scholarly journals Dynamic critical curve of a synthetic antiferromagnet

2009 ◽  
Vol 95 (22) ◽  
pp. 222513 ◽  
Author(s):  
Huy Pham ◽  
Dorin Cimpoesu ◽  
Andrei-Valentin Plamadă ◽  
Alexandru Stancu ◽  
Leonard Spinu
Keyword(s):  
Critical Curve ◽  
Synthetic Antiferromagnet

scholarly journals Measurement of the critical curve of a synthetic antiferromagnet

2008 ◽  
Vol 93 (2) ◽  
pp. 022506 ◽  
Author(s):  
Cosmin Radu ◽  
Dorin Cimpoesu ◽  
Alexandru Stancu ◽  
Leonard Spinu
Keyword(s):  
Critical Curve ◽  
Synthetic Antiferromagnet

scholarly journals Generalised model-independent characterisation of strong gravitational lenses

2018 ◽  
Vol 613 ◽  
pp. A6 ◽  
Author(s):  
J. Wagner ◽  
N. Tessore
Keyword(s):  
Quadrupole Moment ◽  
Galaxy Cluster ◽  
Transformation Matrix ◽  
Critical Curve ◽  
Reference Points ◽  
Quadrupole Moments ◽  
Multiple Images ◽  
Lower Accuracy ◽  
Cusp Points ◽  
Model Independent

We determine the transformation matrix that maps multiple images with identifiable resolved features onto one another and that is based on a Taylor-expanded lensing potential in the vicinity of a point on the critical curve within our model-independent lens characterisation approach. From the transformation matrix, the same information about the properties of the critical curve at fold and cusp points can be derived as we previously found when using the quadrupole moment of the individual images as observables. In addition, we read off the relative parities between the images, so that the parity of all images is determined when one is known. We compare all retrievable ratios of potential derivatives to the actual values and to those obtained by using the quadrupole moment as observable for two- and three-image configurations generated by a galaxy-cluster scale singular isothermal ellipse. We conclude that using the quadrupole moments as observables, the properties of the critical curve are retrieved to a higher accuracy at the cusp points and to a lower accuracy at the fold points; the ratios of second-order potential derivatives are retrieved to comparable accuracy. We also show that the approach using ratios of convergences and reduced shear components is equivalent to ours in the vicinity of the critical curve, but yields more accurate results and is more robust because it does not require a special coordinate system as the approach using potential derivatives does. The transformation matrix is determined by mapping manually assigned reference points in the multiple images onto one another. If the assignment of the reference points is subject to measurement uncertainties under the influence of noise, we find that the confidence intervals of the lens parameters can be as large as the values themselves when the uncertainties are larger than one pixel. In addition, observed multiple images with resolved features are more extended than unresolved ones, so that higher-order moments should be taken into account to improve the reconstruction precision and accuracy.

Langmuir turbulence as a critical phenomenon. Part 2. Application of the dynamical renormalization group method

1980 ◽  
Vol 24 (3) ◽  
pp. 421-443 ◽  
Author(s):  
Guy Pelletier
Keyword(s):  
Renormalization Group ◽  
Large Scale ◽  
Critical Phenomenon ◽  
Critical Curve ◽  
Group Method ◽  
Renormalization Group Method ◽  
Scaling Invariance ◽  
Correlation Spectrum ◽  
Scale Properties ◽  
Modulation Regime

In part 1 of this work, we have found a ‘critical curve’ which separates the unstable self-modulation regime from the stable one for a Gibbs ensemble of interacting modes. On this critical curve, the correlation length diverges and scaling invariance occurs; in particular, the Langmuir correlation spectrum is proportional to k-2. Simple laws have been derived for the neighbourhood of the critical curve. However these derivations are based on equilibrium statistical mechanics and the results are obtained with a Hartree approximation which has not been checked. So, in this second part, we elaborate a direct statistical theory of Zakharov's equations completed by excitation sources and dissipations. In spite of infra-red divergences and a large fluctuation level, large-scale properties are derived in the neighbourhood of the critical curve, by the renormalization group method. The laws obtained in part 1 are slightly modified; however, the same spectrum is obtained.

Dynamics on the Interaction between Vegetation Growth and Aeolian Dust Deposition

2011 ◽  
Vol 356-360 ◽  
pp. 2430-2433 ◽  
Author(s):  
Fei Fan Zhang ◽  
Hua Yong Zhang ◽  
Tou Sheng Huang
Keyword(s):  
Theoretical Basis ◽  
Equilibrium Distribution ◽  
Simulation Analysis ◽  
Critical Curve ◽  
The Other ◽  
Dust Deposition ◽  
Vegetation Growth ◽  
Aeolian Dust ◽  
Interior Equilibrium ◽  
The Stability

From the holistic perspective, a new dynamic model is proposed in this research to investigate the interaction between vegetation growth and aeolian dust deposition. Three cases of equilibrium distribution can be obtained and the stability of interior equilibriums is determined. When there is a stable interior equilibrium, a critical curve exists and separates the coexistent area where vegetation can survive in the environment of aeolian dust deposition, from the other area where vegetation is to be excluded. Simulation analysis further reveals the variation of the critical curve with the parameters and the anthropic influences. The critical curve and the coexistent equilibrium described by the model may be used as a theoretical basis to evaluate the feasibility of vegetation restoration in the environment of aeolian dust deposition.

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