Schroedinger equation on a generic radial grid

In this note, we discuss the choice of radial grid in the numerical resolution of the Schroedinger equation. We detail the transformation of the equation resulting from a change of variable and function for a generic radial grid, using either the explicit or implicit form of the relation describing the change of variable, and apply it to the $a r + b \ln(r)$ log-linear mesh. It is shown that, in the former case, the first three derivatives of the Lambert $W$ function are required. This complication becomes unnecessary if we adopt the implicit relation instead.Comment: submitted to High Energy Density Phy

Towards the Fully-coupled Numerical Modelling of Floating Wind Turbines

AbstractThe aim of this study is to model the interactions between fluids and solids using fully nonlinear models. Non- linearity is important in the context of floating wind turbines, for example, to model breaking waves impacting on the structure and the effect of the solid's elasticity. The fluid- and solid-dynamics equations are solved using two unstructured finite-element models, which are coupled at every time step. Importantly, the coupling ensures that the action-reaction principle is satisfied at a discrete level, independently of the order of representation of the discrete fields. To the authors’ knowledge, the present algorithm is novel in that it can simultaneously handle: (i) non- matching fluid and solid meshes, (ii) different polynomial orders of the basis functions on each mesh, and (iii) different fluid and solid time steps. First, results are shown for the flow past a fixed actuator-disk immersed in a uniform flow and representing a wind turbine. The present numerical results for the velocity deficit induced by the disk are shown to be in good agreement with the semi-analytical solution, for three values of thrust coefficients. The presence of a non-zero fluid viscosity in the numerical simulation affects wake recovery and fluid entrainment around the disk. Second, the dynamic response of a cylindrical pile is computed when placed at an interface between air and water. The results qualitatively demonstrate that the present models are applicable to the modelling of multiple fluids interacting with a floating solid. This work provides a first-step towards the fully coupled simulation of offshore wind turbines supported by a floating spar

GAN for time series prediction, data assimilation and uncertainty quantification

We propose a new method in which a generative adversarial network (GAN) is used to quantify the uncertainty of forward simulations in the presence of observed data. Previously, a method has been developed which enables GANs to make time series predictions and data assimilation by training a GAN with unconditional simulations of a high-fidelity numerical model. After training, the GAN can be used to predict the evolution of the spatial distribution of the simulation states and observed data is assimilated. In this paper, we describe the process required in order to quantify uncertainty, during which no additional simulations of the high-fidelity numerical model are required. These methods take advantage of the adjoint-like capabilities of generative models and the ability to simulate forwards and backwards in time. Set within a reduced-order model framework for efficiency, we apply these methods to a compartmental model in epidemiology to predict the spread of COVID-19 in an idealised town. The results show that the proposed method can efficiently quantify uncertainty in the presence of measurements using only unconditional simulations of the high-fidelity numerical model.Comment: arXiv admin note: text overlap with arXiv:2105.0772

Social communication between virtual characters and children with autism

Children with ASD have difficulty with social communication, particularly joint attention. Interaction in a virtual environment (VE) may be a means for both understanding these difficulties and addressing them. It is first necessary to discover how this population interacts with virtual characters, and whether they can follow joint attention cues in a VE. This paper describes a study in which 32 children with ASD used the ECHOES VE to assist a virtual character in selecting objects by following the character’s gaze and/or pointing. Both accuracy and reaction time data suggest that children were able to successfully complete the task, and qualitative data further suggests that most children perceived the character as an intentional being with relevant, mutually directed behaviour

Numerical Modelling of Melt Behaviour in the Lower Vessel Head of a Nuclear Reactor

Acknowledgements The authors would like to thank the EPSRC MEMPHIS multi-phase programme grant, the EPSRC Computational modelling for advanced nuclear power plants project and the EU FP7 projects THINS and GoFastR for helping to fund this work.Peer reviewedPublisher PD

An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high-fidelity model results. Reduced-order models based on an autoencoder and a novel hybrid SVD-autoencoder are developed. These methods are compared with the standard POD-Galerkin approach and are applied to two test cases taken from the field of nuclear reactor physics.Comment: 35 pages, 33 figure

Numerical Modelling of Debris Bed Water Quenching

Acknowledgements The authors would like to thank the EPSRC MEMPHIS multi-phase programme grant, the EPSRC Computational modelling for advanced nuclear power plants project, the EU FP7 projects THINS and GoFastR and ExxonMobil for helping to fund this work.Peer reviewedPublisher PD