Mathematical treatment of environmental models

Large-scale environmental models can successfully be used in different important for the modern society studies as, for example, in the investigation of the influence of the future climatic changes on pollution levels in different countries. Such models are normally described mathematically by non-linear systems of par- tial differential equations, which are defined on very large spatial domains and have to be solved numerically on very long time intervals. Moreover, very often many different scenarios have also to be developed and used in the investigations. There- fore, both the storage requirements and the computational work are enormous. The great difficulties can be overcome only if the following four tasks are successfully resolved: (a) fast and sufficiently accurate numerical methods are to be selected, (b) reliable and efficient splitting procedures are to be applied, (c) the cache memories of the available computers are to be efficiently exploited and (d) the codes are to be parallelized

Ordinary kriging for on-demand average wind interpolation of in-situ wind sensor data

We have developed a domain agnostic ordinary kriging algorithm accessible via a standards-based service-oriented architecture for sensor networks. We exploit the Open Geospatial Consortium (OGC) Sensor Web Enablement (SWE) standards. We need on-demand interpolation maps so runtime performance is a major priority.Our sensor data comes from wind in-situ observation stations in an area approximately 200km by 125km. We provide on-demand average wind interpolation maps. These spatial estimates can then be compared with the results of other estimation models in order to identify spurious results that sometimes occur in wind estimation.Our processing is based on ordinary kriging with automated variogram model selection (AVMS). This procedure can smooth time point wind measurements to obtain average wind by using a variogram model that reflects the wind phenomenon characteristics. Kriging is enabled for wind direction estimation by a simple but effective solution to the problem of estimating periodic variables, based on vector rotation and stochastic simulation.In cases where for the region of interest all wind directions span 180 degrees, we rotate them so they lie between 90 and 270 degrees and apply ordinary kriging with AVMS directly to the meteorological angle. Else, we transform the meteorological angle to Cartesian space, apply ordinary kriging with AVMS and use simulation to transform the kriging estimates back to meteorological angle.Tests run on a 50 by 50 grid using standard hardware takes about 5 minutes to execute backward transformation with a sample size of 100,000. This is acceptable for our on-demand processing service requirements

MEDICO-APPLIED CHARACTERISTICS OF SOME BICOMPONENT POLYMER SYSTEMS. FIRST COMMUNICATION. EVALUATION OF ACUTE TOXICITY

The acute toxicity of polymer compositions when introduced perorally in rats and intraperitonealy in mice has been determined. The materials examined are plaster-like. Their production is based on a hydrophilized unsaturated polyester resin. The latter is object of investigations elsewhere and enables the obtaining bicomponent polymer systems in combination with a carbamide-formaldehyde or mclamine-formaldehyde resins. Experimental animals are selected and observed prior to and after the introduction of polymer substances during different periods of time according to the kind of investigation. Neither changes in animal appearance and behaviour, nor mortality cases for all doses examined are registered. These results define polymer composites as low-toxic ones (according to the IVth class of chemical compounds) and present the first stage in the course of research aiming at evaluating their safety when applied in both medical and stomatological practices

On the scattering of torsional elastic waves from axisymmetric defects in coated pipes

Long range ultrasonic testing is now a well established method for examining in-service degradation in pipelines. In order to protect pipelines from the surrounding environment it is common for viscoelastic coatings to be applied to the outer surface. These coatings are, however, known to impact on the ability of long range ultrasonic techniques to locate degradation, or defects, within a coated pipe. The coating dissipates sound energy travelling along the pipe, attenuating both the incident and reflected signals making responses from defects difficult to detect. This article aims to investigate the influence of a viscoelastic coating on the ability of long range ultrasonic testing to detect a defect in an axisymmetric pipe. The article focuses on understanding the behaviour of the fundamental torsional mode and quantifying the effect of bitumen coatings on reflection coefficients generated by axisymmetric defects. Reflection coefficients are measured experimentally for coated and uncoated pipes and compared to theoretical predictions generated using numerical mode matching and a hybrid finite element technique. Good agreement between prediction and measurement is observed for uncoated pipes, and it is shown that the theoretical methods presented here are fast and efficient making them suitable for studying long pipe runs. However, when studying coated pipes agreement between theory and prediction is observed to be poor for predictions based on those bulk acoustic properties currently reported in the literature for bitumen. Good agreement is observed only after conducting a parametric study to identify more appropriate values for the bulk acoustic properties. Furthermore, the reflection coefficients obtained for the fundamental torsional mode in a coated pipe show that significant sound attenuation is present over relatively short lengths of coating, thus quantifying those problems commonly encountered with the use of long range ultrasonic testing on coated pipes in the field. © 2012 Elsevier Ltd

