Морозов А. Н., Скрипкин А. В.

25
3, 2011
535.2
,
. .
, . .
,
,
,
.
,
,
.
PACS: 05.40.Ca, 44.40.+a
:
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C—
S—
—
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(
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)
(1))
(
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T0
T (t )
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(2)
3 ST03
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C
-
t )1/3
(1
-
T0 —
t = 0.
.
4
I (t )
-
ST (t ),
(2),
I(t)
J(t)
.
,
(
)
-
I (t )
I0 —
-
I0
t )4/3
(1
t = 0.
,
,
(3)
,
(3) (
-
,
C dT
S dt
T 4,
(1)
),
(
,
) [1].
,
.
,
.
-
J,
. . .
.
, 105005,
, . 2, 5.
. (499) 263-67-35. E-mail: a.skripkin@mail.ru
18
. .,
-
,
. ., 2011
2010 .
t<
t= ,
I (t )
J
(1
(t
)) 4/3
,
t< .
26
3, 2011
,
,
,
).
J( )
( ;
d )
dI (t )
d
d (1
-
J( )
)) 4/3
(t
J0.
d .
,
-
,
J( ),
I (t )
4
3
t
0
,
(t
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,
(4)
d .
7/3
(4)
,
,
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,
I(t),
-
(4),
t = 0,
J(t)
.
J(t)
I(t)
,
(4)
,
-
(4).
,
,
[5].
g1 ( ; t )
[2].
,
.
.
1
-
g L ( 1 ,...,
exp iJ 0
-
,
—
,
.
-
,
[4]
.
,
-
exp
L
-
2
11/3
t)
(5)
,
l 1
(tl
(1
2
l
2
4/3
(1
1
11/3
(tl
t1 ))
L
tk )
F(a, b, c; x) —
[6].
,
tl )11/3
(tl tk ) 7/3
F( 4 / 3,7 / 3, 1/ 3;1/ ( (tl
(1
(1
l k
l , k 1, k l
F ( 4 / 3,7 / 3, 1/ 3;(1
l
tl )4/3
1
1
7/3
1
t1 ))
1 L
11 l 1 (1
8
3
L ; t1 ,..., t L )
1
. .).
,
1
L
g L ( 1 ,..., L ; t1 ,..., t L )
[3].
t ) 4/3
(1
8
1
33
(1
exp
-
,
,
I(t)
g1 ( ; t ) exp iJ 0 1
,
(
-
,
-
.
,
J(t)
.
-
,
J( )
1
,
,
tk )))
tk ) / ( (tl tk )))
4/3
, (6)
27
3, 2011
F(a, b, c; x)
x < 1.
1 tk
1;
(tl tk )
1
1
(tl tk )
.
,
(6)
1 tk
1,
(tl tk )
(6)
-
1
12,00
2
8,00
4,00
.
(5)
(6)
3
0
0,02
0,04
. 2.
0,1
2
4
=1
,
c = 380
/(
)
(1), R = 2
(2) R = 3
(3)
R=1
DI(t)
0,08
DI(t)
I(t)
[7],
I(t)
0,06
t,
-
I(t).
4
16,00
0,00
,
2
DI(t),
20,00
-
:
g1 ( ; t )
(i )
I (t )
2
DI (t )
I (t )
J0 1
0
2
I (t )
(7)
1
t ) 4/3
(1
16
1
33
(1
(8)
(7)
;
I
I
1
n
I
n
I
0, n —
( n 1)!! D n / 2 (t ), n —
.
K(t,t – )
(
)
I(t)
,
,
-
g 2 ( 1,
-
2 ; t1 , t 2 ).
(6)
,
J0
16 /33.
(7) (8)
.1
2
K (t , t
,
1
(1
1
(1
)
4/3
(1
t)
)) 4/3
(t
1
4/3
J 02
F ( 4 / 3,7 / 3, 1/ 3;1 /
2
F ( 4 / 3,7 / 3, 1/ 3;(1
0,80
(1
1
0,60
(t
))
(t
4/3 7/3
2
)
)) /
4/3
)
.
(9)
2
3
(6),
0,40
1
0,20
0,00
)
1
.
< I(t) >,
1,00
,
. (8)
t )11/3
,
t
;
0
0,02
0,04
0,06
0,08
)
.3
0,1
t,
(t
1
(9)
t 1/
.
2
),
K(t,t –
t 1/
2
,
(9)
. 1.
I(t)
R=1
J0 = 1
c = 380
/(
(1), R = 2
(2) R = 3
2
,
)
(3)
J 02
t.
-
28
3, 2011
-
K(t, t– )/ J 02
7
6
GI( ),
5
I(t),
4
1
0
,
Iˆ( s)
i .
3
2
-
(7)
3
1
0
0,02
2
0,04
0,06
0,08
0,1
K(t,t– )/J02
= 10
t = 0,1 (1), t = 0,2 (2) t = 1 (3)
4 s ˆ
,
J ( s ),
3
es/
s—
ˆ
J ( s) —
t,
. 3.
