SELF-ORGANIZED CRITICALITY VIA STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

被引：0
作者：
Barbu, Viorel [1 ]
Blanchard, Philippe
Da Prato, Giuseppe
Roeckner, Michael
机构：
[1] Octav Mayer Inst Math, Iasi, Romania
来源：
POTENTIAL THEORY AND STOCHASTICS IN ALBAC: AUREL CORNEA MEMORIAL VOLUME, CONFERENCE PROCEEDINGS | 2009年
关键词：
Stochastic porous media equations; self-organized criticality; finite-time extinction; SYSTEMS; CONSERVATION; DIFFUSION; SANDPILES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Models of self-organized criticality which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models) are analyzed. Existence and uniqueness of nonnegative strong solutions are proved. Previously numerically predicted transition to the critical state in 1-D is confirmed by a rigorous proof that this indeed happens in finite time with high probability.
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页码：11 / +
页数：3
相关论文
共 22 条
  • [1] SELF-ORGANIZED CRITICALITY
    BAK, P
    TANG, C
    WIESENFELD, K
    [J]. PHYSICAL REVIEW A, 1988, 38 (01): : 364 - 374
  • [2] SELF-ORGANIZED CRITICALITY - AN EXPLANATION OF 1/F NOISE
    BAK, P
    TANG, C
    WIESENFELD, K
    [J]. PHYSICAL REVIEW LETTERS, 1987, 59 (04) : 381 - 384
  • [3] SELF-ORGANIZATION AND ANOMALOUS DIFFUSION
    BANTAY, P
    JANOSI, IM
    [J]. PHYSICA A, 1992, 185 (1-4): : 11 - 18
  • [4] Barbu V, 1976, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste Romania
  • [5] Barbu V, 2008, INDIANA U MATH J, V57, P187
  • [6] Stochastic Porous Media Equations and Self-Organized Criticality
    Barbu, Viorel
    Da Prato, Giuseppe
    Roeckner, Michael
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 285 (03) : 901 - 923
  • [7] What can one learn about self-organized criticality from dynamical systems theory?
    Blanchard, P
    Cessac, B
    Krüger, T
    [J]. JOURNAL OF STATISTICAL PHYSICS, 2000, 98 (1-2) : 375 - 404
  • [8] LOCAL RIGIDITY AND SELF-ORGANIZED CRITICALITY FOR AVALANCHES
    CAFIERO, R
    LORETO, V
    PIETRONERO, L
    VESPIGNANI, A
    ZAPPERI, S
    [J]. EUROPHYSICS LETTERS, 1995, 29 (02): : 111 - 116
  • [9] SELF-ORGANIZED CRITICALITY AND SINGULAR DIFFUSION
    CARLSON, JM
    CHAYES, JT
    GRANNAN, ER
    SWINDLE, GH
    [J]. PHYSICAL REVIEW LETTERS, 1990, 65 (20) : 2547 - 2550
  • [10] SELF-ORGANIZED CRITICALITY IN SANDPILES - NATURE OF THE CRITICAL PHENOMENON
    CARLSON, JM
    CHAYES, JT
    GRANNAN, ER
    SWINDLE, GH
    [J]. PHYSICAL REVIEW A, 1990, 42 (04): : 2467 - 2470
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