Cauchy Distribution Research Articles

Measurement of the Dispersion of χ(3)$\chi ^{(3)}$ of SiO2${\rm SiO}_2$ and SiN Across the THz and Far‐Infrared Frequency Bands

AbstractTerahertz (THz) radiation sources based on two‐color femtosecond plasmas in air are becoming a mature technology for coherent spectroscopy and strong‐field physics across the extended THz range to several tens of THz. The field‐resolved detection of such THz transients relies on the third‐order nonlinearity of the detection medium. Here, a comparative measurement is demonstrated with air‐biased coherent detection (ABCD) and solid‐state biased detection (SSBCD) as a novel method to measure the dispersion of the magnitude and phase of the relevant third‐order nonlinearity for fused silica () and silicon nitride (SiN). Based on the development of the ultrabroadband SSBCD device with a detection bandwidth exceeding 30 THz, measurements are obtained across the 1–28 THz frequency range, hence covering the THz and far‐infrared. It is shown that the vibrational modes in and SiN in the THz range lead to strong resonant enhancement and dispersion of the nonlinearity. The SSBCD devices operate down to nanojoule (nJ) probe energy, and their is demonstrated by measuring the dielectric function of the Lorentzian line profile of transverse‐optical (TO) phonon mode at 9 THz in single‐crystal gallium arsenide (GaAs) and observing the weak phonon combination bands near the TO phonon.

Similar experimental study on diffusion and distribution of diesel exhaust in confined space of a coal mine.

In the confined space of the underground coal mine, which is dominated by transportation lanes, explosion-proof diesel-powered trackless rubber-wheeled vehicles are becoming the main transportation equipment, and the exhaust gas produced by them is hazardous to the health of workers and pollutes the underground environment. In this experiment, a similar test platform is built to study the effects of wind speed, vehicle speed, and different wind directions on the diffusion characteristics of exhaust gas. In this paper, CO and SO2 are mainly studied. The results show that the diffusion of CO and SO2 gas is similar and the maximum SO2 concentration only accounts for 11.4% of the CO concentration. Exhaust gas is better diluted by increasing the wind speed and vehicle speed, respectively. Downwind is affected by the reverse wind flow and diffuses to the driver's position, which is easy to cause occupational diseases. When the wind is a headwind, the exhaust gases spread upwards and make a circumvention movement, gathering at the top. When the wind speed and vehicle speed are both 0.6m/s, the CO concentration corresponds to the change trend of the Lorentz function when the wind is downwind and the CO concentration corresponds to the change trend of the BiDoseResp function when the wind is headwind. The study of exhaust gas diffusion characteristics is of great significance for the subsequent purification of the air in the restricted mine space and the protection of the workers' occupational health.

High-Quality Multi-Emitter LED-Based Retrofits for Incandescent Photometric A Illuminant Reliability of R2 Evaluation

This research deals with the design problems of LED-based spectrally tunable light sources (LSTLSs). The study aims to assess the reliability of popular models for the spectral modeling of LED radiation and a typically used curve-fitting criterion (R2) in the development of high-quality multi-emitter LED retrofits for incandescent photometric illuminant. The research methodology involves modeling each LED channel using Lorentz and Gaussian functions and combining multiple channels to approximate the desired spectral power distribution (SPD). After the optimization, 20 various LED sets were designed, which allowed us to replicate the SPD of CIE illuminant A with a very high R2 value. Two sets were constructed and measured to recognize the reliability of the simulation approach. The results suggest that for planning the LSTLS for photometric applications, these models are unreliable as they do not reflect the real effect of changes in the characteristics of the components nor reveal the share of various spectral ranges. Therefore, the decisions made on these criteria may not be the best solutions in the context of specific applications.

