Dynamical symmetry breaking through AI: The dimer self-trapping transition

The nonlinear dimer obtained through the nonlinear Schrödinger equation has been a workhorse for the discovery the role nonlinearity plays in strongly interacting systems. While the analysis of the stationary states demonstrates the onset of a symmetry broken state for some degree of nonlinearity, the full dynamics maps the system into an effective [Formula: see text] model. In this later context, the self-trapping transition is an initial condition-dependent transfer of a classical particle over a barrier set by the nonlinear term. This transition that has been investigated analytically and mathematically is expressed through the hyperbolic limit of Jacobian elliptic functions. The aim of this work is to recapture this transition through the use of methods of Artificial Intelligence (AI). Specifically, we used a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition and its dependence on initial conditions. Exploitation of this result in the case of the nondegenerate nonlinear dimer gives additional information on the more general dynamics and helps delineate linear from nonlinear localization. This work shows how AI methods may be embedded in physics and provide useful tools for discovery.

A Cooperative Localization Method based on V2I Communication and Distance Information in Vehicular Networks

Relative positions are recent solutions to overcome the limited accuracy of GPS in urban environment. Vehicle positions obtained using V2I communication are more accurate because the known roadside unit (RSU) locations help predict errors in measurements over time. The accuracy of vehicle positions depends more on the number of RSUs; however, the high installation cost limits the use of this approach. It also depends on nonlinear localization nature. They were neglected in several research papers. In these studies, the accumulated errors increased with time due to the linearity localization problem. In the present study, a cooperative localization method based on V2I communication and distance information in vehicular networks is proposed for improving the estimates of vehicles’ initial positions. This method assumes that the virtual RSUs based on mobility measurements help reduce installation costs and facilitate in handling fault environments. The extended Kalman filter algorithm is a well-known estimator in nonlinear problem, but it requires well initial vehicle position vector and adaptive noise in measurements. Using the proposed method, vehicles’ initial positions can be estimated accurately. The experimental results confirm that the proposed method has superior accuracy than existing methods, giving a root mean square error of approximately 1 m. In addition, it is shown that virtual RSUs can assist in estimating initial positions in fault environments.

Distributed networked localization using neighboring distances only through a computational topology control approach

For large-scale wireless sensor networks, the nonlinear localization problem where only neighboring distances are available to each individual sensor nodes have been attracting great research attention. In general, distributed algorithms for this problem are likely to suffer from the failures that localizations are trapped in local minima. Focusing on this issue, this article considers a fully distributed algorithm by introducing a novel mechanism, where each individual node is allowed to computationally interact with a random subset of its neighbors, for helping localizations escape from local minima. Theoretical analyses reveal that with the proposed algorithm, any local minimum of the localization will be unstable, and the global optimum would finally be achieved with probability 1 after enough time of iterations. Numerical simulations are given as well to demonstrate the effectiveness of the algorithm.

Interplay of Linear and Nonlinear Localization Mechanisms in Spin-Torque Oscillators with a Field Well

The magnetization dynamics in a spin-torque oscillator with nonuniform profile of a static magnetic field creating a field well is studied by analytic calculations and numerical simulations. It is demonstrated that, in the case of sufficiently deep and narrow field well, the linear localization in the field well dominates the nonlinear self-localization, despite a negative nonlinear frequency shift. A change of the localization mechanism results in a qualitatively different dependence of the generation power on the driving current. For the dominant linear localization, the soft generation mode is realized, while, for the nonlinear self-localization, we observe a hard mode of auto-oscillator excitation. Simultaneously, a difference in the profiles of the excited spin-wave mode can become evident and distinguishable in experiments only in the case of a nonsymmetric field well.