Infinite Simple 3D Cubic Lattice of Identical Resistors (Two Missing Bonds)

An infinite regular three-dimensional network is composed of identical resistors each of resistance joining adjacent nodes. What is the equivalent resistance between the lattice site and the lattice site, when two bonds are removed from the perfect network? Three cases are considered here, and some numerical values are calculated. Finally, the asymptotic behavior of the equivalent resistance is studied for large distances between the two sites.Comment: 11 pages, 3 figures, published in EPJ-A

Infinite Networks of Identical Capacitors

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors is studied. The method is generalized to infinite Simple Cubic (SC) lattice. We make use of the superposition principle and the symmetry of the infinite gridComment: 16 pages, 5 figures, 2 table

Investigation of transdermal permeation of atorvastatinloaded microemulsions

Purpose: To develop microemulsions containing atorvastatin for transdermal application, which will improve the bioavailability and reduce the side effects associated with the oral administration of atorvastatin.Methods: Atorvastatin-loaded microemulsions (MEs) were developed using tween 80 as a nonionic surfactant, isopropyl myristate, polyethylene glycol 400 and dimethyl sulfoxide. Their droplets’ size, and rheological properties were estimated, with the diffusion through the rat’s skin being evaluated using Franz diffusion cells. Furthermore, the in vivo transdermal and oral bioavailability, as well as the toxicity of formulation, were assessed in rats.Results: The results showed that the MEs have a droplet size lower than 100 nm and low Newtonian viscosity. In addition, a flux rate of atorvastatin as high as 10.078 μg/cm2.h was achieved after the loading of the MEs. The in vivo transdermal application maintained a steady state concentration of 1.02μg/mL for 48 h, in comparison to a maximum concentration of 7.7 μg/mL after 2.74 h following oral administration at the same dosing level. Moreover, the transdermally treated rats did not elicit skin irritation.Conclusion: The developed atorvastatin MEs for transdermal application delivers the drug to achieve a controlled plasma level, as well as reduce dosing frequency and toxicity in rats when compared to oral administration. Therefore, the formulation has a potential for development for use in humans

Uniform tiling with electrical resistors

The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagom\'e, the diced and the decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.Comment: 22 pages, 14 figure