ɇɚɲɟ

ɦɟɫɬɨ

ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟɉɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ

ɢɢ

ɜɪɟɦɟɧɧɵɟɜɪɟɦɟɧɧɵɟ

ɦɚɫɲɬɚɛɵɦɚɫɲɬɚɛɵ..

ȼɵɱɢɫɥɢɬɟɥɶɧɵɟȼɵɱɢɫɥɢɬɟɥɶɧɵɟ

ɦɟɬɨɞɵɦɟɬɨɞɵ

Ȼɭɩɧɶ

ɇɩɦɠɥɮɦɶ ɇɩɦɠɥɮɦɺɫɨɶɠ

ɛɨɬɛɧɜɦɣ Ʌɩɨɟɠɨɬ. ɬɣɬɭɠɧɶ

Ʌɩɧɪɩɢɣɭɶ Ʌɩɨɭɣɨɮɮɧmicroscopic (1microscopic (1--10 nm, 10 nm, fs/psfs/ps)) mesoscopicmesoscopic

(10(10--1000 nm, ns/1000 nm, ns/μμs)s) macroscopic (~1 mm, macroscopic (~1 mm, μμs/s)s/s)

QM DFT QMD MM MD MC SMD CG-MC/MD DPDLattice Models

MC-RISM RISM SCFT MD/DDFT DDFT FT-CLD

Particle-in-CellHydrodynamicsFinite ElementsFinite VolumesPeridynamics

ɘɦɠɥɭɫɩɨɨɶɠ

ɬɩɬɭɩɺɨɣɺ,ɰɣɧɣɲɠɬɥɣɠ

ɫɠɛɥɱɣɣ,ɬɭɫɮɥɭɮɫɛ

ɧɩɦɠɥɮɦ,ɬɪɠɥɭɫɶ, ɟɣɨɛɧɣɥɛ

ɋɛɝɨɩɝɠɬɨɛɺ

ɧɠɢɩɬɥɩɪɣɲɠɬɥɛɺ

ɬɭɫɮɥɭɮɫɛ,ɥɩɦɦɠɥɭɣɝɨɶɠ

ɬɝɩɤɬɭɝɛ/ɟɣɨɛɧɣɥɛ,ɪɫɩɱɠɬɬɶ

ɬɛɧɩɩɫɞɛɨɣɢɛɱɣɣ

ɧɩɦɠɥɮɦ,ɯɛɢɩɝɶɠ

ɪɠɫɠɰɩɟɶ

Ʌɫɮɪɨɩɧɛɬɳɭɛɜɨɛɺ

ɬɭɫɮɥɭɮɫɛ,ɟɠɯɩɫɧɛɱɣɺ, ɫɛɢɫɮɳɠɨɣɠ,ɭɠɲɠɨɣɠ, ɞɣɟɫɩɟɣɨɛɧɣɥɛ

ɚɬɨɦɵɚɬɨɦɵ

ɱɚɫɬɢɰɵɱɚɫɬɢɰɵ

ɱɚɫɬɢɰɵɱɚɫɬɢɰɵ//ɩɨɥɹɩɨɥɹ

ɩɨɥɹɩɨɥɹ

ɤɨɧɬɢɧɭɭɦɤɨɧɬɢɧɭɭɦee--

pp++

10-15

10-12

10-9

10-6

10-3

100

10-10 10-9 10-8 10-7 10-6 10-5 10-4

(nm) (μm)

(fs)

(ps)

(ns)

(μs)

(ms)

ɪɚɫɫɬɨɹɧɢɟ

/m

ɜɪɟɦɹ /s

Ɇɟɡɨɫɤɨɩɢɤɚ

ɩɨɥɭɷɦɩɢɪɢɱɟɫɤɢɟɦɟɬɨɞɵ

Ab initio

ɦɟɬɨɞɵ

MɋMD

Tight-Binding

MNDO, INDO/S

Ʉɨɧɬɢɧɭɚɥɶɧɵɟ

ɦɟɬɨɞɵ

Lattice Monte Carlo

Brownian Dynamics

Dissipative Particle Dynamics

Field Theoretic Methods

Ⱥɬɨɦɢɫɬɢɱɟɫɤɢɟ

ɦɟɬɨɞɵ

~102 ~103

~106

~109

~NAv

Ƚɥɚɜɧɵɣ

ɜɵɡɨɜ: ɦɭɥɶɬɢɦɚɫɲɬɚɛɧɨɟ

ɦɨɞɟɥɢɪɨɜɚɧɢɟ

ɍɍɫɪɟɞɧɟɧɢɟɫɪɟɞɧɟɧɢɟ

ɩɨɩɨ

ɜɪɟɦɟɧɢɜɪɟɦɟɧɢɋɪɟɞɧɟɟ

ɡɧɚɱɟɧɢɟ

<Ⱥ> ɧɟɤɨɬɨɪɨɝɨ

ɫɜɨɣɫɬɜɚ

Ⱥ(r,v), ɡɚɜɢɫɹɳɟɝɨ

ɨɬ

ɤɨɨɪɞɢɧɚɬ

{r} ɢ

ɫɤɨɪɨɫɬɟɣ

{v} ɱɚɫɬɢɰ, ɨɩɪɟɞɟɥɹɸɬ

ɩɭɬɟɦ

ɭɫɪɟɞɧɟɧɢɹ

ɦɧɨɠɟɫɬɜɚ

"ɦɝɧɨɜɟɧɧɵɯ" ɡɧɚɱɟɧɢɣ

A[r(t),v(t)], ɧɚɛɥɸɞɚɟɦɵɯ

ɜ

ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ

ɦɨɦɟɧɬɵ

ɜɪɟɦɟɧɢ

t. Ɍɚɤɨɣ

ɩɨɞɯɨɞ

ɢɫɯɨɞɢɬ

ɢɡ

ɬɨɝɨ, ɱɬɨ

ɧɚɦ

ɢɡɜɟɫɬɧɵ

ɡɚɤɨɧɵ

ɞɜɢɠɟɧɢɹ

ɱɚɫɬɢɰ

ɫɢɫɬɟɦɵ.

ɍɍɫɪɟɞɧɟɧɢɟɫɪɟɞɧɟɧɢɟ

ɩɨɩɨ

ɚɧɫɚɦɛɥɸɚɧɫɚɦɛɥɸɇɚɛɥɸɞɚɟɦɨɟ

ɫɜɨɣɫɬɜɨ

ɪɚɫɫɦɚɬɪɢɜɚɸɬ

ɤɚɤ

ɫɪɟɞɧɟɟ

ɩɨɦɧɨɠɟɫɬɜɭ

ɪɚɡɥɢɱɧɵɯ

ɫɨɫɬɨɹɧɢɣɫɢɫɬɟɦɵ, ɤɨɬɨɪɵɟ

ɜɨɡɧɢɤɚɸɬ

ɫɨɩɪɟɞɟɥɟɧɧɨɣ

ɜɟɪɨɹɬɧɨɫɬɶɸ. ȼɟɪɨɹɬɧɨɫɬɶ

(ɱɚɫɬɨɬɚ) ɜɨɡɧɢɤɧɨɜɟɧɢɹ

ɬɨɝɨ

ɢɥɢ

ɢɧɨɝɨɫɨɫɬɨɹɧɢɹ

ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ

ɟɝɨɫɬɚɬɢɫɬɢɱɟɫɤɨɦɭ

ɜɟɫɭ

e–U/kT,ɝɞɟ

U

–

ɩɨɬɟɧɰɢɚɥɶɧɚɹ

ɷɧɟɪɝɢɹ

ɞɚɧɧɨɣɤɨɧɮɢɝɭɪɚɰɢɢ, k

–

ɤɨɧɫɬɚɧɬɚ

Ȼɨɥɶɰɦɚɧɚ, T –ɚɛɫɨɥɸɬɧɚɹ

ɬɟɦɩɟɪɚɬɭɪɚ.

ȾɜɚȾɜɚ

ɩɨɞɯɨɞɚɩɨɞɯɨɞɚ

ɜɜ

ɫɬɚɬɢɫɬɢɱɟɫɤɨɣɫɬɚɬɢɫɬɢɱɟɫɤɨɣ

ɬɟɨɪɢɢɬɟɨɪɢɢ

ɈɛɚɈɛɚ

ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ

ɩɪɢɧɰɢɩɚɩɪɢɧɰɢɩɚ

ɦɨɝɭɬɦɨɝɭɬ

ɛɵɬɶɛɵɬɶ

ɩɨɥɨɠɟɧɵɩɨɥɨɠɟɧɵ

ɜɜ

ɨɫɧɨɜɭɨɫɧɨɜɭ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯɜɵɱɢɫɥɢɬɟɥɶɧɵɯ

ɫɯɟɦɫɯɟɦ, , ɪɟɚɥɢɡɭɟɦɵɯɪɟɚɥɢɡɭɟɦɵɯ

ɧɚɧɚ

ɤɨɦɩɶɸɬɟɪɟɤɨɦɩɶɸɬɟɪɟ. . ɇɇɟɨɛɯɨɞɢɦɨɟɨɛɯɨɞɢɦɨ

ɡɧɚɬɶɡɧɚɬɶ

ɥɢɲɶɥɢɲɶɫɩɨɫɨɛɫɩɨɫɨɛ

ɪɚɫɱɟɬɚɪɚɫɱɟɬɚ

ɩɨɬɟɧɰɢɚɥɶɧɨɣɩɨɬɟɧɰɢɚɥɶɧɨɣ

ɷɧɟɪɝɢɢɷɧɟɪɝɢɢ

ɫɢɫɬɟɦɵɫɢɫɬɟɦɵ

UU

ɤɚɤɤɚɤ

ɮɭɧɤɰɢɢɮɭɧɤɰɢɢ

ɤɨɨɪɞɢɧɚɬɤɨɨɪɞɢɧɚɬ rr..

