CC BY
15DOI: 10.24412/cl-37100-2023-12-90-98
A. Bushuev
Trends of physical effects
ABSTRACT
A method for finding an invariant, i.e., the same property for effects of different physical and geometric nature, based on the theory of the dimension of physical quantities in the Bartini LT-basis, is proposed. The invariant is determined by the transfer matrix of proportionality between the input and output matrices of the effect. Effects with the same invariant form trends in the development of spatial, temporal and Su-field resources. One example is the well-known trend "point-line-surface-volume". According to the law of folding-unfolding, the trends of effects are collapsed and expanded into trends of invariants. For invariant trends, equivalent electrical analogs are proposed that allow numerical comparison of effects by degree of complexity. The methodology is supposed to be used for the classification of effects by invariant properties, for the synthesis of the operating physical principle, as well as in the process of studying inventive physics in TRIZ.
Keywords: invariant of the physical effect, trends of effects and invariants, numerical estimation of the complexity of the effect
FOREWORD
In the theory of inventive problem solving many basic notions are considered as a process, i.e., as a sequence of certain events, objects, which precondition reference points of direction of development. Such sequences are called evolution lines [1]. Historically speaking, the first line of development can be understood as an ARIZ structure, which is at bottom a graph with summits, consisting of known contradictions and with directed edges, pointing out the order of algorithm. In the fullest sense the graphs are presented in the trends of technical systems evolution. [2, 3]. Each peak of these graphs possesses a certain feature, which is common with all peaks. Let us call this common feature an invariant. For example, in the ARIZ line an invariant is the fact that each peak of the graph is a contradiction, in the trend for trimming and deployment of technical systems according to the line 1-2-many each peak has an invariant -certain numerical value. The second important feature of the lines: each peak of the graph, preserving an invariant is a transformer of an input feature into an output one. In the famous abbreviation MATHEM an invariant is the notion of a field as an action of one substance upon another, while a feature of transforming is the transformation of the field of one kind of energy into a field of another kind of energy. Consequently, the peaks in the MATHEM graph are the physical effects, while the entire graph could be called the line of evolution of kinds of physical effects. For particular physical effects the name of the kind becomes an invariant. According to this invariant the effects are classified in indices of physical effects [4, 5] into mechanical, thermal, electrical and magnetic.
It is proposed to conduct further search for invariants already inside the effects listed in [6] with the aid of criteria of similarity. As it is known, «criterion of similarity is a dimensionless value, composed of dimensional physical parameters, which determine the analyzed physical phenomenon». With physical effects the dimensional parameters will be understood as input and output values of effect. If with two effects the criterion of similarity is the same, the effects are also similar, i.e., the invariants in reference to criterion of similarity. Examples of criteria of similarity are the Reynolds number in hydro- and gas dynamic, Prandtl number in heat transfer processes, etc. [7]
However, criteria of similarity are characterized by disadvantages, which are associated with the loss of information regarding the dimensionality of physical values. At the same time inventive problem solving has accumulated certain experience in using theory of dimensionality. In [8] it is proposed to use theory of dimensionality for obtainment of high-quality mathematical model of engineering systems. A couple of contradictory parameters is identified as part of this model and then paramet-rical method is used for resolving contradictions. In the work [9] a structural model of the system in the form of a graph is created based on expert evaluation of cause/effect connections. System of dimensionality in the basis of MLT (mass, length, time) are used for checking the authenticity of structural model and for finding the peaks of localizing physical contradictions, i.e., the violation of cause/effect connections. The report [10] is focused at the research of known trend «Point-Line-PlaneVolume», which is related to the trend of increasing coordination. The peaks of the graph within the trend form spatial resources, while the invariant is the length L - main unit within the system of dimensions of physical units. In this case the peaks can be set up with the aid of their dimensionalities Ln, where n=0,1,2,3, while the trend can be regarded as a chain of geometrical effects for transforming the space of one dimensionality into a space of another dimensionality.
This work is focused at the methodology for creating trends of physical and physical-and-geometrical effects for the purpose of obtaining the general regularities of evolution of effects and technical devices, which are used for implementing them. The effect is understood here as a transformation of each measurable physical or geometrical value into another similar value.
