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Distribution of innovations

For the account of influence of an environment interesting comparison of processes of distribution of an innovation with physical process of diffusion of molecules is represented.

Diffusion is understood caused by chaotic movement of molecules as process of gradual mutual penetration of two substances adjoining with one another [165, with.

367]. The diffusion phenomenon finds out itself everywhere, it has the important displays in the nature. Diffuzionnymi processes usually name processes of spontaneous redistribution of substance in the environment by dissipatsii or its directed carrying over under the influence of a gradient of any potential, and in the elementary case, a gradient of concentration [166]. In the systems including diverse particles, diffusion is shown in aspiration to alignment of local potential differences. It is necessary to notice, that generally carrying over diffundirujushchih particles can be caused not only heterogeneity of distributions of concentration, but also heterogeneity of fields of other physical sizes, for example, by a difference of temperatures.

The first quantitative description of processes of diffusion has been given by physicist A.E.Fick in 1855. The analogy has been put in a basis of this theory between
Processes of carrying over in liquid solutions and heat at the expense of the heat conductivity, defined equation Fure. Fick's laws widely use not only for the description of process of diffusion of molecules, but also for modelling of spatial processes of distribution of viruses [120], evolution of minieconomic institutes [167], processes of technological evolution [168], for definition of factor of distribution of innovations in the market [11] etc.

Leading problem of the analytical theory of diffusion is definition and studying of existential change of such physical size, as concentration Cu = f (x, y, t), where h, at - spatial co-ordinates; t - time. The laws operating existential development of concentration, are called Fick's as laws [166].

Under density of a stream of molecules Jпонимают the relation of number of molecules dN, transferred in time dt, to the area dS:

Fick's first law: Diffuzionnyj the stream for lack of external effects is proportional to its concentration [166].

Let's admit for a linear case concentration it is changed in an axis direction h, and in planes, perpendicular to a diffusion direction it is constant. Then the elementary expression for a linear case looks like:

Where J - it is stream density diffundirujushchego substances;

D - Proportionality factor, or diffusion factor;

C - concentration, place and time function: C = f (h, t).

Dimension for molecular diffusion:

Diffusion factor - a constant depending on properties of environment, by nature diffundirujushchego substances and from conditions at which are environment and diffundirujushchee substance. The sign a minus indicates that a substance stream
It is directed towards concentration reduction.

Thereof in the closed system there is a tendency to disappearance of concentration gradients.

Fick's second law connects spatial and time changes of concentration:

The law considers change of a stream of molecules in the course of diffusion and describes such change of the general concentration diffundirujushchego substances in each point of environment, thus, taking into consideration nestatsionarnost a stream. Thus speed of accumulation diffundirujushchego substances in the given volume is a difference between entering and leaving streams for individual time. The more strongly significances of potentials in different parts of system, the more size diffuzionnyh streams differ.

Used analogy for an explanation of behaviour of an innovation from the point of view of molecular distribution: innovations, as well as molecules, extend in the market from high potential in an index point to lower, will not reach yet certain levels. Unlike the considered models in paragraph 1.3, operating in indirect parametres, in the presented model the accent is done not on the influence made on behaviour of the market (advertising, mutual relation between buyers etc.), and on interaction between innovations in the market.

In the environment there are innovations, name their "charged" molecules, and becoming outdated products (services, technologies etc.) as which we will name as a background. If to apply by Wednesday a certain force which would move innovations from the manufacturer to consumers for lack of a background the innovation would extend in regular intervals, yet has not reached all consumers. But the availability of a background changes business: speed of distribution of an innovation increases until faces other substances and does not lose the impulse. As a result the innovation is compelled to move on a broken way, i.e. to drift with the average speed proportional to a gradient of a field.

Unlike work [11] in which application of laws of Fick to modelling of process of distribution of innovations is justified, it is offered to use as motive power a difference between a supply and demand (a technological push), as causes a potential difference. A difference between a supply and demand, and also a condition of environment will influence speed of process of distribution.

The basic operated concepts of models of distribution of molecules and innovations are resulted in table 2.2.

