Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Compressive Sensing for Spectroscopy and Polarimetry

We demonstrate through numerical simulations with real data the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into one consistent framework. Signals are recovered thanks to a sparse reconstruction scheme from projections of the signal of interest onto appropriately chosen vectors, typically noise-like vectors. The compressibility properties of spectral lines are analyzed in detail. The results shown in this paper demonstrate that, thanks to the compressibility properties of spectral lines, it is feasible to reconstruct the signals using only a small fraction of the information that is measured nowadays. We investigate in depth the quality of the reconstruction as a function of the amount of data measured and the influence of noise. This change of paradigm also allows us to define new instrumental strategies and to propose modifications to existing instruments in order to take advantage of compressive sensing techniques.Comment: 11 pages, 9 figures, accepted for publication in A&

Stress-dependent electrical transport and its universal scaling in granular materials

We experimentally and numerically examine stress-dependent electrical transport in granular materials to elucidate the origins of their universal dielectric response. The ac responses of granular systems under varied compressive loadings consistently exhibit a transition from a resistive plateau at low frequencies to a state of nearly constant loss at high frequencies. By using characteristic frequencies corresponding to the onset of conductance dispersion and measured direct-current resistance as scaling parameters to normalize the measured impedance, results of the spectra under different stress states collapse onto a single master curve, revealing well-defined stress-independent universality. In order to model this electrical transport, a contact network is constructed on the basis of prescribed packing structures, which is then used to establish a resistor-capacitor network by considering interactions between individual particles. In this model the frequency-dependent network response meaningfully reproduces the experimentally observed master curve exhibited by granular materials under various normal stress levels indicating this universal scaling behaviour is found to be governed by i) interfacial properties between grains and ii) the network configuration. The findings suggest the necessity of considering contact morphologies and packing structures in modelling electrical responses using network-based approaches.Comment: 12 pages, 4 figure