Nonstationary Field Research Articles

Free and Forced Oscillations of Charged Particles in the Presence of Inertially Nonstationary Fast Oscillating Quadrupole Electric Fields

Free and forced oscillations of charged particles in the presence of inertially nonstationary quadrupole HF electric fields are studied. Polyharmonic oscillations of charged particles in the presence of fast oscillating fields with slowly varying parameters are represented using a model of a nonstationary harmonic oscillator with the aid of linear relationships of the coefficients of series that serve as solutions to the Mathieu differential equation. The Green function is used to derive expressions for resonance oscillations of charged particles in the presence of nonstationary HF fields with superimposed uniform excitation fields. A particular case of a polyharmonic oscillator with a linearly varying natural oscillation frequency is considered, and expressions for parameters of the excitation function are derived. Analytical expressions are proven by the results of computer simulation.

Effect of spatially variable saturated hydraulic conductivity with non-stationary characteristics on the stability of reservoir landslides

Conventional landslide analyses, based on deterministic methods or simple random variable methods, cannot consider the spatial variability and the depth-dependent nature of saturated hydraulic conductivity (Ks) in accumulative landslides. However, studies show that these conditions exist objectively and have a large impact on the seepage and deformation of landslides. Thus, the non-stationary characteristics of Ks need to be properly accounted for. In this paper, the Baishuihe landslide is taken as a case study. First, based on surface nuclear magnetic resonance (surface-NMR) technology, spatial variability and the depth-dependent nature of the Ks are obtained. Then, a non-stationary random field model is established to model the trend and fluctuating components of the Ks individually, and a deterministic model is established to model the trend of the Ks with depth. Finally, numerical simulations of the stochastic model and deterministic model under reservoir water fluctuation conditions are carried out by the non-intrusive stochastic finite element method, and the seepage-deformation and stability characteristics of the landslide are analyzed. The results show that compared with that in the deterministic model, the change in pore pressure in the stochastic model obviously lags, during reservoir water drawdown, the displacement of the trailing edge in the stochastic model is larger than that in the deterministic model, with increasing reservoir water deceleration, the hysteresis of the pore pressure in the stochastic model is more notable, and the deformation is larger and the stability is worse in the stochastic model. It is demonstrated that ignoring the spatial variability of the Ks will overestimate the stability of the landslide.

Stochastic response of a cable-stayed bridge under non-stationary winds and waves using different surrogate models

The prediction of the structural stochastic response under strong winds and waves is important in the design of cross-sea bridges with longer spans, while the non-stationary characteristics of winds and waves may affect the accuracy. This paper investigates the effects of non-stationary winds and waves on the stochastic response of a cable-stayed bridge based on a wind-wave-bridge (WWB) system. In order to improve the computational efficiency, three surrogate models, i.e., the support vector regression (SVR), the BP neural network (BPN), and the Gaussian process regression (GPR), are established by correlating the environmental parameters with the bridge response. A comparison among the three models is conducted to find the optimal one, and the effects of the mean wind speed, the significant wave height, and the peak wave period on the bridge response are further investigated. The bridge responses of the stationary wind and wave fields are 0.05%–16% larger than those of the non-stationary wind and wave fields. Different surrogate models are applicable to different parts of the bridge. The SVR, BPN, and GPR models are recommended for predicting the response of the tower, the foundation, and the girder, respectively, and the sensitivity analysis reveals the effects of non-stationary winds and waves.

A non-stationary random field model for earthquake slip

The present work aims at building a non-stationary random field model for the slip distribution on the rupture plane. The estimates are arrived based on 230 slip fields available in the SRCMOD database. The evaluation is performed by segregating and quantifying the trend and fluctuation components of the field. Here, the trend portion of the slip is extracted by fitting a 2D elliptical Gaussian surface. The remaining fluctuation part is observed to be stationary following a normal distribution. Further, we propose scaling relations as a function of magnitude for all the unknowns in trend and fluctuation part of the field. Furthermore, an additive model to generate a slip field for a given magnitude combining the deterministic trend part and randomly generated fluctuation part is also developed in the study. Ground motion simulations performed with the components of the slip field showed that the trend portion controls the low frequency, and the fluctuation portion influences the high-frequency characteristics of ground motion. The model developed from the study can be used to generate an ensemble of slip fields for ground motion simulations.

