scholarly journals Representations of Polycrystalline Microstructure by n-Point Correlation Tensors

1993 ◽  
Vol 21 (1) ◽  
pp. 17-37 ◽  
Author(s):  
Pavel Etingof ◽  
Brent L. Adams
Keyword(s):  
Representation Theory ◽  
Crystal Lattice ◽  
Spatial Coherence ◽  
Central Problem ◽  
Important Class ◽  
Lower Dimension ◽  
Lattice Orientation ◽  
Minimum Dimension ◽  
Point Correlation ◽  
Polycrystalline Microstructure

An important class of representations of polycrystalline microstructure consists of the n-point correlation tensors. In this paper the representation theory of groups is applied to a consideration of symmetries in the n-point correlation tensors. Three sources of symmetry are included in the development: indicial symmetry in the coefficients of tensors, symmetry associated with the crystal lattice, and statistical symmetries in the microstructure induced by processing. The central problem discussed here is the “residence space”, or the space of minimum dimension occupied by correlation tensors possessing such symmetries. In addition to the general case of correlation tensors possessing such symmetries, a model microstructure is also considered which embodies an assumption of no spatial coherence of lattice orientation between neighboring grains or crystallites. It is shown that the model microstructure generally results in residence spaces of lower dimension.

On the Positivity of $\mathbf{{a}}$-Linear with Random Finitely

2020 ◽  
Author(s):  
Amanda Bolton
Keyword(s):  
Representation Theory ◽  
Central Problem ◽  
Numerical Representation

Let $\rho$ be an ultra-unique, reducible topos equipped with a minimal homeomorphism. We wish to extend the results of \cite{cite:0} to trivially Cartan classes. We show that $d$ is comparable to $\mathcal{{M}}$. This leaves open the question of uniqueness. Moreover, a central problem in numerical representation theory is the description of irreducible, orthogonal, hyper-unique graphs.

Bending and branching of calcite laths in the foliated microstructure of pectinoidean bivalves occurs at coherent crystal lattice orientation

2019 ◽  
Vol 205 (3) ◽  
pp. 7-17
Author(s):  
Antonio G. Checa ◽  
María E. Yáñez-Ávila ◽  
Alicia González-Segura ◽  
Francisco Varela-Feria ◽  
Erika Griesshaber ◽  
...  
Keyword(s):  
Crystal Lattice ◽  
Lattice Orientation ◽  
Coherent Crystal

Periodically arranged co-flowing jets

1994 ◽  
Vol 263 ◽  
pp. 63-92 ◽  
Author(s):  
E. Villermaux ◽  
E. J. Hopfinger
Keyword(s):  
Large Scale ◽  
Travelling Waves ◽  
Spatial Coherence ◽  
Low Frequency ◽  
Periodic Pattern ◽  
Low Frequency Oscillation ◽  
Recirculating Flow ◽  
Point Correlation ◽  
Spatio Temporal ◽  
New Formulation

The problem of a periodic planar arrangement of a large number of co-flowing, interacting jets is investigated. It is shown that this interaction gives rise to strong nearfield oscillations of large-scale spatial coherence and to far-field inhomogeneities. In the experiments performed, the jets were produced behind a flat plate perforated by holes arranged in a square or triangular periodic pattern and placed perpendicular to a uniform flow. At moderate Reynolds numbers, the interaction results in a remarkable low-frequency oscillation of the merging distance of the jets downstream of the plate. A detailed description of the recirculating flow in the cavities between the jets emphasizes the role of the backflow in the cavities on the oscillatory behaviour. This description is supported by measurements of the local fluctuating velocity and pressure, two-point correlation measurements and quantitative flow visualizations. These experimental observations suggest a new formulation for the instability dynamics of such unstable recirculating flows. This formulation, based on the nonlinear delayed saturation of the jet's shear layer instability (NLDS model) predicts successfully the dependence of the oscillation of the merging distance on the jet Reynolds number and on the local geometrical features of the confinement of the jets. Furthermore, it is shown that the diffusion of mass coming from one jet, seeded with an inert dye, gives rise to an exponential diffusion front over a distance corresponding to a few mesh sizes indicating a strong local coupling of the jets. At the scale of the whole jet assembly, the oscillations are organized as large-scale travelling waves, propagating from the boundaries of the domain to its centre. This symmetry-breaking property is discussed and supplemented by a spatio-temporal simulation of an array of coupled oscillators.

scholarly journals Producing desired ice faces

2015 ◽  
Vol 112 (45) ◽  
pp. E6096-E6100 ◽  
Author(s):  
Mary Jane Shultz ◽  
Alexandra Brumberg ◽  
Patrick J. Bisson ◽  
Ryan Shultz
Keyword(s):  
Catalytic Activity ◽  
Heterogeneous Catalysis ◽  
Single Crystal ◽  
Crystal Lattice ◽  
Surface Reactivity ◽  
Lattice Plane ◽  
Lattice Orientation ◽  
High Quality ◽  
Hexagonal Ice ◽  
Single Crystal Faces

The ability to prepare single-crystal faces has become central to developing and testing models for chemistry at interfaces, spectacularly demonstrated by heterogeneous catalysis and nanoscience. This ability has been hampered for hexagonal ice, Ih––a fundamental hydrogen-bonded surface––due to two characteristics of ice: ice does not readily cleave along a crystal lattice plane and properties of ice grown on a substrate can differ significantly from those of neat ice. This work describes laboratory-based methods both to determine the Ih crystal lattice orientation relative to a surface and to use that orientation to prepare any desired face. The work builds on previous results attaining nearly 100% yield of high-quality, single-crystal boules. With these methods, researchers can prepare authentic, single-crystal ice surfaces for numerous studies including uptake measurements, surface reactivity, and catalytic activity of this ubiquitous, fundamental solid.

Probing the Chain and Crystal Lattice Orientation in Polyethylene Thin Films by Near Edge X-ray Absorption Fine Structure (NEXAFS) Spectroscopy

2010 ◽  
Vol 43 (19) ◽  
pp. 8153-8161 ◽  
Author(s):  
Yantian Wang ◽  
Ying Zou ◽  
Tohru Araki ◽  
Jan Lüning ◽  
A. L. D. Kilcoyne ◽  
...  
Keyword(s):  
Thin Films ◽  
Fine Structure ◽  
Crystal Lattice ◽  
Lattice Orientation ◽  
X Ray ◽  
Absorption Fine ◽  
Nexafs Spectroscopy ◽  
X Ray Absorption
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