Análisis competencial de una tarea de modelización abierta

Según diversos autores, las actividades dirigidas al desarrollo conjunto de las competencias matemáticas deben relacionarse con la realidad y los procesos de modelización matemática. El objetivo del presente trabajo es describir, a partir de la producción de un grupo de alumnos de tercer curso de ESO, las competencias que los alumnos han de poner en juego para resolver una tarea genuina y completa de modelización y que formarían parte de la propia competencia en Modelizació

Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials

We develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. This approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. The interparticle distances in the lattice kinks with high energy are physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with a single velocity and a single energy which are independent on the excitation conditions. The found kinks are ultra-discrete and can be described with the "magic wave number" $q\simeq 2\pi/3a$, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the supersonic kinks, with basically two particles moving at the same time, allows the interpretation of their double-kink structure. The energy of the supersonic kinks is between the possible source of $^{40}$K recoil in beta decay and the energy necessary for the ejection of an atom at the border as has been found experimentally.Comment: 14 pages, 15 figure

Nonlinear waves in a chain of magnetically coupled pendula

A motivation for the study of reduced models like one-dimensional systems in Solid State Physics is the complexity of the full problem. In recent years our group has studied theoretically, numerically and experimentally wave propagation in lattices of nonlinearly coupled oscillators. Here, we present the dynamics of magnetically coupled pendula lattices. These macroscopic systems can model the dynamical processes of matter or layered systems. We report the results obtained for harmonic wave propagation in these media, and the different regimes of mode conversion into higher harmonics strongly influenced by dispersion and discreteness, including the phenomenon of acoustic dilatation of the chain, as well as some results on the propagation of localized waves i.e., solitons and kinks.Generalitat Valenciana APOSTD/2017/042Umiversitat Politècnica de València PAID-01-14Ministerio de Economía y Competitividad (MINECO), Spain FIS2015-65998-C2-2-PJunta de Andalucía 2017/FQM-28

Quodons in Mica 2013

Quodons in Mica 2013 INDEX 1. Introduction. 3. JFR Archilla, SMM Coelho, FD Auret, V Dubinko and V Hizhnyakov. Experimental observation of moving discrete breathers in germanium. 5. L Brzihik. Bisolectrons in harmonic and anharmonic lattices. 6. AP Chetverikov. Solitons and charge transport in triangular and quadratic Morse lattices. 7. LA Cisneros-Ake. Travelling coherent structures in the electron transport in 2D anharmonic crystal lattices. 8. SMM Coelho, FD Auret, JM Nel and JFR Archilla. The origin of defects induced in ultra-pure germanium by Electron Beam Deposition. 10. S Comorosan and M Apostol. Theory vs. Reality - Localized excitations induced by optical manipulation of proteins, as a different approach to link experiments with theory. 12. L Cruzeiro. The amide I band of crystalline acetanilide: old data under new light. 13. SV Dmitriev and AA Kistanov. Moving discrete breathers in crystals with NaCl structure. 15. V Dubinko, JFR Archilla, SMM Coelho and V Hizhnyakov. Modeling of the annealing of radiation-induced defects in germanium by moving discrete breathers. 16. JC Eilbeck. Numerical simulations of nonlinear modes in mica: past, present and future. 17. A Ferrando, C Mili\'an, DE Ceballos-Herrera and Dmitry V. Skryabin. Soliplasmon resonances at metal-dielectric interfaces. 19. YuB Gaididei. Energy localization in nonlinear systems with flexible geometry. 20. D Hennig. Existence and non-existence of breather solutions in damped and driven nonlinear lattices. 21. P Jason and M Johansson. Existence, dynamics and mobility of Quantum Compactons in an extended Bose-Hubbard model. 22. N. Jiménez, JFR Archilla, Y. Kosevich, V. Sánchez-Morcillo and LM García-Raffi. A crowdion in mica. Between K40 recoil and transmission sputtering. 24. M Johansson. Strongly localized moving discrete solitons (breathers): new ways to beat the Peierls-Nabarro barrier. 26. YA Kosevich and AV Savin. Energy transport in molecular chains with combined anharmonic potentials of pair interatomic interaction. 28. B Malomed, C Mejía-Cortés and RA Vicencio. Mobile discrete solitons in the one-dimensional lattice with the cubic-quintic nonlinearity. 29. FM Russell. Recording process in iron-rich muscovite crystals. 30. L Salasnich. Bright solitons of attractive Bose-Einstein condensates confined in quasi-1D optical lattice. 31. V Sánchez-Morcillo, LM, Garcíaa-Raffi, V. Romero-Garcíaa, R. Picó, A. Cebrecos, and Kestutis Staliunas. Wave localization in chirped sonic crystals. 32. P Selyschev, V Sugakov and T Didenko. Peculiarities of the change of temperature and heat transfer under irradiation. 33. K Staliunas. Taming of Modulation Instability: Manipulation, and Complete Suppression of Instability by Spatio-Temporal Periodic Modulation. 34. G Tsironis. Gain-Driven Breathers in PT-Symmetric Metamaterials. 36. JAD Wattis and IA Butt. Moving breather modes in two-dimensional lattices.Ministerio de Ciencia e Innovación FIS2008-0484

