смод
.pdfɁɚɩɢɲɟɦ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɫ ɭɱɟɬɨɦ ɧɟɢɡɜɟɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ȼ f(X,B) = f(X)f(X/B) = f(B)f(X/B). Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɡɚɩɢɫɚɧɵ ɞɥɹ ɫɥɭɱɚɹ ɧɚɥɢɱɢɹ ɨɛɧɚɪɭɠɢɜɚɟɦɨɝɨ ɫɢɝɧɚɥɚ. ɉɨɞɟɥɢɦ ɨɛɟ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜɚ ɧɚ f(X/s0) ɢ ɩɪɨɢɧɬɟɝɪɢɪɭɟɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɩɨ ɦɧɨɠɟɫɬɜɭ ɧɟɢɡɜɟɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ:
f(X/s1)/f(X/s0)= ³ (f(X/B)/f(X/s0))dB=¢l(X/B)²B.
:B
Ɍɨ ɟɫɬɶ ɡɚɩɢɫɵɜɚɟɦ ɭɫɥɨɜɧɨɟ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɧɟɢɡɜɟɫɬɧɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɚ ɡɚɬɟɦ ɟɝɨ ɭɫɪɟɞɧɹɟɦ ɩɨ ɜɫɟɦ ɧɟɢɡɜɟɫɬɧɵɦ ɩɚɪɚɦɟɬɪɚɦ, ɭɱɢɬɵɜɚɹ ɢɯ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɫɜɨɣɫɬɜɚ, ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɥɨɬɧɨɫɬɶɸ ɜɟɪɨɹɬɧɨɫɬɢ f(B).
8.5.ɋɢɧɬɟɡ ɭɫɬɪɨɣɫɬɜɚ ɨɛɧɚɪɭɠɟɧɢɹ ɞɥɹ ɫɢɝɧɚɥɚ ɫɨ ɫɥɭɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ
ɋɢɝɧɚɥ ɫ ɧɟɢɡɦɟɧɧɨɣ ɚɦɩɥɢɬɭɞɨɣ, ɧɨ ɫɥɭɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɬɚɤɨɣ ɮɨɪɦɟ: s(t,M)=s(t)cos[Z0t+Is(t)+M)], ɝɞɟ s(t)-ɫɨɦɧɨɠɢɬɟɥɶ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɮɨɪɦɭ ɫɢɝɧɚɥɚ; Z0 - ɮɢɤɫɢɪɨɜɚɧɧɚɹ ɱɚɫɬɨɬɚ; Is(t) - ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɚɹ ɮɭɧɤɰɢɹ ɮɚɡɨɜɨɣ ɦɨɞɭɥɹɰɢɢ; M - ɫɥɭɱɚɣɧɚɹ ɮɚɡɚ ɫ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ, ɪɚɜɧɨɦɟɪɧɵɦ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 0 ɞɨ 2S.
ɉɪɟɨɛɪɚɡɭɟɦ ɤɨɫɢɧɭɫ ɫɭɦɦɵ ɜ ɜɵɪɚɠɟɧɢɢ ɞɥɹ ɫɢɝɧɚɥɚ ɩɨ ɢɡɜɟɫɬɧɨɣ ɮɨɪɦɭɥɟ ɢ ɩɨɥɭɱɢɦ s(t,M) = sc(t)cos M - ss(t)sin M. ɉɨɞɫɬɚɜɢɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɜ
ɮɨɪɦɭɥɭɞɥɹ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ:
z(X/M) = zccosM-zssinM = Zcos(M-]), ɝɞɟ Z = (zc2+zs2)1/2, ]=
T T
= arctg(zs/zc); zc= ³ |
sc(t)x(t)dt zs=³ss(t)x(t)dt. ȼɵɪɚɠɟɧɢɟ ɞɥɹ ɷɧɟɪɝɢɢ ɫɢɝɧɚɥɚ: E(M |
0 |
0 |
T
)= ³s2(t)cos2[Z0t+Is(t)+M]dt|E ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɡɚɜɢɫɢɦɵɦ ɨɬ M, ɟɫɥɢ ɞɥɢɬɟɥɶ-
0
ɧɨɫɬɶ ɫɢɝɧɚɥɚ ɦɧɨɝɨ ɛɨɥɶɲɟ ɩɟɪɢɨɞɚ ɡɚɩɨɥɧɟɧɢɹ 1/f0. Ɍɨɝɞɚ ɞɥɹ ɩɪɢɟɦɚ ɫɢɝɧɚɥɚ ɧɚ ɮɨɧɟ ɧɨɪɦɚɥɶɧɨɝɨ ɲɭɦɚ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɜ ɬɚɤɨɦ ɜɢɞɟ:
2S
lM(X) = exp(-E/S0)(2S)-1 ³ exp[Zcos(M-])]dM = exp(-E/S0)I0(Z),
0
ɝɞɟ I0(x) - ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɚɹ ɮɭɧɤɰɢɹ Ȼɟɫɫɟɥɹ ɧɭɥɟɜɨɝɨ ɩɨɪɹɞɤɚ. ɗɬɚ ɮɭɧɤɰɢɹ ɦɨɧɨɬɨɧɧɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɜɨɟɝɨ ɚɪɝɭɦɟɧɬɚ, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɪɟɲɚɸɳɟɟ ɩɪɚɜɢɥɨ: Z t z0. ɋɬɪɭɤɬɭɪɚ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɪɢɟɦɧɨ-ɪɟɲɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɫɨɞɟɪɠɢɬ ɞɜɚ "ɤɜɚɞɪɚɬɭɪɧɵɯ" ɤɚɧɚɥɚ, ɤɜɚɞɪɚɬɨɪɵ ɜ ɤɚɠɞɨɦ ɢɡ ɧɢɯ, ɫɭɦɦɚɬɨɪ ɢ ɩɨɪɨɝɨɜɨɟ ɭɫɬɪɨɣɫɬɜɨ. ɉɪɢ ɫɥɭɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɟ, ɟɫɥɢ ɫɢɝɧɚɥ ɧɟ ɫɨɡɞɚɟɬ
ɷɮɮɟɤɬɚ ɜ ɨɞɧɨɦ ɢɡ ɞɜɭɯ ɤɚɧɚɥɨɜ, ɨɧ ɨɛɹɡɚɬɟɥɶɧɨ ɫɨɡɞɚɫɬ ɟɝɨ ɜɨ ɜɬɨɪɨɦ ɤɚɧɚɥɟ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɫɧɢɠɚɸɬɫɹ ɩɨɬɟɪɢ ɜ ɨɛɧɚɪɭɠɟɧɢɢ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɧɟɢɡɜɟɫɬɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ. Ɏɭɧɤɰɢɹ ɜɵɛɨɪɨɱɧɵɯ ɞɚɧɧɵɯ Z ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɥɭɱɚɣɧɨɝɨ ɩɚɪɚɦɟɬɪɚ - ɮɚɡɵ M ɢ ɹɜɥɹɟɬɫɹ ɢɧɜɚɪɢɚɧɬɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ (ɞɥɢɧɚ ɜɟɤɬɨɪɚ).
ɇɚɣɞɟɦ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ ɢ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚɪɭɠɟɧɢɹ. Ⱦɥɹ ɷɬɨɝɨ ɨɩɪɟɞɟɥɢɦ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɜɟɥɢɱɢɧɵ Z:
2S |
2S |
f(Z) = ³ f(M)f(Z/M)dM = [1/(2S)] ³ f(Z/M)dM. ɉɪɢ ɧɚɥɢɱɢɢ ɫɢɝɧɚɥɚ:
0 |
0 |
f(Z/s1)= Z/E exp[-E/S0(1+Z2/Q2)]I0(Z),
ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɫɢɝɧɚɥɚ
f(Z/s0)=Z/E exp(-Z2/Q2).
ɋɪɚɜɧɢɬɟɥɶɧɵɣ ɚɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɜɵɪɚɠɟɧɢɣ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɦɨɞɭɥɹ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ ɩɪɢ ɧɚɥɢɱɢɢ ɫɢɝɧɚɥɚ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɬɚɤɨɝɨ ɠɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɧɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɫɢɝɧɚɥɚ) ɫɦɟɳɟɧɢɟɦ ɜɩɪɚɜɨ. ɗɬɨ ɫɦɟɳɟɧɢɟ ɡɚɜɢɫɢɬ ɨɬ Q. ɂ ɱɟɦ ɛɨɥɶɲɟ Q, ɬɟɦ ɛɨɥɶɲɟ ɫɦɟɳɟɧɢɟ. Ɍɟɦ ɫɚɦɵɦ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚɪɭɠɟɧɢɹ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɩɨɪɨɝɨɜɨɦ ɭɪɨɜɧɟ (ɮɢɤɫɢɪɨɜɚɧɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ).
