Solitons and Volume Preserving Flow

Solitons arise as solutions to non-linear partial differential equations. These equations are only analytically solvable in very few special cases. Other solutions must be found numerically. A useful technique for obtaining static solutions is gradient flow. Gradient flow evolution is in a direction which never increases energy, leading to solutions which are local minima. Here, a modified version of gradient flow referred to as volume preserving flow is introduced. This flow is constructed to evolve solutions towards local minima, while leaving a number of global quantities unaltered. Volume preserving gradient flow will be introduced and demonstrated in some simple models. Volume preserving flow will be used to investigate minimal surfaces in the context of double bubbles. Work will reproduce explicit results for double bubbles on the two-torus and construct a range of possible minimisers on the three-torus. Domain walls in a Wess-Zumino model with a triply degenerate vacuum will be used to represent the surfaces of the bubbles. Volume preserving flow will minimise the energy of the domain walls while maintaining the volumes of the space they contain. Global minima will represent minimal surfaces in the limit in which the domain wall thickness tends to zero. Numerical simulations of solitons in models which have conformal symmetry are problematic. Discretisation breaks the zero modes associated with changes of scale to negative modes. These lead to the collapse of solutions. Volume preserving flow provides a framework in which minimisation occurs orthogonally to these zero modes, maintaining a scale for the minimisation. Two such conformal models which permit Hopf solitons are the Nicole and AFZ models. They are comprised of the two components of the Skyrme-Faddeev model, taken to fractional powers to allow for solitons. Volume preserving flow will be used to find static solutions for a range of Hopf charges for each model. Comparisons will be made with the Skyrme-Faddeev model and general features of Hopf solitons will be discussed. A one parameter family of conformal Skyrme-Faddeev models will also be introduced. These models will be the set of linear combinations of the Nicole and AFZ models where the coefficients sum to one. Energy and topology transitions through this set of models will be investigated

Numerical characterisation of stably stratified flows past spheres

A numerical study of stably stratified flows past spheres at moderate Reynolds numbers is presented. The resolved flows can adequately describe a wide class of geophysical, environmental, and engineering flows characterised by the density stratification of the terrestrial atmosphere and oceanic thermocline. The range of physical phenomena developing when stratified flows impact single and multiple spheres constitute a convenient benchmark for complex geometry applications, e.g. mountains, islands, wind turbines, and buildings. Solutions of Navier-Stokes equations, in the incompressible Boussinesq limit, are obtained by applying a semi-implicit finite volume (FV) non-oscillatory forward-in-time (NFT) integration scheme enhanced by MPI parallelization. The developed model is applied for a systematic investigation of stratified flow patterns arising for a range of Froude numbers Fr ∈ [0.1,∞] at Reynolds numbers Re = 200 and Re = 300, for which the neutrally stratified flows induces distinctly different near-wake features

Hopf solitons in the Nicole model

The Nicole model is a conformal field theory in a three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to construct soliton solutions numerically for all Hopf charges from 1 to 8. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than 2 and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme–Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories

A class of finite-volume models for atmospheric flows across scales

The paper examines recent advancements in the class of Nonoscillatory Forward-in-Time (NFT) schemes that exploit the implicit LES (ILES) properties of Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The reported developments address both global and limited area models spanning a range of atmospheric flows, from the hydrostatic regime at planetary scale, down to mesoscale and microscale where flows are inherently nonhydrostatic. All models operate on fully unstructured (and hybrid) meshes and utilize a median dual mesh finite volume discretisation. High performance computations for global flows employ a bespoke hybrid MPI-OpenMP approach and utilise the ATLAS library. Simulations across scales—from a global baroclinic instability epitomising evolution of weather systems down to stratified orographic flows rich in turbulent phenomena due to gravity-wave breaking in dispersive media, verify the computational advancements and demonstrate the efficacy of ILES both in regularizing large scale flows at the scale of the mesh resolution and taking a role of a subgrid-scale turbulence model in simulation of turbulent flows in the LES regime

A point particle model of lightly bound skyrmions

A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number 1≤B≤8 obtained by numerical simulation of the full field theory. For 9≤B≤23, a large number of static solutions of the point particle model are found, all closely resembling size B subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised

Skyrmions with low binding energies

Nuclear binding energies are investigated in two variants of the Skyrme model: the first replaces the usual Skyrme term with a term that is sixth order in derivatives, and the second includes a potential that is quartic in the pion fields. Solitons in the first model are shown to deviate significantly from ansätze previously assumed in the literature. The binding energies obtained in both models are lower than those obtained from the standard Skyrme model, and those obtained in the second model are close to the experimental values

The mechanisms and processes of connection: developing a causal chain model capturing impacts of receiving recorded mental health recovery narratives.

BACKGROUND: Mental health recovery narratives are a core component of recovery-oriented interventions such as peer support and anti-stigma campaigns. A substantial number of recorded recovery narratives are now publicly available online in different modalities and in published books. Whilst the benefits of telling one's story have been investigated, much less is known about how recorded narratives of differing modalities impact on recipients. A previous qualitative study identified connection to the narrator and/or to events in the narrative to be a core mechanism of change. The factors that influence how individuals connect with a recorded narrative are unknown. The aim of the current study was to characterise the immediate effects of receiving recovery narratives presented in a range of modalities (text, video and audio), by establishing the mechanisms of connection and the processes by which connection leads to outcomes. METHOD: A study involving 40 mental health service users in England was conducted. Participants were presented with up to 10 randomly-selected recovery narratives and were interviewed on the immediate impact of each narrative. Thematic analysis was used to identify the mechanisms of connection and how connection leads to outcome. RESULTS: Receiving a recovery narrative led participants to reflect upon their own experiences or those of others, which then led to connection through three mechanisms: comparing oneself with the narrative and narrator; learning about other's experiences; and experiencing empathy. These mechanisms led to outcomes through three processes: the identification of change (through attending to narrative structure); the interpretation of change (through attending to narrative content); and the internalisation of interpretations. CONCLUSIONS: This is the first study to identify mechanisms and processes of connection with recorded recovery narratives. The empirically-based causal chain model developed in this study describes the immediate effects on recipients. This model can inform selection of narratives for use in interventions, and be used to support peer support workers in recounting their own recovery narratives in ways which are maximally beneficial to others