Asymptotic scaling in a model class of anomalous reaction-diffusion equations

Anomalous scaling for 3d Cahn-Hilliard fronts

We prove the stability of the one dimensional kink solution of the Cahn-Hilliard equation under d-dimensional perturbations for d > 2. We also establish a novel scaling behavior of the large time asymptotics of the solution. The leading asymptotics of the solution is characterized by a length scale proportional to the cubic root of t instead of the usual square root of t scaling typical to parabolic problems.

Anomalous scaling behavior in Takens-Bogdanov bifurcations

A general algorithm is presented for estimating the nonlinear instability threshold, $σ_c$, for subcritical transitions in systems where the linearized dynamics is significantly non-normal (i.e. subcritical bifurcations of {\em Takens-Bogdanov} type). The $N$-dimensional degenerate node is presented as an example. The predictions are then compared to numerical studies with excellent agreement.

From continuous-time random walks to controlled-diffusion reaction

Daily, are reported systems in nature that present anomalous diffusion phenomena due to irregularities of medium, traps or reactions process. In this scenario, the diffusion with traps or localised--reactions emerge through various investigations that include numerical, analytical and experimental techniques. In this work, we construct a model which involves a coupling of two diffusion equations to approach the random walkers in a medium with localised reaction point (or controlled diffusion). We present the exact analytical solutions to the model. In the following, we obtain the survival prob…

异质弹性线的异常标度：从样本到样本波动的新图景

Anomalous scaling of heterogeneous elastic lines: a new picture from sample to sample fluctuations

研究异质弹性线在不同μ值下的标度行为，揭示异常标度现象及其与样本波动的关系