Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm (Liu \textit{et al.,} Phys. Rev. E \textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatment disregarding the intrinsic non-stationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for non-stationary stochastic processes like fBm.Comment: 8 pages, 6 figure

Complex anisotropy beneath the Peruvian flat slab from frequency-dependent, multiple-phase shear wave splitting analysis

Flat or shallow subduction is a relatively widespread global occurrence, but the dynamics remain poorly understood. In particular, the interaction between flat slabs and the surrounding mantle flow has yet to be studied in detail. Here we present measurements of seismic anisotropy to investigate mantle flow beneath the Peruvian flat-slab segment, the largest present-day region of flat subduction. We conduct a detailed shear wave splitting analysis at a long-running seismic station (NNA) located near Lima, Peru. We present measurements of apparent splitting parameters (fast direction ? and delay time ?t) for SKS, ScS, and local S phases from 80 events. We observe well-defined frequency dependence and backazimuthal variability, indicating the likely presence of complex anisotropy. Forward modeling the observations with two or three layers of anisotropy reveals a likely layer with a trench-normal fast direction underlying a layer with a more trench-oblique (to trench-subparallel) fast direction. In order to further constrain the anisotropic geometry, we analyzed the source-side splitting from events originating within the slab measured at distant stations. Beneath the flat-slab segment, we found trench-normal fast splitting directions in the subslab mantle, while within the dipping portion of the slab further to the east, likely trench-subparallel anisotropy within the slab itself. This subslab pattern contradicts observations from elsewhere in South America for “normal” (i.e., more steeply dipping) slab conditions. It is similar, however, to inferences from other shallowly dipping subduction zones around the world. While there is an apparent link between slab dip and the surrounding mantle flow, at least beneath Peru, the precise nature of the relationship remains to be clarified

Gels under stress: the origins of delayed collapse

Attractive colloidal particles can form a disordered elastic solid or gel when quenched into a two-phase region, if the volume fraction is sufficiently large. When the interactions are comparable to thermal energies the stress-bearing network within the gel restructures over time as individual particle bonds break and reform. Typically, under gravity such weak gels show a prolonged period of either no or very slow settling, followed by a sudden and rapid collapse - a phenomenon known as delayed collapse. The link between local bond breaking events and the macroscopic process of delayed collapse is not well understood. Here we summarize the main features of delayed collapse and discuss the microscopic processes which cause it. We present a plausible model which connects the kinetics of bond breaking to gel collapse and test the model by exploring the effect of an applied external force on the stability of a gel.Comment: Accepted version: 10 pages, 7 figure

Estimation, Analysis and Smoothing of Self-Similar Network Induced Delays in Feedback Control of Nuclear Reactors

This paper analyzes a nuclear reactor power signal that suffers from network induced random delays in the shared data network while being fed-back to the Reactor Regulating System (RRS). A detailed study is carried out to investigate the self similarity of random delay dynamics due to the network traffic in shared medium. The fractionality or selfsimilarity in the network induced delay that corrupts the measured power signal coming from Self Powered Neutron Detectors (SPND) is estimated and analyzed. As any fractional order randomness is intrinsically different from conventional Gaussian kind of randomness, these delay dynamics need to be handled efficiently, before reaching the controller within the RRS. An attempt has been made to minimize the effect of the randomness in the reactor power transient data with few classes of smoothing filters. The performance measure of the smoothers with fractional order noise consideration is also investigated into.Comment: 6 pages, 6 figure