Simulation of nonstationary wind in one-spatial dimension with time-varying coherence by wavenumber-frequency spectrum and application to transmission line

Practical non-synoptic fluctuating wind often exhibits nonstationary features and should be modeled as nonstationary random processes. Generally, the coherence function of the fluctuating wind field has time-varying characteristics. Some studies have shown that there is a big difference between the fluctuating wind field of the coherent function model with and without time variability. Therefore, it is of significance to simulate nonstationary fluctuating wind field with time-varying coherent function. However, current studies on the numerical simulation of nonstationary fluctuating wind field with time-varying coherence are very limited, and the proposed approaches are usually based on the traditional spectral representation method with low simulation efficiency. Especially, for the simulation of multi-variable wind field of large span structures such as transmission tower-line, not only the simulation is inefficient but also the matrix decomposition may have singularity problem. In this paper, it is proposed to conduct the numerical simulation of nonstationary fluctuating wind field in one-spatial dimension with time-varying coherence based on the wavenumber-frequency spectrum. The simulated multivariable nonstationary wind field with time-varying coherence is transformed into one-dimensional nonstationary random waves in the simulated spatial domain, and the simulation by wavenumber frequency spectrum is derived. So, the proposed simulation method can avoid the complicated Cholesky decomposition. Then, the proper orthogonal decomposition is employed to decompose the time-space dependent evolutionary power spectral density and the Fourier transform of time-varying coherent function, simultaneously, so that the two-dimensional Fast Fourier transform can be applied to further improve the simulation efficiency. Finally, the proposed method is applied to simulate the longitudinal nonstationary fluctuating wind velocity field along the transmission line to illustrate its performances.

Importance of Distribution Type on Bearing Capacity of an Embedded Foundation in Spatially Varying Soils

The objective of this paper is to investigate the effect of soil variability on bearing capacity of an embedded foundation in the presence of nonstationary undrained shear strength. The nonstationary undrained shear strength is simulated by a nonstationary random field generator based on the spectral representation method. An embedded foundation buried into the soil to two times of width is presented to investigate the influence of spatially variable undrained shear strength on bearing capacity. Firstly, Monte Carlo simulations are carried out to discuss the effect of distribution type, nonstationary gradient parameter, and horizontal autocorrelation length on the bearing capacity from the standpoint of mean value and standard deviation. Then, the influence of the distribution type on the failure probability of nonstationary random soil is also investigated, with the failure probability for the Beta distribution being demonstrated to be always larger than that for the Lognormal and Gamma distribution.

ON THE NATURE OF A CLASSICAL PSEUDODIFFERENTIAL EQUATION

The work is devoted to the study of the general nature of one classical parabolic pseudodi- fferential equation with the operator M.Rice of fractional differentiation. At the corresponding values of the order of fractional differentiation, this equation is also known as the isotropic superdiffusion equation. It is a natural generalization of the classical diffusion equation. It is also known that the fundamental solution of the Cauchy problem for this equation is the density distribution of probabilities of stable symmetric random processes by P.Levy. The paper shows that the fundamental solution of this equation is the distribution of probabilities of the force of local influence of moving objects in a nonstationary gravitational field, in which the interaction between masses is subject to the corresponding potential of M.Rice. In this case, the classical case of Newton’s gravity corresponds to the known nonstationary J.Holtsmark distribution.

A New Rapid Method of Determining the Thermal Diffusivity of Materials and Finished Articles

A new nonstationary nondestructive rapid method of determining the thermal diffusivity of materials and finished articles has been suggested and tested experimentally without cutting out samples from them and preparation of the latter. The method is based on using an infrared imager to video record the infrared radiation of the surface originating as a result of its local stepwise heating by, say, a focused laser beam. Subsequent computer processing of the patterns of the nonstationary thermal field by the developed models and algorithms makes it possible to determine the thermal diffusivity of a material or an article in the case of one-sided access to them.