8.6.Ɉɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɧɚɪɭɠɟɧɢɹ ɞɥɹ ɫɢɝɧɚɥɚ ɫɨ ɫɥɭɱɚɣɧɵɦɢ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ ɢ ɚɦɩɥɢɬɭɞɨɣ
ɋɢɝɧɚɥ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧ ɜ ɬɚɤɨɦ ɜɢɞɟ: s(t,A,M) =As(t)cos[Z 0t+Is(t)+M], ɝɞɟ M - ɫɥɭɱɚɣɧɚɹ ɧɚɱɚɥɶɧɚɹ ɮɚɡɚ, ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɪɚɜɧɨɦɟɪɧɨɦɭ ɡɚɤɨɧɭ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 0 ɞɨ 2S; Ⱥ - ɫɥɭɱɚɣɧɚɹ ɚɦɩɥɢɬɭɞɚ, ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɪɟɥɟɟɜɫɤɨɦɭɡɚɤɨɧɭ
f(A)=AV-2exp(-A2/(2V2)), At0. ɋɥɭɱɚɣɧɵɟ ɜɟɥɢɱɢɧɵ M ɢ Ⱥ ɧɟɡɚɜɢɫɢɦɵ ɢ ɢɯ ɫɨɜɦɟɫɬɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ f(M,Ⱥ) ɪɚɜɧɨ ɩɪɨɢɡɜɟɞɟɧɢɸ ɨɞɧɨɦɟɪɧɵɯ ɡɚɤɨɧɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɉɪɢ ɬɚɤɢɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɭɫɥɨɜɧɨɟ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɢɦɟɟɬ ɜɢɞ l(X/M,A) =AZcos(M - ]). ɗɧɟɪɝɢɹ ɫɢɝɧɚɥɚ ɡɚɜɢɫɢɬ ɨɬ ɫɥɭɱɚɣɧɵɯ ɩɚɪɚɦɟɬɪɨɜ Ⱥ ɢ M ɢ ɞɨɥɠɧɚ ɛɵɬɶ ɭɫɪɟɞɧɟɧɚ ɩɨ ɜɫɟɦ ɷɬɢɦ ɩɚɪɚɦɟɬɪɚɦ. Ⱦɥɹ Ⱥ/V ɷɬɚ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɪɚɜɧɚ ȿ (ɩɪɢɛɥɢɠɟɧɧɨ ɩɪɢ ɬɟɯ ɠɟ ɫɨɨɬɧɨɲɟɧɢɹɯ, ɱɬɨ ɢ ɞɥɹ ɫɥɭɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɵ). ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ ɩɪɟɞɵɞɭɳɟɝɨ ɩɨɞɪɚɡɞɟɥɚ, ɨɩɪɟɞɟ-
ɥɢɦ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ, ɭɫɪɟɞɧɢɜ ɟɝɨ ɩɨ Ⱥ ɢ M: lAM(X)= =S0/(E+S0)exp[Z2S0/(4(E+S0))]. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɬɪɭɤɬɭɪɭ ɨɛɧɚɪɭɠɢɬɟɥɹ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɩɪɨɥɨɝɚɪɢɮɦɢɪɨɜɚɜ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ. Ɉɛɧɚɪɭɠɢɬɟɥɶ ɞɥɹ ɫɥɭɱɚɣɧɵɯ ɚɦɩɥɢɬɭɞɵ ɢ ɧɚɱɚɥɶɧɨɣ ɮɚɡɵ ɧɟ ɨɬɥɢɱɚɟɬɫɹ ɩɨ ɫɬɪɭɤɬɭɪɟ ɨɬ ɨɛɧɚɪɭɠɢɬɟɥɹ ɞɥɹ ɫɥɭɱɚɣɧɨɣ ɮɚɡɵ. Ɉɬɥɢɱɢɟ ɜɵɪɚɠɚɟɬɫɹ ɬɨɥɶɤɨ ɜ ɩɨɪɨɝɨɜɨɦ ɭɪɨɜɧɟ, ɫ ɤɨɬɨɪɵɦ ɫɪɚɜɧɢɜɚɟɬɫɹ ɤɜɚɞɪɚɬ ɦɨɞɭɥɹ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ Z ɜ ɨɛɥɚɫɬɢ ɝɢɩɨɬɟɡɵ (G0) ɢ ɚɥɶɬɟɪɧɚɬɢɜɵ (G1) ɨɬɥɢɱɚɟɬɫɹ ɬɨɥɶɤɨ ɜɟɥɢɱɢɧɨɣ ɞɢɫɩɟɪɫɢɢ:
f(Z/s0) =Z/Eexp(-Z2/Q2); f(Z/s1)=ZS0/[E(E+S0)]exp[-Z2S02/(4E(E+S0)).
Ɍɨɝɞɚ ɜɟɪɨɹɬɧɨɫɬɢ ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ pF ɢ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚɪɭɠɟɧɢɹ pD ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ:
f
pF= ³ f(Z/s0)dZ=exp(-S02/(2Q2)); pD=(pF)(1-Q2/2)-1.
z0
Ƚɪɚɮɢɤɢ ɤɪɢɜɵɯ ɨɛɧɚɪɭɠɟɧɢɹ ɞɥɹ ɬɪɟɯ ɬɢɩɨɜ ɫɢɝɧɚɥɨɜ ɩɨɤɚɡɚɧɵ ɜ [6, ɪɢɫ.8.2], ɝɞɟ ɜɢɞɧɨ, ɱɬɨ ɱɟɦ ɛɨɥɶɲɟ ɚɩɪɢɨɪɧɨɟ ɧɟɡɧɚɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɚɪɚɦɟɬɪɨɜ ɫɢɝɧɚɥɨɜ, ɬɟɦ ɛɨɥɶɲɟ ɬɪɟɛɭɟɬɫɹ ɨɬɧɨɲɟɧɢɟ ɫɢɝɧɚɥ/ɲɭɦ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɪɚɜɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɚɜɢɥɶɧɨɝɨ ɨɛɧɚɪɭɠɟɧɢɹ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɥɨɠɧɨɣ ɬɪɟɜɨɝɢ. Ɉɞɧɚɤɨ ɩɪɢ ɦɚɥɵɯ ɨɬɧɨɲɟɧɢɹɯ ɫɢɝɧɚɥ/ɲɭɦ ɷɬɚ ɬɟɧɞɟɧɰɢɹ ɧɚɪɭɲɚɟɬɫɹ: ɫɢɝɧɚɥ ɫ ɮɥɸɤɬɭɢɪɭɸɳɟɣ ɚɦɩɥɢɬɭɞɨɣ ɢ ɧɟɢɡɜɟɫɬɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ ɨɛɧɚɪɭɠɢɜɚɟɬɫɹ ɥɭɱɲɟ, ɱɟɦ ɫɢɝɧɚɥ ɫ ɧɟɢɡɜɟɫɬɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ. ɗɬɨ ɦɨɠɧɨ ɨɛɴɹɫɧɢɬɶ ɭɜɟɥɢɱɟɧɢɟɦ ɞɢɫɩɟɪɫɢɢ ɨɬɧɨɲɟɧɢɹ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɡɚ ɫɱɟɬ ɮɥɸɤɬɭɢɪɭɸɳɟɣ ɚɦɩɥɢɬɭɞɵ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɟɜɵɲɟɧɢɹ ɩɨɪɨɝɨɜɨɝɨ ɭɪɨɜɧɹ z0.
8.7. Ɉɛɧɚɪɭɠɟɧɢɟ ɩɚɱɤɢ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ ɧɚ ɮɨɧɟ ɛɟɥɨɝɨ ɲɭɦɚ
ɋɢɝɧɚɥ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɚɱɤɭ (ɩɚɤɟɬ) ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ ɫɨ ɫɥɭɱɚɣɧɵɦɢ ɧɟɡɚɜɢɫɢɦɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɮɚɡɚɦɢ ɨɬɞɟɥɶɧɵɯ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ
m
s(t,M1,...,Mm) = ¦ si(t)cos[Z0t+Ii(t)+Mi] ɢ ɫ ɩɥɨɬɧɨɫɬɶɸ ɜɟɪɨɹɬɧɨɫɬɢ ɧɚɱɚɥɶɧɵɯ
i 1
ɮɚɡ, ɪɚɜɧɨɣ ɩɪɨɢɡɜɟɞɟɧɢɸ ɨɞɧɨɦɟɪɧɵɯ ɩɥɨɬɧɨɫɬɟɣ ɜɟɪɨɹɬɧɨɫɬɟɣ ɤɚɠɞɨɣ ɢɡ ɧɚɱɚɥɶɧɵɯ ɮɚɡ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ, ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɪɚɜɧɨɦɟɪɧɨ ɨɬ 0 ɞɨ 2S.
ɉɨɫɤɨɥɶɤɭ ɨɛɧɚɪɭɠɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɚ ɮɨɧɟ ɧɨɪɦɚɥɶɧɨɝɨ ɲɭɦɚ, ɬɨ ɫɬɪɭɤɬɭɪɚ ɨɛɧɚɪɭɠɢɬɟɥɹ ɞɨɥɠɧɚ ɛɵɬɶ ɨɫɧɨɜɚɧɚ ɧɚ ɤɨɪɪɟɥɹɰɢɨɧɧɨɦ ɢɧɬɟɝɪɚɥɟ, ɡɚɩɢɫɚɧɧɨɦ ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɟ i-ɝɨ ɢɦɩɭɥɶɫɚ:
m
z[x(t)/M1,...,Mm]=¦Zicos(Mi-]i),
i1
ɝɞɟ Zi=(zci2+zsi2)1/2, ]=arctg[x(t)/M1,...,Mm]. ȿɫɥɢ ɜ ɩɪɟɞɟɥɚɯ ɞɥɢɬɟɥɶɧɨɫɬɢ ɤɚɠɞɨɝɨ ɪɚɞɢɨɢɦɩɭɥɶɫɚ ɭɤɥɚɞɵɜɚɟɬɫɹ ɦɧɨɝɨ (ɛɨɥɶɲɟ 100) ɩɟɪɢɨɞɨɜ ɡɚɩɨɥɧɟɧɢɹ, ɬɨ ɷɧɟɪɝɢɹ ɩɚɱɤɢ ɢɦɩɭɥɶɫɨɜ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɥɭɱɚɣɧɵɯ ɧɚɱɚɥɶɧɵɯ ɮɚɡ ɢ ɪɚɜɧɚ ɫɭɦɦɟ ɷɧɟɪɝɢɣ ɤɚɠɞɨɝɨ ɢɡ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ.
