On a degenerate parabolic equation arising in pricing of Asian options

We study a certain one-dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary condition, regularity of the generalized solution of such a problem remained unclear. We prove that the generalized solution of the problem is indeed a classical solution.     

Adaptive mesh refinement for simulation of thin film flows

We present a robust and accurate numerical method for simulating gravity-driven, thin-film flow problems. The convection term in the governing equation is treated by a semi-implicit, essentially non-oscillatory scheme. The resulting nonlinear discrete equation is solved using a nonlinear full approximation storage multigrid algorithm with adaptive mesh refinement techniques. A set of representative numerical experiments are presented. We show that the use of adaptive mesh refinement reduces computational time and memory compared to the equivalent uniform mesh results. Our simulation results are consistent with previous experimental observations.     

Phase separation and gelation of polymer-dispersed liquid crystals

Polymerization-induced phase separation in polymer-dispersed liquid crystal is studied by computer simulations in two dimensions. The domain morphology resulting from phase separation is investigated by solving the coupled set of equations for the local volume fraction and the nematic order parameter, taking into account the viscoelastic effects and gelation due to polymerization. Comparing the morphology of phase separation by temperature quench, it is shown that the viscoelastic effects and gelation enable the polymer-rich phase to form a stable interconnected domain even when the polymer component is minority. The experimental evidence consistent with this characteristic feature is also given.     

Thermal activation and thermal transfer of localized excitons in InAs self-organized quantum dots

We have investigated the temperature dependence of photoluminescence (PL) properties of a number of InAs/GaAs heterostructures with InAs layer thickness ranging from 0.5 monolayer (ML) to 3 ML. The temperature dependence of the InAs exciton energy and linewidth was found to display a significant difference when the InAs layer thickness is smaller or larger than the critical thickness around 1.7 ML, indicating spontaneous formation of quantum dots (QDs). A model, involving exciton recombination and thermal activation and transfer, is proposed to explain the experimental data. In the PL thermal quenching study, the measured thermal activation energies of different samples demonstrate that the InAs wetting layer may act as a barrier for thermionic emission of carriers in high quality InAs multilayers, while in InAs monolayers and submonolayers the carriers are required to overcome the GaAs barrier to thermally escape from the localized states.     

Magnetic resonance image enhancement using highly sparse input

Lately, the Magnetic Resonance scans have struggled with its own inherent limitations, such as spatial resolution as well as long examination times. In this paper, a novel, rapid compressively-sensed magnetic resonance high resolution image resolution algorithm is presented. This technique addresses these two key issues by employing a highly-sparse sampling scheme and super-resolution reconstruction (SRR) method. Due to highly challenging requirements for the accuracy of diagnostic images registration, the presented technique exploits image priors, deblurring, parallel imaging, and a discrete dense displacement sampling for the deformable human body and motion analysis. The clinical trials as well as phantom based studied have been conducted. It has been proven that the proposed algorithm is able to enhance image spatial resolution, reduce motion artefacts and scan times.