**4.3. Applications in the field of multiple pollution**

The natural environment can be polluted chemically, electromagnetically, thermally, nucle‐ arly, etc. To date, the individual maximum/allowable concentrations of various pollutants affecting the environment and the living organisms have been identified [25–36]. The crucial issue lies in determining when the critical state is reached in case two or several pollutants act simultaneously and/or successively.

Actually, one has to deal with the superposition of pollutant action, or the cumulation of their action and sometimes with the superposition and cumulation of their action. The problem is solved relatively simply by using PCE, according to which the total participation of pollutant action is equal to the sum of their individual participations. By analogy with Eq. (4) we may write:

$$P\_T\left(t\right) = \sum\_{i} P\_i \left[ \left( c\_{p,i} \right) : t\_i \right],\tag{35}$$

where *cp*,*<sup>i</sup>* is the pollutant concentration *i* acting over time *ti* .

For the sake of generality, one allows that the relation between the pollutant and its effect is a power law, similar to law (6), namely:

$$\mathcal{L}\_{p,l}\left(t\right) = \mathcal{M}\_{c\_{p,l}} \cdot e\_{p,l}^{k\_{p,l}}\left(t\right) \tag{36}$$

where *Mcp*,*<sup>i</sup>* şi *k <sup>p</sup>*,*<sup>i</sup>* are constants while *ep*,*<sup>i</sup>* (*t*) is the effect of the pollutant upon the natural environment, living organisms, plants, etc.

By analogy with the general relation (12) one gets the total participation caused by pollutant action:

$$P\_T\left(c\_p\right) = \sum \left[\frac{c\_{p,i}\left(t\right)}{\left(c\_{p,i}\right)\_{cr}}\right]^{a\_{p,i}+1} \tag{37}$$

where (*cp*,*<sup>i</sup>* )*cr* is the critical concentration of the pollutant *i*, while α*p*,*<sup>i</sup>* =1 / *k <sup>p</sup>*,*<sup>i</sup>* . The critical or allowable value of the concentration is specific to the biophysical factor that is being calculated (water, air, earth, some plant, some living organism...), as shown in the examples listed in Tables 2 and 3.

#### The Principle of Critical Energy as a Transdisciplinary Principle with Interdisciplinary Applications http://dx.doi.org/10.5772/64914 15


Other applications of the PCE have been summarized in [1, 2, 12], such as the superposition of mechanical and electrical effects, the superposition of the mechanical loads and magnetic

Proceedings of the International Conference on Interdisciplinary Studies (ICIS 2016) - Interdisciplinarity and Creativity

The natural environment can be polluted chemically, electromagnetically, thermally, nucle‐ arly, etc. To date, the individual maximum/allowable concentrations of various pollutants affecting the environment and the living organisms have been identified [25–36]. The crucial issue lies in determining when the critical state is reached in case two or several pollutants act

Actually, one has to deal with the superposition of pollutant action, or the cumulation of their action and sometimes with the superposition and cumulation of their action. The problem is solved relatively simply by using PCE, according to which the total participation of pollutant action is equal to the sum of their individual participations. By analogy with Eq. (4) we may

> ( ) ( , ) ;, *<sup>T</sup> i pi i i*

For the sake of generality, one allows that the relation between the pollutant and its effect is a

*p i*

( ) ( ) , , , ,

*p i k*

By analogy with the general relation (12) one gets the total participation caused by pollutant

, α 1

+

*p i*

( )

*c*

is the critical concentration of the pollutant *i*, while α*p*,*<sup>i</sup>* =1 / *k <sup>p</sup>*,*<sup>i</sup>*

allowable value of the concentration is specific to the biophysical factor that is being calculated (water, air, earth, some plant, some living organism...), as shown in the examples listed in

*p i cr*

, ,

*c t*

é ù = ê ú ê ú ë û

*p i*

( ) ( )

*T p*

*P c*

is the pollutant concentration *i* acting over time *ti*

are constants while *ep*,*<sup>i</sup>*

*Pt P c t* <sup>=</sup> é ù å ë û (35)

*p i c pi ct M e t* = × (36)

(*t*) is the effect of the pollutant upon the natural

å (37)

. The critical or

.

field by shells/buckling, the superposition of effects in thermoelectromagnetism, etc.

**4.3. Applications in the field of multiple pollution**

simultaneously and/or successively.

in the Knowledge Society

14

power law, similar to law (6), namely:

environment, living organisms, plants, etc.

şi *k <sup>p</sup>*,*<sup>i</sup>*

write:

where *cp*,*<sup>i</sup>*

where *Mcp*,*<sup>i</sup>*

action:

where (*cp*,*<sup>i</sup>*

Tables 2 and 3.

)*cr*

**Table 2.** Maximum allowable concentration for environment factors in air (extracted with permission from [27])


**Table 3.** Maximum allowable concentration for environment factors in water (extracted with permission from [29])

The total participation thus calculated is compared to the critical participation,

$$P\_{cr}\left(t\right) = 1 - D\_T\left(-t\right) \tag{38}$$

where *DT* (−*t*) previously produced deterioration (−*t*) upon the biophysical factor.

If *PT* (*cp*) <*Pcr* (*t*) the status of the biophysical factor is subcritical, while if *PT* (*cp*) ≥*Pcr* (*t*) —the state is critical or supercritical.

Sometimes the interaction of pollutants from a mixture produces a change in their behaviour, as they mutually enhance their obnoxious effects. One can get a positive synergistic effect, meaning that the effect of the mixture is greater than the sum of the individual effects of the pollutants [14]. Positive synergism does not mean that one can get more out of 'something plus something else', but it means that the behaviour of that 'something' changes in the presence of the 'something else' which makes the whole effect be greater than the sum of the composing effects!