METHODOLOGY FOR SEARCH OF TRENDS OF EFFECTS IN LT-BASIS
The search is based on the method of analogies in defining the trends of Su-Field resources in LT-basis of the B artini system of kinematic values [11]. For example, the trend of «Point-Line-Plane-Volume» is located according to its geometric dimensions L0T0^L1T0^ L2T0^ L3T0. In Fig. 1 this trend is shown by red arrows.
D. I? xc Ll Ia L<5 1}
L'] L°Ts Surface power LT-i Power
r-4 L'lT* L°T Specific gravity, pressure gradient Pressure Surface tension Force Farce momentum, energy
rd i-ir-3 £0r-3 Current density bliCtro-magnetic field strength Current, loss mass Motion quantity, impulse №
r*a liT2 Mass density, angular accelerator Magnetic displacement f pccele ration Potential difference jb "Mass. quantity of magnetism or electricity Magnetic momentum Moment of inertia
r1 Volume charge density Frequency X Velocity r Two- dimensional abundance Loss volume L4T.i TFr*
j-0 Curvature G Cinnension-le s s consiarts #- L Length. • capacity self- induction »» Surface —- Volume of space l*Ta ¿Jj-0
T\ Conductivity Period, duration VTl L2Tl LAJ\
Fig. 1. Examples of dimensional and temporal trends and trends of Su-Field resources within the Bartini system of kinematic values
The trend is dimensional, its invariant L1T0 is located with respect to dimensionalities of adjacent cells at the trend: L3T0/L2T0=L2T0/L1T0=L1T0/ L0T0=L1T0, while the dimensionality of the output cell is divided into the dimensionality of the input cell. An example of a temporal trend is shown with blue arrows, its invariant is equal to L1T-2/L1T-1=L1T-1/L1T0= L0T-1.
The trends of Su-Field resources are located at the diagonals of Bartini table. For example, green arrows on the main diagonal line show the trend of L0T0^L1T-1^L2T-2^L3T-3 ^L4T-4^ L5T-5, reflecting the work of rotating electrical machine (Fig.2) on transforming mechanical energy into electric energy (generator) and back (motor). The invariant of the trend is equal to dimensionality of line speed [V]= L1T-1.
Fig. 2. Electrical machine and the trend of evolution of ideas concerning it
The trend enables to imagine the manifestation of a physical effect of electromagnetic induction, in which the law of Faraday is implemented. In fact the first stage is the angle u of pivoting (rotation) of a conductor in a magnetic field. The second stage is the idea that the rotation takes place at a linear speed of V. The next idea is the generation of difference of potentials U at the poles of the conductor. Further on, after short-circuiting of the conductor, electric current I is generated in it. The current possesses power action F. Force F, multiplied by linear speed V of rotation of conductor, yields power P, developed by induction machine.
The search for an invariant of trends of effects makes us formulate the task in the following way. Let us know the assigned input (x) and output (y) values of the effect, i.e., their dimensionality in the basis of LT [x]=LaT , [y]=LcT is known. Let us introduce matrices X and Y of input and output values respectively
Ho Tü4 Y=[
And we shall obtain a transfer matrix of W-effect
0
'pd
W = YX
■ H
0
rpd
] ]
(1)
La 01 _ rLc-a 0 1 = TLm 0 0 TbJ [ 0 Td - bj [0 xr
Transfer matrix shall be treated as an invariant, i.e., all effect, which have one and the same transfer matrix, are included with one trend. The trend of effects will be created in the following way.
• We select in Bartini table any trend of spatial, temporal or Su-field resources.
• We shall treat one of the values within a trend as the input action of the effect.
• Based on reference lists of physical effects and scientific literature we find the name of the effect and, consequently, output value as well.
• Based on the dimensionality of input and output we find an invariant - transfer matrix of W-effect.
• We move along the trend consequently by one cell to this and (or) to that side and find new input action by their dimensionalities in Bartini table.
• We multiply new input action by invariant W and find the yield of effect and thereby we determine its name.
