CN104091057B - Method for generating fractal unit matrix and growth matrix of special energy gathering structure - Google Patents

Abstract

The invention discloses a method for generating a fractal unit matrix and a growth matrix of a special energy gathering structure. The method includes the following steps that first, digital quality of each element of the fractal unit matrix is defined; second, a growth matrix is determined, wherein the growth matrix with any i-dimension special energy gathering structure parameters is derived; third, whether the designed parameter matrix meets the requirement for optimization of a parameter matrix of the special energy gathering structure or not is checked; fourth, the parameter matrix of the special energy gathering structure is determined, wherein after a physical quantity is selected, the constant c is determined, and the parameter matrix of the designed structure is obtained; fifth, the material for use, the total size and the shape of the special energy gathering structure and the shape and the size of each structural unit are designed as required. The method for generating the fractal unit matrix and the growth matrix of the special energy gathering structure has the advantages that generation of the energy gathering structure is irrelevant to the material, the shape and the size of the made structure but only relevant to the sequence of all constitutional units of the structure.

Description

Method for generating fractal unit matrix and growth matrix of special energy-gathering structure

Technical Field

The invention relates to a signal processing technology, application of a fractal theory and application of a complex system modeling theory, in particular to a method for generating a fractal unit matrix and a growth matrix with fractal characteristics.

Background

Different structures can cause different physical characteristics, complex nonlinear systems can cause different influences on signals due to different arrangement sequences of the constituent units of the complex nonlinear systems, and some special structures also have strong energy effects. At present, the research aiming at the relationship between the structure, the system, the information and the energy is very little at home and abroad, for example, the invention is a structure consisting of 64 metal cylinders designed in patents such as 'universal energy collector' of 'patent 94117538.3 patent, energy-collecting field effect instrument' of 200410102761.4 patent, and 'Spatial field effect physical therapy device' of U.S. patent 7445009 patent, and the like, and experiments and practical clinical application show that the structure has the effect of energy collection around the structure, and can amplify electromagnetic signals. However, these patents do not analyze the characteristics and features of this particular energy-concentrating structure, nor do they describe the physical mechanism of its operation.

According to the maximum entropy principle, when the characteristics of the system are uniformly distributed, the system reaches an equilibrium state, and the entropy value at the moment is maximum. The special energy gathering structure designed by the invention has high symmetry and balance, all characteristic values of a structural system appear at equal probability, and the structure has the maximum characteristic information entropy value. Therefore, the maximum information entropy value is the target function in the design of the structural parameters of the invention, the constraint condition is that the characteristic set has equal digital density in all directions, the mathematical iterative formula of the growth matrix of the structure belongs to the initiative, and the structure designed and realized according to the growth matrix generated by the mathematical iterative formula and the parameter matrix of the structure is named as a special energy gathering structure.

The research of the fractal theory and the application thereof obtains remarkable results in many aspects, and in the analysis of the complex network, a plurality of networks in the real world are found to be fractal networks, certain inherent self-similarity exists, the relation existing between the scale-free characteristic and the fractal characteristic in the complex network is revealed, and the fractal theory provides a new angle for the research of the complex network. The invention firstly analyzes the characteristics of the special energy-gathering structure, and indicates that the structure has fractal characteristics, and self-similarity exists between local parts and between local parts and the whole body. And then, by utilizing the self-similarity, a mathematical model of the special energy-gathering structure is established, and a mathematical iterative formula of a parameter matrix of the special energy-gathering structure is deduced.

The special energy gathering structure with fractal characteristics, high symmetry and balance can gather electromagnetic energy and has an amplification effect on electromagnetic signals, the structure has small limitation on the requirements of materials and shapes, can be a three-dimensional structure or a planar structure, and has the functions of gathering the electromagnetic energy and amplifying the electromagnetic signals as long as the arrangement sequence of the components of the structure meets the mathematical iteration formula and the constraint condition of the invention. The device can be used in various fields needing to amplify and gather energy of electromagnetic signals, and has strong practicability and wide application prospect.