ɆɨɥɟɤɭɥɹɪɧɚɹɆɨɥɟɤɭɥɹɪɧɚɹ

ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ

mmii

aaii

((tt) = ) = FFii

((tt) ) [[ɦɚɫɫɚɦɚɫɫɚ

××

ɭɫɤɨɪɟɧɢɟɭɫɤɨɪɟɧɢɟ

= = ɫɢɥɚɫɢɥɚ]]

aaii

((tt) = d) = dvvii

((tt)/)/ddtt

= d= d22rrii

((tt)/d)/dtt22

FFii

((tt) = ) = ––∂∂UU((rr11

,,……, , rrNN

))//∂∂rrii

ɇɭɠɧɨ

ɡɧɚɬɶ

ɥɢɲɶ

U(r1,…, rN)

ɢɥɢ

F

!

mm

ii

dd22rrii

((tt)/d)/dtt22

= = FFii

((tt))

John von

NeumannGrand Monaco ɋasino

ɆɨɧɬɟɆɨɧɬɟ--ɄɚɪɥɨɄɚɪɥɨ

SA

=nA

/n

ǞǸȀȄǭǶǺǭȌ

ǯȈǮǻǽǷǭ

∑ωω=−ωj

jjjjj pkTU /)/exp(~

∑∑

−

−

=

j

kTU

j

kTU

j

j

j

e

eA

A /

/

ǞǿǭǿǵǾǿǵȄDzǾǷǵǶ

ǯDzǾ

ǷǻǺȁǵǰȀǽǭȃǵǵ

1944 ǰǻDZ

ɆɨɧɬɟɆɨɧɬɟ--ɄɚɪɥɨɄɚɪɥɨ

((ɦɟɬɨɞɦɟɬɨɞ

ɆɟɬɪɨɩɨɥɢɫɚɆɟɬɪɨɩɨɥɢɫɚ

––

""ɫɭɳɟɫɬɜɟɧɧɚɹɫɭɳɟɫɬɜɟɧɧɚɹ

ɜɵɛɨɪɤɚɜɵɛɨɪɤɚ")")

(1953) Metropolis, (1953) Metropolis, RosenbluthRosenbluth, , RosenbluthRosenbluth, Teller, Teller, Teller, Teller

= = MRMR22TT22

∑=

=s

n

nAs

A1

1

{r}→U {r'}→U' Ⱦɥɹ

{r} ɧɚɣɬɢ

U

ɢ

ω=exp(-U/kT)

ɋɥɭɱɚɣɧɨ

ɜɵɛɪɚɬɶ

ɱɚɫɬɢɰɭ

i

ɋɥɭɱɚɣɧɨ

ɩɟɪɟɦɟɫɬɢɬɶ

ɱɚɫɬɢɰɭ

i:r'i

→ri

+Δr; {r}→{r'}

ɇɚɣɬɢ

U' ɢ ɜɟɫ ω'=exp(-U'/kT)

Ɂɚɦɟɧɢɬɶ

{r}

ɧɚ

{r'}

ɫ

ɜɟɪɨɹɬɧɨɫɬɶɸ

p

= min{1, ω'/ ω}

ɉɟɪɢɨɞɢɱɟɫɤɢɟɉɟɪɢɨɞɢɱɟɫɤɢɟ

ɝɪɚɧɢɱɧɵɟɝɪɚɧɢɱɧɵɟ

ɭɫɥɨɜɢɹɭɫɥɨɜɢɹ

3D

ǿǻǽ

/ 2D ǾǵǾǿDzǹǭ ←←

LL →→

4D

ǷȀǮ

-

ǿDzǾǾDzǽǭǷǿ

ǻǮǽǭǴ

Ɉɩɪɟɞɟɥɟɧɢɟ

1. ɉɨɧɹɬɢɟɉɨɧɹɬɢɟ

""ɦɨɞɟɥɶɦɨɞɟɥɶ

ɫɢɫɬɟɦɵɫɢɫɬɟɦɵ" " ɡɚɤɥɸɱɚɟɬɫɹɡɚɤɥɸɱɚɟɬɫɹ

ɜɜ

ɜɵɛɨɪɟɜɵɛɨɪɟ

ɩɪɚɜɢɥɩɪɚɜɢɥ, , ɨɩɢɫɵɜɚɸɳɢɯɨɩɢɫɵɜɚɸɳɢɯ

ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɜɡɚɢɦɨɞɟɣɫɬɜɢɟ

ɱɚɫɬɢɰɱɚɫɬɢɰ

ɦɟɠɞɭɦɟɠɞɭ

ɫɨɛɨɣɫɨɛɨɣ

ɢɢ//ɢɥɢɢɥɢ

ɫɫ

ɜɧɟɲɧɢɦɢɜɧɟɲɧɢɦɢ

ɩɨɥɹɦɢɩɨɥɹɦɢ, , ɬɬ..ɟɟ. . ɜɜ

ɮɨɪɦɭɥɢɪɨɜɤɟɮɨɪɦɭɥɢɪɨɜɤɟ

ɜɢɞɚɜɢɞɚ

ɢɢ

ɫɩɨɫɨɛɚɫɩɨɫɨɛɚ

ɜɵɱɢɫɥɟɧɢɹɜɵɱɢɫɥɟɧɢɹ

ɮɭɧɤɰɢɢɮɭɧɤɰɢɢ

ɩɨɬɟɧɰɢɚɥɶɧɨɣɩɨɬɟɧɰɢɚɥɶɧɨɣ

ɷɧɟɪɝɢɢɷɧɟɪɝɢɢ..

ǚȀdzǺǻ

ǴǺǭǿȉ:

U(r1

,…, rN

)

ɏɨɪɨɲɚɹ

ɬɟɨɪɢɹ

ɫɥɨɠɧɵɯ

ɫɢɫɬɟɦ

ɞɨɥɠɧɚ ɩɪɟɞɫɬɚɜɥɹɬɶ

ɫɨɛɨɣ

ɥɢɲɶ

ɯɨɪɨɲɭɸ "ɤɚɪɢɤɚɬɭɪɭ" ɧɚ

ɷɬɢ

ɫɢɫɬɟɦɵ, ɭɬɪɢɪɭɸɳɭɸɬɟ

ɫɜɨɣɫɬɜɚ

ɢɯ, ɤɨɬɨɪɵɟ

ɹɜɥɹɸɬɫɹ

ɧɚɢɛɨɥɟɟɬɢɩɢɱɟɫɤɢɦɢ, ɢ

ɭɦɵɲɥɟɧɧɨ

ɢɝɧɨɪɢɪɭɸɳɭɸɜɫɟ

ɨɫɬɚɥɶɧɵɟ

-

ɧɟɫɭɳɟɫɬɜɟɧɧɵɟ

ɫɜɨɣɫɬɜɚ.

ə.ɂ. Ɏɪɟɧɤɟɥɶ

Ɉɩɪɟɞɟɥɟɧɢɟ

2. Ʉɨɦɩɶɸɬɟɪɧɚɹ

ɢɦɢɬɚɰɢɹ

ɦɟɬɨɞɚɦɢ

ɦɨɥɟɤɭɥɹɪɧɨɣ

ɞɢɧɚɦɢɤɢ

ɢɥɢ

Ɇɨɧɬɟ-Ʉɚɪɥɨ

ɦɨɞɟɥɢ

ɮɢɡɢɱɟɫɤɨɣ

ɫɢɫɬɟɦɵ

ɫ

ɰɟɥɶɸ

ɢɡɭɱɟɧɢɹ

ɟɟ

ɯɚɪɚɤɬɟɪɢɫɬɢɤ

ɜ

ɡɚɜɢɫɢɦɨɫɬɢ

ɨɬ

ɡɚɞɚɧɧɵɯ

ɩɚɪɚɦɟɬɪɨɜ

ɩɪɟɞɫɬɚɜɥɹɟɬ

ɫɨɛɨɣ

ɱɢɫɥɟɧɧɵɣ

(ɤɨɦɩɶɸɬɟɪɧɵɣ) ɷɤɫɩɟɪɢɦɟɧɬ

ɫ ɷɬɨɣ

ɦɨɞɟɥɶɸ.

ɍɬɜɟɪɠɞɟɧɢɟ

1. ɉɨɫɤɨɥɶɤɭ

ɦɟɬɨɞɵ

ɆȾ

ɢ

ɆɄ

ɨɫɧɨɜɵɜɚɸɬɫɹ

ɧɚ

ɜɟɫɶɦɚ

ɨɛɳɢɯ

ɩɪɢɧɰɢɩɚɯ

ɤɥɚɫɫɢɱɟɫɤɨɣ

ɮɢɡɢɤɢ, ɨɧɢ ɜ ɫɭɳɧɨɫɬɢ

ɩɪɟɞɫɬɚɜɥɹɸɬ

ɫɨɛɨɣ

ɥɢɲɶ

ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ

(ɱɢɫɥɟɧɧɭɸ) ɪɟɚɥɢɡɚɰɢɸ

ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ

ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ

ɩɨɞɯɨɞɨɜ

ɤ

ɨɩɪɟɞɟɥɟɧɢɸ

ɯɚɪɚɤɬɟɪɢɫɬɢɤ

ɫɢɫɬɟɦɵ

ɢɫɯɨɞɹ

ɢɡ

ɡɚɞɚɧɧɵɯ

ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɯ

ɡɚɤɨɧɨɜ

ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ

ɱɚɫɬɢɰ.

ɉɨɷɬɨɦɭ, ɟɫɥɢ

ɜ

ɦɨɞɟɥɢɪɭɸɳɟɣ

ɩɪɨɝɪɚɦɦɟ

ɧɟɬ

ɨɲɢɛɨɤ

ɢ

ɩɪɟɞɭɫɦɨɬɪɟɧ

ɧɚɞɥɟɠɚɳɢɣ

ɤɨɧɬɪɨɥɶ

ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ

ɩɨɝɪɟɲɧɨɫɬɟɣ, ɬɨ

ɩɨɥɭɱɟɧɧɵɟ

ɪɟɡɭɥɶɬɚɬɵ

ɛɭɞɭɬ

ɫɬɪɨɝɢɦɢ, ɬɨ

ɟɫɬɶ

ɢɦɟɸɳɢɦɢ

ɫɢɥɭ

ɚɤɫɢɨɦɵ

ɞɥɹ

ɜɵɛɪɚɧɧɨɣ

ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ

ɦɨɞɟɥɢ

ɮɢɡɢɱɟɫɤɨɣ

ɫɢɫɬɟɦɵ.

