1 / 3

R.A. Fisher , Ann. Eugenics 7 , 353 ~ 19 37 Kolmogoroff, I.Petrovsky, and N. Piscounoff,

R.A. Fisher , Ann. Eugenics 7 , 353 ~ 19 37 Kolmogoroff, I.Petrovsky, and N. Piscounoff, Moscow Univ. Bull. Math. 1 , 1 - 19 37 . P.W. Anderson, Phys. Rev. 109 , 1492 ~ 19 58 . M. Doi , J. Phys. A 9 , 1465 ~ 19 76 ; H.K. Janssen , Z. Physik. 42 , 141 ~ 19 81 .

effie
Télécharger la présentation

R.A. Fisher , Ann. Eugenics 7 , 353 ~ 19 37 Kolmogoroff, I.Petrovsky, and N. Piscounoff,

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. R.A. Fisher, Ann. Eugenics 7, 353 ~1937 Kolmogoroff, I.Petrovsky, and N. Piscounoff, Moscow Univ. Bull. Math. 1, 1-1937. P.W. Anderson, Phys. Rev. 109, 1492 ~1958. M. Doi, J. Phys. A 9, 1465 ~1976; H.K. Janssen, Z. Physik. 42, 141 ~1981. P. Grassberger, Z. Phys. B: Condens. Mat 47, 465 ~1982 L. Peliti, J. Phys. ~France! 46, 1469 ~1985. M. Kardar, G. Parisi, and Y.-C. Zhang, PRL 56,889 ~1986. J.L. Cardy and U.C. Tauber, PRL 77, 4780 ~1996 D.C. Mattis, M.L. Glasser, Rev. Mod. Phys. 70, 979 ~1998

  2. Q- Discreteness / microscopic fluctuations were known to • influence the approach to the equilibrium state (e.g. Fisher waves; annihilation) • Make perturbative corrections the value of a phase transition point. • Doi, Janssen, Grassberger, Peliti, Zeldovich, Michailov, Cardy, Mattis and Glasser etc etc • SO What is the novelty? • A- Here the very character of the final state is totally changed (for all values)- Discreteness makes the difference between life and death. N.M. Shnerb, Y. Louzoun, E. Bettelheim, and S. Solomon, Proc. Natl. Acad. Sci. 97, 10322 ~2000.

  3. For Experts(usually they can ask, but in such a big room I have to anticipate their thoughts): Don’t look for cheap escapes: Once a continuous a(x,t) is accepted, the death sentence for la 0 – m< 0is unavoidable Q- slow a(x,t)  a0convergence: A- it is enough a(x,t) < m/ l to have decay at all x Q- non-linear features in PDE b. = (al- m)b + Db D bA-the equation is linear in b Q -instability of the homogenousb(x,t)= b(0,t) solution: A- The solution is stable for la 0 – m< 0

More Related