Physical model of neutron scattering by clathrate hydrate and C 60 hosting paramagnetic oxygen molecules

This paper describes the physical modelling of neutron scattering in two polycrystalline inclusion compounds, fully deuterated clathrate hydrate and C60 , each with paramagnetic oxygen as guest molecules. For studying the suitability of these materials for neutron moderation to very low energies, the model includes, in addition to the magnetic neutron scattering by the oxygen, the nuclear scattering by all constituents. The theoretical total cross sections are calculated based on the phonon density of states obtained by density functional theory and molecular dynamics simulations. At low temperatures, the developed scattering kernels are in good agreement with experimental neutron scattering data reported in the literature. At 20 K and above, a Lorentzian distribution for the zero-field splitting of the magnetic substates of the spin triplet of the oxygen molecules helps to reproduce magnetic peaks observed in inelastic neutron scattering experiments better than the original theory based on a single-valued splitting constant. Neutron spectra obtained by Monte Carlo simulations in infinite media are presented, highlighting the potential use of O2 -containing fully deuterated clathrate hydrate as a neutron moderator for the production of very cold neutrons.

Forecasting VIX using Bayesian deep learning

AbstractRecently, deep learning techniques are gradually replacing traditional statistical and machine learning models as the first choice for price forecasting tasks. In this paper, we leverage probabilistic deep learning for inferring the volatility index VIX. We employ the probabilistic counterpart of WaveNet, Temporal Convolutional Network (TCN), and Transformers. We show that TCN outperforms all models with an RMSE around 0.189. In addition, it has been well known that modern neural networks provide inaccurate uncertainty estimates. For solving this problem, we use the standard deviation scaling to calibrate the networks. Furthermore, we found out that MNF with Gaussian prior outperforms Reparameterization Trick and Flipout models in terms of precision and uncertainty predictions. Finally, we claim that MNF with Cauchy and LogUniform prior distributions yield well-calibrated TCN, and Transformer and WaveNet networks being the former that best infer the VIX values for one and five-step-ahead forecasting, and the probabilistic Transformer model yields an adequate forecasting for the COVID-19 pandemic period.

Nonzero current due to coherent dynamic electron transport through a dimer with no external bias

We have proposed a mechanism of the interplay of injected coherence and decoherence dynamics of the system in electron transport through an excitonic dimer when it is simultaneously connected to thermocoherent electron source and a thermal electron sink. Due to such an interplay, the variation of current with the energy gap between two excitonic states which is the internal bias of the system, is largely affected and it markedly bears the signature of the decoherence dynamics. We have also shown an extension in the modification of Landauer conductance formula for electron transport through excitonic dimer. The current has the property of an asymmetry in spectral width which can be understood in terms of sum of two Lorentzian profiles. More remarkably we have shown that current due to electron transport through the dimer can also arise at zero external bias which is a purely quantum coherent effect of the source fermionic reservoir having zero thermal occupation number.

Nonplanar ion acoustic waves in e-p-i plasmas with non-Maxwellian distributed electrons and positrons

The process of propagation of cylindrical and spherical ion acoustic solitary waves in an electron, positron, and ion plasma system is studied. The electrons are considered to have the generalized (r, q) distribution, while the positrons are supposed to have the kappa distribution, also known as the Lorentzian distribution. The classic nonlinear equation, Korteweg de-Vries (KdV), has been numerically solved by employing appropriate mathematical transformations. The role of various plasma parameters and nonplanar geometry on the widths and amplitudes of nonlinear ion acoustic structures has been numerically investigated. The current study could be helpful to understand the significance of cylindrical and spherical solitary waves in laboratory, astrophysical as well as in space plasmas.

Enhancement of third-harmonic generation in all-dielectric kite-shaped metasurfaces driven by quasi-bound states in the continuum

Abstract We develop a new all-dielectric metasurface for designing high quality-factor (Q-factor) quasi-bound states in the continuum (quasi-BICs) using asymmetry kite-shaped nanopillar arrays. The Q-factors of quasi-BICs follow the quadratic dependence on the geometry asymmetry, and meanwhile their resonant spectral profiles can be readily tuned between Fano and Lorentzian lineshapes through the interplay with the broadband magnetic dipole mode. The third-harmonic signals of quasi-BIC modes exhibit a gain from 43.4- to 634-fold enhancement between samples with an axial-length difference of 15 nm and 75 nm when reducing the numerical aperture of the illuminating objective lenses in nonlinear measurement, which is attributed to the increasing illumination spot size and the less contribution from the large oblique incident light for establishing quasi-BIC modes with high-Q spectral profile and strong near-field intensity. The silicon-based metasurfaces with their simple geometry are facile for large-area fabrication and open new possibilities for the optimization of upconversion processes to achieve efficient nonlinear devices.

