Mathematical Modelling of flow in Schlemm's canal and its influence on primary open angle glaucoma

POAG (Primary Open Angle Glaucoma) is a major cause of blindness. This normally occurs when the IOP (intraocular pressure) increases. High pressure can be caused by an imbalance in the production and drainage of fluid (aqueous humour, AH) in the eye. AH is continually being produced but sometimes cannot be drained because of improperly functioning drainage channels (trabecular meshwork, TM). A mathematical model is presented for the flow of AH through the TM and into the SC (canal of Schlemm) and to couple this flow in order to predict changes in IOP. The governing equations have been developed by using the lubrication theory limit of the Navier-Stokes equations. To close the model, Friedenwald’s law has been used to predict changes of IOP. Several different cases have been examined in the model, relating AH flow to changes in IOP for various submodels: (i) the permeability, k in Darcy’s law may be either constant or not constant; (ii) the TM may be deformable so that the general theory of a beam under axial load is applicable - a number of different subcases where either ? or ?, may be either large or small have been considered. However only the subcase ? is small has been discussed in this study by assuming the permeability, k is constant and the TM is deformable. This subcase has been solved by using the regular perturbation method. The results show that the IOP rises continually when ? is small and may cause blindness

Period doubling in glow discharges: local versus global differential conductivity

Short planar glow discharges coupled to a resistive layer exhibit a wealth of spontaneous spatio-temporal patterns. Several authors have suggested effective reaction-diffusion-models to explore similarities with other pattern forming systems. To test these effective models, we here investigate the temporal oscillations of a glow discharge layer coupled to a linear resistor. We find an unexpected cascade of period doubling events. This shows that the inner structure of the discharge is more complex than can be described by a reaction-diffusion-model with negative differential conductivity.Comment: 4 pages, 4 figures, submitted to PR

Decentralised distributed fountain coding: asymptotic analysis and design

A class of generic decentralised distributed fountain coding schemes is introduced and the tools of analysis of the performance of such schemes are presented. It is demonstrated that the developed approach can be used to formulate a robust code design methodology in a number of instances. We show that two non-standard applications of fountain codes, fountain codes for distributed source coding and fountain codes for unequal error protection lie within this decentralised distributed fountain coding framework

Rate adaptive binary erasure quantization with dual fountain codes

In this contribution, duals of fountain codes are introduced and their use for lossy source compression is investigated. It is shown both theoretically and experimentally that the source coding dual of the binary erasure channel coding problem, binary erasure quantization, is solved at a nearly optimal rate with application of duals of LT and raptor codes by a belief propagation-like algorithm which amounts to a graph pruning procedure. Furthermore, this quantizing scheme is rate adaptive, i.e., its rate can be modified on-the-fly in order to adapt to the source distribution, very much like LT and raptor codes are able to adapt their rate to the erasure probability of a channel

Fountain coding with decoder side information

In this contribution, we consider the application of Digital Fountain (DF) codes to the problem of data transmission when side information is available at the decoder. The side information is modelled as a "virtual" channel output when original information sequence is the input. For two cases of the system model, which model both the virtual and the actual transmission channel either as a binary erasure channel or as a binary input additive white Gaussian noise (BIAWGN) channel, we propose methods of enhancing the design of standard non-systematic DF codes by optimizing their output degree distribution based oil the side information assumption. In addition, a systematic Raptor design has been employed as a possible solution to the problem

New Physics of the 30∘30^\circ Partial Dislocation in Silicon Revealed through {\em Ab Initio} Calculation

Based on {\em ab initio} calculation, we propose a new structure for the fundamental excitation of the reconstructed 30$^\circ$ partial dislocation in silicon. This soliton has a rare structure involving a five-fold coordinated atom near the dislocation core. The unique electronic structure of this defect is consistent with the electron spin resonance signature of the hitherto enigmatic thermally stable R center of plastically deformed silicon. We present the first {\em ab initio} determination of the free energy of the soliton, which is also in agreement with the experimental observation. This identification suggests the possibility of an experimental determination of the density of solitons, a key defect in understanding the plastic flow of the material.Comment: 6 pages, 5 postscript figure