Ȼɟɡɭɫɥɨɜɧɨɟ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɩɨɥɭɱɚɟɬɫɹ ɩɨɫɥɟ ɭɫɪɟɞɧɟɧɢɹ ɭɫ-
m
ɥɨɜɧɨɝɨ ɨɬɧɨɲɟɧɢɹ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɩɨ ɜɫɟɦ ɧɚɱɚɥɶɧɵɦ ɮɚɡɚɦ l(X)= exp(-
i 1
Ei/S0)I0(Zi), ɤɨɬɨɪɨɟ ɩɨɫɥɟ ɥɨɝɚɪɢɮɦɢɪɨɜɚɧɢɹ ɩɪɢɧɢɦɚɟɬ ɜɢɞ lnl(X) =
m |
m |
¦ lnI0(Zi) - |
¦ Ei/S0. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɨɥɭɱɟɧɧɨɣ ɮɨɪɦɭɥɨɣ ɦɨɠɧɨ ɫɢɧɬɟ- |
i 1 |
i 1 |
ɡɢɪɨɜɚɬɶ ɨɛɧɚɪɭɠɢɬɟɥɶ ɫɢɝɧɚɥɚ ɜ ɜɢɞɟ ɩɚɱɤɢ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ ɫ ɧɟɡɚɜɢɫɢɦɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɮɚɡɚɦɢ ɨɬɞɟɥɶɧɵɯ ɢɦɩɭɥɶɫɨɜ. Ɉɧ ɫɨɞɟɪɠɢɬ ɮɨɪɦɢɪɨɜɚɬɟɥɶ ɨɬɧɨɲɟɧɢɹ ɩɪɚɜɞɨɩɨɞɨɛɢɹ, ɛɥɨɤ ɜɵɱɢɫɥɟɧɢɹ ɮɭɧɤɰɢɢ Ȼɟɫɫɟɥɹ, ɥɨɝɚɪɢɮɦɚɬɨɪ, ɫɭɦɦɚɬɨɪ (ɧɚɤɨɩɢɬɟɥɶ) ɢ ɩɨɪɨɝɨɜɨɟ ɭɫɬɪɨɣɫɬɜɨ. ɇɚɥɢɱɢɟ ɧɚɤɨɩɢɬɟɥɹ ɨɛɭɫɥɨɜɥɟɧɨ ɩɟɪɟɯɨɞɨɦ ɨɬ ɨɞɧɨɝɨ ɢɦɩɭɥɶɫɚ ɤ ɩɚɱɤɟ ɨɞɢɧɚɤɨɜɵɯ ɢɦɩɭɥɶɫɨɜ. ɇɟɨɛɯɨɞɢɦɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɟɫɥɢ ɚɦɩɥɢɬɭɞɵ ɢɦɩɭɥɶɫɨɜ ɜ ɩɚɱɤɟ ɨɬɥɢɱɚɸɬɫɹ ɩɨ ɜɟɥɢɱɢɧɟ ɢ ɷɬɨ ɨɬɥɢɱɢɟ ɢɡɜɟɫɬɧɨ, ɬɨ ɧɚɤɨɩɥɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɫ ɜɟɫɨɜɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɫɨɨɬɧɨɲɟɧɢɸ ɚɦɩɥɢɬɭɞ ɢɦɩɭɥɶɫɨɜ ɜ ɩɚɱɤɟ. Ʉɪɨɦɟ ɬɨɝɨ, ɧɚɤɨɩɥɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɤɨɝɟɪɟɧɬɧɵɦ ɢ ɧɟɤɨɝɟɪɟɧɬɧɵɦ. Ɉɬɥɢɱɢɟ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɢɡɜɟɫɬɧɵ ɢɥɢ ɧɟɢɡɜɟɫɬɧɵ ɧɚɱɚɥɶɧɵɟ ɮɚɡɵ ɪɚɞɢɨɢɦɩɭɥɶɫɨɜ. ȿɫɥɢ ɢɡɜɟɫɬɧɵ, ɬɨ ɧɚɤɨɩɥɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɚ ɪɚɞɢɨɱɚɫɬɨɬɟ, ɟɫɥɢ ɧɟɢɡɜɟɫɬɧɵ - ɬɨ ɧɚ ɜɢɞɟɨɱɚɫɬɨɬɟ, ɬ.ɟ. ɩɨ ɨɝɢɛɚɸɳɟɣ. ȼ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɩɟɪɟɞ ɧɚɤɨɩɥɟɧɢɟɦ ɢɥɢ ɨɩɪɟɞɟɥɹɸɬ ɦɨɞɭɥɶ ɤɜɚɞɪɚɬɭɪɧɵɯ ɤɨɪɪɟɥɹɰɢɨɧɧɵɯ ɢɧɬɟɝɪɚɥɨɜ, ɢɥɢ ɜɤɥɸɱɚɸɬ ɚɦɩɥɢɬɭɞɧɵɣ ɞɟɬɟɤɬɨɪ. ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɩɟɪɟɞ ɧɚɤɨɩɥɟɧɢɟɦ ɨɩɪɟɞɟɥɹɸɬ ɜɟɥɢɱɢɧɭ, ɧɟ ɡɚɜɢɫɹɳɭɸ ɨɬ ɧɚɱɚɥɶɧɨɣ ɮɚɡɵ ɪɚɞɢɨɢɦɩɭɥɶɫɚ ɜ ɩɚɱɤɟ. ɉɟɪɟɯɨɞ ɤ ɩɚɱɤɟ ɨɬ ɨɞɢɧɨɱɧɨɝɨ ɢɦɩɭɥɶɫɚ ɩɨɡɜɨɥɹɟɬ ɭɜɟɥɢɱɢɬɶ ɨɬɧɨɲɟɧɢɟ ɫɢɝɧɚɥ/ɲɭɦ ɧɚ ɜɵɯɨɞɟ ɧɚɤɨɩɢɬɟɥɹ ɜ (m)1/2 ɪɚɡ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɨɞɢɧɨɱɧɵɦ ɢɦɩɭɥɶɫɨɦ.
Ⱥɧɚɥɨɝɨɜɨɟ ɧɚɤɨɩɥɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɡɚɦɟɧɟɧɨ ɰɢɮɪɨɜɵɦ, ɟɫɥɢ ɦɨɧɨɬɨɧɧɭɸ ɮɭɧɤɰɢɸ lnI0(Z) ɡɚɦɟɧɢɬɶ ɛɢɧɚɪɧɵɦ ɤɜɚɧɬɨɜɚɧɢɟɦ ɫ ɩɨɪɨɝɨɜɵɦ ɭɪɨɜɧɟɦ z0. ɋɬɪɭɤɬɭɪɚ ɨɛɧɚɪɭɠɢɬɟɥɹ ɩɪɢ ɷɬɨɦ ɢɡɦɟɧɹɟɬɫɹ: ɩɨɹɜɥɹɟɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɩɨɪɨɝɨɜɨɟ ɭɫɬɪɨɣɫɬɜɨ, ɚ ɧɚɤɨɩɢɬɟɥɶ ɚɧɚɥɨɝɨɜɵɣ ɡɚɦɟɧɹɟɬɫɹ ɰɢɮɪɨɜɵɦ, ɜ ɤɨɬɨɪɨɦ ɜɵɩɨɥɧɹɟɬɫɹ ɫɥɨɠɟɧɢɟ ɟɞɢɧɢɰ ɢ ɧɭɥɟɣ, ɱɬɨ ɨɫɭɳɟɫɬɜɢɬɶ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɨɳɟ. ɉɪɢ ɷɬɨɦ ɩɨɥɭɱɚɟɬɫɹ ɮɚɤɬɢɱɟɫɤɢ ɤɜɚɡɢɨɩɬɢɦɚɥɶɧɵɣ ɨɛɧɚɪɭɠɢɬɟɥɶ, ɬ.ɟ. ɞɨɩɭɫɤɚɸɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɨɬɟɪɢ ɜ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɨɛɧɚɪɭɠɟɧɢɹ, ɧɨ ɭɩɪɨɳɚɟɬɫɹ ɭɫɬɪɨɣɫɬɜɨ ɨɛɧɚɪɭɠɢɬɟɥɹ. ɉɪɢɦɟɧɹɟɬɫɹ ɬɚɤɨɣ ɜɢɞ ɧɚɤɨɩɥɟɧɢɹ, ɤɨɝɞɚ ɜ ɩɚɱɤɟ ɦɧɨɝɨ ɢɦɩɭɥɶɫɨɜ ɢ ɩɟɪɟɯɨɞ ɤ ɰɢɮɪɨɜɨɦɭ ɨɛɧɚɪɭɠɟɧɢɸ ɧɟ ɩɪɢɜɨɞɢɬ ɤ ɡɧɚɱɢɬɟɥɶɧɵɦ ɩɨɬɟɪɹɦ ɜ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɨɛɧɚɪɭɠɟɧɢɹ. Ɍɚɤ, ɟɫɥɢ ɱɢɫɥɨ ɢɦɩɭɥɶɫɨɜ ɛɨɥɟɟ 10, ɬɨ ɩɨɬɟɪɢ ɜ ɨɬɧɨɲɟɧɢɢ ɫɢɝɧɚɥ/ɲɭɦ ɧɟ ɩɪɟɜɵɲɚɸɬ 2 ɞȻ.
ɇɚɤɨɩɥɟɧɢɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɧɟ ɬɨɥɶɤɨ ɩɪɢ ɨɛɧɚɪɭɠɟɧɢɢ ɩɚɱɤɢ ɢɦɩɭɥɶɫɨɜ, ɧɨ ɢ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɫɢɝɧɚɥɨɜ ɜ ɪɚɞɢɨɫɜɹɡɢ, ɩɪɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ ɪɚɡɧɟɫɟɧɧɨɦ ɩɪɢɟɦɟ, ɤɨɝɞɚ ɫɢɝɧɚɥɵ, ɩɪɢɧɢɦɚɟɦɵɟ ɪɚɡɥɢɱɧɵɦɢ ɚɧɬɟɧɧɚɦɢ, ɧɟɡɚɜɢɫɢɦɵ ɞɪɭɝ ɨɬ ɞɪɭɝɚ.
9. ɈɋɇɈȼɕ ɌȿɈɊɂɂ ɈɐȿɇɈɄ
ɋɭɳɟɫɬɜɭɟɬ ɰɟɥɵɣ ɤɥɚɫɫ ɡɚɞɚɱ, ɜ ɤɨɬɨɪɵɯ ɨɛɪɚɛɨɬɤɚ ɫɢɝɧɚɥɨɜ ɫɜɨɞɢɬɫɹ ɤ ɩɨɥɭɱɟɧɢɸ ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɜɵɜɨɞɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɤɨɬɨɪɵɯ ɧɟɢɡɜɟɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɫɢɝɧɚɥɨɜ ɢ ɩɨɦɟɯ.
Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɩɪɢɦɟɪɵ, ɜ ɤɨɬɨɪɵɯ ɢɫɩɨɥɶɡɭɸɬɫɹ ɨɫɧɨɜɧɵɟ ɩɨɧɹɬɢɹ ɬɟɨɪɢɢ ɨɰɟɧɨɤ.
ɇɚ ɜɯɨɞ ɭɫɬɪɨɣɫɬɜɚ, ɩɪɨɢɡɜɨɞɹɳɟɝɨ ɨɰɟɧɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɩɚɪɚɦɟɬɪɚ ɚ ɩɨɫɬɭɩɚɟɬ ɚɞɞɢɬɢɜɧɚɹ ɫɦɟɫɶ ɫɢɝɧɚɥɚ ɢ ɲɭɦɚ x(t) = s(t,a)+[(t). Ɉɰɟɧɤɚ ɩɪɨɢɡɜɨɞɢɬɫɹ ɜ ɬɟɱɟɧɢɟ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ Ɍ, ɧɚɡɵɜɚɟɦɨɝɨ ɢɧɬɟɪɜɚɥɨɦ ɧɚɛɥɸɞɟɧɢɹ. Ɏɨɪɦɚ ɫɢɝɧɚɥɚ ɬɨɱɧɨ ɢɡɜɟɫɬɧɚ, ɧɟɢɡɜɟɫɬɟɧ ɬɨɥɶɤɨ ɟɝɨ ɩɚɪɚɦɟɬɪ ɚ. Ɉɛɨɡɧɚɱɢɦ ɨɰɟɧɤɭ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɱɟɪɟɡ a*, ɢɫɬɢɧɧɨɟ ɡɧɚɱɟɧɢɟ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ - ɱɟɪɟɡ a0. ɉɭɫɬɶ ɨɰɟɧɤɚ ɩɪɨɢɡɜɨɞɢɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɚɥɝɨɪɢɬɦɨɦ ɚ*=G [x(t)]. ɇɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɚɥɝɨɪɢɬɦ, ɩɨɡɜɨɥɹɸɳɢɣ ɧɚɯɨɞɢɬɶ ɨɰɟɧɤɭ ɭɤɚɡɚɧɧɨɝɨ ɩɚɪɚɦɟɬɪɚ ɧɚɢɥɭɱɲɢɦ ɨɛɪɚɡɨɦ. ɉɨɫɤɨɥɶɤɭ ɧɚ ɜɯɨɞ ɭɫɬɪɨɣɫɬɜɚ ɨɩɪɟɞɟɥɟɧɢɹ ɨɰɟɧɤɢ ɩɨɫɬɭɩɚɟɬ ɫɦɟɫɶ ɫɢɝɧɚɥɚ ɢ ɫɥɭɱɚɣɧɨɝɨ ɩɪɨɰɟɫɫɚ, ɬɨ ɢ ɧɚ ɜɵɯɨɞɟ ɛɭɞɟɬ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ, ɢɦɟɸɳɚɹ ɭɫɥɨɜɧɭɸ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ f(a*/a0), ɚ ɡɧɚɱɢɬ, ɩɨɥɭɱɟɧɧɚɹ ɨɰɟɧɤɚ ɢɦɟɟɬ ɩɨɝɪɟɲɧɨɫɬɢ ɫɥɭɱɚɣɧɨɝɨ ɢ ɧɟɫɥɭɱɚɣɧɨɝɨ ɯɚɪɚɤɬɟɪɚ.
ɇɚɣɞɟɦ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɰɟɧɤɢ ɚ*, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɟ ɟɟ ɤɚɱɟɫɬɜɨ.
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɨɲɢɛɤɢ ɢɡɦɟɪɟɧɢɹ
f
M(a*/a0) = ³ (a*-a0)f(a*/a0)da*
f
ɟɫɬɶ ɫɢɫɬɟɦɚɬɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ; ɜɬɨɪɨɣ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɫɬɟɩɟɧɶ ɪɚɡɛɪɨɫɚɧɧɨɫɬɢ ɨɰɟɧɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫɬɢɧɧɨɝɨ ɡɧɚɱɟɧɢɹ (ɧɚɡɨɜɟɦ ɟɝɨ ɞɢɫɩɟɪɫɢɟɣ, ɯɨɬɹ ɷɬɨ ɱɚɫɬɧɵɣ ɫɥɭɱɚɣ ɜɬɨɪɨɝɨ ɦɨɦɟɧɬɚ, ɤɨɝɞɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɩɨɝɪɟɲɧɨɫɬɢ ɪɚɜɧɨ ɧɭɥɸ) ɢɦɟɟɬ ɜɢɞ
f
V2(a*/a0) = ³ (a*-a0)2f(a*/a0) da*.
f
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɨɰɟɧɤɢ ɧɚɡɵɜɚɸɬ ɫɢɫɬɟɦɚɬɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɶɸ ɢɥɢ ɫɦɟɳɟɧɢɟɦ ɨɰɟɧɤɢ. ȿɫɥɢ ɨɧɨ ɪɚɜɧɨ ɧɭɥɸ, ɬɨ ɨɰɟɧɤɭ ɧɚɡɵɜɚɸɬ ɧɟɫɦɟɳɟɧɧɨɣ. ȿɫɥɢ ɫɪɟɞɢ ɜɫɟɯ ɩɪɨɱɢɯ ɨɰɟɧɨɤ ɨɞɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɩɚɪɚɦɟɬɪɚ (ɪɚɡɥɢɱɧɵɯ ɭɫɬɪɨɣɫɬɜ ɩɨɥɭɱɟɧɢɹ ɨɰɟɧɤɢ) ɞɢɫɩɟɪɫɢɹ ɨɞɧɨɣ ɢɡ ɨɰɟɧɨɤ ɦɢɧɢɦɚɥɶɧɚ, ɬɨ ɬɚɤɭɸ ɨɰɟɧɤɭɧɚɡɵɜɚɸɬ ɷɮɮɟɤɬɢɜɧɨɣ.
9.1. Ɇɟɬɨɞɵ ɩɨɥɭɱɟɧɢɹ ɨɰɟɧɨɤ (ɤɪɢɬɟɪɢɢ ɨɰɟɧɨɤ)
1.Ɉɰɟɧɤɚ ɩɨ ɦɢɧɢɦɭɦɭ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɣ (ɫɥɭɱɚɣɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ) ɨɲɢɛɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɫɥɨɜɢɹ Va2=min. Ɉɩɬɢɦɚɥɶɧɵɣ ɚɥɝɨɪɢɬɦ ɩɨɥɭɱɟɧɢɹ ɬɚɤɨɣ ɨɰɟɧɤɢ ɫɬɪɨɢɬɫɹ, ɢɫɯɨɞɹ ɢɡ ɪɟɲɟɧɢɹ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ:
wVa2/wa*=0 ɢ w2Va2/(wa*)2 !0.
2.Ɉɰɟɧɤɚ ɩɨ ɦɚɤɫɢɦɭɦɭ ɚɩɨɫɬɟɪɢɨɪɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ a*=aɦɚɤɫ ɟɫɬɶ ɚɛɫɰɢɫɫɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɦɚɤɫɢɦɭɦɭ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɢ
f(am/X). Ɉɩɬɢɦɚɥɶɧɵɣ ɚɥɝɨɪɢɬɦ ɧɚɯɨɠɞɟɧɢɹ ɬɚɤɨɣ ɨɰɟɧɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɟɲɟ-
ɧɢɟɦ ɫɢɫɬɟɦɵ ɢɡ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ:
wf(a*/X)/wa* = 0 ɢ w2f(a*/X)/(wa*)2<0.
3.Ɉɰɟɧɤɚ ɩɨ ɦɚɤɫɢɦɭɦɭ ɮɭɧɤɰɢɢ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫɤɨɦɨɣ ɨɰɟɧɤɢ a*: wL(a*)/w(a*)=0, ɝɞɟ L(a*) = f(X/a). ȿɫɥɢ ɷɬɚ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɢɦɟɟɬ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣ ɜɢɞ, ɬɨ ɭɞɨɛɧɟɟ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɬɶ ɥɨɝɚɪɢɮɦ ɮɭɧɤɰɢɢ ɩɪɚɜɞɨɩɨɞɨɛɢɹ l(a*)=lnL(a*);
wl(a*)/wa*=0.
