scholarly journals On the Computation of the Dispersion Diagram of Symmetric One-Dimensionally Periodic Structures

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 307 ◽  
Author(s):  
Francisco Mesa ◽  
Raúl Rodríguez-Berral ◽  
Francisco Medina
Keyword(s):  
Periodic Structures ◽  
Network Models ◽  
General Purpose ◽  
Critical Discussion ◽  
Simulation Software ◽  
Dispersion Diagram ◽  
Full Wave ◽  
Unit Cells ◽  
Relevant Role ◽  
Finite Sections

A critical discussion on the computation of the dispersion diagram of electromagnetic guiding/radiating structures with one-dimensional periodicity using general-purpose electromagnetic simulation software is presented in this work. In these methods, full-wave simulations of finite sections of the periodic structure are combined with appropriate simplifying network models. In particular, we analyze the advantages and limitations of two different combined methods, with emphasis on the determination of their range of validity. Our discussion is complemented with several selected numerical examples in order to show the most relevant aspects that a potential user of these methods should be aware of. Special attention is paid to the relevant role played by the high-order coupling between adjacent unit cells and between the two halves of unit cells exhibiting reflection, inversion, and glide symmetries.

scholarly journals On the Computation of the Dispersion Diagram of Symmetric Periodic One-dimensional Structures

2018 ◽  
Author(s):  
Francisco Mesa ◽  
Raul Rodriguez-Berral ◽  
Francisco Medina
Keyword(s):  
Equivalent Circuit Model ◽  
Critical Discussion ◽  
Post Processing ◽  
Dispersion Diagram ◽  
Numerical Examples ◽  
One Dimensional ◽  
Full Wave ◽  
Software Packages ◽  
Relevant Role ◽  
Pros And Cons

A critical discussion on the computation of the dispersion diagram in periodic one-dimensional guiding structures is carried out. In particular, an analysis is presented of the pros and cons of combined methods that make use of full-wave simulations done with commercial software packages with further analytical post-processing based on simplifications brought by an equivalent circuit model of the structure. Some of the most common methods reported in the literature are reviewed and their advantanges and limitations highlighted. Our discussion is complemented with several selected numerical examples in order to discuss the most relevant aspects that a potential user of these methods should be aware of. Special attention is paid to the relevant role played by the high-order coupling between the two halves of a symmetric unit cell of the periodic structure.

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

Hierarchical Design of Phononic Materials and Structures

2005 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Wave Scattering ◽  
Design Methodology ◽  
Periodic Structures ◽  
Building Blocks ◽  
Hierarchical Design ◽  
Material Interfaces ◽  
Dynamical Characteristics ◽  
Constituent Material ◽  
Unit Cells ◽  
Damping Materials

Within periodically heterogeneous materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. A novel multiscale dispersive design methodology is presented by which periodic unit cells are designed for desired frequency band structures, and are used as building blocks for forming fully or partially periodic structures, typically at larger length scales. Structures resulting from this hierarchical design approach are tailored to desired dynamical characteristics without the necessity for altering the overall geometric shape of the structure nor employing dissipative damping materials. Case studies are presented for shock isolation and frequency sensing.

scholarly journals Design and Modeling of New UWB Metamaterial Planar Cavity Antennas with Shrinking of the Physical Size for Modern Transceivers

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Mohammad Alibakhshi Kenari
Keyword(s):  
Transmission Lines ◽  
Patch Antenna ◽  
Patch Antennas ◽  
Frequency Bandwidth ◽  
Left Handed ◽  
Full Wave ◽  
Radiation Properties ◽  
Unit Cells ◽  
Constitutive Parameters ◽  
Large Frequency

A variety of antennas have been engineered with MTMs and MTM-inspired constructs to improve their performance characteristics. This report describes the theory of MTMs and its utilization for antenna's techniques. The design and modeling of two MTM structures withε-μconstitutive parameters for patch antennas are presented. The framework presents two novel ultrawideband (UWB) shrinking patch antennas filled with composite right-/left-handed transmission line (CRLH-TL) structures. The CRLH-TL is presented as a general TL possessing both left-handed (LH) and right-handed (RH) natures. The CRLH-TL structures enhance left-handed (LH) characteristics which enable size reduction and large frequency bandwidth. The large frequency bandwidth and good radiation properties can be obtained by adjusting the dimensions of the patches and CRLH-TL structures. This contribution demonstrates the possibility of reducing the size of planar antennas by using LH-transmission lines. Two different types of radiators are investigated—a planar patch antenna composed of fourO-formed unit cells and a planar patch antenna composed of sixO-shaped unit cells. A CRLH-TL model is employed to design and compare these two approaches and their realization with a varying number ofL-Cloaded unit cells. Two representative antenna configurations have been selected and subsequently optimized with full-wave electromagnetic analysis. Return loss and radiation pattern simulations of these antennas prove the developed concept.

