3 diffusion r1

7/22/2019 3 Diffusion r1

1/29

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrens 2

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrensprlpbrlm iy

Zd. K. Jbrhbnm, Sreflsser, Mlpbrtdlnt ef Lnjonllronj Sgyso`s,

D`Dbstlr \novlrsoty, Gbdohten, Entbroe, @bnbmbQIbslm en @gbptlr < ef Hbdbrsg son`l tgl trlbtdlnt tglrl os jeemT

Derl bieut tgos meùdlnt

Puddbry;

Nlutren devldlnt os demlhhlm glrlon bs b moffusoen pre`lss. Dene-lnlrjlto` nlutrens brl uslm

fer ohhustrbtoen purpesls. Bnbhyto`bh sehutoens ef tgl nlutren mostroiutoen brl seujgt fer sedl

sodphl `bsls onvehvonj foxlm seur`ls.

]bihl ef @entlnts

2 Ontremu`toen............................................................................................................................. 02.2 Hlbrnonj Eutèdls......................................................................................................... =

9 Zgy Moffusoen ........................................................................................................................ > 4 ènstbnt.

Ot sgeuhm il netlm gewlvlr tgbt P(r) `bn hlbm te hbrjl vbhuls ef ( )

rr

wgo`g voehbtls

bssudptoen (l).

0. Peur`ls. Bs plr bssudptoen (b), wl `bn jlt bwby wotg seur`ls bs henj bs tgly brl derl

tgbn b flw dlbn frll pbtgs bwby.

=. Osetrepo` s`bttlronj. Bnosetrepo` s`bttlronj `bn il èrrl`tlm fer iy mltbohlm

ènsomlrbtoens ef trbnspert tglery on wgo`g M os rl-lvbhubtlm;

+ /M 2 + 0M M t bs s hn9 2 + 0M /M

b st b

4

Zglrl

ès (bvlrbjl ef tgl s`bttlronj bnjhl on tgl hbi systld)9

0B4 Lxpbnmonj tgl lqubtoen on M, bievl;

2M 4

0 (2 )(2 = /


14/29

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrens 2=

42

0 (2 )t

fer b /t882

tr

M 4 0 bs prlvoeushy mlfonlm on tgl supphldlntbh dbtlrobh bt tgl lnm ef tgl `gbptlrenIbso` Mlfonotoens bnm Slrspl`tovls


15/29



16/29


7 ]gl Moffusoen Lqubtoen

Zl rlturn new te tgl nlutren ibhbn`l lqubtoen;

n( ,t) 4 s( ,t) ( ) ( ,t) ( ,t)bt

r r r r K ro (7.2)

bnm suistotutl4 M ( ,t) K r

te jovl

n( ,t) 4 s( ,t) ( ) ( ,t)+ M ( ,t)bt

r r r r ro

Of M 4 ènstbnt w.r.t. rtgln (usonj n v 4 )9

b

2 ( , t) 4 P( ,t) ( ) ( , t) + M ( ,t)

v t

r r r r r Nlutren moffusoen lqubtoen

Fer stlbmy stbtl 2 ( ,t) 4 3v t

r . ]gos stlbmy stbtl moffusoen lqubtoens os bhse anewn bs tgl

s`bhbr Glhdgehtz lqubtoen. Of s (r) 4 3 bs wlhh, ot os sedltodls `bhhlm tgl iuàhonj lqubtoen

on bnbhejy te tgl lqubtoen jevlrnonj tgl iuàhonj ef ilbds on strlnjtg ef dbtlrobhs. Ot os bhse

anewn bs tgl wbvl lqubtoen on bnbhejy te voirbtonj stronjs, lt`.

L;X]LB@GXLS=M0XtlxtX0-moffusoenXmoffusoen-r2.me` 933=-37-2:


17/29

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrens 2:

? Ieunmbry @enmotoens fer tgl Ptlbmy Ptbtl Moffusoen Lqubtoen

Fer tgos typl ef lqubtoen tgl fehhewonj bpphols;

En tgl ieunmbrols ef b rljoen on wgo`g sbtosfols tgl mofflrlntobh lqubtoen, lotglr , er tglnerdbh mlrovbtovl ef , er b honlbr èdionbtoen ef tgl twe dust il splòfolm. Ietg bnm otsnerdbh mlrovbtovl `bnnet il splòfolm onmlplnmlnthy.

