Spectral Density Function Research Articles

Modeling and simulating nonhomogeneous non-Gaussian corrosion fields on buried pipelines and its use in predicting burst capacities of corroded pipelines

The present study proposes an iterative algorithm to simulate nonhomogeneous non-Gaussian corrosion fields on buried oil and gas pipeline's external surfaces. The algorithm incorporates the concepts of the discrete orthonormal S-transform and the iterative amplitude adjusted Fourier transform algorithm. This results in the space-wavenumber power spectral density function and marginal distribution function of the simulated corrosion field matching, respectively, their corresponding targets that could be determined from the high-resolution corrosion measurement data obtained from naturally corroded pipe segments. The simulation results demonstrate that the use of the proposed algorithm is able to capture the statistical characteristics of naturally occurring corrosion fields on pipelines. Three-dimensional elasto-plastic finite element analyses are carried out to evaluate the burst capacities of pipe segments containing simulated corrosion fields. Combined with finite element analyses, this algorithm can be employed to conduct virtual full-scale burst tests of corroded pipe specimens, which is of great value to the pipeline corrosion management practice.

Some remarks on X(6900) * *Supported in part by National Nature Science Foundations of China (11975028, 10925522) and China Postdoctoral Science Foundation (2020M680500)

The analysis of the LHCb data on found in the di- system was performed using a momentum-dependent Flatté-like parameterization. The use of the pole counting rule and spectral density function sum rule provides consistent evidence that both confining and molecular states are possible. Alternatively, the nature of cannot be distinguished if only the di- experimental data with current statistics are available. Nevertheless, we found that the lowest state in the di- system likely has the same quantum numbers as , and is probably not interpreted as a molecular state.

Novel analysis using magnetic resonance cholangiography for patients with pancreaticobiliary maljunction.

We used a novel diagnostic Fourier transform (FT) algorithm of the entire extrahepatic bile duct (EHBD) measured by magnetic resonance cholangiography (MRC) to evaluate subtle deformation of bile duct lumen, indicating the malignant potential of EHBD, in patients with pancreaticobiliary maljunction (PBMJ) and in a comparative group of controls without PBMJ. From the workstation, the EHBD lumen was traced automatically and a 2D diagram cross section was measured at 0.5mm-longitudinal intervals. The FT-based integrated power spectral density function value (FTPSDI) of the diameter or area (mm2 or mm4/Hz) and the phase value distribution entropy (PVDE) were also measured. There were 16 patients with undilated PBMJ and 7 with dilated PBMJ. The control group comprised 10 patients with a normal bile duct, 20 with bile duct carcinoma (BDC), and 1 with primary sclerosing cholangitis. Both the diameter and area of the dilated bile ducts and the ducts with early- or advanced-stage BDC were significantly greater than those of the normal duct (p < 0.05). The undilated type of PBMJ tended to have a larger FTPSDI diameter than a normal bile duct, which had a smaller diameter than the dilated type of PBMJ or BDC. BDC had a significantly larger FTPSDI diameter (p < 0.05) and the cutoff value for accuracy was 168mm2Hz-1. The novel mathematical FTPSDI is a promising indicator of whether preventive EHBD resection is necessary for patients with PBMJ, which can be widely applied in the early diagnosis of other biliary diseases.

Empirical evaluation of kinematic soil-structure interaction effects in structures with large footprints and embedment depths

Kinematic soil-structure interaction (SSI) effects cause foundation-level motions to deviate from free-field motions. Simplified procedures to account for kinematic SSI effects are available in design guidelines for regular buildings and have been calibrated for regular buildings with limited foundation size and depth of embedment. As a result, their application to structures with much larger foundation footprints and deeper embedment depths is questionable. Kinematic interaction effects can be used to reduce foundation-level ground motions relative to those specified in the free-field, and this can be cost-effective especially for structures with larger footprints and embedment depths. The objective of this study is to quantify the extent of deviations between the use of available simplified procedures and empirical data for a select group of structures with larger footprints and embedment depths. In this study, a dataset of earthquake motions recorded at the instrumented structures in Japan is used to evaluate kinematic SSI effects, which are quantified in terms of the transfer function and the ratio of response spectra between foundation motions and corresponding free-field motions. Transfer functions represent the ratio between the free-field and the foundation level of a structure motion in the frequency domain and can be obtained by dividing Power Spectral Density functions of foundation motion and corresponding free-field motion. Finally, these empirical functions are compared to the available simplified formulations such as the semi-empirical transfer function and the ASCE/SEI 41–17 recommended ratio of response spectra, and the results are presented in terms of residuals. The overall trends of residuals indicate that the current simplified procedures tend to overestimate the foundation motions in structures with large footprints and embedment depths, and the extent of overestimation is higher for the ratio of response spectra compared to transfer functions. Thus, in future studies, these simplified procedures should be revised for applications in structures with large footprints and embedment depths.

