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Malakaviy bitiruv ishida quyidagi xulosa olindi:


Tirqish kengligi davriy ravishda

funksiya bilan o’zgarganda quyidagi natijalar olindi:



  • Tirqish funksiyasining amplitudasi va chastotasi ortishi bilan sistemadagi zarrachalar yashash vaqtlari kamayib borar ekan.

  • Tirqish doimiy bo’lganiga nisbata o’zgaruvchan bo’lganida zarrachalarning yashash vaqtlari ortadi.

Оlingan natijalardan ko’rinadiki, dеmak nurni prоfili aylana ko’rinishdagi nurtоlaga nisbatan kеsilgan aylana ko’rinishdagi nurtоlada uzоq masоfaga uzatish mumkin. Bundan tashqari, olingan natijalar ushbu geometiryaga ega xaqiqiy fizik muhitlardagi ( optik nurtolalar, optik rezonatorlar, fazaviy bir jinsli bo’lmagan muhitlarda sochilish va boshqalar) jarayonlarni baholashda muvofaqqiyatli qo’llanilishi mumkin.

ILOVA

program cut_circle_bill_tirqishli

REAL*8 x1,x2,y1,y2,h,w0,vyi,x01,x10,y10,number,nnd(10000000)

common/param/x1,x2,y1,y2,h,w0,vyi,x01,x10,y10

INTEGER i,t,jj

real*8 x,y,x0,y0, b(4),beta0,beta,pi,n,gamma,alpha,psi,rr,ni

common/param/ x,y,x0,y0, b,beta0,beta,pi,n,gamma,alpha,psi,rr,ni

real*8 delta,delsent,psii,psiii,df,Ns,w,a

common/param/ delta,delsent,psii,psiii,df,w,a

open(1,file='Number_w=0.25.txt',status='unknown')

open(2,file='time_w=0.25.txt',status='unknown')

open(3,file='Np_Ns.txt',status='unknown')

pi=4.d0*datan(1.d0)

Nt=1000000

nd=1000000000

b(1)=1.0d0 ! aylana radiusi

w0=0.05d0 ! nurtolaning vertikal kengligi kesilish

number=10000 ! sistemadagi zarrachalar soni

w=15.d0 ! tirqishning o'zgarish funksiyasi chastotasi

a=10.0d0 ! tirqishning o'zgarish funksiyasi yarim

dd=0.0d0 ! tirqishning o'zgarish funksiyasi erkin

n=10000.d0 !devor bilan to'qnashuvlar soni

delsent=90.0d0 !tirqish markazining burchak koordinatasi ! psii=(delsent delta)*pi/180

r=0


rr=0

do t=1,nd

! random drop to a cell

x01=rand(0)*1.e 10

x10=mod(x01 t*1.0,1.0)

y10=mod(x01 t*1.0,1.2)

beta0=int(mod(1 t*1.0,358.0))

if(sqrt(x10**2 y10**2).gt.b(1)) goto 4

if(y10.lt.b(1)*(1-w0)) goto 4

r=r 1


if(r.gt.number) goto 5

write(*,*) r

x0=x10 ! boshlangich x0 nuqta

y0=y10 ! boshlangich y0 nuqta

beta=beta0*pi/180

h=2*b(1)-w0*b(1) ! nurtolaning vertikal qirqilgan qismi

b(2)=tan(beta) ! y=kx b dagi k

b(3)=y0-x0*b(2) ! y=kx b dagi b

call kvdr(x1,x2,y1,y2,b)

if(beta0.eq.90.)then

x0=x0

y0=(b(1)**2-x0**2)**0.5



goto 1

endif


if(beta0.eq.270.)then

x0=x0


y0=-(b(1)**2-x0**2)**0.5

goto 1


endif

if(beta0.gt.0.and.beta0.lt.180.)then

y0=max(y1,y2)

x0=(y0-b(3))/b(2)

endif

if(beta0.gt.180.and.beta0.lt.360.)then



y0=min(y1,y2)

x0=(y0-b(3))/b(2)

endif

if(beta0.eq.0.or.beta0.eq.360.)then



y0=y0

x0=(b(1)**2-y0**2)**0.5

endif

if(beta0.eq.180.)then



y0=y0

x0=-(b(1)**2-y0**2)**0.5

endif

ni=0


1 do i=1,Nt

delta=dd a*dsin(w*i)

psii=(delsent delta)*pi/180

psiii=(delsent-delta)*pi/180

if(y0.le.b(1)*(1-w0))then

ni=ni 1


call cut(x0,y0,b,beta,w0)

call kvdr(x1,x2,y1,y2,b)

if(abs(b(2)).gt.1.e 10)then

x0=x0


y0=(b(1)**2-x0**2)**0.5

goto 2


endif

y0=max(y1,y2)

x0=(y0-b(3))/b(2)

endif


2 call imu(x0,y0,b,gamma,beta)

ni=ni 1


alpha=atan(y0/x0)

