The mechanics of granitoid systems and maximum entropy production rates

2010 ◽  
Vol 368 (1910) ◽  
pp. 53-93 ◽  
Author(s):  
Bruce E. Hobbs ◽  
Alison Ord
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Melt Inclusions ◽  
Selection Process ◽  
Finite Thickness ◽  
Control Valve ◽  
Entropy Production Rate ◽  
Constitutive Behaviour ◽  
Maximum Entropy Production ◽  
Physical Height

A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10 4 –10 7 years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson–Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient ‘ponds’ of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic–viscous at high temperatures to elastic–plastic–viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate.

A Criteria for Size Separation Using Maximum Entropy Production

2009 ◽  
Author(s):  
Chuan-ping Liu ◽  
Li Wang ◽  
Min Jia ◽  
Lige Tong
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Stable State ◽  
Irreversible Processes ◽  
Entropy Production Rate ◽  
Absolute Maximum ◽  
Kinetic Temperature ◽  
Granular Mixture ◽  
Maximum Entropy Production ◽  
Size Separation

In order to study analytically the nature of the size separation in granular mixture, we present the maximum entropy production principle based on kinetic temperature of granular mixture. For simplicity we apply this principle to size separation of a sphere binary mixture in vibrated bed, and we find a new thermodynamic mechanism of size separation phenomenon. With the irreversible processes such as elastic collisions and frictions, the kinetic energy is dissipated rapidly in system, which induces the entropy production. By the fact that the entropy production rate always has the absolute maximum at the stable state of granular mixture, we find the crossover from “Brazil Nut Effect” to its reverse by changing particles size and density, and our result is about satisfied with Schnautz’s experiment.

Morphological instability at the solid–liquid interface by the maximum entropy production rate principle

2018 ◽  
Vol 96 (12) ◽  
pp. 1314-1320 ◽  
Author(s):  
Yaw Delali Bensah
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Production Rate ◽  
Liquid Interface ◽  
Instability Criterion ◽  
Entropy Production Rate ◽  
Morphological Instability ◽  
Maximum Entropy Production ◽  
Solid Liquid Interface ◽  
Solid Liquid

We examine the morphological instability from planar to non-planar cellular morphology with the maximum entropy production rate (MEPR) principle. An expression that quantifies the MEPR density at the solid–liquid interface (SLI) during direction solidification is presented, which leads to an instability criterion for dilute binary alloys. The instability criterion also affords to theoretically calculate the instability solidification growth velocity. The model considers steady state solidification at close-to and far-from equilibrium conditions.

scholarly journals Solidification Morphology and Bifurcation Predictions with the Maximum Entropy Production Rate Model

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 40 ◽  
Author(s):  
Yaw Delali Bensah ◽  
J. A. Sekhar
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Production Rate ◽  
Materials Science ◽  
Morphological Evolution ◽  
Diffusion Constant ◽  
Solute Diffusion ◽  
Diffuse Interface ◽  
Entropy Production Rate ◽  
Maximum Entropy Production

The use of the principle of maximum entropy generation per unit volume is a new approach in materials science that has implications for understanding the morphological evolution during solid–liquid interface growth, including bifurcations with or without diffuseness. A review based on a pre-publication arXiv preprint is first presented. A detailed comparison with experimental observations indicates that the Maximum Entropy Production Rate-density model (MEPR) can correctly predict bifurcations for dilute alloys during solidification. The model predicts a critical diffuseness of the interface at which a plane-front or any other form of diffuse interface will become unstable. A further confidence test for the model is offered in this article by comparing the predicted liquid diffusion coefficients to those obtained experimentally. A comparison of the experimentally determined solute diffusion constant in dilute binary Pb–Sn alloys with those predicted by the various solidification instability models (1953–2011) is additionally discussed. A good predictability is noted for the MEPR model when the interface diffuseness is small. In comparison, the more traditional interface break-down models have low predictiveness.

scholarly journals Relaxation Processes and the Maximum Entropy Production Principle

Entropy ◽  
2010 ◽  
Vol 12 (3) ◽  
pp. 473-479 ◽  
Author(s):  
Paško Županović ◽  
Srećko Botrić ◽  
Davor Juretić ◽  
Domagoj Kuić
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Relaxation Processes ◽  
Maximum Entropy Production
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