Числовий метод знаходження ефективного показника заломлення пористих композиційних матеріалів на основі мікрорівневих моделей

The application of the developed numerical method for finding an effective refractive index of porous nanocomposites is shown. The numerical method of finding an effective refractive index of porous composites is developed on the basis of the use of the micro-level cellular structure model, the method of generation of random fibrous inclusions with the help of Bezier curves and micro-level cellular models. The cellular models are used in this paper for generation of porous composites structural models. They describe composite structure by representative volume elements that contains big amount of regular voxel cells that can be simultaneously used as finite element discretization. Voxel cells contain scalar intensities in diapason from 0 to 1. This enables the description of nanostructural heterogeneity of material within a model, and its direct use as a regular finite-element discretization. This method allows considering complex structural inhomogeneities of the material within the framework of a similar model and to synthesize the corresponding refractive index on the basis of numerical simulation of the electrostatic field. The method of finding an effective index of refraction of porous composite structures described in this paper was programmed in C++ 11 algorithmic language using OpenCL version 1.2 and Qt SDK version 5.4.1. The proposed implementation is simpler and requires less computation poser and resources comparing to similar analytical methods. Due to the regular structure, the obtained micro-level model can be used directly as finite-element sampling, since the use of Bezier curves enables the pores to be modeled taking into account nanostructural heterogeneities. The proposed method was tested by comparing with existing analytical models for finding an effective refractive index, such as Maxwell-Garnett model, Bruggeman model and Drude (Silberstein) model. Based on the estimation of the upper bound of the finite element method approximation error, the obtained results indicate greater accuracy compared to the Drude (Silberstein) analytical model.Розглянуто застосування розробленого числового методу знаходження ефективного показника заломлення для випадку пористих нанокомпозитів. На основі використання мікрорівневої коміркової моделі структури, методу генерування випадкових волокнистих включень з допомогою кривих Без'є та мікрорівневих коміркових моделей структури розвинено числовий метод знаходження ефективного показника заломлення пористих композитів, що дає змогу в рамках однотипної моделі розглядати складні структурні неоднорідності матеріалу та синтезувати відповідний показник заломлення на основі числового моделювання електростатичного поля. Така реалізація є простішою та потребує меншої кількості обчислень та ресурсів порівняно з аналогічними аналітичними методами. Завдяки регулярній структурі отриману мікрорівневу модель можна використовувати безпосередньо як скінченно-елементну дискретизацію, оскільки використання кривих Без'є дає змогу моделювати пори з урахуванням наноструктурних неоднорідностей. Запропонований метод було перевірено шляхом порівняння з наявними аналітичними моделями знаходження ефективного показника заломлення, такими як: Максвелла-Гарнета, моделлю Брюгемана та моделлю Друде (Сільберштейна). Спираючись на оцінку верхньої границі похибки апроксимації використаного методу скінченних елементів, отримані результати свідчать про більшу точність порівняно з аналітичною моделлю Друде (Сільберштейна)

Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets

A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets can be analyzed whithin the anyon theory. Thus, we show that static magnetic vortices correspond to the self-dual Chern - Simons solitons and are described by the Liouville equation. The related magnetic topological charge is associated with the electric charge of anyons. Furthermore, vortex - antivortex configurations are described by the sinh-Gordon equation and its conformally invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199

Time as an operator/observable in nonrelativistic quantum mechanics

The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated with a quantum state solution to the equation. Under the physical assumption that each spatial, as well as the temporal, component of this current is observable, the position in time becomes an operator and an observable in that the weighted average value of the time of the particle's crossing of a complete hyperplane can be simply defined: ... When the space-time coordinates are (t,x,y,z), the paper analyzes in detail the case that the hyperplane is of the type z=constant. Particles can cross such a hyperplane in either direction, so it proves convenient to introduce an indefinite metric, and correspondingly a sesquilinear inner product with non-Hilbert space structure, for the space of quantum states on such a surface. >... A detailed formalism for computing average crossing times on a z=constant hyperplane, and average dwell times and delay times for a zone of interaction between a pair of z=constant hyperplanes, is presented.Comment: 31 pages, no figures. Differs from published version by minor corrections and additions, and two citation

Superposition in nonlinear wave and evolution equations

Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages, 2 figures, style change

Liquid metals as a divertor plasma facing material explored using the Pilot-PSI and Magnum-PSI linear devices

