Effective conductivity tensor of ordered and disordered composite media: exact relations and numerical simulations

2003 ◽  
Vol 330 (1-2) ◽  
pp. 291-294 ◽  
Author(s):  
Yakov M. Strelniker ◽  
David J. Bergman ◽  
Shlomo Havlin ◽  
Emma Mogilko ◽  
Leonid Burlachkov ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Effective Conductivity ◽  
Conductivity Tensor ◽  
Composite Media ◽  
Exact Relations

Using quasiconvex functionals to bound the effective conductivity of composite materials

1993 ◽  
Vol 123 (4) ◽  
pp. 633-679 ◽  
Author(s):  
V. Nesi
Keyword(s):  
Composite Materials ◽  
Arbitrary Number ◽  
Effective Conductivity ◽  
Spatial Dimension ◽  
Conductivity Tensor ◽  
Volume Fractions

SynopsisIn this paper we establish bounds constraining the effective conductivity tensor of composites made of an arbitrary number n of possibly anisotropic phases in prescribed volume fractions. The bounds are valid in any spatial dimension d≧2. The bounds have a very simple and concise form and include those previously obtained by Hashin and Shtrikman, Murat and Tartar, Lurie and Cherkaev, Kohn and Milton, Avellaneda, Cherkaev, Lurie and Milton and Dell'Antonio and Nesi.

Exact relations between the thermoelectroelastic moduli of heterogeneous materials

1993 ◽  
Vol 441 (1913) ◽  
pp. 549-557 ◽  
Keyword(s):  
Thermal Expansion ◽  
Heterogeneous Media ◽  
Composite Media ◽  
Two Phase ◽  
Elastic Fields ◽  
Piezoelectric Coupling ◽  
Effective Thermal Expansion ◽  
The Individual ◽  
Exact Relations ◽  
Pyroelectric Response

Exact relations are obtained between the effective thermoelectroelastic moduli of two-phase heterogeneous media and their corresponding isothermal effective electroelastic moduli. The relations are obtained by generalizing the results of V. M. Levin, and B. W. Rosen and Z. Hashin to the inherently anisotropic coupling between the electric and elastic fields in thermoelectroelastic composites. The explicit expressions that are obtained can be used to obtain the effective thermal expansion and pyroelectric coefficients of the composite when the effective electroelastic (elastic, piezoelectric and dielectric) moduli are known, either by theory or experiment. The results also provide a means to assess the internal consistency of any micromechanics model that is proposed to estimate the thermoelectroelastic and electroelastic moduli of the composite. It is verified that when piezoelectric coupling is absent, the expressions reduce to those of B. W. Rosen and Z. Hashin for thermoelastic composite media. Finally, the resulting exact relations are exploited to prove the interesting phenomena that two-phase heterogeneous media can exhibit a net pyroelectric response even though neither of the individual phases exhibits pyroelectricity.

scholarly journals Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 225
Author(s):  
Mahendra Verma ◽  
Manohar Sharma ◽  
Soumyadeep Chatterjee ◽  
Shadab Alam
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Numerical Simulations ◽  
Inertial Range ◽  
Energy Fluxes ◽  
Mhd Turbulence ◽  
Conservation Of Energy ◽  
Exact Relations ◽  
The Magnetic Field ◽  
Variable Energy

In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range.

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