Cauchy Model Research Articles

Locally optimum watermark decoder in NSST domain using RSS-based Cauchy distribution

It is important to consider the tradeoff between imperceptibility and robustness requirements in developing an image-watermarking technique, some statistical model-based image watermarking schemes have been designed in the past decade. The effectiveness of a statistical watermark decoder depends highly on the modeling of the transform-domain coefficients and the use of hypothesis testing. In this study, a multiplicative image watermarking scheme is proposed in the nonsubsampled Shearlet transform (NSST) domain, where NSST coefficients are modeled by ranked set sample (RSS) based Cauchy statistical distribution and locally most powerful (LMP) test criterion is applied. Digital image watermarking technique consists of two parts, namely, embedding and extracting. In the embedding process, to achieve relatively good imperceptibility and robustness, watermark data is inserted into the significant NSST directional subband that has the highest energy value, by modifying nonlinearly the significant NSST coefficients. In the extracting phase, a scheme is proposed for designing a blind NSST domain watermark decoder incorporating the RSS based Cauchy statistical distribution and LMP test criterion. Here, the RSS method is used to estimate the location parameter and shape parameter of Cauchy statistical distribution instead of traditional maximum-likelihood (ML) method, which can provide the Cauchy model with higher precision parameters. Experimental results on a set of standard test images show significant improvements in imperceptibility and robustness using the proposed method compared with the best known state-of-the-art approaches.

Quaternions and Cauchy Classical Theory of Elasticity

AbstractDeveloped by French mathematician Augustin-Louis Cauchy, the classical theory of elasticity is the starting point to show the value and the physical reality of quaternions. The classical balance equations for the isotropic, elastic crystal, demonstrate the usefulness of quaternions. The family of wave equations and the diffusion equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic solid. Using the quaternion algebra, we present the derivation of the quaternion form of the multiple wave equations. The fundamental consequences of all derived equations and relations for physics, chemistry, and future prospects are presented.

Impact force and moment problems on random mass density fields with fractal and Hurst effects.

This paper reports the application of cellular automata to study the dynamic responses of Lamb-type problems for a tangential point load and a concentrated moment applied on the free surface of a half-plane. The medium is homogeneous, isotropic and linear elastic while having a random mass density field with fractal and Hurst characteristics. Both Cauchy and Dagum random field models are used to capture these effects. First, the cellular automata approach is tested on progressively finer meshes to verify the code against the continuum elastodynamic solution in a homogeneous continuum. Then, the sensitivity of wave propagation on random fields is assessed for a wide range of fractal and Hurst parameters. Overall, the mean response amplitude is lowered by the mass density field's randomness, while the Hurst parameter (especially, for β < 0.2) is found to have a stronger influence than the fractal dimension on the response. The resulting Rayleigh wave is modified more than the pressure wave for the same random field parameters. Additionally, comparisons with previously studied Lamb-type problems under normal in-plane and anti-plane loadings are given. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

The compound truncated Poisson Cauchy model: A descriptor for multimodal data

Multimodal data are often present in synthetic aperture radar (SAR) image processing. Such images are often modeled by probability mixtures, but such solution may involve a large number of parameters and its inference becomes challenging. To address this issue, we proposed a probability distribution capable of describing multimodal data with only three parameters. The introduced model is defined by the sum of a random number, following the truncated Poisson law, of independent random variables with the Cauchy model, called compound truncated Poisson Cauchy (CTPC) distribution. We derived the characteristic function (cf), a distance measure between cfs, and provided estimators for the CTPC parameters: maximum likelihood estimators (MLEs) and quadratic distance estimators (QDEs). Furthermore, we derived a goodness-of-fit (GoF) distance based on the CTPC law and its empirical cf. To quantify the performance of the proposed estimators and GoF statistic, we employed a Monte Carlo simulation and the results suggest that QDEs outperform MLEs. Finally, we detail a numerical experiment with actual SAR data which describes a segment of SAR intensities with at least two types of textures. Our model could outperform six SAR intensities models: Weibull, gamma, generalized gamma, K, G0, and beta generalized normal.

Optical-energy properties of CdSe thin film

The optical constants and thickness of CdSe thin films prepared by quasi close-space sublimation method are determined. The structural investigations performed by means of XRD technique showed that the films have a polycrystalline and hexagonal structure. The optical constants and the band gap of the films under study have been determined (Eg= 1.68 eV). Optical properties (refractive index n(λ), absorption coefficient α(λ), and extinction coefficient k(λ)) of thin films and thickness d can be determined from the transmission spectrum. The dispersion of the refractive index was explained using a single oscillator model. Single oscillator energy and dispersion energy are obtained from fitting. Optical parameters of the films were determined using the Cauchy, Sellmeier and Wemple models.

