Tensor conductivity

The effective thermal conductivity tensor depends on the transformation vec-... 

Fffective thermal conductivity tensor Kinetic coefficients Flectric potential... 

Section II deals with the general formalism of Prigogine and his co-workers. Starting from the Liouville equation, we derive an exact transport equation for the one-particle distribution function of an arbitrary fluid subject to a weak external field. This equation is valid in the so-called "thermodynamic limit , i.e. when the number of particles N —> oo, the volume of the system 2-> oo, with Nj 2 = C finite. As a by-product, we obtain very easily a formulation for the equilibrium pair distribution function of the fluid as well as a general expression for the conductivity tensor. 

Before closing this chapter, let us note the formal expression for the conductivity tensor per unit volume. We have ... 

Izawa K, Yamaguchi H, Sasaki T, Matsuda Y (2002) Superconducting gap stmcture of /c-(BEDT-TTF)2Cu(NCS)2 probed by thermal conductivity tensor. Phys Rev Lett 88 27002/1 ... 

X is the rank-two conductivity tensor for a particular material. In Eq. 1.24, x is the material property that relates both the magnitude of effect Jq to the cause E and their directions—Jq is not necessarily parallel to E. 

Of particular interest is the case of anisotropic tensorial conductivity, which couples together the various field and current components. It is then, of course, impossible to obtain a separate equation for Hz and, in principle, a dynamo is possible with an increment determined by the off-diagonal (in x, y, z coordinates) components of the conductivity tensor. Usually the direction of anisotropy is related to the magnetic field, but then the whole problem becomes nonlinear. 

This means that the resistivity and thermal conductivity tensors are no longer symmetric. For example,... 

The thermal conductivity tensor may likewise be split into symmetric and antisymmetric parts, with expansions in powers of B as in eqs. (35) and (36). But Z is not necessarily a symmetric tensor at B = 0, and so the expansion of the antisymmetric part of Z in an equation like eq. (36) is not applicable. Instead,... 

The ionic susceptibility/conductivity is a function of the trajectories of the charges at equilibrium that is, y (m (o>) is proportional to the ACF spectrum of the E-projection of the steady-state velocity. One may regard Eq. (394) as a convenient (for numerical calculations) form of the Kubo formula [69] for the diagonal component of the conductivity tensor... 

Magnetic field acts on moving electrons by the Lorentz force directed perpendicularly to both the electron velocity and magnetic field. This leads to the appearance of non-diagonal components of the conductivity tensor. Namely, these components cause an electric field perpendicular to both the current flowing through a sample and to the external magnetic field ... 

The crystal symmetry of most organic metals is low, often only monoclinic, and the principal axes of the conductivity tensor (cr) are not precisely defined. However, in practice the conductivity along the chain direction (cr,) is particularly high, usually 300 to 2500 (Q-cm) 1 at room temperature, while that in one direction perpendicular to the chains (07) is very low [2]. Therefore, these two directions must be very close to the principal axes of ex. The third perpendicular direction has intermediate conductivity (07). So in the situation, where > 07, which is quite common, the principal axes of the conductivity and resistivity (p) tensors are known reasonably well. When measuring these quantities on a single crystal, care must be taken either to ensure that the current distribution is uniform, or alternatively, special methods such as those of Montgomery [11] or van der Pauw [12] must be used. Some insight into these problems can be obtained by consideration of the equivalent isotropic sample [11,13]. 

None. From Eq. 6.6, it is seen that the conductivity tensor is isotropic in the ab plane perpendicular to the c axis. 

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