scholarly journals Systematic derivation of coarse-grained fluctuating hydrodynamic equations for many Brownian particles under nonequilibrium conditions

2006 ◽  
Vol 74 (3) ◽  
Author(s):  
Takenobu Nakamura ◽  
Shin-ichi Sasa
2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Nicodemo Di Pasquale ◽  
Thomas Hudson ◽  
Matteo Icardi

Author(s):  
Steven A. Orszag ◽  
I. Staroselsky,

The renormalization group (RNG) and related e-expansion methods are a powerful technique that allow the systematic derivation of coarse-grained equations of motion for turbulent flows and, in particular, the derivation of sophisticated turbulence models based on the fundamental underlying physics. The RNG method provides a convenient calculus for the analysis of complex physical effects in complex flows. The details of the RNG method applied to fluid mechanics differ in some crucial respects from how renormalization group techniques are applied to field theories in other branches of physics. At the present time, the RNG methods for fluid dynamics are by no means rigorously justified, so their utility must be based on the quality and quantity of results to which they lead. In this paper we discuss the basis for the RNG method and then illustrate its application to a variety of turbulent flow problems, emphasizing those points where further analysis is needed. The application of a field-theoretic method like the RNG technique to turbulence is based on the fundamental assumption of universality of small scales in turbulent flows. Such universal behavior was first suggested over 50 years ago in the seminal work of A. N. Kolmogorov who argued that the small-scale spectrum of incompressible turbulence is universal and characterized by two numbers, the rate of energy dissipation ε per unit mass and the kinematic viscosity v.


Author(s):  
Dominic Spiller ◽  
Aaron Brunk ◽  
Oliver Habrich ◽  
Herbert Egger ◽  
Maria Lukacova-Medvidova ◽  
...  

2020 ◽  
Vol 43 (11) ◽  
Author(s):  
Florian Vogel ◽  
Matthias Fuchs

Abstract. We determine the non-local stress autocorrelation tensor in an homogeneous and isotropic system of interacting Brownian particles starting from the Smoluchowski equation of the configurational probability density. In order to relate stresses to particle displacements as appropriate in viscoelastic states, we go beyond the usual hydrodynamic description obtained in the Zwanzig-Mori projection-operator formalism by introducing the proper irreducible dynamics following Cichocki and Hess, and Kawasaki. Differently from these authors, we include transverse contributions as well. This recovers the expression for the stress autocorrelation including the elastic terms in solid states as found for Newtonian and Langevin systems, in case that those are evaluated in the overdamped limit. Finally, we argue that the found memory function reduces to the shear and bulk viscosity in the hydrodynamic limit of smooth and slow fluctuations and derive the corresponding hydrodynamic equations. Graphical abstract


2009 ◽  
Vol 11 (12) ◽  
pp. 1977 ◽  
Author(s):  
Xiaoyu Chen ◽  
Paola Carbone ◽  
Giuseppe Santangelo ◽  
Andrea Di Matteo ◽  
Giuseppe Milano ◽  
...  

Author(s):  
R. E. Ferrell ◽  
G. G. Paulson

The pore spaces in sandstones are the result of the original depositional fabric and the degree of post-depositional alteration that the rock has experienced. The largest pore volumes are present in coarse-grained, well-sorted materials with high sphericity. The chief mechanisms which alter the shape and size of the pores are precipitation of cementing agents and the dissolution of soluble components. Each process may operate alone or in combination with the other, or there may be several generations of cementation and solution.The scanning electron microscope has ‘been used in this study to reveal the morphology of the pore spaces in a variety of moderate porosity, orthoquartzites.


Author(s):  
J. M. Walsh ◽  
K. P. Gumz ◽  
J. C. Whittles ◽  
B. H. Kear

During a routine examination of the microstructure of rapidly solidified IN-100 powder, produced by a newly-developed centrifugal atomization process1, essentially two distinct types of microstructure were identified. When a high melt superheat is maintained during atomization, the powder particles are predominantly coarse-grained, equiaxed or columnar, with distinctly dendritic microstructures, Figs, la and 4a. On the other hand, when the melt superheat is reduced by increasing the heat flow to the disc of the rotary atomizer, the powder particles are predominantly microcrystalline in character, with typically one dendrite per grain, Figs, lb and 4b. In what follows, evidence is presented that strongly supports the view that the unusual microcrystalline structure has its origin in dendrite erosion occurring in a 'mushy zone' of dynamic solidification on the disc of the rotary atomizer.The critical observations were made on atomized material that had undergone 'splat-quenching' on previously solidified, chilled substrate particles.


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