CLASSICAL BAND STRUCTURE OF PERIODIC ELASTIC COMPOSITES

1996 ◽  
Vol 10 (09) ◽  
pp. 977-1094 ◽  
Author(s):  
MANVIR S. KUSHWAHA
Keyword(s):  
Band Structure ◽  
Band Gap ◽  
Binary Systems ◽  
Spectral Gaps ◽  
Wave Localization ◽  
Band Theory ◽  
Phononic Band Gap ◽  
Rich Diversity ◽  
Wide Range ◽  
The Rich

The rich diversity and the fundamental character of the essential theoretical problems associated with it have given band theory a width of interest which contrasts strongly with the apparent narrowness of its subject matter. This review, dealing mainly with the classical band structures of periodic elastic and acoustic binary systems, offers briefly a systematic survey of the historical development of the principles, tools, and applications of band theory for electrons, phonons, photons, and vibrations giving what may be called the "background" to the more recent developments in the fields of photonic and phononic band-gap crystals. Attention is given to survey the physical conditions required to achieve the complete spectral gaps within which the respective propagating modes are utterly forbidden irrespective of the direction of propagation. The existence of complete spectral gaps for cleverly synthesized photonic crystals guarantees the observability of classical Anderson localization of photons and the influence on the spontaneous emission which was, until the 1980's, often regarded as a natural and uncontrollable phenomenon. The phononic band-gap crystals, on the other hand, offer the feasibility of constructing the ultrasound filters, polarization filters, and improvements in designing the transducers, as well as the observability of classical elastic or acoustic wave localization. Abiding by the central theme of the review, numerous theoretical results on the band structure related problems for periodic elastic and acoustic binary sytems have been gathered and reviewed. This survey is preceded by a detailed mathematical machinery that provides the reader with numerous useful analytical results applicable to a wide range of systems of varying interest. Finally, the report concludes with a summary of anticipated implications of photonic and phononic band-gap crystals and proposes some interesting relevant problems concerned with the spectral gaps and the classical wave localization. Our satisfaction in writing this review, like any other review which covers a considerably longer period, was to reach a reasonably self-contained unity by wanting to "leave nothing unexplained". The background provided is believed to make less formidable the task of future writers of reviews in this rather general field and hence enable them to deal more readily with particular aspects of the subject, or with recent advances in those directions in which notable progress may have been made.

Band Gap Engineering in N-Dimensional Phononic Crystals

2006 ◽  
Author(s):  
Manvir S. Kushwaha
Keyword(s):  
Photonic Crystals ◽  
Band Structure ◽  
Band Gap ◽  
Photonic Band Gap ◽  
Phononic Crystals ◽  
Spectral Gaps ◽  
Phononic Band Gap ◽  
Acoustic Waveguides ◽  
Photonic Band Gap Materials ◽  
Acoustic Filters

Periodic binary elastic/acoustic composites can give rise to genuine band gaps in the band structure. The term genuine refers to the complete gaps, which persist independently of the polarization of the wave and of its direction of propagation. Within these complete gaps sound and vibrations are forbidden, the "acoustic crystals" stand still, and the total silence reigns. Thus a vibrator (or defect) introduced into a periodic elastic composite would be unable to generate sound or vibrations within the gap. The existence of complete gaps in the band structure is closely associated with the (classical) Anderson localization of sound and vibrations. The search for phononic band-gap materials is of comparable interest to the pursuit of photonic band-gap materials. Thus the phononic crystals are to acoustics as photonic crystals are to optics. In comparison to the photonic crystals, there are additional parameters (the mass densities and two velocities - longitudinal and transverse) involved in the phononic crystals, which make the physics richer and leaves us with more options in the quest of creating full stop bands in the system. As regards the applications, the phononic crystals are envisioned to find ways in the acoustic waveguides, improvements in designing the transducers, elastic/acoustic filters, noise control, ultrasonics, and medical imaging, to name a few. Since the interesting phenomena emerging from the phononic crystals are all consequences of the existence of the gap(s), a major part of the research efforts has focused on the search for phononic band-gap crystals. As such, we report and emphasize on the spectral gaps in the band structure for cleverly synthesized N-dimensional (N = 1, 2, 3) phononic crystals. PACS numbers:

Full Band-Gap Silicon Phononic Crystals for Surface Acoustic Waves

2006 ◽  
Author(s):  
Saeed Mohammadi ◽  
Abdelkrim Khelif ◽  
Ryan Westafer ◽  
Eric Massey ◽  
William D. Hunt ◽  
...  
Keyword(s):  
Band Gap ◽  
Acoustic Waves ◽  
Phononic Crystal ◽  
Surface Acoustic Waves ◽  
Hexagonal Lattice ◽  
Phononic Crystals ◽  
Bulk Wave ◽  
Filling Fraction ◽  
Phononic Band Gap ◽  
Wide Range

Periodic elastic structures, called phononic crystals, show interesting frequency domain characteristics that can greatly influence the performance of acoustic and ultrasonic devices for several applications. Phononic crystals are acoustic counterparts of the extensively-investigated photonic crystals that are made by varying material properties periodically. Here we demonstrate the existence of phononic band-gaps for surface acoustic waves (SAWs) in a half-space of two dimensional phononic crystals consisting of hexagonal (honeycomb) arrangement of air cylinders in a crystalline Silicon background with low filling fraction. A theoretical calculation of band structure for bulk wave using finite element method is also achieved and shows that there is no complete phononic band gap in the case of the low filling fraction. Fabrication of the holes in Silicon is done by optical lithography and deep Silicon dry etching. In the experimental characterization, we have used slanted finger interdigitated transducers deposited on a thin layer of Zinc oxide (sputtered on top of the phononic crystal structure to excite elastic surface waves in Silicon) to cover a wide range of frequencies. We believe this to be the first reported demonstration of phononic band-gap for SAWs in a hexagonal lattice phononic crystal at such a high frequency.

scholarly journals Temperature dependent Band gap Correction model using tight-binding approach for UTB device simulations

2022 ◽  
Author(s):  
Nalin Vilochan Mishra ◽  
Ravi Solanki ◽  
Harshit Kansal ◽  
Aditya S Medury
Keyword(s):  
Band Structure ◽  
Band Gap ◽  
Tight Binding ◽  
Thin Body ◽  
Temperature Dependent ◽  
Minor Variation ◽  
Correction Model ◽  
Wide Range ◽  
Channel Thickness ◽  
Semi Empirical

<div>Ultra-thin body (UTB) devices are being used in many electronic applications operating over a wide range of temperatures. The electrostatics of these devices depends on the band structure of the channel material, which varies with temperature as well as channel thickness. The semi-empirical tight binding (TB) approach is widely used for calculating channel thickness dependent band structure of any material, at a particular temperature, where TB parameters are defined. For elementary semiconductors like Si, Ge and compound semiconductors like GaAs, these TB parameters are generally defined at only 0 K and 300 K. This limits the ability of the TB approach to simulate the electrostatics of these devices at any other intermediate temperatures.</div><div>In this work, we analyze the variation of band structure for Si, Ge and GaAs over different channel thicknesses at 0 K and 300 K (for which TB parameters are available), and show that the band curvature at the band minima has minor variation with temperature, whereas the change of band gap significantly affects the channel electrostatics. Based on this finding, we propose an approach to simulate the electrostatics of UTB devices, at any temperature between 0 K and 300 K, using TB parameters defined at 0 K, along with a suitable channel thickness and temperature dependent band gap correction. </div>

Rays of the World

2016 ◽  
Keyword(s):  
Comprehensive Overview ◽  
Life Project ◽  
Rich Diversity ◽  
Research Initiative ◽  
Wide Range ◽  
The World ◽  
Distributional Information ◽  
Living Species ◽  
The Rich ◽  
Book Collectors

Rays are among the largest fishes and evolved from shark-like ancestors nearly 200 million years ago. They share with sharks many life history traits: all species are carnivores or scavengers; all reproduce by internal fertilisation; and all have similar morphological and anatomical characteristics, such as skeletons built of cartilage. Rays of the World is the first complete pictorial atlas of the world’s ray fauna and includes information on many species only recently discovered by scientists while undertaking research for the book. It includes all 26 families and 633 valid named species of rays, but additional undescribed species exist for many groups. Rays of the World features a unique collection of paintings of all living species by Australian natural history artist Lindsay Marshall, compiled as part of a multinational research initiative, the Chondrichthyan Tree of Life Project. Images sourced from around the planet were used by the artist to illustrate the fauna. This comprehensive overview of the world’s ray fauna summarises information such as general identifying features and distributional information about these iconic, but surprisingly poorly known, fishes. It will enable readers to gain a better understanding of the rich diversity of rays and promote wider public interest in the group. Rays of the World is an ideal reference for a wide range of readers, including conservationists, fishery managers, scientists, fishers, divers, students and book collectors.

