Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane

This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffraction of a time harmonic plane wave by a quarter-plane, including the secondary radiated waves. This leads to a precise representation of the diffraction coefficient describing the diffraction occurring at the corner of the quarter-plane. Our results for the secondary radiated waves are an important step towards finding a formula giving the corner diffraction coefficient everywhere. © 2012 The authors.

On the application of differential geometry to MDO

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: Differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface

Mishuris, G; Kuhn, G., (2001) 'Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface', Zeitschrift f?r Angewandte Mathematik und Mechanik 81(12) pp.811-826 RAE2008

Depolarization of sperm membrane potential is a common feature of men with subfertility and is associated with low fertilization rate at IVF

STUDY QUESTION. Are significant abnormalities in outward (K+) conductance and resting membrane potential (Vm) present in the spermatozoa of patients undertaking IVF and ICSI and if so, what is their functional effect on fertilization success? SUMMARY ANSWER. Negligible outward conductance (≈5% of patients) or an enhanced inward conductance (≈4% of patients), both of which caused depolarization of Vm, were associated with a low rate of fertilization following IVF. WHAT IS KNOWN ALREADY. Sperm-specific potassium channel knockout mice are infertile with defects in sperm function, suggesting that these channels are essential for fertility. These observations suggest that malfunction of K+ channels in human spermatozoa might contribute significantly to the occurrence of subfertility in men. However, remarkably little is known of the nature of K+ channels in human spermatozoa or the incidence and functional consequences of K+ channel defects. STUDY DESIGN, SIZE AND DURATION. Spermatozoa were obtained from healthy volunteer research donors and subfertile IVF and ICSI patients attending a hospital assisted reproductive techniques clinic between May 2013 and December 2015. In total, 40 IVF patients, 41 ICSI patients and 26 normozoospermic donors took part in the study. PARTICIPANTS/MATERIALS, SETTING, METHODS. Samples were examined using electrophysiology (whole-cell patch clamping). Where abnormal electrophysiological characteristics were identified, spermatozoa were further examined for Ca2+ influx induced by progesterone and penetration into viscous media if sufficient sample was available. Full exome sequencing was performed to specifically evaluate potassium calcium-activated channel subfamily M α 1 (KCNMA1), potassium calcium-activated channel subfamily U member 1 (KCNU1) and leucine-rich repeat containing 52 (LRRC52) genes and others associated with K+ signalling. In IVF patients, comparison with fertilization rates was done to assess the functional significance of the electrophysiological abnormalities. MAIN RESULTS AND THE ROLE OF CHANCE. Patch clamp electrophysiology was used to assess outward (K+) conductance and resting membrane potential (Vm) and signalling/motility assays were used to assess functional characteristics of sperm from IVF and ICSI patient samples. The mean Vm and outward membrane conductance in sperm from IVF and ICSI patients were not significantly different from those of control (donor) sperm prepared under the same conditions, but variation between individuals was significantly greater (P< 0.02) with a large number of outliers (>25%). In particular, in ≈10% of patients (7/81), we observed either a negligible outward conductance (4 patients) or an enhanced inward current (3 patients), both of which caused depolarization of Vm. Analysis of clinical data from the IVF patients showed significant association of depolarized Vm (≥0 mV) with low fertilization rate (P= 0.012). Spermatozoa with electrophysiological abnormities (conductance and Vm) responded normally to progesterone with elevation of [Ca2+]i and penetration of viscous medium, indicating retention of cation channel of sperm (CatSper) channel function. LIMITATIONS, REASONS FOR CAUTION. For practical, technical, ethical and logistical reasons, we could not obtain sufficient additional semen samples from men with conductance abnormalities to establish the cause of the conductance defects. Full exome sequencing was only available in two men with conductance defects. WIDER IMPLICATIONS OF THE FINDINGS. These data add significantly to the understanding of the role of ion channels in human sperm function and its impact on male fertility. Impaired potassium channel conductance (Gm) and/or Vm regulation is both common and complex in human spermatozoa and importantly is associated with impaired fertilization capacity when the Vm of cells is completely depolarized.

