Modeling and simulation: Examples in Materials and Biology

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Examples on mathematical modeling and simulation in physics and biology: crystals, nerves and muscles, semiconductors, nucleation
[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, On the modelling of instabilities in dislocation interactions, Philosophical Magazine B 78 (2), 155-157, 1998 [3] 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 [4] A Carpio, LL Bonilla, A Wacker, E Schöll, Wave fronts may move upstream in semiconductor superlattices, Physical Review E 61 (5), 4866, 2000 [5] A Carpio, P Hernando, M Kindelan, Numerical study of hyperbolic equations with integral constraints arising in semiconductor theory, SIAM Journal on Numerical Analysis 39 (1), 168-191, 2001 [6] A Carpio, SJ Chapman, JJL Velázquez, Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals, SIAM Journal on Applied Mathematics 61 (6), 2168-2199, 2001 [7] A Carpio, LL Bonilla, Wave front depinning transition in discrete one-dimensional reaction-diffusion systems, Physical Review Letters 86 (26), 6034, 2001 [8] A Carpio, LL Bonilla, G Dell’Acqua, Motion of wave fronts in semiconductor superlattices, Physical Review E 64 (3), 036204, 2001 [9] A Carpio, E Cebrian, FJ Mustieles, Long time asymptotics for the semiconductor Vlasov-Poisson-Boltzmann equations, Mathematical Models and Methods in Applied Sciences 11 (09), 1631-1655, 2001 [10] A Carpio, LL Bonilla, A Luzón, Effects of disorder on the wave front depinning transition in spatially discrete systems, Physical Review E 65 (3), 035207, 2002 [11] A Carpio, Wavefronts for discrete two-dimensional nonlinear diffusion equations, Applied Mathematics Letters 15 (4), 415-421, 2002 [12] A Carpio, LL Bonilla, Depinning transitions in discrete reaction-diffusion equations, SIAM Journal on Applied Mathematics 63 (3), 1056-1082, 2003 [13] A Carpio, LL Bonilla, Pulse propagation in discrete systems of coupled excitable cells, SIAM Journal on Applied Mathematics 63 (2), 619-635, 2003 [14] A Carpio, LL Bonilla, Edge dislocations in crystal structures considered as traveling waves in discrete models, Physical Review Letters 90 (13), 135502, 2003 [15] A Carpio, LL Bonilla, Oscillatory wave fronts in chains of coupled nonlinear oscillators, Physical Review E 67 (5), 056621, 2003 [16] A Carpio, Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators, Physical Review E 69 (4), 046601, 2004 [17] JC Neu, LL Bonilla, A Carpio, Igniting homogeneous nucleation, Physical Review E 71 (2), 021601, 2005 [18] A Carpio, LL Bonilla, Discrete models of dislocations and their motion in cubic crystals, Physical Review B 71 (13), 134105, 2005 [19] A Carpio, Asymptotic construction of pulses in the discrete Hodgkin-Huxley model for myelinated nerves, Physical Review E 72 (1), 011905, 2005 [20] A Carpio, Wave trains, self-oscillations and synchronization in discrete media, Physica D: Nonlinear Phenomena 207 (1-2), 117-136, 2005 [21] LL Bonilla, A. Carpio, Y. Farjoun, JC Neu, Asymptotic and numerical studies of the Becker-Döring model for transient homogeneous nucleation, Markov processes and related fields, 12, 341-365, 2006 [22] LL Bonilla, A Carpio, JC Neu, WG Wolfer, Kinetics of helium bubble formation in nuclear materials, Physica D: Nonlinear Phenomena 222 (1-2), 131-140, 2006 [23] LL Bonilla, A Carpio, I Plans, Dislocations in cubic crystals described by discrete models, Physica A: Statistical Mechanics and its Applications 376, 361-377, 2007 [24] 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 [25] A Carpio, ML Rapún, Topological derivatives for shape reconstruction, In: Bonilla, L.L. (eds) Inverse Problems and Imaging. Lecture Notes in Mathematics, vol 1943. Springer, Berlin, Heidelberg, 2008 [26] A Carpio, LL Bonilla, F de Juan, MAH Vozmediano, Dislocations in graphene, New Journal of Physics 10 (5), 053021, 2008 [27] A Carpio, ML Rapún, Solving inhomogeneous inverse problems by topological derivative methods, Inverse Problems 24 (4), 045014, 2008 [28] A Carpio, LL Bonilla, Periodized discrete elasticity models for defects in graphene, Physical Review B 78 (8), 085406, 2008 [29] A Carpio, ML Rapún, Domain reconstruction using photothermal techniques, Journal of Computational Physics 227 (17), 8083-8106, 2008 [30] JC Neu, A Carpio, LL Bonilla, Theory of surface deposition from boundary layers containing condensable vapour and particles, Journal of fluid mechanics 626, 183-210, 2009 [31] E Cebrián, LL Bonilla, A Carpio, Self-sustained current oscillations in the kinetic theory of semiconductor superlattices, Journal of Computational Physics 228 (20), 7689-7705, 2009 [32] I Plans, A Carpio, LL Bonilla, Toy nanoindentation model and incipient plasticity, Chaos, Solitons & Fractals 42 (3), 1623-1630, 2009