Symmetry coupling coefficients for point groups and the importance of Racah's Lemma for the standardization of phase

1973 ◽  
Vol 32 (1) ◽  
pp. 27-40 ◽  
Author(s):  
Edgar K�nig ◽  
Stefan Kremer
Keyword(s):  
Coupling Coefficients ◽  
Point Groups

Symmetric Form of Coupling Coefficients for Single and Double Point Groups and the Application of Time-Reversal Symmetry

1974 ◽  
Vol 29 (8) ◽  
pp. 1179-1187 ◽  
Author(s):  
E. König ◽  
S. Kremer
Keyword(s):  
Time Reversal ◽  
Point Group ◽  
Time Reversal Symmetry ◽  
Coupling Coefficients ◽  
Covering Group ◽  
Group I ◽  
Symmetry Properties ◽  
Point Groups ◽  
Expansion Coefficients ◽  
Definition Of

Symmetrized coupling coefficients, the 3-Γ symbols, are investigated for an arbitrary molecular point group G ⊂ SO (3) or d G ⊂ SU(2). The definition employs the 3-j symbols of the full covering group SO (3) [or SU(2)] and the expansion coefficients of the basis functions. 〈j m | j Γ γ a〉 . Considerable simplification is achieved by taking into account time-reversal symmetry in conjunction with the lemma of Racah. It is found that the 3-Γ symbols have the same symmetry properties as the 3-j symbols of SO (3). The definition of 6-Γ symbols is likewise introduced. The treatment covers non-simply reducible groups and complex representations as well. For illustration, 3-Γ symbols of the point group I are calculated and presented.

scholarly journals Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination

2021 ◽  
Author(s):  
J. F. Cass ◽  
S. J. Hogan
Keyword(s):  
Motor Coordination ◽  
Nonlinear Damping ◽  
Numerical Continuation ◽  
Arbitrary Parameter ◽  
Relevant Parameter ◽  
Coupling Coefficients ◽  
Dimensionless Parameters ◽  
Biologically Relevant ◽  
Mechanical Analogue ◽  
Partner Interaction

AbstractThe widely cited Haken–Kelso–Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.

Darstellung, Schwingungsspektren und Normalkoordinatenanalyse von Chloro-Bromo-Rhodaten(III) / Preparation, Vibration Spectra and Normal Coordinate Analysis of Chloro-Bromo-Rhodates(III)

1989 ◽  
Vol 44 (10) ◽  
pp. 1221-1227 ◽  
Author(s):  
W. Preetz ◽  
W. Kuhr
Keyword(s):  
Exchange Chromatography ◽  
Trans Isomers ◽  
Normal Coordinate ◽  
Valence Force ◽  
Trans Influence ◽  
Diethylaminoethyl Cellulose ◽  
Point Groups ◽  
First Time ◽  
Ir And Raman ◽  
Good Agreement

The mixed chloro-bromo-rhodates(III) [RhClnBr6-n]3-, n = 1-5, have been separated for the first time by ion exchange chromatography on diethylaminoethyl-cellulose. Due to the stronger trans-effect of Br, as compared with Cl, on treatment of [RhBr6]3- with conc. HCl nearly pure cis/fac-isomers for n = 2, 3, 4 are formed. The reaction of [RhCl6]3- with conc. HBr yields mixtures of the cis/trans-isomers for n = 2, 4, which cannot be separated, but mer-[RhCl3Br3]3 is formed stereospecifically. The IR and Raman spectra of all isolated mixed ligand complexes are completely assigned according to point groups Oh, D3d, C4v, C3v and C2v, supported by normal coordinate analyses based on a general valence force field. The good agreement of calculated and observed frequencies confirms the assignments. Due to the stronger trans-influence of Br as compared to Cl, in all asymmetric Cl—Rh—Br axes the Rh—Br bonds are strengthened and the Rh—Cl bonds are weakened, indicated by valence force constants for Rh—Br approximately 14% higher, for Rh—Cl 10% lower, as compared with the values calculated for symmetric Br—Rh—Br and Cl—Rh—Cl axes, respectively.

