Geometric analysis of the effect of symmetry breaking perturbations on an 𝑂(2) invariant homoclinic cycle

Symmetry Breaking of a Time-2D Space Fractional Wave Equation in a Complex Domain

Axioms ◽

10.3390/axioms10030141 ◽

2021 ◽

Vol 10 (3) ◽

pp. 141

Author(s):

Rabha W. Ibrahim ◽

Dumitru Baleanu

Keyword(s):

Wave Equation ◽

Symmetry Breaking ◽

Symmetric Operator ◽

Geometric Analysis ◽

Analytic Solutions ◽

Complex Domain ◽

Open Unit ◽

Function Type ◽

Fractional Wave Equation ◽

2D Space

(1) Background: symmetry breaking (self-organized transformation of symmetric stats) is a global phenomenon that arises in an extensive diversity of essentially symmetric physical structures. We investigate the symmetry breaking of time-2D space fractional wave equation in a complex domain; (2) Methods: a fractional differential operator is used together with a symmetric operator to define a new fractional symmetric operator. Then by applying the new operator, we formulate a generalized time-2D space fractional wave equation. We shall utilize the two concepts: subordination and majorization to present our results; (3) Results: we obtain different formulas of analytic solutions using the geometric analysis. The solution suggests univalent (1-1) in the open unit disk. Moreover, under certain conditions, it was starlike and dominated by a chaotic function type sine. In addition, the authors formulated a fractional time wave equation by using the Atangana–Baleanu fractional operators in terms of the Riemann–Liouville and Caputo derivatives.

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Geometric Analysis of Bifurcation and Symmetry Breaking in a Gross–Pitaevskii Equation

Journal of Statistical Physics ◽

10.1023/b:joss.0000037238.94034.75 ◽

2004 ◽

Vol 116 (1-4) ◽

pp. 881-905 ◽

Cited By ~ 64

Author(s):

R. K. Jackson ◽

M. I. Weinstein

Keyword(s):

Symmetry Breaking ◽

Geometric Analysis ◽

Pitaevskii Equation

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Forced reflectional symmetry breaking of an O(2)-symmetric homoclinic cycle

Nonlinearity ◽

10.1088/0951-7715/6/5/003 ◽

1993 ◽

Vol 6 (5) ◽

pp. 723-731 ◽

Cited By ~ 23

Author(s):

P Chossat

Keyword(s):

Symmetry Breaking ◽

Homoclinic Cycle

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Liquid crystalline ordering of paired helical filaments in neurofibrillary tangles of Alzheimer's disease

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143365 ◽

1986 ◽

Vol 44 ◽

pp. 348-349

Author(s):

D.F. Clapin ◽

V.J.A. Montpetit

Keyword(s):

Alzheimer’S Disease ◽

Alzheimer's Disease ◽

Neurofibrillary Tangles ◽

Liquid Crystalline ◽

Amyloid Fibrils ◽

Geometric Analysis ◽

Paired Helical Filaments ◽

Microscopic Level ◽

Light Microscopic Level ◽

Regular Spacing

Alzheimer's disease is characterized by the accumulation of abnormal filamentous proteins. The most important of these are amyloid fibrils and paired helical filaments (PHF). PHF are located intraneuronally forming bundles called neurofibrillary tangles. The designation of these structures as "tangles" is appropriate at the light microscopic level. However, localized domains within individual tangles appear to demonstrate a regular spacing which may indicate a liquid crystalline phase. The purpose of this paper is to present a statistical geometric analysis of PHF packing.

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Symmetry breaking in convergent-beam diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154378 ◽

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

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

Biochemical Society Transactions ◽

10.1042/bst20200298 ◽

2020 ◽

Vol 48 (3) ◽

pp. 1243-1253 ◽

Cited By ~ 1

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.

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