ȺɞɢɚɛɚɬɢɱɟɫɤɨɟȺɞɢɚɛɚɬɢɱɟɫɤɨɟ

ɩɪɢɛɥɢɠɟɧɢɟɩɪɢɛɥɢɠɟɧɢɟ((ɦɟɬɨɞɦɟɬɨɞ

ɦɨɥɟɤɭɥɹɪɧɨɣɦɨɥɟɤɭɥɹɪɧɨɣ

ɦɟɯɚɧɢɤɢɦɟɯɚɧɢɤɢ))

ɉɪɢɛɥɢɠɟɧɢɟɉɪɢɛɥɢɠɟɧɢɟ

ȻɨɪɧɚȻɨɪɧɚ--ɈɩɩɟɧɝɟɣɦɟɪɚɈɩɩɟɧɝɟɣɦɟɪɚ

ɞɥɹɞɥɹ

ɭɪɭɪ. . ɒɪɺɞɢɧɝɟɪɚɒɪɺɞɢɧɝɟɪɚ..ǬȍȒȖȔȗȖȏȐȞȐȧǬȍȒȖȔȗȖȏȐȞȐȧ

ȊȖȓȕȖȊȖȑȊȖȓȕȖȊȖȑ

ȜțȕȒȞȐȐȜțȕȒȞȐȐ

ȕȈȕȈ

ȥȓȍȒȚȘȖȕȕțȦȥȓȍȒȚȘȖȕȕțȦ

ȐȐ

ȧȌȍȘȕțȦȧȌȍȘȕțȦ

ȟȈșȚȐȟȈșȚȐ::……ȌȊȐȎȍȕȐȍȌȊȐȎȍȕȐȍ

ȒȈȎȌȖȋȖȒȈȎȌȖȋȖ

ȥȓȍȒȚȘȖȕȈȥȓȍȒȚȘȖȕȈ

ȊȊ

ȈȚȖȔȍȈȚȖȔȍ

ȐȓȐȐȓȐ

ȔȖȓȍȒțȓȍȔȖȓȍȒțȓȍ

ȔȖȎȍȚȔȖȎȍȚ

ȘȈșșȔȈȚȘȐȊȈȚȤșȧȘȈșșȔȈȚȘȐȊȈȚȤșȧȕȍȏȈȊȐșȐȔȖȕȍȏȈȊȐșȐȔȖ

ȖȚȖȚ

ȌȊȐȎȍȕȐȧȌȊȐȎȍȕȐȧ

ȈȚȖȔȕȖȋȖȈȚȖȔȕȖȋȖ

ȧȌȘȈȧȌȘȈ

ȐȓȐȐȓȐ

șȐșȚȍȔȣșȐșȚȍȔȣ

ȈȚȖȔȕȣȝȈȚȖȔȕȣȝ

ȧȌȍȘȧȌȍȘ......

"ɉɨɥɭɤɥɚɫɫɢɱɟɫɤɢɟ" ɩɪɢɛɥɢɠɟɧɢɟ.ɋɬɚɬɢɫɬɢɱɟɫɤɚɹ

ɫɭɦɦɚ:

Q = Qclass

Qquant

((M/mM/mee

=1830)=1830)

ɆɟɯɚɧɢɱɟɫɤɚɹɆɟɯɚɧɢɱɟɫɤɚɹ

ɦɨɞɟɥɶɦɨɞɟɥɶ

ɦɨɥɟɤɭɥɵɦɨɥɟɤɭɥɵ((ɦɨɥɟɤɭɥɹɪɧɚɹɦɨɥɟɤɭɥɹɪɧɚɹ

ɦɟɯɚɧɢɤɚɦɟɯɚɧɢɤɚ))

ɷɥɟɤɬɪɨɧɧɨɷɥɟɤɬɪɨɧɧɨ--ɹɞɟɪɧɚɹɹɞɟɪɧɚɹ

ɫɢɫɬɟɦɚɫɢɫɬɟɦɚ""ȺɬɨɦȺɬɨɦ""

""ɆɨɥɟɤɭɥɚɆɨɥɟɤɭɥɚ""

∑ ∑+= nvvalmol UUU

∑=molecules

molUU

ǜǻǿDzǺȃǵǭǸȉǺǭȌ

ȊǺDzǽǰǵȌ

ǹǻǸDzǷȀǸȈ

ǵ

ǹǻǸDzǷȀǸȌǽǺǻǶ

ǾǵǾǿDzǹȈ

ɆɟɯɚɧɢɱɟɫɤɚɹɆɟɯɚɧɢɱɟɫɤɚɹ

ɦɨɞɟɥɶɦɨɞɟɥɶ

ɦɨɥɟɤɭɥɵɦɨɥɟɤɭɥɵ:: ȼɧɭɬɪɟɧɧɢɟȼɧɭɬɪɟɧɧɢɟ

ɤɨɨɪɞɢɧɚɬɵɤɨɨɪɞɢɧɚɬɵ

)]cos(1[

)(

)(

02

1

202

1

202

1

ϕ±=

Θ−Θ=

−=

Θ

nVU

kU

bbkU

tors

angle

bbond

ȼɧɭɬɪɢɦɨɥɟɤɭɥɹɪɧɵɟ"ɜɚɥɟɧɬɧɵɟ" ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ

...

∑∑∑

+

+

+=

tors

tors

angle

angle

bond

bondval

U

U

UU

ɆɟɯɚɧɢɱɟɫɤɚɹɆɟɯɚɧɢɱɟɫɤɚɹ

ɦɨɞɟɥɶɦɨɞɟɥɶ

ɦɨɥɟɤɭɥɵɦɨɥɟɤɭɥɵ:: ɇɟɜɚɥɟɧɬɧɵɟɇɟɜɚɥɟɧɬɧɵɟ

ɜɡɚɢɦɨɞɟɣɫɬɜɢɹɜɡɚɢɦɨɞɟɣɫɬɜɢɹ

⎟⎟⎠

⎞⎜⎜⎝

⎛ σ−

σε=

6

6

12

12

4)(rr

rUVdW

YH...OX10

10

12

12

cos4)( −−− Θ⎟⎟⎠

⎞⎜⎜⎝

⎛ σ−

σε=

rrrU HbondH

r

qqU el

o

21

∈=

ɉɨɬɟɧɰɢɚɥɉɨɬɟɧɰɢɚɥ

ɅɟɧɧɚɪɞɚɅɟɧɧɚɪɞɚ--ȾɠɨɧɫɚȾɠɨɧɫɚ

ȼɨɞɨɪɨɞɧɚɹȼɨɞɨɪɨɞɧɚɹ

ɫɜɹɡɶɫɜɹɡɶ

ɗɥɟɤɬɪɨɫɬɚɬɢɤɚɗɥɟɤɬɪɨɫɬɚɬɢɤɚ

((ɩɨɬɟɧɰɢɚɥɩɨɬɟɧɰɢɚɥ

ɄɭɥɨɧɚɄɭɥɨɧɚ))

2/1

,1

2

,1

)1(2exp

)1(exp

⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡−−−

−⎥⎦

⎤⎢⎣

⎡−−⋅=

∑

∑

≠=

≠=

jij Me

ij

jij Me

ij

i

D

rQB

D

rCAu

ȼɡɚɢɦɨɞɟɣɫɬɜɢɟȼɡɚɢɦɨɞɟɣɫɬɜɢɟ

ɦɟɬɚɥɥɦɟɬɚɥɥ--ɦɟɬɚɥɥɦɟɬɚɥɥ

( ) K1010

88

66

r

C

r

C

r

Crudis −−−=

( ) ( ) Br

overlap erAru −≈

ǟǽǵǟǽǵ

ǼȀǿǵǼȀǿǵ

ǷǷ

NanoNano…… ǵǵ

DZǭǸDzDzDZǭǸDzDz

•• ǗǽȀǼǺǻǹǭǾȅǿǭǮǺǻDzǗǽȀǼǺǻǹǭǾȅǿǭǮǺǻDz

ǭǿǻǹǵǾǿǵȄDzǾǷǻDzǭǿǻǹǵǾǿǵȄDzǾǷǻDz ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz

––

ǽǭǾǼǭǽǭǸǸDzǸDzǺǺȈDzǽǭǾǼǭǽǭǸǸDzǸDzǺǺȈDz

ǵǵ ǽǭǾǼǽDzDZDzǸDzǺǺȈDzǽǭǾǼǽDzDZDzǸDzǺǺȈDz

ǯȈȄǵǾǸDzǺǵȌǯȈȄǵǾǸDzǺǵȌ ((ǾȀǼDzǽǷǻǹǼȉȋǿDzǽȈǾȀǼDzǽǷǻǹǼȉȋǿDzǽȈ

ǵǵ

GRIDGRID--ǾǵǾǿDzǹȈǾǵǾǿDzǹȈ))..

•• ǕǾǼǻǸȉǴǻǯǭǺǵDzǕǾǼǻǸȉǴǻǯǭǺǵDz

ǻǰǽȀǮǸDzǺǺȈȂǻǰǽȀǮǸDzǺǺȈȂ

ǹǻDZDzǸDzǶǹǻDZDzǸDzǶ: : ǹDzǴǻǾǷǻǼǵȄDzǾǷǵDzǹDzǴǻǾǷǻǼǵȄDzǾǷǵDz

ǹDzǿǻDZȈǹDzǿǻDZȈ..

•• ǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDzǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDz

ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz:: ȄǭǾǿǵȃȈȄǭǾǿǵȃȈ

+ + ǼǻǸȌǼǻǸȌ..

ȼɵɫɨɤɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɵɟȼɵɫɨɤɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɵɟ

ɜɵɱɢɫɥɢɬɟɥɶɧɵɟɜɵɱɢɫɥɢɬɟɥɶɧɵɟ

ɫɢɫɬɟɦɵɫɢɫɬɟɦɵ

Cluster SKIF-MSU5080 CPUs4-core Intel Xeon E5472 3.0 GHz~70 TFLOPS

Blue Gene/P8192 CPUs

GRID-ǾǵǾǿDzǹȈ

((1 1 TFLOPS = TFLOPS = 1 1 ȚȘȓȕȚȘȓȕ

ȖȗȍȘȈȞȐȑȖȗȍȘȈȞȐȑ

ȊȊ

șȍȒțȕȌțșȍȒțȕȌț))

ȼɢɪɭɫɵȼɢɪɭɫɵ

VirusX: 713,580 ɚɬɨɦɨɜ

Satellite Tobacco Mosaic Virus:

932,508 ɚɬɨɦɨɜPenicillium

stoloniferum

F

(PsV-F):

5,000,000 ɚɬ. (120 ɤɨɩɢɣ ɨɞɧɨɝɨ ɛɟɥɤɚ)

ȼɢɪɭɫɵȼɢɪɭɫɵ: : ɆɨɥɟɤɭɥɹɪɧɚɹɆɨɥɟɤɭɥɹɪɧɚɹ

ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ

Satellite Tobacco Mosaic Virus:

932,508 ɚɬɨɦɨɜ

20 Ǻǹ~10 ǺǾ

ɉɨɥɢɦɟɪɧɵɟɉɨɥɢɦɟɪɧɵɟ

ɷɥɟɤɬɪɨɥɢɬɧɵɟɷɥɟɤɬɪɨɥɢɬɧɵɟ

ɬɨɩɥɢɜɧɵɟɬɨɩɥɢɜɧɵɟ

ɷɥɟɦɟɧɬɵɷɥɟɦɟɧɬɵ

Ƀɩɨɩɧɠɫɨɛɺ

ɧɠɧɜɫɛɨɛ

–

ɸɭɩ

ɩɜɶɲɨɩ

Nafion®

:

water/methanol + mobile ions

Ⱦɣɟɫɩɯɣɦɷɨɶɠ

ɥɛɨɛɦɶ

–ɣɧɠɨɨɩ

ɩɨɣ

ɪɫɩɝɩɟɺɭ

ɭɩɥ.