Personalized brain revascularization: computer modeling of the reconstruction zone for carotid endarterectomy

To develop a technique of computer modeling of hemodynamics before conventional CEE. Classical CEE is performed according to conventional patch technique. Duplex parameters of stenosis and blood flow velocity in the carotid arteries were analyzed by using of a linear transducer 7-7.5 MG (Acuson 128XP scanner, Acuson, USA). Multispiral computed tomography with angiography and subsequent processing of data using the Clear canvas software were performed to visualize the main geometric characteristics of the carotid arteries and features of atherosclerotic plaque. Blood flow hemodynamics is essential in the occurrence of postoperative restenosis. Therefore, computer simulation of blood flow using CFD (Computational Fluid Dynamics) methods based on particular patient's data makes it possible to assess localization of zones with high risk of restenosis. CFD approach implies construction of blood flow parameters at absolutely every point of the vessel considering geometric shape of the vessel and flow characteristics at the entrance and exit from the vessel. Pressure curves at the inlet and outlet are constructed using blood flow velocity curves. Pressure curves are subsequently used in the CFD model. The result of blood flow CFD modeling is non-stationary three-dimensional fields of pressure and velocity in the investigated area. Visual analysis of blood flow dynamics in these fields makes it possible to judge possible problem areas along the blood flow and on the inner wall of the vessel. Patch technique of classical CEE is characterized by great risk of parietal thrombosis and hyperproliferation of neointima that explains more frequent development of restenosis. Computer modeling is valuable to consider some important technical aspects in implementation of various surgical techniques for carotid artery reconstruction. This result demonstrates an importance of achieving the optimal ratio of the diameter of common, internal and external carotid arteries. Modification of patch based on computer simulation is required for these purposes.

Evolution equations of translational-rotational motion of a non-stationary triaxial body in a central gravitational field

The translational-rotational motion of a triaxial body with constant dynamic shape and variable size and mass in a non-stationary Newtonian central gravitational field is investigated. Differential equations of motion of the triaxial body in the relative coordinate system with the origin at the center of a non-stationary spherical body are obtained. The axes of the Cartesian coordinate system fixed to the non-stationary triaxial body are coincident with its principal axes and their relative orientation is assumed to remain unchanged in the course of evolution. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is obtained. Differential equations of translational-rotational motion of the non-stationary triaxial body are derived in Jacobi osculating variables and are studied with the perturbation theory methods. The perturbing function is expanded in power series in terms of the Delaunay–Andoyer elements up to the second harmonic element inclusive. The evolution equations of the translational-rotational motion of the non-stationary triaxial body are obtained in the osculating elements of Delaunay–Andoyer.

Nonstationary Porosity and Density Fields at the Stage of Withdrawal of An Acid Solution from a Carbonate Stratum

The authors have considered the problem on concentration fields of hydrochloric acid with account taken of the chemical reaction as applied to the stage of withdrawal of the active solution from a carbonate stratum. Analytical expressions to determine the porosity of the carbonate skeleton and the density of the hydrochloric acid solution, which are applicable for engineering calculations, have been found with account of the preceding technological processes. The results of computational experiments on the process of acidic stimulation have been analyzed, and it has been shown that the obtained dependences can be used for calculations of cyclic stimulation of oil and gas reservoirs, which is implemented to enhance the oil recovery.

ОПРЕДЕЛЕНИЕ НЕСТАЦИОНАРНОГО ТЕМПЕРАТУРНОГО ПОЛЯ КОЛЕСА ПАССАЖИРСКОГО ВАГОНА ПРИ ТОРМОЖЕНИИ

The paper is devoted to modeling of nonstationary field of a passenger car wheel at braking. The calculation is based on formulation of thermal conductivity equation for the wheel tread as a curved rod with the application of linear approximation of thermal field. At formulation of thermal conductivity equation it is necessary to consider a balance of heat in small volume of tread with the consideration for thermal flow from braking shoe, thermal emission to the environment and thermal conductivity in circular direction. The authors have set for the initial equation of thermal conductivity a functional and have formulated conditions of stationarity that leads after integration to the system of the first order differential equations of time. The authors have applied the Euler method at integration. The developed method has been realized in the C++ program. With the use of this application the authors have conducted a research of the thermal field of the passenger car wheel. The method can be used at designing of new rolling stock and for the analysis of reasons of flaws appearance on the surface of car wheels.