Items 1 and 2 needn't be fulfilled, if some effect is already assigned, and we would like to create a trend, with which this effect is going to be included. EXAMPLE OF FINDING EFFECTS OF INDUCTIVE TREND
As one of the effects of the trend let us select direct piezoelectrical effect [5], in which the input action is the force F, applied to piezo-crystal, while the output is the electric charge Q, generated on plates (Fig.3c). We find transfer matrix W1
W = OF-1 = [L3 0 1 [L4 0 1_1 = [L_1 0 1 1 ^ [0 T - 2 ][0 T - 4j [0 T 2 j'
Let us move along Bartini table with respect to the cell of force L4T-4 by one cell to the right, i.e., i.e., we move along the trend of spatial resources. We get to the cell L5T-4, in which the energy and static temperature, measured in SI system in joules are located. However, at the same time this very cell contains the dimensionality of the moment of rotation Mrot., measured in SI system in newtons, multiplied by meter (1 joule =1 N-m). Let us consider the moment of rotation Mrot. to be the input action of the following element of trend. Physics and geometry of such transition has the following simple explanation. In piezoeffect the force F is applied to the point and acts along the straight line upon the piezo crystal. From the standpoint of fields, used in TRIZ, this action is similar to the mechanical field of pressure. The follwong effect, which is heretofore unknown, the input action is the moment Mrot., acting along circularly and being defined according to the known formula Mrot=F-£, where I is the arm of force. Therefore, this action could be related to the mechanical field of centrifugal forces.
Based on the assigned input and transfer matrix W1 of the trend we find the output value
wiM„t = [L- 1 T° ][05 T-4H0 T°-2j = M'
where M is a magnetic moment. In SI system the magnetic moment M is equal to the product of current I by area S of the circuit and has dimensionality of A-m2, however, in the system of CGS, at which the names of physical entities within the Bartini system are oriented, the magnetic moment has the dimensionality A-m-s ( M=I-S/C, where C is the light speed in m/s).
In the reference book [5] such input and output is characterized by Barnett effect. The effect shows the association between the atomic magnetic moments and mechanical moments and is contained in magnetizing of the bodies by rotating them under th conditions of absense of external magnetic field. This effect is implemented in ferromagnetics, like Cioffi iron, nickel, cobalt, permalloy (nickel-iron), transformer steel, armco iron, etc. In a specimen, which is rotating at a constant rotation speed ro around the unchangeable axis z (Fig. 3d), elementary small magnets of its material are regarded as sorts of gyroscopes, possessing mechanical moment of amount of movement and magnetic moment. The effect manifests itself on bodies with elongated geometrical shape and also reveals itself throughout the entire volume of a ferromagnetic. The resultant of a magnetic field is directed along the axis of rotation. It was discovered by Samuel Barnett in 1909. The physical effect is applied for research of nature and structure of ferromagnetic substances.
Fig. 3. Inductive trend of evolution of effects
We shall look for other effects of graph of trend, moving from the cell of force of L4T-4 to the left. Let us understand the input as a value with dimensionality L3T-4. In this case we shall obtain the output by multiplying by transfer matrix of effect.
L3 0 ] = [L2 0 ] (2) o T_4- [0 T" 2 - (2)
where E - difference of potentials or electromotive force (EMF), measured in the SI system in volts. The input value is superficial tension or rigidity. Physical effect of transforming these mechanical values into electric voltage or into EMF has not yet been found. Therefore, let us act in the following way: let us find an electric value with the dimensionality of assigned input H L3T-4. For this purpose, let us go
3 4 3 3
down from the cell L T- lower, to the cell L T-, where we find the electric current, measured in the SI system in amperes. A conclusion can be drawn there from that in the cell L3T-4 there is an electric value - rate of current changing in time dI/dt, where t is time. Consequently, the generation of EMF as a result of changing the current in the conductor is a manifestation of effect of self-induction, discovered by J.Henry in 1831. The value of EMF of self-induction generated in the coil with current (Fig.3c), could be found according to the law of electromagnetic induction of Faraday.
E = —Lr
= [■
0
0
T2
dl
-3T- (3)
where Lc is coil inductivity. The formula (3) written for dimensions of physical values completely coincides with the formula (2). Transfer matrix of the trend of effects in terms of dimensionality coincides with the inductiveness of the coil, therefore the trend is called inductive.
