Corrigendum to: The Horton–Rogers–Lapwood problem for an inclined porous layer with permeable boundaries
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications t...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
Many problems in fluid mechanics and acoustics can be modelled by Helmholtz scattering off poro-elastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function expansions, for Helmholtz scattering off multiple variable poro-elastic plates in two dimensions. Such boundary conditions, namely the varying physical ...
Maxwell tipping points: the hidden mechanics of an axially compressed cylindrical shell
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
Numerical results for the axially compressed cylindrical shell demonstrate the post-buckling response snaking in both the applied load and corresponding end-shortening. Fluctuations in load, associated with progressive axial formation of circumferential rings of dimples, are well known. Snaking in end-shortening, describing the evolution from a sin...
How rare are power-law networks really?
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
The putative scale-free nature of real-world networks has generated a lot of interest in the past 20 years: if networks from many different fields share a common structure, then perhaps this suggests some underlying ‘network law’. Testing the degree distribution of networks for power-law tails has been a topic of considerable discussion. Ad hoc sta...
Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applic...
Core–periphery structure in directed networks
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
Empirical networks often exhibit different meso-scale structures, such as community and core–periphery structures. Core–periphery structure typically consists of a well-connected core and a periphery that is well connected to the core but sparsely connected internally. Most core–periphery studies focus on undirected networks. We propose a generaliz...
Atmospheric composition of exoplanets based on the thermal escape of gases and implications for habitability
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
The detection of habitable exoplanets is an exciting scientific and technical challenge. Owing to the current and most likely long-lasting impossibility of performing in situ exploration of exoplanets, their study and hypotheses regarding their capability to host life will be based on the restricted low-resolution spatial and spectral information o...
Preface to a special feature dedicated to the memory of Prof. Peter Chadwick FRS
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
Structure and function in human and primate social networks: implications for diffusion, network stability and health
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
The human social world is orders of magnitude smaller than our highly urbanized world might lead us to suppose. In addition, human social networks have a very distinct fractal structure similar to that observed in other primates. In part, this reflects a cognitive constraint, and in part a time constraint, on the capacity for interaction. Structure...
A fluid mechanic’s analysis of the teacup singularity
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with the swirl. The simulations reproduce and corroborate aspects of prior studies reporting strong evidence for a finite-time singularity. ...
