Published in Proceedings. Mathematical, Physical, and Engineering Sciences
We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear Schrödinger equation as a model example, we show that the solution of the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbe...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
This study develops a modelling framework for simulating the spread of infectious diseases within real cities. Digital copies of Birmingham (UK) and Bogotá (Colombia) are generated, reproducing their urban environment, infrastructure and population. The digital inhabitants have the same statistical features of the real population. Their motion is a...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a cl...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
The next generations of wireless networks will work in frequency bands ranging from sub-6 GHz up to 100 GHz. Radio signal propagation differs here in several critical aspects from the behaviour in the microwave frequencies currently used. With wavelengths in the millimetre range (mmWave), both penetration loss and free-space path loss increase, whi...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
By modelling the evaporation and settling of droplets emitted during respiratory releases and using previous measurements of droplet size distributions and SARS-CoV-2 viral load, estimates of the evolution of the liquid mass and the number of viral copies suspended were performed as a function of time from the release. The settling times of a dropl...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
Wave fields obeying the two-dimensional Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing ideal boundary conditions. This is for example the case for the classical canonical problems of diffr...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
As of July 2020, COVID-19 caused by SARS-COV-2 is spreading worldwide, causing severe economic damage. While minimizing human contact is effective in managing outbreaks, it causes severe economic losses. Strategies to solve this dilemma by considering the interrelation between the spread of the virus and economic activities are urgently needed to m...
We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers-Kronig relations and sum rules for the linear susceptibilities obtained thro...
Published in Proceedings. Mathematical, Physical, and Engineering Sciences
We use synchrotron X-ray micro-tomography to investigate the displacement dynamics during three-phase—oil, water and gas—flow in a hydrophobic porous medium. We observe a distinct gas invasion pattern, where gas progresses through the pore space in the form of disconnected clusters mediated by double and multiple displacement events. Gas advances i...
