Correlation Function Method Research Articles

Elucidating lipid conformations in the ripple phase: Machine learning reveals four lipid populations

A new mixed radial-angular, three-particle correlation function method in combination with unsupervised machine learning was applied to examine the emergence of the ripple phase in dipalmitoylphosphatidylcholine (DPPC) lipid bilayers using data from atomistic molecular dynamics simulations of system sizes ranging from 128 to 4096 lipids. Based on the acyl tail conformations, the analysis revealed the presence of four distinct conformational populations of lipids in the ripple phases of the DPPC lipid bilayers. The expected gel-like (ordered; Lo) and fluid-like (disordered; Ld) lipids are found along with their splayed tail equivalents (Lo,s and Ld,s). These lipids differ, based on their gauche distribution and tail packing. The disordered (Ld) and disordered-splayed (Ld,s) lipids spatially cluster in the ripple in the groove side, that is, in an asymmetric manner across the bilayer leaflets. The ripple phase does not contain large numbers of Ld lipids; instead they only exist on the interface of the groove side of the undulation. The bulk of the groove side is a complex coexistence of Lo,Lo,s, and Ld,s lipids. The convex side of the undulation contains predominantly Lo lipids. Thus, the structure of the ripple phase is neither a simple coexistence of ordered and disordered lipids nor a coexistence of ordered interdigitating gel-like (Lo) and ordered-splayed (Lo,s) lipids, but instead a coexistence of an ordered phase and a complex mixed phase. Principal component analysis further confirmed the existence of the four lipid groups.

Multi-sensor optimal placement of rotor-bearing system based on fault diagnosability

In view of the current situation that there are few studies on whether the fault signals that may occur in the rotor bearing system can be identified and analyzed in the sensor arrangement, fault diagnosability is applied to the optimal arrangement of the sensors in the rotor bearing system. The preliminary layout of the multi-sensor is carried out by analyzing the transmission path of the vibration signals in the rotor bearing system and based on the minimum path. Secondly, the nonparametric kernel density estimation method calculates the state information’s probability density function. The K-L divergence value is further used to measure fault detectability, fault separability, and fault diagnosability. Then, the correlation function method is used to fuse the multi-sensor information, and the optimal sensor layout is given with the fault diagnosability as an index. Finally, the validity of the method is proved by the experimental laboratory data and the correlation coefficient.

Revisiting the continuum reverberation lags in the AGN PKS 0558−504

ABSTRACT We present a revised analysis of the photometric reverberation mapping campaign of the narrow-line Seyfert 1 galaxy PKS 0558 − 504 carried out with the Swift Observatory during 2008–2010. Previously, Gliozzi et al. (2013) found using the Discrete Correlation Function (DCF) method that the short-wavelength continuum variations lagged behind variations at longer wavelengths, the opposite of the trend expected for thermal reprocessing of X-rays by the accretion disc, and they interpreted their results as evidence against the reprocessing model. We carried out new DCF measurements that demonstrate that the inverted lag-wavelength relationship found by Gliozzi et al. resulted from their having interchanged the order of the driving and responding light curves when measuring the lags. To determine the inter-band lags and uncertainties more accurately, we carried out new measurements with four independent methods. These give consistent results showing time delays increasing as a function of wavelength, as expected for the disc reprocessing scenario. The slope of the re-analysed delay spectrum appears to be roughly compatible with the predicted τ ∝ λ4/3 relationship for reprocessing by an optically thick and geometrically thin accretion disc, although the data points exhibit a large scatter about the fitted power-law trend.

Theoretical insights into room temperature phosphorescence emission with anti-Kasha behavior in aggregate

Organic room temperature phosphorescence (RTP) materials with long lifetimes have shown promising applications in organic light emitting diodes and bioimaging fields. However, the inner luminescent mechanisms for RTP especially for high lying triplet state emission, have not been unveiled. Herein, based on density functional theory (DFT) and time-dependent density functional theory (TD-DFT), the photophysical properties of four RTP systems with triphenylethylene derivatives as skeletons are studied. Excited state dynamic process in aggregate is systematically studied by combining quantum mechanics with molecular mechanics (QM/MM) method coupled with thermal vibration correlation function (TVCF) method. Moreover, the intermolecular interactions are measured by the independent gradient model based on Hirshfeld partition (IGMH) method, the Huang-Rhys factor, reorganization energy and spin-orbit coupling (SOC) constant are calculated, radiative and non-radiative decay as well as intersystem crossing (ISC) and reverse intersystem crossing (RISC) processes are all investigated. Results indicate that the radiative decay process from the lowest triplet excited state (T1) to ground state (S0) is low and the non-radiative decay process is high, various calculations are also performed to exclude the emission process from T1 to S0, thus non-luminescence is determined for T1. Furthermore, a large energy gap between T2 and T1 is observed, and high radiative decay and low non-radiative decay processes from T2 to S0 are confirmed. Thus, the mechanisms of RTP from high lying triplet state T2 are revealed. Furthermore, through wise molecular design and detailed calculations, the mechanical insights are detected that the RTP emissions with anti-Kasha behavior are largely related to the unique molecular configurations with triphenylethylene derivatives as skeletons. Our studies give reasonable explanations for the previous experimental measurements and provide underlying perspectives for RTP mechanisms from high lying triplet state T2, which could promote the development of new efficient RTP emitters.

