научная статья по теме PSEUDO-SCALED AND SCALED DESCRIPTION AND SCALEPORTATION OF INORGANIC AND ORGANIC POLYMER AND POLYMER COMPOSITES PROPERTIES Комплексное изучение отдельных стран и регионов

Текст научной статьи на тему «PSEUDO-SCALED AND SCALED DESCRIPTION AND SCALEPORTATION OF INORGANIC AND ORGANIC POLYMER AND POLYMER COMPOSITES PROPERTIES»

НАНОСТРУКТУРЫ

NANOSTRUCTURES

Статья поступила в редакцию 12.03.10. Ред. рег. № 760 The article has entered in publishing office 12.03.10. Ed. reg. No. 760

PACS: 87.10.-e, 87.16.A-, 82.35.Pq, 82.35.Lr, 82.45.Yz, 34.10.+x, 46.05.+b

ПСЕВДОМАСШТАБНОЕ И МАСШТАБНОЕ ОПИСАНИЕ И ПЕРЕНОС ПО МАСШТАБАМ СВОЙСТВ НЕОРГАНИЧЕСКИХ И ОРГАНИЧЕСКИХ ПОЛИМЕРОВ И ПОЛИМЕРНЫХ КОМПОЗИТОВ

1 12 В.С. Травкин , Н.Н. Болотина '

hierarchical Scaled Physics and Technologies (HSPT), Los Angeles, CA, USA E-mail: travkin@travkin-hspt.com 2University of Applied Sciences, Rheinbach, Germany

Заключение совета рецензентов: 01.04.10 Заключение совета экспертов: 11.04.10 Принято к публикации: 24.04.10

Мы начинаем с краткого очерка, в котором представлены некоторые определения из физики нескольких масштабов и некоторый полученный объем результатов, используемых в современной физике. Далее мы напоминаем об истории связи между структурой и свойствами материалов так, как они были сформулированы в 80-х и 90-х годах, включая и постепенное угасание этой кампании, и затем мы обсуждаем подходы, предлагаемые в настоящее время. Получение искомых специфических свойств сложных материалов, биоматериалов и искусственных биологических тканей вряд ли возможно без компонентов на полимерной основе. Для этого и необходимо изучение многомасштабных явлений в этих материалах и их композитах. Мы оцениваем новые технологии «многомасштабности», которые якобы соединяют свойства различных масштабов в полимерах и композитах, материалах на полимерной основе. Критический обзор будет главным образом посвящен попыткам «много-масштабности», псевдомасштабности, квазимасштабности, произвольной масштабности в физических методах и технологиях, в основном в механике сплошных сред и материаловедении, и в областях, связанных с моделированием полимеров, биополимеров и материалов на полимерной основе и их композитов. Претензии такого рода было бы лучше назвать методами множественного разрешения одного масштаба. В то же время мы сравниваем и описываем в деталях истинные полимасштабные механизмы, вытекающие из использования гетерогенных аналогов теоремы Гаусса-Остроградского (GOT) и дальнейшего использования этих теорем (WSAM) для тех же целей, для которых используется однородная теорема Гаусса-Остроградского в физике. В обзоре специальное внимание уделяется некоторым проблемам многомасштабных материалов, композитов с разномасштабными, гетерогенными, нелокальными и нелинейными свойствами.

Ключевые слова: полимеры, биополимеры, органические полимеры, полимерные композиты, гетерогенный, многомасштабный, полимасштабный, моделирование, многомасштабное моделирование, физическая модель, теорема Гаусса-Остроград-ского, теории осреднения, перенос по масштабам.

PSEUDO-SCALED AND SCALED DESCRIPTION AND SCALEPORTATION OF INORGANIC AND ORGANIC POLYMER AND POLYMER COMPOSITES PROPERTIES

V.S. Travkin1, N.N. Bolotina

1,2

'Hierarchical Scaled Physics and Technologies (HSPT), Los Angeles, CA, USA E-mail: travkin@travkin-hspt.com 2University of Applied Sciences, Rheinbach, Germany

Referred: 01.04.10 Expertise: 11.04.10 Accepted: 24.04.10

We start with a short outline in which some definitions of a few scales physics and a developed volume of results used in the contemporary physics will be introduced. We continue with the reminding of the history of structure-properties relation as it was formulated in the 80s-90s including the calm fading of that campaign, and then we go on with the currently proposed approaches. The specific attributes of complex materials, biomedia and tissue engineering are hardly to be achieved without polymer-based constituents. That is of interest in promoting the understanding of multiscale studies. We consider the new techniques of "multiscaling" that allegedly connect different scale properties of polymers and polymer-based composites, materials. The critical review will be dealing mostly with the attempts to "multiscale", pseudo-scale, quasi-scale, ad-hoc scaling approaches and techniques in physics, mostly in continuum mechanics and materials science and related to polymer and polymer-based materials and composite modeling fields. The claims of this kind would be better to name as the multi-resolution ones. At the same time, we compare and describe in some detail the true multiscaling mechanisms stemmed from the heterogeneous analogs of Gauss-Ostrogradsky theorem (GOT) and further use of these theorems (WSAM) for the same purposes in which the homogeneous GOT is used. The interests will be focused on the problems of scaled materials, composites with multiscale, heterogeneous, nonlocal and nonlinear character.

