STOCHASTIC LANDAU EQUATION WITH TIME-DEPENDENT DRIFT

被引:30
作者
SWIFT, JB
HOHENBERG, PC
AHLERS, G
机构
[1] UNIV TEXAS, CTR NONLINEAR DYNAM, AUSTIN, TX 78712 USA
[2] AT&T BELL LABS, MURRAY HILL, NJ 07974 USA
[3] UNIV CALIF SANTA BARBARA, DEPT PHYS, SANTA BARBARA, CA 93106 USA
[4] UNIV CALIF SANTA BARBARA, CTR NONLINEAR SCI, SANTA BARBARA, CA 93106 USA
来源
PHYSICAL REVIEW A | 1991年 / 43卷 / 12期
关键词
D O I
10.1103/PhysRevA.43.6572
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
The stochastic differential equation tau-0-partial-t A = epsilon(t) A - g3 A3 + f(t)BAR, where f(t)Bar is Gaussian white noise, is studied for arbitrary time dependence of epsilon(t). In particular, cases are considered where epsilon(t) goes through the bifurcation of the deterministic system, which occurs at epsilon = 0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P (A,t). The results compare favorably with a numerical simulation of the stochatic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of epsilon(t). The procedure can be generalized to an arbitrary deterministic part partial-t A = D (A,t) + fBAR(t), but the deterministic equation may then have to be solved numerically.
引用
收藏
页码:6572 / 6580
页数:9
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共 18 条
  • [1] THE AMPLITUDE EQUATION NEAR THE CONVECTIVE THRESHOLD - APPLICATION TO TIME-DEPENDENT HEATING EXPERIMENTS
    AHLERS, G
    CROSS, MC
    HOHENBERG, PC
    SAFRAN, S
    [J]. JOURNAL OF FLUID MECHANICS, 1981, 110 (SEP) : 297 - 334
  • [2] INFLUENCE OF WHITE-NOISE ON DELAYED BIFURCATIONS
    BROGGI, G
    COLOMBO, A
    LUGIATO, LA
    MANDEL, P
    [J]. PHYSICAL REVIEW A, 1986, 33 (05): : 3635 - 3637
  • [3] PASSAGE TIMES FOR THE DECAY OF A TIME-DEPENDENT UNSTABLE STATE
    CACERES, MO
    BECKER, A
    [J]. PHYSICAL REVIEW A, 1990, 42 (02): : 696 - 702
  • [4] CACERES MO, IN PRESS PHYS REV A
  • [5] ON FLUCTUATIONS AND RELAXATION IN SYSTEMS DESCRIBED BY A ONE-DIMENSIONAL FOKKER-PLANCK EQUATION WITH A TIME-DEPENDENT POTENTIAL
    CAROLI, B
    CAROLI, C
    ROULET, B
    STJAMES, D
    [J]. PHYSICA A, 1981, 108 (01): : 233 - 256
  • [6] TRANSIENT STATISTICS IN A CO2-LASER WITH A SLOWLY SWEPT PUMP
    CIOFINI, M
    MEUCCI, R
    ARECCHI, FT
    [J]. PHYSICAL REVIEW A, 1990, 42 (01): : 482 - 486
  • [7] FLUCTUATIONS AND LIMIT OF METASTABILITY IN A PERIODICALLY DRIVEN UNSTABLE SYSTEM
    DEPASQUALE, F
    RACZ, Z
    SANMIGUEL, M
    TARTAGLIA, P
    [J]. PHYSICAL REVIEW B, 1984, 30 (09): : 5228 - 5238
  • [8] SWEEPING THROUGH THE CRITICAL REGION
    GROSSMANN, S
    MIKHAILOV, AS
    [J]. ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1990, 78 (01): : 1 - 10
  • [9] NUMERICAL-INTEGRATION OF STOCHASTIC DIFFERENTIAL-EQUATIONS
    HELFAND, E
    [J]. BELL SYSTEM TECHNICAL JOURNAL, 1979, 58 (10): : 2289 - 2299
  • [10] POSTPONED BIFURCATIONS OF A SWEPT PARAMETER RING LASER MODEL WITH ADDITIVE WHITE-NOISE
    MANNELLA, R
    MCCLINTOCK, PVE
    MOSS, F
    [J]. PHYSICS LETTERS A, 1987, 120 (01) : 11 - 14