Theoretical Study on the Light-Emitting Mechanism of Multifunctional Thermally Activated Delayed Fluorescence Molecules

Multifunctional thermally activated delayed fluorescence (TADF) molecules have recently attracted great attention. The light-emitting mechanisms of the TADF molecule PTZ-AQ with aggregation-induced emission (AIE) and mechanochromic luminescence (MCL) in three different aggregation states are studied using the combined quantum mechanics and molecular mechanics (QM/MM) method as well as the thermal vibration correlation function method. It is found that different aggregation patterns would induce different intermolecular interaction and molecular geometries. The different energy diagram of excited states also induce variation of emission colors and (reverse) intersystem crossing processes. By comparing with the light-emitting properties in solvent, the AIE property is confirmed, which is induced by enhanced radiative rate and decreased nonradiative rates in aggregation. The bicolor switch mechanism for the molecule in the solid state should have a close relationship with the dihedral angle change between the donor and the acceptor. The calculation results provide valuable information for understanding the light-emitting mechanism of the PTZ-AQ based polymorphs with AIE and MCL properties, which would favor the design of a new type multifunctional TADF molecules.

The mechanism of intramolecular halogen bonding enhanced the quantum efficiency of ultralong organic phosphorescence in the aggregated state.

Ultralong organic phosphorescence (UOP) has broad application prospects in many fields, but realizing its high quantum efficiency is still full of challenges. One of the main reasons is that the internal luminescence mechanism is unclear and theoretical investigations to reveal the inner structure-property relationship are highly desired. Herein, the internal mechanism of halogen bonding enhancing the quantum efficiency of UOP is studied through the combination of quantum mechanics and molecular mechanics methods coupled with the thermal vibration correlation function (TVCF) method. Geometric and electronic data are obtained by density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations. Transition properties, energy gaps, intermolecular interactions, excited state dynamics as well as Huang-Rhys factors and reorganization energies are analyzed in detail. The results show that the high phosphorescence quantum efficiency benefits from the fast intersystem crossing (ISC) process and the slow non-radiative decay process. The halogen bonding, which cooperates with the effects of aromatic carbonyl and heavy atoms, not only accelerates the ISC rate by increasing the spin-orbit coupling effect, but also restricts the molecular motion and reduces the non-radiative energy consumption. Furthermore, through wise molecular design, an efficient UOP molecule with fast ISC and slow non-radiative decay rates is proposed. This work provides an insight into realizing efficient UOP emission via intramolecular halogen bonding.

Triplet exciton dynamics of pure organics with halogen substitution boosted two photon absorption and room temperature phosphorescence: A theoretical perspective

Organic room temperature phosphorescence (RTP) molecules have shown promising applications in organic light emitting diodes and vivo imaging. Thus, triplet exciton dynamics in solid phase should be revealed and the molecule should possess large two photon absorption (TPA) cross sections under near-infrared excitation. The effects of halogen substitution and intermolecular interaction on RTP and TPA properties are studied at molecular level for a series of derivatives. Surrounding environment in solid phase is considered by combined quantum mechanics and molecular mechanics method. Intermolecular interactions are evaluated by the independent gradient model and calculated through the molecular force field energy decomposition method. Minimum energy crossing point, Huang-Rhys factor and reorganization energy are discussed, triplet exciton dynamics are investigated by thermal vibration correlation function method. Results indicate that the largest TPA cross sections are found for molecule in water. The halogen substitution can enlarge the proportion of (π, π*) and facilitate the intersystem crossing process. Restricted intramolecular rotation motions of dihedral angle in low frequency regions are found for Br-Np-Cz-BF2 in solid phase. While enhanced vibrations of bond length and bond angle in high frequency regions are detected for I-Np-Cz-BF2. Effects of halogen substitution and intermolecular interaction on triplet exciton dynamics are highlighted.

