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Philip Broadbridge      
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Philip Broadbridge published an article in March 2018.
Top co-authors See all
Colin Rogers

183 shared publications

M. J. Ward

121 shared publications

Yi-Ping Phoebe Chen

120 shared publications

Kenji Kajiwara

117 shared publications

Meg E. Morris

111 shared publications

Publication Record
Distribution of Articles published per year 
(1970 - 2018)
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Publications See all
Article 0 Reads 0 Citations Nonclassical Symmetry Solutions for Fourth-Order Phase Field Reaction–Diffusion Philip Broadbridge, Dimetre Triadis, Dilruk Gallage, Pierlui... Published: 17 March 2018
Symmetry, doi: 10.3390/sym10030072
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Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a “mushy” zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.
Article 0 Reads 0 Citations Integrable Discrete Model for One-Dimensional Soil Water Infiltration Dimetre Triadis, Philip Broadbridge, Kenji Kajiwara, Ken-ich... Published: 28 February 2018
Studies in Applied Mathematics, doi: 10.1111/sapm.12208
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We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection–diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self-adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost.
Article 0 Reads 0 Citations On approximation for fractional stochastic partial differential equations on the sphere Vo V. Anh, Philip Broadbridge, Andriy Olenko, Yu Guang Wang Published: 16 February 2018
Stochastic Environmental Research and Risk Assessment, doi: 10.1007/s00477-018-1517-1
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This paper gives the exact solution in terms of the Karhunen–Loève expansion to a fractional stochastic partial differential equation on the unit sphere \({\mathbb {S}}^{2} \subset {\mathbb {R}}^{3}\) with fractional Brownian motion as driving noise and with random initial condition given by a fractional stochastic Cauchy problem. A numerical approximation to the solution is given by truncating the Karhunen–Loève expansion. We show the convergence rates of the truncation errors in degree and the mean square approximation errors in time. Numerical examples using an isotropic Gaussian random field as initial condition and simulations of evolution of cosmic microwave background are given to illustrate the theoretical results.
Article 0 Reads 0 Citations Foreword: Proceedings of the 4th International Electronic Conference on Entropy and Its Applications Philip Broadbridge Published: 24 January 2018
Proceedings, doi: 10.3390/proceedings2040196
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Note: In lieu of an abstract, this is an excerpt from the first page.Excerpt This volume presents papers contributed to the 4th E-Conference on Entropy (ECEA-4), of November 2017.
PREPRINT 0 Reads 0 Citations Nonclassical Symmetry Solutions for 4th Order Phase Field Reaction-Diffusion Philip Broadbridge, Dimetre Triadis, Dilruk Gallage, Pierlui... Published: 18 January 2018
doi: 10.20944/preprints201801.0169.v1
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Article 0 Reads 1 Citation Exact Solutions of the Richards Equation With Nonlinear Plant-Root Extraction Philip Broadbridge, Edoardo Daly, Joanna Goard Published: 01 November 2017
Water Resources Research, doi: 10.1002/2017wr021097
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The Richards equation, commonly used to model water flow in unsaturated soils, is highly nonlinear, thus making it very challenging to solve analytically for situations meaningful in practical applications. The inclusion of realistic forms of root-water uptake rates in this equation adds complications in deriving exact solutions. This study provides for the first time analytical solutions of the Richards equation with a sink term nonlinearly dependent on soil water content. These solutions are applied to irrigation furrows, using Cartesian coordinates, and irrigation from a circular plate, in cylindrical coordinates.