Non-zero Mean Value Research Articles

D'Alembert‐type solution of the Cauchy problem for the Boussinesq‐Klein‐Gordon equation

AbstractIn this paper, we construct a weakly‐nonlinear d'Alembert‐type solution of the Cauchy problem for the Boussinesq‐Klein‐Gordon (BKG) equation. Similarly to our earlier work based on the use of spatial Fourier series, we consider the problem in the class of periodic functions on an interval of finite length (including the case of localized solutions on a large interval), and work with the nonlinear partial differential equation with variable coefficients describing the deviation from the oscillating mean value. Unlike our earlier paper, here we develop a novel multiple‐scales procedure involving fast characteristic variables and two slow time scales and averaging with respect to the spatial variable at a constant value of one or another characteristic variable, which allows us to construct an explicit and compact d'Alembert‐type solution of the nonlinear problem in terms of solutions of two Ostrovsky equations emerging at the leading order and describing the right‐ and left‐propagating waves. Validity of the constructed solution in the case when only the first initial condition for the BKG equation may have nonzero mean value follows from our earlier results, and is illustrated numerically for a number of instructive examples, both for periodic solutions on a finite interval, and localized solutions on a large interval. We also outline an extension of the procedure to the general case, when both initial conditions may have nonzero mean values. Importantly, in all cases, the initial conditions for the leading‐order Ostrovsky equations by construction have zero mean, while initial conditions for the BKG equation may have nonzero mean values.

Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows.

We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing non-zero mean values of a shear flow. Using theoretical analyses of limiting cases, as well as numerical solutions of the full Fokker–Planck equation, we present a thorough parameter study of PDFs for different values of the correlation time and amplitude of stochastic forcing. From time-dependent PDFs, we calculate the information length (), which is the total number of statistically different states that a system passes through in time and utilise it to understand the information geometry associated with the formation of bimodal or unimodal PDFs. We identify the difference between the relaxation and build-up of the shear gradient in view of information change and discuss the total information length () which maps out the underlying attractor structures, highlighting a unique property of which depends on the trajectory/history of a PDF’s evolution.

On wave propagation in a random conducting magneto-non-simple thermo-viscoelastic medium

• The waves in a random magneto-non-simple thermo-visco-elastic medium is studied. • The couple dispersion equation for longitudinal and transverse waves is analyzed. • The effect of thermal field to attenuate longitudinal waves is discussed. • Effect of magnetic conductivity is studied both theoretically and numerically. • Effect of visco-elasticity is discussed both analytically and numerically. The paper examines the problem of wave propagation in a random conducting magneto- non-simple thermo-viscoelastic medium. The medium has been assumed to be weakly conducting and weakly thermal. The thermomechanical coupling parameter and the conductivity are random functions, proportional to ε, with non-zero mean values, ε measuring the smallness of the scale of random fluctuation of inhomogeneities of the medium. The smooth perturbation technique enunciated by Keller (1964) has been employed to analyze the appropriate dispersion equation in non-simple thermoelastic medium. The longitudinal and transverse waves were discussed by using a particular form of thermomechanical coupling parameter representing the corresponding auto-correlation function. The effect of magnetic conductivity has been investigated. The phenomena of attenuation of waves and change of phase speed were discussed numerically in details.

Orientation Analysis of Simulated Tornadic Debris

AbstractPolarimetric weather radars are capable of detecting tornadic debris signatures (TDSs), which result from debris being lofted to the level of the radar beam and can be modulated by centrifuging and debris fallout. TDSs have been used in promising applications, such as enhanced tornado detection, improved warning and assessment of a potential tornado threat, and estimating tornado damage potential and intensity. Regions with negative differential reflectivity have been found in TDS observations but a physical explanation is yet to be determined. Some hypotheses suggest a common alignment of debris or non-Rayleigh scattering to be the cause. However, because it is inherently difficult and extremely dangerous to verify this, a simulated environment can aid in this context to reveal information that would otherwise be impossible to retrieve in practice. Under the simulation environment, the true construct of the debris is known, wherefrom the bulk distributions of position and orientation data can be extracted for statistical analysis. The primary focus of this work is to investigate the cause of nonzero mean values of in TDSs with simulated data from SimRadar, which is a polarimetric radar time series simulator developed for tornadic debris studies. The 6-degrees-of-freedom (DOF) model shows that for both small and large platelike debris, the debris face tends to have some common degree of alignment normal to the wind direction, which may be a plausible cause for the occurrence of negative in real polarimetric radar observations. Potential explanations for other hypotheses regarding tornado and debris dynamics are also briefly discussed.

