Publication:
Fronts in lattices

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2012-06
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Abstract
Simple models of defect motion in lattices identify dislocations [1] and cracks [8,9] with discrete traveling waves [4,10]. In overdamped limits, such lattice models often become discrete bistable equations [3,5], similar to the ones encountered in biology (to describe nerve propagation [7], for instance). In this talk, we will review recent results on front propagation in spatially discrete models, discussing existence of stationary and travelling wave fronts [2,5,6] together with strategies to predict their speeds and the thresholds for propagation failure [3].
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Física-Modelos matemáticos , Análisis matemático
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1202 Análisis y Análisis Funcional
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[1] A Carpio, SJ Chapman, SD Howison, JR Ockendon, Dynamics of line singularities, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 355(1731), 2013-2024, 1997 [2] A Carpio, SJ Chapman, S Hastings, JB McLeod, Wave solutions for a discrete reaction-diffusion equation, European Journal of Applied Mathematics 11 (4), 399-412, 2000 [3] A Carpio, LL Bonilla, Depinning transitions in discrete reaction-diffusion equations, SIAM Journal on Applied Mathematics 63 (3), 1056-1082, 2003 [4] A Carpio, LL Bonilla, Edge dislocations in crystal structures considered as traveling waves in discrete models, Physical Review Letters 90 (13), 135502, 2003 [5] A Carpio, LL Bonilla, Oscillatory wave fronts in chains of coupled nonlinear oscillators, Physical Review E 67 (5), 056621, 2003 [6] A Carpio, Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators, Physical Review E 69 (4), 046601, 2004 [7] A Carpio, Asymptotic construction of pulses in the discrete Hodgkin-Huxley model for myelinated nerves, Physical Review E 72 (1), 011905, 2005 [8] I Plans, A Carpio, LL Bonilla, Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model, EPL (Europhysics Letters) 81 (3), 36001, 2008 [9] I Plans, A Carpio, LL Bonilla, Toy nanoindentation model and incipient plasticity, Chaos, Solitons & Fractals 42 (3), 1623-1630, 2009 [10] LL Bonilla, A Carpio, A Prados, RR Rosales, Ripples in a string coupled to Glauber spins, Physical Review E 85 (3), 031125, 2012
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https://hdl.handle.net/20.500.14352/45980
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