Structural Isomerization Effect on the Triplet Energy Consumption Process of Organic Room-Temperature Phosphorescence Molecules: A QM/MM Study

Organic room-temperature phosphorescence (RTP) materials with long lifetimes and high efficiency have attracted great attention in recent studies. Structural isomerism with ester substituents at different positions could intrinsically influence the luminescence efficiency and operational lifetime of RTP molecules. A theoretical study to reveal the intrinsic structure–property relationship is highly desired. Herein, based on density functional theory (DFT) and time-dependent density functional theory (TD-DFT), the geometric and electronic properties of three isomers (o-MCBA, m-MCBA, and p-MCBA proposed by Tang) are investigated. Furthermore, the Huang–Rhys factor and reorganization energy are analyzed, and exciton dynamic processes, such as the intersystem crossing (ISC) process and three decay channels for the energy consumption process of the first triplet excited state (T1) based on the thermal vibration correlation function (TVCF) method, are discussed in detail. The results show that intermolecular interactions can restrict the rotation motions of the dihedral angle and the vibration motions of the bond angle for o-MCBA and m-MCBA. In addition, decreased Huang–Rhys factor and reorganization energy are found and a hindered nonradiative consumption process is determined. For p-MCBA in the solid phase, the rotation motions are partly restricted by the solid-state effect and the vibration motions of the bond length are effectively promoted by intermolecular H-bond interactions. In addition, the spin–orbit coupling (SOC) effect is enhanced by the solid-state effect, which is helpful to facilitate the ISC process. Through this study, we pursue opportunities to detect the relationship between basic molecular structures and RTP properties, which could take advantage of the unique molecular design to develop high-performance emitting molecules.

Evaluation of Serviceability of Canal Lining Based on AHP–Simple Correlation Function Method–Cloud Model: A Case Study in Henan Province, China

In the process of sustainable development within modern agriculture, in order to ensure that agricultural production has adequate water resources, canal lining (CL) is often used to transport water in order to reduce water seepage, thus promoting the sustainable utilization of water resources. However, due to the influence of the terrain, environment, human factors and other factors, the CL often suffers a certain degree of damage. Therefore, it is necessary to evaluate the serviceability of the CL, so to realize the sustainable use of the CL strategy. Aiming at the weight assignment of CL evaluation indices that are subjective and not combined with actual index data, a weight calculation method based on the Analytic Hierarchy Process (AHP)–simple correlation function (SCF) method was proposed, and game theory was used to achieve combination weighting. For the evaluation indices with the characteristics of fuzziness and randomness, the cloud model (CM) was used to comprehensively consider these characteristics in order to realize the evaluation. Finally, a method to measure serviceability of CL based on AHP–SCF–CM was proposed. Taking a CL project in China as an example, this method was used to evaluate the serviceability of the CL. The evaluation result showed that the serviceability of the CL was poor, and the qualitative evaluation result was consistent with the actual damage condition of the project; meanwhile, a comparative study was performed in combination with the AHP–Entropy Weight (EW)–unascertained measurement theory (UMT). The quantitative evaluation results of the two methods displayed the same grade of serviceability, which verifies that the method proposed in this paper is more reasonable, objective and feasible from both qualitative and quantitative perspectives. Furthermore, the evaluation results lay the foundation for subsequent maintenance and fault prevention of the canal.

Effects of cement particle distribution on the hydration process of cement paste in three-dimensional computer simulation

This study investigated the influences of cement particle distribution on the hydration process of cement paste using three-dimensional computer simulation. The pre-hydrated models of cement paste were generated by using both the correlation function (CF) method based on SEM images and the random distribution (RD) method. The hydration process of cement paste was simulated using the model based on the CEMHYD3D. The RD method was simpler and required less time in generating a pre-hydrated model than the CF method. In addition, the simulation results of the RD method were similar to those of the CF method in the properties of cement paste using the cement 133 with water-to-cement ratio of 0.3. Although the simulation results of the RD method was in good agreement with those of the CF method, authors highly recommended that the cement particles larger than a critical diameter (13 µm) in the simulation contain multiple cement crystalline phases whereas the other ones smaller than the critical diameter should contain a single phase. The proposed RD method was validated by using the previously reported experimental results using ordinary Portland cement as well.

