Modern methods of direct numerical simulations of transfer processes in random media

The paper considers the methods of direct numerical investigation of the behaviour of dynamical systems of explosive type under the influence of random noise. Dynamical systems are described by a system of nonstationary ordinary differential equations (ODE). The dynamics of the system, taking into account random noise, is described by a system of stochastic ordinary differential equations (SODE). The paper provides an overview of modern algorithms based on modifications of Runge – Kutta integration methods. The features of the analysis of weak and strong convergence of the SODE integration methods are described. Methods for generating random noise with complex temporal structure (color noise) are described. The method of numerical solution of the system of SODE is used to generate random color noise. Examples of the study of the influence of random noise on biological and mechanical systems of explosive type are presented. It is shown that random noises acting on such systems qualitatively change the character of their behaviour.

Response Analysis of Asymmetric Monostable Harvesters Driven by Color Noise and Band-Limited Noise

In this paper, we investigate the response of asymmetric potential monostable energy harvesters (MEHs) excited by color noise and band-limited noise. The motivation for this study is that environmental vibrations always have the characteristic of randomness, and it is difficult to modulate a perfectly symmetric MEH. For the excitation of exponentially correlated color noise, the moment differential equation was applied to evaluate the output performance of the asymmetric potential MEHs. Numerical and theoretical analyses were carried out to investigate the influence of noise intensity and internal system parameters on the output power of the system. Our results demonstrate that the output performance of the asymmetric MEH decreases with the increase in the correlation time, which determines the character of the color noise. On the contrary, the increase in the asymmetric degree enhances the output power of the asymmetric MEH subjected to color noise. For the band-limited noise excitation, numerical simulation is undertaken to consider the response of the asymmetric MEHs, and outcomes indicate that the frequency bandwidth and center frequency have a significant influence on the output performance. Regarding the asymmetric potential, its appearance leads the MEHs to generate higher output power at lower frequencies and this phenomenon is more obvious with the increase in the degree of asymmetry. Finally, we observed that the characteristics of the response bandwidth of asymmetric MEHs subjected to band-limited noise excitation are similar to the response under harmonic excitation.

A fourth-order cumulant orthonormal propagator rooting method based on Toeplitz approximation

A novel Toeplitz fourth-order cumulant (FOC) orthonormal propagator rooting method (TFOC ‐ OPRM) of direction-of-arrival (DOA) estimation for uniform linear array (ULA) is proposed in this paper. Specifically, the modified (i.e., reduced-dimension) FOC (MFOC) matrix is achieved at first via removing the redundant information encompassed in the primary FOC matrix; then, the TFOC matrix which possesses Toeplitz structure can be recovered by utilizing the Toeplitz approximation method. To reduce the computational complexity, an effective method based on the polynomial rooting technology is adopted. Finally, the DOAs of incident signals can be estimated by exploiting orthonormal propagator rooting method. The theoretical analysis coupled with simulation results show that the proposed resultant algorithm can reduce the computational complexity significantly, as well as improve the estimation performance in both spatially white noise environment and spatially color noise environment.

Data Adaptive Analysis on Vertical Surface Deformation Derived from Daily ITSG-Grace2018 Model

With the widely used monthly gravity models, it is hard to determine the sub-monthly variations. Thanks to the high temporal resolution, a daily ITSG-Grace2018 gravity model is employed to derive the vertical deformation of the China region in 1.0° × 1.0° grids. The standard deviations of residuals between the daily and monthly averaged displacement range from 1.0 to 3.5 mm, reaching half of the median residuals, which indicates that a higher temporal resolution gravity model is quite necessary for the analysis of crustal displacement. For the signal analysis, traditional least square (LS) is limited in its analysis of signals with constant amplitude. However, geophysical signals in a geodetic time series usually fluctuate over long periods, and missing data happen. In this study, the data adaptive approach called enhanced harmonic analysis (EHA), which is based on an Independent Point (IP) scheme, is introduced to deal with these issues. To demonstrate the time-varying signals, the relative differences between EHA and LS are calculated. It illustrates that the median percentage of epochs at grids with a relative difference larger than 10% is 69.7% and the proportions for the ranges of 30%, 50%, and 70% are about 30.1%, 18.4%, and 13.0%, respectively. The obvious discrepancy suggests the advantage of EHA over LS in obtaining time-varying signals. Moreover, the spatial distribution of the discrepancy also demonstrates the regional characteristics, suggesting that the assumption of constant amplitude is not appropriate in specific regions. To further validate the effectiveness of EHA, the comprehensive analysis on the different noise types, number of IPs, missing data, and simultaneous signals are carried out. Specifically, EHA can deal with series containing white or color noise, although the stochastic model for the color noise should be modified. The signals are slightly different when selecting different numbers of IPs within a range, which could be accepted during analysis. Without interpolation, EHA performs well even with continuously missing data, which is regarded as its feature. Meanwhile, not only a single signal but also simultaneous signals can be effectively identified by EHA.