Robust colored point cloud alignment based on L*a*b* guided and Cauchy kernel

AbstractPrecision agriculture benefits from point set registration, which can monitor plant health and growth in real time, promote the precise application of fertilizers and pesticides, and provide technical support for achieving sustainable development of agriculture. In this work, we propose a robust point set registration method for precision agriculture based on L*a*b* color guidance, bidirectional search and Cauchy distribution. First, the L*a*b* color guidance is applied to establish accurate correspondences between agricultural RGB‐D data. Second, the bidirectional nearest neighbor search strategy between point sets improves the reliability of establishing correspondences and broadens the convergence domain of the algorithm. Third, Cauchy distribution is utilized as an energy function for noise suppression, which further improves the robustness of the algorithm in dealing with complex vegetation scenes. Finally, results of ablation and simulation experiments indicate that the proposed registration algorithm can achieve more accurate and robust alignment results than other classic and state‐of‐the‐art point cloud registration algorithms to achieve monitoring and comparison of plant growth.

An enhanced NSGA-II and a fast constraint repairing method for combined heat and power dynamic economic emission dispatch

In this paper, an enhanced NSGA-II (ENSGA-II) is presented for the combined heat and power dynamic economic emission dispatch (CHPDEED). ENSGA-II produces offspring individuals by a novel crossover of the Cauchy distribution with adaptive location and scale parameters. It can not only sufficiently explore and exploit the decision space but also remain a relatively high population diversity. Also, ENSGA-II adopts a modified crowding distance to penalize crowded individuals, seeking to evenly distribute the individuals in the objective space. In addition, a fast constraint repairing method (FCRM) is proposed to significantly reduce the constraint violations and guide infeasible individuals to move towards feasible zones rapidly. The proposed ENSGA-II is applied to a number of multi-objective optimization problems and compared with the other eight multi-objective evolutionary algorithms (MOEAs). ENSGA-II is found to produce better results on most problems, such as smaller inverse generational distances, larger hypervolumes, larger coverage rates and smaller spacings. Therefore, ENSGA-II can obtain a satisfactory Pareto set with broad spread, high diversity, strong convergence and good evenness, and it is an efficient alternative for CHPDEED.

A new goodness-of-fit test for the Cauchy distribution

A new goodness-of-fit test for the Cauchy distribution

Transport-entropy and functional forms of Blaschke–Santaló inequalities

We explore alternative functional or transport-entropy formulations of the Blaschke–Santaló inequality. In particular, we obtain new Blaschke–Santaló inequalities for s -concave functions. We also obtain new sharp symmetrized transport-entropy inequalities for a large class of spherically invariant probability measures, including the uniform measure on the unit Euclidean sphere and generalized Cauchy and Barenblatt distributions.

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Fast-Field-Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a powerful, non-destructive magnetic resonance technique that enables, among other things, the investigation of slow molecular dynamics at low magnetic field intensities. FFC-NMR relaxometry measurements provide insight into molecular motion across various timescales within a single experiment. This study focuses on a model-free approach, representing the NMRD profile R1 as a linear combination of Lorentzian functions, thereby addressing the challenges of fitting data within an ill-conditioned linear least-squares framework. Tackling this problem, we present a comprehensive review and experimental validation of three regularization approaches to implement the model-free approach to analyzing NMRD profiles. These include (1) MF-UPen, utilizing locally adapted L2 regularization; (2) MF-L1, based on L1 penalties; and (3) a hybrid approach combining locally adapted L2 and global L1 penalties. Each method’s regularization parameters are determined automatically according to the Balancing and Uniform Penalty principles. Our contributions include the implementation and experimental validation of the MF-UPen and MF-MUPen algorithms, and the development of a “dispersion analysis” technique to assess the existence range of the estimated parameters. The objective of this work is to delineate the variance in fit quality and correlation time distribution yielded by each algorithm, thus broadening the set of software tools for the analysis of sample structures in FFC-NMR studies. The findings underline the efficacy and applicability of these algorithms in the analysis of NMRD profiles from samples representing different potential scenarios.

