Gradients of density

This part of the chapter will deal with the distribution of the DA receptors in the brain, in order to provide an overview of the sites of DA action. As in the previous sections, we will mainly refer to the rat brain, with a comparison with humans and nonhuman primates. Data on DA receptors in the human brain are also dealt with in the chapter of Hurd and Hall in this volume. 

Since the concentration of receptors provides clues for the efficacy of DA action at given brain sites, the distribution of each receptor subtype will be presented according to an overall indicative criterion of high, intermediate and low density, based on the comparison between literature data. The definition of high, intermediate and low density and their illustration in the distributional maps refer to the relative density of each receptor subtype and are not indicative of a relationship in density across different receptor subtypes. 

The wide distribution of DA receptors in the brain brings about the obvious consequences of the presence of more than one subtype of these receptors in the same brain sites. This does not necessarily imply, however, a colocalization of different DA receptors in single cells. 

---

Around each sink, the density of the diffusing particles is reminiscent of the Smoluchowski density [3]. However, as discussed in Chap. 8, Sect. 2.3, the depletion of the density around any sink affects the density in the vicinity of a neighbouring sink. This occurs because the density midway between the sinks (the effective boundary) is reduced and this reduction may not be the same on opposite sides of the sink. There is an overall gradient of density imposed across the region around the sink of interest as well as a reduction of density. Some distance (> 1QR) away from this sink, the density is approximately... 

From the density of the diffusing species around the two, sinks, a rate coefficient can be calculated using the gradient of density at the sinks. Samson and Deutch [258] showed that Hi is is... 

As a reference to something more familiar, consider the case of a fluid where incompressibility is enforced via a Lagrange multiplier. For a Stokesian fluid, it is assumed that the constitutive variables (stress, energy, heat flux) are a function of density, p, temperature, T, rate of deformation tensor, d, and possibly other variables (such as the gradients of density and temperature). Exploiting the entropy inequality in this framework produces the following constitutive restriction for the Cauchy stress tensor [10]... 

In a non-equilibrium gas system there are gradients in one or more of the macroscopic properties. In a mono-atomic gas the gradients of density, fluid velocity, and temperature induce molecular transport of mass, momentum, and kinetic energy through the gas. The mathematical theory of transport processes enables the quantification of these macroscopic fluxes in terms of the distribution function on the microscopic level. It appears that the mechanism of transport of each of these molecular properties is derived by the same mathematical procedure, hence they are collectively represented by the generalized property (/ ... 

An entirely different line of thought eventually found its way into the theory of critical correlations. In the late nineteenth century it was realized that the treatment of capillary and surface phenomena by continuum mechanics required that the free-energy density depend on the gradient of density or composition, as well as on the density itself. These efforts are reviewed by Bakker, particularly in Chapter 15. Many years later this work was taken up by Cahn and Hilliard, particularly for its application to nucleation theory, and given a firm thermodynamic foundation by... 

Using (4.6), (4.4) and the following definitions of space gradients of densities and temperature... 

For long duration experiments, t > 10 —20 s, natural convection due to gradients of density can also take place. 

Apart from diffusion and migration, transport by convection can also take place due to different internal and external forces. Thus, natural convection due to gradients of density can occur when the electrode reaction provokes a significant local change in the solution composition or due to thermal variations. The modelling of this case is difficult and so electrochemical experiments are usually restricted to short time scales, low concentration of analyte, and thermostated cells such that the influence of natural convection is minimised. 

The above conditions, however, are not fulfilled by other processes such as shock waves, highly rarefied gases. Many biological systems have gradients of density, energy density etc. over a distance of 10 A (such as material near or in a membrane or a cell nucleus) which would not have true local equilibrium. 

Density gradient gra-de-9nt n. A gradient of density such as in a gradient column for measuring density of plastic materials. 

Consider a plume, as shown in Figure 5.14, whose main driving force consists of a gradient of density caused by a difference in temperature (natural convection). 

Anticipating that near the critical point the gradients of density or... 

Mpemba paradox arises intrinsically from heating and undercoordination induced 0 H-0 bond relaxation. Heat emission proceeds at a rate depending on the initial energy storage, and the skin supersolidity creates the gradients of density, specific heat, and thermal conductivity for heat conduction in Fourier s equation of fluid thermodynamics. 

---