SHORT-TIME CRITICAL BEHAVIOR OF THE GINZBURG–LANDAU MODEL WITH QUENCHED DISORDER

2001 ◽  
Vol 15 (02) ◽  
pp. 43-55 ◽  
Author(s):  
Z. B. LI ◽  
Y. CHEN ◽  
S. H. GUO
Keyword(s):  
Long Range ◽  
Scaling Laws ◽  
Quenched Disorder ◽  
Long Range Correlations ◽  
Time Dynamics ◽  
Time Regime ◽  
Renormalization Group Approach ◽  
Long Time ◽  
Logarithmic Decay ◽  
Short Time

The theoretic renormalization-group approach is applied to the study of short-time dynamics of the d-dimensional n-component spin systems with long-range interactions r-(d+σ) and quenched disorder which has long-range correlations r-(d-ρ). Asymptotic scaling laws are obtained in a frame of double expansions in ∊=2σ-d and ρ with ρ of the order ∊. The static exponents are obtained exactly to all the order. The initial slip exponents θ′ for the order parameter and θ for the response function, as well as the dynamic exponent z, are calculated upto the first order in ∊. In d=2σ, in contrast to the unique logarithmic decay in the long-time regime which does not depend on σ, ρ, n and the disorder, we find rich scaling structures including logarithmic and exponential-logarithmic scalings in the short-time regime. Non-universal critical scalings of Ising systems are also discussed for d=2σ.

SHORT-TIME DYNAMICS OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2003 ◽  
Vol 17 (23) ◽  
pp. 1227-1236 ◽  
Author(s):  
YUAN CHEN ◽  
ZHI-BING LI
Keyword(s):  
Long Range ◽  
High Temperature Phase ◽  
Vector Model ◽  
Temperature Phase ◽  
Range Interaction ◽  
Time Dynamics ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Short Time ◽  
N Vector

The short-time critical behavior of the random n-vector model with long-range interaction is studied by the theoretic renormalization-group approach. After a sudden quench to the critical temperature from the high temperature phase, the system is released to an evolution within model A dynamics. The initial slip exponents and the dynamic exponent are calculated to two-loop order.

THE AGING BEHAVIOR OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2007 ◽  
Vol 21 (23) ◽  
pp. 1555-1568 ◽  
Author(s):  
YUAN CHEN
Keyword(s):  
Long Range ◽  
Vector Model ◽  
Aging Behavior ◽  
Range Interaction ◽  
Fluctuation Dissipation ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Long Time ◽  
Short Time ◽  
N Vector

The aging behavior of the random n-vector model with long-range interaction decaying as r-(d+σ) (where d is the dimensionality), is investigated by the theoretic renormalization-group approach. The system initially disordered at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with model A dynamics. The aging properties are studied by the short-time expansions. The scaling behavior of two-time response and correlation functions are obtained in a frame of the expansion in ∊ = 2σ-d. In dimensions d < 2σ, the long-time limit of the critical fluctuation dissipation ratio X∞ is calculated up to one-loop order. The simulation of X∞ is discussed.

THE COMPLETE TREATMENT OF THE TIME EVOLUTION IN THE CASE OF A DISCRETIZED ATOM-FIELD INTERACTION MODEL

2001 ◽  
Vol 15 (21) ◽  
pp. 883-894
Author(s):  
J. SEKE ◽  
A. V. SOLDATOV ◽  
N. N. BOGOLUBOV
Keyword(s):  
State Energy ◽  
Interaction Model ◽  
Time Interval ◽  
Short Time Interval ◽  
Field Interaction ◽  
Markovian Dynamics ◽  
Complete Treatment ◽  
Time Regime ◽  
Long Time ◽  
Short Time

The dynamics of a discretized atom-field interaction model with a physically relevant form factor is analyzed. It is shown that after some short time interval only a small fraction of eigenvalues and eigenstates (belonging to the close vicinity of the excited atomic state energy E = ω0/2) contributes to the nondecay probability amplitudes in the long-time regime, whereas the contribution of all other eigenstates and eigenvalues is negligible. Nevertheless, to describe correctly the non-Markovian dynamics in the short-time regime the contribution of all eigenstates and eigenvalues must be taken into account.