Disclosure of Invention

The invention aims to provide a fractal unit matrix of a special energy gathering structure and a method for generating a growth matrix by utilizing a fractal theory and a maximum entropy principle, wherein parameters of the structure in the method have fractal characteristics. The structure can gather various electromagnetic energy in the space, the energy field of the structure has a time delay memory function and has an amplification effect on various electromagnetic signals, and the special energy gathering structure can penetrate through the metal electromagnetic shielding net to act on the periphery of the structure. The parameter matrix generated by the mathematical iteration of the invention accords with the constraint condition of the structure in the invention to design and realize the structure, and has special energy accumulation effect. The invention provides conditions which accord with special energy-gathering structure parameters and conditions for obtaining optimal energy-gathering effect. The special energy gathering structure can be applied to various related fields needing energy gathering and electromagnetic signal amplification, and analysis of complex systems.

The purpose of the invention is realized by the following technical scheme: the invention relates to a method for producing a fractal unit matrix and a growth matrix of a special energy-gathering structure, which calculates and generates required parameters by a structure parameter matrix provided by the invention, selects materials according to application objects and occasions and designs and realizes the required special energy-gathering structure according to the generated parameter matrix, and specifically comprises the following steps:

step one, determining a fractal unit S_iDefine matrix X ═ (X)_ij) Is m, then:

m＝x_ij， (1)

defining a path from one element to another as l_n，l_nIs the number n of elements passed; the numerical density of the line segment is defined as:

the parameter matrix of the special energy gathering structure has a fractal characteristic, and a fractal unit of the parameter matrix consists of two mutually orthogonal straight line segments with equal digital density and equal length. The parameter matrix of the special energy gathering structure has fractal characteristics, and the two-dimensional plane affine change is as follows:

wherein,

A. t can be taken as follows:

zoom(k is an integer), rotationTranslation

In summary, the parameter matrix of a particular shaped structure is a matrix having the structure shown in fig. 2(a), 2(b) and 2 (c).

The special energy gathering structure has high symmetry and balance, and according to the maximum entropy principle, the system characteristics of the structure are uniformly distributed and have the maximum characteristic information entropy value. Therefore, let the feature set of the parameter matrix be: s_i＝(s_i1s_i2s_i3s_i4s_i5s_i6s_i7s_i8)_1×8Wherein s is_ij∈ N (integer) element s_ijRepresenting the characteristic category of the special energy-gathering structure state, the characteristic information entropy of the structure is as follows:

wherein:

probability p(s)_ij) Is a status feature s_ijSet of features S_iSpecific gravity, w_ijAre weighting coefficients.

S_iMay form a matrixF to reach the maximum information entropy value, F should have symmetry in each direction of digital density, and each w_ijAre equal in value, so that each s_ijP(s) of_ij) Are equal. Then S_iThe following equation (6) should be satisfied:

s_i1+s_i5＝s_i3+s_i7＝s_i4+s_i8＝s_i2+s_i6， (6)

so S_iEach element of (1) is a solution of formula (7);

(7) the solution of the formula is a family of solutions, and a proper solution can be selected from the family of solutions to execute the step two;

step two, determining a growth matrix, finding an iteration mode of a special energy-gathering structure, and deducing the growth matrix Y for obtaining any i-dimensional special energy-gathering structure parametersⁱS calculated according to the step one_iThe growth matrix for obtaining the i-dimensional special energy-gathering structure is shown as the formula (8):

Yⁱis an i-dimensional growth matrix, wherein: e_i×jIs a matrix with dimension i × j and all elements of 1, Y¹And S of said step one_iSame, Y¹＝(y₁₁y₁₂y₁₃y₁₄y₁₅y₁₆y₁₇y₁₈)_1×8Is a one-dimensional growth matrix, Y for short, wherein, s_ij,y_ij∈ N. if a one-dimensional special energy-gathering structure is required, then Y¹＝S_iDirectly using S determined in step one_i＝(s_i1s_i2s_i3s_i4s_i5s_i6s_i7s_i8)_1×8Then the method is finished; if the designed special energy-gathering structure with more than two dimensions is adopted, determining a growth matrix according to the formula (8);

step three: checking whether the designed parameter matrix meets the optimization requirement of the parameter matrix of the special energy gathering structure;

the parameter growth matrix of the special energy-gathering structure has the following three characteristics, and the three characteristics can be used as conditions for checking whether the designed growth matrix and the parameter matrix meet the special energy-gathering structure;

condition (1): the growth matrix has the fractal characteristics described in the first step;

condition (2): since the feature set of the parameter matrix is derived from equation (7), and the solution of equation (7) is not the only solution, it is checked whether the resulting structural parameter matrix reaches an optimal value.

