Stable localised roll structures have been observed in many physical problems and model equations, notably in the 1D Swift–Hohenberg equation. Reflection-symmetric localised rolls are often found to lie on two “snaking” solution branches, so that the spatial width of the localised rolls increases when moving along each branch. Recent numerical results by Burke and Knobloch indicate that the two...

Design of optimal distributed controllers with a priori assigned localisation constraints is a difficult problem. Alternatively, one can ask the following question: given a localised distributed exponentially stabilising controller, is it inversely optimal with respect to some cost functional? We study this problem for linear spatially invariant systems and establish a frequency domain criterio...

Abstract Controlled breakdown has recently emerged as a highly accessible technique to fabricate solid-state nanopores. However, in its most common form, controlled creates single nanopore at an arbitrary location the membrane. Here, we introduce new strategy whereby is performed by applying electric field between on-chip electrode and electrolyte solution contact with opposite side of We demon...

Differences between exchange methods in exchange-only Kohn-Sham theory are highlighted by calculations of diatomic molecule total energies, uncoupled isotropic NMR shieldings, and HOMO-LUMO eigenvalue differences. Optimised effective potential (OEP) and Wu-Yang (WY) results are very similar. Localised Hartree-Fock (LHF) and Krieger-Li-Iafrate (KLI) results are close to one another, but are diff...

AIMS Pigmented villonodular synovitis (PVNS) is a rare, locally aggressive and potentially recurrent synovial disease. We present the largest single-centre experience of knee PVNS. Our aim was to evaluate our tertiary hospital's experience in the management of knee PVNS. PATIENTS AND METHODS Retrospective data collection of consecutive cases of knee PVNS from 2002 to 2015. RESULTS In total,...