ȼɫɟ ɩɟɪɟɱɢɫɥɟɧɧɵɟ ɨɰɟɧɤɢ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɪɚɡɥɢɱɧɵɦ ɤɪɢɬɟɪɢɹɦ ɨɰɟɧɤɢ ɤɚɱɟɫɬɜɚ ɨɰɟɧɤɢ ɢ ɨɩɪɟɞɟɥɹɸɬ ɨɩɬɢɦɚɥɶɧɵɣ ɚɥɝɨɪɢɬɦ ɨɰɟɧɢɜɚɧɢɹ.
ɋɪɚɜɧɢɦ ɚɥɝɨɪɢɬɦɵ ɨɰɟɧɤɢ ɩɨ ɫɦɟɳɟɧɧɨɫɬɢ, ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢ ɫɨɫɬɨɹɬɟɥɶɧɨɫɬɢ.
ɇɚɩɨɦɧɢɦ, ɱɬɨ ɫɨɫɬɨɹɬɟɥɶɧɨɫɬɶ ɤɪɢɬɟɪɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɬɪɟɦɥɟɧɢɟɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɠɢɞɚɧɢɹ ɨɰɟɧɤɢ ɤ ɢɫɬɢɧɧɨɦɭ ɡɧɚɱɟɧɢɸ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɨɛɴɟɦɚ ɜɵɛɨɪɤɢ, ɩɨ ɤɨɬɨɪɨɣ ɩɪɨɢɡɜɨɞɢɬɫɹ ɨɰɟɧɤɚ (ɢɥɢ ɭɜɟɥɢɱɟɧɢɢ ɜɪɟɦɟɧɢ ɧɚɛɥɸɞɟɧɢɹ Ɍ). Ⱦɨɫɬɚɬɨɱɧɨɣ ɧɚɡɵɜɚɟɬɫɹ ɨɰɟɧɤɚ, ɩɪɢ ɩɨɥɭɱɟɧɢɢ ɤɨɬɨɪɨɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜɫɹ ɢɧɮɨɪɦɚɰɢɹ ɨɛ ɢɡɦɟɪɹɟɦɨɦ ɩɚɪɚɦɟɬɪɟ, ɫɨɞɟɪɠɚɳɚɹɫɹ ɜ ɢɫɯɨɞɧɨɣ ɜɵɛɨɪɤɟ X.
ȿɫɥɢ ɫɭɳɟɫɬɜɭɟɬ ɷɮɮɟɤɬɢɜɧɚɹ ɧɟɫɦɟɳɟɧɧɚɹ ɨɰɟɧɤɚ, ɬɨ ɨɧɚ ɹɜɥɹɟɬɫɹ ɟɞɢɧɫɬɜɟɧɧɵɦ ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ ɦɚɤɫɢɦɭɦɚ ɩɪɚɜɞɨɩɨɞɨɛɢɹ (3-ɹ ɨɰɟɧɤɚ). ȿɫɥɢ ɠɟ ɫɭɳɟɫɬɜɭɟɬ ɞɨɫɬɚɬɨɱɧɚɹ ɨɰɟɧɤɚ ɩɚɪɚɦɟɬɪɚ, ɬɨ ɤɚɠɞɨɟ ɪɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɞɨɫɬɚɬɨɱɧɨɣ ɨɰɟɧɤɢ.
ȼɬɨɪɚɹ ɨɰɟɧɤɚ ɫɨɫɬɨɹɬɟɥɶɧɚ ɢ ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɷɮɮɟɤɬɢɜɧɚ (ɟɟ ɞɢɫɩɟɪɫɢɹ ɫɬɪɟɦɢɬɫɹ ɤ ɦɢɧɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ ɩɪɢ ɜɨɡɪɚɫɬɚɧɢɢ ɨɛɴɟɦɚ ɜɵɛɨɪɤɢ). ȿɫɥɢ ɚɩɪɢɨɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ f(a) ɨɰɟɧɤɢ ɪɚɜɧɨɦɟɪɧɨ ɧɚ ɤɨɧɟɱɧɨɦ ɢɧɬɟɪɜɚɥɟ, ɬɨ ɨɰɟɧɤɢ 2 ɢ 3 ɫɨɜɩɚɞɚɸɬ ɢ ɞɥɹ ɨɰɟɧɤɢ 2 ɬɨɠɟ ɦɨɠɟɬ ɫɭɳɟɫɬɜɨɜɚɬɶ ɷɮɮɟɤɬɢɜɧɚɹ ɨɰɟɧɤɚ.
ȼɫɟ ɩɟɪɟɱɢɫɥɟɧɧɵɟ ɩɪɚɜɢɥɚ ɧɚɯɨɠɞɟɧɢɹ ɨɰɟɧɨɤ ɢɡɦɟɪɹɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɞɚɸɬ ɬɨɱɟɱɧɵɟ ɨɰɟɧɤɢ. ɋɭɳɟɫɬɜɭɸɬ ɢ ɢɧɬɟɪɜɚɥɶɧɵɟ ɨɰɟɧɤɢ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɞɨɜɟɪɢɬɟɥɶɧɵɦɢ ɢɧɬɟɪɜɚɥɚɦɢ ɢ ɞɨɜɟɪɢɬɟɥɶɧɵɦɢ ɜɟɪɨɹɬɧɨɫɬɹɦɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɚɩɨɫɬɟɪɢɨɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɨɰɟɧɤɢ (ɢɥɢ ɜɵɞɜɢɝɚɟɬɫɹ ɝɢɩɨɬɟɡɚ ɨ ɟɝɨ ɜɢɞɟ) ɢ ɭɤɚɡɵɜɚɟɬɫɹ ɢɧɬɟɪɜɚɥ, ɜ ɤɨɬɨɪɵɣ ɩɨɩɚɞɚɟɬ ɨɰɟɧɢɜɚɟɦɵɣ ɩɚɪɚɦɟɬɪ ɫ ɡɚɞɚɧɧɨɣ ɞɨɜɟɪɢɬɟɥɶɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ.
Ɉɰɟɧɢɜɚɟɦɵɟ ɩɚɪɚɦɟɬɪɵ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɞɜɟ ɨɫɧɨɜɧɵɟ ɝɪɭɩɩɵ: ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ (ɜɥɢɹɸɳɢɟ ɧɚ ɷɧɟɪɝɢɸ ɫɢɝɧɚɥɚ: ɚɦɩɥɢɬɭɞɚ, ɞɥɢɬɟɥɶɧɨɫɬɶ) ɢ ɧɟɷɧɟɪɝɟɬɢɱɟɫɤɢɟ (ɧɚɱɚɥɶɧɚɹ ɮɚɡɚ, ɱɚɫɬɨɬɚ, ɜɪɟɦɹ ɡɚɞɟɪɠɤɢ - ɞɚɥɶɧɨɫɬɶ ɜ ɥɨɤɚɰɢɢ).
ɂɦɟɸɬɫɹ ɢ ɩɪɨɰɟɞɭɪɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɨɰɟɧɢɜɚɧɢɹ. ȼ ɩɪɨɰɟɫɫɟ ɩɪɨɜɟɞɟɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɨɰɟɧɤɚ ɩɚɪɚɦɟɬɪɚ ɧɚ ɤɚɠɞɨɦ ɷɬɚɩɟ ɩɨɥɭɱɟɧɢɹ ɟɞɢɧɢɱɧɵɯ ɢɡɦɟɪɟɧɢɣ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɩɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɧɟ ɛɭɞɟɬ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɨɞɧɨɦɭɢɡ ɤɪɢɬɟɪɢɟɜ ɤɚɱɟɫɬɜɚ.
Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪɵ ɫɢɧɬɟɡɚ ɚɥɝɨɪɢɬɦɨɜ ɨɰɟɧɤɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɢ ɧɟɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫɢɝɧɚɥɨɜ.
9.2.Ɉɩɬɢɦɚɥɶɧɚɹ ɨɰɟɧɤɚ ɚɦɩɥɢɬɭɞɵ ɫɢɝɧɚɥɚ
ɂɫɩɨɥɶɡɭɟɦ ɫɥɟɞɭɸɳɭɸ ɦɨɞɟɥɶ ɫɢɝɧɚɥɚ: s(t) = a c(t), ɝɞɟ ɚ - ɚɦɩɥɢɬɭɞɚ, ɩɨɞɥɟɠɚɳɚɹ ɨɰɟɧɤɟ; ɫ(t) - ɡɚɞɚɟɬ ɮɨɪɦɭ ɫɢɝɧɚɥɚ ɫ ɟɞɢɧɢɱɧɨɣ ɚɦɩɥɢɬɭɞɨɣ. Ɍɨɝɞɚ ɢɫɯɨɞɧɚɹ ɜɵɛɨɪɤɚ ɫɨɞɟɪɠɢɬ ɞɜɚ ɫɥɚɝɚɟɦɵɯ: x(t)=s(t)+[(t); ɜɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɟɫɬɶ ɲɭɦ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɚɥɝɨɪɢɬɦɚ ɨɰɟɧɤɢ ɚɦɩɥɢɬɭɞɵ ɨɩɪɟɞɟɥɢɦ ɮɭɧɤɰɢɨɧɚɥ ɩɪɚɜɞɨɩɨɞɨɛɢɹ L(ɚ), ɤɨɬɨɪɵɣ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɜɦɟɫɬɧɭɸ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɟɞɢɧɢɱɧɵɯ ɢɡɦɟɪɟɧɢɣ X, ɩɨɥɭɱɟɧɧɵɯ ɧɚ ɨɫɧɨɜɟ ɞɢɫɤɪɟɬɢɡɚɰɢɢ x(t) ɩɨ ɬɟɨɪɟɦɟ Ʉɨɬɟɥɶɧɢɤɨɜɚ. Ɍɚɤɢɟ ɢɡɦɟɪɟɧɢɹ, ɟɫɥɢ ɲɭɦ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɧɨɪɦɚɥɶɧɵɣ ɫɥɭɱɚɣɧɵɣ ɩɪɨɰɟɫɫ, ɛɭɞɭɬ ɧɟɡɚɜɢɫɢɦɵɦɢ, ɢ ɢɯ ɫɨɜɦɟɫɬɧɚɹ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɟɣ ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɨɞɧɨɦɟɪɧɵɯ ɩɥɨɬɧɨɫɬɟɣ ɜɟɪɨɹɬɧɨɫɬɟɣ:
n
L(a)=f(X/a)=(2S)-n/2V-nexp{-0,5V-2 ¦ [xi-ac(ti)]2}
i 1
n
ɢɥɢ l(a)=(2S)n/2Vnln[L(a) 2V2] =¦[xi-ac(ti)]2.