Wykorzystanie gier decyzyjnych/symulacyjnych w naukach społecznych. Wybrane problemy

Treścią publikacji jest przedstawienie wybranych problemów prognozowania w naukach społecznych. W artykule skoncentrowano się na metodzie gier decyzyjnych/symulacyjnych, które – zwłaszcza wraz z rozwojem teorii gier oraz komputerów – są coraz częściej wykorzystywane w wielu dziedzinach. Na wybranych przykładach gier decyzyjnych/symulacyjnych – Poznań International Model United Nations 2013/POZiMUN; S.E.N.S.E. a także gry sieciowej EVE Online – wskazano jak ważne są takie ćwiczenia, by móc precyzyjniej przewidywać przyszłość. Zwrócono także szczególną uwagę na kwestię przypadku oraz czynników zakłócających, które mogą destabilizować proces przewidywania. Poruszono ponadto problem podejmowania decyzji w aspekcie klasycznej oraz kwantowej logiki.

The numerical modelling of multi-physics phenomena: The shape casting process

In this paper a computer simulation tool capable of modelling multi-physics processes in complex geometry has been developed and applied to the casting process. The quest for high-quality complex casting components demanded by the aerospace and automobile industries, requires more precise numerical modelling techniques and one that need to be generic and modular in its approach to modelling multi-processes problems. For such a computer model to be successful in shape casting, the complete casting process needs to be addressed, the major events being:-• Filling of hot liquid metal into a cavity mould • Solidification and latent heat evolution of liquid metal • Convection currents generated in liquid metal by thermal gradients • Deformation of cast and stress development in solidified metal • Macroscopic porosity formation The above phenomena combines the analysis of fluid flow, heat transfer, change of phase and thermal stress development. None of these events can be treated in isolation as they inexorably interact with each other in a complex way. Also conditions such as design of running system, location of feeders and chills, moulding materials and types of boundary conditions can all affect on the final cast quality and must be appropriately represented in the model.

PHYSICA - A software environment for the modelling of multi-physics phenomena

A brief description of a software environment in FORTRAN77 for the modelling of multi-physics phenomena is given. The numerical approach is based on finite volume methods but extended to unstructured meshes (ie. FV-UM). A range of interacting solution procedures for turbulent fluid flow, heat transfer with solidification/melting and elasto-visco-plastic solid mechanics are implemented in the first version of PHYSICA, which will be released in source code form to the academic community in late 1995.

Using an interactive software environment for the parallelization of real-world scientific applications

The parallelization of real-world compute intensive Fortran application codes is generally not a trivial task. If the time to complete the parallelization is to be significantly reduced then an environment is needed that will assist the programmer in the various tasks of code parallelization. In this paper the authors present a code parallelization environment where a number of tools that address the main tasks such as code parallelization, debugging and optimization are available. The ParaWise and CAPO parallelization tools are discussed which enable the near automatic parallelization of real-world scientific application codes for shared and distributed memory-based parallel systems. As user involvement in the parallelization process can introduce errors, a relative debugging tool (P2d2) is also available and can be used to perform nearly automatic relative debugging of a program that has been parallelized using the tools. A high quality interprocedural dependence analysis as well as user-tool interaction are also highlighted and are vital to the generation of efficient parallel code and in the optimization of the backtracking and speculation process used in relative debugging. Results of benchmark and real-world application codes parallelized are presented and show the benefits of using the environment

Design of parallel algorithms for fractal video compression

The intrinsic independent features of the optimal codebook cubes searching process in fractal video compression systems are examined and exploited. The design of a suitable parallel algorithm reflecting the concept is presented. The Message Passing Interface (MPI) is chosen to be the communication tool for the implementation of the parallel algorithm on distributed memory parallel computers. Experimental results show that the parallel algorithm is able to reduce the compression time and achieve a high speed-up without changing the compression ratio and the quality of the decompressed image. A scalability test was also performed, and the results show that this parallel algorithm is scalable.

Parallel genetic algorithms for the solution of inverse heat conduction problems

A parallel genetic algorithm (PGA) is proposed for the solution of two-dimensional inverse heat conduction problems involving unknown thermophysical material properties. Experimental results show that the proposed PGA is a feasible and effective optimization tool for inverse heat conduction problems

Reviews: making mathematics with needlework

Review of Making Mathematics with Needlework, edited by Sarah-Marie Belcastro and Carolyn Yackel, published by AK Peters Ltd, 2007 (ISBN 978-1-56881-331-8).