Multilevel approximation of Gaussian random fields: Fast simulation

We propose and analyze several multilevel algorithms for the fast simulation of possibly nonstationary Gaussian random fields (GRFs) indexed, for example, by the closure of a bounded domain [Formula: see text] or, more generally, by a compact metric space [Formula: see text] such as a compact [Formula: see text]-manifold [Formula: see text]. A colored GRF [Formula: see text], admissible for our algorithms, solves the stochastic fractional-order equation [Formula: see text] for some [Formula: see text], where [Formula: see text] is a linear, local, second-order elliptic self-adjoint differential operator in divergence form and [Formula: see text] is white noise on [Formula: see text]. We thus consider GRFs on [Formula: see text] with covariance operators of the form [Formula: see text]. The proposed algorithms numerically approximate samples of [Formula: see text] on nested sequences [Formula: see text] of regular, simplicial partitions [Formula: see text] of [Formula: see text] and [Formula: see text], respectively. Work and memory to compute one approximate realization of the GRF [Formula: see text] on the triangulation [Formula: see text] of [Formula: see text] with consistency [Formula: see text], for some consistency order [Formula: see text], scale essentially linearly in [Formula: see text], independent of the possibly low regularity of the GRF. The algorithms are based on a sinc quadrature for an integral representation of (the application of) the negative fractional-order elliptic “coloring” operator [Formula: see text] to white noise [Formula: see text]. For the proposed numerical approximation, we prove bounds of the computational cost and the consistency error in various norms.

Nonlinear flutter control of a long-span closed-box girder bridge with vertical stabilizers subjected to various turbulence flows

This study investigated the influence of different heights of upward vertical central stabilizers (UVCS) in flutter performance of long-span suspension bridges through developing nonlinear three-dimensional Finite Element (FE) bridge model using large-deformation beam elements with 14 degrees of freedom (DOFs). Using Runyang Yangtze River Bridge as a case study, the developed FE model firstly incorporates a nonlinear aerodynamic force model of the 2D closed-box girder with various UVCS, and the model predicted critical flutter wind velocities of the bridges were validated using wind tunnel testing results. A series of parametric studies were then carried out to study the aerodynamic performance of the bridge under different vertical intensities of incoming turbulence flow (Iw) by developing multi-variable non-stationary stochastic wind fields. The numerical results show that the installation of UVCS could not only modify from first-order to second-order symmetrical vertical oscillation configuration, but also change the coupled oscillation from the stable condition to the unstable limit cycle of flutter divergence. Furthermore, UVCS mainly governs the vertical DOF partication in the coupled bending-torsional oscillation of the bridge, while the increase of the height of UVCS results in a higher critical flutter wind velocity but a lower torsional frequency, particularly for the 1.1 m UVCS when Iw is over 2.84%.

Numerical analysis of layered composite panel behavior with interlaminar defects subject to dynamic loads

Aims of research. Polymer unidirectional composite laminate panel behavior with interlaminate defects under action of different dynamic loads is consider. Methods. Normal modes and eigenvalues of rectangular composite panels in the presence multiple delamination different sizes ellipsoidal form are calculated. The dependences of the maximum deflections from the frequency of the stationary pressure field action are constructed. Distribution field of panels plies failure index under action of nonstationary pressure field by using different failure criteria for composites is determined. Results. Modeling methodology composite panels behavior in the presence multiple interlaminar defects under action of different dynamic loads is developed. Analysis of failure panel with the use of different failure criteria for composites is carried out.

Non-Stationary Turbulent Wind Field Simulation of Long-Span Bridges Using the Updated Non-Negative Matrix Factorization-Based Spectral Representation Method

Numerical simulation of the turbulent wind field on long-span bridges is an important task in structural buffeting analysis when it comes to the system non-linearity. As for non-stationary extreme wind events, some efforts have been paid to update the classic spectral representation method (SRM) and the fast Fourier transform (FFT) has been introduced to improve the computational efficiency. Here, the non-negative matrix factorization-based FFT-aided SRM has been updated to generate not only the horizontal non-stationary turbulent wind field, but also the vertical one. Specifically, the evolutionary power spectral density (EPSD) is estimated to characterize the non-stationary feature of the field-measured wind data during Typhoon Wipha at the Runyang Suspension Bridge (RSB) site. The coherence function considering the phase angles is utilized to generate the turbulent wind fields for towers. The simulation accuracy is validated by comparing the simulated and target auto-/cross-correlation functions. Results show that the updated method performs well in generating the non-stationary turbulent wind field. The obtained wind fields will provide the research basis for analyzing the non-stationary buffeting behavior of the RSB and other wind-sensitive structures in adjacent regions.