i 1
Ɉɩɪɟɞɟɥɢɦ ɷɤɫɬɪɟɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɷɬɨɝɨ ɮɭɧɤɰɢɨɧɚɥɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɪɟɬɶɢɦ ɤɪɢɬɟɪɢɟɦ ɢɡ ɩɪɢɜɟɞɟɧɧɨɝɨ ɪɚɧɟɟ ɫɩɢɫɤɚ. Ⱦɥɹ ɷɬɨɝɨ ɩɪɨɞɢɮɮɟɪɟɧɰɢɪɭɟɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɩɨ ɚ ɢ ɩɪɢɪɚɜɧɹɟɦ ɩɨɥɭɱɟɧɧɭɸ ɩɪɨɢɡɜɨɞɧɭɸ ɤ ɧɭɥɸ, ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɪɚɫɤɪɵɜ ɤɜɚɞɪɚɬ ɪɚɡɧɨɫɬɢ ɜ ɫɤɨɛɤɚɯ:
|
n |
n |
|
|
wl(a)/wa = 2 ¦ xic(ti)+2a*¦c2(ti) = 0, |
|
|
|
i 1 |
i 1 |
|
|
|
n |
n |
ɨɬɤɭɞɚ ɧɚɣɞɟɦ |
ɨɰɟɧɢɜɚɟɦɭɸ ɚɦɩɥɢɬɭɞɭ: |
a* = ¦ xic(ti)/ ¦ c2(ti)= |
|
|
|
i 1 |
i 1 |
n |
n |
|
|
=(1/E0) ¦ xic(ti), ɝɞɟ E = |
¦ c2(ti) - ɷɧɟɪɝɢɹ ɟɞɢɧɢɱɧɨɝɨ ɫɢɝɧɚɥɚ. ɉɨɫɥɟ ɩɟɪɟ- |
i 1 |
i 1 |
|
T |
ɯɨɞɚ ɤ ɧɟɩɪɟɪɵɜɧɨɣ ɪɟɚɥɢɡɚɰɢɢ x(t) ɩɪɢ nof ɩɨɥɭɱɢɦ a*= = ³ x(t)c(t)dt, ɫɥɟɞɨ- 0
ɜɚɬɟɥɶɧɨ, ɚɥɝɨɪɢɬɦ ɨɰɟɧɤɢ ɚɦɩɥɢɬɭɞɵ ɨɫɧɨɜɚɧ ɧɚ ɜɡɚɢɦɨɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɨɛɪɚɛɨɬɤɟ ɪɟɚɥɢɡɚɰɢɢ x(t) ɢ ɢɡɜɟɫɬɧɨɝɨ ɟɞɢɧɢɱɧɨɝɨ ɫɢɝɧɚɥɚ c(t). Ɉɩɪɟɞɟɥɢɦ ɤɚɱɟɫɬɜɨ ɩɨɥɭɱɟɧɧɨɣ ɨɰɟɧɤɢ, ɬ.ɟ. ɫɦɟɳɟɧɢɟ ɢ ɞɢɫɩɟɪɫɢɸ. ɋɦɟɳɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ ɨɠɢɞɚɧɢɟɦ ɨɰɟɧɤɢ a*:
T |
T |
¢a*²=(1/E0)¢ ³ |
[[(t)+a0c(t)]c(t)dt² = ¢(a0/E0) ³ c2(t)dt² = a0, |
0 |
0 |
ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɥɭɱɟɧɧɚɹ ɨɰɟɧɤɚ ɹɜɥɹɟɬɫɹ ɧɟɫɦɟɳɟɧɧɨɣ ɩɪɢ ɥɸɛɨɣ ɞɥɢɬɟɥɶɧɨɫɬɢ ɫɢɝɧɚɥɚ Ɍ. Ʉɜɚɞɪɚɬ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɝɨ ɨɬɤɥɨɧɟɧɢɹ ɨɰɟɧɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɢɫɬɢɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɚɦɩɥɢɬɭɞɵ a0 ɢɦɟɟɬ ɜɢɞ |
T |
|
T |
T |
|
¢(a*-a0)2²=¢ ³ ³ [(t1) [(t2) c(t1) c(t2)dt1dt2²/[ ³ c2(t)dt]2. |
||
0 |
0 |
0 |
ɉɨɫɤɨɥɶɤɭ ɜ ɱɢɫɥɢɬɟɥɟ ɫɥɭɱɚɣɧɵɦ ɹɜɥɹɟɬɫɹ ɬɨɥɶɤɨ [(t), ɚ ɩɪɢɟɦ ɩɪɨɢɡɜɨ-
ɞɢɬɫɹ ɧɚ ɮɨɧɟ ɛɟɥɨɝɨ ɲɭɦɚ, ɬɨ ¢[(t1)[(t2)²=S0G(W)/2. ɍɱɢɬɵɜɚɹ ɮɢɥɶɬɪɭɸɳɟɟ ɫɜɨɣɫɬɜɨ G-ɮɭɧɤɰɢɢ, ɩɨɥɭɱɢɦ ¢(a*-a0)2² = S0/(2E0). Ɉɬɧɨɫɢɬɟɥɶɧɭɸ ɫɪɟɞɧɟɤɜɚɞ-
ɪɚɬɢɱɟɫɤɭɸ ɩɨɝɪɟɲɧɨɫɬɶ ɨɰɟɧɤɢ ɚɦɩɥɢɬɭɞɵ ɨɩɪɟɞɟɥɢɦ ɩɨ ɮɨɪɦɭɥɟ ¢(a*-a0)2² /a02 =S0/(a022E0)=S0/(2E)=1/Q2, ɝɞɟ ȿ - ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ ɫɢɝɧɚɥɚ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɨɲɢɛɤɚ ɢɡɦɟɪɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɫɢɝɧɚɥɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɮɨɪɦɵ ɫɢɝɧɚɥɚ, ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɨɬɧɨɲɟɧɢɟɦ ɫɢɝɧɚɥ/ɲɭɦ Q. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ Q ɩɨɝɪɟɲɧɨɫɬɶ ɭɦɟɧɶɲɚɟɬɫɹ.
ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɟɫɥɢ ɤɪɨɦɟ ɨɰɟɧɢɜɚɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɫɢɝɧɚɥɚ ɟɫɬɶ ɧɟɢɡɦɟɪɹɟɦɵɟ ɩɚɪɚɦɟɬɪɵ, ɬɨ ɮɭɧɤɰɢɨɧɚɥ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɭɫɪɟɞɧɹɟɬɫɹ ɩɨ ɜɫɟɦ ɷɬɢɦ ɩɚɪɚɦɟɬɪɚɦ.
9.3.Ɉɰɟɧɤɚ ɧɟɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫɢɝɧɚɥɨɜ ɢɡɜɟɫɬɧɨɣ ɮɨɪɦɵ
ɉɭɫɬɶ ɫɢɝɧɚɥ s(t) ɡɚɜɢɫɢɬ ɨɬ ɤɚɤɨɝɨ-ɥɢɛɨ ɧɟɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɬ.ɟ. s(t) = s(t,a), ɤɨɬɨɪɵɦ ɦɨɠɟɬ ɛɵɬɶ, ɧɚɩɪɢɦɟɪ, ɡɚɞɟɪɠɤɚ ɫɢɝɧɚɥɚ ɢɥɢ ɫɦɟɳɟɧɢɟ ɱɚɫɬɨɬɵ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɷɮɮɟɤɬɨɦ Ⱦɨɩɥɟɪɚ. Ɍɨɝɞɚ ɮɭɧɤɰɢɨɧɚɥ ɩɪɚɜɞɨɩɨɞɨɛɢɹ (ɟɫɥɢ ɩɪɢɟɦ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɚ ɮɨɧɟ ɧɨɪɦɚɥɶɧɨɝɨ ɲɭɦɚ) ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧ ɜ
T
ɜɢɞɟ L(a) = exp[-E/S0 + +z(a)], ɝɞɟ z(a) = 2/S0 ³ |
x(t)s(t,a)dt - ɤɨɪɪɟɥɹɰɢɨɧɧɵɣ |
0 |
|
ɢɧɬɟɝɪɚɥ ɩɨ ɢɡɦɟɪɹɟɦɨɦɭɩɚɪɚɦɟɬɪɭ |
|
T |
T |
z(a) = 2/S0 ³ [s(t)+[(t)]s(t,a)dt = 2/S0 ³ s(t)s(t,a)dt+ |
|
0 |
0 |
T
+2/S0 ³ [(t)s(t,a)dt = zs(a)+z [(a),
0
ɝɞɟ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ - ɫɢɝɧɚɥɶɧɚɹ ɮɭɧɤɰɢɹ ɢɥɢ ɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɮɭɧɤɰɢɹ ɫɢɝɧɚɥɚ ɩɨ ɢɡɦɟɪɹɟɦɨɦɭ ɩɚɪɚɦɟɬɪɭ, ɚ ɜɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ - ɲɭɦɨɜɚɹ ɮɭɧɤɰɢɹ. ɋɢɝɧɚɥɶɧɚɹ ɮɭɧɤɰɢɹ ɟɫɬɶ ɜɡɚɢɦɨɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɮɭɧɤɰɢɹ ɢɫɯɨɞɧɨɝɨ (ɨɩɨɪɧɨɝɨ) ɫɢɝɧɚɥɚ ɢ ɫɢɝɧɚɥɚ, ɢɦɟɸɳɟɝɨ ɢɡɦɟɪɹɟɦɵɣ ɩɚɪɚɦɟɬɪ (ɡɚɞɟɪɠɤɚ ɢɥɢ ɫɦɟɳɟɧɢɟ ɱɚɫɬɨɬɵ), ɢ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɜɨɣɫɬɜɚ ɫɚɦɨɝɨ ɫɢɝɧɚɥɚ ɛɟɡ ɭɱɟɬɚ ɲɭɦɚ. ɗɬɚ ɮɭɧɤɰɢɹ ɱɟɬɧɚɹ ɨɬ-
ɧɨɫɢɬɟɥɶɧɨ ɩɚɪɚɦɟɬɪɚ a. ȿɟ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɪɚɜɧɨ 2E/S0, ɬ.ɟ. ɩɪɢ a = a0,
ɤɨɝɞɚ ɩɚɪɚɦɟɬɪɵ ɨɩɨɪɧɨɝɨ ɫɢɝɧɚɥɚ ɢɢɫɫɥɟɞɭɟɦɨɝɨ ɫɢɝɧɚɥɚ ɫɨɜɩɚɞɚɸɬ, ɢɦɟɟɦ
T
(2/S0) Øs2(t,a)dt = 2E/S0.
