Low-Dimensionality Representations and Matching

2009 ◽  
pp. 147-179
Keyword(s):  
Low Dimensionality

Cooperative Self-Assembly of Pyridine-2,6-Diimine-Linked Macrocycles into Mechanically Robust Nanotubes

2019 ◽  
Author(s):  
Michael J. Strauss ◽  
Darya Asheghali ◽  
Austin Evans ◽  
Rebecca Li ◽  
Anton Chavez ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Self Assembly ◽  
Gel Permeation Chromatography ◽  
Synthetic Polymers ◽  
Young’S Moduli ◽  
Structural Rigidity ◽  
Assembly Mechanism ◽  
Low Dimensionality ◽  
Harsh Conditions

<p>Nanotubes assembled from macrocyclic precursors offer a unique combination of low dimensionality, structural rigidity, and distinct interior and exterior microenvironments. Usually the weak stacking energies of macrocycles limit the length or strength of the resultant nanotubes. Imine-linked macrocycles were recently found to assemble into high-aspect ratio (>10<sup>3</sup>), lyotropic nanotubes in the presence of excess acid. Yet these harsh conditions are incompatible with many functional groups and processing methods, and lower acid loadings instead catalyze macrocycle degradation. Here we report pyridine-2,6-diimine-linked macrocycles that assemble into high-aspect ratio nanotubes in the presence of less than 1 equiv of CF<sub>3</sub>CO<sub>2</sub>H per macrocycle. Analysis by gel permeation chromatography and fluorescence spectroscopy revealed a cooperative self-assembly mechanism. Nanofibers obtained by touch-spinning the pyridinium-based nanotubes exhibit Young’s moduli of 1.48 GPa, which exceeds that of many synthetic polymers and biological filaments. These findings will enable the design of structurally diverse nanotubes from synthetically accessible macrocycles. </p>

scholarly journals Half-Dirac Semimetal and Quantum Anomalous Hall Effect in Kagome Cd2N3 Lattice

2020 ◽  
Author(s):  
Xinyang Li ◽  
Weixiao Ji ◽  
Peiji Wang ◽  
Chang-wen Zhang
Keyword(s):  
Hall Effect ◽  
Quantum State ◽  
Anomalous Hall Effect ◽  
Topological Phases ◽  
Dirac Semimetal ◽  
Quantum Anomalous Hall Effect ◽  
Dirac Materials ◽  
Low Dimensionality ◽  
Dirac Semimetals ◽  
Topological Phases Of Matter

Half-Dirac semimetals (HDSs), which possess 100% spin-polarizations for Dirac materials, are highly desirable for exploring various topological phases of matter, as low-dimensionality opens unprecedented opportunities for manipulating the quantum state...

Ionothermal effects on low-dimensionality uranyl compounds using task specific ionic liquids

CrystEngComm ◽  
2014 ◽  
Vol 16 (31) ◽  
pp. 7244-7250 ◽  
Author(s):  
P. A. Smith ◽  
P. C. Burns
Keyword(s):  
Ionic Liquids ◽  
Uranyl Compounds ◽  
Low Dimensionality

Task specific ionic liquids are employed in the development of two new low-dimensionality uranyl compounds.

scholarly journals Local Low Dimensionality of Atmospheric Dynamics

2001 ◽  
Vol 86 (26) ◽  
pp. 5878-5881 ◽  
Author(s):  
D. J. Patil ◽  
Brian R. Hunt ◽  
Eugenia Kalnay ◽  
James A. Yorke ◽  
Edward Ott
Keyword(s):  
Atmospheric Dynamics ◽  
Low Dimensionality

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

Phosphate tungsten bronze series: crystallographic and structural properties of low-dimensional conductors

2001 ◽  
Vol 57 (5) ◽  
pp. 603-632 ◽  
Author(s):  
P. Roussel ◽  
O. Pérez ◽  
Ph. Labbé
Keyword(s):  
Crystal Structures ◽  
Structural Properties ◽  
Tungsten Bronze ◽  
Structural Description ◽  
X Ray ◽  
X Ray Scattering ◽  
Modulated Structures ◽  
Low Dimensionality ◽  
Low Dimensional ◽  
Thickness Function

Phosphate tungsten bronzes have been shown to be conductors of low dimensionality. A review of the crystallographic and structural properties of this huge series of compounds is given here, corresponding to the present knowledge of the different X-ray studies and electron microscopy investigations. Three main families are described, monophosphate tungsten bronzes, Ax (PO2)4(WO3)2m , either with pentagonal tunnels (MPTBp) or with hexagonal tunnels (MPTBh), and diphosphate tungsten bronzes, Ax (P2O4)2(WO3)2m , mainly with hexagonal tunnels (DPTBh). The general aspect of these crystal structures may be described as a building of polyhedra sharing oxygen corners made of regular stacking of WO3-type slabs with a thickness function of m, joined by slices of tetrahedral PO4 phosphate or P2O7 diphosphate groups. The relations of the different slabs with respect to the basic perovskite structure are mentioned. The structural description is focused on the tilt phenomenon of the WO6 octahedra inside a slab of WO3-type. In this respect, a comparison with the different phases of the WO3 crystal structures is established. The various modes of tilting and the different possible connections between two adjacent WO3-type slabs involve a great variety of structures with different symmetries, as well as the existence of numerous twins in MPTBp's. Several phase transitions, with the appearance of diffuse scattering and modulation phenomena, were analysed by X-ray scattering measurements and through the temperature dependence of various physical properties for the MPTBp's. The role of the W displacements within the WO3-type slabs, in two modulated structures (m = 4 and m = 10), already solved, is discussed. Finally, the complexity of the structural aspects of DPTBh's is explained on the basis of the average structures which are the only ones solved.

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