arXiv subjects

Simon Horsley

Publications and source records attributed to Simon Horsley.

5 recordsLinked to original sources

arXiv2025

Plane-Wave Decomposition and Randomised Training; a Novel Path to Generalised PINNs for SHM

In this paper, we introduce a formulation of Physics-Informed Neural Networks (PINNs), based on learning the form of the Fourier decomposition, and a training methodology based on a spread of randomly chosen boundary conditions. By training in this way we produce a PINN that generalises; after training it can be used to correctly predict the solution for an arbitrary set of boundary conditions and interpolate this solution between the samples that spanned the training domain. We demonstrate for a toy system of two coupled oscillators that this gives the PINN formulation genuine predictive capability owing to an effective reduction of the training to evaluation times ratio due to this decoupling of the solution from specific boundary conditions.

physics.comp-ph↗

arXiv2024

SpiDy.jl: open-source Julia package for the study of non-Markovian stochastic dynamics

SpiDy.jl solves the non-Markovian stochastic dynamics of interacting classical spin vectors and harmonic oscillator networks in contact with a dissipative environment. The methods implemented allow the user to include arbitrary memory effects and colored quantum noise spectra. In this way, SpiDy.jl provides key tools for the simulation of classical and quantum open systems including non-Markovian effects and arbitrarily strong coupling to the environment. Among the wide range of applications, some examples range from atomistic spin dynamics to ultrafast magnetism and the study of anisotropic materials. We provide the user with Julia notebooks to guide them through the various mathematical methods and help them quickly set up complex simulations.

physics.comp-ph↗

arXiv2018

Designing scattering-free isotropic index profiles using phase-amplitude equations

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this phase, we designed two-dimensional graded-index media which do not scatter light. We give two illustrative examples, the first of which is a periodic grating for which diffraction is completely suppressed at a single frequency at normal incidence to the periodicity. The second example is a medium which behaves as a 'beam shifter' at a single frequency; acting to laterally shift a plane wave, or sufficiently wide beam, without reflection.

physics.optics↗

arXiv2017

Zero reflection and transmission in graded index media

Graded index media whose electric susceptibility satisfies the spatial Kramers-Kronig relations are known to be one-way reflectionless to electromagnetic radiation, for all angles of incidence. We demonstrate how a family of these media, in addition to being reflectionless, also have negligible transmission. To this end, we discuss how the transmission coefficient for the propagation of waves through a medium whose permittivity is built from poles in the complex position plane, with residues that sum to infinity, can be controlled by tuning the positions and residues of the poles. In particular, we have shown how to make the transmission arbitrarily small, and hence maximise the absorption of the wave's energy. This behaviour is confirmed by numerical simulations.

physics.optics↗

arXiv2017

Perfect Transmission through Disordered Media

The transmission of a wave through a randomly chosen `pile of plates' typically decreases exponentially with the number of plates, a phenomenon closely related to Anderson localisation. In apparent contradiction we construct disordered planar permittivity profiles which are complex-valued (i.e. have reactive and dissipative properties) that appear to vary randomly with position, yet are one-way reflectionless for all angles of incidence and exhibit a transmission coefficient of unity. We contrast these complex-valued 'random' planar permittivity profiles with a family of real-valued, two-way reflectionless and perfectly transmitting disordered permittivity profiles that function only for a single angle of incidence and frequency.

physics.class-ph↗