Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws

2001 ◽  
Vol 8 (6) ◽  
pp. 2883-2889 ◽  
Author(s):  
D. Oron ◽  
L. Arazi ◽  
D. Kartoon ◽  
A. Rikanati ◽  
U. Alon ◽  
...  
Keyword(s):  
Scaling Laws ◽  
Late Time ◽  
Time Scaling

Scaling law of static liquefaction mechanism in geocentrifuge and corresponding hydromechanical characterization of an unsaturated silty sand having a viscous pore fluid

2015 ◽  
Vol 52 (6) ◽  
pp. 708-720 ◽  
Author(s):  
Amin Askarinejad ◽  
Alexander Beck ◽  
Sarah M. Springman
Keyword(s):  
Pore Pressure ◽  
Scaling Laws ◽  
Scaling Law ◽  
Pore Fluid ◽  
Silty Sand ◽  
Excess Pore Pressure ◽  
Geotechnical Centrifuge ◽  
Time Scaling ◽  
Static Liquefaction ◽  
Viscous Solution

Fast landslides induced by rainfall impose considerable damage on infrastructure and cause major casualties worldwide. Static liquefaction is one of the triggering mechanisms mentioned frequently in the literature as a cause of this type of landslide. The scaling laws required to model this mechanism in the geotechnical centrifuge are developed, and it is shown that either a reduction in the soil pore size or use of a viscous pore fluid is needed to unify the time scaling factors of contractive volume change of the saturated voids and dissipation of the excess pore pressure generated. The latter option was used in this research; therefore, the influences of the viscous pore fluid on the hydromechanical characteristics of a silty sand were investigated. Subsequently, geocentrifuge tests were conducted to compare the behaviour of a slope having a viscous solution as the pore fluid with that of a model with water as the pore fluid. Both slopes were subjected to rainfall, and the evolution of the pore pressure and surface movements were monitored.

scholarly journals Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Márton Kormos
Keyword(s):  
Scaling Limit ◽  
Transverse Field ◽  
Late Time ◽  
Ising Chain ◽  
Initial State ◽  
Equilibrium Dynamics ◽  
Time Scaling ◽  
Point Correlation ◽  
Lattice Effect ◽  
Non Equilibrium

We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.

scholarly journals Constant-rate inflation: primordial black holes from conformal weight transitions

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Kin-Wang Ng ◽  
Yi-Peng Wu
Keyword(s):  
Black Holes ◽  
Power Spectrum ◽  
Analytic Solutions ◽  
Conformal Weight ◽  
Late Time ◽  
Primordial Black Holes ◽  
De Sitter ◽  
Slow Roll ◽  
Time Scaling ◽  
Constant Rate

Abstract Constant-rate inflation, including ultra-slow-roll inflation as a special case, has been widely applied to the formation of primordial black holes with a significant deviation from the standard slow-roll conditions at both the growing and decaying phases of the power spectrum. We derive analytic solutions for the curvature perturbations with respect to the late-time scaling dimensions (conformal weights) constrained by the dilatation symmetry of the de Sitter background and show that the continuity of conformal weights across different rolling phases is protected by the adiabatic condition of the inflaton perturbation. The temporal excitation of subleading states (with the next-to-lowest conformal weights), recorded as the “steepest growth” of the power spectrum, is triggered by the entropy production in the transition from the slow-roll to the constant-rate phases.

scholarly journals Linking scales in sea ice mechanics

2017 ◽  
Vol 375 (2086) ◽  
pp. 20150352 ◽  
Author(s):  
Jérôme Weiss ◽  
Véronique Dansereau
Keyword(s):  
Sea Ice ◽  
Scaling Laws ◽  
Thickness Distribution ◽  
Ice Cover ◽  
Ice Thickness ◽  
Elastic Stresses ◽  
Multi Scale ◽  
Modelling Framework ◽  
Time Scaling ◽  
Energy Exchanges

Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell–elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws. This article is part of the themed issue ‘Microdynamics of ice’.

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