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Register a new userEffect of discrete breathers on the specific heat of a nonlinear chain
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A nonlinear chain with six-order polynomial on-site potential is used to analyze the evolution of the total to kinetic energy ratio during development of modulational instability of extended nonlinear vibrational modes. For the on-site potential of hard-type (soft-type) anharmonicity, the instability of $q=pi$ mode ($q=0$ mode) results in the appearance of long-living discrete breathers (DBs) that gradually radiate their energy and eventually the system approaches thermal equilibrium with spatially uniform and temporally constant temperature. In the hard-type (soft-type) anharmonicity case, the total to kinetic energy ratio is minimal (maximal) in the regime of maximal energy localization by DBs. It is concluded that DBs affect specific heat of the nonlinear chain and for the case of hard-type (soft-type) anharmonicity they reduce (increase) the specific heat.
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The effect of discrete breathers (DBs) on macroscopic properties of the Fermi-Pasta-Ulam chain with symmetric and asymmetric potentials is investigated. The total to kinetic energy ratio (related to specific heat), stress (related to thermal expansion), and Youngs modulus are monitored during the development of modulational instability of the zone boundary mode. The instability results in the formation of chaotic DBs followed by the transition to thermal equilibrium when DBs disappear due to energy radiation in the form of small-amplitude phonons. It is found that DBs reduce the specific heat for all the considered chain parameters. They increase the thermal expansion when the potential is asymmetric and, as expected, thermal expansion is not observed in the case of symmetric potential. The Youngs modulus in the presence of DBs is smaller than in thermal equilibrium for the symmetric potential and for the potential with a small asymmetry, but it is larger than in thermal equilibrium for the potential with greater asymmetry. Our results can be useful for setting experiments on the identification of DBs in crystals by measuring their macroscopic properties.
In the present work we explore a pre-stretched oscillator chain where the nodes interact via a pairwise Lennard-Jones potential. In addition to a homogeneous solution, we identify solutions with one or more (so-called) `breaks, i.e., jumps. As a function of the canonical parameter of the system, namely the precompression strain $d$, we find that the most fundamental one break solution changes stability when the monotonicity of the Hamiltonian changes with $d$. We provide a proof for this (motivated by numerical computations) observation. This critical point separates stable and unstable segments of the one break branch of solutions. We find similar branches for 2 through 5 break branches of solutions. Each of these higher `excited state solutions possesses an additional unstable pair of eigenvalues. We thus conjecture that $k$ break solutions will possess at least $k-1$ (and at most $k$) pairs of unstable eigenvalues. Our stability analysis is corroborated by direct numerical computations of the evolutionary dynamics.
We study the properties of discrete breathers, also known as intrinsic localized modes, in the one-dimensional Frenkel-Kontorova lattice of oscillators subject to damping and external force. The system is studied in the whole range of values of the coupling parameter, from C=0 (uncoupled limit) up to values close to the continuum limit (forced and damped sine-Gordon model). As this parameter is varied, the existence of different bifurcations is investigated numerically. Using Floquet spectral analysis, we give a complete characterization of the most relevant bifurcations, and we find (spatial) symmetry-breaking bifurcations which are linked to breather mobility, just as it was found in Hamiltonian systems by other authors. In this way moving breathers are shown to exist even at remarkably high levels of discreteness. We study mobile breathers and characterize them in terms of the phonon radiation they emit, which explains successfully the way in which they interact. For instance, it is possible to form ``bound states of moving breathers, through the interaction of their phonon tails. Over all, both stationary and moving breathers are found to be generic localized states over large values of $C$, and they are shown to be robust against low temperature fluctuations.
In this paper, interstitial migration generated by scattering with a mobile breather is investigated numerically in a Frenkel-Kontorova one-dimensional lattice. Consistent with experimental results it is shown that interstitial diffusion is more likely and faster than vacancy diffusion. Our simulations support the hypothesis that a long-range energy transport mechanism involving moving nonlinear vibrational excitations may significantly enhance the mobility of point defects in a crystal lattice.
By applying a staggered driving force in a prototypical discrete model with a quartic nonlinearity, we demonstrate the spontaneous formation and destruction of discrete breathers with a selected frequency due to thermal fluctuations. The phenomenon exhibits the striking features of stochastic resonance (SR): a nonmonotonic behavior as noise is increased and breather generation under subthreshold conditions. The corresponding peak is associated with a matching between the external driving frequency and the breather frequency at the average energy given by ambient temperature.
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