4/3
4 s
3
Iˆ( s )
–1
(10)
t;
J(t);
x, y —
,
-
g1 ( ; t ),
(5),
t x 1e t dt .
( x, y )
I(t)
(11)
y
(10)
(11)
-
.
(12)
,
p( I , t )
,
1
2
g1 ( ; t ) exp( i I )d
1
2 D (t )
(I
exp
I )
2 D (t )
,
8/3
16
9
GI ( )
2
GI( )
,
I(t)
,
p(I,t)
,
t.
I(t) "
I, "
GI( ),
-
"
.
0,6
3
0,4
0
2
1
0
2
4
6
8
10
,
1
. 5.
0,0953
0,0949
4
1
0,2
2
0,0957
0,0951
2
0,8
,
0,0955
-
1,2
"
t
p(I, t),
GI( )
. 5.
.
. 4
4
,
3
2
I(t)
= 10 -1, = 20
2
-1
DI( )
-1
,
= 30
-
-1
,
3
0,0947
0,4
0,6
0,8
. 4.
1
1,2
I,
1,4
,
-
2
.
p(I,t)
R=1
t = 0,1 (2)
-
t = 0,07 (1),
(
1/ )
t = 0,13 (3)
,
-
(4),
.
-
29
3, 2011
-
0,
w( )
: w( )
,
-
(
0 ),
.
J(t)
N0
-
.
.
h( ) exp i
(15)
.
0
(15)
(13)
(14)
-
J0 (
)
0 —
N0 0,
I(t):
,
n 1
.
g1 ( ; t ) exp N 0
,
, . .
-
.
g1 ( ; t )
L
g L ( 1 ,...,
g1 ( ; t ) exp N0
g L ( 1 ,...,
4
3
t
h
0
4
3 (1
L ; t1 ,..., t L )
(t
))
exp N 0
L
d
))7/3
(tk
(17)
.
)
)
(
(16)
(17),
-
(7)—(9),
h
J0
0
N0
N 0 02 .
0
-
k
k 1 (1
n
3n n !
n 1
k
,
min(t1 ,...,t L )
0)
(
1 d ; (13)
7/3
(4i
n
L
k 1 (1
0
(16)
;
1
L ; t1 ,..., t L ) exp N 0
min(t1 ,...,t L )
J(t),
t )7 n /3
(1
)n
0
3n n !(7n / 3 1)
n 1
1
1
h( ),
g ( 1,..., L ; t1,..., tL )
I(t)
-
(4i
1 d
))7/3
(tk
(14)
.
,
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,
-
(
).
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0
2
0.
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I
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I
I
4
32
243
3
I
256
2
N0
2
4
0
N 0 30 ,
N0
363
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;
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D
0.
w( ),
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. .
w( )
1
2 D
exp
(
0)
2D
2
,
30
3, 2011
,
-
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,
. .
h( ) exp(i
1
D
2
) exp
0
2
2
0 N0
.
N 02 ,
—
(13)
g1 ( ; t )
(14),
g ( 1,...,
L
.
-
,
L ; t1,..., t L )
,
-
,
I(t)
,
,
-
.
-
N0:
g1 ( ; t ) exp N 0
exp
t
exp
exp
0
8 L
9 k 1 (1
,
))7/3
,
,
.
2 2
1 d
))14/3
(t
g L ( 1,...,
t
0
(t
3(1
0
8
D
9
(1
exp N 0
4i
exp
(18)
,
L ; t1 ,..., t L )
4 L
3 k 1 (1
i
,
,
))7/3
(tk
,
2 2
k
D
1 d
))14/3
( tk
,
0 k
.
,
,
,
I(t) ,
,
,
J0
N 0 0 ).
(8),
,
,
-
.
(18) (7) ( DI(t)
,
-
,
,
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1.
N 0 (2
2
0
D ),
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-
.
(12),
.
[8],
,
. .
. — .:
, 1964.
2.
. .
. — .:
. . .
3.
. .,
. . //
. 2009. . 52. 2. . 66.
4.
. .,
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, 1997.
.
.—
1976.
5.
2004.
6.
7.
.
. //
. .
,
.
.
. .C
, 1984.
. .
, 1990.
.—
-
3. . 47.
.
.
.,
.—
.:
.,
.—
8.
.:
-
.
.:
.:
, 1988.
31
3, 2011
Thermal radiation of the body subjected to the fluctuating
external influence
A. N. Morozov, A. V. Skripkin
Bauman Moscow State Technical University, 5 2-nd Bauman str., Moscow, 105005, Russia
E-mail: a.skripkin@mail.ru
Considered are fluctuations of a radiation intensity of the body which is subjected to the external
influence having a character of the white or shot noise. The general statistical characteristics of radiation, such as characteristic functions, dispersion, spectral density, etc, are defined.
PACS: 05.40.Ca, 44.40.+a
Keywords: thermal radiation, intensity fluctuations, non-Markovian process, charasteric function, spectral
density
Bibliography — 8 references.
Received February 18, 2010