scholarly journals The Rich Diversity of Urban Allotment Gardens in Europe: Contemporary Trends in the Context of Historical, Socio-Economic and Legal Conditions

2021 ◽  
Vol 13 (19) ◽  
pp. 11076
Author(s):  
Lidia Poniży ◽  
Monika J. Latkowska ◽  
Jürgen Breuste ◽  
Andrew Hursthouse ◽  
Sophie Joimel ◽  
...  
Keyword(s):  
Fruits And Vegetables ◽  
Geographical Location ◽  
Economic Benefits ◽  
Main Function ◽  
Allotment Gardens ◽  
Urban Gardening ◽  
Rich Diversity ◽  
Wide Range ◽  
The Rich ◽  
The Uk

Urban allotment gardens (AGs) provide a unique combination of productive and recreational spaces for the inhabitants of European cities. Although the reasons behind the decision to have a plot, as well as the mode of use and gardening practices, are well recognised in the literature, these issues are mainly considered in relation to particular case studies within a single country. The regional diversity of European allotment gardens is still poorly understood, however. This knowledge gap became an incentive for us to carry out the present study. The research was conducted in seven countries: Austria, Estonia, Germany, France, Portugal, Poland and the UK. Surveys were used to assess the motivations of users regarding plot uses and gardening practices. Information was also collected during desk research and study visits, making use of available statistical data. Allotment gardens in Europe are currently very diverse, and vary depending on the historical, legal, economic and social conditions of a given country, and also as determined by geographical location. Three main types of plots were distinguished, for: cultivation, recreation–cultivation, and cultivation–recreation. The recreational use of AGs has replaced their use for food production in countries with a long history of urban gardening. The only exception is the UK. In some countries, the production of food on an AG plot is still its main function; however, the motivations for this are related to better quality and taste (the UK), as well as the economic benefits of self-grown fruits and vegetables (Portugal, Estonia). Among the wide range of motivations for urban gardening in Europe, there is increasing emphasis on active recreation, contact with nature and quality food supply.

scholarly journals Paulus en mag: Raamwerke en aansprake

2012 ◽  
Vol 68 (1) ◽  
Author(s):  
Jeremy Punt
Keyword(s):  
Rich Diversity ◽  
Wide Range ◽  
Imperial Ideology ◽  
The Rich ◽  
Interpretive Strategies ◽  
And Function

Paul and power: Framing claims. Evidently an important theme in the Pauline letters, discussions of the nature, scope and function of power have given rise to a wide range of explanations and interpretative positions. Engaging the rich diversity regarding the content and nature of power in Paul, this contribution argues that the Roman imperial context is indicative and instrumental for understanding the construction and regulation of power in the Pauline letters. Coming to terms with the significance of imperial ideology in the understanding of power in Paul requires appropriate interpretive strategies such as a postcolonial interpretation.

scholarly journals Temperature dependent Band gap Correction model using tight-binding approach for UTB device simulations

2022 ◽  
Author(s):  
Nalin Vilochan Mishra ◽  
Ravi Solanki ◽  
Harshit Kansal ◽  
Aditya S Medury
Keyword(s):  
Band Structure ◽  
Band Gap ◽  
Tight Binding ◽  
Thin Body ◽  
Temperature Dependent ◽  
Minor Variation ◽  
Correction Model ◽  
Wide Range ◽  
Channel Thickness ◽  
Semi Empirical