Exact benchmark solutions of random vibration responses for thin-walled orthotropic cylindrical shells

The exact solutions of random vibration responses of orthotropic thin cylindrical shells are imperative for verifying numerical approaches. This study proposes the discrete analytical method (DAM) and achieves the exact benchmark responses of thin-walled orthotropic cylindrical shells under stationary and nonstationary random excitations for the first time. Firstly, by revisiting the governing motion equations of elastic orthotropic shells based on the Flügge shell theory, the closed-form modal shape functions of orthotropic cylindrical shell with shear diaphragm boundary condition are introduced into stationary and nonstationary random vibration analyses. The power spectral density functions and root mean squares (RMSs) for stochastic responses of thin shell subjected to various random excitations, including the point, surface, base acceleration and moving excitations, are analytically derived by using the pseudo excitation method. Moreover, DAM is proposed to enhance the computational efficiency by implementing the discretization of the modal coordinates, frequency and temporal domains. Finally, the exact benchmark solutions of stationary and nonstationary stochastic responses are achieved, and the results indicate high accuracy and efficiency of proposed DAM. The excitation bandwidth and spatial distribution have significantly different effects on various types of responses, and maximum response RMS declines with increasing of acceleration of moving load.

Random vibrations of a structure modified by damped absorbers

The problem of reducing the level of vibrations in various constructions has been considered for many years. This is an important element of analyzing the technical condition of buildings and the comfort of users. Various ways and means of preventing unacceptable vibrations are known and the search for an optimal absorber is still ongoing. Different kinds of vibration absorbers are applied for reducing the vibration level in various engineering structures. Vibrations caused by traffic do not pose a threat to a structure, but are often a nuisance for people. There is a need to reduce them, especially in cities where there is more traffic. In order to be able to analyze an excited structure, traffic was modeled. A model that is a structure and an absorber system with two degrees of freedom is proposed in the paper. The first eigenfrequency of the structure was included in the analysis. As a result, the authors obtained closed equations of motion. The work examines the problem of the absorber effect on the vibrations of traffic-induced structures. It was assumed that the shocks occurring at random moments, and which form the Poisson process, are determined by random amplitude, a deterministic shape function and two different forms of envelope functions. The problem was discussed in the field of correlation theory and spectral density function. Numerical analysis of the displacement of the two-degree system is considered.

Spectral behaviors of diffracted chirped Gaussian pulsed beam propagating in slant turbulent atmosphere path

The analytical expression for the cross spectral density function of chirped Gaussian pulsed beam diffracted by a circular aperture propagating in the slant turbulent atmosphere path is derived based on the extended Huygens-Fresnel principle, which enables us to investigate spectral behaviors of diffracted chirped Gaussian pulsed beam. The change properties of spectrum for the apertured case are studied in comparison with those of spectrum for the unapertured case. The discussions show that the spectral changes are closely related to the aperture size, position parameter, propagation distance, zenith angle, pulse duration and chirp parameter. Our research results have potential applications in realizing the information encoding and transmission in slant turbulent atmosphere.

Edgeworth Expansion for the Whittle Maximum Likelihood Estimator of Linear Regression Processes with Long Memory Residuals

We establish an Edgeworth expansion for the distribution of the Whittle maximum likelihood estimator of the parameter of a time series generated by a linear regression model with Gaussian, stationary, and long-memory residuals. This is done by imposing an extra condition on coefficients of the regression model in addition to the standard conditions imposed on the the spectral density function and the parameter values and making use of the results of Andrews et al. (2005), who provided an Edgeworth expansion for the residual component.

Spectral density functions of bivariable stable polynomials

The relationship between a stable multivariable polynomial p(z) and the Fourier coefficients of its spectral density function $$1/|p(z)|^2$$ , is further investigated. In this paper we focus on the radial asymptotics of the Fourier coefficients for a specific choice of a two variable polynomial. Hypergeometric functions appear in the analysis, and new results are derived for these as well.

An algorithm to simulate nonstationary and non-Gaussian stochastic processes

We proposed a new iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary and non-Gaussian processes. The proposed algorithm is rooted in the concept of defining the stochastic processes in the transform domain, which is elaborated and extend. The algorithm extends the iterative amplitude adjusted Fourier transform algorithm for generating surrogate and the spectral correction algorithm for simulating stationary non-Gaussian process. The IPAC algorithm can be used with different popular transforms, such as the Fourier transform, S-transform, and continuous wavelet transforms. The targets for the simulation are the marginal probability distribution function of the process and the power spectral density function of the process that is defined based on the variables in the transform domain for the adopted transform. The algorithm is versatile and efficient. Its application is illustrated using several numerical examples.

