Linearization and symmetry breaking in nonlinear SU(3) x SU(3)

1972 ◽  
Vol 5 (12) ◽  
pp. 1689-1697 ◽  
Author(s):  
P H Dondi
Keyword(s):  
Symmetry Breaking

Symmetry breaking in convergent-beam diffraction

1989 ◽  
Vol 47 ◽  
pp. 480-481
Author(s):  
D.J. Eaglesham
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
Space Groups ◽  
Atomic Displacements ◽  
Small Probe ◽  
Phase Sensitive ◽  
Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

Centrosome Aurora A gradient ensures single polarity axis in C. elegans embryos

2020 ◽  
Vol 48 (3) ◽  
pp. 1243-1253 ◽  
Author(s):  
Sukriti Kapoor ◽  
Sachin Kotak
Keyword(s):  
Symmetry Breaking ◽  
Cell Fate ◽  
Cell Cortex ◽  
Axis Formation ◽  
Aurora A Kinase ◽  
Aurora A ◽  
C Elegans ◽  
Cell Embryo ◽  
Polarity Establishment

Cellular asymmetries are vital for generating cell fate diversity during development and in stem cells. In the newly fertilized Caenorhabditis elegans embryo, centrosomes are responsible for polarity establishment, i.e. anterior–posterior body axis formation. The signal for polarity originates from the centrosomes and is transmitted to the cell cortex, where it disassembles the actomyosin network. This event leads to symmetry breaking and the establishment of distinct domains of evolutionarily conserved PAR proteins. However, the identity of an essential component that localizes to the centrosomes and promotes symmetry breaking was unknown. Recent work has uncovered that the loss of Aurora A kinase (AIR-1 in C. elegans and hereafter referred to as Aurora A) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin flow dynamics results in the occurrence of two polarity axes. Notably, the role of Aurora A in ensuring a single polarity axis is independent of its well-established function in centrosome maturation. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of Rho-dependent contractility. In this mini-review, we will discuss the unconventional role of Aurora A kinase in polarity establishment in C. elegans embryos and propose a refined model of centrosome-dependent symmetry breaking.

A Symmetry-Breaking Theory of False Pop Out

2011 ◽  
Author(s):  
Kimberley D. Orsten ◽  
Mary C. Portillo ◽  
James R. Pomerantz
Keyword(s):  
Symmetry Breaking

Symmetry Breaking and the Turn-On Fluorescence of Small, Highly Strained Carbon Nanohoops

2019 ◽  
Author(s):  
Terri Lovell ◽  
Curtis Colwell ◽  
Lev N. Zakharov ◽  
Ramesh Jasti
Keyword(s):  
Symmetry Breaking ◽  
Theoretical Work ◽  
P Systems ◽  
Quantum Yields ◽  
Size Dependent ◽  
New Class ◽  
Carbon Carbon Bond ◽  
Conjugated Macrocycles ◽  
Structural Manipulation ◽  
Highly Strained

<p>[<i>n</i>]Cycloparaphenylenes, or “carbon nanohoops,” are unique conjugated macrocycles with radially oriented p-systems similar to those in carbon nanotubes. The centrosymmetric nature and conformational rigidity of these molecules lead to unusual size-dependent photophysical characteristics. To investigate these effects further and expand the family of possible structures, a new class of related carbon nanohoops with broken symmetry is disclosed. In these structures, referred to as <i>meta</i>[<i>n</i>]cycloparaphenylenes, a single carbon-carbon bond is shifted by one position in order to break the centrosymmetric nature of the parent [<i>n</i>]cycloparaphenylenes. Advantageously, the symmetry breaking leads to bright emission in the smaller nanohoops, which are typically non-fluorescent due to optical selection rules. Moreover, this simple structural manipulation retains one of the most unique features of the nanohoop structures-size dependent emissive properties with relatively large extinction coefficents and quantum yields. Inspired by earlier theoretical work by Tretiak and co-workers, this joint synthetic, photophysical, and theoretical study provides further design principles to manipulate the optical properties of this growing class of molecules with radially oriented p-systems.</p>

Symmetry Breaking and the Turn-On Fluorescence of Small, Highly Strained Carbon Nanohoops

2019 ◽  
Author(s):  
Terri Lovell ◽  
Curtis Colwell ◽  
Lev N. Zakharov ◽  
Ramesh Jasti
Keyword(s):  
Symmetry Breaking ◽  
Theoretical Work ◽  
P Systems ◽  
Quantum Yields ◽  
Size Dependent ◽  
New Class ◽  
Carbon Carbon Bond ◽  
Conjugated Macrocycles ◽  
Structural Manipulation ◽  
Highly Strained

<p>[<i>n</i>]Cycloparaphenylenes, or “carbon nanohoops,” are unique conjugated macrocycles with radially oriented p-systems similar to those in carbon nanotubes. The centrosymmetric nature and conformational rigidity of these molecules lead to unusual size-dependent photophysical characteristics. To investigate these effects further and expand the family of possible structures, a new class of related carbon nanohoops with broken symmetry is disclosed. In these structures, referred to as <i>meta</i>[<i>n</i>]cycloparaphenylenes, a single carbon-carbon bond is shifted by one position in order to break the centrosymmetric nature of the parent [<i>n</i>]cycloparaphenylenes. Advantageously, the symmetry breaking leads to bright emission in the smaller nanohoops, which are typically non-fluorescent due to optical selection rules. Moreover, this simple structural manipulation retains one of the most unique features of the nanohoop structures-size dependent emissive properties with relatively large extinction coefficents and quantum yields. Inspired by earlier theoretical work by Tretiak and co-workers, this joint synthetic, photophysical, and theoretical study provides further design principles to manipulate the optical properties of this growing class of molecules with radially oriented p-systems.</p>

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