An exhaustive exploration of Zn0.15Sn0.85(Se0.95S0.05)2 crystal-based photodetector and its potential application as a photocatalytic material

The research pioneers the exploration of synthesized quaternary Zn0.15Sn0.85(Se0.95S0.05)2 (ZSSS) crystals, demonstrating remarkable efficacy as optoelectronic switching devices and potent photocatalysts. The ZSSS photodetector recorded a stable photoresponse with remarkable rapid rise and decay times. The Langmuir-Hinshelwood kinetic model was used to look at the photocatalytic activity at different methylene blue concentrations. The researchers grew highly pure ZSSS crystals using the direct vapour transport (DVT) method. Field effect scanning electron microscopy (FESEM) and high-resolution transmission electron microscopy (HRTEM) images reveal the layer growth mechanism in the grown crystals. The structural analyses of the grown crystals were carried out using an X-ray diffraction (XRD) pattern and temperature-dependent Raman spectroscopy. The Lorentzian function was fitted to experimental data to carry out the temperature-dependent Raman analysis. The grown crystals exhibit a direct optical bandgap of 1.69 eV. The electrical analyses explain the semiconducting nature of the crystals.

Full-Scale Observations for the Combined Wind-Induced Responses of a Cylindrical Tower

This paper presents full-scale observations of wind-induced vibrations on a 140[Formula: see text]m high cylindrical reinforced concrete tower under non-stationary and strong wind conditions. The vibration responses of the tower in two planar orthogonal axes and rotation, in conjunction with wind speed and direction data, have been utilized to extract the response characteristics. The primary focus is on discussing the correlation of wind-induced responses in three components: Along-wind, across-wind, and torsion. Throughout the varying levels of oscillation, the tower’s responses clearly exhibit correlations among these components. The correlation coefficients between along-wind and across-wind responses, as well as along-wind and torsional responses, remain negligible across the entire dataset. In contrast, during intense oscillations, there is a near-perfect correlation between the across-wind and torsional responses. Furthermore, the probability density functions (PDFs) of the response components under strong wind conditions significantly deviate from the Gaussian distribution and closely resemble the Cauchy distribution. The joint PDFs also indicate that the along-wind response is statistically independent of the other response components, while the across-wind response correlates well with the torsion, as indicated by the non-Gaussian distribution. This paper also includes distinct observations regarding dominant oscillating frequencies, torsional amplitudes, and vertical vibration amplitudes. The importance of this research lies in its examination of the relationship between different response components, a crucial aspect in understanding how structures behave under wind loading. By emphasizing the need for full-scale measurements, this study aims to provide valuable validation for previous theoretical and experimental research findings.

Development and application of a three-dimensional pseudo-Voigt function for muon spin relaxation analysis of weakly magnetic materials.

We present a three-dimensional pseudo-Voigt function to analyze muon spin relaxation (μSR) in weakly magnetic materials. Our approach approximates the Voigt function by superimposing Gaussian and Lorentzian functions using a one-dimensional method proposed by Di Rocco and Cruzado [Acta Phys. Pol., A 122, 666 (2012)]. We derive the peak of the Voigt function analytically and express the Half Width at Half Maximum (HWHM) of the Voigt function as a function of the HWHMs of the Gaussian and Lorentzian functions. We compare the pseudo-Voigt function to the exact Voigt function and find a maximum normalized discrepancy of ∼20% at the tail of the distribution function, depending on the ratio of Lorentzian to Gaussian HWHMs and internal magnetic field. We apply the derived three-dimensional pseudo-Voigt function to calculate μSR functions for zero- and longitudinal-field experiments and use them to fit μSR time spectra of La2-xSrxCuO4 with 2.4% Sr, employing a strong collision model with the static-based pseudo-Voigt muon spin relaxation function as the initial condition. Our results show that the Gaussian- and Lorentzian-fitted parameters and fluctuation rate are in good agreement with results from the exact Voigt function for a temperature range of 30-200K, with the deviation of Gaussian and Lorentzian width parameters reaching ∼0.15G below 30K.