ɋɬɪɭɤɬɭɪɚɋɬɪɭɤɬɭɪɚ

ɧɚɮɢɨɧɨɜɨɣɧɚɮɢɨɧɨɜɨɣ

ɦɟɦɛɪɚɧɵɦɟɦɛɪɚɧɵ

C O S F H

ɇɚɧɨɤɨɦɩɨɡɢɬɵɇɚɧɨɤɨɦɩɨɡɢɬɵȺɥɸɦɨɫɢɥɢɤɚɬ

Na+, K+ ɉɨɥɢɦɟɪ/ɜɨɞɚ

xxxxxxx

y x

z

US US TeraGrid/GridSAMTeraGrid/GridSAM

~107

ɚɬɨɦɨɜ

ɆɨɥɟɤɭɥɹɪɧɵɟɆɨɥɟɤɭɥɹɪɧɵɟ

ɦɚɲɢɧɵɦɚɲɢɧɵ

ɢɢ

ɦɨɬɨɪɵɦɨɬɨɪɵ

Boron-NitrideɎɭɥɥɟɪɟɧɵ

ɢ

ɧɚɧɨɬɪɭɛɤɢ

ɆɨɥɟɤɭɥɹɪɧɵɟɆɨɥɟɤɭɥɹɪɧɵɟ

ɦɚɲɢɧɵɦɚɲɢɧɵ

ɇɚɧɨɩɪɨɜɨɞɚɇɚɧɨɩɪɨɜɨɞɚ

2. ɇɚɧɨɬɪɭɛɤɢ

3. ȾɇɄ1. Ɉɤɫɢɞɵ

ɦɟɬɚɥɥɨɜ

ɇɚɧɨɩɪɨɜɨɞɚɇɚɧɨɩɪɨɜɨɞɚ

ɧɚɧɚ

ɨɫɧɨɜɟɨɫɧɨɜɟ

ȾɇɄȾɇɄ

Ɇɟɬɚɥɥɢɱɟɫɤɢɟ

ɩɪɨɜɨɞɚ:

Ȼɨɥɶɲɨɟ

ɩɨɜɟɪɯɧɨɫɬɧɨɟ

ɧɚɬɹɠɟɧɢɟɜɟɞɟɬ

ɤ

ɞɟɮɨɪɦɚɰɢɢ

ɢ

ɪɚɡɪɵɜɭ

Ɇɟɬɚɥɥɢɡɚɰɢɹ

ȾɇɄ:1. Ʉɨɧɞɟɧɫɚɰɢɹ

Au+3

2. ȼɨɫɫɬɚɧɨɜɥɟɧɢɟ

Au+3

→ Au

Ȼɦɷɭɠɫɨɛɭɣɝɛ

MD with many-body potential

ɋɚɦɨɫɛɨɪɤɚ

ɧɚɧɨɱɚɫɬɢɰ

ɡɨɥɨɬɚɧɚ

ɩɨɜɟɪɯɧɨɫɬɢ

ȾɇɄ.

ɉɪɨɛɥɟɦɚɉɪɨɛɥɟɦɚ ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢ ɦɨɥɟɤɭɥɦɨɥɟɤɭɥ

ɋɬɪɚɬɟɝɢɹ:1.

ɉɪɟɞɫɤɚɡɚɬɶ

ɤɪɢɫɬɚɥɥ.2.

Ɋɚɡɦɧɨɠɢɬɶ

ɤɪɢɫɬɚɥɥ.3.

ɆȾ

ɦɨɞɟɥɢɪɨɜɚɧɢɟ.

ɬɢɨɮɟɧ

ɩɟɩɬɢɞ

ɈɝɪɭɛɥɟɧɧɵɟɈɝɪɭɛɥɟɧɧɵɟ ɦɨɞɟɥɢɦɨɞɟɥɢ (Coarse(Coarse--graining)graining)

•• ǜǻǺǵdzDzǺǵDzǜǻǺǵdzDzǺǵDz

ȄǵǾǸǭȄǵǾǸǭ

ǾǿDzǼDzǺDzǶǾǿDzǼDzǺDzǶ

ǾǯǻǮǻDZȈǾǯǻǮǻDZȈ [United Atoms (UA), Mapping/Reverse [United Atoms (UA), Mapping/Reverse

MappingMapping, , SMD, DPD].SMD, DPD].

•• ǛǮǻǸǻȄǷǵǛǮǻǸǻȄǷǵ

[Shape[Shape--based Models, Patchy based Models, Patchy Particles, Granular Models]Particles, Granular Models]..

•• ǑǵǾǷǽDzǿǺȈDzǑǵǾǷǽDzǿǺȈDz

ǽDzȅDzǿǻȄǺȈDzǽDzȅDzǿǻȄǺȈDz

ǹǻDZDzǸǵǹǻDZDzǸǵ. .

ɋɬɨɯɚɫɬɢɱɟɫɤɚɹɋɬɨɯɚɫɬɢɱɟɫɤɚɹ

ɦɨɥɟɤɭɥɹɪɧɚɹɦɨɥɟɤɭɥɹɪɧɚɹ

ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ

Robert Brown (1773-1858)

6 /frictiona F vγ πη= = −Ɂɚɤɨɧ

ɋɬɨɤɫɚ

ɞɥɹ

ɤɨɷɮɮɢɰɢɟɧɬɚ

ɬɪɟɧɢɹ

6

kTD

aπη=

)(tvvm σςγ +−=&ɍɪɚɜɧɟɧɢɟ

Ʌɚɧɠɟɜɟɧɚ

0)( =tς )()()( tttt ′−=′ δςς

σTkB2/2σ=γ

RandomFrictionveConservatidt

dm FFF

r++=

2

2

RandomveConservatidt

dm FF

r+=

Ʌɚɧɠɟɜɟɧɨɜɚ

ɞɢɧɚɦɢɤɚ

Ȼɪɨɭɧɨɜɫɤɚɹ

ɞɢɧɚɦɢɤɚ

ɈɝɪɭɛɥɟɧɢɟɈɝɪɭɛɥɟɧɢɟ

ɦɨɞɟɥɢɦɨɞɟɥɢ

((CoarseCoarse--Graining, CG)Graining, CG)ɉɨɧɢɠɟɧɢɟɉɨɧɢɠɟɧɢɟ

ɱɢɫɥɚɱɢɫɥɚ

ɫɬɟɩɟɧɟɣɫɬɟɩɟɧɟɣ

ɫɜɨɛɨɞɵɫɜɨɛɨɞɵ

MappingMapping

ɆɨɞɟɥɶɆɨɞɟɥɶ

ɩɨɥɢɦɟɪɢɡɚɰɢɢɩɨɥɢɦɟɪɢɡɚɰɢɢ

((ɯɢɦɢɱɟɫɤɚɹɯɢɦɢɱɟɫɤɚɹ

ɫɟɬɤɚɫɟɬɤɚ))

ɋɯɟɦɚɋɯɟɦɚ

ɫɜɹɡɟɣɫɜɹɡɟɣ

ɌɨɩɨɥɨɝɢɹɌɨɩɨɥɨɝɢɹ

ɫɟɬɤɢɫɟɬɤɢ

Reverse MappingReverse Mapping

ɆɄɆɄ

ɆȾɆȾ

23867

points

500

points

100

points

ɒɚɪɧɢɪɵɒɚɪɧɢɪɵ

ɢɢ

ɨɛɨɥɨɱɤɢɨɛɨɥɨɱɤɢ

Shape-based coarse-graining Ⱦɟɮɨɪɦɢɪɭɟɦɵɟ

ɢ

ɠɟɫɬɤɢɟ

ɨɛɨɥɨɱɤɢ

Ɇɟɬɨɞ

ɧɟɣɪɨɧɧɵɯ

ɫɟɬɟɣ

ɄɚɤɄɚɤ

ɨɩɪɟɞɟɥɢɬɶɨɩɪɟɞɟɥɢɬɶ

ɜɡɚɢɦɨɞɟɣɫɬɜɢɹɜɡɚɢɦɨɞɟɣɫɬɜɢɹ

ɞɥɹɞɥɹ

CGCG--ɦɨɞɟɥɢɦɨɞɟɥɢ ??

•• ǜǻDZǰǻǺǷǭǜǻDZǰǻǺǷǭ

ǽDzǴȀǸȉǿǭǿǻǯǽDzǴȀǸȉǿǭǿǻǯ

ǼǻDZǼǻDZ

ȊǷǾǼDzǽǵǹDzǺǿȊǷǾǼDzǽǵǹDzǺǿ..•• ǜǻDZǰǻǺǷǭǜǻDZǰǻǺǷǭ

ǽDzǴȀǸȉǿǭǿǻǯǽDzǴȀǸȉǿǭǿǻǯ

ǼǻDZǼǻDZ

ǭǿǻǹǵǾǿǵȄDzǾǷǻDzǭǿǻǹǵǾǿǵȄDzǾǷǻDz ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz..

ǕǿDzǽǭǿǵǯǺǭȌǕǿDzǽǭǿǵǯǺǭȌǎǻǸȉȃǹǭǺǻǯǾǷǭȌǎǻǸȉȃǹǭǺǻǯǾǷǭȌ

ǵǺǯDzǽǾǵȌǵǺǯDzǽǾǵȌ1

meso-scale

atomistic

g(R) + kT

g(R)

eff eff

i iu u lni

+

⎛ ⎞⎜ ⎟=⎜ ⎟⎝ ⎠

0effu = ɉɨɬɟɧɰɢɚɥ

ɫɪɟɞɧɟɣ

ɫɢɥɵ: -kT ln

g(R)atomistic

ueff

ȼɢɪɭɫɵȼɢɪɭɫɵ: : CG CG ɆɨɥɟɤɭɥɹɪɧɚɹɆɨɥɟɤɭɥɹɪɧɚɹ

ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ

Reovirus

Core

CGCG

CGCG--MDMD

ȻɢɨɧɚɧɨɦɨɬɨɪȻɢɨɧɚɧɨɦɨɬɨɪ

(Flagellum)(Flagellum)

ǼȓȈȋȍȓȓțȔ

-

ȔȖȓȍȒțȓȧȘȕȣȑ

ȔȖȚȖȘ

(ȕȈȕȖȔȈȠȐȕȈ) ȐșȗȖȓȤȏțȍȔȣȑ

ȉȈȒȚȍȘȐȧȔȐ

Ȍȓȧ

ȗȘȖȌȊȐȎȍȕȐȧ

ȟȍȘȍȏ

șȘȍȌț. ǩȈȒȚȍȘȐȈȓȤȕȣȑ

flagellum ȥȚȖ

șȗȐȘȈȓȤȕȖȍ

ȊȖȓȖȒȕȖ

ȒȖȚȖȘȖȍ

ȊȘȈȡȈȍȚșȧ

ȒȈȒ

"ȕȈȊȍșȕȖȑ

ȔȖȚȖȘ".

