کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7155553 | 1462623 | 2015 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Early-warning signs for pattern-formation in stochastic partial differential equations
ترجمه فارسی عنوان
نشانه های زودرس برای شکل گیری الگوی در معادلات دیفرانسیل مجدد تصادفی
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کلمات کلیدی
Critical transition - انتقال انتقادیCovariance operator - اپراتور کوواریانسBifurcation - تقسیم بندیOrnstein–Uhlenbeck process - روند Ornstein-UhlenbeckStochastic partial differential equation - معادله دیفرانسیل تقسیم بندی تصادفیScaling law - مقیاس قانونTipping point - نقطه اوجGinzburg–Landau - گینزبورگ-لاندو
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی مکانیک
چکیده انگلیسی
There have been significant recent advances in our understanding of the potential use and limitations of early-warning signs for predicting drastic changes, so called critical transitions or tipping points, in dynamical systems. A focus of mathematical modeling and analysis has been on stochastic ordinary differential equations, where generic statistical early-warning signs can be identified near bifurcation-induced tipping points. In this paper, we outline some basic steps to extend this theory to stochastic partial differential equations with a focus on analytically characterizing basic scaling laws for linear SPDEs and comparing the results to numerical simulations of fully nonlinear problems. In particular, we study stochastic versions of the Swift-Hohenberg and Ginzburg-Landau equations. We derive a scaling law of the covariance operator in a regime where linearization is expected to be a good approximation for the local fluctuations around deterministic steady states. We compare these results to direct numerical simulation, and study the influence of noise level, noise color, distance to bifurcation and domain size on early-warning signs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 22, Issues 1â3, May 2015, Pages 55-69
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 22, Issues 1â3, May 2015, Pages 55-69
نویسندگان
Karna Gowda, Christian Kuehn,