Definition matrix YⁱHas a numerical mass of m per element of_ij，YⁱHas a total numerical mass of G (Y)ⁱ)：

m_ij＝y_ij， (9)

Growth matrix YⁱThe digital centroid of all elements of (a) is at the geometric centroid of the structure;

condition (3): taking the modulus 5 of each element of the growth matrix to obtain the matrix ofThe digital centroid of all elements remains at the geometric centroid of their structure;

s if the designed special energy-gathering structure reaches the optimal value_i、Y¹The formulas (7) and (8) are satisfied, and the three conditions are satisfied at the same time;

step four, determining a parameter matrix, determining the parameter matrix of the special energy gathering structure according to an application object, wherein each element in the parameter matrix is a parameter value of each unit of the special energy gathering structure, determining the parameters to be area, volume, height, current intensity, electromagnetic wave frequency or other required various physical quantities according to requirements, and determining a constant c (c is a complex number) after selecting the physical quantities to obtain the parameter matrix (11) of the designed structure:

X＝cYⁱ， (11)

and step five, designing the used materials, the overall size and the shape of the special energy gathering structure and the shape and the size of each structural unit according to the requirements.

Compared with the prior art, the invention has the following advantages and effects:

(1) energy accumulation occurs around the structure, and the tested components include electromagnetic signals of various frequency bands and other unknown components that may be present.

(2) The structure can amplify electromagnetic signals of various frequency bands.

(3) After the structure is removed, the original energy field has a memory delay function and still exists for a period of time.

(4) The energy field of the special energy-gathering structure can penetrate through metal, and the characteristics of (1), (2) and (3) are still obtained under the condition that the structure is shielded by the metal.

(5) The above four points are not related to the material, shape and size of the manufacturing structure. The structure is tested by using samples made of various materials such as various metals, mineral crystals, wood, high polymer materials, cement and the like, and the four characteristics exist.

Drawings

Fig. 1 is a two-dimensional design of a special energy-gathering structure.

FIG. 2(a) shows_nA fractal characteristic diagram of a special energy-gathering structure of 8.

FIG. 2(b) is a drawing l_nFractal characteristic diagram of special energy-gathering structure of 4

FIG. 2(c) is a drawing l_n2, a fractal characteristic diagram of a special energy-gathering structure.

Fig. 3 is a two-dimensional special energy-concentrating structure parameter list diagram.

FIG. 4 is the electric and magnetic field increment above the particular energy concentrating structure shown in FIG. 1 in units of: and (7) DB.

Fig. 5 is a graph of the power increase in units above the particular energy concentrating structure shown in fig. 1: microwatts per square meter.

FIG. 6 is a memory delay time, in units, for the particular energy concentrating structure shown in FIG. 1: and second.

Fig. 7 is the increase in electric field strength in units of: and (7) DB.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.

Examples

As shown in figure 1, the single-sided copper-clad plate for the design of the two-dimensional special energy-gathering structure of the invention sets S according to the step I_i＝(3 8 2 7 1 6 4 9)＝Y¹，S_iIn accordance with formula (7).

Calculating a two-dimensional growth matrix according to equation (8):

the parameter matrix X of the structure is calculated as 4Y according to equation (11)²The elements of X are shown in FIG. 3.

Sixty-four rectangles with different sizes are manufactured according to the element values of the calculated parameter matrix X, the interval of each rectangle in the same row is 2mm, the total size of the structure is 80 × 80mm rectangles, the structure is shown in figure 1, the structure is composed of 64 small rectangles, the black part in figure 1 is a copper-clad part, the area data of the copper-clad rectangle is shown in a table in figure 3, and the unit is mm²。

The Y is²The conditions (1), (2) and (3) of the step three are met.