0
ɋɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɲɭɦɨɜɨɣ ɮɭɧɤɰɢɢ ɪɚɜɧɨ ɧɭɥɸ, ɬɚɤ ɤɚɤ <[(t)>=0, ɚ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɤɜɚɞɪɚɬɚ ɷɬɨɣ ɮɭɧɤɰɢɢ ɟɫɬɶ 2ȿ/S0. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɲɭɦɨɜɚɹ ɮɭɧɤɰɢɹ ɟɫɬɶ ɜɡɚɢɦɨɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɮɭɧɤɰɢɹ ɫɢɝɧɚɥɚ ɢ ɩɨɦɟɯɢ. Ʉɨɪɪɟɥɹɰɢɨɧɧɵɣ ɢɧɬɟɝɪɚɥ ɩɨ ɢɡɦɟɪɹɟɦɨɦɭ ɩɚɪɚɦɟɬɪɭ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɬɧɨɲɟɧɢɹ ɫɢɝɧɚɥ/ɲɭɦ ɢɦɟɟɬ ɬɚɤɢɟ ɨɫɨɛɟɧɧɨɫɬɢ: ɱɟɦ ɛɨɥɶɲɟ Q, ɬɟɦ ɨɫɬɪɟɟ ɷɬɚ ɮɭɧɤɰɢɹ, ɚ ɡɧɚɱɢɬ, ɬɨɱɧɟɟ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɟɞɟɧɚ ɨɰɟɧɤɚ ɩɚɪɚɦɟɬɪɚ a. Ɉɞɧɚɤɨ ɟɫɬɶ ɜɟɪɯɧɢɣ ɩɪɟɞɟɥ (ɩɨɬɟɧɰɢɚɥɶɧɵɣ) ɩɨɝɪɟɲɧɨɫɬɢ ɨɰɟɧɤɢ ɩɚɪɚɦɟɬɪɚ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɫɚɦɨɝɨ ɫɢɝɧɚɥɚ ɛɟɡ ɭɱɟɬɚ ɲɭɦɨɜɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ. ȿɫɥɢ Q>>1, ɬɨ <(a*-a0)>=0, ɚ ɟɟ ɞɢɫɩɟɪɫɢɹ ɪɚɜɧɚ
Va2 = [d2zs(a)/da2]-1/ a a0 = -1/[(2E/S0) (d 2ks(a)/da2)],
T
ɝɞɟ ks(a) =(1/S0) ³ s(t)s(t,a)dt - ɧɨɪɦɢɪɨɜɚɧɧɚɹ ɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɮɭɧɤɰɢɹ ɩɨ ɢɡ-
0
ɦɟɪɹɟɦɨɦɭ ɩɚɪɚɦɟɬɪɭ. ɉɟɪɟɞ ɜɵɪɚɠɟɧɢɟɦ ɞɥɹ Va2 ɫɬɨɢɬ ɦɢɧɭɫ ɢɡ-ɡɚ ɬɨɝɨ, ɱɬɨ ɫɢɝɧɚɥɶɧɚɹ ɮɭɧɤɰɢɹ ɩɪɢ ɡɧɚɱɟɧɢɢ a = a0 ɦɚɤɫɢɦɚɥɶɧɚ ɢ ɟɟ ɜɬɨɪɚɹ ɩɪɨɢɡɜɨɞɧɚɹ ɨɬɪɢɰɚɬɟɥɶɧɚ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɞɢɫɩɟɪɫɢɹ - ɜɟɥɢɱɢɧɚ ɩɨɥɨɠɢɬɟɥɶɧɚɹ.
ȿɫɥɢ a ɟɫɬɶ ɡɚɞɟɪɠɤɚ W, ɬɨ ɨɩɪɟɞɟɥɢɬɶ W* - ɡɧɚɱɢɬ ɧɚɣɬɢ ɩɨɥɨɠɟɧɢɟ ɦɚɤɫɢɦɭɦɚ ɧɚ ɨɫɢ W, ɢ ɱɟɦ ɨɫɬɪɟɟ ks(W)ɩɪɢ W = W0, ɬɟɦ ɜɵɲɟ ɬɨɱɧɨɫɬɶ ɨɰɟɧɤɢ W (ɛɨɥɶɲɟ ɡɧɚɱɟɧɢɟ ɜɬɨɪɨɣɩɪɨɢɡɜɨɞɧɨɣ).
Ⱥɧɚɥɨɝɢɱɧɨ ɦɨɠɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ks('Z)ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɱɚɫɬɨɬɵ ɩɪɢɯɨɞɹɳɟɝɨ ɫɢɝɧɚɥɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɱɚɫɬɨɬɵ ɩɟɪɟɞɚɜɚɟɦɨɝɨ ɫɢɝɧɚɥɚ (ɪɚɞɢɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɨɛɴɟɤɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɭɧɤɬɚ ɧɚɛɥɸɞɟɧɢɹ).
Ɍɨɱɧɨɫɬɢ ɨɰɟɧɨɤ W ɢ 'Z ɦɨɝɭɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɵ ɩɨ ɮɨɪɦɭɥɚɦ:
VW2= =1/(2EE2/S0) ɢ V:2=1/(2ED2/S0),
ff
ɝɞɟ E2 = ³ Z2F 2(Z)d Z/ ³ F 2(Z)d Z = 'Zɷ2; 'Zɷ - ɷɮɮɟɤɬɢɜɧɚɹ ɲɢɪɢɧɚ ɫɩɟɤ-
f f
ɬɪɚ ɫɢɝɧɚɥɚ; ɱɢɫɥɢɬɟɥɶ ɜɵɪɚɠɟɧɢɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɲɢɪɢɧɭ ɫɩɟɤɬɪɚ ɢ ɩɨɞɨɛɟɧ ɜɵɪɚɠɟɧɢɸ ɞɥɹ ɞɢɫɩɟɪɫɢɢ, ɤɨɬɨɪɚɹ ɩɨɤɚɡɵɜɚɟɬ ɫɬɟɩɟɧɶ ɪɚɡɛɪɨɫɚɧɧɨɫɬɢ ɋȼ, ɚ ɜ ɩɪɢɜɟɞɟɧɧɨɣ ɮɨɪɦɭɥɟ - ɫɬɟɩɟɧɶ ɪɚɫɫɟɹɧɢɹ ɫɩɟɤɬɪɚɥɶɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɨɬɧɨɫɢɬɟɥɶɧɨ Z0;
ff
D2= ³ |
t2c2(t)dt/ ³ c2(t)dt = ('t)ɷ2; 'tɷ - ɷɮɮɟɤɬɢɜɧɚɹ ɞɥɢɬɟɥɶɧɨɫɬɶ ɫɢɝɧɚɥɚ. |
f |
f |
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɬɨɛɵ ɩɨɜɵɫɢɬɶ ɬɨɱɧɨɫɬɶ ɢɡɦɟɪɟɧɢɹ ɜɪɟɦɟɧɢ ɡɚɞɟɪɠɤɢ, ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɲɢɪɢɬɶ ɫɩɟɤɬɪ ɫɢɝɧɚɥɚ, ɚ ɷɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɞɥɢɬɟɥɶ-
ɧɨɫɬɢ 't (ɞɥɹ ɫɢɝɧɚɥɨɜ ɫ ɟɞɢɧɢɱɧɨɣ ɛɚɡɨɣ) ɢ ɫɧɢɠɟɧɢɸ ɬɨɱɧɨɫɬɢ ɢɡɦɟɪɟɧɢɹ ɞɨɩɥɟɪɨɜɫɤɨɝɨ ɩɪɢɪɚɳɟɧɢɹ ɱɚɫɬɨɬɵ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɨɬɧɨɲɟɧɢɹ ɫɢɝɧɚɥ/ɲɭɦ ɬɨɱɧɨɫɬɶ ɢɡɦɟɪɟɧɢɹ ɤɚɤ W, ɬɚɤ ɢ 'Z ɜɨɡɪɚɫɬɚɟɬ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɨɫɬɵɯ ɫɢɝɧɚɥɨɜ ɧɟɜɨɡɦɨɠɧɨ ɨɞɧɨɜɪɟɦɟɧɧɨ ɭɜɟɥɢɱɢɜɚɬɶ ɪɚɡɪɟɲɟɧɢɟ ɩɨ ɡɚɞɟɪɠɤɟ ɢ ɩɨ ɞɨɩɥɟɪɨɜɫɤɨɦɭ ɩɪɢɪɚɳɟɧɢɸ ɱɚɫɬɨɬɵ, ɬɚɤ ɤɚɤ ɭɜɟɥɢɱɟɧɢɟ ɲɢɪɢɧɵ ɫɩɟɤɬɪɚ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɷɧɟɪɝɢɢ, ɚ ɡɧɚɱɢɬ, ɤ ɭɦɟɧɶɲɟɧɢɸ ɨɬɧɨɲɟɧɢɹ ɫɢɝɧɚɥ/ɲɭɦ. ȼɥɢɹɧɢɟ ɷɬɨɝɨ ɩɪɨɬɢɜɨɪɟɱɢɹ ɧɚ ɬɨɱɧɨɫɬɶ ɢɡɦɟɪɟɧɢɹ ɦɨɠɟɬ ɛɵɬɶ ɫɧɢɠɟɧɨ ɩɪɢɦɟɧɟɧɢɟɦ ɫɥɨɠɧɵɯ ɫɢɝɧɚɥɨɜ, ɭ ɤɨɬɨɪɵɯ ɫɨɱɟɬɚɟɬɫɹ ɛɨɥɶɲɚɹ ɞɥɢɬɟɥɶɧɨɫɬɶ ɫ ɲɢɪɨɤɢɦ ɫɩɟɤɬɪɨɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɨɱɧɨɫɬɶ ɢɡɦɟɪɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɡɚɜɢɫɢɬ ɧɟ ɬɨɥɶɤɨ ɨɬ ɨɬɧɨɲɟɧɢɹ ɫɢɝɧɚɥ/ɲɭɦ, ɧɨ ɢɨɬ ɮɨɪɦɵ ɫɢɝɧɚɥɚ. (ɍ ɫɥɨɠɧɵɯ ɫɢɝɧɚɥɨɜ - ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ ɩɪɨɢɡɜɟɞɟɧɢɣ ɲɢɪɢɧɵ ɫɩɟɤɬɪɚ ɧɚ ɞɥɢɬɟɥɶɧɨɫɬɶ, ɱɬɨ ɧɚɡɵɜɚɟɬɫɹ ɛɚɡɨɣ ɫɢɝɧɚɥɚ). ɇɚ ɩɪɚɤɬɢɤɟ ɢɫɩɨɥɶɡɭɸɬ ɫɢɝɧɚɥɵ, ɛɚɡɚ ɤɨɬɨɪɵɯ ɞɨɫɬɢɝɚɟɬ ɞɟɫɹɬɤɨɜ ɬɵɫɹɱ.
10.ɈȻɇȺɊɍɀȿɇɂȿ ɋɂȽɇȺɅɈȼ ɉɊɂ ȺɉɊɂɈɊɇɈɃ ɇȿɈɉɊȿȾȿɅȿɇɇɈɋɌɂ
Ɋɚɧɟɟ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɥɢ ɫɢɧɬɟɡ ɨɩɬɢɦɚɥɶɧɵɯ ɫɬɪɭɤɬɭɪ ɨɛɧɚɪɭɠɟɧɢɹ ɩɪɢ ɢɡɜɟɫɬɧɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹɯ ɩɚɪɚɦɟɬɪɨɜ ɢɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɫɢɝɧɚɥɨɜ ɢ ɩɨɦɟɯ. ȼ ɪɟɚɥɶɧɵɯ ɩɪɚɤɬɢɱɟɫɤɢɯ ɫɢɬɭɚɰɢɹɯ ɩɚɪɚɦɟɬɪɵ ɫɢɝɧɚɥɨɜ ɢ ɩɨɦɟɯ ɦɨɝɭɬ ɢɡɦɟɧɹɬɶɫɹ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ ɩɨ ɪɚɡɥɢɱɧɵɦ ɩɪɢɱɢɧɚɦ. ɇɚɩɪɢɦɟɪ, ɦɟɧɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɨɬɪɚɠɟɧɢɣ ɨɬ ɩɨɜɟɪɯɧɨɫɬɟɣ ɪɚɡɞɟɥɚ ɫɪɟɞ (ɩɚɫɫɢɜɧɚɹ ɩɨɦɟɯɚ ɜ ɪɚɞɢɨɥɨɤɚɰɢɢ ɢɥɢ ɪɟɜɟɪɛɟɪɚɰɢɹ ɜ ɝɢɞɪɨɥɨɤɚɰɢɢ) ɢɡ-ɡɚ ɢɡɦɟɧɟɧɢɹ ɭɫɥɨɜɢɣ ɨɬɪɚɠɟɧɢɹ ɡɨɧɞɢɪɭɸɳɢɯ ɫɢɝɧɚɥɨɜ ɨɬ ɷɬɢɯ ɩɨɜɟɪɯɧɨɫɬɟɣ. ɉɚɪɚɦɟɬɪɵ ɚɤɬɢɜɧɵɯ ɩɨɦɟɯ ɦɨɝɭɬ ɢɡɦɟɧɹɬɶɫɹ ɢ ɢɫɤɭɫɫɬɜɟɧɧɨ, ɞɥɹ ɜɜɟɞɟɧɢɹ ɩɪɨɬɢɜɧɢɤɚ ɜ ɡɚɛɥɭɠɞɟɧɢɟ ɢɥɢ ɭɯɭɞɲɟɧɢɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɨɛɧɚɪɭɠɟɧɢɹ. Ⱦɚɠɟ ɩɚɪɚɦɟɬɪɵ ɜɧɭɬɪɢɩɪɢɟɦɧɨɝɨ ɲɭɦɚ ɧɟ ɨɫɬɚɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ, ɚ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɪɚɡɥɢɱɧɵɦ ɩɪɢɱɢɧɚɦ: ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ, ɧɚɩɪɹɠɟɧɢɹ ɩɢɬɚɧɢɹ ɢ ɬ.ɞ. ȿɫɥɢ ɢɦɟɟɬɫɹ ɨɛɧɚɪɭɠɢɬɟɥɶ, ɫɢɧɬɟɡɢɪɨɜɚɧɧɵɣ ɜ ɭɫɥɨɜɢɹɯ ɫɬɚɰɢɨɧɚɪɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɨɦɟɯ, ɬɨ ɟɝɨ ɩɨɤɚɡɚɬɟɥɢ ɢɡɦɟɧɹɸɬɫɹ ɜ ɪɟɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɪɚɛɨɬɵ ɩɪɢɢɡɦɟɧɟɧɢɢ ɷɬɢɯɩɚɪɚɦɟɬɪɨɜ [6. ɋ. 61-62]
11.ɂɇɌȿɊȼȺɅɖɇɕȿ ɈɐȿɇɄɂ ɉȺɊȺɆȿɌɊɈȼ ɋɂȽɇȺɅɈȼ
Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɬɨɱɟɱɧɵɟ ɨɰɟɧɤɢ ɩɚɪɚɦɟɬɪɨɜ ɫɢɝɧɚɥɨɜ ɧɟ ɩɨɡɜɨɥɹɸɬ ɨɰɟɧɢɬɶ ɫɬɟɩɟɧɶ ɛɥɢɡɨɫɬɢ ɩɨɥɭɱɟɧɧɨɣ ɨɰɟɧɤɢ ɤ ɢɫɬɢɧɧɨɦɭ ɡɧɚɱɟɧɢɸ ɨɰɟɧɢɜɚɟɦɨɝɨ ɩɚɪɚɦɟɬɪɚ. Ȼɨɥɟɟ ɫɨɞɟɪɠɚɬɟɥɶɧɚ ɩɪɨɰɟɞɭɪɚ ɨɰɟɧɤɢ ɩɚɪɚɦɟɬɪɚ, ɫɜɹɡɚɧɧɚɹ ɫ ɩɨɫɬɪɨɟɧɢɟɦ ɢɧɬɟɪɜɚɥɚ, ɤɨɬɨɪɵɣ "ɩɟɪɟɤɪɵɜɚɟɬ" ɨɰɟɧɢɜɚɟɦɵɣ ɩɚɪɚɦɟɬɪ ɫ ɢɡɜɟɫɬɧɨɣ ɫɬɟɩɟɧɶɸ ɞɨɫɬɨɜɟɪɧɨɫɬɢ. ɇɚɩɪɢɦɟɪ, ɩɭɫɬɶ ɨɰɟɧɤɚ mx* ɫɪɟɞɧɟɝɨ ɡɧɚɱɟɧɢɹ ɜɵɱɢɫɥɟɧɚ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɦɟɬɨɞɚ ɫɪɟɞɧɟɝɨ ɚɪɢɮɦɟɬɢɱɟɫɤɨɝɨ ɩɨ n ɧɟɡɚɜɢɫɢɦɵɦ ɧɚɛɥɸɞɟɧɢɹɦ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɏ. ɉɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɨɰɟɧɢɬɶ mx ɜ ɩɪɟɞɟɥɚɯ ɧɟɤɨɬɨɪɨɝɨ ɢɧɬɟɪɜɚɥɚ m*±'m, ɜ ɤɨɬɨɪɵɣ mx ɩɨɩɚɞɚɟɬ ɫ ɡɚɞɚɧɧɨɣ ɫɬɟ-