Electromagnetic Burst Generation during Annihilation of Magnetic Field in Relativistic Laser-Plasma Interaction

We present the results of theoretical studies of formation and evolution of the current sheet in a colliosionless plasma during magnetic reconnection in relativistic limit. Relativistic magnetic reconnection is driven by parallel laser pulses interacting with underdense plasma target. Annihilation of laser created magnetic field of opposite polarity generates strong non-stationary electric field formed in between the region with opposite polarity magnetic field accelerating charged particles within the current sheet. This laser-plasma target configuration is discussed in regard with the laboratory modeling of charged particle acceleration and gamma flash generation in astrophysics. We present the results of 3-dimensional kinetic simulations and theoretical studies on the formation and evolution of the current sheet in a collisionless plasma during magnetic field annihilation in the ultra-relativistic limit. Annihilation of oppositively directed magnetic fields driven by two laser pulses interacting with underdense plasma target is accompanied by an electromagnetic burst generation. The induced strong non-stationary longitudinal electric field accelerates charged particles within the current sheet. Properties of the laser-plasma target configuration are discussed in the context of the laboratory modeling for charged particle acceleration and gamma flash generation in astrophysics.

Методика побудови розв’язку двовимірної задачі електродинаміки для електропровідного тіла з плоскопаралельними межами за дії зов-нішнього нестаціонарного електромагнітного поля

A two-dimensional initial-boundary value problem of electrodynamics for an electroconductive non-ferromagnetic body with planar-parallel boundaries is formulated under the action of an external non-stationary electromagnetic field. The electromagnetic field is given by the values of the inhomogeneous longitudinal coordinate of the component of the magnetic field intensity vector at its bases. To construct a general solution of the formulated initial boundary value problem under such electromagnetic action, a cubic approximation by thickness coordinate and an integral Fourier transform along a longitudinal coordinate was used for a key function — a given component of the magnetic field intensity vector. As a result, the initial two-dimensional initial boundary value problem for the key function is reduced to the one-dimensional initial boundary value problem. This initial boundary value problem is on the integral key function. These characteristics are the functions of time variable and the thickness coordinate. The coefficients of the polynomial approximating the key function are given by the transformants of the integral characteristics of the key function and given its values on the bases of the body as corresponding functions of time and longitudinal coordinate. The general solutions of the one-dimensional initial boundary value problem are obtained as a convolution of functions. These functions describe homogeneous solutions and key function boundary values on the bases of the body. Using the inverse Fourier transforms, the solution of the original electrodynamics problem under the action of an arbitrary variable in time and by the longitudinal coordinate of a non-stationary electromagnetic field is written. On the basis of such a common solution, as a partial case, we also write the solutions of the original two-dimensional initial boundary value problem under the action of a stationary harmonic in time variable electromagnetic field. In order to improve the accuracy of the approximate solution of the problem under consideration, an independent approximation of the corresponding component of the electric field intensity vector along the thickness coordinate is proposed. Systems of equations are formulated to determine the integral characteristics of this component, both under the action of an arbitrary variable in time and for a longitudinal coordinate non-stationary and the stationary electromagnetic field.

On the Cauchy Problem for the Wave Equation with Data on the Boundary

We consider the Cauchy problem for the wave equation in $\Omega\times{\mathbb R}$ with data given on some part of the boundary $\partial\Omega\times{\mathbb R}$. We provide a reconstruction algorithm for this problem based on analytic expressions. Our result is applicable to the problem of determining nonstationary wave field arising in geophysics, photoacoustic tomography, tsunami wave source recovery.

Frequency dependence of microwave-assisted electron-transfer chemical reactions

In this paper, the electron transfer reactions in the microwave field are studied. A classical theory is developed for a mix of reagents and polar frequency-dispersive and lossy solvent filling vessels excited by microwaves. These reactors are described by a system of non-linear partial self-consistent differential equations for non-stationary microwave field, heat and liquid dynamics, and chemical molecular kinetics. A particular solution of this system is considered for the isothermic electron-transfer reactions in the microwave field varying its frequency with the calculation of the normalised Marcus rate coefficient. It is found that for the small normalised reaction free energy, the chemical reactions are supported by microwaves in a wide frequency band with an increased value of the exponent in the Marcus rate coefficient. At higher values of this energy, these reactions are driven only by conventional microwave heating. The restrictions for the given theory are reviewed, and further experimental and semi-classical and quantum-mechanical studies are found essential for practical applications of these findings.