Design of tuned liquid sloshing dampers using nonlinear constraint optimization for across-wind response control of benchmark tall building

The present study proposes an optimal design methodology of tuned liquid sloshing dampers (TLSDs) installed in wind-excited benchmark tall building. The TLSDs design parameters were determined using proposed optimal design methodology based on nonlinear constraint optimization technique. Top floor peak acceleration was considered as the objective function and maximum value of sloshing depth of liquid as a nonlinear constraint for the design purpose. The classical nonlinear shallow water wave theory was used for the simulation of liquid sloshing, and the basic equations of nonlinear liquid sloshing were solved using the Lax Finite Difference Scheme. The governing equations of motion of combined structure-TLSDs system were expressed as state-space variables and structural response was numerically simulated. The findings were presented and assessed on the basis of a comparison between power spectral density functions, time history analysis, root mean square, peak response, and performance criteria for benchmark building with and without TLSDs. The off-tuning effect of TLSDs due to ±15% uncertainty in the building stiffness was also investigated. Further, an attempt has been made to present the control effectiveness of TLSDs in time–frequency domain (wavelet scalogram) using continuous wavelet transformation technique. The optimal TLSDs design based on the proposed methodology was found to be quite effective in serviceability-based design of benchmark tall building under wind loads and can be very useful for the practical design of TLSDs.

Theoretical study on the exciton dynamics of coherent excitation energy transfer in the phycoerythrin 545 light-harvesting complex

The experimental observation of long-lived quantum coherence in the excitation energy transfer (EET) process of the several photosynthetic light-harvesting complexes at low and room temperatures has aroused hot debate. It challenges the common perception in the field of complicated pigment molecular systems and evokes considerable theoretical efforts to seek reasonable explanations. In this work, we investigate the coherent exciton dynamics of the phycoerythrin 545 (PE545) complex. We use the dissipation equation of motion to theoretically investigate the effect of the local pigment vibrations on the population transfer process. The result indicates that the realistic local pigment vibrations do assist the energy transmission. We demonstrate the coherence between different pigment molecules in the PE545 system is an essential ingredient in the EET process among various sites. The coherence makes the excitation energy delocalized, which leads to the redistribution of the excitation among all the chromophores in the steady state. Furthermore, we investigate the effects of the complex high-frequency spectral density function on the exciton dynamics and find that the high-frequency Brownian oscillator model contributes most to the exciton dynamic process. The discussions on the local pigment vibrations of the Brownian oscillator model suggest that the local heterogeneous protein environments and the effects of active vibration modes play a significant role in coherent energy transport.

Train Wheel Force Analysis by Dynamic Analysis of High-speed Train Bridge

A dynamic numerical analysis of the wheel forces of a Korea Train express (KTX) vehicle is conducted to investigate the traffic safety of railway bridge. It is carried out to solve the structural responses which is especially focused on either the dynamic amplification factor (DAF; vertical deflections, stresses, moments, and accelerations) of the bridge or the differences of wheel forces (DWF) and three directions rotations of the train while travelling between on the ground and on the pre-stressed concrete (PSC) box bridge with an analysed range of running speeds from 100 km/h to 600 km/h by 10 km/h increments. The numerical finite element method (FEM) with fourth order Runge−Kutta method is used to analyse the traffic safety of the bridge considering wheel-track forces between a 38 degree-of -freedom vehicle model and a track irregularity generated by the power spectral density (PSD) function. It will be proposed as indies of evaluation method (DAF, DWF, and KTX rotations) are recommended as the enforced traffic safety of the existing PSC box bridges due to the increasing speed of next generation KTX.

Topological Atomic Chains on 2D Hybrid Structure.

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

Dynamic analysis of an array of semi-rigid “sea station” fish cages subjected to waves

The dynamic behaviour of an array of 6 × 6 semi-rigid “sea station” fish cages is studied under the effect of waves. The semi-rigid sea station system is discretized into a lumped mass model, that is used as the dynamic simulation model. The tension in the mooring lines of the mooring system is obtained in the time domain for different wave directions. The rotations of three degrees of freedom of each semi-rigid sea station under different wave directions are analysed, and the spectral density function of the mooring tension is obtained by Fast Fourier Transform of the time domain response. The results provide a basis for the design of the semi-rigid sea station system and have a certain guiding significance for the specific engineering practice.