?.2 Ieunmbry @enmotoens bt Purfb`ls

Enl typl ef ieunmbry ènmotoen e`ùrs bt surfb`ls, ol., ontlrfb`ls iltwlln mlnsl bnm spbrsl

dlmob rl`bhh tgbt Foàs Hbw (bnm gln`l Moffusoen ]glery) os net vbhom nlbr b surfb`l. ]glrlferl

splòbh ènsomlrbtoen dust il jovln.

Zl bssudl b ieunmbry

ènmotoen bt tgl surfb`l ef tgl

ferd

Ylb`ter Vbùud

mostbn`lm

moffusoen tglery

trbnspert tglery

m/mn4shepl4-/m

Ieunmbry2.fhb

2 m 2 4mn m

wglrl m 4 lxtrbpehbtlm hlnjtg

bnm

m

mn

4 nerdbh mlrovbtovl bttgl surfb`l. Netl tgbt tgos

lqubtoen sbtosfols tgl bievl

ènmotoen rljbrmonj ieunmbry

ènmotoen ferds.

Fojurl : Lxtrbpehbtlm hlnjtg

Odpesonj tgos I.@. en b nen rl-lntrbnt surfb`l (enl on wgo`g nlutrens `bnnet rl-lntlr en`l tgly

gbvl hlft tgl dlmoud) jovls;

m 4 3.:2 trfer phbnbr surfb`ls

fred trbnspert tglery. Ot `bn il sgewn tgbt tgos I.@. jovls bn b`ùrbtl vbhul ef fer ontlroerpeonts iut net nlbr er bt tgl surfb`l.


On volw ef tgl fb`t tgbt 4 3 bt tgl lxtrbpehbtlm hlnjtg bnm son`l m 88 systld modlnsoens on


18/29


prb`to`bh sotubtoens, tgl bievl I.@. os rlphb`lm wotg hotthl lrrer iy;

]gl sehutoen te tgl moffusoen lqubtoen vbnosgls bt tgl lxtrbpehbtoen mostbn`l ilyenm tgl lmjl ef b

frll surfb`l.

]gl bssudptoens onglrlnt on tgl bievl sgeuhm il `brlfuhhy netlm.

Pon`l M 4 moffusoen èlffoòlnt 4

tr0

bnm M ~ 2 `d,

m 4 .:2 ~.:2 0 ~ 9 `d 88 rlb`ter sozl (dltlrs)tr

(surfb`l) 3

?.9 Ieunmbry @enmotoens bt bn Ontlrfb`l

Bt bn ontlrfb`l, tglrl os ne b`ùduhbtoen ef nlutrens. ]glrlferl;

(KB)n4 (KI)n wglrl n4nerdbh morl`toen

ol. tgl nlutren ùrrlnt on rljoen B 4 tgbt ef I

Bhse, n (r, t, ) bnm (r, t, ) brl èntonueus b`ress tgl ontlrfb`l.

?.0 Etglr @enmotoens

Sgyso`bh rlquorldlnts;

2. B nljbtovl er odbjonbry fhux gbs ne dlbnonj. Gln`l; tgl sehutoen te tglmoffusoen lqubtoen dust il rlbh, nen-nljbtovl bnm sonjhl vbhulm on tgesl rljoens

wglrl tgl lqubtoen bpphols.

9. lx`lpt fer sonjuhbr peonts ef seur`l mostroiutoens. ]glsl twe ènstrbontsslrvl te lhodonbtl lxtrbnleus fun`toens fred tgl sehutoen.



19/29

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrens 2?

?.= Puddbry ef Ieunmbry @enmotoens

2. 4 bt bn ontlrfb`l

9. K 4 K

0. mlfonlmbt b surfb`l

=. K 4 mlfonlm

3 bnm rlbh



20/29


23Lhldlntbry Pehutoens ef tgl Ptlbmy Ptbtl Moffusoen Lqubtoen

Zl gbvl prlvoeushy sgewn tgl Ptlbmy Ptbtl Moffusoen Lqubtoen te il

93 P( ) ( ) ( )+M ( )b

4 r r r r

MlfononjM9 9H 4 Q`d T1 H moffusoen hlnjtg

b

29 49 MH

P (23.2)

23.2Onfonotl Shbnbr Peur`l

(x) 4 3, x 3

Peur`l, P nlutrens/d9-s

x

ShbnbrOnfonotl2.fhb

i

b(x) mx 4 2, b 8 3 8 i

4 3 etglrwosl

Fojurl 7 Fhux mostroiutoen fer b phbnbr seur`l

Lqubtoen (23.2) rlmu`ls te;

9m (x) 2 P (x)4

9 9 Mmx H

(x) (23.9)

bnm fer x 39m (x) (x)

4 39 9mx H

(23.0)



21/29


@ensomlr tgl phbnbr seur`l (bs sgewn on fojurl ?)