A Fourth-Order Cumulants Orthonormal Propagator Rooting Method Based on Toeplitz Approximation

A novel Toeplitz fourth-order cumulantsAorthonormal propagator rooting method of direction-of-arrivalnestimation for uniform linear arrayois proposed in this paper. Specifically, the modified (i.e., reduced-dimension)vmatrix is achieved at first via removing the redundant information encompassed in the primaryematrix, then the lmatrix which possesses Toepltiz structure can be recovered by utilizing the Toepltiz approximation method. To reduce the computational complexity, an effective method based on the polynomial rooting technology is adopted. Finally, the DOAs of incident signals can be estimated by exploiting orthonormal propagator rooting method. The theoretical analysis coupled with simulation results show that the proposed resultant algorithm can reduce the computational complexity signify- cantly, as well as improve the estimation performance in both spatially-white noise environment and spatially-color noise environment.

A Fourth-Order Cumulants Orthonormal Propagator Rooting Method Based on Toeplitz Approximation

A novel Toeplitz fourth-order cumulants (\operatorname{FOC} ) orthonormal propagator rooting method {\text{(TFOC-OPRM)}} to direction-of-arrival (DOA) estimation for uniform linear array (ULA) is addressed in this paper. Specifically, the modified (reduced-dimension) FOC{\kern 1pt} {\kern 1pt} (MFOC) matrix is achieved at first via removing the redundant information encompassed in the primary FOC matrix, and then the TFOC matrix which possesses Toepltiz structure can be recovered by utilizing the Toepltiz approximation method. To reduce computational complexity, we adopt an effective method which depends on the polynomial rooting technology. Finally, the DOAs of incident signals can be estimated by exploiting orthonormal propagator rooting method. The theoretical analysis coupled with simulation results show that the proposed resultant algorithm can reduce computational complexity significantly, as well as improve the estimation performance in both spatially-white noise and spatially-color noise environments.

Chameleonic noise in GPS position series: what is the true color of the GPS error spectra?

<p><em>Chameleonic: readily changing color or other attributes.</em></p><p><em>Chameleon: a lizard that changes skin color to match what surrounds it so that it cannot be seen.</em></p><p>The error spectrum of decadal long GPS position time series is typically represented by a combination of flicker (pink) noise at long periods and white noise at short periods. It is known that when fitting a linear trend to the series, part of the flicker noise at the longest observed period will be absorbed by the trend. Here, using real and synthetic GPS position series, we show how the error spectrum is even more altered by the position discontinuities that populate the series. The fitted position offsets at the discontinuity epochs absorb a significant portion of the power spectrum at periods longer than the separation between the discontinuity epochs. The resulting error spectrum is flattened at long periods and this implies that:</p><ul><li>the estimated content of colored noise is biased low and can even apparently change its color towards whiter noise, i.e. the true noise color is not observable due to the discontinuities,</li> <li>the red (random walk) noise , most probably present in the series in small quantity, becomes undetectable even if long series are used,</li> <li>the pink (flicker) noise is not the best color noise to represent the error spectrum in long series containing discontinuities,</li> <li>the colored noise content cannot be compared between series with different sets of discontinuities.</li> </ul><p>These findings need to be considered when comparing the noise levels between series from different solutions, networks or monuments. In particular, and contrary to a recently published recommendation, station operators should make every effort to avoid adding new discontinuities into their station time series if reliable velocity estimates are expected.</p>