BREAKING OF LINEAR SYMMETRIES AND MICHEL'S THEORY: GRASSMANN MANIFOLDS, AND INVARIANT SUBSPACES

2008 ◽  
Vol 23 (03n04) ◽  
pp. 547-565
Author(s):  
GIUSEPPE GAETA
Keyword(s):  
Symmetry Breaking ◽  
Group Action ◽  
Invariant Manifolds ◽  
Invariant Subspaces ◽  
Geometric Approach ◽  
Symmetry Type ◽  
Original Formulation ◽  
Grassmann Manifolds ◽  
Nonlinear Flows

Michel's theory of symmetry breaking in its original formulation has some difficulty in dealing with problems with a linear symmetry, due to the degeneration in the symmetry type implied by the linearity of group action. Here we propose a fully geometric, approach to the problem, making use of Grassmann manifolds. In this way Michel theory can also be applied to the determination of dynamically invariant manifolds for equivariant nonlinear flows.

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

SINGULAR SWITCHED LINEAR SYSTEMS: SOME GEOMETRIC ASPECTS

2012 ◽  
Vol 26 (25) ◽  
pp. 1246006
Author(s):  
H. DIEZ-MACHÍO ◽  
J. CLOTET ◽  
M. I. GARCÍA-PLANAS ◽  
M. D. MAGRET ◽  
M. E. MONTORO
Keyword(s):  
Linear Systems ◽  
Group Action ◽  
Lie Group ◽  
Equivalence Relation ◽  
Geometric Approach ◽  
Differentiable Manifold ◽  
Equivalence Classes ◽  
Switched Linear Systems ◽  
Lie Group Action

We present a geometric approach to the study of singular switched linear systems, defining a Lie group action on the differentiable manifold consisting of the matrices defining their subsystems with orbits coinciding with equivalence classes under an equivalence relation which preserves reachability and derive miniversal (orthogonal) deformations of the system. We relate this with some new results on reachability of such systems.

scholarly journals The determination of point groups from imprecise molecular geometries

2021 ◽  
Author(s):  
Peter J. Knowles
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
Simple Function ◽  
Coordinate Frame ◽  
New Approach ◽  
Measure Of Symmetry ◽  
Point Groups

AbstractWe present a new approach for the assignment of a point group to a molecule when the structure conforms only approximately to the symmetry. It proceeds by choosing a coordinate frame that minimises a measure of symmetry breaking that is computed efficiently as a simple function of the molecular coordinates and point group specification.

Determination of Maximal Singularity-Free Workspace of Parallel Mechanisms Using Constructive Geometric Approach

2013 ◽  
pp. 307-314
Author(s):  
Mohammad Hadi Farzaneh Kaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Behnam Mashhadi Gholamali
Keyword(s):  
Geometric Approach ◽  
Parallel Mechanisms ◽  
Maximal Singularity

New Investigation on the Geometry of the Contact in Gear Generation

2003 ◽  
Author(s):  
Marco Gabiccini ◽  
Massimo Guiggiani ◽  
Francesca Di Puccio
Keyword(s):  
Reference Frame ◽  
Relative Position ◽  
Geometric Approach ◽  
Gear Ratio ◽  
Reference Systems ◽  
Geometric Properties ◽  
Envelope Surface ◽  
Enveloping Surface ◽  
Contact Matrix

Based on a recently developed geometric approach to the theory of gearing that does not make use of any reference systems [1], this paper presents some useful relations between the geometric properties of the enveloping surface and those of its envelope. Treating vectors as such, that is without expressing their components in any reference systems, it is possible to obtain compact expressions for the coefficients of the first and second fundamental forms of the envelope surface. These coefficients show to be central in the determination of the contact matrix between mating surfaces. Moreover, since this approach is coordinate free, it is valid regardless of the reference frame actually employed to perform calculations and allows a, hopefully, clearer understanding of the roles played by the intrinsic geometric properties of the enveloping surface, the relative position of the gear axes and the gear ratio.

RADIATIVE EFFECTS AND ELECTROWEAK SYMMETRY BREAKING IN A SUPERSYMMETRIC PREON MODEL

1999 ◽  
Vol 14 (09) ◽  
pp. 1389-1427
Author(s):  
JONGBAE KIM
Keyword(s):  
Symmetry Breaking ◽  
Dynamical Symmetry ◽  
Electroweak Symmetry Breaking ◽  
Effective Theory ◽  
Supersymmetric Particle ◽  
Electroweak Symmetry ◽  
Radiative Effects ◽  
Yukawa Couplings ◽  
Lepton Universality

We construct the low energy effective theory of composite quarks, leptons, and Higgs bosons for a supersymmetric preon model and study the effects of renormalization-group based radiative corrections. The study on the evolution of scalar masses for avoiding color and charge breakings leads us to conclude that Yukawa couplings are bounded from above. The implementation of electroweak symmetry breaking requires that only the purely dynamical symmetry breaking should be needed for the model, but the combined scheme of dynamical and radiative symmetry breaking as well as the purely radiative symmetry breaking scheme be disfavored. Our analysis of [Formula: see text] including radiative effects shows that, should a discrepancy be found between the observed and the theoretical value of [Formula: see text] after experimental determination of supersymmetric particle masses, it would imply that the complete quark–lepton universality in the supersymmetric preon model does not hold either for the Yukawa couplings, or for the condensates, or for both.

Structural Determination of the Symmetry-Breaking Parameter intrans-(CH)x

1982 ◽  
Vol 48 (2) ◽  
pp. 100-104 ◽  
Author(s):  
C. R. Fincher ◽  
C. -E. Chen ◽  
A. J. Heeger ◽  
A. G. MacDiarmid ◽  
J. B. Hastings
Keyword(s):  
Symmetry Breaking ◽  
Structural Determination ◽  
Breaking Parameter

Determination of Grassmann Manifolds Which are Boundaries

1991 ◽  
Vol 34 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Parameswaran Sankaran
Keyword(s):  
Grassmann Manifold ◽  
Vector Subspace ◽  
Complex Numbers ◽  
Sufficient Condition ◽  
Grassmann Manifolds

AbstractLetFGn,kdenote the Grassmann manifold of allk-dimensional (left)F-vector subspace ofFnfor F = ℝ, the reals,C, the complex numbers, orHthe quaternions. The problem of determining which of the Grassmannians bound was addressed by the author in [4]. Partial results were obtained in [4] for the caseF= ℝ, including a sufficient condition, due to A. Dold, on n and k for ℝGn,kto bound. Here, we show that Dold's condition is also necessary, and obtain a new proof of sufficiency using the methods of this paper, which cover the complex and quaternionic cases as well.

Superfluid 4He

Quantum 20/20 ◽  
2019 ◽  
pp. 243-260
Author(s):  
Ian R. Kenyon
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Critical Velocity ◽  
Superfluid Transition ◽  
Superfluid 4He ◽  
Long Range Order ◽  
Second Sound ◽  
Superfluid Fraction ◽  
Fraction Versus

The superfluid transition of 4He at 2.17K to He-II and the inference of an underlying condensate are introduced. The fountain effect is interpreted. Andronikashvili’s experiment and the determination of superfluid fraction versus temperature are discussed. Sound and second sound are described. Relationships between the condensate and superfluid fractions, and to off diagonal long-range order (ODLRO) are deduced. The revelation of topological quantization of circulation by Vinen’s experiment is recounted. Spontaneous symmetry breaking by the condensate’s phase coherence is explained. Excitations and their dispersion relations described with Landau’s interpretation, including the explanation of the critical velocity of superflow. Vortices, their interpretation in terms of quantized circulation, and their visualization are described.

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