29,902 research outputs found
Spectral algorithms for reaction-diffusion equations
No full textA collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness associated with the diffusive terms in a reaction-diffusion model allowing explicit high order timestepping to be used. This is particularly valuable for two (and higher) space dimension problems. Our aim here is to provide codes, together with examples, to allow practioners to easily utilize, understand and implement these ideas; we incorporate recent theoretical advances such as exponential time differencing methods and provide timings and error comparisons with other more standard approaches.
The examples are chosen from the literature to illustrate points and queries that naturally arise
Elastic Orbital Angular Momentum
No full textWe identify that flexural guided elastic waves in elastic pipes carry a well-defined orbital angular momentum associated with the compressional dilatational potential. This enables the transfer of elastic orbital angular momentum, that we numerically demonstrate, through the coupling of the compressional potential in a pipe to the acoustic pressure field in a surrounding fluid in contact with the pipe
Platonic Localisation: One Ring to Bind Them
No full textIn this paper, we present an asymptotic model describing localised flexural
vibrations along a structured ring containing point masses or spring-mass
resonators in an elastic plate. The values for the required masses and
stiffnesses of resonators are derived in a closed analytical form. It is shown
that spring-mass resonators can be tuned to produce a "negative inertia" input,
which is used to enhance localisation of waveforms around the structured ring.
Theoretical findings are accompanied by numerical simulations, which show
exponentially localised and leaky modes for different frequency regimes
Shallow viscoplastic flow on an inclined plane
No full textEvolving viscoplastic flows upon slopes are an important idealization of many flows in a variety of geophysical situations where yield stress is thought to play a role. For such models, asymptotic expansions suitable for slowly moving shallow fluid layers (lubrication theory) reduce the governing equations to a simpler problem in terms of the fluid thickness. We consider the version of the theory for fluids described by the Herschel-Bulkley constitutive law, and provide a variety of solutions to the reduced equation, both numerical and analytical. For extruded inclined domes, we derive the characteristic temporal behavior of measures of the dome's dimensions
Viscoplastic flow over an inclined surface
No full textWe review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material. Lubrication theory is used for shallow and slow flows to reduce the governing equations to a nonlinear diffusion-type equation for the local fluid depth; this model is used as the basis for exploration of the problem. Theory is compared to experiments. A number of complications and additional physical effects are discussed that enrich real situations
Reinforcement learning optimisation for graded metamaterial design using a physical-based constraint on the state representation and action space
No full textThe energy harvesting capability of a graded metamaterial is maximised via reinforcement learning (RL) under realistic excitations at the microscale. The metamaterial consists of a waveguide with a set of beam-like resonators of variable length, with piezoelectric patches, attached to it. The piezo-mechanical system is modelled through equivalent lumped parameters determined via a general impedance analysis. Realistic conditions are mimicked by considering either magnetic loading or random excitations, the latter scenario requiring the enhancement of the harvesting capability for a class of forcing terms with similar but different frequency content. The RL-based optimisation is empowered by using the physical understanding of wave propagation in a such local resonance system to constrain the state representation and the action space. The procedure outcomes are compared against grading rules optimised through genetic algorithms. While genetic algorithms are more effective in the deterministic setting featuring the application of magnetic loading, the proposed RL-based proves superior in the inherently stochastic setting of the random excitation scenario
Dynamics of cooling viscoplastic domes
No full textA variety of problems in engineering and geology involve spreading cooling non-Newtonian fluids. If the fluid is relatively shallow and spreads slowly, lubrication-style asymptotic approximations can be used to build reduced models for the spreading dynamics. The centrepiece of such models is a nonlinear diffusion equation for the local fluid thickness, and ideally this should become coupled to a correspondingly simple equation determining the local temperature field. However, when heat diffuses relatively slowly as the fluid flows, we cannot usefully reduce the temperature equation, and the asymptotic reduction couples the local thickness equation to an advection diffusion equation that crucially involves diffusion in the vertical. We present an efficient computational algorithm for numerically solving this more complicated type of lubrication model, and describe a suite of solutions that illustrate the dynamics captured by the model in the case of an expanding Bingham fluid with a temperature-dependent viscosity. Based on these solutions, we evaluate two simpler models that further approximate the temperature equation: a vertically isothermal theory, and a ‘skin theory’. The latter is based on the integral-balance method of heat-transfe
Topological Rainbow Trapping for Elastic Energy Harvesting in Graded Su-Schrieffer-Heeger Systems
No full textWe amalgamate two fundamental designs from distinct areas of wave control in physics, and place them in the setting of elasticity. Graded elastic metasurfaces, so-called metawedges, are combined with the now classical Su-Schrieffer-Heeger (SSH) model from the field of topological insulators. The resulting structures form one-dimensional graded-SSH metawedges that support multiple, simultaneous, topologically protected edge states. These robust, enhanced localized modes are leveraged for applications in elastic energy harvesting using the piezoelectric effect. The designs we develop are first motivated by applying the SSH model to mass-loaded Kirchhoff-Love thin elastic plates. We then extend these ideas to using graded resonant rods, and create SSH models, coupled to elastic beams and full elastic half-spaces
Viscoplastic flow over an inclined surface (Erratum)
No full textWe review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material. Lubrication theory is used for shallow and slow flows to reduce the governing equations to a non-linear diffusion-type equation for the local fluid depth; this model is used as the basis for exploration of the problem. Theory is compared to experiments. A number of complications and additional physical effects are discussed that enrich real situations. © 2006 Elsevier B.V. All rights reserved
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