# 3.2. Unified model of the generalized physical process

V. I. Melnikov

Specific character of physics as a science about the most general laws of nature is the availability of a significant amount of independent and weakly coupled branches. In spite of the fact that physics is the exact science, each rule and law of which demand a clear and reliable experimental justification, the inevitable limitation and approximateness of adopted initial concepts of each branch do not allow one to construct an integral monolithic noncontradictory structure of the whole physics. The process of harmonization of different branches depends on the level of the development of the experimental base and the capabilities of theoretical reduction and generalization of boundless sets of experimental data, including a regularity of interpretation of the results obtained.

In this situation the ТCS by virtue of its generality can play the role of a link between different branches of physics. The capabilities of the ТCS as a methodological tool can be exhibited most effectively at considering a number of debatable problems of modern physics with the corresponding adaptation of the rules of the theory to specific character of the modern physical picture of the universe.

For the indicated adaptation we synthesize a physical analog of the ТCS on the basis of the generalization of quite representative body of theoretical and experimental data of different branches of physics.

The analysis of the structure of a number of basic physical laws and corresponding mathematical models from different branches of physics (mechanics, thermodynamics, acoustics, electromagnetism, etc.) as well as the comparison of their physical nature show essential similarity of these relations both in the formal structural notation and in their actual physical nature.

Some results of such an analysis are presented in Table 2, which contains information about different physical processes, the quantities and parameters describing these processes, and the relations connecting them.

The upper half of Table 2 lists in the vertical direction the well-studied physical processes from different branches of physics, including mechanical motion, fluid and gas flow, heat transfer, direct current, diffusion, and acoustic flow.

Main physical quantities or their complexes describing these processes are presented to the right of each of these processes. These physical quantities and the complexes of different processes are arranged with respect to one another in such a manner that in the vertical direction they form groups of parameters with identical functions: initiation, deceleration, accumulation, change, etc. The first group unites the parameters which represent the moving active component of all processes (i.e. the "difference" of force system known as a resultant, pressure difference, potential difference, concentration difference, temperature difference, i.e. the difference of any like parameters of the physical condition of bodies). The second group embraces the parameters characterizing the intensity of processes (*I*, *v*, *Q*).

The third group connects the parameters which limit (decelerate) the process (viscosity, resistance, friction, etc.). The fourth group includes the parameters which reflect the quantitative result of the process flow (length, volume, heat quantity, amount of matter, etc.). The fifth group reflects the energy level of the process, its power. The sixth group unites the parameters of the energetic efficiency of the process (it shows the total amount of energy changes which took place in the system as well as the work accomplished during the process).

Each of these groups, in view of the functional similarity of their components, can be considered as a whole, and it can be denoted by a unified generalized parameter. The naming and notation of generalized parameters for each group are presented in the head of Table 3. They are *U*,* R*,* I*,* L*,* N*,* W*. The last two parameters, power and energy, have already been used as generalized parameters valid for any process independently of its nature. One more generalized parameter, which is implicitly present in the listed processes, is time .

Thus, it is possible to assume that any physical process can be described in terms of seven generalized parameters *U*,* R*,* I*,* t*,* L*,* N*,* W*. Three well-known and widely used parameters can be supplemented with four other parameters: *U*,* R*,* I*,* L*.

The presented system of generalized parameters allows one to speak about the "existence" of some generalized physical process corresponding to them.

Let us consider in more detail the conditions of its origination, regularities of behaviour and description, and the causes and conditions of process termination.

The analysis of the presented partial and generalized processes allows one to extract the following general features.

1. The general criterion of the existence of any physical process is the availability of two or more different physical objects (system of objects), including different positions of objects in space.

2. The practical criterion of the existence of interaction process can also be the appearance of new experimentally discovered features, characteristics or parameters at least for one of the objects of the system in contrast to its isolated state (position).

3. The objects and processes participating in interaction can be of any physical nature: single-type as well as multiple-type (thermocouple, heat expansion, electroheating, light pressure, etc.).

4. Any physical process can include simultaneously, sequentially, or in any combination a set of multidirectional and more small-sized (partial) processes of different physical nature (heat exchanging, acoustic, diffusive, mechanical, electromagnetic, and others), on which the presented conditions and relationships are applied to as well.

5. The objects can be both with lamped and with distributed parameters possessing the features of integrity and without them.

6. Any process means a mutual change of parameters of the objects participating in the process (i.e. interaction), energy and (or) matter transmission between interacting objects, i.e. the existence of some material flow between them.

