ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
100
1 2
0
0
1/ 2
0
exp
(
)
f
a
f
w
a
a w
D p
E
D
p
R
§ ·
§
·
¨ ¸
¨
¸
© ¹
©
¹
P
T T
T
(5)
ɂɡ ɜɵɪɚɠɟɧɢɹ (5) ɩɨɥɭɱɢɦ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨ-
ɪɨɫɬɢ ɝɨɪɟɧɢɹ
f
D
ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɜɟɪɯɧɨɫɬɢ
w
T
ɢ ɫɬɟɩɟɧɧɭɸ ɡɚ-
ɜɢɫɢɦɨɫɬɶ ɨɬ ɞɚɜɥɟɧɢɹ
0
p
ɫɨ ɫɬɟɩɟɧɶɸ, ɪɚɜɧɨɣ 1/2. Ɍɚɤɨɣ ɠɟ ɪɟɡɭɥɶ-
ɬɚɬ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɬɢɩɚ Ⱥɪɪɟɧɢ-
ɭɫɚ [9], ɨɞɧɚɤɨ ɜ ɮɨɪɦɭɥɟ (5) ɩɪɟɞɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣ ɦɧɨɠɢɬɟɥɶ
0
f
D
ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɤɚɤ ɨɛɵɱɧɨ ɞɥɹ ɮɨɪɦɭɥ ɬɢɩɚ Ⱥɪ-
ɪɟɧɢɭɫɚ, ɚ ɫ ɩɨɦɨɳɶɸ ɪɚɫɱɟɬɨɜ ɩɨ ɮɨɪɦɭɥɟ (4). ɗɬɨ ɨɫɧɨɜɧɚɹ ɨɫɨ-
ɛɟɧɧɨɫɬɶ ɩɪɟɞɥɚɝɚɟɦɨɣ ɦɨɞɟɥɢ.
Ɍɟɦɩɟɪɚɬɭɪɚ ɩɨɜɟɪɯɧɨɫɬɢ
w
T
ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟ-
ɧɢɹ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɫ ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨɜɢɹɦɢ
2
2
;
D
k
x x
t
c x
w
w
t
w
w
T
T
U
(6)
4
SB
e
w f
D
k
q
D e x x
x
w
'
w
T
HV T
U
(7)
ɝɞɟ
e
'
—
ɬɟɩɥɨɬɚ ɝɚɡɢɮɢɤɚɰɢɢ ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ;
SB
V
—
ɤɨɧɫɬɚɧɬɚ
ɋɬɟɮɚɧɚ—Ȼɨɥɶɰɦɚɧɚ;
H
—
ɫɬɟɩɟɧɶ ɱɟɪɧɨɬɵ;
D
x x
—
ɩɨɥɨɠɟɧɢɟ
ɩɨɜɟɪɯɧɨɫɬɢ ɝɨɪɟɧɢɹ ɜ ɤɨɨɪɞɢɧɚɬɚɯ
Ox
;
t
—
ɜɪɟɦɹ.
ɂɡ ɭɪɚɜɧɟɧɢɣ (6) ɢ (7) ɧɚɣɞɟɦ
w
T
ɤɚɤ ɮɭɧɤɰɢɸ ,
e
q
ɚ ɬɚɤɠɟ
k
,
U
,
c
,
H
ɢ
.
e
'
ȿɫɥɢ ɧɚɝɪɟɜ ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɦɟɞ-
ɥɟɧɧɵɦ, ɬ. ɟ. ɬɚɤɢɦ, ɱɬɨ ɝɪɚɞɢɟɧɬ ɬɟɦɩɟɪɚɬɭɪɵ (
)
x
w w
T
ɨɬɧɨɫɢɬɟɥɶɧɨ
ɦɚɥ, ɬɨ ɬɟɩɥɨɩɟɪɟɧɨɫ ɜ ɝɥɭɛɶ ɦɚɬɟɪɢɚɥɚ ɛɭɞɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɢɦ,
ɱɟɦ ɨɬɬɨɤ ɬɟɩɥɨɬɵ ɜɫɥɟɞɫɬɜɢɟ ɢɡɥɭɱɟɧɢɹ:
4
SB
(
)
.
w
w
| k
x |
w w
T
HV T
Ɍɨɝɞɚ
ɬɟɦɩɟɪɚɬɭɪɭ ɩɨɜɟɪɯɧɨɫɬɢ
w
T
ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɪɢɛɥɢɠɟɧɧɨ ɢɡ
ɭɪɚɜɧɟɧɢɹ (7):
1 4
SB
( )
e
f
w e
q D e
q
§
· '
¨
¸
¨
¸
©
¹
U
T
HV
(8)
ɉɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɟ (8) ɞɥɹ
w
T
ɜ (5), ɩɨɥɭɱɢɦ ɫɤɨɪɨɫɬɶ
f
D
ɜ
ɜɢɞɟ ɮɭɧɤɰɢɢ ɨɬ
0
p
ɢ
e
q
(3).
ɋɤɨɪɨɫɬɶ ɜɧɭɬɪɟɧɧɟɝɨ ɷɪɨɡɢɨɧɧɨɝɨ ɝɨɪɟɧɢɹ
i
D
.
ɋɜɨɛɨɞɧɨɟ
ɝɨɪɟɧɢɟ — ɷɬɨ ɢɞɟɚɥɢɡɢɪɨɜɚɧɧɚɹ ɫɯɟɦɚ ɝɨɪɟɧɢɹ ɪɟɚɥɶɧɵɯ ɦɚɬɟɪɢɚ-
ɥɨɜ. Ɍɜɟɪɞɵɟ ɬɨɩɥɢɜɚ ɞɚɠɟ ɞɜɭɯɨɫɧɨɜɧɨɝɨ ɬɢɩɚ ɹɜɥɹɸɬɫɹ ɝɟɬɟɪɨ-