FlagellumFlagellum: : CG CG ɆɨɥɟɤɭɥɹɪɧɚɹɆɨɥɟɤɭɥɹɪɧɚɹ

ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ

70,000,000 ɚɬɨɦɨɜ

ɉɪɨɰɟɫɫɵɉɪɨɰɟɫɫɵ

ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢɈɝɪɭɛɥɟɧɧɵɟɈɝɪɭɛɥɟɧɧɵɟ

ɦɨɞɟɥɢɦɨɞɟɥɢ

((ShapeShape--Based Coarse Graining)Based Coarse Graining)

ɈɛɨɥɨɱɤɢɈɛɨɥɨɱɤɢ

ɜɢɪɭɫɨɜɜɢɪɭɫɨɜ

((ɤɚɩɫɢɞɵɤɚɩɫɢɞɵ))

ɉɪɨɰɟɫɫɵɉɪɨɰɟɫɫɵ

ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢǛǰǽȀǮǸDzǺǺȈDzǛǰǽȀǮǸDzǺǺȈDz

ǹǻDZDzǸǵǹǻDZDzǸǵ

((Patchy Particles Patchy Particles ––

""ǜȌǿǺǵǾǿȈDzǜȌǿǺǵǾǿȈDz

ȄǭǾǿǵȃȈȄǭǾǿǵȃȈ""))

12 X

Patchy ParticlePatchy Particle

ɉɪɨɰɟɫɫɵɉɪɨɰɟɫɫɵ

ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢɈɝɪɭɛɥɟɧɧɵɟɈɝɪɭɛɥɟɧɧɵɟ

ɦɨɞɟɥɢɦɨɞɟɥɢ

((Patchy ParticlesPatchy Particles))

•

Ɇɚɬɟɪɢɚɥɵ, ɫɨɫɬɨɹɳɢɟ

ɢɡ

ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɯ

ɝɪɚɧɭɥ•

ɉɟɫɨɤ, ɫɧɟɝ,

ɝɪɚɜɢɣ, ɤɪɭɩɚ

ɢ

ɨɪɟɲɤɢ•

ɉɨɜɟɞɟɧɢɟ

ɭɩɪɚɜɥɹɟɬɫɹ

ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɦɢ

ɫɢɥɚɦɢ•

Ɍɪɟɧɢɟ, ɝɪɚɜɢɬɚɰɢɹ, ɮɨɪɦɚ

ɱɚɫɬɢɰ

ȽɪɚɧɭɥɹɪɧɵɟȽɪɚɧɭɥɹɪɧɵɟ

ɦɨɞɟɥɢɦɨɞɟɥɢ

ɊɟɲɟɬɨɱɧɵɟɊɟɲɟɬɨɱɧɵɟ

((ɞɢɫɤɪɟɬɧɵɟɞɢɫɤɪɟɬɧɵɟ) ) ɦɨɞɟɥɢɦɨɞɟɥɢ

CC BB AA

DD EEİED

İEA

İEC

İEB

1.

ɉɨɥɨɠɟɧɢɟ

ɱɚɫɬɢɰ

ɜ

ɩɪɨɫɬɪɚɧɫɬɜɟ

ɨɝɪɚɧɢɱɟɧɨ

ɭɡɥɚɦɢ

ɩɪɚɜɢɥɶɧɨɣ

ɪɟɲɟɬɤɢ.2.

ȼɡɚɢɦɨɞɟɣɫɬɜɭɸɬ

ɬɨɥɶɤɨ

ɱɚɫɬɢɰɵ

ɜ

ɫɨɫɟɞɧɢɯ

ɭɡɥɚɯ.3.

ɉɟɪɟɫɟɱɟɧɢɹ

ɰɟɩɢ

ɡɚɩɪɟɳɟɧɵ.

AA AA BB BB AB ABE N N Nε ε ε= + +

ɐɟɩɶ

ɫ

"ɮɥɭɤɬɭɢɪɭɸɳɢɦɢ" ɫɜɹɡɹɦɢ(bond fluctuation model)

"Ɋɟɩɬɚɰɢɨɧɧɚɹ" ɦɨɞɟɥɶ

ǞǵǺǿDzǴ

ǼǻǸȀǼǽǻǯǻDZȌȆǵȂ

ǺǭǺǻǾǿǽȀǷǿȀǽ

ɄɜɚɧɬɨɜɵɟɄɜɚɧɬɨɜɵɟ

ɬɨɱɤɢɬɨɱɤɢ

((NanodotsNanodots))

ǙǺǻǰǻǰǽǭǺǺǵǷǏǻǽǻǺǻǰǻ

ȾɢɫɫɢɩɚɬɢɜɧɚɹȾɢɫɫɢɩɚɬɢɜɧɚɹ ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ ɱɚɫɬɢɰɱɚɫɬɢɰ (DPD)(DPD)

DPD-ȄǭǾǿǵȃǭ

ǞǯǻǶǾǿǯǭ

DPD ȄǭǾǿǵȃȈ

∑ −−=ψl

lkk ss )(/)()( rxrxx

)/exp()( 22 dxs −=x

∑ψ=i

ikk mM )(x

i

i

ikk mvxP ∑ψ= )(

∑ ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+ψ=+

<i ij

ijMDiikkkk rUmvUVM )()( 2

2

12

2

1 x

kkkk M/PVr ≡=&

ȾɢɫɫɢɩɚɬɢɜɧɚɹȾɢɫɫɢɩɚɬɢɜɧɚɹ ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ ɱɚɫɬɢɰɱɚɫɬɢɰ (DPD)(DPD)

V2

V1

F1dissipative

F2dissipative

F1random

F2random

RandomDissCons

ij ijijijFFFF ++=

"Ȼɥɨɛ"(ɫɬɚɬ. ɫɟɝɦɟɧɬ)

ijijij

C

ij ra rF )(ω=

ijijijij

D

ij r rvrF ))((2 ⋅γω−=

ijijijB

R

ij rTk rF )(2 ωξγ=

⎩⎨⎧

>≤−

=ωcutij

cutijcutij

ij rr

rrrrr

0

/1)(

);;( κδχ= solvFHij fa

)'(2)'()( ttTktt ijB

R

j

R

i −δδγδ= αββα FF

ɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹ

ɩɨɥɢɦɟɪɧɵɯɩɨɥɢɦɟɪɧɵɯ

ɧɚɧɨɫɬɪɭɤɬɭɪɧɚɧɨɫɬɪɭɤɬɭɪ: : ɍɪɨɤɍɪɨɤ

ʋʋ 11

Ɇɢɤɪɨɮɚɡɧɨɟ

ɪɚɡɞɟɥɟɧɢɟ:Ɇɚɫɲɬɚɛ

ɧɚɧɨɫɬɪɭɤɬɭɪ

~10-100 ɧɦ

100 ɧɦ

ɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹ

ɩɨɥɢɦɟɪɧɵɯɩɨɥɢɦɟɪɧɵɯ

ɧɚɧɨɫɬɪɭɤɬɭɪɧɚɧɨɫɬɪɭɤɬɭɪ: : ɍɪɨɤɍɪɨɤ

ʋʋ 22

ɑɚɫɬɢɰɵ ɉɨɥɟɜɨɟ

ɩɪɟɞɫɬɚɜɥɟɧɢɟ

LAM HEX BCC GYR

ȾɢɡɚɣɧȾɢɡɚɣɧ

ɩɨɥɢɦɟɪɧɵɯɩɨɥɢɦɟɪɧɵɯ

ɧɚɧɨɫɬɪɭɤɬɭɪɧɚɧɨɫɬɪɭɤɬɭɪ: : ɄɪɚɫɨɬɚɄɪɚɫɨɬɚ

ɇɚɧɨɦɢɪɚɇɚɧɨɦɢɪɚ

ɎɢɡɢɱɟɫɤɢɣɎɢɡɢɱɟɫɤɢɣ

ɫɢɧɬɟɡɫɢɧɬɟɡ: : ɂɧɠɟɧɟɪɢɹɂɧɠɟɧɟɪɢɹ

ɧɚɧɨɫɬɪɭɤɬɪɧɚɧɨɫɬɪɭɤɬɪ

timeɝɶɭɫɛɝɦɣɝɛɨɣɠ

~5 nm 30-50% ɪɩɫ

ɇɚɧɨɩɨɪɢɫɬɵɟ

ɦɚɬɟɪɢɚɥɵ

(ɦɟɦɛɪɚɧɵ, ɧɚɧɨɮɢɥɶɬɪɵ…)

ǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDzǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDz

ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz:: ǤǭǾǿǵȃȈǤǭǾǿǵȃȈ

+ + ǜǻǸȌǜǻǸȌ

Ƚɥɚɜɧɚɹ

ɢɞɟɹ:

Ⱦɟɤɨɦɩɨɡɢɰɢɹ

ɫɥɨɠɧɨɣ

ɫɢɫɬɟɦɵ

ɧɚ

2 ɱɚɫɬɢ:

Subsystem A(ɨɫɧɨɜɧɨɣ

ɢɧɬɟɪɟɫ)

Subsystem B(ɤɨɧɬɢɧɭɚɥɶɧɵɣ

ɮɨɧ)

Ɇɟɬɨɞɵ

ɱɚɫɬɢɰ(MC, MD, DPD)

ɉɨɥɟɜɨɟ

ɨɩɢɫɚɧɢɟ(RISM/PRISM, SCFT, DDFT)

ɑɚɫɬɢɰɵɑɚɫɬɢɰɵ ɉɨɥɟɉɨɥɟ

ǑǵǺǭǹǵȄDzǾǷǭȌǑǵǺǭǹǵȄDzǾǷǭȌ

ǿDzǻǽǵȌǿDzǻǽǵȌ

ȁȀǺǷȃǵǻǺǭǸǭȁȀǺǷȃǵǻǺǭǸǭ

ǼǸǻǿǺǻǾǿǵǼǸǻǿǺǻǾǿǵ

ȼ

ɨɬɥɢɱɢɟ

ɨɬ

ɦɟɬɨɞɨɜ

ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɨɝɨ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ

(ɬɚɤɢɯ, ɤɚɤ

Ɇɨɧɬɟ-Ʉɚɪɥɨɢɥɢ

ɦɨɥɟɤɭɥɹɪɧɚɹ

ɞɢɧɚɦɢɤɚ), ɝɞɟ

ɜɵɱɢɫɥɟɧɢɹ

ɩɪɨɜɨɞɹɬɫɹ

ɞɥɹ

ɚɬɨɦɨɜ

ɢɥɢ

ɦɨɥɟɤɭɥ, ɜɦɟɡɨɫɤɨɩɢɱɟɫɤɨɦ

ɦɨɞɟɥɢɪɨɜɚɧɢɢ

ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ

ɩɨɜɟɞɟɧɢɟɤɨɥɥɟɤɬɢɜɧɵɯ

ɩɟɪɟɦɟɧɧɵɯ

–

ɮɭɧɤɰɢɣ

ɪɚɫɩɪɟɞɟɥɟɧɢɹ

ɩɥɨɬɧɨɫɬɟɣ

ɢ

ɩɨɥɟɣ.