Properties of a Lorentz correlated beam in uniaxial crystal

AbstractThe equation of a Lorentz‐correlated Schell‐model beam (LCSMB) in a uniaxial crystal is derived, and the relation of spreading properties and coherence with and are analyzed during propagation. The intensity of an LCSMB in the uniaxial crystal will evolve from Lorentz distribution into diamond distribution, and the LCSMB with smaller will evolve from Gaussian distribution into Lorentz distribution faster. The distribution of coherence of an LCSMB will lose the Lorentz distribution and become an elliptical distribution as increases.

Spot size measurement of a deuterium-tritium dense plasma focus using neutron radiography.

Neutron radiography is a technique uniquely suited to applications in nuclear diagnostics, non-destructive testing, and subcritical experiments. The spatial resolution of neutron radiographs is degraded by optical blur in the imaging system and the neutron source size, where the ideal source is point-like to optimize the point-spread function. A potential neutron source for radiography is the dense plasma focus (DPF), a coaxial Z-pinch that produces thermonuclear and beam-target neutrons. To assess if the source size is suitable for radiography, a neutron imaging system was used to measure the source size of the 4 MA Sodium DPF at the Nevada National Security Site operating with deuterium-tritium gas-fill. The source size was measured using the edge-spread function of tungsten objects, each having a rolled (convex) edge. The spot size was found to be 7-12mm full-width at half-max(FWHM) assuming a Gaussian source, though comparison is presented for Lorentzian and Bennett distributions. The average FWHM was found to be 8.6 ± 1.2mm vertically and 10.8 ± 1.2mm horizontally with respect to the image plane, averaging over varied edges and alignments. The results were sensitive to source alignment and edge metrology, which introduced notable uncertainties. These results are consistent with separate experimental measurements as well as magnetohydrodynamics simulations of this DPF, which suggest that neutron production can originate from pinches ∼5-7mm off-axis. These results suggest that the DPF should be used for radiography at low magnification (M < 1) where spot size does not dominate spatial blur.

Variability of Blue Supergiants in the LMC with TESS

The blue supergiant (BSG) problem, namely, the overabundance of BSGs inconsistent with classical stellar evolution theory, remains an open question in stellar astrophysics. Several theoretical explanations have been proposed, which may be tested by their predictions for the characteristic time variability. In this work, we analyze the light curves of a sample of 20 BSGs obtained from the Transiting Exoplanet Survey Satellite (TESS) mission. We report a characteristic signal in the low-frequency (f ≲ 2 day−1) range for all our targets. The amplitude spectrum has a peak frequency of ∼0.2 day−1, and we are able to fit it by a modified Lorentzian profile. The signal itself shows strong stochasticity across different TESS sectors, suggesting its driving mechanism happens on short (≲months) timescales. Our signals resemble those obtained for a limited sample of hotter OB stars and yellow supergiants, suggesting their possible common origins. We discuss three possible physical explanations: stellar winds launched by rotation, convection motions that reach the stellar surface, and waves from the deep stellar interior. The peak frequency of the signal favors processes related to the convective zone caused by the iron opacity peak, and the shape of the spectra might be explained by the propagation of high-order, damped gravity waves excited from that zone. We discuss the uncertainties and limitations of all these scenarios.

Transform coefficient distribution modeling based frame-level adaptive rate control for VVC

Rate control is a key issue in the research of video coding optimization. In this work, we propose a statistical modeling based frame-level distortion estimation model and a distortion dependency based rate control optimization algorithm for Versatile Video Coding (VVC). VVC has incorporated into more advanced coding tools, resulting in the distribution of transform coefficient more sharper. In response to this phenomenon, the TCD of VVC is modeled by the probability density function (PDF) of Cauchy distribution and generalized Gaussian distribution (GGD) individually. Then, a sliding window-based frame-level distortion model is proposed, which is used for derivation of inter-frame distortion dependency factor. According to the derived distortion dependency factor, a frame-level rate control optimization algorithm is presented to update the coding parameters in practical coding process. Experiments have shown that the proposed method could effectively improve rate–distortion performance, achieving an average rate distortion performance improvement of 0.72% in sequences blow 4K resolution, and 1.47% in 4K sequences in low delay P frame (LDP) configuration.