Dynamical scaling laws and time dependent Landau-Ginzburg equation

1969 ◽  
Vol 29 (8) ◽  
pp. 458-459 ◽  
Author(s):  
C. Di Castro ◽  
F. Ferro-Luzzi ◽  
J.A. Tayson
Keyword(s):  
Scaling Laws ◽  
Time Dependent ◽  
Dynamical Scaling

Critical dynamics and renormalization group (RG)

2021 ◽  
pp. 875-898
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Renormalization Group ◽  
Time Evolution ◽  
Langevin Equation ◽  
Scaling Laws ◽  
Transport Coefficients ◽  
Time Dependent ◽  
Critical Systems ◽  
Static Properties ◽  
Critical Domain ◽  
Dynamical Scaling

Time evolution, near a phase transition in the critical domain of critical systems not far from equilibrium, using a Langevin-type evolution is studied. Typical quantities of interest are relaxation rates towards equilibrium, time-dependent correlation functions and transport coefficients. The main motivation for such a study is that, in systems in which the dynamics is local (on short time-scales, a modification of a dynamic variable has an influence only locally in space) when the correlation length becomes large, a large time-scale emerges, which characterizes the rate of time evolution. This phenomenon called critical slowing down leads to universal behaviour and scaling laws for time-dependent quantities. In contrast with the situation in static critical phenomena, there is no clean and systematic derivation of the dynamical equations governing the time evolution in the critical domain, because often the time evolution is influenced by conservation laws involving the order parameter, or other variables like energy, momentum, angular momentum, currents and so on. Indeed, the equilibrium distribution does not determine the driving force in the Langevin equation, but only the dissipative couplings are generated by the derivative of the equilibrium Hamiltonian, and directly related to the static properties. The purely dissipative Langevin equation specifically discussed, corresponding to static models like the f4 field theory and two-dimensional models. Renormalization group (RG) equations are derived, and dynamical scaling relations established.

scholarly journals Time-dependent energetic proton acceleration and scaling laws in ultraintense laser-pulse interactions with thin foils

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
Yongsheng Huang ◽  
Yuanjie Bi ◽  
Yijin Shi ◽  
Naiyan Wang ◽  
Xiuzhang Tang ◽  
...  
Keyword(s):  
Laser Pulse ◽  
Scaling Laws ◽  
Time Dependent ◽  
Proton Acceleration ◽  
Energetic Proton ◽  
Thin Foils

Phase Separation Dynamics of Blends of Telechelic Epoxy Terminated Polybutadiene and Maltene

1995 ◽  
Vol 68 (1) ◽  
pp. 158-166 ◽  
Author(s):  
Tsunehiro Yamamoto ◽  
Thein Kyu
Keyword(s):  
Phase Separation ◽  
Scaling Laws ◽  
Phase Region ◽  
Solution Temperature ◽  
Two Phase ◽  
Time Resolved ◽  
Thermally Induced ◽  
Dynamical Scaling ◽  
Upper Critical Solution Temperature ◽  
Deep Temperature

Abstract Thermally induced phase separation in a mixture of telechelic epoxy terminated polybutadiene (ETPB) and maltene has been studied by means of time-resolved light scattering and optical microscopy. Maltene, consisting of various hydrocarbon derivatives, was extracted from asphalt with n-heptane and isolated by centrifugation. The cloud point studies of the ETPB/maltene mixture showed an upper critical solution temperature (UCST) which is thermally reversible. Several deep temperature quench experiments were conducted at an off-critical composition (27/73 ETPB/maltene) from a single phase (80°C) to a two-phase region (27, 29, 31 and 33 °C). The time-evolution of the structure factor for the late stage of spinodal decomposition (SD) was analyzed in the framework of nonlinear and dynamical scaling laws. The reverse quench experiments were also undertaken to elucidate the phase dissolution process.