),()(

)]([F),( 2 tt

tr

r

rrα

α

αα

α η+δφφδ

∇Λ=∂

φ∂

F

–

ɮɭɧɤɰɢɨɧɚɥ

ɫɜɨɛɨɞɧɨɣ

ɷɧɟɪɝɢɢ, Λα

–

ɤɨɷɮɮɢɰɢɟɧɬɵ

ɩɨɞɜɢɠɧɨɫɬɢ

ɤɨɦɩɨɧɟɧɬɚ

α, η

–ɫɬɨɯɚɫɬɢɱɟɫɤɢɣ

ɲɭɦ, ɪɚɫɩɪɟɞɟɥɟɧɢɟ

ɤɨɬɨɪɨɝɨ

ɩɨɞɱɢɧɹɟɬɫɹ

ɮɥɭɤɬɭɚɰɢɨɧɧɨ-ɞɢɫɫɢɩɚɬɢɜɧɨɣ

ɬɟɨɪɟɦɟ.

ɗɜɨɥɸɰɢɹ

ɥɨɤɚɥɶɧɨɣ

ɩɥɨɬɧɨɫɬɢ

φ(r) ɤɨɦɩɨɧɟɧɬɚ

Į:

)]([)()]/([F rrr φμ≡δφφδ ααα

ȼɜɨɞɹɬɫɹ

ɝɢɩɨɬɟɬɢɱɟɫɤɢɟ

ɜɧɟɲɧɢɟ

ɩɨɥɹ

ȦĮ

(r), ɤɨɬɨɪɵɟ

ɞɟɣɫɬɜɭɸɬ

ɧɚ

ɤɨɦɩɨɧɟɧɬɭ

α

ɢ

ɩɨɞɛɢɪɚɸɬɫɹ

ɬɚɤ, ɱɬɨ

ɜ

ɤɚɠɞɵɣ

ɦɨɦɟɧɬ

ɜɪɟɦɟɧɢ

t

ɪɚɫɩɪɟɞɟɥɟɧɢɟ

ɩɥɨɬɧɨɫɬɟɣ

φα

(r,t) ɨɬɜɟɱɚɟɬ

ɪɚɜɧɨɜɟɫɧɨɦɭ

ɫɨɫɬɨɹɧɢɸ

→ ɩɪɨɛɥɟɦɚ

ɜɵɱɢɫɥɟɧɢɹ

ɯɢɦɢɱɟɫɤɢɯ

ɩɨɬɟɧɰɢɚɥɨɜ

μα

(r) ɩɟɪɟɮɨɪɦɭɥɢɪɭɟɬɫɹ

ɜ

ɩɪɨɛɥɟɦɭ, ɫɜɹɡɚɧɧɭɸ

ɫ

ɜɵɱɢɫɥɟɧɢɟɦ

ɜɧɟɲɧɢɯ

(ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɵɯ) ɩɨɥɟɣ

ȦĮ

(r).

Ɋɚɜɧɨɜɟɫɢɟ:

įF[φ]/įφĮ

= 0

ǗǭǷǗǭǷ

ȊǿǻȊǿǻ

ǽǭǮǻǿǭDzǿǽǭǮǻǿǭDzǿ

? ? ǜǽǻǾǿǻǶǜǽǻǾǿǻǶ

ǼǽǵǹDzǽǼǽǵǹDzǽ..

ɊɚɡɞɟɥɟɧɢɟɊɚɡɞɟɥɟɧɢɟ

ɫɦɟɫɢɫɦɟɫɢ

ɛɟɧɡɨɥɚɛɟɧɡɨɥɚ

ɫɫ

ɜɨɞɨɣɜɨɞɨɣ

(1:1(1:1

ɫɦɟɫɶɫɦɟɫɶ))ɉɨɥɟɜɨɣɉɨɥɟɜɨɣ

ɲɚɛɥɨɧɲɚɛɥɨɧ: Im3m : Im3m ((ɊɊ--ɫɬɪɭɤɬɭɪɚɫɬɪɭɤɬɭɪɚ

ɒɜɚɪɰɚɒɜɚɪɰɚ))

MDMD

ɎɢɧɚɥɶɧɚɹɎɢɧɚɥɶɧɚɹ

ɫɬɪɭɤɬɭɪɚɫɬɪɭɤɬɭɪɚ

MD/SCFTMD/SCFTSCFTSCFT

ǗǻǺǾǿǽȀǵǽǻǯǭǺǵDzǗǻǺǾǿǽȀǵǽǻǯǭǺǵDz

ǺǭǺǻǾǿǽȀǷǿȀǽǺǭǺǻǾǿǽȀǷǿȀǽ

ɆɟɯɚɧɢɤɚɆɟɯɚɧɢɤɚ

ɫɩɥɨɲɧɨɣɫɩɥɨɲɧɨɣ

ɫɪɟɞɵɫɪɟɞɵ::ɆɟɬɨɞɆɟɬɨɞ

ɤɨɧɟɱɧɵɯɤɨɧɟɱɧɵɯ

ɷɥɟɦɟɧɬɨɜɷɥɟɦɟɧɬɨɜ

x1 x2 x3 x4 x5 x6

U1

U6

U5U4

U3U2

U

1 2 3 4 5

a b

1

2

3

N(r)

N(r)+dN(r)

dx

q(r)(x)

i

j

u(r)(x) – ɩɟɪɟɦɟɳɟɧɢɟ

ɭɡɥɚq(r)(x) – ɢɧɬɟɧɫɢɜɧɨɫɬɶ

ɧɚɝɪɭɡɤɢq(r)(x)dx – ɧɚɝɪɭɡɤɚN(r)(x) – ɜɧɭɬɪɟɧɧɹɹ

ɫɢɥɚdN(r) + q(r)(x)dx = 0 – ɪɚɜɧɨɜɟɫɢɟ

ui

uj

)(

2

)(2)(

)()()(

rr

r

rrr

qdx

udc

dx

ducN

=−

=

ǔǭǷǻǺ

ǐȀǷǭ:

DZǭǯǸDzǺǵDz

ǞDZǯǵǰǻǯǻDz

ǺǭǼǽȌdzDzǺǵDz

ǝǭǾǼǽDzDZDzǸDzǺǵDz

ǺǭǼǽȌdzDzǺǵǶǼǽǵ

DZDzȁǻǽǹǭȃǵǵ

ǹDzǹǮǽǭǺȈ

ɆɟɬɨɞɆɟɬɨɞ

ɤɨɧɟɱɧɵɯɤɨɧɟɱɧɵɯ

ɷɥɟɦɟɧɬɨɜɷɥɟɦɟɧɬɨɜɆɟɦɛɪɚɧɚ

ɬɨɩɥɢɜɧɵɯ

ɷɥɟɦɟɧɬɨɜ

ɉɟɪɢɞɢɧɚɦɢɤɚɉɟɪɢɞɢɧɚɦɢɤɚ

((PeridynamicsPeridynamics

= = PeriPeri

+ + DynaDyna))

∫ +−′−′=ρ ′R

x txbdVxxxtxutxuftxux ),(];);,(),([),()( &&

ɍɪɚɜɧɟɧɢɟ

ɞɜɢɠɟɧɢɹ:

x

x'

f

–

ɩɥɨɬɧɨɫɬɶ

ɫɢɥ

(x'→x)ρ(x) –

ɩɥɨɬɧɨɫɬɶ

ɦɚɬɟɪɢɚɥɚu

–

ɜɟɤɬɨɪ

ɫɦɟɳɟɧɢɹ

V

ɉɟɪɢɞɢɧɚɦɢɤɚ

–

ɝɢɛɪɢɞ

ɦɨɥɟɤɭɥɹɪɧɨɣ

ɞɢɧɚɦɢɤɢ

ɢ

ɤɥɚɫɫɢɱɟɫɤɨɣ

ɬɟɨɪɢɢ

ɷɥɚɫɬɢɱɧɨɫɬɢ

f

= fbond

+ f

short

100 ǹ\ǾDzǷ

70 ǹǹ

550 ǹǹ

Ʌɸɛɨɣ

ɦɚɬɟɪɢɚɥɶɧɵɣ

ɩɪɟɞɦɟɬ

−

ɷɬɨ

ɜɫɟɝɨ

ɥɢɲɶ ɫɤɨɩɥɟɧɢɟ

ɚɬɨɦɨɜ

ɜ

ɩɪɨɫɬɪɚɧɫɬɜɟ. Ɍɨ, ɤɚɤ

ɷɬɢ

ɚɬɨɦɵ ɫɨɛɪɚɧɵ

ɜ

ɫɬɪɭɤɬɭɪɭ, ɨɩɪɟɞɟɥɹɟɬ, ɱɬɨ

ɷɬɨ

ɛɭɞɟɬ

ɡɚ ɩɪɟɞɦɟɬ. ɂ

ɦɵ

ɬɨɥɶɤɨ

ɞɢɪɢɠɢɪɭɟɦ

ɨɪɤɟɫɬɪɨɦ

ɢɡ

ɷɬɢɯ ɚɬɨɦɧɵɯ

ɫɬɪɭɤɬɭɪ. ɗɬɨɬ

ɨɪɤɟɫɬɪ

ɫɭɳɟɫɬɜɨɜɚɥ

ɫ ɫɨɬɜɨɪɟɧɢɹ

ɦɢɪɚ

ɢ

ɥɢɲɶ

ɠɞɟɬ, ɤɨɝɞɚ

ɩɨɹɜɢɬɫɹ

ɞɢɪɢɠɟɪ

...

ɋɬɚɧɢɫɥɚɜ

Ʌɟɦ, 1982 ɝ.

