Inverse square distance matrix

Charge Indices Charge indices G and are calculated from the matrix product M=(A x D ), where D is the inverse square distance matrix [16] ... 

During gel electrophoresis, the migration of macromolecules is obstructed by the polymer matrix, and thus depends on the molecular weight as well as the frictional coefficient with the matrix. In the reptation model, DNA is assumed to move in a worm-like fashion through virtual tubes in the gel polymer matrix (Fig. 9.1A). The central result is that the electrophoretic mobility depends on the mean-square end-to-end distance of the macromolecule, and inversely on length (L) or molecular weight. The electrophoretic mobility is expressed as... 

Values of the e.s.d.s of parameters can be obtained, as shown in Figure 10.13, in the least-squares refinement from values of the diagonals of the inverse matrix. Similarly, any correlations between parameters, such as is often found to occur between occupancy and atomic displacement parameters, can be identified and taken into account in the description of the resulting molecular structure. The e.s.d.s for the refined parameters can then be used to calculate e.s.d.s of derived parameters, such as distances, angles, and torsion angles. ... 

Both diffusion and advection of solutes are important in biofilms. The biofilm matrix hinders both phenomena obviously the matrix is an effective barrier not only for water movement (advection) but also for the random movement of solutes (diffusion). The effective diffusion coefficient (Deff) is proportional to the biofilm porosity (6) and inversely proportional to the square of the diffusional distance, the average path length (cp) ... 

---