Let us find the next effect of the trend. Using the input of the effect we select pressure P with
••24
dimension L T- and multiply it by transfer matrix of the trend
WXP = [
-l
0
0
T2
L2 0
0 rp - 4 |
] [ 0 T- 2 ]■
0 T - 21
In Bartini table the corresponding cell contains a linear acceleration, which has dimensionality m/s in the system SI. Being oriented at the adjacent cell on the right, in which the dimension of the difference of potentials is expressed in volts, while the shift by one cell to the left means subdivision into meters, we obtain at the output of the effect a value of tension of electric field, measured in V/m. The electric strength of dielectrics, for example, disruption voltage Ud is measured in the same units. Effect of variation of electric strength of gasses depending upon pressure is known from physics [12] (Fr.Paschen's law, 1889) and moreover, its use is analyzed by G.S.Altshuller in [1] as part of solving the problem of lightning arrester in (Fig.3a) for the sake of protection of radiotelescope antennae. [13]. Physical-and-geometrical effects of inductive trend are quoted in Fig. 4 (marked with red arrows).
EXAMPLE OF IDENTIFYING THE EFFECTS OF TREND OF CONDUCTIVITY
Let us create a trend of effects based on temporary trend of input actions. Let us select the phenomenon of electroosmosis [5] as a source effect. Electroosmosis is the motion of fluid in a capillary under the action of applied EMF. The effect is assigned by the following mathematic expression
V =
Jfl]
4Ttr|f
where V is linear speed of the fluid, Z - is a zeta-potential, E is a potential of external field, S -cross-section of the capillary, n - viscosity of fluid, and I is the distance between electrodes.
Based on known dimensions of input E and output V we find the transfer matrix of the effect
W, = VE
- i = [L1 Lo
0 T_!
L2 0
0 1" =[L- 1 01
r- 2J [ 0 T 1 J"
Physical entity in this cell of Bartini table is called conductivity (however, in SI system this value has the dimension Ohm), therefore, the trend of effects will be called by us the trend of conductivity.
We move one step higher and get into the cell of voltage of electromagnetic field H. We find the outcome of effect
W,H
[
-l
0
0
T1
1 [ 1
TL2
0 T_ 3J LO T ■
where a is a linear acceleration.
Such effect could be related to electromagnetic acceleration of charged particles, at which the Lorenz force F, depending upon the voltage of electromagnetic field H acts upon a charged particle, for example, in a solenoid. With the mass m under the action of force F the particle acquires linear acceleration a = F/m. This effect is also used in electromagnetic weapons, in which a charged body, flying from the field, performs the killing action [14].
For the next effect of the trend the input action is the pressure P. We find the output value
TIT1 0 \L2 0 1 = TL1 01.
0 T _ 4- [0 T _ 3 ] , where j - density of flow or, as applied to the flow of charged particles, density of current, measured in SI system in A/m . The variation of density of current depending upon gas pressure is characteristic of gas discharge in electric vacuum devices [15]. At atmospheric pressure inside the glass bulb with electrodes there is no discharge, because even at high voltage the discharge cannot break through a gap between electrodes. When the gas is pumped out the pressure drops down and a breakdown in the form of an arc discharge - thin crimson rope (for air). At the further reduction of pressure, the arc discharge is transformed into a glow discharge, the current density grows and the discharge occupies the entire glass bulb. The effects of conductivity trend are presented in Fig. 4 with blue lines.
W,P
[
Fig. 4. Physical-and-geometrical effects of inductive trend (red arrows) And conductivity trend (blue arrows)
Trends for other effects could be created in a similar way.
BASIC RESULTS
Introduction of transfer matrix of the effect, which formally coincides (visually) with the matrices of physical values, enables to place the effects in the cells of the Bartini table. Several effects, which have got into one and the same cell, form a trend. Thus, all effects of the trend possess the same specific feature or an invariant. Bartini table of dimensions can be used as a means of classification, coding and storage of effects, which makes it easier to search for them for the purpose of solving inventive problems. Fig. 5 quotes a fragment of LT-table, in which the effects are placed under the serial numbers.