3`urrlnt fred lotglr lnm

hod K(x) 4x

-x/H x/H(x) 4 B l + @ l

-x/H (x) 4 B l , x > 3

P

9

(23.=)

SohhIex.fhb

x x

KK

]gl sehutoen te Lqubtoen (23.0) gbs tgl fehhewonj ferd;

(23. 3, @ 4 3, etglrwosl os nen-fonotl bs x

(23.6)

Fojurl ? @urrlnt "pohh iex"

Fred Fo`as Hbwm MB MB-x/HK 4 M 4 + l 4 4

3 mx H H 93 3

P

PHB 4

9M

PH -x/H (x) 4 l x > 39M

(23.:)

Podohbrhy fer x 8 3, jovonj- x /HPH

(x) 4 l9M

. Yl`bhh tgbt tgos net vbhom bt er nlbr x 4 3.

]gos sehutoen sgeuhm dbal pgyso`bh slnsl te yeu. ]gl fhux ml`bys lxpenlntobhhy bwby fred tgl

seur`l bs ot os biserilm iy tgl dlmoud. ]gos bjrlls wotg tgl ilbd biserptoen hbws tgbt wl gbvl

prlvoeushy mlrovlm.



22/29


23.9Seont Peur`l on bn Onfonotl Dlmoud

Fer b peont seur`l, ot os bppreprobtl te wera on spglro`bh

`eermonbtls;

surfb`l brlb 4 =r9

r

P(r)

Peur`l2.fhb

9

9 9

2 m m 2r

mr mr r H

4 P (r) (23.7)

wglrl tgl seur`l, P, os bt r 4 3.

Fojurl 23 Seont seur`l

New9= r K(r) P (r) P 4 4

9

r 3

Phod r K(r)

= 4

(23.?)

Zl mlfonl b `gbnjl ef vbrobihl9

9 9

24r - 43

r H

(23.23)

bnm, tglrlferl, bs ilferl;-r/H r / H4Bl @l +

er-r/H r/Hl l

4B +@ bnm @43 bs ilferl.

r r

New,

r / H

9

m 2 2K4-M MB l

mx rH r

4 +

9 r / H 3/ H

r 3r 3

r Pr K MB 2 l MBl MB

H =

4

4

4 + 4 4 4

r / HP PB4 , 4 l=M = Mr

Netl; On tgl bievl twe `bsls, bs on dest rlb`ter `bsls, tgl fhux, , os prepertoenbh te tgl seur`l

strlnjtg, P.



23/29




24/29

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrens 9=

23.0Pystlds wotg b Frll Purfb`l

Ylb`ter


lxtrbpehbtlm

hlnjtg

b/9

ShbnbrFonotl2.fhb

b/9

Fojurl 22 Shbnbr seur`l on b fonotl shbi

@ensomlr bn onfonotl shbi ef tgo`anlss b-9m, wglrl m43.:2 tr, gln`l (b/9) 4 3. ]gl jevlrnonj2 spllm nlutren moffusoen lqubtoen on stlbmy stbtl os

9m (x) 2 P (x)4

9 9 Mmx H

(x)

Zl try b sehutoen ef tgl ferd;

-x/H x/H(x) 4 B l + @ l

Fer x>3,

( )

( )

b / H b / Hb9

b / H

x / H (x b) / H

3 Bl @l

@ Bl

B l l

+

+

4 4 +

4

4

Bs ilferlx / H (x b / H)

x 3

b / H

m P MBK M l l

mx 9 H

MB2 l

H

4

4 4 4 + +

4 +


( )2

b / H x / H (x b) / HPH 2 l l l9M

4 +


25/29



26/29


23.=Duhto-rljoen Sreihlds

@ensomlr tgl onfonotl shbi ef tgl prlvoeus dlmoud surreunmlm iy b slènm dlmoud ef onfonotl

tgoànlss.

Yljoen 2


Yljoen 9 Yljoen 9

pgyso`bh

ontlrfb`l

pgyso`bh

ontlrfb`l

b/9

Shbnbr9Yljoen2.fhb

b/9

Zl gbvl;9

2 b2 99 9

2

99 b

9 99 99

m 23 fer x , x 3

mx H

m 2

3 fer xmx H

4

4

Ieunmbry ènmotoens

2. 9 fonotl bs x 4

9.x 3

Phod K(x) (seur`l enmotoen, nerdbhozbtoen)

94

0. ( ) ( )2 9b / 9 b / 9 èntonuoty ef fhux bt tgl ontlrfb`l 4

=. 2 92 9x b / 9 x b / 9

m mM M èntonuoty ef urrlnt bt tgl ontlrfb`l

mx mx4 4

4

Zl try;

9 9

2 2 2 2

x / H x / H9 9 9

(x) B èsg(x / H ) @ song(x / H )

(x) B l @ l

4 +

4 +

2

]gus wl gbvl = unanewns bnm = ieunmbry ènmotoens.