Fracture of beams with random field properties: Fractal and Hurst effects

The classical problem of peeling a beam off a substrate is studied through a re-examination of Griffith's fracture criterion in the presence of multiscale random properties. Four types of wide-sense homogeneous Gaussian random fields of the vector {Young's modulus E, surface energy density γ}, parametrized by the beam axis, are considered: Ornstein–Uhlenbeck, Matérn, Cauchy, and Dagum. The latter two are multiscale and allow decoupling of the fractal dimension and Hurst effects. Also calculated is the variance of the crack driving force G with any given type of random field in terms of the covariances of E and γ, under either fixed-grip or dead-load conditions. This investigation is complemented by a study of the stochastic crack stability which involves a stochastic competition between potential and surface energies. Overall, we find that, for Cauchy and Dagum models, the introduction of fractal-and-Hurst effects strongly influences the fracture mechanics results. Notably, while the Cauchy and Dagum models represent a more realistic scenario of random fields, given the same covariance on input, the response on output is strongest for Matérn, then Ornstein–Uhlenbeck, then Cauchy and, finally, Dagum model.

Characterization of e-beam evaporated Ge, YbF3, ZnS, and LaF3 thin films for laser-oriented coatings.

Thin films of Ge, ZnS, YbF3, and LaF3 produced using e-beam evaporation on ZnSe and Ge substrates were characterized in the range of 0.4-12 µm. It was found that the Sellmeier model provides the best fit for refractive indices of ZnSe substrate, ZnS, and LaF3 films; the Cauchy model provides the best fit for YbF3 film. Optical constants of Ge substrate and Ge film as well as extinction coefficients of ZnS, YbF3, LaF3, and ZnSe substrate are presented in the frame of a non-parametric model. For the extinction coefficient of ZnS, the exponential model is applicable. Stresses in Ge, ZnS, YbF3, and LaF3 were estimated equal to (-50)MPa, (-400)MPa, 140 MPa, and 380 MPa, respectively. The surface roughness does not exceed 5 nm for all films and substrates.

Spectroscopic studies on liquid crystalline n-hexyloxy-cyanobiphenyl with dispersed citrate-capped gold nanoparticles in visible region

ABSTRACTIn the present manuscript, the characterisation was done on liquid crystalline n-hexyloxycyanobiphenyl (6ocb) compound with dispersed citrate-capped gold nanoparticles (Au NPs) at different concentrations. It is observed that the birefringence enhances with increase in concentration of Au NPs. Also, strong Vander Waal’s interaction takes place due to well capping between the Au NPs and 6ocb molecules. The refractive indices are determined by using modified spectrometer at different wavelengths. The orientational order parameter has been determined from various theoretical molecular internal field models namely, Kuczynski, Effective geometry, Haller’s extrapolation and Vuks. The dispersive power ω is estimated for two consecutive wavelengths for the case of <n>, ne and no at different wavelengths found to be constant with temperature. The values of cross-over temperature, TCO determined from the temperature gradients of ne and no. Further, the refractive indices measured are fitted with two and three coefficient Cauchy model. Three coefficient Cauchy model is favourable than two coefficient Cauchy model for high birefringence liquid crystals. The results obtained are compared and discussed. Further, the phase transitions can be easily identified by GMSD Image processing method with Matlab tool to reduce the costly equipment’s usage in finding the heat flow with respect to temperature.

On how swarm robotics can be used to describe particle system’s deformation

In previous works, we have described time evolution of a two-dimensional particle lattice, subject to deformation, without the use of Newton’s law. According to our experience, in control of robotic swarm, the new position of a particle is determined by the spatial position of its neighbours; therefore, we have used an interaction law based on the spatial position of the particles themselves. The tool that we have realized reproduced some behaviour of deformable bodies both according to the standard Cauchy model and the second gradient theory. In this paper, we try to stress what is still under investigation, like the relationship describing the interaction rule and its physical meaning; moreover, we shall describe as some solutions do not agree with the behaviour of the classical solution coming out from differential equations.