Scaling laws for time-dependent stagnant lid convection in a spherical shell

2005 ◽  
Vol 149 (3-4) ◽  
pp. 361-370 ◽  
Author(s):  
C.C. Reese ◽  
V.S. Solomatov ◽  
J.R. Baumgardner
Keyword(s):  
Spherical Shell ◽  
Scaling Laws ◽  
Time Dependent

TIME, SPACE AND MAGNITUDE CORRELATIONS IN EARTHQUAKE OCCURRENCE

2009 ◽  
Vol 23 (28n29) ◽  
pp. 5583-5596 ◽  
Author(s):  
E. LIPPIELLO ◽  
L. DE ARCANGELIS ◽  
C. GODANO
Keyword(s):  
Earthquake Magnitude ◽  
Time Dependent ◽  
Scaling Relation ◽  
Earthquake Occurrence ◽  
Time And Space ◽  
Dynamical Scaling ◽  
Time Space ◽  
Temporal And Spatial ◽  
Magnitude Difference ◽  
Space Distance

Clustering in time and space is a widely accepted feature of seismicity. Much more questionable is the existence of magnitude correlations. The standard approach to time-dependent seismic hazard generally assumes that magnitudes are independent and therefore, in principle, the next earthquake magnitude is unpredictable. We will show that an earthquake magnitude depends on previous ones: earthquakes occur with higher probability close, not only in time and space, but also in magnitude to previous events. Moreover, the magnitude difference fixes the characteristic temporal and spatial scale controlling correlations between events. As a consequence, the next earthquake tends to have a magnitude similar but smaller than the previous one. We will discuss a dynamical scaling relation between energy, time and space distance that reproduces the main statistical properties of experimental catalogs.

scholarly journals Kibble–Zurek mechanism in the Ising Field Theory

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Kristóf Hódsági ◽  
Márton Kormos
Keyword(s):  
Field Theory ◽  
Scaling Laws ◽  
Time Window ◽  
Quantum Phase Transitions ◽  
Quantum Critical Point ◽  
Continuous Phase ◽  
Scaling Properties ◽  
Dynamical Scaling ◽  
Dynamical Aspect ◽  
Dimensional Coupling

The Kibble--Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble--Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.

scholarly journals Universal dynamical scaling laws in three-state quantum walks

2021 ◽  
Vol 104 (5) ◽  
Author(s):  
P. R. N. Falcão ◽  
A. R. C. Buarque ◽  
W. S. Dias ◽  
G. M. A. Almeida ◽  
M. L. Lyra
Keyword(s):  
Scaling Laws ◽  
Quantum Walks ◽  
Dynamical Scaling

Fundamentals of laminar free convection in internally heated fluids at values of the Rayleigh–Roberts number up to

2018 ◽  
Vol 846 ◽  
pp. 966-998 ◽  
Author(s):  
Kenny Vilella ◽  
Angela Limare ◽  
Claude Jaupart ◽  
Cinzia G. Farnetani ◽  
Loic Fourel ◽  
...  
Keyword(s):  
Scaling Laws ◽  
Flow Characteristics ◽  
Internal Heat ◽  
Three Dimensions ◽  
Time Dependent ◽  
Free Boundaries ◽  
Cylindrical Structures ◽  
Thermal Anomalies ◽  
Split And Merge ◽  
Isothermal Fluid

Motions in the solid mantle of silicate planets are predominantly driven by internal heat sources and occur in laminar regimes that have not been systematically investigated. Using high-resolution numerical simulations conducted in three dimensions for a large range of Rayleigh–Roberts numbers ($5\times 10^{3}\leqslant Ra_{H}\leqslant 10^{9}$), we have determined the characteristics of flow in internally heated fluid layers with both rigid and free slip boundaries. Superficial planforms evolve with increasing $Ra_{H}$ from a steady-state tessellation of hexagonal cells with axial downwellings to time-dependent clusters of thin linear downwellings within large areas of nearly isothermal fluid. The transition between the two types of planforms occurs as a remarkable flow polarity reversal over a small $Ra_{H}$ range, such that downwellings go from isolated cylindrical structures encircled by upwellings to thin interconnected linear segments outlining polygonal cells. In time-dependent regimes at large values of $Ra_{H}$, linear downwellings dominate the flow field at shallow depth but split and merge at intermediate depths into nearly cylindrical plume-like structures that go through the whole layer. With increasing $Ra_{H}$, the number of plumes per unit area and their velocities increase whilst the amplitude of thermal anomalies decreases. Scaling laws for the main flow characteristics are derived for $Ra_{H}$ values in a $10^{6}$–$10^{9}$ range. For given $Ra_{H}$, plumes are significantly colder, narrower and wider apart beneath free boundaries than beneath rigid ones. From the perspective of planetary studies, these results alert to the dramatic changes of convective planform that can occur along secular cooling.

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