DSpace Collection:
https://dspace.lboro.ac.uk/2134/2484
2017-06-23T13:38:45Z[Mathematical experiment of the track problem]
https://dspace.lboro.ac.uk/2134/25452
Title: [Mathematical experiment of the track problem]
Authors: Zhou, Diwei; Han, Shuguang
Abstract: After establishing and solving the mathematical model of the track problem, a mathematical experiment on the problem is designed in this paper. Mathematical modelling is established and the solution is obtained. It has been proved that the three factors, namely the curve of the child, the length and the angle of the stick, influence the track of the toy considerably. Using the MATLAB software, the effect of each factor is modelled clearly. Furthermore, several meaningful findings are obtained by detecting the track of the toy.2005-01-01T00:00:00ZUniversal formula for Hilbert series of minimal nilpotent orbits
https://dspace.lboro.ac.uk/2134/25427
Title: Universal formula for Hilbert series of minimal nilpotent orbits
Authors: Matsuo, A.; Veselov, A.P.
Abstract: We show that the Hilbert series of the projective variety X = P(Omin), corresponding to the minimal nilpotent orbit Omin, is
universal in the sense of Vogel: it is written uniformly for all simple Lie algebras in terms of Vogel’s parameters α, β, γ and represents a special case of the generalized hypergeometric function 4F3. A universal formula for the degree of X is then deduced.
Description: This paper is closed access until it is published.2017-01-01T00:00:00ZModelling the evaporation of nanoparticle suspensions from heterogeneous surfaces
https://dspace.lboro.ac.uk/2134/25393
Title: Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces
Authors: Chalmers, Christopher; Smith, Roger; Archer, Andrew J.
Abstract: We present a kinetic Monte Carlo (KMC) grid-based model for the drying of drops of a nanoparticle suspension upon a heterogeneous surface. The model consists of a generalised lattice-gas in which the interaction parameters in the Hamiltonian can be varied to model different properties of the materials involved. We show how to choose correctly the interactions, to minimise the effects of the underlying grid so that hemispherical droplets form. We also include the effects of surface roughness to examine the effects of contact-line pinning on the dynamics. When there is a `lid' above the system, which prevents evaporation, equilibrium drops form on the surface, which we use to determine the contact angle and how it varies as the parameters of the model are changed. This enables us to relate the interaction parameters to the materials used in applications. The model has also been applied to drying on heterogeneous surfaces, in particular to the case where the suspension is deposited on a surface consisting of a pair of hydrophilic conducting metal surfaces that are either side of a band of hydrophobic insulating polymer. This situation occurs when using inkjet printing to manufacture electrical connections between the metallic parts of the surface. The process is not always without problems, since the liquid can dewet from the hydrophobic part of the surface, breaking the bridge before the drying process is complete. The KMC model reproduces the observed dewetting, allowing the parameters to be varied so that the conditions for the best connection can be established. We show that if the hydrophobic portion of the surface is located at a step below the height of the neighbouring metal, the chance of dewetting of the liquid during the drying process is significantly reduced.
Description: This paper is closed access until 12 months after publication.2017-01-01T00:00:00ZSelf-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows
https://dspace.lboro.ac.uk/2134/25372
Title: Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows
Authors: Dallaston, Michael C.; Tseluiko, Dmitri; Zheng, Zhong; Fontelos, Marco; Kalliadasis, Serafim
Abstract: A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finitetime rupture. The self-similar nature of the rupture has been studied before
by utilising the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent n = 3 has been used, namely, Π(h) ∝ −1/h3, where h is the film thickness. In
the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at nc ≈ 1.485. We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, nplane c ≈ 1.499. Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures.
Description: This paper is closed access until 19th May 2018.2017-01-01T00:00:00Z