English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the dynamics of particles undergoing the reaction $A+A \to\emptyset$ in one dimension with a dynamic bias. Here the particles movetowards their nearest neighbour with probability $0.5+\epsilon$ where $-0.5\leq \epsilon < 0$. $\epsilon_c = -0.5$ is the deterministic limit where thenearest neighbour interaction is strictly repulsive. We show that the negativebias changes drastically the behaviour of the fraction of surviving particles$\rho(t)$ and persistence probability $P(t)$ with time $t$. $\rho(t)$ decays as$a/ (\log t)^b$ where $b$ increases with $\epsilon - \epsilon_c$. $P(t)$ showsa stretched exponential decay with non-universal decay parameters. Theprobability $\Pi(x,t)$ that a tagged particle is at position $x$ from itsorigin is found to be Gaussian for all $\epsilon<0$; the associated scalingvariable is $x/t^\alpha$ where $\alpha$ approaches the known limiting value$1/4$ as $\epsilon \to \epsilon_c$, in a power law manner. Some additionalfeatures of the dynamics by tagging the particles are also studied. The resultsare compared to the case of positive bias, a well studied problem.

$A+ A \to \emptyset$ reaction for particles with a dynamic bias to move away from their nearest neighbour in one dimension