Sharp MD-M11Z Manuel d'utilisateur télécharger pdf (Page 13)

76 D, Renter

method, the variance of the variance may increase. thus invulidzuing convectional

error bar estimates. sec [9].

As in the case of conditional expectation Monte (`urlo We can design an cmrcnne

case 0{impmtancc sampling with zum srarisrical corm Africa only one maple: Let u<

scar ff.) gfx),/[_ Chuck: I cams. Monte Carlo integration pmcccds hy

wnmpling {mm [his di<u·ihuri0nff.r) which, inMs.c ofourpmricem*c:<mx1plc can

hc done by [hc rqicctinu technique. Then, indcpcndcm 0I`[hc implying, I is <cm*cd.

Unfortunately we needed the knowledge of the Gal result 1 already to design this

perfect zero variance scheme.

3.3.0.5 5f Monte Carlo

Finally we use our simple integral to ilhlslrale the concept of the 6/ lv[¤n1c(`m·1¤>

method, which is widely used in kinetic particle uzmsporl sinmllulions. Starting point

is the idea to split the unknown purunnctcr imo u large known nearby quantity and

<mal| unknown pcrturhaticm. Len particle <Imo|ari0n< hi< can also hc theca <ing|c parti—

clc dktriluutimx I`uncut<m ff.) sox ing some kinetic cumin or moments nfrhis pd.`.

lu near equilibrium situariom wc haw

[Qu) : [€W(.¤) + ¤5_f(w) c3.17>

with, for example, the Muxwelliun equilibrium distribution _fWm and a small pcmlr

balun 6f.Ilcuntl1cn be udvanlugcotxs to solvé. by lV[on1c(`ur1u sampling, only for

{if rather [han for theca {ull disuihmion.

S0 lc us consider our integral again, and write. accordingly, lv Lv 4 6] with

In [hc known pan

` ` I I , 2 I

1 + lu q I ) lu T » rw 7) <3.1s» U &_14 ¤<> e_14 2 3€_1

and 6] [hc roc<t. Clearly.

»! 1 2 / ` 0 — I — rr — rr /2 0] dm . (3.19;

H 0 — I

Figure 3.6 <haws theca roc<u|t 0{roc csrimarc for I, with In known and {XI cx alumcd

by crude Nlnurc Carlo. Clearly by eliminating a large, known, cmurihmion m I theca

rclariw errors of [hc csrimarcs for any gig sample <i/c `\' are greatly reduced a<

ccmxparcdm prcxi0u<mc[hm1s.

Hi< method is mlm relaxed to theca <0 called correlation sampling ruchuiquc. in

which one would evahmc both 1 and lg. by Monte (`urlo techniques. but using the

same random numbers. Both EMS's are men positively corrclumcd and me Swiss

Lilac precision of the Monte (`urlo cstinmtc for the difference 61 can be subslamiully

better than in indcpcndcm cstinmtcs of! and lg. or ufl alone.

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Sharp MD-M11Z Manuel d'utilisateur Page 13