Cauchy, Cauchy–Santos–Sartori–Faria, Logit, and Probit Functions for Estimating Seed Longevity in Soybean

Seed longevity is characterized as the time for which seed remains viable during storage. Seed longevity can be estimated by a Probit model that determines the period in which 50% of seeds have lost viability (P50). The transformed data are binary and when they are not normally distributed, it is necessary to modify the Probit model or apply other functions to estimate longevity. This work aimed studied the use of the Logit, Cauchy, and Cauchy–Santos–Sartori–Faria (Cauchy‐SSF) functions to estimate the longevity of soybean seed [Glycine max (L.) Merr.] and compared Probit longevity models for the ordinary least squares (OLS) adjustment method and the generalized linear model (GLM). Ten seed lots were used to estimate water content, germination, and longevity. The P50 data were transformed via the Probit, Logit, Cauchy, and Cauchy‐SSF functions to estimate the coefficients of determination, the Akaike information criterion, deviance, dispersion, and the regression residuals. The effect on the results was observed, depending on the link function. The Cauchy‐SSF function as part of the OLS method estimated longevity in eight seed lots within the interval of interest (II), and the Cauchy function as part of the GLM estimated longevity in nine seed lots. The Cauchy, Cauchy‐SSF, and Logit models were capable of estimating the longevity of soybean seeds (P50) slightly better than the Probit model. We suggest the Cauchy‐SSF function for the OLS method and the Cauchy function for the GLM method to estimate soybean seed longevity when the data are not normally distributed.Core Ideas The Cauchy, Cauchy–Santos–Sartori–Faria Cauchy‐SSF, and Logit functions estimated longevity in soybean seeds more robustly than the Probit function. The ordinary least squares method combined with the Cauchy‐SSF function is as good as the generalized linear model method with the Cauchy function. The selection of the function changes the estimated time when 50% of seeds have lost viability, emphasizing the importance of the correct choice.

Morphology, UV–visible and ellipsometric studies of sodium lithium orthovanadate

Sodium lithium orthovanadates were prepared by the classic ceramic method technique. Structure, phase purity, composition, and morphology were characterized by X-ray powder diffraction, infrared spectroscopy, energy dispersive spectroscopy, scanning-electron microscopy and atomic force microscopy. The optical properties of NaxLi1−xCdVO4 (x = 0.5, 1) compounds prepared were recorded at room temperature using ultra-visible and ellipsometric spectroscopies in the spectral range (200–800) nm. The average reflectance of the pellets showed high reflectivity (over 80%) in the visible spectrum. The UV–Vis absorption bands are assigned to the charge transfer from the oxygen ligands to the central vanadium atom inside the [VO4]3− groups in the orthovanadate compounds. The optical band gaps Eg of both samples are evaluated using Kubelka–Munk function. The analysis of the data revealed the existence of optical allowed direct transition for NaxLi1−xCdVO4 (x = 0.5, 1). Spectroscopic ellipsometry measurements have been performed on NaxLi1−xCdVO4 (x = 0.5, 1) specimens and their optical properties were analyzed using the Cauchy model.

An Asymmetric Bimodal Distribution with Application to Quantile Regression

In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data.

On Discrete Wrapped Cauchy Model

Modeling angular data throws many challenges in practical situations. Good number of circular / semicircular models are developed for modeling continuous circular / angular data. Scant attention was paid in analysis of discrete angular data, in particular, construction of discrete angular models for fitting angular data is not touched so far. Hence an attempt is made to develop method for constructing Discrete l - axial models and study their population characteristics. Keywords: China insurance industry, Foreign fund, Challenge DOI : 10.7176/MTM/9-4-02 Publication date : April 30 th 2019.

Group and phase birefringence dispersion of pure and doped lithium niobate crystals obtained by analysis of interference pattern observed behind a plane polariscope

A sample of lithium niobate crystal with known thickness is set on a vertical rotary stage, placed in between two crossed plane polarizers and illuminated by a collimated beam of white light. The sample is rotated to an appropriate position, and interference fringes observed behind an analyzer are recorded by a fiber-optic spectrometer. The recorded channeled spectrum is then analyzed, and from measured positions of interference minima (dark fringes) and known crystal’s thickness, the group birefringence of the crystal sample is obtained as a function of wavelength. The fringe order versus position of the fringe within the spectrum is fitted by appropriate dispersion function, and as the result phase birefringence as a function of wavelength is found. The measurement is performed for a sample declared as undoped, a sample doped with 0.025 wt. % of Fe, and a sample doped with 0.025 wt. % of Fe and 0.075 wt. % of Mn in the wavelength ranges (470 to 780) nm and (900 to 1700) nm. A good agreement between group birefringence dispersion obtained from positions of interference minima and known sample’s thickness and that calculated from phase birefringence dispersion given by Sellmeier dispersion model (used for undoped sample) and Cauchy model (used for doped samples) is found.