Multiaxial fatigue life estimation in low-cycle fatigue regime including the mean stress effect

The goal of the present paper is to discuss the reliability of a strain-based multiaxial Low-Cycle Fatigue (LCF) criterion in estimating the fatigue lifetime of metallic structural components subjected to multiaxial sinusoidal loading with zero and non-zero mean value. Since it is well-known that a tensile mean normal stress reduces the fatigue life of structural components, three different models available in the literature are implemented in the present criterion in order to take into account the above mean stress effect. In particular, such a criterion is formulated in terms of strains by employing the displacement components acting on the critical plane and, then, by defining an equivalent strain related to such a plane. The Morrow model, the Smith-Watson-Topper model and the Manson-Halford model are applied to define such an equivalent strain. The effectiveness of the new formulations is evaluated through comparison with some experimental data reported in the literature, related to biaxial fatigue tests performed on metallic specimens under in-and out-of-phase loadings characterised by non-zero mean stress values.

Mean stress effect in stress-life fatigue prediction re-evaluated

The paper compares various methods for computing the equivalent stress amplitude for stress cycles of non-zero mean value in stress-life fatigue prediction. A set of 11 calculation methods is evaluated. In addition to formulations based on common static or fatigue properties, the Walker formula and the generalized Linear formula are included in the investigation. These two methods use an optimization routine to find the material parameters. The final response of the methods is compared and discussed. The Walker method provides a better solution. The generalized Linear method produces inferior results, i.e. the linear fit of the segment of the Haigh diagram is not an optimal solution.

PWR Effect On Crack Initiation Under Equi-biaxial Loading

The lifetime extension of the nuclear power stations is considered as an energy challenge worldwide. That is why, the risk analysis and the study of various effects of different factors that could potentially prevent safe long term operation are necessary. These structures, often of great dimensions, are subjected during their life to complex loading combining varying mechanical loads, multiaxial, with nonzero mean values associated with temperature fluctuations and also PWR environment. Based on more recent fatigue data (including tests at 300°C in air and PWR environment, etc…), some international codes (RCC-M, ASME and others) have proposed and suggested a modification of the austenitic stainless steels fatigue curve combined with a calculation of an environmental penalty factor, namely Fen, which has to be multiplied by the usual fatigue usage factor. The aim of this paper is to present a new device "FABIME2E" developed in the LISN in collaboration with EDF and AREVA. These new tests allow quantifying the effect of PWR environment on disk specimen. This new device combines the structural effect like equi-biaxiality and mean strain and the environmental penalty effect with the use of PWR environment during the fatigue tests.

PWR EFFECT ON CRACK INITIATION UNDER EQUI-BIAXIAL LOADING: DEVELOPMENT OF THE EXPERIMENT

The lifetime extension of the nuclear power stations is considered as an energy challenge worldwide. That is why, the risk analysis and the study of various effects of different factors that could potentially represent a hazard to a safe long term operation are necessary. These structures, often of great dimensions, are subjected during their life to complex loading combining varying mechanical loads, multiaxial, with non-zero mean values associated with temperature fluctuations and also PWR environment.Historically, the methodology for fatigue dimensions of the Pressurized Water Reactor components (PWR) (ASME, RCC-M, KTA, …) is based on the use of design curves established from tests carried out in air at 20°C on smooth specimens by integrating safety coefficients that cover, among other parameters, the dispersion of tests associated with the effects of structures.Based on more recent fatigue data (including tests at 300°C in air and PWR environment, etc…), some international codes (RCC-M, ASME and others) have proposed and suggested a modification of the austenitic stainless steels fatigue curve combined with a calculation of an environmental penalty factor, namely Fen, which has to be multiplied by the usual fatigue usage factor.The aim of this paper is to present a new device "FABIME2E" developed in the LISN in collaboration with EDF and AREVA. These new tests allow quantifying accurately the effect of PWR environment on semi-structure specimen. This new device combines the structural effect like equi-biaxiality and mean strain and the environmental penalty effect with the use of PWR environment during the fatigue tests.

New analytical expression for speckle contrast of spectral light broadening

A new analytical expression for the average speckle contrast is derived for surfaces of random roughness at reflection. Rayleigh and Simpson phase probability density distributions of non-zero phase mean value are assumed for the roughness of the surface. The behavior of a speckle contrast with a roughness root mean square of phase deviation is presented. The effect of the spectral light profile, its spectral width, the density of the scatterers of the rough surface and the average time delay between the interfering beams are taken into consideration.