And compared with a smooth copper-clad plate, the test signal is 50MHz-3.5GHz, and the test result is shown in figure 4, figure 5, figure 6 and figure 7. FIG. 4 shows the increment of electric field strength and magnetic field strength of the structure shown in FIG. 1 compared with a smooth copper-clad plate, and the test result shows that the structure has obvious enhancement effect on electromagnetic signals. FIG. 5 is an increase in power density for the structure shown in FIG. 1 compared to a smooth CCL. FIG. 6 shows that after the special energy-gathering structure shown in FIG. 1 is removed, an energy field still exists in the original position of the sample, an amplification effect still exists on the signal, and the energy field delay time tau is approximately equal to 380 seconds. The result of fig. 7 is a comparison of the electric field intensity of the sample with the smooth copper clad laminate after the sample with the special energy-gathering structure penetrates the metal shield, and the result shows that the energy of the sample with the structure can penetrate the metal shield to act on the signals around the structure.

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (6)

1. A method for generating a fractal unit matrix and a growth matrix of a special energy gathering structure is characterized by comprising the following steps:

step one, determining a fractal unit S_iDefining fractal unit matrix X ═ X_ij) The numerical mass m of each element of (a), then:

m_ij＝x_ij， (1)

defining a path from one element to another as l_n，l_nIs the number n of elements passed; the numerical density of the defined line segments is:

${\mathrm{\ρ}}_l=\frac{{\mathrm{\Σm}}_{ij}}{n},---\left(2\right)$

the fractal unit S_iIs formed into a matrixIf F is to reach the maximum information entropy value, F should have symmetry in each direction of the number density, and each w_ijAre equal in value, so that each s_ijP(s) of_ij) Are equal, then S_iThe formula (6) should be satisfied:

s_i1+s_i5＝s_i3+s_i7＝s_i4+s_i8＝s_i2+s_i6， (6)

therefore, S_iIs a solution of formula (7):

objective function max H (S)_i) The constraint of (2):

$s.t.\left\{\begin{array}{c}{s}_{i1}+s_{i5}=s_{i3}+s_{i7}=s_{i4}+s_{i8}=s_{i2}+s_{i6}\\ s_{ij}\≥0,s_{ij}\∈N\end{array}\right.,---\left(7\right)$

wherein H (S)_i) Is the characteristic entropy of the structure, s_ijIs a fractal sheetYuan S_iThe value of each element of (a);

(7) the solution of the formula is a family solution, one solution is selected from the family solution, and the step two is executed;

step two, determining a growth matrix, finding an iteration mode of a special energy-gathering structure, and deducing the growth matrix Y for obtaining any i-dimensional special energy-gathering structure parametersⁱS calculated according to the step one_iObtaining a growth matrix of an i-dimensional special energy gathering structure;

step three, checking whether the designed parameter matrix meets the optimization requirement of the parameter matrix of the special energy gathering structure;

determining a parameter matrix, determining the parameter matrix of the special energy gathering structure according to an application object, determining that each element in the parameter matrix is a parameter value of each unit of the special energy gathering structure, determining that the parameter is area, volume, height, current intensity, electromagnetic wave frequency or other required various physical quantities according to requirements, and determining a constant c after selecting the physical quantities to obtain the parameter matrix of the designed structure;

and step five, designing the used materials, the overall size and the shape of the special energy gathering structure and the shape and the size of each structural unit according to the requirements.

2. The method for generating fractal element matrix and growth matrix for special energy-gathering structure as claimed in claim 1, wherein in step three, the method for checking whether the designed parameter matrix meets the requirement of optimization of parameter matrix for special energy-gathering structure is as follows:

the following three conditions are used as conditions for checking whether the designed growth matrix and parameter matrix meet the special energy-gathering structure;

condition (1): the growth matrix has the fractal characteristics described in the first step;

condition (2): since the feature set of the parameter matrix is obtained from equation (7), where equation (7) has multiple solutions, it is checked whether the resulting structural parameter matrix reaches an optimal value;

definition matrix YⁱHas a numerical mass of m per element of_ij，YⁱHas a total numerical mass of G (Y)ⁱ)：

m_ij＝y_ij， (9)

$G\left(Y^i\right)=\underset{i,j}{\Σ}{m}_{ij}=\underset{i,j}{\Σ}{y}_{ij},---\left(10\right)$

Growth matrix YⁱThe digital centroid of all elements of (a) is at the geometric centroid of the structure;

condition (3): taking the modulus 5 of each element of the growth matrix to obtain the matrix ofThe digital centroid of all elements remains at the geometric centroid of their structure;

s if the designed special energy-gathering structure reaches the optimal value_i、Y¹The expressions (7) and (8) are satisfied, and the above-described conditions (1), (2), and (3) are satisfied.