Fox H-kernel and θ-deformation of the Cauchy Two-Matrix Model and Bures Ensemble

Abstract A $\theta $-deformation of the Laguerre weighted Cauchy two-matrix model, and the Bures ensemble, is introduced. Such a deformation is familiar from the Muttalib–Borodin ensemble. The $\theta $-deformed Cauchy–Laguerre two-matrix model is a two-component determinantal point process. It is shown that the correlation kernel, and its hard edge scaled limit, can be written in terms of particular Fox H-functions, generalising the Meijer G-function class known from the study of the case $\theta = 1$. In the $\theta =1$ case, it is shown that the Laguerre–Bures ensemble is related to the Laguerre–Cauchy two-matrix model, notwithstanding the Bures ensemble corresponding to a Pfaffian point process. This carries over to the $\theta $-deformed case, allowing explicit expressions involving Fox H-functions for the correlation kernel, and its hard edge scaling limit, to also be obtained for the $\theta $-deformed Laguerre–Bures ensemble. The hard edge scaling limit is in the Raney class $(\theta /2+1,1/2)$.

Optical properties and charge transport of textured Sc2O3 thin films obtained by atomic layer deposition

Scandium oxide films with thickness d = 20–100 nm were deposited by atomic layer deposition (ALD) using tris(methylcyclopentadienyl) scandium (III) Sc(MeCp)3 and water vapors as precursors at reactor temperature range of 200–400 °C. The ALD-window was detected in the range of 230–370 °C. Growth per cycle remained constant and was 0.080–0.084 nm/cycle in this range. O/Sc ratio was found to be 1.49 which is close to stoichiometric Sc2O3. The films were polycrystalline. The grains were more apparent for the films grown at higher temperatures. The grain size increased with thickness. Cubic Sc2O3 phase was determined by FTIR, Raman spectroscopy and X-rays diffraction.In general, different crystallographic directions are more preferential for different process conditions. Films were textured and their growth occurred mainly in the (400) direction. The refractive index dispersions of deposited films were well described by the Cauchy model. Optical properties depended weakly on process parameters (temperature or thickness). As it was detected for the films with close thickness the refractive index slightly increased with deposition temperature increase. The Nasyrov-Gritsenko (N-G) multiphonon trap ionization model well describes the charge transport. The trap parameters were determined to be: concentration N = 1.5 × 1019 cm−3, thermal energy Wt = 0.83 eV, and optical energy Wopt = 1.66 eV.

Anti-plane shear Lamb's problem on random mass density fields with fractal and Hurst effects

This paper reports a study of transient dynamic responses of the anti-plane shear Lamb's problem on random mass density field with fractal and Hurst effects. Cellular automata (CA) is used to simulate the shear wave propagation. Both Cauchy and Dagum random field models are used to capture fractal dimension and Hurst effects in the mass density field. First, the dynamic responses of random mass density are evaluated through a comparison with the homogenerous computational results and the classical theoretical solution. Then, a comprehensive study is carried out for different combinations of fractal and Hurst coefficients. Overall, this investigation determines to what extent fractal and Hurst effects are significant enough to change the dynamic responses by comparing the signal-to-noise ratio of the response versus the signal-to-noise ratio of the random field.

Nanostructured device based on coated ZnO layer as a window in solar cell applications

Abstract This work highlights some physical properties related to the influence of aluminum, tin and copper incorporation on nanostructured zinc oxide (ZnO:M; M:Al, Sn and Cu) thin films prepared by ultrasonic spray pyrolysis technique (USP) on glass substrate at 350±5 °C. For the as-grown layers, M- to Zn-ratio was fixed at 1.5 %. The effects of metal doping on structural, morphological, optical and electrical properties were investigated. X-ray diffraction pattern revealed that the as-prepared thin films crystallized in hexagonal structure with (0 0 2) preferred orientation. The surface topography of the films was performed by atomic force microscopy. AFM images revealed inhibition of grain growth due to the doping elements incorporation into ZnO matrix, which induced the formation of ZnO nanoparticles. Optical measurements showed a high transparency around 90 % in visible range. Some optical parameters, such as optical band gap, Urbach energy, refractive index, extinction coeffi-cient and dielectric constant were studied in terms of doping element. Particularly, dispersion of refractive index was discussed in terms of both Cauchy and single oscillator model proposed by Wemple and DiDomenico. Cauchy parameters and single oscillator energy E0 as well as dispersion energy Ed were calculated. Finally, electrical properties were investigated by means of electrical conductivity and Hall effect measurements. The measurements confirmed n type conductivity of the prepared thin films and a good agreement between the resistivity values and the oxidation number of doping element. The main aim of this work was the selection of the best candidate for doping ZnO for optoelectronics applications. The comparative study of M doped ZnO (M:Al, Sn and Cu) was performed. High rectifying efficiency of the Al/n-ZnO/p-Si/Al device was achieved and non-ideal behavior was revealed with n &gt; 4.

