Анизотропные жидкости. Биологические структуры. Петрова Г.П. - 10 стр.

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МГУ | Москва

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9
—
c
T
(«clearing point»).
a
—
sin cos ,
sin sin , cos .
x
yz
a
aa
ϑϕ
ϑϕ ϑ
=
==
cos
ϑ
cos 0an
ϑ
=≡
,
nn
=−
()
2
1
3cos 1
2
Q
ϑ
=−
0
ϑ
=
—
1
Q
=
2
1
cos
3
ϑ
=
–
=
. (1)
()
,
f
θϕ
sin
ddd
ω ϑϑϕ
=
-
f
ϕ
n
2).
-
()
ϑ
dhe_[Zgby \hdjm] gZijZ\e_gby mkj_^g_gghc hjb_glZpbb :fieblm
^Z wlbo dhe_[Zgbc \hajZklZ_l ih f_j_ ijb[eb`_gby d l_fi_jZlmj_
i_j_oh^Z \ bahljhigmx `b^dhklv lZd gZau\Z_fhc l_fi_jZlmj_
ijhk\_le_gby beb ijhykg_gby — Tc («c le a rin g p o in t»).
     JZkkfhljbf ijhkl_crbc kemqZc jbk fhe_dme bf_xsbo
nhjfm djm]euo l\_j^uo kl_j`g_c a — _^bgbqguc \_dlhj \^hev
hkb kl_j`gy
    a x = sin ϑ cosϕ ,
    a y = sin ϑ sin ϕ , a z = cosϑ.

     OZjZdl_jbklbdm mihjy^h
q_gby ^ebgguo hk_c fh`gh [u
eh [u hij_^_eblv kj_^gbf
cosϑ  h^gZdh cosϑ = an ≡ 0 ,
lZd dZd n = −n kj_^gbc ih Zg
kZf[ex ^bihevguc fhf_gl jZ
\_g   Ihkdhevdm kj_^gbc ^b
ihevguc fhf_gl hlkmlkl\m_l Jbk  Hjb_glZpby fhe_dme- kl_j`g_c
ke_^mxsbf we_dljbq_kdbf fh hlghkbl_evgh \_dlhjZ ^bj_dlhjZ
f_glhf dhlhjuc fh`_l [ulv
bkihevah\Zg ^ey hij_^_e_gby mihjy^hq_gby fhe_dme kj_^u y\ey_l
ky d\Z^jmihevguc fhf_gl

 Q=
      1
      2
        (
        3cos2 ϑ − 1  )      ^ey ϑ = 0 —   Q = 1  ^ey cos2 ϑ =
                                                                  1
                                                                  3
                                                                    – 4 = .   (1 )


     WlZ \_ebqbgZ \ dZq_kl\_ iZjZf_ljZ ihjy^dZ g_fZlbq_kdhc kj_
^u [ueZ ij_^eh`_gZ <G P\_dh\uf
     < h[s_f kemqZ_ mihjy^hq_g
gmx g_fZlbq_kdmx nZam fh`gh hoZ
jZdl_jbah\Zlv nmgdpb_c jZkij_^_
e_gby f (θ ,ϕ )  dhlhjZy hij_^_ey_l
\_jhylghklv lh]h qlh \ kemqZ_ _keb
aZ^ZgZ hjb_glZpby fhe_dmeu  lh
^ebggZy hkv fhe_dmeu  [m^_l aZ
dexq_gZ         \    l_e_kghf    m]e_
d ω = sin ϑ dϑ dϕ  hlghkbl_evgh hjb
_glZpbb - c fhemdmeu
     Nmgdpby f g_ aZ\bkbl hl ϕ  ld
bf__lky ihegZy kbff_ljby \jZs_          Jbk  =jZnbd ^ey I (ϑ )
gby hlghkbl_evgh n jbk 2 ).
                                                                                 9

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