Search Results (4)

The signal detection problem for cyclostationary signals is addressed within the fraction-of-time probability framework, where statistical functions are constructed starting from a single time series, without introducing the concept of stochastic process. Single-cycle detectors and quadratic-form detectors based on measurements of the Fourier coefficients of the almost-periodically time-variant cumulative distribution and probability density functions are proposed. The adopted fraction-of-time approach provides both methodological and implementation advantages for the proposed detectors. For single-cycle detectors, the decision statistic is a function of the received signal and the threshold is derived using side data under the null hypothesis. For quadratic-form detectors, the decision statistic can be expressed as a function of the received signal without using side data, at the cost of some performance degradation. The threshold can be derived analytically. Performance analysis is carried out using Monte Carlo simulations in severe noise and interference environments, where the proposed detectors provide better performance with respect to the analogous detectors based on second- and higher-order cyclic statistic measurements. Full article

The Gulf of California (GC) is the only interior sea in the Eastern Pacific Ocean and is the most important fishing area in the northwestern region of the Mexican Pacific. This study focuses on the oceanographic variability of the GC, including its southern portion, which is an area with a high flow of energy and exchange of properties with the Pacific Ocean (PO), in order to determine its role in physical–biological cycles and climate change. The purpose of this work is to analyze the sea surface temperature (SST) and chlorophyll a concentration (Chl-a) during the period from 1998–2022 as indicators of long-term physical and biological processes, oceanographic variability, and primary production in the GC. In total, 513 subareas in the GC were analyzed, and a cluster analysis was applied to identify similar areas in terms of SST and Chl-a via the K-means method and using the silhouette coefficient (>0.5) as a metric to validate the clusters obtained. The trends of the time series of both variables were analyzed, and a fast Fourier analysis was performed to evaluate cycles in the series. A descriptive analysis of the SST and Chl-a series showed that the SST decreased from south to north. Six bioregions were identified using a combined of both SST and Chl-a data. The spectral analysis of the SST showed that the main frequencies in the six bioregions were annual and interannual (3–7 years), and the frequencies of their variations were associated with basin-level weather events, such as El Niño and La Niña. The SST in the GC showed a heating trend at an annual rate of ~0.036 °C (~0.73 °C in 20 years) and a decrease in Chl-a at an annual rate of ~0.012 mg/m³ (~0.25 mg/m³ in 20 years), with potential consequences for communities and ecosystems. Additionally, cycles of 10–13 and 15–20 years were identified, and the 10–13-year cycle explained almost 40–50% of the signal power in some regions. Moreover, mesoscale features (eddies and filaments) were identified along the GC, and they were mainly associated with the clusters of the SST. All these spatial and temporal variabilities induce conditions that generate different habitats and could explain the high biodiversity of the GC. If the warming trend of the SST and the decreasing trend of the Chl-a continue in the long term, concerns could be raised, as they can have important effects on the dynamics of this important marine ecosystem, including habitat loss for numerous native species, declines in the catches of the main fishery resources, and, consequently, support for the arrival of harmful invasive species. Full article

Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space and one-time dimensions (1+1 NLS) is an important tool in this analysis. We demonstrate that small-time asymptotic spectral solutions of the 2+1 NLS equation can be constructed as the nonlinear superposition of many 1+1 NLS equations, each corresponding to a particular radial direction in the directional spectrum of the waves. The radial 1+1 NLS equations interact nonlinearly with one another. We determine practical asymptotic spectral solutions of the 2+1 NLS equation that are formed from the ratio of two phase-lagged Riemann theta functions: Surprisingly this construction can be written in terms of generalizations of periodic Fourier series called (1) quasiperiodic Fourier (QPF) series and (2) almost periodic Fourier (APF) series (with appropriate limits in space and time). To simplify the discourse with regard to QPF and APF Fourier series, we call them NLF series herein. The NLF series are the solutions or approximate solutions of the nonlinear dynamics of water waves. These series are indistinguishable in many ways from the linear superposition of sine waves introduced theoretically by Paley and Weiner, and exploited experimentally and theoretically by Barber and Longuet-Higgins assuming random phases. Generally speaking NLF series do not have random phases, but instead employ phase locking. We construct the asymptotic NLF series spectral solutions of 2+1 NLS as a linear superposition of sine waves, with particular amplitudes, frequencies and phases. Because of the phase locking the NLF basis functions consist not only of sine waves, but also of Stokes waves, breather trains, and superbreathers, all of which undergo complex pair-wise nonlinear interactions. Breather trains are known to be associated with rogue waves in solutions of nonlinear wave equations. It is remarkable that complex nonlinear dynamics can be represented as a generalized, linear superposition of sine waves. NLF series that solve nonlinear wave equations offer a significant advantage over traditional periodic Fourier series. We show how NLFA can be applied to numerically model nonlinear wave motions and to analyze experimentally measured wave data. Applications to the analysis of SINTEF wave tank data, measurements from Currituck Sound, North Carolina and to shipboard radar data taken by the U. S. Navy are discussed. The ubiquitous presence of coherent breather packets in many data sets, as analyzed by NLFA methods, has recently led to the discovery of breather turbulence in the ocean: In this case, nonlinear Fourier components occur as strongly interacting, phase locked, densely packed breather modes, in contrast to the previously held incorrect belief that ocean waves are weakly interacting sine waves. Full article

A series of poly(lactic acid) (PLA) and poly(lactic acid)-based bio-composites (sisal PLA) were prepared and studied by spectroscopic and microscopic techniques as such and after immersion at room temperature in different degradation mediums (i.e., distilled and natural sea water and solutions at pH = 2, 6, and 8). In these conditions, some of their macroscopic and microscopic properties were monitored during a period of 30 days. Water absorption increased with the increasing fiber content regardless of the immersion medium. The maximum water absorption was achieved at pH = 8 (~16%), indicating a more severe action of the alkaline mediums on the samples. The diffusivity, D, of PLA decreased with the addition of fibers and acidic mediums showed higher D, indicating higher diffusivity of water through the specimens with respect to those submerged in moderate or alkaline mediums. Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM) analysis evidenced a weak interaction between the PLA matrix and the sisal fibers. Very limited degradation phenomena occur in our conditions: Despite some changes in the microstructure, the PLA backbone seems to be largely resistant to hydrolysis, almost regardless of the pH value and even at the highest sisal content. Full article