Theoretical Spectral Density Research Articles

АНАЛИЗ ПРОЦЕССОВ ФОРМИРОВАНИЯ МИКРОПРОФИЛЯ ПОВЕРХНОСТЕЙ ДЕТАЛЕЙ МАШИН НА ЭТАПАХ ОБРАБОТКИ И ПРИРАБОТКИ В УСЛОВИЯХ ГРАНИЧНОГО ТРЕНИЯ

An approach is proposed which is based on the theory of random processes and which allows carrying out an objective comparative analysis of the results of forming of surface roughness profiles of sliding friction joint elements both after machining and during operational run-in. The research relevance is determined by the task of forming a surface roughness profile by various technological methods, which corresponds to or is close to the operational one formed during the running-in of the sliding friction joint elements, that would allow manufacturing products which would start operating in conditions close to normal wear. The studies evaluate the influence of technological factors on forming roughness profiles by turning options and round grinding methods followed by surface plastic deformation by diamond smoothing, electromechanical machining, etc., as well as the influence of the run-in processes carried out on the test bench. A qualitative assessment of the forms of amplitude-frequency characteristics of models forming element surfaces is accepted as the identity criterion of processes forming microprofiles of element surfaces. The paper presents a method of experimental verification of the surface roughness profile for stationarity and ergodicity, which can be used to analyze other random sequences appearing in the practice of tribotechnological research. The construction of autocorrelation functions of the surface roughness profile before and after running-in makes it possible to find out the influence of technological heredity on forming a microprofile while surface machining and running-in of parts. The calculation of indicators to evaluate the theoretical spectral densities of roughness profiles and the construction of amplitude-frequency characteristics of forming surface roughness by various technological methods and during run-in allows choosing an effective method of machining parts, which significantly reduces the run-in time of sliding friction pairs. Studies have shown that surface plastic deformation should be used as the finishing treatment of parts, which allows to obtain a roughness profile of sliding friction surfaces close to the operational one.

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex.

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneities in the Fenna-Matthews-Olson (FMO) complex. However, challenges persist in numerically simulating these systems, both in terms of parameterizing them and following their dynamics over long periods of time because of long non-Markovian memories. We investigate the dynamics of FMO with the exact treatment of various theoretical spectral densities using the new tensor network path integral-based methods, which are uniquely capable of addressing the difficulty of long memory length and incoherent Förster theory. It is also important to be able to analyze the pathway of EET flow, which can be difficult to identify given the non-trivial structure of connections between bacteriochlorophyll molecules in FMO. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some new routes of transport. The combination of exact and approximate methods sheds light on the role of coherences in affecting the fine details of the transport and promises to be a powerful toolbox for future exploration of other open systems with quantum transport.

Weak-light phase locking aided by frequency division phase meter for intersatellite laser interferometry

Weak light phase locking is an important part of intersatellite laser interference ranging. Phase-locked loop (PLL) is used to track the phase of heterodyne interference optical signal. Owing to shot noise, laser frequency and other kinds of noise, there is a phase difference between the internal PLL local oscillator and the heterodyne signal, while the phase detection range of the PLL is only one period. If the phase difference exceeds the phase detection range at a certain time, the local oscillator may enter the wrong operating point under feedback regulation, resulting in cycle clip, which leads to subsequent phase reconstruction errors. In this paper, a cycle clip diagnosis method based on the detection background of gravitational waves is proposed. Based on the original PLL, an auxiliary frequency phase divider with larger phase detection range is introduced, which can provide a basis for judging whether the cycle clip occurs in the PLL. In this paper, a digital weak-light PLL model is established to evaluate the influence of various noise. The theoretical spectral density of the error phase is given according to the two main kinds of noise (laser phase noise and particle noise). Considering the limited detection range of PLL, large error phase may lead to cycle clip, making the PLL work at the wrong locking point. A phase meter with smaller frequency division phase range can be used to solve this problem. First, the input heterodyne sine signal is converted into in-phase square wave N frequency division. Then the phase difference is determined by comparing the output signal with output signal reduced by 1/<i>N</i> through the time-to-degital converter (TDC) Based on the theory of PLL and noise, the theoretical model of frequency division phase meter is established. The simulation results show that the frequency division phase meter can realize a wide range of phase detection under the current theoretical framework and has the ability to judge the cycle clip of weak light phase locking. It can be used in the weak- light phase locking task represented by LISA.

