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

In this paper we extend the results proposed in [36] and study the problem of active control in the context of the scalar Helmholtz equation. Given a source region Da and {v0, v1, ..., vn}, a set of solutions of the homogeneous scalar Helmholtz equation in n mutually disjoint ”control” regions {D0, D1, ..., Dn} of R2 or R3 respectively, the main objective of the paper is to characterize the necessary boundary data on ∂Da so that the solution to the corresponding exterior scalar Helmholtz problem will closely approximate vi in Di respectively for each i ∈ {0, .., n}. Building up on the previous ideas presented in [36] we show the existence of a class of solutions to the problem, provide numerical support of the results in 2D and 3D and discuss the existence of a minimal energy solution and its stability.

Active manipulation of fields modeled by the Helmholtz equation