Suboptimal Anisotropy-based Control for Linear Discrete Time Varying Systems with Noncentered Disturbances

This paper is concerned with a γ-optimal control for linear discrete time varying systems on bounded time intervals driven by statistically uncertain random disturbances with nonzero mean values. The uncertainty is described in information theoretic terms using a previously introduced anisotropy functional. It is shown that, under additional constraints on the mean value and the covariance matrix of the input disturbance, the γ-optimal anisotropy-based controller design problem can be reduced to a multiobjective control problem. In comparison with the original anisotropy-based control setting, which uses the anisotropic norm of a system as a performance criterion, the suboptimal control approach, considered in the present paper, employs a modified version of the norm. The modified anisotropic norm is related to the original norm at a reduced anisotropy level and the H∞-norm of the system. Using this connection, we obtain sufficient conditions for γ-optimal anisotropy-based control. The resulting controller involves the solution of a certain convex optimization problem. A numerical example is presented in order to demonstrate the method proposed.

Flow around an oscillating circular disk at low to moderate Reynolds numbers

Direct numerical simulations of the flow induced by a circular disk oscillating sinusoidally along its axis are performed. The aspect ratio ($\unicode[STIX]{x1D712}=\text{diameter}/\text{thickness}$) of the disk is 10. The Reynolds number ($\mathit{Re}$), based on the maximum speed and the diameter of the disk, is in the range of $50\leqslant \mathit{Re}\leqslant 800$. The Keulegan–Carpenter number ($KC$) is in the range of $1\leqslant KC\leqslant 24$. Five flow regimes are observed in the considered $\mathit{Re}$–$KC$ space: (I) axisymmetric flow (AS), (II) planar symmetric flow in the low-$KC$ region (PSL), (III) azimuthally rotating flow in the low-$KC$ region (ARL), (IV) planar symmetric flow in the high-$KC$ region (PSH) and (V) azimuthally rotating flow in the high-$KC$ region (ARH). The critical boundaries between different flow regimes are identified based on the evolutions of the magnitude and direction of transverse force acting on the disk. For the non-axisymmetric flow regimes, the flow is one-sided with respect to the axis of the disk and is associated with a non-zero mean value of the transverse force acting on the disk.

Coupling effects on the dynamic response of moored floating platforms for offshore wind energy plants

The increasing importance of offshore deep-water wind energy together with the complexity of the wind-wave-structure interaction problem makes the dynamic analysis of floating platforms a case of considerable interest. In this work, the dynamics of moored floating platforms for deep-water wind energy purposes is analysed in regular waves in order to discuss the effects on the motion due to the coupling of different degrees of freedom, usually associated with the operation of the mooring system and the hydrodynamic action, and the role of the main parameters affecting the motion. The platform is modelled as a rigid body and the associated differential dynamic problem is solved by using a suitable Lie group time integrator. The loads associated with mooring lines and waves are respectively assessed through a quasi-static model and a linear hydrodynamic model. The coupling of different degrees of freedom is usually related to loads with higher-frequency components and non-zero mean value that could bring the system into a mean dynamic configuration rather different from the static equilibrium configuration. Moreover, very interesting to limit the oscillations of the body is the effect of the location of the center of mass, the lower the center the lower the amplitude of pitch and roll response.

Optimization of Wavefront Coding Phase Mask Applied to 5X-40X Micro-Objectives Simultaneously

A wavefront coding (WFC) technique provides an extension of the depth of field for a microscopy imaging system with slight loss of image spatial resolution. Through the analysis of the relationship between the incidence angle of light at the phase mask and the system pupil function, a mixing symmetrical cubic phase mask (CPM) applied to 5X-40X micro-objectives is optimized simultaneously based on point-spread function (PSF) invariance and nonzero mean values of the modulation transfer function (MTF) near the spatial cut-off frequency. Optimization results of the CPM show that the depth of field of these micro-objectives is extended 3-10 times respectively while keeping their resolution. Further imaging simulations also prove its ability in enhancing the defocus imaging.

Baryon and chiral symmetry breaking in holographic QCD

We study the relationship between chiral symmetry breaking and baryons in holographic QCD. We construct a soliton with unit baryon charge in the presence of a nonzero mean value of the scalar bifundamental field, which is dual to the chiral condensate. We obtain a relation between the chiral condensate and the mass of the baryon and find in a clear-cut way that at large values of the condensate the holographic soliton is no longer located on the IR wall. Instead it is split into two halves, which are symmetrically located on the left and right flavor branes. On the other hand we find that the local value of the quark condensate is suppressed in the core of the soliton, which is evidence for a partial chiral symmetry restoration inside the baryon.