Rectangular hollow twisted multi-Gaussian Schell-model source

We obtained a twisted far field with rectangular hollow distribution by designing a new type of light source, which can rotates around the axis during propagation. Then, we derived the expression of cross spectral density function on propagation of such source and analyzed the characteristics of spectral intensity distribution of beam field. In addition, we discussed the influence of corresponding parameters of such a source on the behavior of the beam field, including thickness of the hollow edge, the size of the hollow, and direction of beam rotation in detail.

A stochastic analysis method of transient responses using harmonic wavelets, part 2: Time-dependent vehicle-bridge systems

Conventional stochastic response analysis methods of vehicle-bridge (VB) systems involve a brute-force calculation based on a large number of simulations, which imposes huge computational burdens because the dynamic analysis of a time-dependent VB system requires repeated assembles of system matrices. This paper proposes a novel stochastic analysis method of transient responses for time-dependent VB systems based on periodic generalized harmonic wavelets (GHW). We establish the equations of motion of the VB system and reveal the orthogonal characteristic relationships between the time-dependent system matrices and the wavelet functions. Then, two sets of linear algebraic equations of wavelet coefficients are established for describing the time-dependent VB system, and the time-varying power spectral density functions of system responses are obtained in a semi-analytical form. The stochastic response analysis of the time-dependent VB system is therefore converted into solving a set of linear algebraic equations, which significantly simplifies the stochastic response analysis. The accuracy and efficiency of the proposed method are validated via comparison against the Monte Carlo simulations of nonstationary stochastic analyses of a highway bridge and a railway bridge, respectively. The proposed method provides a high-efficient way to estimate the time-varying power spectral density functions of stochastic responses of time-dependent VB systems.

Superconducting coherence length of hole-doped cuprates obtained from electron\u2013boson spectral density function

Electron–boson spectral density functions (EBSDFs) can be obtained from measured spectra using various spectroscopic techniques, including optical spectroscopy. EBSDFs, known as glue functions, are suggested to have a magnetic origin. Here, we investigated EBSDFs obtained from the measured optical spectra of hole-doped cuprates with wide doping levels, from underdoped to overdoped cuprates. The average frequency of an EBSDF provides the timescale for the spin fluctuations to form Cooper pairs. This timescale is directly associated with retarded interactions between electrons. Using this timescale and Fermi velocity, a reasonable superconducting coherence length, which reflects the size of the Cooper pair, can be extracted. The obtained coherence lengths were consistent with those measured via other experimental techniques. Therefore, the formation of Cooper pairs in cuprates can be explained by spin fluctuations, the timescales of which appear in EBSDFs. Consequently, EBSDFs provide crucial information on the timescale of the microscopic mechanism of Cooper pair formation.

A practical method for recovering Sturm–Liouville problems from the Weyl function

In the paper we propose a direct method for recovering the Sturm–Liouville potential from the Weyl–Titchmarsh m-function given on a countable set of points. We show that using the Fourier–Legendre series expansion of the transmutation operator integral kernel the problem reduces to an infinite linear system of equations, which is uniquely solvable if so is the original problem. The solution of this linear system allows one to reconstruct the characteristic determinant and hence to obtain the eigenvalues as its zeros and to compute the corresponding norming constants. As a result, the original inverse problem is transformed to an inverse problem with a given spectral density function, for which the direct method of solution from Kravchenko and Torba (2021 Inverse Problems 37 015015) is applied. The proposed method leads to an efficient numerical algorithm for solving a variety of inverse problems. In particular, the problems in which two spectra or some parts of three or more spectra are given, the problems in which the eigenvalues depend on a variable boundary parameter (including spectral parameter dependent boundary conditions), problems with a partially known potential and partial inverse problems on quantum graphs.

Experimental investigation on the effect of particles on large scale vortices of an isolated hemispherical roughness element

Particle image velocimetry (PIV) was used to investigate the effect of 155 μm polystyrene particles on the wake structure of an isolated hemispherical roughness element placed in a laminar boundary layer of a flat plate. The main purpose of this study was to investigate the influence of particles on the large-scale vortices induced by the hemisphere. The turbulence statistics and the main modes of proper orthogonal decomposition (POD) in whole field of view (FOV) were comparatively analyzed. The shedding frequency was analyzed by the power spectral density (PSD) function, and the hairpin vortex head structure was conditionally detected by the spatial multi-scale local average function. The results showed that by introducing particles, the statistics in the near-wall region downstream of the hemisphere were significantly changed. PSD results showed that the existence of particles led to the shedding of structures with multiple frequencies and inhibited the shedding of primary structures. Further conclusions could be drawn through POD and hairpin vortex head extraction: the existence of particles changed the type of vortex shedding behind the hemisphere, thereby reducing the number and the vorticity intensity of hairpin vortex heads in the range near the peak, and promoting the scale of the prograde vortex structure.