NON-TRIVIAL BEHAVIOR OF THE LINEAR RESPONSE FUNCTION IN PHASE ORDERING KINETICS

Drawing from exact, approximate and numerical results an overview of the properties of the out of equilibrium response function in phase ordering kinetics is presented. Focusing on the zero field cooled magnetization, emphasis is on those features of this quantity which display non trivial behavior when relaxation proceeds by coarsening. Prominent among these is the dimensionality dependence of the scaling exponent aχ which leads to failure of the connection between static and dynamic properties at the lower dimensionality dL, where aχ=0. We also analyse the mean spherical model as an explicit example of a stochastic unstable system, for which the connection between statics and dynamics fails at all dimensionalities.

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Scaling of the linear response function from zero-field-cooled and thermoremanent magnetization in phase-ordering kinetics

Physical Review E ◽

10.1103/physreve.68.046131 ◽

2003 ◽

Vol 68 (4) ◽

Cited By ~ 42

Author(s):

Federico Corberi ◽

Eugenio Lippiello ◽

Marco Zannetti

Keyword(s):

Response Function ◽

Linear Response ◽

Zero Field ◽

Thermoremanent Magnetization ◽

Ordering Kinetics ◽

Linear Response Function ◽

Phase Ordering

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Multifaceted phase ordering kinetics of an antiferromagnetic spin-1 condensate

Scientific Reports ◽

10.1038/s41598-021-88454-7 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Joanna Pietraszewicz ◽

Aleksandra Seweryn ◽

Emilia Witkowska

Keyword(s):

Scaling Laws ◽

Study Phase ◽

One Dimensional ◽

Phase Domain ◽

Ordering Kinetics ◽

Domain Coarsening ◽

Long Time ◽

Phase Ordering ◽

Kinetics Of ◽

Antiferromagnetic Spin

AbstractWe study phase domain coarsening in the long time limit after a quench of magnetic field in a quasi one-dimensional spin-1 antiferromagnetic condensate. We observe that the growth of correlation length obeys scaling laws predicted by the two different models of phase ordering kinetics, namely the binary mixture and vector field. We derive regimes of clear realization for both of them. We demonstrate appearance of atypical scaling laws, which emerge in intermediate regions.

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Response Prediction and Dynamic Substructuring for Coupled Structures in the Frequency Domain

Journal of Mechanics ◽

10.1017/jmech.2020.49 ◽

2020 ◽

Vol 36 (6) ◽

pp. 867-879

Author(s):

X. H. Liao ◽

W. F. Wu ◽

H. D. Meng ◽

J. B. Zhao

Keyword(s):

Frequency Response ◽

Response Function ◽

Frequency Response Function ◽

Dynamic Properties ◽

Main Idea ◽

Prediction Method ◽

Response Prediction ◽

Synthesis Methods ◽

Dynamic Substructuring ◽

Coupled Structures

ABSTRACTTo evaluate the dynamic properties of a coupled structure based on the dynamic properties of its substructures, this paper investigates the dynamic substructuring issue from the perspective of response prediction. The main idea is that the connecting forces at the interface of substructures can be expressed by the unknown coupled structural responses, and the responses can be solved rather easily. Not only rigidly coupled structures but also resiliently coupled structures are investigated. In order to further comprehend and visualize the nature of coupling problems, the Neumann series expansion for a matrix describing the relation between the coupled and uncoupled substructures is also introduced in this paper. Compared with existing response prediction methods, the proposed method does not have to measure any forces, which makes it easier to apply than the others. Clearly, the frequency response function matrix of coupled structures can be derived directly based on the response prediction method. Compared with existing frequency response function synthesis methods, it is more straightforward and comprehensible. Through demonstration of two examples, it is concluded that the proposed method can deal with structural coupling problems very well.

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On anomalous diffusion and the out of equilibrium response function in one-dimensional models

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/2011/01/l01002 ◽

2011 ◽

Vol 2011 (01) ◽

pp. L01002 ◽

Cited By ~ 20

Author(s):

D Villamaina ◽

A Sarracino ◽

G Gradenigo ◽

A Puglisi ◽

A Vulpiani

Keyword(s):

Response Function ◽

Anomalous Diffusion ◽

One Dimensional ◽

Equilibrium Response ◽

Dimensional Models

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Photophysics of the lowest triplet state in 2-benzoylpyridine crystals. II. Optically detected e. p. r. in zero and high magnetic fields

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1979.0159 ◽

1979 ◽

Vol 369 (1737) ◽

pp. 187-206 ◽

Cited By ~ 4

Keyword(s):

Triplet State ◽

Rate Constants ◽

Radiative Decay ◽

Dynamic Properties ◽

Deep Trap ◽

Lattice Relaxation ◽

Spin Lattice Relaxation ◽

Zero Field ◽

Spin Lattice ◽

Optically Detected

Optically detected zero-field resonance has been used to characterize the intrinsic and deep trap 3 nπ * states in single crystals of 2-benzoylpyridine at 4.2 K. The dynamic properties of these states were studied by means of time-resolved modulated phosphorescence (t. r. m. p.) and estimates for the rate constants for depopulation and spin-lattice relaxation of the magnetic sub-levels obtained by computer simulation. For all species, depopulation from ז z dominates, having rates of order 100 s -1 , but the ז x and ז y sub-states have substantial radiative activity. The orientations of the fine-structure tensors of the magnetic species were determined from high-field e. p. r. spectra. Assuming that z is parallel to C = O, excitation causes the C = O direction to change by 8 ± 2° for the intrinsic species and by an in-significant amount for the deep trap. These spectra also demonstrated that the intrinsic triplet state is mobile. This species is believed to be a polaron with slow intersite hopping rate. A maximum energy transfer rate of 10 4 -10 5 s -1 was found for transfer between translationally inequivalent sites symmetry-related by twofold rotation about the crystal b -axis. Rate estimates for transfer to the other two translationally inequivalent sites established the two dimensional nature of the polaron. The sign and shape of the zero-field resonances for the intrinsic species were found to depend on whether excitation was through S 1 or T 1 . From the parameters required to simulate the corresponding t. r. m. p. signals it is inferred that the changes are largely due to differences in the rate constants for non-radiative decay. The deep trap was shown to have an orientation and magnetic properties similar to those of the intrinsic species, and is believed to be a physical defect. It has radiative activity from the ז x sub-level which is significantly less than for the intrinsic species. Spin-lattice relaxation is fast for the mobile intrinsic species ( ca . 10 4 s -1 ) compared with the deep trap rate ( ca . 50 4 s -1 ). For the intrinsic species a field dependence for spin-lattice relaxation is apparent.

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