TECHNICAL NOTE. TWO-DIMENSIONAL TREATMENT OF COMPLEX STRUCTURES.

1972 ◽  
Vol 53 (3) ◽  
pp. 589-596 ◽  
Author(s):  
IA MACLEOD ◽  
D GREEN ◽  
W WILSON ◽  
P BHATT
Keyword(s):  
Technical Note ◽  
Complex Structures ◽  
Two Dimensional

A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method

1969 ◽  
Vol 73 (697) ◽  
pp. 55-65 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Computational Analysis ◽  
Three Dimensional ◽  
Technical Note ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Displacement Method ◽  
Stress Concentrations ◽  
The Past ◽  
The Matrix ◽  
Triangular Elements

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.

High-resolution complex structures for two-dimensional photonic crystals realized by x-ray diffraction lithography

2003 ◽  
Vol 21 (2) ◽  
pp. 748 ◽  
Author(s):  
L. Businaro ◽  
F. Romanato ◽  
P. Candeloro ◽  
E. Di Fabrizio ◽  
M. Patrini ◽  
...  
Keyword(s):  
High Resolution ◽  
Photonic Crystals ◽  
Complex Structures ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray

Formation of Two-Dimensional Crystals of Membrane-Anchored and Water-Soluble Proteins

1993 ◽  
Vol 330 ◽  
Author(s):  
Harald Engelhardt ◽  
T. Scheybani ◽  
W. Von Gustedt ◽  
W. Baumeister
Keyword(s):  
Molecular Sieves ◽  
Soluble Proteins ◽  
Water Soluble ◽  
Biological Macromolecules ◽  
Complex Structures ◽  
Two Dimensional ◽  
Protein Species ◽  
Future Developments ◽  
Multiple Protein ◽  
Support Devices

ABSTRACTThe formation of two-dimensional (2-D) crystals of biological macromolecules is of interest for nanotechnological applications. Protein 2-D crystals may be used as molecular sieves and/or support devices as components of biosensors etc. [1]. Functionally specialized 2-D crystals, containing transport or catalytic proteins, provide a certain function in a highly efficient and vectorial manner. Future developments may allow the design of more complex structures such as multilayers made from different proteins or arrays of functionally linked oligo- or multimeric complexes consisting of multiple protein species [2]. Regular 2-D arrays, either truely crystalline or densely packed molecules, are one of the basic structures taht might be used to construct more sophisticated protein-based devices. 2-D crystals have some interesting features:

Homoclinic and Heteroclinic Situations Specific to Two-Dimensional Noninvertible Maps

1997 ◽  
Vol 07 (01) ◽  
pp. 39-70 ◽  
Author(s):  
Gilles Millerioux ◽  
Christian Mira
Keyword(s):  
Qualitative Change ◽  
Closed Curve ◽  
Stable Set ◽  
Complex Structures ◽  
Two Dimensional ◽  
Parameter Region ◽  
Critical Curves ◽  
Rank One ◽  
Stable And Unstable Sets ◽  
Noninvertible Maps

These situations are put in evidence from two examples of (Z0 - Z2) maps. It is recalled that such maps (the simplest type of non-invertible ones) are related to the separation of the plane into a region without preimage, and a region each point of which has two rank-one preimages. With respect to diffeomorphisms, non-invertibility introduces more complex structures of the stable and unstable sets defining the homoclinic and heteroclinic situations, and the corresponding bifurcations. Critical curves permit the analysis of this question. More particularly, a basic global contact bifurcation (contact of the map critical curve with a non-connected saddle stable set Ws) plays a fundamental role for explaining the qualitative change of Ws, which occurs between two boundary homoclinic bifurcations limiting a parameter region related to the disappearing of an attracting invariant closed curve.

scholarly journals Development of three-dimensional wetting and drying algorithm for the Geophysical Scale Transport Multi-Block Hydrodynamic Sediment and Water Quality Transport Modeling System (GSMB)

2021 ◽  
Author(s):  
Ray Chapman ◽  
Phu Luong ◽  
Sung-Chan Kim ◽  
Earl Hayter
Keyword(s):  
Water Quality ◽  
Water Wave ◽  
Large Scale ◽  
Three Dimensional ◽  
The United States ◽  
Technical Note ◽  
Three Dimensions ◽  
Transport Modeling ◽  
Two Dimensional ◽  
Wetting And Drying

The Environmental Laboratory (EL) and the Coastal and Hydraulics Laboratory (CHL) have jointly completed a number of large-scale hydrodynamic, sediment and water quality transport studies. EL and CHL have successfully executed these studies utilizing the Geophysical Scale Transport Modeling System (GSMB). The model framework of GSMB is composed of multiple process models as shown in Figure 1. Figure 1 shows that the United States Army Corps of Engineers (USACE) accepted wave, hydrodynamic, sediment and water quality transport models are directly and indirectly linked within the GSMB framework. The components of GSMB are the two-dimensional (2D) deep-water wave action model (WAM) (Komen et al. 1994, Jensen et al. 2012), data from meteorological model (MET) (e.g., Saha et al. 2010 - http://journals.ametsoc.org/doi/pdf/10.1175/2010BAMS3001.1), shallow water wave models (STWAVE) (Smith et al. 1999), Coastal Modeling System wave (CMS-WAVE) (Lin et al. 2008), the large-scale, unstructured two-dimensional Advanced Circulation (2D ADCIRC) hydrodynamic model (http://www.adcirc.org), and the regional scale models, Curvilinear Hydrodynamics in three dimensions-Multi-Block (CH3D-MB) (Luong and Chapman 2009), which is the multi-block (MB) version of Curvilinear Hydrodynamics in three-dimensions-Waterways Experiments Station (CH3D-WES) (Chapman et al. 1996, Chapman et al. 2009), MB CH3D-SEDZLJ sediment transport model (Hayter et al. 2012), and CE-QUAL Management - ICM water quality model (Bunch et al. 2003, Cerco and Cole 1994). Task 1 of the DOER project, “Modeling Transport in Wetting/Drying and Vegetated Regions,” is to implement and test three-dimensional (3D) wetting and drying (W/D) within GSMB. This technical note describes the methods and results of Task 1. The original W/D routines were restricted to a single vertical layer or depth-averaged simulations. In order to retain the required 3D or multi-layer capability of MB-CH3D, a multi-block version with variable block layers was developed (Chapman and Luong 2009). This approach requires a combination of grid decomposition, MB, and Message Passing Interface (MPI) communication (Snir et al. 1998). The MB single layer W/D has demonstrated itself as an effective tool in hyper-tide environments, such as Cook Inlet, Alaska (Hayter et al. 2012). The code modifications, implementation, and testing of a fully 3D W/D are described in the following sections of this technical note.