Fig.5. Fragment of LT-table of trends of effects
The following effects are included with the inductive trend with invariant W1: 5. 1.Barnett effect
3. Direct piezoelectric effect
4. Effect of self-induction,
5. Effect of variation of electrical strength of gasses depending upon pressure
6. The following effects are included with the trend of conductivity with invariant W1 :
7. 5.Effect of electroosmosis
6. Effect of electromagnetic acceleration
7. Effect of variation of current density in a gas discharge
8. Besides, the following effects are shown as an example of filling-in the table:
9. Radio metrical effect of manifestation of repulsion force between two surfaces in a rarefied gas, which have different temperature, input - temperature difference L5 T-4, output - force L4 T-4
10. Doppler effect, input - linear speed L1T-1, output - frequency L0 T-1
3 0
11. Mechanical-and-geometrical effect of slab rolling into a sheet, input - volume L T , out
2гтЮ
put - surface L T
12. Dorne effect (sedimentation), input - force of gravity (or centrifugal force) L4 T-4, output difference of potentials L2 T-2
13. Faraday's law (electromagnetic induction), input - force L4T-4, output - EMF L2T-2 13. Piezoresistive effect, input - linear deformation L1T0, output - electric resistance L-1T1
14. Hooke's law, input - force L4 T-4, output - mechanical tension, pressure L2 T-4
15. Doppler effect, input - linear velocity L1T-1, output - length of the wave L1T0.
The main difference of this table indicator consists in the fact that certain structural specific features of technical implementation of the effect are taken into account in it. Many physical effects are characterized by several different input and output actions. For example, tens resistive effect (No.13) can have a linear deformation at the input, i.e., tens resistor is elongated or compressed along its length, but it may also be a film effect. With a film effect pressure will be an input, and the
3 5 • •
tens effect with a film tens resistor will get into a different cell - L- T . Similarly for the outcomes -the Doppler effect (No.9 and No.13) is placed in different cells depending upon what is obtained at the output of Doppler's meter of speed, wavelength or frequency.
The analyzed trends are related to the trend of trimming and deployment of technical systems, not only to the trend of increasing coordination. [10]. In fact, the trend «Point-Line-Plane-Volume» is trimmed into the cell L1T0 of Bartini table, in which the invariant L1T0 Mcan be included with the
trends of invariants with neighboring cells. Fig. 5 presents the temporal trend of such kinds of invariants L"1T0^L"1T1^L"1T2 in brown, blue and red cells respectively. For the trend of effects located in the brown cell the transfer matrix W3 is equal to
w3=[l; t°O].
While in Bartini system the dimensionality L-1T0 is presented by the values of curvature (Fig. 1). The trend of invariants L-1T0^L-1T1^L-1T2 can be presented by its electric equivalent. If instead of dimensions in the basis of LT we include the conventional notation of elements of electric circuit, we shall obtain the following circuit:
1/C^R^L,
In which C is capacitance, Ф, R - electric resistance, Ohm, L is inductivity, henry. With effects No. 1,2,3,4 in an inductive trend with invariant W1 the inductivity L is an ideal model reflecting the main feature of transforming of input into output. This feature consists in the fact that if we feed to the input the effect of the flow (or the current - for charged particles), certain force is generated in the effect, which hinders the variation of this flow (current). The energy of interaction is not dissipated, it remains in the effect. From the informational viewpoint it could be said that the memory is generated, which remembers this state.
In a similar way with effects No. 5,6,7 an ideal model in the trend of conductivity with invariant W2 is the active Ohm resistance R. The resistance also hinders the input flow (or current), however, the result is not remembered, since the energy of interaction is dissipated in the form of heat.
A characteristic example is the phenomenon of electromagnetic induction, it is used in effects No.3 (self-induction) and No. 6 (electromagnetic acceleration). While the current changes, in terms of value or direction, the feature of inductivity L is retained. When the current becomes constant, the feature of inductivity disappears and the feature of Ohm resistance R appears, the energy gets dissipated as a result of heating of the conductor. The effect is transferred to the trend of conductivity. Of course, this example relates to the ideal conductor, which possesses either only inductivity or only active resistance. In case with electromagnetic acceleration the shell flying out of the gun, carries the energy of the field, which is dissipated as a result of friction during the flight.
Effects could be numerically compared in terms of complexity degree of their models in the form of transfer matrices. If the effect is assigned by the transfer matrix W (1), them the number of complexity Nc is found from the formula Nc=|m|+|n|. With all effects in inductive trend Nc=3, with effects in conductivity trend Nc=2. The complexity number of the Число сложности effect reflects the expenditures of spatial and temporal resources on transforming the input action into an output one.
CONCLUSION
In analysis of physical effects in LT-basis of kinematic values, the methodology of hidden regularities, trends of evolution of effects. This methodology can be used
• In search and classification of technological effects
• For synthesis of a physical principle of operation of technical systems [16] and comparative evaluation of information-and-energy schemes for the purpose of patenting
• For teaching inventive physics as part of TRIZ
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