Second harmonic propagation in Coupled Oscillators

[EN] In this work, we studied numerically, analytically and experimentally the nonlinear dynamics for a chain of magnates. Propagation the second harmonic depends on the medium parameters and the excitation signal (amplitude and frequency). From the experimental results which have a good agreement with the theoretical results, several phenomenons in nonlinear behavior can be study. The experiment also shows the generation of subharmonics.This research was partially supported by Ministerio de Economía y ompetitividad under grant FIS2015-65998-C2-2. LJSC and AM acknowledge UPV for predoctoral contract FPI-Subprograma 1Mehrem, A.; Sánchez Morcillo, VJ.; Jimenez, N.; Salmerón Contreras, LJ.; García-Andrés, FX.; Picó Vila, R.; García-Raffi, LM. (2016). Second harmonic propagation in Coupled Oscillators. Universidade do Porto. 1-4. http://hdl.handle.net/10251/181098S1

Gap Solitons in acoustic layered media

[EN] In this work we study numerically the existence of gap solitons in an acoustic media. To approach the problem a set of coupled-mode equations are given. In order to obtain a solitary wave in a real media, it is necessary of two phenomena, dispersion and nonlinearity. Acoustic media, usually can present nonlinearity but also low dispersions. To increase dispersion, it is proposed to use a multi-layered medium, a kind of sonic crystal in 1D, that it is demonstrated to have high dispersion near some frequency bands. In this kind of media, it is possible to observe soliton wavesThis research was partially supported by Ministerio de Economía y ompetitividad under grant FIS2015-65998-C2-2. LJSC and AM acknowledge UPV for redoctoral contract FPI-Subprograma 1Salmerón Contreras, LJ.; García-Raffi, LM.; Jimenez, N.; Mehrem, A.; Picó Vila, R.; Sánchez Morcillo, VJ.; Staliunas, K. (2016). Gap Solitons in acoustic layered media. Universidade do Porto. 1-4. http://hdl.handle.net/10251/181071S1

Rate Theory of Acceleration of Defect Annealing Driven by Discrete Breathers

Siendo un capítulo de libro es un poco estraño que los campos correspondan a una revista. Tal vez, en vez de coordinador/director deberían ser editores, y en vez de editor, editorial. En cambio faltarían campos como volumen y serieNovel mechanisms of defect annealing in solids are discussed, which are based on the large amplitude anharmonic lattice vibrations, a.k.a. intrinsic localized modes or discrete breathers (DBs). A model for amplification of defect annealing rate in Ge by low energy plasma-generated DBs is proposed, in which, based on recent atomistic modelling, it is assumed that DBs can excite atoms around defects rather strongly, giving them energy ≫ kBT for ~100 oscillation periods. This is shown to result in the amplification of the annealing rates proportional to the DB flux, i.e. to the flux of ions (or energetic atoms) impinging at the Ge surface from inductively coupled plasma (ICP)

Supersonic Kinks in Coulomb lattices

There exist in nature examples of lattices of elements for which the interaction is repulsive, the elements are kept in place because different reasons, as border conditions, geometry (e.g., circular) and, certainly, the interaction with other elements in the system, which provides an external potential. A primer example are layered silicates as mica muscovite, where the potassium ions form a two dimensional lattice between silicate layers. We propose an extremely simplified model of this layer in order to isolate the properties of a repulsive lattice and study them. We find that they are extremely well suited for the propagation of supersonic kinks and multikinks. Theoretically, they may have as much energy and travel as fast as desired. This striking results suggest that the properties of repulsive lattices may be related with some yet not fully explained direct and indirect observations of lattice excitations in muscovite

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

In this paper, a new methodology for the determination of the boundaries between oscillatory and non-oscillatory motion for nonviscously damped nonproportional systems is proposed. It is assumed that the damping forces are expressed as convolution integrals of the velocities via hereditary exponential kernels. Oscillatory motion is directly related to the complex nature of eigensolutions in a frequency domain and, in turn, on the value of the damping parameters. New theoretical results are derived on critical eigenmodes for viscoelastic systems with multiple degrees of freedom, with no restrictions on the number of hereditary kernels. Furthermore, these outcomes enable the construction of a numerical approach to draw the critical curves as solutions of certain parameter-dependent eigenvalue problems. The method is illustrated and validated through two numerical examples, covering discrete and continuous systems

Hyperuniformity of quasiperiodic tilings generated by continued fractions

Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small wavenumbers. In this paper quasiperiodic tilings constructed by word concatenation are under study. The lattice is generated from a parameter given by its continued fraction so that quasiperiodicity emerges for infinite when irrational generators are into consideration. Numerical simulations show a quite regular quadratic decay of Fourier intensities, regardless of the number considered for the generator parameter, which leads us to formulate the hypothesis that this type of media is strongly hyperuniform of order 3. Theoretical derivations show that the density fluctuations scale in the same proportion as the wavenumbers. Furthermore, it is rigorously proved that the structure factor decays around the origin according to the pattern $S(k) \sim k^4$. This result is validated with several numerical examples with different generating continued fractions