Abstract For DEMO and beyond liquid metal plasma facing components are considered due to their resilience to erosion through flowed replacement, potential for cooling beyond conduction and inherent immunity to many of the issues of neutron loading compared to solid materials. The development curve of liquid metals is behind that of e.g. tungsten however and tokamak-based research is currently somewhat limited in scope. Therefore investigation in linear plasma devices can provide faster progress under controlled and well-diagnosed conditions in assessing many of the issues surrounding the use of liquid metals. The linear plasma devices Magnum-PSI and Pilot-PSI are capable of producing DEMO relevant plasma fluxes which well replicate expected divertor conditions, and the exploration of physics issues for tin (Sn) and lithium (Li) such as vapour-shielding, erosion under high particle flux loading and overall power handing are reviewed here. A deeper understanding of erosion and deposition through this work indicates that stannane formation may play an important role in enhancing Sn erosion, while on the other hand the strong hydrogen isotope affinity reduces the evaporation rate and sputtering yields for Li. In combination with the strong re-deposition rates which have been observed under this type of high density plasma this implies an increase in the operational temperature range, implying a power handling range of 20-25 MW m -2 for Sn and up to 12.5 MW m -2 for Li could be achieved. Vapour shielding may be expected to act as a self-protection mechanism in reducing the heat load to the substrate for off-normal events in the case of Sn, but may potentially be a continual mode of operation for Li.</p

СТРУКТУРНЫЙ АНАЛИЗ ТАЗА ДО И ПОСЛЕ ПРОЦЕДУРЫ ЗАМЕНЫ ТАЗОБЕДРЕННОГО СУСТАВА

The paper presents the results of a preliminary study on the structural analysis of the pelvic girdle, comparing results for the analysis performed before and after the hip replacement procedure with taking into account changes in the mechanical properties of the articular cartilage of the joint. Basic anatomy and biomechanics of the hip joint is introduced. The mechanical analysis of the hip joint model in each case is conducted. Final results of analysis are presented. The numerical model of the tested objects was made on the basis of CT and CAD modeling. Hip bone models were made using specialist software such as Materialise Mimics. The model is made in the program was then exported to a data exchange file in order to obtain the editable CAD files. Thus obtained models were the starting point for the implementation of the numerical model of personalized hip replacement. Numerical models of bone and implant were performed in Solidworks environment.Mechanical analysis was carried out using finite element analysis. During performing of calculations with the use of finite element analysis other physical quantities are also being discretized: loads, tensions, restraints or other examples represented in the system with the use of continuous function. While performing the process of discretization software aims at maximally approximation of discreet and continuous form using approximation methods.В статье представлены результаты предварительного исследования структурного анализа тазового пояса, сравниваются результаты анализа, проведенного до и после процедуры замены тазобедренного сустава, с учетом изменений механических свойств суставного хряща. Вводится базовая анатомия и биомеханика тазобедренного сустава. В каждом случае проводится механический анализ модели тазобедренного сустава. Приводятся окончательные результаты анализа. Численная модель испытуемых объектов сделана на основе компьютерной томографии и CAD-моделирования, модели костного мозга выполнены с использованием специализированного программного обеспечения Materialise Mimics. Модель, сделанная в программе, затем экспортировалась в файл обмена данными, чтобы получить редактируемые файлы CAD. Таким образом, полученные модели стали отправной точкой для внедрения численной модели персонализированной замены тазобедренного сустава. Численные модели кости и имплантата были выполнены в среде SolidWorks. Механический анализ проводился с использованием метода конечных элементов. Во время выполнения расчетов с использованием МКЭ-анализа также дискретируются другие физические величины – нагрузки, напряжения, ограничения, представленные в системе с использованием непрерывной функции. При выполнении процесса дискретизации программное обеспечение нацелено на максимальное сближение дискретной и континуальной моделей с использованием методов аппроксимаци

Energy efficiency considerations in integrated IT and optical network resilient infrastructures

The European Integrated Project GEYSERS - Generalised Architecture for Dynamic Infrastructure Services - is concentrating on infrastructures incorporating integrated optical network and IT resources in support of the Future Internet with special emphasis on cloud computing. More specifically GEYSERS proposes the concept of Virtual Infrastructures over one or more interconnected Physical Infrastructures comprising both network and IT resources. Taking into consideration the energy consumption levels associated with the ICT today and the expansion of the Internet in size and complexity, that incurring increased energy consumption of both IT and network resources, energy efficient infrastructure design becomes critical. To address this need, in the framework of GEYSERS, we propose energy efficient design of infrastructures incorporating integrated optical network and IT resources, supporting resilient end-to-end services. Our modeling results quantify significant energy savings of the proposed solution by jointly optimizing the allocation of both network and IT resources

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM-The International Journal on Mathematics Education-by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers' and didacticians' engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. © 2014 FIZ Karlsruhe