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Ana Carpio, Applied Mathematics - Materials Science
Graphene is a two dimensional crystal
with promising properties. Atoms are arranged
forming a honeycomb lattice. We have characterized
defects experimentally observed in the atomic
lattice as cores of dislocations and dislocation
groups:
heptagon-pentagon pairs, vacancies, divacancies,
Stone-Wales defects... We use periodized discrete
elasticity models and singular solutions of
elasticity equations to study the dynamical
stability of such defects. Our predictions
have been corroborated by experimental observations.
We have coupled Foppl-Von Karman descriptions of
graphene plates to stochastic effects producing
domains forming ripples and studying out-of-plane
deformations around the core of defects.
Earlier, we observed a similar depinning transition in experiments of domain wall relocations in semiconductor superlattices. Predictions of thresholds for controlling parameters and of propagation speeds are obtained reducing the dynamics of the whole lattice to a small set of active points.
By asymptotic studies of Becker-Döring type models we have obtained descriptions of particle nucleation and coarsening processes. We performed further studies of bubble formations in the context of radioactive waste.
In all cases, asymptotic and analytical predictions are validated by numerical simulations whose results are then compared to available experimental information. In the course of the simulations, we have developed specific numerical schemes for hyperbolic and kinetic models, as well as also nonreflecting boundary conditions for waves.
Graphene
defects
Periodized discrete
elasticity models allow us to understand dislocation
nucleation in cubic crystals during indentation
tests in terms of bifurcations. We have shown that
bifurcations also characterize the Peierls stresses
and depinning transition of such defects, whose
motion may be described by travelling wave
solutions.  Ripples in graphene
|
 Out of plane
displacements for heptagon-pentagon
pairs forming a dipole |
Earlier, we observed a similar depinning transition in experiments of domain wall relocations in semiconductor superlattices. Predictions of thresholds for controlling parameters and of propagation speeds are obtained reducing the dynamics of the whole lattice to a small set of active points.
By asymptotic studies of Becker-Döring type models we have obtained descriptions of particle nucleation and coarsening processes. We performed further studies of bubble formations in the context of radioactive waste.
In all cases, asymptotic and analytical predictions are validated by numerical simulations whose results are then compared to available experimental information. In the course of the simulations, we have developed specific numerical schemes for hyperbolic and kinetic models, as well as also nonreflecting boundary conditions for waves.
Graphene
- Measuring strain and rotation fields at the dislocation core in graphene (with L.L. Bonilla, C. Gong, J.H. Warner), Physical Review B 92(15), 155417, 2015 [pdf] [arxiv]
- Driving
dislocations in graphene (with L.L.
Bonilla), Science 337(6091), 161-162,
2012 [pdf]
- Model of ripples in graphene (with L.L. Bonilla), Physical Review B 86(19), 195402, 2012 [pdf] [arxiv]
- Ripples in a graphene membrane coupled to Glauber spins (with L.L. Bonilla), Journal of Statistical Mechanics- Theory and Experiment, P09015, 2012 [pdf] [archivo]
- Ripples in a string coupled to Glauber spins (with L.L. Bonilla, A. Prados, R.R. Rosales), Physical Review E 85(3), 031125, 2012 [pdf] [arxiv]
- Theory of defect dynamics in graphene: defect groupings and their stability (with LL Bonilla), Continuum Mechanics and Thermodynamics 23(4), 337-346, 2011 [pdf] [arxiv]
- Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins (with L.L. Bonilla and A. Prados), Journal of Statistical Mechanics-Theory and Experiment, P09019, 2010 [pdf] [arxiv]
- Phase transitions in a mechanical system coupled to Glauber spins (with A. Prados, L.L. Bonilla), Journal of Statistical Mechanics-Theory and Experiment, P06016, 2010 [pdf] [arxiv]
- Periodized discrete elasticity models for defects in graphene (with L.L. Bonilla), Physical Review B 78(8), 085406, 2008 [pdf] [arxiv]
- Dislocations in graphene (with L.L. Bonilla, F. de Juan, M.A.H. Vozmediano), New Journal of Physics 10, 053021, 2008 [pdf]
Dislocations and plasticity in crystals
- Nonreflecting boundary conditions for discrete waves (with B. Tapiador), Journal of Computational Physics 229(5), 1879-1896, 2010 [pdf] [archivo]
- Toy
nanoindentation model and incipient
plasticity (with I. Plans, L.L.