7. Any process is characterized by a number of required basic parameters relating to active (moving) and passive (stabilizing) parts.

Table 3. Structural scheme of partial and generalized physical processes

Processes | Partial and generalized parameters | |||||

Level, U | Resistance, R | Intensity, I | Quantity, L | Power, N | Energy, W | |

Uniform rectilinear motion | F | F/v | v | L | Fv | FL |

Motion of fluid flow or gas | ΔP | ΔP/Q | Q | V | ΔPQ | ΔPV |

Heat transfer | ΔТ | Δl_{T} /λS_{T} |
Q_{T}/t |
Q_{T} |
k_{T} ΔTQ_{T} /t |
K_{T} ΔTQ_{T} |

Diffusion | ΔС | Δl_{d} /DS_{d} |
M_{d} /t |
M_{d} |
k_{d} ΔCM_{d} /t |
k_{d}CM_{d} |

Direct electric current | Δφ | Δφ /I_{e} |
I_{e} |
I_{e}t |
Δφ I_{e} |
Δφ I_{e} t |

Electrostatic interaction (q) | 1 **q | ε_{0}r^{2} |
E | E t | k_{эс} E q |
k_{эс} E q t |

Electrostatic interaction (q_{1} q_{2}) |
q_{1}q_{2} |
ε_{0}r^{2} |
F_{эс} |
F_{эс}t |
K_{эс}F_{эс}q_{1}q_{2} |
K_{эс}F_{эс}q_{1}q_{2}t |

Magnetostatic interaction (J_{1}J_{2}) |
J_{1}J_{2} |
μ_{0}r^{2} |
F_{M} |
F_{M}t |
k_{M}F_{M}J_{1}J_{2} |
k_{M}F_{M}J_{1}J_{2}t |

Interaction of mass with vacuum (m) | 1** m | r^{2}/G |
E_{m} |
E_{m} t |
k_{m} E_{m} m |
k_{m} E_{m} m t |

Gravitational interaction (m_{1}m_{2}) |
m_{1}m_{2} |
r^{2} /G |
F_{гр} |
F_{гр} t |
k_{гр} F_{гр} m_{1}m_{2} |
k_{гр} F_{гр} m_{1}m_{2} t |

Inertial interaction | m^{2} |
m /a (m /a G)* | F_{ИН} |
F_{ИН} t |
k_{ИН}F_{ИН} am^{2} |
k_{ИН} F_{ИН} am^{2} t |

Generalized process | U | U / I | I | L | U I | U I t |

* outside of SI system.

** unit charge and mass.

Conventional designations adopted in Table :

*Generalized*: *I* – intensity; *U *- level; *L *- quantity; *R* – resistance; *N* – power; *W* – energy; *t *- time.

*Partial*: *v* – velocity of motion; *Q*- output of hydropneumatic flow; Δ*Р* – differential pressure in hydropneumatic line; *V* – volume; *I _{e}* – current;

*U*– potential of the electric circuit, field;

*E*– electric field strength;

*q*– electric charge;

*Q*– quantity of heat; Δ

_{T}*Т*– temperature difference;

*М*– mass of diffusing matter;

_{d}*С*– concentration of matter; Δ

_{d}*l*– path length of heat or matter transfer;

_{i}*λ*– thermal conductivity;

*S*– cross-sectional area of heat or matter flow;

_{i}*D*– diffusion coefficient;

*F*– gravitational force;

_{гр}*m*– mass of matter;

*Em*– tension of gravitational field;

*G*– gravitational constant;

*F*– force of electrostatic attraction-repulsion;

_{эс}*ε*

_{0}– dielectric permeability of vacuum;

*r*– distance between masses, between charges, between mass and field point;

*F*– force of magnetic attraction-repulsion;

_{M}*J*– magnetization;

*F*– inertial force;

_{ИН}*a*– tangential acceleration of mechanical motion;

*k*– dimensional coefficients of proportionality.

_{i}8. The active part is determined by two parameters: the level U (F, ΔT, ΔP, Δφ, ΔC etc.) and the intensity of interaction I (v, I, Q etc.) forming in the aggregate the parameter of power N.

9. The passive part is determined by one basic parameter – the resistance of different physical nature (*R _{e}, F/u, ΔP/Q, S_{a}/I_{a}, l_{T}/ΔS_{T}*), thus R = U/I.