Tetrahedron Elements with Linearly Varying Strain for the Matrix Displacement Method

1965 ◽  
Vol 69 (660) ◽  
pp. 877-880 ◽  
Author(s):  
J. H. Arcyris,
Keyword(s):  
Three Dimensional ◽  
Technical Note ◽  
Considerable Improvement ◽  
Elastic Behaviour ◽  
Large Displacements ◽  
Two Dimensional ◽  
Displacement Method ◽  
The Matrix ◽  
Cardinal Point ◽  
Natural Strains

The author mentioned in his Main Lecture(1) the success achieved in the analysis of three-dimensional media, for small and large displacements, as well as anisotropic and non-elastic behaviour, by the introduction of tetrahedron elements of constant strain and stress(2), see also technical note 1 of this series(3). A cardinal point of the theory is the specification of natural strains, stresses and stiffness. At the same time attention was drawn to certain difficulties arising in the interpretation of the stresses at the nodal or other points, which are more severe than for constant strain triangles, the corresponding elements in the two-dimensional case. It was suggested in the lecture that a considerable improvement might be achieved by the specification of a linearly varying strain or stress state within the tetrahedron. The solution of this problem, limited to small displacements, is summarised in this fifth technical note and its application is to be demonstrated on an example in the printed lecture.

scholarly journals Technical Note: Fast two-dimensional GC-MS with thermal extraction for anhydro-sugars in fine aerosols

2010 ◽  
Vol 10 (9) ◽  
pp. 4331-4341 ◽  
Author(s):  
Y. Ma ◽  
M. D. Hays ◽  
C. D. Geron ◽  
J. T. Walker ◽  
M. J. Gatari Gichuru
Keyword(s):  
Biomass Burning ◽  
Atmospheric Aerosols ◽  
Analytical Techniques ◽  
Technical Note ◽  
Two Dimensional ◽  
Relative Standard ◽  
The Us ◽  
Thermal Extraction ◽  
Biomass Burning Aerosol ◽  
The Stability

Abstract. A fast two-dimensional gas chromatography (GC-MS) method that uses heart-cutting and thermal extraction (TE) and requires no chemical derivatization was developed for the determination of anhydro-sugars in fine aerosols. Evaluation of the TE-GC-GC-MS method shows high average relative accuracy (≥90%), reproducibility (≤10% relative standard deviation), detection limits of less than 3 ng/μL, and negligible carryover for levoglucosan, mannosan, and galactosan markers. TE-GC-GC-MS- and solvent extraction (SE)-GC-MS-measured levoglucosan concentrations correlate across several diverse types of biomass burning aerosols. Because the SE-GC-MS measurements were taken 8 years prior to the TE-GC-GC-MS ones, the stability of levoglucosan is established for quartz filter-collected biomass burning aerosol samples stored at ultra-low temperature (−50 °C). Levoglucosan concentrations (w/w) in aerosols collected following atmospheric dilution near open fires of varying intensity are similar to those in biomass burning aerosols produced in a laboratory enclosure. An average levoglucosan-mannosan-galactosan ratio of 15:2:1 is observed for these two aerosol sets. TE-GC-GC-MS analysis of atmospheric aerosols from the US and Africa produced levoglucosan concentrations (0.01–1.6 μg/m3) well within those reported for aerosols collected globally and examined using different analytical techniques (0.004–7.6 μg/m3). Further comparisons among techniques suggest that fast TE-GC-GC-MS is among the most sensitive, accurate, and precise methods for compound-specific quantification of anhydro-sugars. In addition, an approximately twofold increase in anhydro-sugar determination may be realized when combining TE with fast chromatography.

Comparison of numerical methods for light propagating in fibers with high steps of refractive index

2012 ◽  
Vol 20 (1) ◽  
Author(s):  
K. Zegadło ◽  
M. Karpierz
Keyword(s):  
Refractive Index ◽  
Numerical Methods ◽  
Light Propagation ◽  
Chromatic Dispersion ◽  
Three Dimensional ◽  
Complex Structures ◽  
Two Dimensional ◽  
Approximate Methods ◽  
Fast Development ◽  
Numerical Tools

AbstractFast development of complex structures like microstructural fibers, photonic nanowires or slot waveguides requires numerical tools to predict a light propagation. There are many works concerning weakly guided case, but the microstructural fibers need algorithm for a high step of the refractive index. In this paper, three approximate methods are compared. The comparison concerns a structure consisting of circular cores surrounded by cladding for different values of the refractive index steps. Application of these methods in chromatic dispersion case is also presented. It is shown that certain conditions prefer two dimensional scalar algorithms (based on approximated methods) than three dimensional ones. This allows us to implement more efficient and less complicated methods.

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