Correlation networks of air particulate matter (hbox {PM}_{2.5}): a comparative study

Over the last decades, severe haze pollution constitutes a major source of far-reaching environmental and human health problems. The formation, accumulation and diffusion of pollution particles occurs under complex temporal scales and expands throughout a wide spatial coverage. Seeking to understand the transport patterns of haze pollutants in China, we review a proposed framework of time-evolving directed and weighted air quality correlation networks. In this work, we evaluate monitoring stations’ time-series data from China and California, to test the sensitivity of the framework to region size, climate and pollution magnitude across multiple years (2014–2020). We learn that the use of hourly hbox {PM}_{2.5} concentration data is needed to detect periodicities in the positive and negative correlations of the concentrations. In addition, we show that the standardization of the correlation function method is required to obtain networks with more meaningful links when evaluating the dispersion of a severe haze event at the North China Plain or a wildfire event in California during December 2017. Post COVID-19 outbreak in China, we observe a significant drop in the magnitude of the assigned weights, indicating the improved air quality and the slowed transport of hbox {PM}_{2.5} due to the lockdown. To identify regions where pollution transport is persistent, we extend the framework, partitioning the dynamic networks and reducing the networks’ complexity through node subsampling. The end result separates the temporal series of hbox {PM}_{2.5} in set of regions that are similarly affected through the year.

Highly Efficient Near-Infrared Thermally Activated Delayed Fluorescence Molecules via Acceptor Tuning: Theoretical Molecular Design and Experimental Verification.

Near-infrared (NIR) thermally activated delayed fluorescence (TADF) materials have shown great application potential in organic light-emitting diodes, photovoltaics, sensors, and biomedicine. However, their fluorescence efficiency (ΦF) is still highly inferior to those of conventional NIR fluorescent dyes, seriously hindering their applications. This study aims to provide theoretical guidance and experimental verification for highly efficient NIR-TADF molecular design. First, the light-emitting mechanism of two deep-red TADF molecules is revealed using first-principles calculation and the thermal vibration correlation function (TVCF) method. Then several acceptors are theoretically designed by changing the position of the cyano group or by introducing the phenanthroline into CNBPz, and 44 molecules are designed and studied theoretically. The photophysical properties of DA-3 in toluene and the amorphous state are simulated using a multiscale method combined with the TVCF method. The NIR-TADF property for DA-3 is predicted both in toluene and in the amorphous state. Experimental measurement further confirms that the TADF emission wavelength of DA-3 is 730 nm and ΦF is as high as 20%. It is the highest fluorescence efficiency reported for TADF molecules with emission wavelengths larger than 700 nm in toluene. Our work provides an effective molecular design strategy, and a good candidate for highly efficient NIR-TADF emitters is also predicted.

Durability evaluation of highway tunnel lining structure based on matter element extension-simple correlation function method-cloud model: A case study.

With the acceleration of infrastructure construction in various countries, more and more highway tunnels have been built. As a permanent structure to maintain the long-term stability and durability of the tunnel, the tunnel lining structure (TLS) is prone to durability damage in the later operation process, which affects the safety of traffic and the whole loading capacity of the tunnel, so it is very important to evaluate the durability of the TLS. Nowadays, the TLS durability evaluation methods ignore the ambiguity and randomness of the lining structure (LS) durability evaluation index, which have certain limitations. In order to evaluate the durability of highway TLS scientifically and rationally, this paper proposes a method for evaluating the durability of highway TLS based on the matter-element extension (MEE)- simple correlation function (SCF) method- cloud model (CM). A case study was carried out by combining the advantages of the above three methods, a LS durability evaluation model was established, and based on the relevant data from the actual inspection of a highway tunnel lining durability disease in China, the model was used to evaluate the durability of the lining of this highway tunnel, and the durability grades were equivalently divided into five grades: in good shape(I), slightly damaged(II), medium damaged(III), severely damaged(IV), extremely dangerous(V). The result show that this tunnel lining belongs to IV, and the result of this evaluation method is in accordance with the actual damage condition of the project, and the accuracy reaches 92.75%. At the same time, a comparative study was carried out in combination with the AHP-Extenics to verify the reasonableness and feasibility of this method. This study provides a new method for durability evaluation of LS, offers a theory basis for judging the durability of highway TLS, and lays a foundation for subsequent maintenance and prevention.

