_{1}

The deterministic description of a wave of solution particle of efavirenz is given. Simulated pharmacokinetic data points from patients on efavirenz are used. The one dimensional wave equation is used to infer on transfer of vibrations due to tension between solution particles. The work investigates movement using wave analogy, but in a different variable space. Two important movement fluxes of a wave are derived an attracting one identified as tension conductivity and a dispersing one identified as tension diffusivity. The Wave Equation can be used to describe another spin-off movement flux formed induced by vibrations in solution particle.

There is a rich history of quantum mechanics that investigates wave-particle duality using light [

This work derives characterisation of a wave and shows it as a spin-off movement flux that is derived from tension in the vibrations of the solution particle. It is described as a spin-off of a solution particle or the pilot wave [

In addition, this work shows that a wave is a system with four primary movement components of flux. The total flux at any given concentration is zero. The system formed is similar to that obtained for the one that facilitates exchange of concentration through gradient [

Simulated projected data on secondary saturation movement, time and concentration was obtained from pharmacokinetic projections made on patients on 600 mg dose of efavirenz considered in Nemaura (2015, 2016). Partial and Ordinary Differential equations are used in the development of models that characterizes wave motion. A statistical Package R, is used to develop nonlinear regression models.

Derivation of Advection Kinetic Flow for the Secondary Saturation Movement Due to TensionConsider

tension advective conductivity flux of solution particle

between

In a homogenous mix,

[tension advective conductivity flux in the solvent of a solute of

Consider a small element of the string (bridge) between the two concentration points

Let

The total vertical tension advective flux acting on the element is

where

and

From Equations (1)-(5) and the approximation formulas for

The concentration-time amount of form movement due to tension in the solution

particle bridge is

place

where,

Thus,

At the limit

The following result is immediate,

where,

is the secondary saturation tension advective conductivity flux

where,

The terms,

are secondary saturation tension base-advection diffusivity flux

turation tension advection diffusivity

rest tension advection conductivity flux

The following relation from Equations (10) and (11) is established between tension advection conductivity and diffusivity fluxes,

where

It is important to note that

We consider the secondary saturation

where,

Following from Equation (13), Equation (10) assume the form of,

and Equation (11) becomes,

The following conditions holds for secondary saturation tension advective diffusivity

Parameters | Estimate | Std Error | t value | |
---|---|---|---|---|

Parameters | Estimate | Std Error | t value | |
---|---|---|---|---|

u | 0.801936 | 0.005934 | 135.1 | |

v | 5.624198 | 0.126684 | 44.4 |

It is noted that for

The reference spin-off advective flux is investigated and the constituent behaviour is suggested by Equation (16) (

Parameters | Estimate | Std Error | t value | |
---|---|---|---|---|

The characterisation of the four main spin-off diffusivity flux entities are shown and magnitudes of effects (

where,

A wave in this work has been shown to be a spin-off movement flux of a solution particle. It also has the same component characterisation as a solution particle at primary level. It consists of the advective, passive, saturation and convective components [

movement flux components [

Considering a different unique space, we obtain similar characterisation of flux of a wave to that of gradient-driven diffusion. These two are system flux movements in time. A conclusion is reached that these two forms are characterised similar pattern of move- ment [

The author would like to thank the following; C. Nhachi, C. Masimirembwa, and G. Kadzirange, AIBST and The College of Health Sciences, University of Zimbabwe.

Nemaura, T. (2016) The Advection Wave-in-Secondary Saturation Movement Equation and Its Application to Concentration Tension-Driven Saturation Kinetic Flow. Journal of Applied Mathematics and Physics, 4, 2126-2134. http://dx.doi.org/10.4236/jamp.2016.412210