Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.

Partial spectral and temporal coherence of plane-wave pulse trains in second-harmonic generation

We study the spectral and temporal coherence effects in the passage of a Gaussian Schell-model (GSM) scalar, plane-wave pulse train through a slab of nonlinear optical crystal exhibiting second-harmonic generation. We show that due to the nonlinear interaction the temporal and spectral degrees of coherence of the fundamental (F) and second-harmonic (SH) pulse trains at the exit facet may deviate markedly from the GSM and the global degree of coherence of the SH wave generally decreases with increasing incident F beam intensity. In addition, we find that due to the partial coherence of the incident GSM field the transmitted SH wave may show a double-peaked intensity distribution.

Displacement-Time Graph of a Point on a Wave Pulse

Using a linear substitution of distance by velocity and time, it is shown how a displacement-time profile of a particle on a wave pulse is graphed.

Temporal and Spatial Development of the EM Field in a Shielding Enclosure with Aperture after Transient Interference Caused by a Subnanosecond High-Energy EM Plane Wave Pulse

A proper assessment of the shielding effectiveness of an enclosure with aperture under subnanosecond transient interference requires a better understanding of the coupling and development mechanisms of the EM field induced inside the enclosure. In this paper, the results of a numerical study of the temporal and spatial development of the electromagnetic (EM) field in a shielding enclosure with aperture after transient interference caused by a subnanosecond high-energy EM plane wave pulse are presented. The interference pulse had Gaussian distribution of the electric and magnetic fields with amplitudes of 106 V/m and 2.68·103 A/m, respectively. The maximum pulse power density was 2.68 GW/m2. The novelty of this study was 2D and 3D images, which visualized the temporal and spatial build-up of electric and magnetic fields in the shielding enclosure within 90 ns after the transient interference. This is 58 times longer than the time needed by any EM wave to travel the distance between the front and rear walls of the enclosure. The presented images, showing the EM field morphology over a relatively long period of time, were crucial for understanding the EM field build-up process inside the shielding enclosure with aperture. They revealed the existence of two unknown phases of the EM field build-up in the enclosure with aperture. We call these two phases the wave phase and the interference phase. In the wave phase, the EM field is generated in the form of so-called primary and secondary wave pulses, traveling towards the enclosure rear wall. In the interference phase, the EM field has the form of temporally and spatially varying pulse-like interference (size-limited) patterns of the associated electric and magnetic fields. The EM field induced in the enclosure is long-lasting compared to the interference pulse duration. The amplitudes of the electric and magnetic fields decreased about threefold in 5 ns and 30-fold in 90 ns, thus exhibiting a severe EM hazard for much longer than the external interference duration. For a long period of time, the highest EM field amplitudes would change their locations in the enclosure, which makes it difficult to assess the shielding effectiveness on the basis of classical definitions. The existence of the long-lasting temporally and spatially varying EM field induced in the enclosure with aperture by the subnanosecond transient interference, visualized in detail in this paper, confirms that a new definition and measurement methods of shielding effectiveness under transient conditions are needed. The obtained results provide a source of data that can be useful when working on the introduction of time-domain parameters to evaluate the transient shielding effectiveness in the case of the ultrashort EM interference.