Repelling Random Walkers in a Diffusion-Coalescence System

Dynamics of a self-repelling random walker

This paper has been withdrawn by the authors.

Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials

We investigate the coalescence of two DNA-bubbles initially located at weak segments and separated by a more stable barrier region in a designed construct of double-stranded DNA. The characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behaviour, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. The results are obtained by mapping the bubble dynamics on the problem of two vi…

Phase Transitions and superuniversality in the dynamics of a self-driven particle

We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior. For self-repelling behavior, we find a phase transition in the dynamics: when the coupling between the field and the walker exceeds a critical value, the particle's behavior changes from renormalized diffusion to one characterized by a diverging diffusion coefficient. The dynamical behavior for all cases is surprisingly independent of dimension and of the noi…

Bubble merging in breathing DNA as a vicious walker problem in opposite potentials

We investigate the coalescence of two DNA-bubbles initially located at weak domains and separated by a more stable barrier region in a designed construct of double-stranded DNA. In a continuum Fokker-Planck approach, the characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behavior, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. In the calculations, we map the bubble dyna…

Passive Random Walkers and River-like Networks on Growing Surfaces

Passive random walker dynamics is introduced on a growing surface. The walker is designed to drift upward or downward and then follow specific topological features, such as hill tops or valley bottoms, of the fluctuating surface. The passive random walker can thus be used to directly explore scaling properties of otherwise somewhat hidden topological features. For example, the walker allows us to directly measure the dynamical exponent of the underlying growth dynamics. We use the Kardar-Parisi-Zhang(KPZ) type surface growth as an example. The word lines of a set of merging passive walkers sho…

一维自相互作用随机游走的精确传播子

Exact propagators of one-dimensional self-interacting random walks

本文研究一维自相互作用随机游走（SIRWs），为一次增强随机游走和多项式自排斥游走两类重要模型提供了精确显式的传播子表达式，从而获取了扩散系数等关键观测量，并揭示了一种驱使游走者远离起始点的内在非马尔可夫机制。