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

The diffusion-controlled reaction $kA\rightarrow\emptyset$ is known to bestrongly dependent on fluctuations in dimensions $d\le d_c=2/(k-1)$. We developa field theoretic renormalization group approach to this system which allowsexplicit calculation of the observables as expansions in $\epsilon^{1/(k-1)}$,where $\epsilon=d_c-d$. For the density it is found that, asymptotically,$n\sim A_k t^{-d/2}$. The decay exponent is exact to all orders in $\epsilon$,and the amplitude $A_k$ is universal, and is calculated to second order in$\epsilon^{1/(k-1)}$ for $k=2,3$. The correlation function is calculated tofirst order, along with a long wavelength expansion for the second order term.For $d=d_c$ we find $n \sim A_k (\ln t/t)^{1/(k-1)}$ with an exact expressionfor $A_k$. The formalism can be immediately generalized to the reaction$kA\rightarrow\ell A$, $\ell < k$, with the consequence that the densityexponent is the same, but the amplitude is modified.Comment: 24 pages (harvmac), 8 figures appended, OUTP-93-39

Renormalization group calculation for the reaction kA to OE