The Statistical Mechanical Derivation of the Stress Tensor and Heat Flux for a System of Spherical Molecules

1971 ◽  
Vol 12 (10) ◽  
pp. 2175-2187 ◽  
Author(s):  
Bruce N. Miller
Keyword(s):  
Heat Flux ◽  
Stress Tensor ◽  
Statistical Mechanical

Statistical Mechanics of Stress Transmission in Static Arrays of Rigid Grains

2000 ◽  
Vol 627 ◽  
Author(s):  
Dmitri V. Grinev ◽  
Sam F. Edwards
Keyword(s):  
Stress Tensor ◽  
Coordination Number ◽  
Complete System ◽  
External Loading ◽  
Contact Network ◽  
Cauchy Equation ◽  
Stress Equilibrium ◽  
Stress Transmission ◽  
Statistical Mechanical ◽  
Fundamental Equations

ABSTRACTWe develop the statistical-mechanical theory that delivers the fundamental equations of stress equilibrium for static arrays of rigid grains. The random geometry of static granular packing composed of rigid cohesionless particles can be visualised as a network of intergranular contacts. The contact network and external loading determine the network of intergranular forces. In general, the contact network can have an arbitrary coordination number varying within the system. It follows then that the network of intergranular forces is indeterminate i.e. the number of unknown forces is larger than the number of Newton's equations of mechanical equilibrium. Thus, in order for the network of intergranular forces to be determined, the number of equations must equal the number of unknowns. We argue that this determines the contact network with a certain fixed coordination number. The complete system of equations for the stress tensor is derived from the equations of intergranular force and torque balance, given the geometric specification of the packing. The granular material fabric gives rise to corrections to the Euler-Cauchy equation that become significant at mesoscopic lengthscales. The stress-geometry equation establishes the relation between various components of the stress tensor, and depends on the topology of the granular array.

Statistical mechanics of inhomogeneous fluids

1982 ◽  
Vol 379 (1776) ◽  
pp. 231-246 ◽  
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Angular Momentum ◽  
Statistical Mechanics ◽  
Stress Tensor ◽  
Pressure Difference ◽  
Strain Tensor ◽  
Pressure Tensor ◽  
Conservation Of Momentum ◽  
Statistical Mechanical

The nature of the microscopic stress tensor in an inhomogeneous fluid is discussed, with emphasis on the statistical mechanics of drops. Changes in free energy for isothermal deformations of a fluid are expressible as volume integrals of the stress tensor ‘times’ a strain tensor. A particular radial distortion of a drop leads to statistical mechanical expressions for the pressure difference across the surface of the drop. We find that the stress tensor is not uniquely defined by the microscopic laws embodying the conservation of momentum and angular momentum and that the am­biguity remains in the ensemble average, or pressure tensor, in regions of inhomogeneity. This leads to difficulties in defining statistical mechanical expressions for the surface tension of a drop.

Siphon Flows in Stratified Coronal Loops

1994 ◽  
Vol 144 ◽  
pp. 185-187
Author(s):  
S. Orlando ◽  
G. Peres ◽  
S. Serio
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Flow Model ◽  
Supersonic Flows ◽  
Coronal Loops ◽  
Characteristic Parameters

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

Rate of Sublimation of Ice by Radiative Heating in Freeze-Etching

1980 ◽  
Vol 38 ◽  
pp. 618-619
Author(s):  
Yeshayahu Talmon
Keyword(s):  
Heat Flux ◽  
Freeze Fracture ◽  
Constant Heat Flux ◽  
Radiative Heating ◽  
Constant Heat ◽  
Entire Sample ◽  
Simplified Method ◽  
Freeze Etching ◽  
Sublimation Rates ◽  
Fractured Surface

To bring out details in the fractured surface of a frozen sample in the freeze fracture/freeze-etch technique,the sample or part of it is warmed to enhance water sublimation.One way to do this is to raise the temperature of the entire sample to about -100°C to -90°C. In this case sublimation rates can be calculated by using plots such as Fig.1 (Talmon and Thomas),or by simplified formulae such as that given by Menold and Liittge. To achieve higher rates of sublimation without heating the entire sample a radiative heater can be used (Echlin et al.). In the present paper a simplified method for the calculation of the rates of sublimation under a constant heat flux F [W/m2] at the surface of the sample from a heater placed directly above the sample is described.

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