<div>Ultra-thin body (UTB) devices are being used in many electronic applications operating over a wide range of temperatures. The electrostatics of these devices depends on the band structure of the channel material, which varies with temperature as well as channel thickness. The semi-empirical tight binding (TB) approach is widely used for calculating channel thickness dependent band structure of any material, at a particular temperature, where TB parameters are defined. For elementary semiconductors like Si, Ge and compound semiconductors like GaAs, these TB parameters are generally defined at only 0 K and 300 K. This limits the ability of the TB approach to simulate the electrostatics of these devices at any other intermediate temperatures.</div><div>In this work, we analyze the variation of band structure for Si, Ge and GaAs over different channel thicknesses at 0 K and 300 K (for which TB parameters are available), and show that the band curvature at the band minima has minor variation with temperature, whereas the change of band gap significantly affects the channel electrostatics. Based on this finding, we propose an approach to simulate the electrostatics of UTB devices, at any temperature between 0 K and 300 K, using TB parameters defined at 0 K, along with a suitable channel thickness and temperature dependent band gap correction. </div>

Conclusion

2018 ◽  
Author(s):  
Stefan Winter
Keyword(s):  
Middle Eastern ◽  
Rich Diversity ◽  
The Social ◽  
Local Contexts ◽  
History Of ◽  
Religious Oppression ◽  
The Rich ◽  
To Come

This concluding chapter summarizes key themes and presents some final thoughts. The book has shown that the multiplicity of lived ʻAlawi experiences cannot be reduced to the sole question of religion or framed within a monolithic narrative of persecution; that the very attempt to outline a single coherent history of “the ʻAlawis” may indeed be misguided. The sources on which this study has drawn are considerably more accessible, and the social and administrative realities they reflect consistently more mundane and disjointed, than the discourse of the ʻAlawis' supposed exceptionalism would lead one to believe. Therefore, the challenge for historians of ʻAlawi society in Syria and elsewhere is not to use the specific events and structures these sources detail to merely add to the already existing metanarratives of religious oppression, Ottoman misrule, and national resistance but rather to come to a newer and more intricate understanding of that community, and its place in wider Middle Eastern society, by investigating the lives of individual ʻAlawi (and other) actors within the rich diversity of local contexts these sources reveal.

PSYCHOLOGICAL FEATURES OF EDUCATION AND TOLERANCE IN STUDENTS

2018 ◽  
Vol 16 (1) ◽  
pp. 112-119
Author(s):  
VLADIMIR GLEB NAYDONOV
Keyword(s):  
Statistical Analysis ◽  
Training Program ◽  
Rich Diversity ◽  
Interethnic Differences ◽  
The World ◽  
The Rich ◽  
Correct Understanding ◽  
Psychological Features ◽  
Different Levels

The article considers the students’ tolerance as a spectrum of personal manifestations of respect, acceptance and correct understanding of the rich diversity of cultures of the world, values of others’ personality. The purpose of the study is to investgate education and the formation of tolerance among the students. We have compiled a training program to improve the level of tolerance for interethnic differences. Based on the statistical analysis of the data obtained, the most important values that are significant for different levels of tolerance were identified.

Efficient Prediction of Structural and Electronic Properties of Hybrid 2D Materials Using DFT and Machine Learning

2018 ◽  
Author(s):  
Sherif Tawfik ◽  
Olexandr Isayev ◽  
Catherine Stampfl ◽  
Joseph Shapter ◽  
David Winkler ◽  
...  
Keyword(s):  
Machine Learning ◽  
Band Gap ◽  
Density Functional ◽  
2D Materials ◽  
Van Der Waals ◽  
Building Blocks ◽  
Machine Learning Techniques ◽  
Interlayer Distance ◽  
Computational Screening ◽  
Wide Range

Materials constructed from different van der Waals two-dimensional (2D) heterostructures offer a wide range of benefits, but these systems have been little studied because of their experimental and computational complextiy, and because of the very large number of possible combinations of 2D building blocks. The simulation of the interface between two different 2D materials is computationally challenging due to the lattice mismatch problem, which sometimes necessitates the creation of very large simulation cells for performing density-functional theory (DFT) calculations. Here we use a combination of DFT, linear regression and machine learning techniques in order to rapidly determine the interlayer distance between two different 2D heterostructures that are stacked in a bilayer heterostructure, as well as the band gap of the bilayer. Our work provides an excellent proof of concept by quickly and accurately predicting a structural property (the interlayer distance) and an electronic property (the band gap) for a large number of hybrid 2D materials. This work paves the way for rapid computational screening of the vast parameter space of van der Waals heterostructures to identify new hybrid materials with useful and interesting properties.

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