Pendry, J Galiffi, E Huidobro, P

Time dependent systems do not in general conserve energy invalidating much of the theory developed for static systems and turning our intuition on its head. This is particularly acute in luminal space time crystals where the structure moves at or close to the velocity of light. Conventional Bloch wave theory no longer applies, energy grows exponent...

Crowdy, D

A class of exact solutions is presented describing the time evolution of insoluble surfactant to a stagnant-cap equilibrium on the surface of deep water in the Stokes flow regime at zero capillary number and infinite surface P´eclet number. This is done by demonstrating, in a two-dimensional model setting, the relevance of the forced complex Burger...

Sassano, M Mylvaganam, T Astolfi, A

We consider optimal control problems for continuous-time systems with time-dependent dynamics, in which the time-dependence arises from the presence of a known exogenous signal. The problem has been elegantly solved in the case of linear input-affine systems, for which it has been shown that the solution has a remarkable structure: it is given by t...

Hamzehloo, A Lusher, D Laizet, S Sandham, N

Counter-flow configurations, whereby two streams of fluid are brought together from opposite directions, are highly efficient mixers due to the high turbulence intensities that can be maintained. In this paper, a simplified version of the problem is introduced that is amenable to direct numerical simulation. The resulting turbulent flow problem is ...

Fagerholm, ED Foulkes, W Friston, KJ Moran, RJ Leech, R

The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion ar...

Gibbon, JD

It is shown how the variable density model that governs the Rayleigh-Taylor instability for the miscible mixing of two incompressible fluids can be transformed into a diffusive version of the inhomogeneous, incompressible Navier-Stokes equations forced by gradients of the composition density ρ of the mixing layer. This demonstrates how buoyancy-dri...

Hager, P Neumann, E

We consider a family of fractional Brownian fields {BH}H∈(0,1) on R d , where H denotes their Hurst parameter. We first define a rich class of normalizing kernels ψ and we rescale the normalised field by the square-root of the gamma function Γ(H), such that the covariance of XH(x) = Γ(H) 1 2 B H(x) − Z Rd B H(u)ψ(u, x)du , converges to the covarian...

Crowdy, D Hauge, J

A new transform pair representing solutions to the complex Helmholtz equation in a convex twodimensional polygon is derived using the theory of Bessel’s functions and Green’s second identity. The derivation is a direct extension of that given by Crowdy [IMA J. Appl. Math, 80, (2015)] for “FourierMellin transform” pairs associated with Laplace’s equ...

Neumann, E Schied, A

We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever-increasing risky position in foreign reserves. We describe this situation mathematically by means of tw...

Wang, T Zheng, H

In this paper we introduce a general framework for time-inconsistent optimal control problems. We characterize the closed-loop equilibrium strategy in both the integral and point wise forms with the newly developed methodology. We recover and improve the results of some well-known models, including the classical optimal control, Bjork et al. (2017)...