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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We analyze the unforced and deterministically forced Burgers equation in theframework of the (diffusive) interpolating dynamics that solves the so-calledSchr\"{o}dinger boundary data problem for the random matter transport. Thisentails an exploration of the consistency conditions that allow to interpretdispersion of passive contaminants in the Burgers flow as a Markovian diffusionprocess. In general, the usage of a continuity equation $\partial_t\rho=-\nabla (\vec{v}\rho)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for theBurgers field and $\rho $ is the density of transported matter, is at variancewith the explicit diffusion scenario. Under these circumstances, we give acomplete characterisation of the diffusive transport that is governed byBurgers velocity fields. The result extends both to the approximate descriptionof the transport driven by an incompressible fluid and to motions in aninfinitely compressible medium. Also, in conjunction with the Born statisticalpostulate in quantum theory, it pertains to the probabilistic (diffusive)counterpart of the Schr\"{o}dinger picture quantum dynamics.Comment: Latex fil

Burgers' flows as Markovian diffusion processes