Bonilla), Chaos, solitons and fractals
42(3), 1623-1630, 2009 [pdf]
[arxiv]
- Homogeneous
nucleation of dislocations as bifurcations
in a periodized discrete
elasticity model (with I. Plans, L.L. Bonilla), EPL (Europhysics
Letters) 81(3), 36001, 2008 [pdf]
[arxiv]
- Dislocations in cubic crystals described by discrete models (with I. Plans, L.L. Bonilla), Physica A, 376, 361-377, 2007 [pdf] [arxiv]
- Discrete models for dislocations and their motion in cubic crystals (with L.L. Bonilla), Physical Review B 71(13) 134105, 2005 [pdf] [arxiv]
- Oscillatory wave fronts in chains of coupled nonlinear oscillators (with L.L. Bonilla) Physical Review E 67(5), 056621, 2003 [pdf] [arxiv]
- Edge dislocations in crystal structures considered as travelling waves in discrete models (with L.L. Bonilla), Physical Review Letters 90(13), 135502, 2003; 91(2), 029901, 2003 [pdf1] [pdf2] [arxiv]
- Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals (with S.J. Chapman and J.J.L. Velazquez), SIAM Journal on Applied Mathematics 61(6), 2168-2199, 2001 [pdf] [arxiv]
- On the modelling
of instabilities in dislocation
interaction (with S.J. Chapman), Philosophical Magazine B 78(2),
155-157, 1998 [pdf]
- Dynamics of line singularities (with S.J. Chapman, S. Howison, J.R. Ockendon), Philosophical Transactions of the Royal Society A 355(1731), 2013-2024, 1997 [pdf] [archivo]
- Analysis of helium bubble growth in radioactive waste (with B. Tapiador), Journal of Nonlinear Analysis-Real World Applications 11(5), 4174-4184, 2010 [pdf] [archivo]
- Theory of surface deposition from boundary layers containing condensable vapour and particles (with J.C. Neu, L.L. Bonilla), Journal of Fluid Mechanics 626, 183-210, 2009 [pdf] [arxiv]
- Kinetics of helium bubble formation in nuclear materials (with J.C. Neu, L.L. Bonilla, W.G. Wolfer), Physica D - Nonlinear Phenomena 222(1-2), 131-140, 2006 [pdf] [arxiv]
- Asymptotic and numerical studies of the Becker-Döring model for transient homogeneous nucleation (with J.C. Neu, L.L. Bonilla, Y. Farjoun), Markov processes and related fields, 12, 341-365, 2006 [arxiv]
- Igniting homogeneous nucleation (with J.C. Neu, L.L. Bonilla), Physical Review E 71(2), 021601, 2005 [pdf] [arxiv]
- Self-sustained current oscillations in the kinetic theory of semiconductor superlattices (with E. Cebrián, L.L. Bonilla), Journal of Computational Physics 228, 7689-7705, 2009 [pdf] [arxiv]
- Effect of disorder on the wave front depinning transition in spatially discrete systems (with L.L. Bonilla, A. Luzon), Physical Review E (RC) 65(3) 035207, 2002 [pdf] [arxiv]
- Numerical study of hyperbolic equations with integral constraints arising in semiconductor theory (with P.J. Hernando, M. Kindelan), SIAM Journal on Numerical Analysis 39(1), 168-191, 2001 [pdf] [arxiv]
- Motion of wave fronts in semiconductor superlattices (with L.L. Bonilla, G. Dell'Acqua), Physical Review E 64(3), 036204, 2001 [pdf] [arxiv]
- Wave fronts may move upstream in semiconductor superlattices (with L.L. Bonilla, A. Wacker, E. Scholl) Physical Review E 61(5), 4866-4876, 2000 [pdf] [arxiv]