Keywords: polymer; biopolymer; organic polymers; polymer composite; heterogeneous; multiscale; polyscale; modeling; multiscale modeling; physical model; Gauss-Ostrogradsky theorem; averaging theories; scaleportation.

g2 International Scientific Journal for Alternative Energy and Ecology № 1 (93) 2011 fl IB [T2

© Scientific Technical Centre «TATA», 2011

Introduction

1. Some definitions of scale dependent physics and hierarchical modeling of scaled phenomena and processes tied to continuum physics and modeling of polymers, polymer composites, and biopolymers as scaled media

In spite of the fact that great progress was achieved regarding the power and speed of scientific computations, still many issues, tasks will remain unsolved in the near future.

It is also the point in discussion whether relying on computer power will solve "all" our problems with scale, interscale dependent issues. Of course, not, it is a too mechanistic human approach to structure and function dependence up to our needs hoping to resolve it with our tools at hand.

By present time, there have been developed numerous mostly experimental (including and numerical experiments) tools, methods for communication of physical properties usually established and applicable at one or another description scale to the other (mostly Upper) scale description methodologies.

This way of doing scale-to-scale [StS] communication has been in need for many decades. Mostly these attempts have been failing throughout this time span. We will talk on the reasons for failure.

Nevertheless, in the latest 8-10 years a huge number of attempts have started again claiming the direct connection, communication of thermal, electrical, mechanical characteristics at different scale description physics.

We start with a short outline in which some definitions of a few scales physics and a developed volume of results used in the contemporary physics will be introduced.

We continue with the reminding of the history of structure-properties relation-formulation in the 80s-90s including the calm fading of that campaign, then the nowadays proposed approaches.

The specific attributes of complex materials, biomedia and tissue engineering are hardly to be achieved without polymer-based constituents. That is of interest in promoting the understanding of multiscale studies.

We consider the new techniques of "multiscaling" that allegedly connect properties of polymers and polymer-based composites, materials. The critical review will be dealing mostly with the attempts to "multiscale", pseudo-scale, quasi-scale, ad-hoc scaling approaches and techniques in physics, mostly in continuum mechanics and materials science and related to polymer and polymer-based materials and composite modeling fields. The claims of this kind would be better to name as multiresolution ones.

The scaled exact governing equations and solutions for classical homogeneous and nonlocal heterogeneous Bottom-Up physical problems in different physical

disciplines, fields, which are under stable development path through more than 40 last years, will be used to analyze the current trends in multiscaling. A few ideas regarding the composites modeling, simulation with the purposes of Scaleportation (Scaleportation was introduced some years ago as a definition for the means and procedures of the direct and strict "transformation" of data at one scale to the data of the neighboring Upper or Lower Scale) would be introduced for the scale ranges from (10-10-10-6) m and up to (10-3-10-2) m.

These ~4 orders of decimal magnitude are at the most of physical theories to provide for the approximate or even ad-hoc adjusting mechanisms for the two-scale Bottom-Up mathematical algorithms. They will be reentered with the examination of the strict Bottom-Up $ Top-Down scale communications.

We should be concerned about the drawbacks within the techniques themselves along with the proper, correct communication of the different scale fields. Having this in mind, we shall try to maintain a balance between the methods employed at this time while demonstrating what arrays of possibilities can be explored in the future studies. In all other nature prescribed cases the physical matters are of scaled or multiscale character by existence.

There is no substance of physical content in our known universe that is not a heterogeneous one. The question is at what scale down the matter is still homogeneous? That answer we don't know yet. And mind the scale: an Upper or Lower one, then we will have the Heterogeneous matter anyway.

There is no action or process that we can name a local one, unless we want to declare that. Obviously, many actions or processes can be separated from their less important, at the moment or case, surroundings or/and forces. But that is always more or less an artificial choice. That says the connections of the scale inherited fields are of great significance/importance.

The strictest definition for the different scale related fields communication - transformation we suggested in 2004 as the Scaleportation. Scaleportation is the means and procedures of the direct and strict "transformation" of data at one scale to the data of the neighbouring Upper or Lower Scale. These interscale communications, scale transformations of data are mostly not by formulae, but using the scal

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