+ +

+

+

+

+

+

_

__

_

_

_

_

ɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵ: : ɈɩɪɟɞɟɥɟɧɢɟɈɩɪɟɞɟɥɟɧɢɟ

ɉɨɥɢɷɥɟɤɬɪɨɥɢɬ

==ɩɨɥɢɦɟɪɩɨɥɢɦɟɪ

ɫɫ

ɡɚɪɹɠɟɧɧɵɦɢɡɚɪɹɠɟɧɧɵɦɢ

ɦɨɧɨɦɟɪɚɦɢɦɨɧɨɦɟɪɚɦɢ

ȾɢɫɫɨɰɢɚɰɢɹȾɢɫɫɨɰɢɚɰɢɹ::ɇɟɣɬɪɚɥɶɧɵɣɇɟɣɬɪɚɥɶɧɵɣ

ɦɨɧɨɦɟɪɦɨɧɨɦɟɪ

⇔⇔ɡɚɪɹɠɟɧɧɵɣɡɚɪɹɠɟɧɧɵɣ

ɦɨɧɨɦɟɪɦɨɧɨɦɟɪ

+ + ɤɨɧɬɪɢɨɧɤɨɧɬɪɢɨɧ

ɑɢɫɥɨɑɢɫɥɨ

ɤɨɧɬɪɢɨɧɨɜɤɨɧɬɪɢɨɧɨɜ

= = ɱɢɫɥɨɱɢɫɥɨ

ɡɚɪɹɠɟɧɧɵɯɡɚɪɹɠɟɧɧɵɯ

ɦɨɧɨɦɟɪɨɜɦɨɧɨɦɟɪɨɜ(N(N++

= N= N--))

ɉɨɥɢɦɟɪ

ɉɨɞɜɢɠɧɵɣ

ɤɨɧɬɪɢɨɧ

ɉɨɥɢɚɧɢɨɧɵɉɨɥɢɚɧɢɨɧɵ

ɢɢ

ɩɨɥɢɤɚɬɢɨɧɵɩɨɥɢɤɚɬɢɨɧɵɉɪɢɦɟɪɵɉɪɢɦɟɪɵ::

(a) sodium (a) sodium polyacrylatepolyacrylate

(b) sodium (b) sodium polymetacrylatepolymetacrylate

(c) (c) polydiallyldimethylammoniumpolydiallyldimethylammonium

chloridechloride

(d) (d) ȾɇɄȾɇɄ

((ɡɚɪɹɞɡɚɪɹɞ

--ee

ɧɚɧɚ

1.7 1.7 ɧɦɧɦ))

(e) (e) ȽɢɫɬɨɧȽɢɫɬɨɧ

––

ɧɭɤɥɟɨɩɪɨɬɟɢɧɧɭɤɥɟɨɩɪɨɬɟɢɧ

(+170(+170e)e)CH

2

CHCH

CH2

N+

CH2

CH2CH

3CH

3

CH3CH

3

CH2

CHCH3

CH3

CO

ONa

+

Cl

CH2

CCH3

CH3

CO

O

CH3

Na+

(a) (b)

(c)

(d) (e)

ɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵ

ɋɢɥɶɧɨɋɢɥɶɧɨ

ɡɚɪɹɠɟɧɧɵɟɡɚɪɹɠɟɧɧɵɟȻɨɥɶɲɚɹȻɨɥɶɲɚɹ

ɞɨɥɹɞɨɥɹ

ɡɚɪɹɠɟɧɧɵɯɡɚɪɹɠɟɧɧɵɯ

ɡɜɟɧɶɟɜɡɜɟɧɶɟɜ((ϕϕ

= = NNqq

/ N / N ≈≈

1)1)

ɋɢɥɶɧɨɋɢɥɶɧɨ

ɩɨɥɹɪɧɚɹɩɨɥɹɪɧɚɹ

ɫɪɟɞɚɫɪɟɞɚ

((ɜɨɞɚɜɨɞɚ, , εε

≈≈

8080))

ɗɥɟɤɬɪɨɫɬɚɬɢɤɚɗɥɟɤɬɪɨɫɬɚɬɢɤɚ

ɞɨɦɢɧɢɪɭɟɬɞɨɦɢɧɢɪɭɟɬ

ɋɥɚɛɨɋɥɚɛɨ

ɡɚɪɹɠɟɧɧɵɟɡɚɪɹɠɟɧɧɵɟɆɚɥɚɹɆɚɥɚɹ

ɞɨɥɹɞɨɥɹ

ɡɚɪɹɠɟɧɧɵɯɡɚɪɹɠɟɧɧɵɯ

ɡɜɟɧɶɟɜɡɜɟɧɶɟɜ((ϕϕ

= = NNqq

/ N / N <<<<

1)1)

ɋɥɚɛɨɋɥɚɛɨ

ɩɨɥɹɪɧɚɹɩɨɥɹɪɧɚɹ

ɫɪɟɞɚɫɪɟɞɚ

((εε

< 10< 10))

ɄɭɥɨɧɨɜɫɤɢɟɄɭɥɨɧɨɜɫɤɢɟ

ɜɡɚɢɦɨɞɟɣɫɬɜɢɹɜɡɚɢɦɨɞɟɣɫɬɜɢɹɤɨɧɤɭɪɢɪɭɸɬɤɨɧɤɭɪɢɪɭɸɬ

ɫɫ

ɞɢɫɩɟɪɫɢɨɧɧɵɦɢɞɢɫɩɟɪɫɢɨɧɧɵɦɢ

ɉɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣɉɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣ

ɢɢ

ɢɨɧɨɦɟɪɧɵɣɢɨɧɨɦɟɪɧɵɣ

ɪɟɠɢɦɵɪɟɠɢɦɵ

ɉɨɥɹɪɧɵɣɉɨɥɹɪɧɵɣ

ɪɚɫɬɜɨɪɢɬɟɥɶɪɚɫɬɜɨɪɢɬɟɥɶ::

εε

>> 1, >> 1, ΓΓ

< 1< 1

→→

ɩɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣɩɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣ

ɪɟɠɢɦɪɟɠɢɦɈɪɝɚɧɢɱɟɫɤɢɣɈɪɝɚɧɢɱɟɫɤɢɣ

ɪɚɫɬɜɨɪɢɬɟɥɶɪɚɫɬɜɨɪɢɬɟɥɶ::

εε

~ 1, ~ 1, ΓΓ

>> 1>> 1

→→

ɢɨɧɨɦɟɪɧɵɣɢɨɧɨɦɟɪɧɵɣ

ɪɟɠɢɦɪɟɠɢɦ

u (r) = q q / rc 1 2 ε

q1 q2

rɗɥɟɤɬɪɨɫɬɚɬɢɤɚɗɥɟɤɬɪɨɫɬɚɬɢɤɚ::

ɉɨɬɟɧɰɢɚɥɶɧɚɹ

ɷɧɟɪɝɢɹ:

e2/εr0

Ɍɟɩɥɨɜɚɹ

ɷɧɟɪɝɢɹ:

~kT

ɉɚɪɚɦɟɬɪ

ɫɜɹɡɢ:

Γ

= e2/εr0 kT

Ⱦɥɢɧɚ

Ȼɶɟɪɪɭɦɚ:

lB

= e2/εkT

|q|q11

| = || = |--qq22

| = | = ɷɥɟɦɟɧɬɚɪɧɵɣɷɥɟɦɟɧɬɚɪɧɵɣ

ɡɚɪɹɞɡɚɪɹɞ ((ee))

ȼɨɞɚȼɨɞɚ

ɩɪɢɩɪɢ

T = 298 KT = 298 K::σσ

≈≈

3.5 3.5 ÅÅ; ; εε

= 81= 81llBB

= 7.1 = 7.1 ÅÅΓΓ

≈≈

22

ȻɟɧɡɨɥȻɟɧɡɨɥ: : ΓΓ

> 20> 20

_

+__

ɂɨɧɨɦɟɪɵɂɨɧɨɦɟɪɵȼȼ

ɨɪɝɚɧɢɱɟɫɤɨɦɨɪɝɚɧɢɱɟɫɤɨɦ

ɪɚɫɬɜɨɪɢɬɟɥɟɪɚɫɬɜɨɪɢɬɟɥɟ

ɤɨɧɬɪɢɨɧɵɤɨɧɬɪɢɨɧɵ ɤɨɧɞɟɧɫɢɪɭɸɬɫɹɤɨɧɞɟɧɫɢɪɭɸɬɫɹ

ɧɚɧɚ

ɦɨɧɨɦɟɪɚɯɦɨɧɨɦɟɪɚɯ

→→ɮɨɪɦɢɪɭɸɬɫɹɮɨɪɦɢɪɭɸɬɫɹ

ɢɨɧɧɵɟɢɨɧɧɵɟ

ɩɚɪɵɩɚɪɵ

ɂɨɧɧɚɹɂɨɧɧɚɹ

ɩɚɪɚɩɚɪɚ

= = ɮɥɭɤɬɭɢɪɭɸɳɢɣɮɥɭɤɬɭɢɪɭɸɳɢɣ

ɞɢɩɨɥɶɞɢɩɨɥɶ ɋɢɥɶɧɨɟɋɢɥɶɧɨɟ

ɞɢɩɨɥɶɞɢɩɨɥɶ--ɞɢɩɨɥɶɧɨɟɞɢɩɨɥɶɧɨɟ

ɩɪɢɬɹɠɟɧɢɟɩɪɢɬɹɠɟɧɢɟ →→ɚɫɫɨɰɢɚɰɢɹɚɫɫɨɰɢɚɰɢɹ

ɞɢɩɨɥɟɣɞɢɩɨɥɟɣ

→→ɮɨɪɦɢɪɨɜɚɧɢɟɮɨɪɦɢɪɨɜɚɧɢɟ

ɦɭɥɶɬɢɩɥɟɬɨɜɦɭɥɶɬɢɩɥɟɬɨɜ::

ɆɭɥɶɬɢɩɥɟɬɆɭɥɶɬɢɩɥɟɬ

= = ɚɝɪɟɝɚɬɚɝɪɟɝɚɬ

ɢɡɢɡ

ɞɢɩɨɥɟɣɞɢɩɨɥɟɣ

ȾɚɥɶɧɨɞɟɣɫɬɜɢɟȾɚɥɶɧɨɞɟɣɫɬɜɢɟ

←←

LL →→2D box2D box 3D box3D box

∑∑≠

ε +=

m mr

N

ji ij

ji

CL

qqU 1

mmxx , m, myy , , mmzz = = 0,1,2,0,1,2,……,,∞∞

1.5

1.0

0.5

0.0

-0.5

-1.0

4321

Lennard-JonesCoulomb + LJ

distance (r)

Ene

rgy,

u(r

)

ɆɚɤɪɨɢɨɧɆɚɤɪɨɢɨɧ

+ + ɤɨɧɬɪɢɨɧɵɤɨɧɬɪɢɨɧɵ

Sun

# run# run0

20

40

60

80

100

1 2

ΓΓ

Simulation protocolSimulation protocol

+1e

-20e

ɋɢɥɶɧɵɟɋɢɥɶɧɵɟ

ɥɚɬɟɪɚɥɶɧɵɟɥɚɬɟɪɚɥɶɧɵɟ ɤɨɪɪɟɥɹɰɢɢɤɨɪɪɟɥɹɰɢɢ. . ɄɨɧɬɪɢɨɧɵɄɨɧɬɪɢɨɧɵ ɮɨɪɦɢɪɭɸɬɮɨɪɦɢɪɭɸɬ

ɫɬɪɭɤɬɭɪɭɫɬɪɭɤɬɭɪɭ

ɬɢɩɚɬɢɩɚ

1D 1D ɤɪɢɫɬɚɥɥɚɤɪɢɫɬɚɥɥɚ

ȼɢɝɧɟɪɚȼɢɝɧɟɪɚ..