Multiwavelength corss-correlation and radio Doppler factor estimation of CGRaBS J2345-1555

In this paper, CGRaBS J2345-1555’s long-term radio band, gamma ray flux and optical V-band magnitude data are collected from Fermi/LAT, Catalina, and OVRO dataset. The correlation between multi-bands is evaluated by the discrete correlation function method. The results show that the correlation coefficient between gamma band and radio band is 0.53, and the time delay is about 90 days, a variation of the gamma band is about 90 days ahead of radio band; the correlation coefficient between radio band and optical V-band is 0.84, and the time delay is about –300 days, a variation of the optical V-band is about 300 days ahead of radio band; there is no significant correlation between gamma and optical V-band. These results show that the optical band is dominated by synchrotron radiation, and the time delay between the radio band and the optical band can be explained as the fact that the radiation region of the optical band is upstream, and the radio band is downstream. The gamma band and the radio band are both homologous. The distribution of brightness temperature is used to calculate the Doppler factor of the celestial body’s radio band. The averaged Doppler factor is 12.64, and it oscillates with the light curve. So the jet has obvious bunching effect, and the variation of radiation flux in radio band comes from the jet.

Effects of Secondary Acceptors on Excited-State Properties of Sky-Blue Thermally Activated Delayed Fluorescence Molecules: Luminescence Mechanism and Molecular Design

The development of efficient sky-blue thermally activated delayed fluorescence (TADF) emitters is highly desired. However, the types and amounts of sky-blue TADF are far from meeting the requirements, and effective molecular design strategies are expected. Herein, the photophysical properties and excited-state dynamics of 12 molecules are theoretically studied based on the thermal vibration correlation function method. Distributions of holes and electrons are analyzed by the heat maps. The frontier molecular orbital distribution, adiabatic singlet-triplet energy gap, and reorganization energy are analyzed in detail. Furthermore, the radiative and non-radiative as well as the intersystem crossing (ISC) and reverse intersystem crossing (RISC) processes are studied, and the up-conversion process is illustrated. Our results indicate that different substitution positions and numbers play an important role in the luminescence properties of TADF molecules. The meta-position substitutions restrict the geometry variations, hinder the non-radiative energy consumption process, and promote the radiative process of TADF molecules. Meanwhile, molecules with ortho-position substitutions possess the smallest energy gaps (ΔEst) and the largest RISC rates. Moreover, molecules with the substitutions of one tBCz group and two PO groups have the smallest ΔEst and the largest spin orbital coupling. Thus, a wise molecular design strategy, namely, ortho-position substitutions as well as substitutions with one tBCz group and two PO groups, is proposed to facilitate the RISC process. Based on this rule, new efficient TADF molecules are theoretically designed and proposed. Our work reasonably elucidates the experimental measurements, and the effects of different substitution numbers and positions of secondary acceptors on TADF properties are highlighted, which could provide a theoretical perspective for designing efficient sky-blue TADF molecules.

An improved phase difference detection method for a Coriolis flowmeter

To detect the phase difference of two vibration signals in a Coriolis flowmeter, the commonly used methods include the zero crossing phase detection method, the correlation function method and the Fourier transform method. However, these methods are subject to low accuracy, entire-cycle sampling and excessive calculation. To solve these problems, a Coriolis flowmeter experimental system was initially modeled, and then a phase difference detection method was built based on least squares and curve fitting. The results showed that this method could reduce the amount of calculation significantly without reducing the detection accuracy or adjusting the entire-cycle sampling. A simulation and a single-phase flow experiment indicated that this method was simple, practical and efficient, and it provided a new method for data processing with a Coriolis flowmeter.

Toward Quantitative Prediction of Fluorescence Quantum Efficiency by Combining Direct Vibrational Conversion and Surface Crossing: BODIPYs as an Example.

Accurate theoretical description of the electronic structure of boron dipyrromethene (BODIPY) molecules has been a challenge, let alone the prediction of fluorescence quantum efficiency. In this Letter, we show that the electronic structures of BODIPYs can be accurately evaluated via the spin-flip time-dependent density functional theory with the B3LYP functional. With the resulting electronic structures, the experimental spectral line shapes of representative BODIPYs are successfully reproduced by our previously developed thermal vibration correlation function method. Most importantly, a two-channel scheme is proposed to describe the internal conversion of S1 to S0 in BODIPYs: channel I via direct vibrational relaxation within the harmonic region and channel II via a distorted S0/S1 minimum energy crossing point well away from the harmonic region. The fluorescence quantum yields are accurately predicted within this two-channel scheme, which can therefore serve as a generalized method for predicting the photophysical parameters of organic fluorescent compounds.