Adventures in pyrolysis II, modeling pyrolysis peaks of petroleum source rocks

Programmed pyrolysis is an integral part petroleum source rock evaluation. The analysis is used to determine the potential of a source rock to generate further petroleum, and with other geochemical measurements, how much it may have generated in the past. An important part of the overall evaluation is an estimate of the source rock thermal maturity. Unfortunately, the addition of any extraneous, non-native hydrocarbons can negatively impact the yield of the samples, and more important, the thermal maturity determination. These extraneous hydrocarbons can be petroleum previously generated and retained within the source rock, fluids that migrated in the subsurface into the rocks, or organic material added during the drilling process. The objective of this study was to determine if mathematical methods could be used to remove these extraneous contributions from the true source rock yields, and arrive at a better determination of thermal maturity.Eighteen samples were studies using the standard pyrolysis method applied in the geochemical services industry. Two aliquots of each sample were analyzed: one as-received and a second after solvent extraction solvents to remove soluble organic matter but not kerogen. The pyrograms typically associate with the conversion of native organic matter in the rock were considered as the sum of up to three underlying components which could be recovered by non-linear least squares methods. Four distribution functions were used to model the pyrograms: classical Gaussian distribution, the Cauchy function, the Logistic function and the Weibull distribution. In addition to the ability of each model to match the measured data, each was evaluated for ease of use. All models reproduced the total pyrolysis yields of the test samples, and generated Tmax values with agreed within 2 °C.•The Gaussian model was marginally better at fitting the measurements than the Logistic or Weibull models, and distinctly better than the Cauchy model. Based upon experience, the Gaussian model was the most forgiving in the choice of initial parameters.•The Cauchy model performed the poorest at fitting the measurements and had the largest differences between extracted and unextracted Tmax values. The deviations from the measured values were most pronounced at high and low temperatures due the longer tail of the Cauchy function.•The Logistic model has marginally lower ability to fit the measured data than the Gaussian model, and similar to the Weibull model. However, the Logistic model was more sensitive to the choice of initial values than the Gaussian model, but less sensitive than the Weibull model.•The Weibull model was marginally poorer at fitting the measurements than the Gaussian model and similar to the Logistic model. It did less well at fitting the four component model for the more complex samples. It was most sensitive to the accurate choices for the initial conditions to insure convergence. For some samples sequential manual choices for these parameters was needed before the Gauss-Newton method could be employed.

Effect of Ni nickel coated porous Si buffers layer on the structural and opto-electronic properties of silicon thin films

In this paper we present an extensive investigation of the effect of Ni metallization on the structural and opto-electronic properties of a dual porous silicon layers elaborated by electrochemical etching. Amorphous silicon thin films were deposited by plasma-enhanced chemical vapor deposition on the metalized porous layer. The microstructure of porous silicon films was systematically studied by atomic force microscopy (AFM), X-ray diffraction (XRD), Raman spectroscopy and Fourier transform infrared spectroscopy (FTIR). It was found that the structure of the porous layer metalized Nickel (SipMNi) strongly depends on the porosity level and on the immersion time in the Ni solution. The optical constants (n and k as a function of wavelength) of the SipMNi were obtained using variable angle spectroscopic ellipsometry (SE) in the UV–vis–NIR regions. The SE spectrum of the SipMNi was modeled as a mixture of void, crystalline silicon and Ni nanoparticles using the Cauchy model approximation. The electrical conductivity, conduction mechanism, relaxation model of the SipMNi/Si samples were studied by means of the impedance spectroscopy technique at various temperatures (340–410 °C). At high frequency a semiconductor to metallic behavior transition has been observed. A full correlation between the microstructure and opto-electrical properties has been presented. It was found that this simple and easy method is effective to produce silicon thin films with high quality suitable for opto-electronic applications.