if(x0.gt.0.and.y0.gt.0)then

psi=alpha

end if


if(x0.lt.0.and.y0.gt.0)then

psi=pi-abs(alpha)

end if

if(x0.lt.0.and.y0.lt.0)then



psi=abs(alpha) pi

end if


if(x0.gt.0.and.y0.lt.0)then

psi=2*pi-abs(alpha)

end if

if(psi.gt.psiii.and.psi.lt.psii) then



nnd(r)=ni

goto 4

endif

call kvdr(x1,x2,y1,y2,b)



if(abs(b(2)).gt.1.e 10)then

x0=x1


y0=-y0

goto 3


endif

if(abs(y1-y0).ge.abs(y2-y0))then

y0=y1

x0=x1


else

y0=y2


x0=x2

endif


3 enddo

4 kkk=max(rr,ni)

rr=kkk

enddo


nub=0

qol=number

5 do jj=1,rr

ss=0


do ii=1,number

if(nnd(ii).eq.jj)then

ss=ss 1

endif


enddo

if(ss.ne.0.)then

nub=nub ss

write(1,*)number-nub

write(2,*)jj

endif


if(nub.eq.number)stop

enddo


close(1)

close(2)

close(3)

end


! kavadrat tenglamaishlanish pod pragrammasi

subroutine kvdr(x1,x2,y1,y2,b)

implicit real*8(a-h,o-z)

real*8 x1,x2,y1,y2,b(4)

x1=(-b(3)*b(2) sqrt((b(1)**2)*(1 b(2)**2)-b(3)**2))/(1 b(2)**2)

x2=(-b(3)*b(2)-sqrt((b(1)**2)*(1 b(2)**2)-b(3)**2))/(1 b(2)**2)

y1=b(3) b(2)*x1

y2=b(3) b(2)*x2

end

! devor bilan tuqnashuvda burchak uzgarishi pod programmasi



subroutine imu(x0,y0,b,gamma,beta)

implicit real*8(a-h,o-z)

real*8 x0,y0,b(4),gamma,beta

if(y0.ge.0.)then

gamma=atan(-x0/(b(1)**2-x0**2)**0.5)

else


gamma=atan(x0/(b(1)**2-x0**2)**0.5)

endif


beta=2*gamma-beta

b(2)=tan(beta)

b(3)=y0-b(2)*x0

end


! aylananing kesilgan qijoyidagi burchak uzgarishi pod programmasi

subroutine cut(x0,y0,b,beta,w0)

implicit real*8(a-h,o-z)

real*8 x0,y0,b(4),w0

y0=b(1)*(1-w0)

x0=(y0-b(3))/b(2)

b(2)=-b(2)

b(3)=y0-x0*b(2)

beta=-beta

end
ADABIYOTLAR



  1. А.Ю.Лоскутов, Динамический хаос. Системы классической механики. УФН. Том 177, №9, 989 (2007).

  2. Н.В. Евдокимов, В.П. Комолов, П.В. Комолов, Интерференция динамического хаоса гамильтоновых систем: Эксперимент и возможности радиофизических приложений. УФН. Том 117, №7, 775 (2001).

  3. В.С. Анищенко, Т.Е Вадивасова, Г.А. Окрокверцхов, Г.И. Стрелкова, Статистические свойства динамического хаоса. УФН. Том 175, №2, 163 (2005).

  4. Мудров А.Е. Численнйе методы для ПЭВМ на языках бейсик, фортран и паскал.Томск. МП”Раско” 1991.

  5. Kuznesov. S. P. Dinamichiskiy xaos. M: Fizmatlit. 2001. 296c.

  6. Kuznesov. A. P, Kuznesov. S. P, Riskin. N. M. Nilineyie kalibaniya. M: Fizmatlit. 2002. 292c.

  7. Berje. P, Pomo. I, Vidal. K. Poryadok v xaose. O determinisnicheskom podxode k turbulentnosti. M: Mir. 1991. 368c.

  8. Mun. F. Xaoticheskie kolekolebaniya. M: Mir, 1990. 312c.

  9. M V Berry. Regularity and chaos in classical mechanics, illustrated by three deformations of а circular billiard. European Journal of Physics,2:91 (1982).

  10. F.Lenz. Time-dependent Classical Billiards. Diploma Thesis in Physics. University of Heidelberg. 2006.

  11. W H Press, S A Teukolsky, W T Vetterling, and B P Flannery. Numerical Recipes in C, theArt of Scientific Computing. Cambridge University Press, 2nd edition edition, 2002.

  12. V. Doya, O. Legrand, F. Mortessagne, and Ch. Miniatura, “Light scarring in an optical fiber”, Phys.Rev. Lett. 88, 014102 (2002).

  13. Suhan Ree. “Fractal analysis on a closed classical hard-wall billiard using a simplified box-counting algorithm” February 4, 2008.

  14. S. Ree, arXiv:nlin.CD/0206003 (will appear in J. KoreanPhys. Soc.) (2002).


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