Table 2.2 - the Parity of concepts between models of distribution of molecules and innovations

The name Molecules Innovations Obozn.
Environment Environment in which molecules extend: gas, a liquid The market on which extend an innovation
Background Molecules of other grade Other innovations or the becoming outdated goods with similar idea TO
Diffundirujushchee

Substance

The investigated substance extending in the environment under the influence of a potential difference Innovative product, service or process, units. And
Motive power Potential difference, usually speak about concentration Difference between a supply and demand And - and U +
Concentration The relation of quantity of substance to volume, for example, mol/l The relation of quantity of innovations to market volume, for example, the relation of quantity of the sold innovative goods to prospective volume of the market WITH
Diffusion factor Characterises speed diffuzionnogo movings of investigated substance. It is defined by properties of environment and type diffundirujushchih particles Shows speed of distribution of an innovation. Depends on properties of the market and characteristics of the innovation D

Then it is possible to express mathematical model of distribution of innovations in the form of following laws.

The first law (analogy of the first law of Fick): Diffuzionnyj the stream for lack of external effects is proportional to its concentration.

It is possible to express the law as follows:

Where Ju - it is density of a stream of extended innovations;

D - proportionality factor, or diffusion factor - a constant depending on properties of environment and the nature of an innovation;

Cu - Concentration, place and time function: Cu = f (x, t), a difference between a supply and demand.

Density of a stream of innovations Juможно to express, as the relation of a stream of innovations dU, accepted in time dt, to a market definite volume dEu:

As a matter of fact, the first law allows to understand, that as the stream of innovations aspires to level difference of a difference of a supply and demand, the diffusion factor (depending on Wednesday) is a measure of speed from which the system is capable to level this difference under beforehand set conditions. The less than competing innovations and less their influence, the passes distribution more fast.

The second law connecting spatial and time changes of concentration, is expressed as follows:

Where x - distance of advancement of an innovation; the parametre which is responsible for spatial distribution of an innovation.

The law considers change of a stream of innovations in the course of diffusion and describes such change of the general concentration diffundirujushchego substances in each point of environment, taking into consideration nestatsionarnost a stream. Thus speed of accumulation diffundirujushchego substances in the given volume is
Difference between entering and leaving streams for individual time. The more strongly significances of potentials in different parts of system, the more size diffuzionnyh streams differ.

Development of comparison of distribution of innovations with the physical phenomenon of diffusion has promoted deeper comprehension of law of the given distribution, introduction of mathematical calculations and on their basis to working out of a management method by distribution of innovations.

2.2.2

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A source: TSvetkova Hope Andreevna. MODELS And the MANAGEMENT METHOD PROCESS of DISTRIBUTION of INNOVATIONS With allowance for THEIR MUTUAL INFLUENCE In SOCIAL AND ECONOMIC SYSTEMS. The DISSERTATION on competition of a scientific degree of a Cand.Tech.Sci. St.-Petersburg - 2018. 2018

More on topic Distribution of innovations:

  1. 1.3 Mathematical models of distribution of innovations
  2. Chapter 3 Management of process of distribution of innovations
  3. Mathematical model of distribution of innovations
  4. Chapter 2 Mutual influence of innovations in the course of their distribution
  5. the Korpuskuljarno-wave approach to the description of process of distribution of innovations
  6. TSvetkova Hope Andreevna. MODELS And the MANAGEMENT METHOD PROCESS of DISTRIBUTION of INNOVATIONS With allowance for THEIR MUTUAL INFLUENCE In SOCIAL AND ECONOMIC SYSTEMS. The DISSERTATION on competition of a scientific degree of a Cand.Tech.Sci. St.-Petersburg - 2018, 2018
  7. Ekosistema innovations
  8. Interaction of innovations
  9. Strategy of introduction of innovations
  10. 4. Strategy of innovations
  11. 2. A principle of continuous innovations.
  12. 3.4. An estimation of possible risks at financing of innovations
  13. 1.1. Concept of innovations and a role of a bank of commerce
  14. the Consequence of the theorem of existence of mutual influence of innovations
  15. the analysis and synthesis of actual creative toolkit on geneyoratsii and to development of innovations: design thinking, TRIZ and lateralnoe myshyolenie
  16. 6.1. Behaviour серы6.1.1. Sulphur distribution between fazamn. The Operational experience of installation ROMELT has shown, that sulphur distribution between fusion products essentially differs from a traditional regenerative fusion in a blast furnace: Products fusion
  17. 1.2. The organisations of competitive production with use of technological innovations.
  18. the Organization of competitive production with use of technological innovations.
  19. the Theorem of existence of mutual influence of innovations