Search Results - "Hydon, Peter"

A New Technique for Preserving Conservation Laws by Frasca-Caccia, Gianluca, Hydon, Peter E.

“…This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove…”
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Why chaotic mixing of particles is inevitable in the deep lung by Tsuda, Akira, Laine-Pearson, Fiona E., Hydon, Peter E.

“…Fine/ultrafine particles can easily reach the pulmonary acinus, where gas is exchanged, but they need to mix with alveolar residual air to land on the septal…”
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Characteristics of Conservation Laws for Difference Equations by Grant, Timothy J., Hydon, Peter E.

“…Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is…”
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Chaotic Mixing Deep in the Lung by Tsuda, Akira, Rogers, Rick A., Hydon, Peter E., Butler, James P.

“…Our current understanding of the transport and deposition of aerosols (viruses, bacteria, air pollutants, aerosolized drugs) deep in the lung has been grounded…”
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Symmetries of Integrable Difference Equations on the Quad-Graph by Rasin, Olexandr G., Hydon, Peter E.

“…This paper describes symmetries of all integrable difference equations that belong to the famous Adler–Bobenko–Suris classification. For each equation, the…”
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Symmetry analysis of initial-value problems by Hydon, Peter E.

“…Symmetry analysis is a powerful tool that enables the user to construct exact solutions of a given differential equation in a fairly systematic way. For this…”
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Asymmetric integrable quad-graph equations by Hydon, Peter E., Viallet, Claude-M.

“…Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use…”
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A Variational Complex for Difference Equations by Hydon, Peter E., Mansfield, Elizabeth L.

“…An analogue of the Poincare lemma for exact forms on a lattice is stated and proved. Using this result as a starting-point, a variational complex for…”
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Difference Forms by Mansfield, Elizabeth L., Hydon, Peter E.

“…Currently, there is much interest in the development of geometric integrators, which retain analogues of geometric properties of an approximated system. This…”
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Numerical preservation of multiple local conservation laws by Frasca-Caccia, Gianluca, Hydon, Peter E.

“…•A novel strategy that uses symbolic algebra to find finite difference methods that preserve conservation laws is applied to the Benjamin-Bona-Mahony (BBM)…”
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Simple bespoke preservation of two conservation laws by Frasca-Caccia, Gianluca, Hydon, Peter Ellsworth

“…Abstract Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference…”
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Moving Frames: Difference and Differential-Difference Lagrangians by White, Lewis C., Hydon, Peter E.

“…This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In…”
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Conservation Laws of Discrete Korteweg-de Vries Equation by Rasin, Olexandr G.

“…All three-point and five-point conservation laws for the discrete Korteweg-de Vries equations are found. These conservation laws satisfy a functional equation,…”
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Self-Invariant Contact Symmetries by Hydon, Peter E

“…Every smooth second-order scalar ordinary differential equation (ODE) that is solved for the highest derivative has an infinite-dimensional Lie group of…”
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Extensions of Noether's Second Theorem: from continuous to discrete systems by Hydon, Peter E., Mansfield, Elizabeth L.

“…A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or…”
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Multi-symplectic formulation of near-local Hamiltonian balanced models by Delahaies, Sylvain, Hydon, Peter E.

“…We transform near-local Hamiltonian balanced models (HBMs) describing nearly geostrophic fluid motion (with constant Coriolis parameter) into multi-symplectic…”
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How to Find Discrete Contact Symmetries by Hydon, Peter E.

“…This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The…”
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Partial Euler operators and the efficient inversion of Div by Hydon, Peter E

“…The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order…”
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The difference variational bicomplex and multisymplectic systems by Peng, Linyu, Hydon, Peter E

“…The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and…”
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Gas flow and mixing in the airways by Pedley, T J, Corieri, P, Kamm, R D, Grotberg, J B, Hydon, P E, Schroter, R C

“…To survey the current state of scientific knowledge of gas flow and mixing in pulmonary airways, especially at high frequencies. Results from the authors' own…”
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