Skip to main content

Research Repository

Advanced Search

Outputs (17)

Computations of the slice genus of virtual knots (2018)
Journal Article
Rushworth, W. (2019). Computations of the slice genus of virtual knots. Topology and its Applications, 253, 57-84. https://doi.org/10.1016/j.topol.2018.11.028

A virtual knot is an equivalence class of embeddings of $ S^1 $ into thickened (closed oriented) surfaces, up to self-diffeomorphism of the surface and certain handle stabilisations. The slice genus of a virtual knot is defined diagrammatically, in d... Read More about Computations of the slice genus of virtual knots.

The swimming of a deforming helix (2018)
Journal Article
Koens, L., Zhang, H., Moeller, M., Mourran, A., & Lauga, E. (2018). The swimming of a deforming helix. European Physical Journal E, 41(10), Article 119. https://doi.org/10.1140/epje/i2018-11728-2

Abstract.: Many microorganisms and artificial microswimmers use helical appendages in order to generate locomotion. Though often rotated so as to produce thrust, some species of bacteria such Spiroplasma, Rhodobacter sphaeroides and Spirochetes induc... Read More about The swimming of a deforming helix.

Early-time jet formation in liquid–liquid impact problems: theory and simulations (2018)
Journal Article
Cimpeanu, R., & Moore, M. R. (2018). Early-time jet formation in liquid–liquid impact problems: theory and simulations. Journal of Fluid Mechanics, 856, 764-796. https://doi.org/10.1017/jfm.2018.704

We perform a thorough qualitative and quantitative comparison of theoretical predictions and direct numerical simulations for the two-dimensional, vertical impact of two droplets of the same fluid. In particular, we show that the theoretical predicti... Read More about Early-time jet formation in liquid–liquid impact problems: theory and simulations.

Booms, busts and heavy tails: the story of Bitcoin and cryptocurrency markets (2018)
Journal Article
Fry, J. (2018). Booms, busts and heavy tails: the story of Bitcoin and cryptocurrency markets. Economics letters, 171, 225-229. https://doi.org/10.1016/j.econlet.2018.08.008

We develop bespoke rational bubble models for Bitcoin and cryptocurrencies that incorporate both heavy tails and the probability of a complete collapse in asset prices. Empirically, we present robustified evidence of bubbles in Bitcoin and Ethereum.... Read More about Booms, busts and heavy tails: the story of Bitcoin and cryptocurrency markets.

Methods to solve half-plane partial slip contact problems (2018)
Journal Article
Hills, D., Ramesh, R., Barber, J., & Moore, M. (2018). Methods to solve half-plane partial slip contact problems. International Journal of Solids and Structures, 155, 155-159. https://doi.org/10.1016/j.ijsolstr.2018.07.019

There exists a family of methods for finding the extent of partial slip in contact problems between elastically similar bodies, capable of idealisation by half-planes. Closed form solutions are given to problems subject to a constant normal load and... Read More about Methods to solve half-plane partial slip contact problems.

Linear groups and computation (2018)
Journal Article
Detinko, A. S., & Flannery, D. L. (2019). Linear groups and computation. Expositiones Mathematicae, 37(4), 454-484. https://doi.org/10.1016/j.exmath.2018.07.002

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for this class of groups are surveyed. We... Read More about Linear groups and computation.

Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces (2018)
Journal Article
Olegovich Manturov, V., & Rushworth, W. (2018). Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces. Journal of Knot Theory and Its Ramifications, 27(9), https://doi.org/10.1142/S0218216518420014

We define additional gradings on two generalisations of Khovanov homology (one due to the first author, the other due to the second), and use them to define invariants of various kinds of embeddings. These include invariants of links in thickened sur... Read More about Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces.

Primordial Gravitational Waves and Reheating in a New Class of Plateau-Like Inflationary Potentials (2018)
Journal Article
Chongchitnan, S. (2018). Primordial Gravitational Waves and Reheating in a New Class of Plateau-Like Inflationary Potentials. Universe, 4(7), Article 77. https://doi.org/10.3390/universe4070077

We study a new class of inflation model parametrized by the Hubble radius, such that aH∝exp(−αφ)n. These potentials are plateau-like, and reduce to the power-law potentials in the simplest case n=2. We investigate the range of model parameters that i... Read More about Primordial Gravitational Waves and Reheating in a New Class of Plateau-Like Inflationary Potentials.

The boundary integral formulation of Stokes flows includes slender-body theory (2018)
Journal Article
Koens, L., & Lauga, E. (2018). The boundary integral formulation of Stokes flows includes slender-body theory. Journal of Fluid Mechanics, 850, Article R1. https://doi.org/10.1017/jfm.2018.483

The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds-number problems analytically and computationally. Alternatively, one can solve the Stokes... Read More about The boundary integral formulation of Stokes flows includes slender-body theory.