scholarly journals Seasonal variability of SST fronts and winds on the southeastern continental shelf of Brazil

2019 ◽  
Vol 69 (11-12) ◽  
pp. 1387-1399 ◽  
Author(s):  
Huan-Huan Chen ◽  
Yiquan Qi ◽  
Yuntao Wang ◽  
Fei Chai
Keyword(s):  
Continental Shelf ◽  
Wind Stress ◽  
Seasonal Variability ◽  
Detection Algorithm ◽  
Coupling Coefficients ◽  
Seafloor Topography ◽  
Wind Stress Curl ◽  
Large Coupling ◽  
The Impact ◽  
Sst Fronts

Abstract Fourteen years (September 2002 to August 2016) of high-resolution satellite observations of sea surface temperature (SST) data are used to describe the frontal pattern and frontogenesis on the southeastern continental shelf of Brazil. The daily SST fronts are obtained using an edge-detection algorithm, and the monthly frontal probability (FP) is subsequently calculated. High SST FPs are mainly distributed along the coast and decrease with distance from the coastline. The results from empirical orthogonal function (EOF) decompositions reveal strong seasonal variability of the coastal SST FP with maximum (minimum) in the astral summer (winter). Wind plays an important role in driving the frontal activities, and high FPs are accompanied by strong alongshore wind stress and wind stress curl. This is particularly true during the summer, when the total transport induced by the alongshore component of upwelling-favorable winds and the wind stress curl reaches the annual maximum. The fronts are influenced by multiple factors other than wind forcing, such as the orientation of the coastline, the seafloor topography, and the meandering of the Brazil Current. As a result, there is a slight difference between the seasonality of the SST fronts and the wind, and their relationship was varying with spatial locations. The impact of the air-sea interaction is further investigated in the frontal zone, and large coupling coefficients are found between the crosswind (downwind) SST gradients and the wind stress curl (divergence). The analysis of the SST fronts and wind leads to a better understanding of the dynamics and frontogenesis off the southeastern continental shelf of Brazil, and the results can be used to further understand the air-sea coupling process at regional level.

Sol-Gel Derived PZT Thick Films with Nano-Sized Microstructure

2002 ◽  
Vol 748 ◽  
Author(s):  
C. L. Zhao ◽  
Z. H. Wang ◽  
W. Zhu ◽  
O. K. Tan ◽  
H. H. Hng
Keyword(s):  
Lead Zirconate Titanate ◽  
Electromechanical Coupling ◽  
Thick Films ◽  
Sol Gel ◽  
Essential Element ◽  
Processing Parameters ◽  
Lead Zirconate ◽  
Piezoelectric Response ◽  
Coupling Coefficients ◽  
Pzt Films

ABSTRACTLead zirconate titanate (PZT) films are promising for acoustic micro-devices applications because of their extremely high electromechanical coupling coefficients and excellent piezoelectric response. Thicker PZT films are crucial for these acoustic applications. A hybrid sol-gel technology has been developed as a new approach to realize simple and cost-effective fabrication of high quality PZT thick films. In this paper, PZT53/47 thick films with a thickness of 5–50 μm are successfully deposited on Pt-coated silicon wafer by using the hybrid sol-gel technology. The obtained PZT thick films are dense, crack-free, and have a nano-sized microstructure. The processing parameters of this technology have been evaluated. The microstructure of the film has been observed using field-emission scanning electron microscopy and the crystallization process has been monitored by the X-ray diffraction. The thick films thus made are good candidates for fabrication of piezoelectric diaphragm which will be an essential element of microspeaker and microphone arrays.

scholarly journals OnSU 3 vector coupling coefficients

1966 ◽  
Vol 41 (4) ◽  
pp. 639-639
Author(s):  
G. Ponzano
Keyword(s):  
Coupling Coefficients ◽  
Vector Coupling
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