Discrete Breathers

Computational assessment of the discrete breathers (also known as intrinsic localised modes) is performed in nickel and palladium hydrides with an even stoichiometry by means of molecular dynamics simulations. The breathers consisting of hydrogen and metallic atoms were excited following the experience obtained earlier by modelling the breathers in pure metallic systems. Stable breathers were only found in the nickel hydride system and only for the hydrogen atoms oscillating along 〈1 0 0〉 and 〈1 1 1〉 polarization axes. At this, two types of the stable breathers involving single oscillating hydrogen and a pair of hydrogen atoms beating in antiphase mode were discovered. Analysis of the breather characteristics reveals that its frequency is located in the phonon gap or lying in the optical phonon band of phonon spectrum near the upper boundary. Analysis of the movement of atoms constituting the breather was performed to understand the mechanism that enables the breather stabilization and long-term oscillation without dissipation its energy to the surrounding atoms. It has been demonstrated that, while in palladium hydride, the dissipation of the intrinsic breather energy due to hydrogen-hydrogen attractive interaction occurs, the stable oscillation in the nickel hydride system is ensured by the negligibly weak hydrogen-hydrogen interaction acting within a distance of the breather oscillation amplitude. Thus, our analysis provides an explanation for the existence of the long-living stable breathers in metallic hydride systems. Finally, the high energy oscillating states of hydrogen atoms have been observed for the NiH and PdH lattices at finite temperatures which can be interpreted as a fingerprint of the finite-temperature analogues of the discrete breathers.

A new mechanism of catalysis is discussed, which is based on the rate-promoting effect of large-amplitude anharmonic lattice vibrations, a.k.a. intrinsic localized modes or 'discrete breathers' (DBs), which can excite atoms at specific 'active sites' rather strongly, giving them energy far exceeding the energy of thermal vibrations for hundreds of oscillation periods. The DB-induced modulation of activation energies (free energy barriers between reactants and products) results in a drastic amplification of the reaction rates, which can be described by a simple analytical expression in the adiabatic limit. The striking site selectiveness of DB excitation dynamics in the presence of spatial (quenched) disorder makes these nonlinear vibrations viable candidates to play the role of 'active modes' in the catalytic process in various physical, chemical and biological systems.

Novel 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 ≫ k B T 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).

Computational assessment of the discrete breathers (also known as intrinsic localised modes) is performed in nickel and palladium hydrides with an even stoichiometry by means of molecular dynamics simulations. The breathers consisting of hydrogen and metallic atoms were excited following the experience obtained earlier by modelling the breathers in pure metallic systems. Stable breathers were only found in the nickel hydride system and only for the hydrogen atoms oscillating along 〈1 0 0〉 and 〈1 1 1〉 polarization axes. At this, two types of the stable breathers involving single oscillating hydrogen and a pair of hydrogen atoms beating in antiphase mode were discovered. Analysis of the breather characteristics reveals that its frequency is located in the phonon gap or lying in the optical phonon band of phonon spectrum near the upper boundary. Analysis of the movement of atoms constituting the breather was performed to understand the mechanism that enables the breather stabilization and long-term oscillation without dissipation its energy to the surrounding atoms. It has been demonstrated that, while in palladium hydride, the dissipation of the intrinsic breather energy due to hydrogen-hydrogen attractive interaction occurs, the stable oscillation in the nickel hydride system is ensured by the negligibly weak hydrogen-hydrogen interaction acting within a distance of the breather oscillation amplitude. Thus, our analysis provides an explanation for the existence of the long-living stable breathers in metallic hydride systems. Finally, the high energy oscillating states of hydrogen atoms have been observed for the NiH and PdH lattices at finite temperatures which can be interpreted as a fingerprint of the finite-temperature analogues of the discrete breathers.

Computational assessment of the discrete breathers (also known as intrinsic localised modes) is performed in nickel and palladium hydrides with an even stoichiometry by means of molecular dynamics simulations. The breathers consisting of hydrogen and metallic atoms were excited following the experience obtained earlier by modelling the breathers in pure metallic systems. Stable breathers were only found in the nickel hydride system and only for the hydrogen atoms oscillating along 〈1 0 0〉 and 〈1 1 1〉 polarization axes. At this, two types of the stable breathers involving single oscillating hydrogen and a pair of hydrogen atoms beating in antiphase mode were discovered. Analysis of the breather characteristics reveals that its frequency is located in the phonon gap or lying in the optical phonon band of phonon spectrum near the upper boundary. Analysis of the movement of atoms constituting the breather was performed to understand the mechanism that enables the breather stabilization and long-term oscillation without dissipation its energy to the surrounding atoms. It has been demonstrated that, while in palladium hydride, the dissipation of the intrinsic breather energy due to hydrogen-hydrogen attractive interaction occurs, the stable oscillation in the nickel hydride system is ensured by the negligibly weak hydrogen-hydrogen interaction acting within a distance of the breather oscillation amplitude. Thus, our analysis provides an explanation for the existence of the long-living stable breathers in metallic hydride systems. Finally, the high energy oscillating states of hydrogen atoms have been observed for the NiH and PdH lattices at finite temperatures which can be interpreted as a fingerprint of the finite-temperature analogues of the discrete breathers.

The article deals with the Fermi-Pasta-Ulam system that describes an infinite system of particles on 2D-lattice. The main result concerns the existence of solitary traveling wave solutions. By means of critical point theory, we obtain sufficient conditions for the existence of such solutions.