응답 파워스펙트럼밀도 적분함수를 이용한 구조물의 감쇠비 추정

The wind-induced vibration of structure is very sensitive to the damping ratio of governing modes of interests. Research to identify the damping ratio from the structural response have been developed for several decades, however is still challenging. A novel estimation technique of damping ratio of a structure is proposed in this research, which is based on the integration of power spectral density (PSD) function. The damping ratio estimation concept is devised on the principle that the integration of PSD have a flattening effect of the external load spectral density so that the integral of spectral density function of decomposed mode can be very closed to the corresponding theoretical integral function. The damping ratio can be identified by comparing the two integral functions. In order to extract the damping ratio, the properties of the integral of theoretical spectral density function is examined, and it is also shown that the estimation technique is applicable to the modal response separated from a non-classically damped system. For the validation of the developed technique in this study, numerical analysis for the mathematical model and application for the site-situ measurement were carried out. From the verification process, it was shown that the technique to estimate the damping ratio is robust and reliable with high stability

Investigation of the damping properties of the process module for a tractor of traction class 1.4

To analyze the positive influence of the technological module on the fluctuations of the external load of the tractor, the methods of statistical dynamics are used. A dynamic model of a process module with two rotating masses is considered: the rim and tire of the drive wheel and the translational mass of the process module. Using the transfer function, the spectral functions of the output process (the horizontal component of the force on the MTZ-82 tractor) were determined when performing a machine-tractor unit (MTA) technological operation with heavy disks (BDT-7) intended for a class 3 tractor. The developed mathematical model of the technological module allowed us to construct theoretical spectral densities of the horizontal component of the force on the tractor hitch when completing it with the technological module. The use of the process module allows the frequency range of forces on the tractor hitch to be shifted to a lower zone from 0 to 2.5 Hz, excluding high-frequency components compared to the standard configuration of the tractor.

Collective optical Thomson scattering in pulsed-power driven high energy density physics experiments (invited).

Optical collective Thomson scattering (TS) is used to diagnose magnetized high energy density physics experiments at the Magpie pulsed-power generator at Imperial College London. The system uses an amplified pulse from the second harmonic of a Nd:YAG laser (3J, 8ns, 532nm) to probe a wide diversity of high-temperature plasma objects, with densities in the range of 1017-1019cm-3 and temperatures between 10eV and a few keV. The scattered light is collected from 100 μm-scale volumes within the plasmas, which are imaged onto optical fiber arrays. Multiple collection systems observe these volumes from different directions, providing simultaneous probing with different scattering K-vectors (and different associated α-parameters, typically in the range of 0.5-3), allowing independent measurements of separate velocity components of the bulk plasma flow. The fiber arrays are coupled to an imaging spectrometer with a gated intensified charge coupled device. The spectrometer is configured to view the ion-acoustic waves of the collective Thomson scattered spectrum. Fits to the spectra with the theoretical spectral density function S(K, ω) yield measurements of the local plasma temperatures and velocities. Fitting is constrained by independent measurements of the electron density from laser interferometry and the corresponding spectra for different scattering vectors. This TS diagnostic has been successfully implemented on a wide range of experiments, revealing temperature and flow velocity transitions across magnetized shocks, inside rotating plasma jets and imploding wire arrays, as well as providing direct measurements of drift velocities inside a magnetic reconnection current sheet.

Whittle Likelihood Estimation of Nonlinear Autoregressive Models With Moving Average Residuals

The Whittle likelihood estimation (WLE) has played a fundamental role in the development of both theory and computation of time series analysis. However, WLE is only applicable to models whose theoretical spectral density function (SDF) is known up to the parameters in the models. In this article, we propose a residual-based WLE, called extended WLE (XWLE), which can estimate models with their SDFs only partially available, including many popular time series models with correlated residuals. Asymptotic properties of XWLE are established. In particular, XWLE is asymptotically equivalent to WLE in estimating linear ARMA models, and is also capable of estimating nonlinear AR models with MA residuals and even with exogenous variables. The finite-sample performances of XWLE are checked by simulated examples and real data analysis.

