Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation

We present the results of direct numerical simulations of flow patterns in a low-Prandtl-number ($Pr = 0.1$) fluid above the onset of oscillatory convection in a Rayleigh-B\'{e}nard system rotating uniformly about a vertical axis. Simulations were carried out in a periodic box with thermally conducting and stress-free top and bottom surfaces. We considered a rectangular box ($L_x \times L_y \times 1$) and a wide range of Taylor numbers ($750 \le Ta \le 5000$) for the purpose. The horizontal aspect ratio $\eta = L_y/L_x$ of the box was varied from $0.5$ to $10$. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes ($0.5 \le \eta < 1$ and $1 < \eta < 2$). The flow patterns observed in boxes with $\eta = 1$ and $\eta = 2$ were different from those with $\eta < 1$ and $1 < \eta < 2$. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell ($\eta = 1$) for $Ta < 2700$, but observed a set of parallel rolls in the form of standing waves for $Ta \geq 2700$. The three-dimensional convection was quasiperiodic or chaotic for $750 \le Ta < 2700$, and then bifurcated into a two-dimensional periodic flow for $Ta \ge 2700$. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle $\phi = \frac{\pi}{2} - \arctan{(\eta^{-1})}$ with the straight rolls.Comment: 32 pages, 14 figures, 1 tabl

Murray polygons as a tool in image processing

This thesis reports on some applications of murray polygons, which are a generalization of space filling curves and of Peano polygons in particular, to process digital image data. Murray techniques have been used on 2-dimensional and 3-dimensional images, which are in cartesian/polar co-ordinates. Attempts have been made to resolve many associated aspects of image processing, such as connected components labelling, hidden surface removal, scaling, shading, set operations, smoothing, superimposition of images, and scan conversion. Initially different techniques which involve quadtree, octree, and linear run length encoding, for processing images are reviewed. Several image processing problems which are solved using different techniques are described in detail. The steps of the development from Peano polygons via multiple radix arithmetic to murray polygons is described. The outline of a software implementation of the basic and fast algorithms are given and some hints for a hardware implementation are described The application of murray polygons to scan arbitrary images is explained. The use of murray run length encodings to resolve some image processing problems is described. The problem of finding connected components, scaling an image, hidden surface removal, shading, set operations, superimposition of images, and scan conversion are discussed. Most of the operations described in this work are on murray run lengths. Some operations on the images themselves are explained. The results obtained by using murray scan techniques are compared with those obtained by using standard methods such as linear scans, quadtrees, and octrees. All the algorithms obtained using murray scan techniques are finally presented in a menu format work bench. Algorithms are coded in PS-algol and the C language

Dynamics of market states and risk assessment

Based on previous developments of the concept of market states using correlation matrices, in the present paper we address the dynamical evolution of correlation matrices in time. This will imply minor modifications to the market states themselves, due to increased attention to the transition matrix between the states. We will introduce trajectories of the correlation matrices by considering one day shifts for the epoch used to calculate the correlation matrices and will visualize both the states and the trajectories after dimensional scaling. This approach using dynamics improves the options of risk assessment and opens the door to dynamical treatments of markets and shows noise suppression in a new light.Comment: 22 pages and 27 figures. arXiv admin note: text overlap with arXiv:2003.0705

The South African Regulatory System: Past, Present, and Future

The drive for improved regulatory systems and the establishment of a more effective regulatory framework in South Africa has been evident for the past two decades but despite political intentions and legislative revisions success has been limited to date. Efforts to address the increasing volume of applications that have been received have to date failed and resources have been stretched to capacity resulting in the development of a significant backlog and extended timelines for product registration. The promulgation of the recently amended Medicines and Related Substance Act of 1965 triggered the establishment of the South African Health Products Regulatory Authority (SAHPRA) as a separate juristic person outside of the National Department of Health to replace the former medicine regulatory authority the Medicines Control Council (MCC). The aim of this review is to provide the historical context supporting the new regulatory environment in South Africa and the transition from the MCC to SAHPRA. Key recommendations to SAHPRA to ensure the full potential of the new regulatory environment in South Africa include: establishing a quality management system to safeguard accountability, consistency and transparency and to streamline the implementation of good review practices including quality decisionmaking practices and benefit-risk assessment; the measurement and monitoring of regulatory performance, targets for overall approval time and key review milestones to instill a culture of accurate metrics collection and measurement of key performance indicators and their continuous improvement and the employment of a risk-based approach to the evaluation of medical products and codify the use of facilitated regulatory pathways in policy and culture. The application of a risk-based approach to regulatory review commensurate with a product’s risk to patients will facilitate the application of increased resources for pharmacovigilance activities and to support the reliance and recognition of reference agencies.Peer reviewe