Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers

While there are many physical processes showing subdiffusion and some useful particle models for understanding the underlying mechanisms have been established, a systematic study of subdiffusive energy transport is still lacking. Here we present convincing evidence that the energy subdiffusion and its antipersistent correlations take place in a Hamiltonian lattice system with both harmonic nearest-neighbor and anharmonic long-range interactions. We further understand the underlying mechanisms from the scattering of phonons and discrete breathers. Our result sheds new light on understanding the extremely slow energy transport.Comment: 5 pages, 5 figure

Discrete breathers assist energy transfer to ac driven nonlinear chains

One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated numerically for different amplitudes $A$ and frequencies $\omega$ within the linear phonon band. The results for the on-site potentials with hard and soft nonlinearity types are compared. For the hard-type nonlinearity, it is shown that when the driving frequency is close to (far from) the {\em upper} edge of the phonon band, the power of the energy source normalized to $A^2$ increases (decreases) with increasing $A$. In contrast, for the soft-type nonlinearity, the normalized power of the energy source increases (decreases) with increasing $A$ when the driving frequency is close to (far from) the {\em lower} edge of the phonon band. Our further demonstrations indicate that, in the case of hard (soft) anharmonicity, the chain can support movable discrete breathers (DBs) with frequencies above (below) the phonon band. It is the energy source quasi-periodically emitting moving DBs in the regime with driving frequency close to the DBs frequency, that induces the increase of the power. Therefore, our results here support the mechanism that the moving DBs can assist energy transfer from the ac driven particle to the chain.Comment: 11 pages, 13 figure

A trade-off formula in designing asymmetric neural networks

NNSF of China [11205032, 11147191, 10925525]; NSF of Fujian province [2013J05008]; Fuzhou University [022390]We show that for asymmetric neural networks the symmetric degree eta of the synaptic coupling can be related to the two main network parameters, the storage capacity alpha and another designing parameter kappa by the formula eta = alpha kappa(2). Such a relation has been well verified by the simulations of our neural network designing. The formula suggests that we cannot improve the network performances by tuning the parameters alpha and kappa simultaneously. The result may provide useful information for optimizing the designing of asymmetric neural networks