On two-dimensional foam ageing

2011 ◽  
Vol 673 ◽  
pp. 147-179 ◽  
Author(s):  
J. DUPLAT ◽  
B. BOSSA ◽  
E. VILLERMAUX
Keyword(s):  
Scaling Laws ◽  
Mean Field Theory ◽  
Mean Field ◽  
Quantitative Agreement ◽  
Two Dimensions ◽  
Straightforward Manner ◽  
Langevin Model ◽  
Common Time ◽  
Set Up ◽  
Facet Number

The present study aims at documenting, making use of an original set-up allowing to acquire well-converged data, the coarsening of foams in two dimensions. Experiments show that a foam behaves quite differently depending on the way it has been prepared. We distinguish between an initially quasi-monodisperse foam and a polydisperse foam. The coarsening laws are initially different, although both foams reach a common, time-dependent asymptotic regime.The ageing process relies on exchanges between adjacent foam cells (von Neumann's law), and on topological rearrangement (1 and 2 processes) whose rates are measured in all regimes. We attempt to make their contribution to the evolution of the area S and facet number n distribution of probability P(S, n, t) quantitative. The corresponding mean field theory predictions represent well the phenomenon qualitatively, and are sometimes in quantitative agreement with the measurements. A simplified version of this theory, taking the form of a Langevin model, explains in a straightforward manner the different scaling laws in the different regimes, for the different foams.

scholarly journals REALISTIC MODELING OF STRONGLY CORRELATED ELECTRON SYSTEMS: AN INTRODUCTION TO THE LDA+DMFT APPROACH

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2611-2625 ◽  
Author(s):  
K. HELD ◽  
I. A. NEKRASOV ◽  
N. BLÜMER ◽  
V. I. ANISIMOV ◽  
D. VOLLHARDT
Keyword(s):  
Quantum Monte Carlo ◽  
Local Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Structure Theory ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Basic Ideas ◽  
Set Up

The LDA+DMFT approach merges conventional band structure theory in the local density approximation (LDA) with a state-of-the-art many-body technique, the dynamical mean-field theory (DMFT). This new computational scheme has recently become a powerful tool for ab initio investigations of real materials with strong electronic correlations. In this paper an introduction to the basic ideas and the set-up of the LDA+DMFT approach is given. Results for the photoemission spectra of the transition metal oxide La 1-x Sr x TiO 3, obtained by solving the DMFT equations by quantum Monte Carlo (QMC) simulations, are presented and are found to be in very good agreement with experiment. The numerically exact DMFT(QMC) solution is compared with results obtained by two approximative solutions, i.e. the iterative perturbation theory and the non-crossing approximation.

Influence of Anisotropic Surfaces on the Friction Behaviour of Hydraulic Seals

2016 ◽  
Author(s):  
Julian Angerhausen ◽  
Hubertus Murrenhoff ◽  
Leonid Dorogin ◽  
Michele Scaraggi ◽  
Boris Lorenz ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Friction Force ◽  
Sliding Friction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Surface Finishing ◽  
Soft Contact ◽  
Rigid Cylinder ◽  
Set Up ◽  
Stribeck Curves

In the modelling of the leakage rate, friction force or contact pressure distribution of hydraulic seals is quite common to assume the mating surfaces to be characterized by a random isotropic roughness. However, due to different surface finishing methods, such as coating, grinding or polishing, roughness with anisotropic characteristics is often generated. In this paper a first experimental investigation of the influence of such anisotropic surfaces on the sliding friction is provided. For this purpose, a test rig has been designed and set up to investigate a soft, lubricated line contact representative of a generic reciprocating hydraulic seal. In particular, an O-ring cord is squeezed into contact with a steady rotating rigid cylinder. In order to adopt a cylinder-on-flat configuration, the diameter of the rigid cylinder is chosen to be significantly larger than the O-ring (cross-section) diameter. Furthermore, three cylinders with different surfaces are used: One (sandblasted) isotropic surface and two anisotropic surfaces roughness, scratched perpendicularly or along the azimuthal direction. Therefore, under temperature control, Stribeck curves have been measured at different squeezing loads and surface roughness, showing a neat influence of the surface roughness characteristics on the friction force. Finally, the experimental results are compared with the predictions provided by a recent mean field theory of soft contact (e.g. rubber) lubrication.

scholarly journals On phase transition behaviors of Kerr–Sen black hole

2020 ◽  
Vol 17 (11) ◽  
pp. 2050169
Author(s):  
A. Belhaj ◽  
A. El Balali ◽  
W. El Hadri ◽  
H. El Moumni ◽  
M. A. Essebani ◽  
...  
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Phase Transitions ◽  
Scaling Laws ◽  
Mean Field Theory ◽  
Mean Field ◽  
Conformal Factor ◽  
Four Dimensions ◽  
Similar Phase ◽  
Second Order Phase Transition

