Numerical RG analysis of SOC in Low Temperature Creep S. I. Zaitsev IMT RAS, Chernogolovka, Russia

Introduction/Motivation –self-organization, SOC in nature –creep, low temperature limit –criticality –renorm. group analysis Physical prototypes of creep in 1D, 2D, 3D Toy models Numerical procedure Single-particle distrubution Analysis and many-particle distribution Discussion Conclusion Landslides Forest/wild fire Earthquakes Landscapes/Coastline River networks quasar noise traffic cardiac activity river flow fractals 1/f noise Many-particle distribution by numerical RG analysis of SOC in Low Temperature Creep S. I. Zaitsev IMT RAS, Chernogolovka, Russia,

Введение/Мотивация -SOC in Nature -два видимых проявления (фракталы, 1/f шум) -парадигма «кучи песка» - есть системы СОК -например, ползучесть -основная цель - поиск метода (подхода, языка) для описания (предсказания) СОК -по аналогии с термодинамикой RG -численное исследование НТ ползучести

X X Xi-1 Xi+1 Xi W(x->x) General framework – Markovian chain (process)

Dislocation gliding: schema

e-beam image Dislocation gliding: observation

Appel, Messerschmidt. Srew dislocation in MgO, 1min per frame Dislocation gliding: observation

Stress=0 Stress 0 set of states y x Dislocation gliding: physical model

fifi

-dislocations 1D -fluxes domain wall2D -grain boundary plastic deformation3D -earthquake Not only dislocation, but ….

Toy model Dislocation gliding:

Toy model

p(f) ~ (f-f c ) γ, γ=1.78 Single-particle distributions, --activated, p(f) --current, pt(f)

fifi 1/a 1.68

xixi Result Reconstruction of many-particle dist. from single-particle ones

Discussion 1.Gaussian for all SOC processes? No, Bak-Sneppen model 2.When Gaussian does appear as limiting distribution 3.Can be applied to critical phenomena

Conclusion: -Numerical RG allows to find limiting form of stationer solution -The stationer solution of the master equ. for creep is Gaussian X X Xi-1 Xi+1 Xi W(x->x)

Evolution model, Bak-Sneppen

Uniform distributionExponential distr. Evolution model, Bak-Sneppen

Conclusion 1.Gaussian as limiting many particle distribution in low temperature creep phenomena 2.Long distance correlation in space 3.Strange results for Bak-Sneppeen model

initial current before act. after act. activated p(f) ~ (f-f c ) γ, γ=1.78