Short Time Dynamics of an Irreversible Probabilistic Cellular Automaton

1998 ◽  
Vol 12 (21) ◽  
pp. 873-879 ◽  
Author(s):  
T. Tomé ◽  
J. R. Drugowich de Fel Icio
Keyword(s):  
Ising Model ◽  
Cellular Automaton ◽  
Early Time ◽  
Universality Class ◽  
Kinetic Ising Model ◽  
Time Dynamics ◽  
Probabilistic Cellular Automaton ◽  
Time Regime ◽  
The One ◽  
Short Time

We study the short-time dynamics of a three-state probabilistic cellular automaton. This automaton, termed TD model, possess "up-down" symmetry similar to Ising models, and displays continuous kinetic phase transitions belonging to the Ising model universality class. We perform Monte Carlo simulations on the early time regime of the two-dimensional TD model at criticality and obtain the dynamic exponent θ associated to this regime, and the exponents β/ν and z. Our results indicate that, although the model do not possess microscopic reversibility, it presents short-time universality which is consistent with the one of the kinetic Ising model.

Non-Equilibrium Critical Dynamics of Ferromagnets with Long Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 31-34
Author(s):  
Dmitry N. Kulikov ◽  
Pavel V. Prudnikov
Keyword(s):  
Critical Exponent ◽  
Long Range ◽  
Critical Behavior ◽  
Disordered Systems ◽  
Asymptotic Series ◽  
Three Dimensional ◽  
Time Regime ◽  
Short Time ◽  
Short Time Evolution ◽  
Non Equilibrium

The simultaneous effect of non-equilibrium initial states and correlation betweendefects of the structure on the evolution of anisotropic disordered systems at the critical pointwas analyzed. The field theory description of the non-equilibrium critical behavior of three-dimensional disordered systems with the long-range correlated defects was given and the dy-namical critical exponent of the short-time evolution was calculated in the two-loop approxima-tion without the use of the "-expansion. The values of the dynamical critical exponent obtainedby using various methods for summing asymptotic series were compared with the results ofthe computer simulation of the non-equilibrium critical behavior of the three-dimensional dis-ordered Ising model in the short-time regime.

SHORT TIME CORRELATIONS IN A TWO-DIMENSIONAL ISING MODEL WITH A LINE OF DEFECTS

2001 ◽  
Vol 15 (25) ◽  
pp. 1141-1146 ◽  
Author(s):  
T. TOMÉ ◽  
C. S. SIMÕES ◽  
J. R. DRUGOWICH DE FELÍCIO
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Ising Model ◽  
Early Time ◽  
Time Correlation ◽  
Two Dimensional ◽  
Time Dynamics ◽  
Time Correlations ◽  
Time Regime ◽  
Short Time

We study the short time dynamics of a two-dimensional Ising model with a line of defects. The dynamical critical exponent θ associated to the early time regime at the critical temperature was obtained by Monte Carlo simulations. The exponent θ was estimated by a method where the quantity of interest is the time correlation of the magnetization.

scholarly journals Free radially expanding liquid sheet in air: time- and space-resolved measurement of the thickness field

2015 ◽  
Vol 764 ◽  
pp. 428-444 ◽  
Author(s):  
C. Vernay ◽  
L. Ramos ◽  
C. Ligoure
Keyword(s):  
High Speed ◽  
Liquid Sheet ◽  
Radial Position ◽  
Maximum Diameter ◽  
Time And Space ◽  
Level Measurement ◽  
Time Regime ◽  
Long Time ◽  
Short Time ◽  
Thickness Field

AbstractThe collision of a liquid drop against a small target results in the formation of a thin liquid sheet that extends radially until it reaches a maximum diameter. The subsequent retraction is due to the air–liquid surface tension. We have used a time- and space-resolved technique to measure the thickness field of this class of liquid sheet, based on the grey-level measurement of the image of a dyed liquid sheet recorded using a high-speed camera. This method enables a precise measurement of the thickness in the range $10{-}450~{\rm\mu}\text{m}$, with a temporal resolution equal to that of the camera. We have measured the evolution with time since impact, $t$, and radial position, $r$, of the thickness, $h(r,t)$, for various drop volumes and impact velocities. Two asymptotic regimes for the expansion of the sheet are evidenced. The scalings of the thickness with $t$ and $r$ measured in the two regimes are those that were predicted by Rozhkov et al. (Proc. R. Soc. Lond. A, vol. 460, 2004, pp. 2681–2704) for the short-time regime and Villermaux and Bossa (J. Fluid Mech., vol. 668, 2011, pp. 412–435) for the long-time regime, but never experimentally measured before. Interestingly, our experimental data also provide evidence for the existence of a maximum of the film thickness $h_{max}(r)$ at a radial position $r_{h_{max}}(t)$ corresponding to the cross-over of these two asymptotic regimes. The maximum moves with a constant velocity of the order of the drop impact velocity, as expected theoretically. Thanks to our visualization technique, we also provide evidence of an azimuthal thickness modulation of the liquid sheets.

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