We investigate phase transitions and critical behaviors of the Kerr–Sen black hole in four dimensions. Computing the involved thermodynamical quantities including the specific heat and using the Ehrenfest scheme, we show that such a black hole undergoes a second-order phase transition. Adopting a new metric form derived from the Gibss free energy scaled by a conformal factor associated with extremal solutions, we calculate the geothermodynamical scalar curvature recovering similar phase transitions. Then, we obtain the scaling laws and the critical exponents, matching perfectly with mean field theory.

scholarly journals Controlled Self-Assembly of Soft-Matter Quasicrystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C889-C889 ◽  
Author(s):  
Kobi Barkan ◽  
Michael Engel ◽  
Haim Diamant ◽  
Ron Lifshitz
Keyword(s):  
Self Assembly ◽  
Soft Matter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Building Blocks ◽  
Two Dimensions ◽  
Pair Potentials ◽  
The Stability ◽  
Dynamics Simulations ◽  
Three Body

A large number of soft-matter systems, whose building blocks range in size from several nanometers to almost a micron, have been shown in recent years to form ordered phases with dodecagonal (12-fold) symmetry (for recent reviews see [1]). Contrary to metallurgic quasicrystals, whose source of stability remains a question of great debate to this day, we show that the stability of certain soft-matter quasicrystals–interacting via pair potentials with repulsive cores, which are either bounded or only slowly diverging–can directly be explained. Their stability is attributed to the existence of two natural length scales in their isotropic pair potentials, along with an effective three-body interaction arising from entropy. We establish the validity of this mechanism at the level of a mean-field theory [2], and then use molecular dynamics simulations in two dimensions to confirm it beyond mean field, and to show that it leads to the formation of cluster crystals [3]. We demonstrate that our understanding of the stability mechanism allows us to generate a variety of desired structures, including decagonal and dodecagonal quasicrystals [3], suggesting a practical approach for their controlled self-assembly in laboratory realizations using synthesized soft-matter particles.

scholarly journals Bosonic mean-field theory for frustrated Heisenberg antiferromagnets in two dimensions

1995 ◽  
Vol 52 (2) ◽  
pp. 1061-1069 ◽  
Author(s):  
R. Chitra ◽  
Sumathi Rao ◽  
Diptiman Sen ◽  
S. Suresh Rao
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Two Dimensions ◽  
Heisenberg Antiferromagnets

scholarly journals Critical Phenomena in Higher Curvature Charged AdS Black Holes

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Arindam Lala
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Critical Phenomena ◽  
Critical Exponents ◽  
Scaling Laws ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Surface ◽  
Thermodynamic Quantities ◽  
Ads Black Holes

In this paper, we have studied the critical phenomena in higher curvature charged AdS black holes. We have considered Lovelock-Born-Infeld-AdS black hole as an example. The thermodynamics of the black hole have been studied which reveals the onset of a higher-order phase transition in the black hole in the canonical ensemble (fixed charge ensemble) framework. We have analytically derived the critical exponents associated with these thermodynamic quantities. We find that our results fit well with the thermodynamic scaling laws and consistent with the mean field theory approximation. The suggestive values of the other two critical exponents associated with the correlation function and correlation length on the critical surface have been derived.

scholarly journals Curvature flows, scaling laws and the geometry of attrition under impacts

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Gergő Pál ◽  
Gábor Domokos ◽  
Ferenc Kun
Keyword(s):  
Scaling Laws ◽  
Mean Field Theory ◽  
Mean Field ◽  
Finite Sample ◽  
Fragmentation Energy ◽  
Ore Processing ◽  
Wall Collision ◽  
Spatio Temporal ◽  
Curvature Driven ◽  
The Impact

AbstractImpact induced attrition processes are, beyond being essential models of industrial ore processing, broadly regarded as the key to decipher the provenance of sedimentary particles. Here we establish the first link between microscopic, particle-based models and the mean field theory for these processes. Based on realistic computer simulations of particle-wall collision sequences we first identify the well-known damage and fragmentation energy phases, then we show that the former is split into the abrasion phase with infinite sample lifetime (analogous to Sternberg’s Law) at finite asymptotic mass and the cleavage phase with finite sample lifetime, decreasing as a power law of the impact velocity (analogous to Basquin’s Law). This splitting establishes the link between mean field models (curvature-driven partial differential equations) and particle-based models: only in the abrasion phase does shape evolution emerging in the latter reproduce with startling accuracy the spatio-temporal patterns (two geometric phases) predicted by the former.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field
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