Simulations of Magnetoviscosity of Dilute Suspensions of Magnetic Ellipsoids

2008 ◽  
Author(s):  
J. H. Sa´nchez ◽  
C. Rinaldi
Keyword(s):  
Brownian Motion ◽  
Angular Momentum ◽  
Momentum Equation ◽  
Orientation Space ◽  
Fluctuation Dissipation ◽  
Ellipsoidal Particles ◽  
Fluctuation Dissipation Theorem ◽  
Dilute Suspensions ◽  
Dilute Suspension ◽  
Rotational Brownian Motion

We studied the rotational Brownian motion of magnetic triaxial ellipsoidal particles (orthotropic particles) suspended in a Newtonian fluid, in the dilute suspension limit, under applied shear and magnetic fields. The algorithm describing the change in the particle magnetization has been derived from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Results are presented for the response of dilute suspensions of ellipsoidal particles to constant magnetic and shear flow fields.

Conclusions

2021 ◽  
pp. 137-148
Author(s):  
Robert W. Batterman
Keyword(s):  
Brownian Motion ◽  
Material Parameter ◽  
Natural Kinds ◽  
Point Of View ◽  
Mesoscale Modeling ◽  
Relation Theory ◽  
Relative Autonomy ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

This concluding chapter focuses on the philosophical lessons to be had from the discussions in the previous chapters. Specifically, it suggests that one interesting and fruitful way to understand the relation “theory X is more fundamental than theory Y” is through mediated mesoscale modeling. This is in contrast to the kind of direction derivational connections often invoked in the debates about reduction that depend on “in principle” mathematical claims. The hierarchical ordering in terms of this relation of relative fundamentality can be understood in terms of the conception of relative autonomy discussed throughout the book. It highlights the fact that this point of view has its genesis in Einstein’s work on Brownian Motion and specifically in his determination of an effective material parameter and the first expression of the Fluctuation-Dissipation theorem. Finally, it recaps the conception of an engineering, middle-out approach to many-body physics and the physical arguments that certain mesoscale variables should be considered to be natural kinds.

Brownian Motion

2021 ◽  
pp. 66-84
Author(s):  
Robert W. Batterman
Keyword(s):  
Brownian Motion ◽  
Many Body ◽  
Hydrodynamic Description ◽  
Representative Volume ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Representative Volume Elements ◽  
Many Body Systems

This chapter discusses the phenomenon of Brownian motion and Einstein’s pioneering arguments that explained various aspects of it. It shows how Einstein presented two arguments that relate directly to the themes of this book. The first is the upscaling or homogenization to effective continuum parameters from correlational structures in representative volume elements at mesoscales. Einstein’s argument is shown to answer the question about autonomy raised in Chapter 2. The second relates to the Fluctuation-Dissipation theorem. This theorem justifies the mesoscale hydrodynamic description of many-body systems and Einstein provided the first statement of the theorem.

scholarly journals The Response to Stratospheric Forcing and Its Dependence on the State of the Troposphere

2009 ◽  
Vol 66 (7) ◽  
pp. 2107-2115 ◽  
Author(s):  
Cegeon J. Chan ◽  
R. Alan Plumb
Keyword(s):  
Time Scale ◽  
Equilibrium Temperature ◽  
Intrinsic Variability ◽  
Winter Solstice ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Order Of Magnitude ◽  
Leading Mode ◽  
Set Up ◽  
Hemisphere Winter

Abstract In simple GCMs, the time scale associated with the persistence of one particular phase of the model’s leading mode of variability can often be unrealistically large. In a particularly extreme example, the time scale in the Polvani–Kushner model is about an order of magnitude larger than the observed atmosphere. From the fluctuation–dissipation theorem, one implication of these simple models is that responses are exaggerated, since such setups are overly sensitive to any external forcing. Although the model’s equilibrium temperature is set up to represent perpetual Southern Hemisphere winter solstice, it is found that the tropospheric eddy-driven jet has a preference for two distinct regions: the subtropics and midlatitudes. Because of this bimodality, the jet persists in one region for thousands of days before “switching” to another. As a result, the time scale associated with the intrinsic variability is unrealistic. In this paper, the authors systematically vary the model’s tropospheric equilibrium temperature profile, one configuration being identical to that of Polvani and Kushner. Modest changes to the tropospheric state to either side of the parameter space removed the bimodality in the zonal-mean zonal jet’s spatial distribution and significantly reduced the time scale associated with the model’s internal mode. Consequently, the tropospheric response to the same stratospheric forcing is significantly weaker than in the Polvani and Kushner case.

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