Time-Domain Simulation of High-Speed Railway Track Irregularity

It was more convenient to describe track irregularity by the spatial frequency.The conventional frequency-domain transfer function can not effectively solve the vibration equation when anlysis of the vibration response to structure of vehicle-track dynamic coupling system, the time domain numerical integration must be used to solve it.The trigonometric series superposition method can be used to convert track irregularity spectrum into time domain frequency power spectral density function, and then turn the simulated irregularity samples into spectral density by the Inverse Fast Fourier Transform (IFFT), which compared with the theoretical spectral density to test the reliability of the sample. The results show that the simulated sample have the same characteristics with the given power spectral density function, which demonstrate the high reliability of this sample and it can be used as the external excitation of the locomotive vehicle system.

Generalized Model-Free Spectral Density Analysis Applied to Rhodopsin Activation in Membranes

Although molecular structures of G-protein-coupled receptors (GPCRs) are becoming increasing available from X-ray crystallography, understanding their functions requires information about molecular dynamics in membranes. Here we use rhodopsin as a model to illuminate general features of GPCR activation. With solid-state 2H NMR spectroscopy we obtain experimental data pertinent to both structure and dynamics. Experimentally, order parameters and relaxation rates are the two observables of solid-state 2H NMR experiments. We propose that the local dynamics of the retinylidene ligand are coupled to large-scale fluctuations of the transmembrane helices of rhodopsin, leading to activation of the receptor. To study the structural dynamics of retinal bound to rhodopsin, we start with an irreducible representation of the correlation function in terms of mean-squared amplitudes and correlation times [1]. The mean-squared amplitudes are related to the orientational order parameter, while the irreducible correlation times include the preexponential factor and energy barrier. To bridge the generalized model-free theory with experimental measurements, we separated the relaxation rates into spectral densities by applying Redfield theory. The spectral densities are Fourier transformation partners of the irreducible correlation functions. By fitting theoretical spectral densities to experimental data we can readily obtain the values of preexponential factors and activation energies [2]. We are currently applying our generalized model-free method to interpret the behavior of active Meta-II rhodopsin. Our aim is to establish if the local fluctuations of the ligand initiate the structural changes of rhodopsin to understand the activation mechanisms of GPCRs in general. Moreover, the results from our generalized model-free analysis method can be used in molecular dynamics (MD) simulations without the limitations of simplified motional models. [1] M.F. Brown (1982) JCP 77, 1576-1599. [2] A.V. Struts et al. (2011) NSMB 18, 392-394.

Surface diffusion of dysprosium on stepped surfaces of tungsten microcrystal

The mobility of W atoms of the (3 2 0) and (2 2 1) regions of the W microcrystal surface with the tip curvature radius ∼300 nm and the surface diffusion of Dy at average coverage ∼0.1 ML on these regions were investigated by spectral analysis of field emission current fluctuations in the temperature range 500–800 K. The diffusion appears to be one-dimensional for the W(3 2 0) regions and two-dimensional for the W(2 2 1). The surface-diffusion coefficients were determined by comparison of the experimental results with the theoretical spectral density functions derived by Gesley and Swanson. The surface-diffusion parameters were calculated. The results are discussed from the aspect of substrate structure.

Protein Dynamics from NMR: The Slowly Relaxing Local Structure Analysis Compared with Model-Free Analysis

(15)N-(1)H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement.

Surface diffusion of dysprosium on the W(1 1 1) facet

Diffusion of dysprosium on the (1 1 1) facet of a tungsten micromonocrystal was investigated by means of spectral analysis of field emission current fluctuations. The experimental spectral density functions of the current fluctuations were analysed by using Gesley and Swanson’s theoretical spectral density function, which enables to determine the surface diffusion coefficient D for dysprosium. Derived from the temperature dependence of D, the diffusion activation energy E is presented for some Dy coverages θ (1 1 1) . In the temperature range 400–600 K, the E first drops from 1.25 eV per atom at θ (1 1 1) ≈0.25 ML to 0.48 eV per atom at θ (1 1 1) ≈1 ML (corresponding to the minimum of the work function of the system), then increases to 1.03 eV per atom at θ (1 1 1) ≈1.3 ML. The results are discussed from the aspects of the substrate structure and interaction in the adsorbed layer.

Kernel Estimation of the Spectral Density of Stationary Random Closed Sets

SummaryA non‐parametric kernel estimator of the spectral density of stationary random closed sets is studied. Conditions are derived under which this estimator is asymptotically unbiased and mean‐square consistent. For the planar Boolean model with isotropic compact and convex grains, an averaged version of the kernel estimator is compared with the theoretical spectral density.