10. The intensity and power accumulate in time and form basic parameters of quantity L and energy W, respectively.

11. The parameter of a level exists up to the beginning of interaction and during interaction process. The parameter of intensity appears only after the beginning of interaction, and it is conserved during the whole time of process flow.

12. The basic parameters of processes in definite relationship:

I = U / R; | |

N = I U; | |

L = I t; | |

W = I U t; | (17) |

where *t* is time.

13. The process can exist only if there are different (with respect to one another) levels of interacting objects.

14. The interaction of objects is directed to rendezvous of their relative levels, i.e. their mutual, counter change.

15. The set of all objects participating in the given process represents a closed system in which the conservation laws are satisfied, including energy conservation.

16. In the course of level equalization, any process going on in a closed system is slowed down in time until it terminates completely .

17. Physical processes of any kind in all closed systems are going on in the same way, i.e. all closed systems are equivalent.

18. Any physical process with the help of the above-listed basic parameters can be represented in the form of the corresponding mathematical model, in particular, in the form of the equation reflecting definite equilibrium of separate physical quantities or their complexes and, therefore, the closure of a system of interacting objects.

19. The degree of fulfillment of presented conditions depends on the degree of the closure of a system of interacting objects, the complete fulfillment is possible only in an absolutely closed system (АCS).

Generalized parameters of generalized (unitized) process presented in the lower line of Table 3 are not expressed in specific dimensional physical quantities of the adopted system of measurements. They are of methodological value. New parameters of processes were obtained with their help (they are underlined), for example, parameters of resistance for the majority of the considered processes (except for uniform rectilinear motion, flow of fluid and gas, direct electric current).

The set of principles, rules, relationships and conditions presented above can be considered as some *unified model of generalized physical process*, which can be used for investigation of new unstudied processes for interpretation of known phenomena as unknowns processes as well as for obtaining new quantitative relations for different physical quantities. As a whole, they can be used as a methodological tool for the solution of various physical problems.

Usage of the presented model allows one to establish the direction of investigations of new processes or phenomena as well as to establish the kind, nomenclature, and quantitative characteristics and parameters of the object under investigation.

This approach can be formulated in the most general form as follows. It is necessary "to impose (to project)" the model on known fragments of the object (process) under investigation, to supplement the model by missing elements in correspondence with its structure, and to obtain its full description in the form of corresponding new concepts of physical quantities and their relationships.

The approximate order of model application for determination and investigation of new or known physical process can look like this.

1. On condition 15 and with allowance for requirements 3, 5 we establish the availability of the system and physical objects included in it.

2. On conditions 1 and 2 and with allowance for 4 we establish the existence of the process of interaction.

3. On condition 11 we establish the nomenclature of the parameters of interaction level and intensity.

4. On condition 12 we establish the value of level and intensity parameters (after the selection of units, techniques, and tools of measurements).

5. On condition 13 we check the availability (existence) of the process of interaction.

6. On relationships 9 and 12 with allowance for 8 and 10 we determine the physical nature and value of the derivative parameters of resistance, quantity, power and energy of the process.

7. On condition 6 and with allowance for 14 and 16 we establish the nature (value) of changes in the parameters of physical objects during interaction. We also establish the corresponding relationships of parameters between themselves and in time.

8. Under requirements 15 and with allowance for 19 we check the fulfillment of the energy conservation law and the condition of system closure.

9. We develop a mathematical model of process and establish thee relationship with the adopted system of measurements of physical quantities. We use different coefficients of conformity or introduce new physical quantities, if necessary.

10. On conditions 16 and 19 we establish final parameters of the process, including the total time of interaction and the final value of its parameters.

Depending on a degree of maturity of a problem it is possible to use all stages or only their part. The presented technique of application of the developed model indicates only the standard structure of a closed system and the principal possibility of detection of the generalized process. It says nothing about possible numerical values of the parameters of the process. In some cases they can be not detectable at the given stage of the experiment development, though they basically should exist. In other cases they can reach large values, but be interpreted completely in another sense. The problem of model in the first case is the logical linkage of a part of the known facts with suspected ones. In the second case with the help of model it is possible to obtain correct explanation of the known facts and on this basis to reduce them to a unified standard closed system. Therefore, in each particular case it is necessary to conduct additional investigation for the solution of the problem.

One of the important consequences of the model presented above is the conclusion that *any physical body is in the state of interaction with environment and that any two or more physical bodies also in a state of interaction between each other*.