Extension of a Plane Wave Integral Representation for Fields in Lossy Reverberation Chambers

This article develops a theoretical extension of a plane wave integral representation to account for fields inside a reverberation chamber with an arbitrary lossy configuration. It is shown that the presented development can explain a general over-moded reverberation chamber with the anisotropy condition; i.e., each of the six complex field components possesses non-zero mean values and different variances from one another. It is found that the ensemble average of the absolute square of the total field can satisfy the homogeneity property (i.e., being independent of position), despite the correlation between the angular spectrum components of the received field. To the of the best authors knowledge, a detailed physical explanation of a high-loss reverberation chamber based on this extended plane wave integral formulation is not currently available due to the difficulty finding a homogeneity property. The theoretical expressions and physical explanations can not only provide fresh insights into the understanding of a lossy reverberation chamber, but they can also be extended to other non-ideal lossy environments and statistical methods. The measured mean power densities inside a reverberation chamber with a variety of lossy configurations are compared with the values obtained from the power balance method, showing the importance of this theoretical development and several future directions for research.

A Fully Analog High Performances Automatic System for Phase Measurement of Electrical and Optical Signals

In this paper, we present a high performance, automatic fully analog phase-to-voltage converter (PVC) circuit for phase shift measurements of periodic waveforms and repeated pulsed signals with zero and nonzero mean values. The PVC operation is fully automatic because an internal closed feedback loop guarantees the self-phase alignment (self-locking) between the reference and input signals. The system has been tested by measuring the phase shifts between the electrical signals generated by digital waveform generators and by photodiodes. The PVC output voltage dynamic range is ±10 V, independently from the phase-shift full-scales equal to ±10°, ±1°, and ±0.1°. The increase of the PVC sensitivity, expressed in volts/degree, which can be easily set to about 1, 10, and 100 V/°, is achieved without any amplification of the signal so avoiding the increasing and/or introduction of additional electronic noise to the measurements. As a consequence, for the smallest phase-shift full-scale equal to ±0.1°, the proposed PVC circuit is capable to achieve phase resolutions in the order of 0.0001°, a value one order of magnitude better than that one of commercial lock-in amplifiers. In the case of optical applications, the PVC is able to detect laser power variations with sensitivity values settable to about 6, 60, and 600 V/ $\mu \!$ W so achieving the best resolution of 16 pW.

Research on the Recursive Method of Real Time Variance Calculation for Non-Zero Mean Value Data

In the area of manufacturing and industrial engineering, variance calculation is the basic method to monitor the performance of instrument. The new improved method of real-time variance calculation is put forward in this paper to calculate the variance of experiment data, despite of zero or non-zero mean value data, Then it is possible to calculate the variance of any kind data at real time without save the historical data. Experiment results shows that the new method for calculate the variance can greatly improve the calculating efficiency with high precision..

Phase Statistics for Strong Scatterers in SAR Interferograms

In synthetic aperture radar interferometry, past studies of interferometric phase statistics are mainly based on the assumption that the interferogram cell size is much larger than the wavelength of the incident radiation and the scene is a homogeneously distributed scatterer. However, strong scatterers are often present in the scene, and in this work, the interferometric phase statistics are studied for this case for single-look interferograms. Its closed-form probability density function is first derived by approximating the complex interferogram signals to two correlated Gaussian random variables with nonzero-mean values. The closed-form mean value and variance are then derived with the assumption that the intensity of the strong scatterer is much larger than that of its background. It is shown that the phase statistics of strong scatterers are related not only to the correlation but also to the intensity of the dominant point and the phase difference variation between the dominant point and the remaining points.

Validity of the Weakly Nonlinear Solution of the Cauchy Problem for the Boussinesq‐Type Equation

We consider the initial‐value problem for the regularized Boussinesq‐type equation in the class of periodic functions. Validity of the weakly nonlinear solution, given in terms of two counterpropagating waves satisfying the uncoupled Ostrovsky equations, is examined. We prove analytically and illustrate numerically that the improved accuracy of the solution can be achieved at the timescales of the Ostrovsky equation if solutions of the linearized Ostrovsky equations are incorporated into the asymptotic solution. Compared to the previous literature, we show that the approximation error can be controlled in the energy space of periodic functions and the nonzero mean values of the periodic functions can be naturally incorporated in the justification analysis.

An Efficient DOA Estimation Algorithm for Spatial-Temporal Correlated Sources

This paper presents a signal direction-of-arrival (DOA) estimation approach that possesses excellent performance in spatial and temporal correlated signals environments. Firstly, an algebraic solution of the null subspace is derived based on the Vandermonde structured steering vectors of uniform linear array when all the sources possess identical nonzero mean value, and then, the DOA estimation is obtained with a polynomial rooting method. The novel algorithm performs much better than the conventional algorithms in the situation that the sources are closely spaced or correlated, and simulations have verified the validity of the algorithm.