Design of Three-Dimensional, Triply Periodic Unit Cell Scaffold Structures for Additive Manufacturing

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Mazher Iqbal Mohammed ◽  
Ian Gibson
Keyword(s):  
Additive Manufacturing ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Unit Cell ◽  
Final Size ◽  
Fused Filament Fabrication ◽  
Cell Structures ◽  
Triply Periodic ◽  
Unit Cells ◽  
Scaffold Structure

Highly organized, porous architectures leverage the true potential of additive manufacturing (AM) as they can simply not be manufactured by any other means. However, their mainstream usage is being hindered by the traditional methodologies of design which are heavily mathematically orientated and do not allow ease of controlling geometrical attributes. In this study, we aim to address these limitations through a more design-driven approach and demonstrate how complex mathematical surfaces, such as triply periodic structures, can be used to generate unit cells and be applied to design scaffold structures in both regular and irregular volumes in addition to hybrid formats. We examine the conversion of several triply periodic mathematical surfaces into unit cell structures and use these to design scaffolds, which are subsequently manufactured using fused filament fabrication (FFF) additive manufacturing. We present techniques to convert these functions from a two-dimensional surface to three-dimensional (3D) unit cell, fine tune the porosity and surface area, and examine the nuances behind conversion into a scaffold structure suitable for 3D printing. It was found that there are constraints in the final size of unit cell that can be suitably translated through a wider structure while still allowing for repeatable printing, which ultimately restricts the attainable porosities and smallest printed feature size. We found this limit to be approximately three times the stated precision of the 3D printer used this study. Ultimately, this work provides guidance to designers/engineers creating porous structures, and findings could be useful in applications such as tissue engineering and product light-weighting.

An Executable Notation, With Illustrations From Elementary Crystallography

1994 ◽  
Author(s):  
Donald B. Mclntyre
Keyword(s):  
Plate Tectonics ◽  
Periodic Structures ◽  
Dimensional Space ◽  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Cubic Symmetry ◽  
Multiple Data ◽  
Special Cases ◽  
Unit Cells ◽  
Crystallographic Axes

Elementary crystallography is an ideal context for introducing students to mathematical geology. Students meet crystallography early because rocks are made of crystalline minerals. Moreover, morphological crystallography is largely the study of lines and planes in real three-dimensional space, and visualizing the relationships is excellent training for other aspects of geology; many algorithms learned in crystallography (e.g., rotation of arrays) apply also to structural geology and plate tectonics. Sets of lines and planes should be treated as entities, and crystallography is an ideal environment for introducing what Sylvester (1884) called "Universal Algebra or the Algebra of multiple quantity." In modern terminology, we need SIMD (Single Instruction, Multiple Data) or even MIMD. This approach, initiated by W.H. Bond in 1946, dispels the mysticism unnecessarily associated with Miller indices and the reciprocal lattice; edges and face-normals are vectors in the same space. The growth of mathematical notation has been haphazard, new symbols often being introduced before the full significance of the functions they represent had been understood (Cajori, 1951; Mclntyre, 1991b). Iverson introduced a consistent notation in 1960 (e.g., Iverson 1960, 1962, 1980). His language, greatly extended in the executable form called J (Iverson, 1993), is used here. For information on its availability as shareware, see the Appendix. Publications suitable as tutorials in , J are available (e.g., Iverson. 1991; Mclntyre, 1991 a, b; 1992a,b,c; 1993). Crystals are periodic structures consisting of unit cells (parallelepipeds) repeated by translation along axes parallel to the cell edges. These edges define the crystallographic axes. In a crystal of cubic symmetry they are orthogonal and equal in length (Cartesian). Those of a triclinic crystal, on the other hand, are unequal in length and not at right angles. The triclinic system is the general case; others are special cases. The formal description of a crystal gives prominent place to the lengths of the axes (a, b, and c) and the interaxial angles ( α, β, and γ). A canonical form groups these values into a 2 x 3 table (matrix), the first row being the lengths and the second the angles.

scholarly journals ExtSim: A Flexible Data Mapping and Synchronization Middleware for Scientific Visualization in Virtual Worlds

2010 ◽  
Vol 2 (5) ◽  
Author(s):  
Johan Berntsson ◽  
Norman Lin ◽  
Zoltan Dezso
Keyword(s):  
Protein Folding ◽  
Real Time ◽  
Virtual Worlds ◽  
Scientific Computing ◽  
General Purpose ◽  
Current Approach ◽  
Simulation Software ◽  
Third Party ◽  
Data Mapping ◽  
Future Work

In this paper we present a general-purpose middleware, called ExtSim that allows OpenSim to communicate with external simulation software, and to synchronize the in-world representation of the simulator state. We briefly present two projects in ScienceSim where ExtSim has been used; Galaxsee which is an interactive real-time N-body simulation, and a protein folding demonstration, before discussing the merits and problems with the current approach. The main limitation is that we until now only have been limited to a third-party viewer, and a fixed server-client protocol, but we present our work on a new viewer, called 3Di Viewer “Rei”, which opens new possibilities in enhancing both performance and richness of the visualization suitable for scientific computing,. Finally we discuss some ideas we are currently studying for future work.

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