27/29

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrens 9:

Oddlmobtlhy; @943 fred I.@. (2) bievl.

Fred (9);

2 2 2 2x / H x / H x / H x / H2 2 2 2 2

22 23

x 3 x 3

P m M B l l M @ l lK(3) M

9 mx H 9 H 9

4 4

+4 4 4

22

2

PH@

9M 4

Fred I.@. (0)

9b / 9H22 9

2 2 2

b PH bB èsg song B l

9H 9M 9H

+ 4

Fred I.@. (=)

9b / 9H2 2 9 9

2 2 2 9

M B b P b M Bsong èsg l

H 9H 9 9H H

+ 4

9 lqubtoens on

9 unanewns

Pehvl fer B2bnm B9

Pehvonj jovls;

2 2 9 2 9 2 22

2 9 2 2 2 9 2

PH M H èsg(b / 9H ) M H song(b / 9H )B

9M M H èsg(b / 9H ) M H song(b / 9H )

+4

+

2b / 9H2 9

99 2 2 2 9 2

PH H lB

9 M H èsg(b / 9H ) M H song(b / 9H )4

+

]glrlferl, wl anew 2bnm 9 .

Netls;

2. 2bnm 9 brl prepertoenbh te P.9. Ot `bn il sgewn tgbt os èntonueus bt b/9 bnm tgbt m/mx os netèntonueus iut M m/mx os. ]gos rlsuhts fred tgl ieunmbryènmotoens odpeslm. Enhy of M24M9os èntonueus.



28/29


22Moffusoen Hlnjtg

Zl gbvl sgewn tgbt, fer b peont seur`l ef nlutrens, P bt r 4 3,r / HPl

( ) ,wglrl H os tgl gbrb`tlrosto` hlnjtg fer fbhh eff ef= rM

4

r

]gl nudilr ef nlutrens biserilm iltwlln r bnm r+mr os;r / H

9bb

r / H r / Hb9

PlmN (r)mV = r mr

M= r

PPl rmr rl mr

M H

4 4

4 4

]gus tgl preibiohoty ef ontlrb`toen (biserptoen) os

r / H

9

mN rp(r)mr l mr

P H

4 4

r / H n bx

9 n3 3 3

r np(r)mr l mr 2 (rl`bhh tgbt x l mx )

H b

+2

! 4 4 4

ol, bhh tgl nlutrens brl biserilm lvlntubhhy.

]gl sl`enm dedlnt ef os mlfonlm;9 r / H

9 9

93

r rlr m

H

4 4 r 6H

]gus

9 92H r6

4

nlutren

ldottlm

ontlrb`toen

nlutrenbiserilm

r

MoffusoenHlnjtg2.fhb

]gbt os, tgl moffusoen hlnjtg

bvlrbjl ef tgl

squbrl ef `rew-fhojgt mostbn`l ef tgl

nlutren.

9bH M / (2/ 6)4 4 x

H9os eftln `bhhlm tgl moffusoen brlb.

Zl mlfonl 92

H6

b

9r . Fer tgl

bpprexodbtoen ef moffusoen tglerybs wlhh.9H M /

Fojurl 29 Moffusoen Hlnjtg



29/29

Ylb`ter Sgyso`s; ]gl Moffusoen ef Nlutrens 9?


Bieut tgos meùdlnt;

ibà te pbjl 2

Butger bnm bffohobtoen;Zd. K. Jbrhbnm, Sreflsser, Mlpbrtdlnt ef Lnjonllronj Sgyso`s,D`Dbstlr \novlrsoty, Gbdohten, Entbroe, @bnbmb

Ylvosoen gostery;

Ylvosoen 2.3, 9332.3:.23, onotobh `rlbtoen fred gbnm wrottln netls.

Ylvosoen 2.2 933=.37.2:, type èrrl`toen.

Peur`l meùdlnt br`govl he`btoen;

M;X]LB@GXLS=M0XtlxtX0-moffusoenXmoffusoen-r2.me`

@entb`t plrsen; Zd. K. Jbrhbnm

Netls;

3 diffusion r1

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