ȽɢɝɚɧɬɫɤɚɹȽɢɝɚɧɬɫɤɚɹ

ɡɧɚɤɨɜɚɹɡɧɚɤɨɜɚɹ

ɢɧɜɟɪɫɢɹɢɧɜɟɪɫɢɹ

Sun

-24e9e -1e

ΓΓ

# run# run0

10

20

30

40

50

1 2

Simulation protocolSimulation protocol ɆɚɤɪɨɢɨɧɆɚɤɪɨɢɨɧ

+ + ɦɭɥɶɬɢɜɚɥɟɧɬɧɵɟɦɭɥɶɬɢɜɚɥɟɧɬɧɵɟ

ɤɨɧɬɪɢɨɧɵɤɨɧɬɪɢɨɧɵ

+ + ɦɨɧɨɜɚɥɟɧɬɧɵɟɦɨɧɨɜɚɥɟɧɬɧɵɟ

ɢɨɧɵɢɨɧɵ

ɉɨɫɥɟɉɨɫɥɟ

ɤɨɧɞɟɧɫɚɰɢɢɤɨɧɞɟɧɫɚɰɢɢ

ɦɚɤɪɨɢɨɧɦɚɤɪɨɢɨɧ

ɩɟɪɟɡɚɪɹɠɚɟɬɫɹɩɟɪɟɡɚɪɹɠɚɟɬɫɹ: : ɟɝɨɟɝɨ

ɡɚɪɹɞɡɚɪɹɞ

ɜɛɥɢɡɢɜɛɥɢɡɢ

ɩɨɜɟɪɯɧɨɫɬɢɩɨɜɟɪɯɧɨɫɬɢ

ɦɟɧɹɟɬɦɟɧɹɟɬ

ɡɧɚɤɡɧɚɤ((ɨɬɨɬ

––2424ee ɞɨɞɨ

66××99e e ––

2424e e = +30= +30ee))

[A. [A. GrosbergGrosberg

and B. and B. ShklovskiiShklovskii]]

ɂɨɧɧɵɟɂɨɧɧɵɟ

ɮɪɚɤɬɚɥɵɮɪɚɤɬɚɥɵΓΓ

> 100 > 100 →→

ɤɪɢɫɬɚɥɥɤɪɢɫɬɚɥɥ

ȼɢɝɧɟɪɚȼɢɝɧɟɪɚ

= = ɮɪɚɤɬɚɥɶɧɵɣɮɪɚɤɬɚɥɶɧɵɣ

ɨɛɴɟɤɬɨɛɴɟɤɬ

ɐɟɩɶɐɟɩɶ

+ + ɦɚɤɪɨɢɨɧɦɚɤɪɨɢɨɧ

Sun

# run# run0

2

4

6

8

10

1 2 3 4 5

ΓΓ

ȾɥɹȾɥɹ

ɨɪɝɚɧɢɡɚɰɢɢɨɪɝɚɧɢɡɚɰɢɢ

ȾɇɄȾɇɄ

ɜɜ ɯɪɨɦɚɬɢɧɯɪɨɦɚɬɢɧ, , ɉɪɢɪɨɞɚɉɪɢɪɨɞɚ

ɢɫɩɨɥɶɡɭɟɬɢɫɩɨɥɶɡɭɟɬ

ɝɢɫɬɨɧɵɝɢɫɬɨɧɵ

–– ɩɪɨɬɟɢɧɵɩɪɨɬɟɢɧɵ

ɫɫ

ɨɝɪɨɦɧɵɦɨɝɪɨɦɧɵɦ ɩɨɥɨɠɢɬɟɥɶɧɵɦɩɨɥɨɠɢɬɟɥɶɧɵɦ

ɡɚɪɹɞɨɦɡɚɪɹɞɨɦ..

-1e

-1e

-1e-1e

-1e

+60e

ȾɇɄȾɇɄ: d = 2 : d = 2 ɧɦɧɦ, , ɡɚɪɹɞɡɚɪɹɞ

--ee

ɧɚɧɚ

1.7 1.7 ɧɦɧɦ

ɉɪɢɉɪɢ

ΓΓ

≥≥

10, 10, ɰɟɩɶɰɟɩɶ

ɮɨɪɦɢɪɭɟɬɮɨɪɦɢɪɭɟɬ ɜɢɬɤɢɜɢɬɤɢ

ɜɨɤɪɭɝɜɨɤɪɭɝ

ɦɚɤɪɨɢɨɧɚɦɚɤɪɨɢɨɧɚ. . ȼɢɬɤɢȼɢɬɤɢ ɭɤɥɚɞɵɜɚɸɬɫɹɭɤɥɚɞɵɜɚɸɬɫɹ

ɜɜ

ɫɨɥɟɧɨɢɞɫɨɥɟɧɨɢɞ..

ɐɟɩɶɐɟɩɶ

+ + ɦɚɤɪɨɢɨɧɵɦɚɤɪɨɢɨɧɵ: : ɋɚɦɨɫɛɨɪɤɚɋɚɦɨɫɛɨɪɤɚ

ɇɚɇɚ

ɛɨɥɶɲɢɯɛɨɥɶɲɢɯ

ɦɚɫɲɬɚɛɚɯɦɚɫɲɬɚɛɚɯ

ɨɞɧɨɢɦɟɧɧɨɨɞɧɨɢɦɟɧɧɨ

ɡɚɪɹɠɟɧɧɵɟɡɚɪɹɠɟɧɧɵɟ

ɫɮɟɪɵɫɮɟɪɵ ɨɬɬɚɥɤɢɜɚɸɬɫɹɨɬɬɚɥɤɢɜɚɸɬɫɹ

→→ ɨɠɟɪɟɥɶɟɨɠɟɪɟɥɶɟ

ɪɚɫɬɹɝɢɜɚɟɬɫɹɪɚɫɬɹɝɢɜɚɟɬɫɹ..

ɋɨɫɟɞɧɢɟɋɨɫɟɞɧɢɟ

ɜɢɬɤɢɜɢɬɤɢ

ɨɬɬɚɥɤɢɜɚɸɬɫɹɨɬɬɚɥɤɢɜɚɸɬɫɹ

ɢɢ ɮɨɪɦɢɪɭɸɬɮɨɪɦɢɪɭɸɬ

ɪɟɝɭɥɹɪɧɵɣɪɟɝɭɥɹɪɧɵɣ

ɫɨɥɟɧɨɢɞɫɨɥɟɧɨɢɞ..

ɑɬɨɑɬɨ

ɩɪɨɢɡɨɣɞɟɬɩɪɨɢɡɨɣɞɟɬ, , ɟɫɥɢɟɫɥɢ

ɞɥɢɧɚɞɥɢɧɚ

ɰɟɩɢɰɟɩɢ

ɜɟɥɢɤɚɜɟɥɢɤɚ? ? ɈɠɢɞɚɟɬɫɹɈɠɢɞɚɟɬɫɹ, , ɱɬɨɱɬɨ

ɱɚɫɬɶɱɚɫɬɶ

ɰɟɩɢɰɟɩɢ

ɛɭɞɟɬɛɭɞɟɬ ɮɨɪɦɢɪɨɜɚɬɶɮɨɪɦɢɪɨɜɚɬɶ

ɜɵɬɹɧɭɬɵɣɜɵɬɹɧɭɬɵɣ

ɯɜɨɫɬɯɜɨɫɬ..ȿɫɥɢȿɫɥɢ

ɰɟɩɶɰɟɩɶ

ɨɱɟɧɶɨɱɟɧɶ

ɞɥɢɧɧɚɹɞɥɢɧɧɚɹ

ɢɢ

ɩɪɢɫɭɬɫɬɜɭɟɬɩɪɢɫɭɬɫɬɜɭɟɬ ɦɧɨɝɨɦɧɨɝɨ

ɦɚɤɪɨɢɨɧɨɜɦɚɤɪɨɢɨɧɨɜ

→→ ɮɨɪɦɢɪɭɟɬɫɹɮɨɪɦɢɪɭɟɬɫɹ ɫɬɪɭɤɬɭɪɚɫɬɪɭɤɬɭɪɚ

ɬɢɩɚɬɢɩɚ

ɨɠɟɪɟɥɶɹɨɠɟɪɟɥɶɹ

((""beadsbeads--onon--stringstring"")): :

ɈɪɝɚɧɢɡɚɰɢɹɈɪɝɚɧɢɡɚɰɢɹ

ȾɇɄȾɇɄ

ɋɬɪɭɤɬɭɪɚɋɬɪɭɤɬɭɪɚ

ɬɢɩɚɬɢɩɚ

ɨɠɟɪɟɥɶɹɨɠɟɪɟɥɶɹ::ɄɚɠɞɚɹɄɚɠɞɚɹ

ɧɭɤɥɟɨɫɨɦɚɧɭɤɥɟɨɫɨɦɚ

ɫɨɞɟɪɠɢɬɫɨɞɟɪɠɢɬ ɨɞɢɧɨɞɢɧ

ɨɤɬɚɦɟɪɨɤɬɚɦɟɪ

ɫɫ

ɡɚɪɹɞɨɦɡɚɪɹɞɨɦ

+170+170ee..ɇɚɇɚ

ɨɤɬɚɦɟɪɨɤɬɚɦɟɪ

ɧɚɦɨɬɚɧɚɧɚɦɨɬɚɧɚ

ɰɟɩɶɰɟɩɶ

ȾɇɄȾɇɄ..

ɌɨɪɨɢɞɚɥɶɧɚɹɌɨɪɨɢɞɚɥɶɧɚɹ

ɨɪɝɚɧɢɡɚɰɢɹɨɪɝɚɧɢɡɚɰɢɹ

ȾɇɄȾɇɄ

Sun

ȽȽ

= 5= 5

ɄɨɧɞɟɧɫɚɰɢɹɄɨɧɞɟɧɫɚɰɢɹ

ɤɨɧɬɪɢɨɧɨɜɤɨɧɬɪɢɨɧɨɜ ɩɪɨɞɭɰɢɪɭɟɬɩɪɨɞɭɰɢɪɭɟɬ

ɩɪɢɬɹɠɟɧɢɟɩɪɢɬɹɠɟɧɢɟ..

ɂɨɧɵɂɨɧɵ

ɢɝɪɚɸɬɢɝɪɚɸɬ

ɪɨɥɶɪɨɥɶ ""ɢɨɧɧɨɝɨɢɨɧɧɨɝɨ

ɤɥɟɹɤɥɟɹ""

Electron micrograph of toroidal DNA,Electron micrograph of toroidal DNA,J.J.--L. L. SikoravSikorav