Progress of experimental studies on two-proton emission

<p indent=0mm>Radioactivity is one of the most significant characteristics of unstable nuclei, the familiar modes including α, β, γ decay and fission. Two-proton (2p) emission is an exotic radioactivity mode of nuclei in the proton drip-line area, which is very significant for studying the structure, mass and correlation between proton pair of extremely proton-rich nuclei and one of the frontiers in radioactive ion beam physics. In this article, progress of experimental studies on two-proton emission was briefly reviewed. Several experimental measurement methods were introduced. The identification method for the mechanism of two-proton emission was discussed. Two-proton emission was predicted to be existed in extremely proton-rich nuclei in 1960. For 2p emission from the ground state of a nucleus with long half-life, it was observed for the first time in 2002 due to the difficulty in the production of a candidate. Only few decay events were observed for the four proton drip-line nuclei with a long half-life ground state. For the detection of 2p emission process, the in-flight decay, implantation decay and optical time projection chamber (OTPC) plus CCD method are the three main experimental methods. The in-flight decay method is suitable for the candidate with very short half-life and almost inapplicable for the candidate with a half-life longer than 1 μs. The implantation decay method is suitable for the candidate with long half-life, especially for β-delayed decay nuclei. In this case, the measured decay signal will be very clear with low background due to the separation recording of the implantation and decay events. The OTPC plus CCD method could record a picture of 2p emission process directly for the candidate. Generally, there are three mechanisms for proton-rich nuclei to emit two protons: (1) ²He cluster emission; (2) three-body emission; (3) sequential emission. The ²He cluster emission is basically two protons constrained by the pair correlation into a quasi-bound singlet, i.e., ¹S₀ configuration. Such a quasi-bound state can only exist for very short time and then becomes separated after penetrating through the Coulomb barrier. Usually, the two-proton relative momentum and the opening angle distributions are used to identify the mechanism of 2p emission in experimental investigations. However, this method can only distinguish it being ²He cluster emission or not. For the three-body and sequential emissions, the key difference is the emission time between the two protons. The proton-proton momentum correlation function (also called HBT) method is a widely used analysis technique in nuclear physics, which can extract the emission time of a particle. It has been demonstrated that the three-body and sequential emissions could be distinguished by using the HBT method. The difficulty in the study of exotic radioactivity is the low production rate of the unstable nuclei in the drip-line area. The high-intensity heavy-ion accelerator facility (HIAF) under construction in China has an advantage of high beam intensity, the most frontier work in the field of exotic radioactivity for nuclei around the drip-line could be performed on it by adopting the superior detection technique and investigation method.

Evaluation of the spatial variability characteristics of the unsaturated clay in Hefei, China

Soil properties (or parameters herein) vary randomly in space because of different depositional conditions. The knowledge of the spatial variability characteristics of unsaturated soils can be critical to the reliability assessment of geological and geotechnical engineering problems such as the stability analysis of unsaturated soil slopes and the seepage analysis of earth dams. To investigate the spatial variability characteristics of unsaturated soils, the soil parameters, including physical, deformation, and hydraulic properties, are measured through laboratory tests in this study. It is found that the variability of the physical parameters is smaller than that of the deformation parameters, and smaller than that of the hydraulic parameters. Five existing methods are adopted to evaluate the horizontal and vertical auto-correlation distances that measure the spatial variability, and it is found that the space average method and the correlation function method are more suitable for evaluating the auto-correlation distances when the number of test data is small. To further explore the spatial variability characteristics, the Wilcoxon rank analysis is conducted, and the results show that the auto-correlation distance is an inherent property of soils and there is little difference among the results obtained based on the physical, deformation, and hydraulic parameters of the unsaturated soils.

The γ-Ray and Optical Variability Analysis of the BL Lac Object 3FGL J0449.4−4350

We have assembled the historical light curves of the BL Lac Object 3FGL J0449.4−4350 at optical and γ-ray bands, the time spanning about 10 yr, analyzed the periodic variability of the light curves by using four different methods (Lomb–Scargle periodogram, REDFIT38, Jurkevich and DACF). We detected a marginally possible quasi-periodic oscillation of ∼450 days. Assuming it originates from the helical motion jet in a supermassive binary black hole system undergoing major merger, we estimate the primary black hole mass M ∼ 7.7 × 109 M⊙. To explore the origin of the γ-ray, we investigated the optical-γ-ray correlations using discrete correlation function method, and found that the correlation between the two bands is very significant. This strong correlation tends to imply lepton self-synchro-Compton model to produce the γ-ray.