Stability Properties of 1-Dimensional Hamiltonian Lattices with Non-analytic Potentials

We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from non-analytic potentials. In particular, we study the dynamics of a model governed by a "graphene-type" force law and one inspired by Hollomon's law describing "work-hardening" effects in certain elastic materials. Our main aim is to show that, although similarities with the analytic case exist, some of the local and global stability properties of non-analytic potentials are very different than those encountered in systems with polynomial interactions, as in the case of 1D Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Our approach is to study the motion in the neighborhood of simple periodic orbits representing continuations of normal modes of the corresponding linear system, as the number of particles $N$ and the total energy $E$ are increased. We find that the graphene-type model is remarkably stable up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks, yet is unstable at low energies and only attains stability at energies where the harmonic force becomes dominant. We suggest that, since our results hold for large $N$, it would be interesting to study analogous phenomena in the continuum limit where 1D lattices become strings.Comment: Accepted for publication in the International Journal of Bifurcation and Chao

Energy transport in one-dimensional oscillator arrays with hysteretic damping

Energy transport in one-dimensional oscillator arrays has been extensively studied to date in the conservative case, as well as under weak viscous damping. When driven at one end by a sinusoidal force, such arrays are known to exhibit the phenomenon of supratransmission, i.e. a sudden energy surge above a critical driving amplitude. In this paper, we study one-dimensional oscillator chains in the presence of hysteretic damping, and include nonlinear stiffness forces that are important for many materials at high energies. We first employ Reid’s model of local hysteretic damping, and then study a new model of nearest neighbor dependent hysteretic damping to compare their supratransmission and wave packet spreading properties in a deterministic as well as stochastic setting. The results have important quantitative differences, which should be helpful when comparing the merits of the two models in specific engineering applications

A Comparison of Machine Learning Methods for the Prediction of Traffic Speed in Urban Places

Rising interest in the field of Intelligent Transportation Systems combined with the increased availability of collected data allows the study of different methods for prevention of traffic congestion in cities. A common need in all of these methods is the use of traffic predictions for supporting planning and operation of the traffic lights and traffic management schemes. This paper focuses on comparing the forecasting effectiveness of three machine learning models, namely Random Forests, Support Vector Regression, and Multilayer Perceptron—in addition to Multiple Linear Regression—using probe data collected from the road network of Thessaloniki, Greece. The comparison was conducted with multiple tests clustered in three types of scenarios. The first scenario tests the algorithms on specific randomly selected dates on different randomly selected roads. The second scenario tests the algorithms on randomly selected roads over eight consecutive 15 min intervals; the third scenario tests the algorithms on random roads for the duration of a whole day. The experimental results show that while the Support Vector Regression model performs best at stable conditions with minor variations, the Multilayer Perceptron model adapts better to circumstances with greater variations, in addition to having the most near-zero errors