We study the interplay between nonlinearity and localization in a model consisting of a quantum quasiparticle interacting with a nonlinear extended lattice. The isolated lattice can support discrete breathers, and the coupling of the quasiparticle to the lattice leads to localized quasiparticle states. Minimum energy states of the full system can have both a breather and a solitonic character. Excited states lead to interesting new phenomena, such as full breather states, which arise from the combination of intrinsic and extrinsic nonlinearity.

We study the existence of discrete breathers (time-periodic and spatially localized oscillations) in a chain of coupled nonlinear oscillators modelling the breathing of DNA. We consider a modification of the Peyrard-Bishop model introduced by Peyrard et al. [Nonlinear analysis of the dynamics of DNA breathing, J. Biol. Phys. 35 (2009), 73-89], in which the reclosing of base pairs is hindered by an energy barrier. Using a new kind of continuation from infinity, we prove for weak couplings the existence of large amplitude and low frequency breathers oscillating around a localized equilibrium, for breather frequencies lying outside resonance zones. These results are completed by numerical continuation. For resonant frequencies (with one multiple belonging to the phonon band) we numerically obtain discrete breathers superposed on a small oscillatory tail.

We dedicate this paper to Professor Apostolos Hadjidimos, whose inspiring research and teaching all these years has demonstrated that Numerical Analysis is a truly fundamental branch of Mathematics and not simply a useful tool for solving scientific problems.

Non-linear localization phenomena in biological lattices have attracted a steadily growing interest and their existence has been predicted in a wide range of physical settings. We investigate the non-linear proton dynamics of a hydrogen-bonded chain in a semiclassical limit using the coherent state method combined with a Holstein-Primakoff bosonic representation. We demonstrate that even a weak inherent discreteness in the hydrogenbonded (HB) chain may drastically modify the dynamics of the non-linear system, leading to instabilities that have no analog in the continuum limit. We suggest a possible localization mechanism of polarization oscillations of protons in a hydrogen-bonded chain through modulational instability analysis. This mechanism arises due to the neighboring protonproton interaction and coherent tunneling of protons along hydrogen bonds and/or around heavy atoms. We present a detailed analysis of modulational instability, and highlight the role of the interaction strength of neighboring protons in the process of bioenergy localization. We perform molecular dynamics simulations and demonstrate the existence of nanoscale discrete breather (DB) modes in the hydrogen-bonded chain. These highly

We discuss the existence of breathers and of energy thresholds for their formation in DNLS lattices with linear and nonlinear impurities. In the case of linear impurities we present some new results concerning important differences between the attractive and repulsive impurity which is interplaying with a power nonlinearity. These differences concern the coexistence or the existence of staggered and unstaggered breather profile patterns. We also distinguish between the excitation threshold (the positive minimum of the power observed when the dimension of the lattice is greater or equal to some critical value) and explicit analytical lower bounds on the power (predicting the smallest value of the power a discrete breather one-parameter family), which are valid for any dimension. Extended numerical studies in one, two and three dimensional lattices justify that the theoretical bounds can be considered as thresholds for the existence of the frequency parametrized families. The discussion reviews and extends the issue of the excitation threshold in lattices with nonlinear impurities while lower bounds, with respect to the kinetic energy, are also discussed for traveling waves in FPU periodic lattices.

This paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

We dedicate this paper to Professor Apostolos Hadjidimos, whose inspiring research and teaching all these years has demonstrated that Numerical Analysis is a truly fundamental branch of Mathematics and not simply a useful tool for solving scientific problems.

http://personal.us.es/jcuevas Collisions between moving localized modes (moving breathers) in nonintegrable lattices present a rich outcome. In this paper, some features of the interaction of moving breathers in Discrete Nonlinear Schrödinger and Klein-Gordon lattices, together with some plausible explanations, are exposed.

Time-periodic localized oscillations occur in a variety of contexts, in particular in weakly coupled anharmonic lattices and in disordered harmonic networks of oscillators, where they are known respectively as discrete breathers and Anderson modes. It is shown numerically in some examples of systems which interpolate between these two limits that discrete breathers can be continued to Anderson modes, modulo small jumps associated with resonance with Anderson modes on other parts of the network.

In this paper, rapidly convergent approximation method (RCAM) is applied for seek of exact solutions of chiral nonlinear Schrodinger’s equation (NLSE) in (1+2)-dimensions. Application of this method gives series solution which converges to the exact analytic solution of NLSE from which several kinds of exact solutions are constructed. The solutions comprise bright, dark, kink, soliton, singular solution and periodic solutions. The parametric conditions for existence of chiral solutions are also presented.

The element of the air has recently started to be welcomed back as a field of knowledge in the social sciences and humanities. The attention to the air has mainly, but not exclusively, been the result of the increasingly tangible effects of particle pollution. Toxic pollutants have made breathing more difficult. It is however not only the atmosphere itself which is congested. This writing is a personal manifesto in which I wish to show how pollution has affected both my physiological as well as my psychological well-being. I sense that the element of the air has in the process of its polluting been robbed from its historical potency to inspire freedom
and imagination. The vital and personal relationship to the air has for a very long time been left ignored as a potential domain for an alternative politics. The air seems instead to have historically been subordinated to a more terrestrially-focused
understanding of politics. This article conveys a personal desire to rethink our relationship to and knowledge of the air. I wish to give the air a renewed voice without confining it to language. I propose to do this by arguing for a poetic awareness and turn in the way we breathe. Through the use of text I attempt to
transcribe the cadence of my breathing.