3. The method for generating fractal element matrix and growth matrix of special energy-gathering structure as claimed in claim 1, wherein in step two, the expression of the growth matrix of i-dimensional special energy-gathering structure is:

Y¹＝(y₁₁y₁₂y₁₃y₁₄y₁₅y₁₆y₁₇y₁₈)_1×8，(i＝1)，

$Y^i={\left(\begin{array}{c}{s}_{i1}{E}_{(i-1)\×8}+Y^{i-1}\\ s_{i2}{E}_{(i-1)\×8}+Y^{i-1}\\ s_{i3}{E}_{(i-1)\×8}+Y^{i-1}\\ s_{i4}{E}_{(i-1)\×8}+Y^{i-1}\\ s_{i5}{E}_{(i-1)\×8}+Y^{i-1}\\ s_{i6}{E}_{(i-1)\×8}+Y^{i-1}\\ s_{i7}{E}_{(i-1)\×8}+Y^{i-1}\\ s_{i8}{E}_{(i-1)\×8}+Y^{i-1}\end{array}\right)}_{8^{i-1}\×8}(i\≥2),---\left(8\right)$

Yⁱis an i-dimensional growth matrix, wherein: e_i×jIs a matrix with dimension i × j and all elements of 1, Y¹And S of said step one_iSame, Y¹＝(y₁₁y₁₂y₁₃y₁₄y₁₅y₁₆y₁₇y₁₈)_1×8Is a one-dimensional growth matrix, Y for short, wherein, s_ij,y_ij∈ N, Y if a one-dimensional special energy-concentrating structure is desired¹＝S_iDirectly using S determined in step one_i＝(s_i1s_i2s_i3s_i4s_i5s_i6s_i7s_i8)_1×8Then the method is finished; if a special energy-gathering structure with more than two dimensions is designed, the growth matrix is determined according to the formula (8).

4. The method for generating fractal element matrix and growth matrix for special energy-gathering structure as claimed in claim 1, wherein in step four, the expression of the parameter matrix is as follows:

X＝cYⁱ， (11)

wherein c is a plurality; the numerical value of each element of the parameter matrix is used for corresponding to the area physical quantity, the volume physical quantity, the height physical quantity, the electromagnetic wave frequency physical quantity, the electric charge physical quantity and the current intensity physical quantity.

5. The method for generating the fractal element matrix and the growth matrix of the special energy gathering structure as claimed in claim 1, wherein in the step one, the parameter matrix of the special energy gathering structure has fractal characteristics, the fractal elements thereof are composed of two mutually orthogonal straight line segments with equal digital density and equal length, the parameter matrix of the special energy gathering structure has fractal characteristics, and the two-dimensional planar affine variation thereof is as follows:

$W\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}e\\ f\end{array}\right)=W\left(X\right)=A\left(X\right)+T,---\left(3\right)$

wherein,

zoomWherein k is an integer; rotateTranslation

The feature set of the parameter matrix of the special energy-gathering structure is set as follows: s_i＝(s_i1s_i2s_i3s_i4s_i5s_i6s_i7s_i8)_1×8Wherein s is_ij∈ N, N being an integer, element s_ijRepresenting a particular energy concentrationAnd (3) the characteristic information entropy of the structure is as follows:

$H\left(T\right)=-\underset{j=1}{\overset{8}{\Σ}}p\left(s_{ij}\right)lbp\left(s_{ij}\right),---\left(4\right)$

wherein:

$p\left(s_{ij}\right)=\frac{w_{ij}n\left(s_{ij}\right)}{\underset{j}{\Σ}{w}_{ij}n\left(s_{ij}\right)},---\left(5\right)$

probability p(s)_ij) Is a status feature s_ijSet of features S_iSpecific gravity, w_ijAre weighting coefficients.

6. The method for generating fractal element matrices and growth matrices for specific energy concentrating structures according to claim 5, wherein the energy concentrating effect of said specific energy concentrating structure is related only to the arrangement order of the constituent elements of the structure.