Microstates of a Neutral Black Hole in M Theory

We consider vacuum solutions in M theory of the form of a five-dimensional Kaluza-Klein black hole cross T^6. In a certain limit, these include the five-dimensional neutral rotating black hole (cross T^6). From a IIA standpoint, these solutions carry D0 and D6 charges. We show that there is a weakly coupled D-brane description which precisely reproduces the Hawking-Bekenstein entropy in the extremal limit, even though supersymmetry is completely broken.Comment: 11 pages. v2: microstate counting extended to generic angular moment

Toxicological Patterns of Multicomponent Polymer Systems

Development of new polymer systems (PS) based on thermo-active resins is important not only from a chemical viewpoint but also because of the opportunity for programmable changing their properties and subsequent application in clinical practice. Some chemical features of a new composition for a multicomponent polymer system (MPS) based on hydrophilized unsaturated polyester resin (HUPR) are presented. Strength parameters of several resins of different compositions are examined. The analysis of the acute oral toxicity of these resins in white Wistar rats proves that they are low toxic. These PS do not demonstrate any harmful effects on human skin after the predicting irritation and sensitization tests using epicutaneous samples. Their main advantages include preliminary water-solubility and capacity to incorporate water, good dilution into water and resin water dispersions, porosity, low relative mass, high strength indices, improved ecological features, thin-founding capacity, good relief impressions in combination with high adhesion ability towards wet surfaces. A wide MPS usage in the manufacture of orthopedic plaster dressings, prostheses, splints, insoles, positive-sample dental imprints, and casts is recommended

Solving advection equations by applying the crank-nicolson scheme combined with the richardson extrapolation

Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples. Copyright Zahari Zlatev et al

Parallel Computations with Large-scale Air Pollution Models

Large-scale mathematical models are very powerful tools in the efforts to provide more information and more detailed information about the pollution levels, especially about pollution levels which exceed certain critical values.. However, the model used must satisfy at least two conditions: (i) it must be verified that the model results are reliable and (ii) it should be possible to carry out different study by using the model. It is clear that comprehensive studies about relationships between different input parameters and the model results can only be carried out (a) if the numerical methods used in the model are sufficiently fast and (b) if the code runs efficiently on the available high-speed computers. Some results obtained recently by a new unified version of the Danish Eulerian Model will be presented in this paper.Великомасштабні математичні моделі – дуже потужний інструмент для одержання більш детальної інформації щодо рівнів забруднень. Проте використовувана модель повинна задовольнити принаймні двом умовам: (i) результати моделювання повинні бути надійними і (ii) повинна існувати можливість уточнення і вивчення різноманітних характеристик моделей. Всебічне вивчення відношень між різноманітними параметрами входу і результатами моделювання може бути виконане, якщо (a) чисельні методи, використовувані в моделі, достатньо швидкі та (b) програмне забезпечення на доступних швидкодіючих комп'ютерах достатньо ефективне. Подані результати рівнобіжної реалізації моделювання забруднення атмосфери, отримані в новій об'єднаній версії датської Ейлерової моделі.Крупномасштабные математические модели – очень мощный инструмент для получения более детальной информации относительно уровней загрязнений. Однако модель должна удовлетво- рить по крайней мере двум условиям: (i) результаты моделирования должны быть надежными и (ii) должна существовать возможность уточнения и изучения характеристик модели. Всестороннее изучение отношений между различными параметрами входа и результатами моделирования может быть выполнено, если (a) численные методы, используемые в модели, достаточно быстры и (b) программное обеспечение на доступных быстродействующих компь- ютерах достаточно эффективно. Представлены результаты параллельной реализации моделирования загрязнения атмосферы, полученные в новой объединенной версии датской Эйлеровой модели