Spectral density of medium strength H-bonds. Direct damping and intrinsic anharmonicity of the slow mode. Beyond adiabatic approximation

The present theory is a new step in our attempt to obtain a flexible tool susceptible to be used by experimentalists working in the realm of the spectra of the infrared ν X–H⋯Y mode of weak and medium strength hydrogen bonds: the spectral density is studied within the linear response theory by Fourier transform of the autocorrelation function of the transition dipole moment of the fast mode. The strong anharmonic coupling theory is used through second-order expansion in the slow-mode coordinate Q of the angular frequency and the equilibrium position of the fast mode. The theory is working beyond the adiabatic approximation. It takes into account the intrinsic anharmonicity of the low frequency mode through Morse potential, and assumes a direct damping of the fast mode. At last, indirect damping, Fermi resonances and Davydov coupling are ignored. When the Morse potential is expanded up to the harmonic approximation, the theoretical spectral density reduces [O. Henri-Rousseau, P. Blaise, Chem. Phys. 250 (1999) 249]. The theory reproduce not only the experimental features obtained in this previous paper but also the increase in magnitude of the first moment with temperature.

Electron distribution in MgO probed by x-ray emission

The relative intensity of the Mg $K\ensuremath{\beta}$ emission band with respect to the $K\ensuremath{\alpha}$ atomic line, obtained by electron-induced x-ray emission spectroscopy, is used to investigate the variation of $p$-like valence electron number located around magnesium in metal and MgO. Calculated spectral intensities of Mg $K$ emissions are obtained within the augmented plane-wave method for the perfect crystal. From experimental and theoretical data, the number of $3p$ electrons present around Mg and involved in the $K\ensuremath{\beta}$ transition does not vary much with the metallic or ionic character of the bonds. This result shows that the charge transfer is weak in the oxide. These experiments can be generalized to other compounds. Spectral densities of states (DOS) around Mg and O are also probed and agreement is found between experimental and theoretical spectral densities of $3p$ Mg and $2p$ O states. Changes of MgO valence DOS with annealing, etching, and aging are discussed.

A Spectral Method for Estimating Parameters in Rainfall Models

One of the most difficult problems in rainfall modelling is often the fitting of theoretical models to data. In this paper a spectral approach is proposed for fitting single-site models, by considering the approximate likelihood functions of collections of sample Fourier coefficients. An objective function is derived, which is the same as that used in Whittle's method for time series parameter estimation, and is shown to have an interpretation as a quasi-likelihood when the time series is non-Gaussian. The method requires knowledge of the theoretical spectral density of models to be fitted; the form of this spectral density is given for a wide class of point-process-based rainfall models. A variant of the method is also developed for when a number of independent replications of a rainfall process are available. Large-sample properties of the estimators are derived, and the method is illustrated with some data from the south-west of England.

Stochastic characteristics of wave kinematics in laboratory-scale random waves

This paper presents the results of analysis of wave kinematics data of Skjelbreia et al. taken in a wave flume using Laser Doppler Velocimetry. This data set is unique with respect to accuracy and amount of data in the vicinity of the mean water level. The present publication of the statistical and spectral characteristics of these data sheds further insight into wave kinematics mechanism in the free surface zone where measurement points are not continuously submerged and when the so called “emergence effect” should be taken into account. Stochastic characteristics estimated from measurements are compared with known theoretical predictions applying the not commonly used approach presented by Tung. Furthermore, the theoretical spectral density of particle velocities, modified by emergence effect, obtained by taking the Fourier transform of the covariance function as derived by Pajouhi and Tung, is compared with measured values. Such a comparison has previously been made by Anastasiou et al. for a data set with limited amount of data above the free surface elevation. Anastasiou et al. have used an approximate formula for the modified covariance function. In this paper, however, the exact modified covariance function is for the first time used for statistical analysis and comparison with measurements of wave kinematics in a wave flume.

Approximate Power Spectral Density of the Response of a Nonlinear System to Stationary Random Excitation

An approximation is obtained for the power spectral density of the response of a hard-spring resonator to a class of random inputs by 2 methods of equivalent linearization. Comparison of the theoretical spectral densities is made with those obtained experimentally from an analog computer with white-noise excitation.