Logarithmic Law Research Articles

Stiffness Hardening Effect of Wire Rope Isolators under Small Cyclic Loads for Vibration Isolation

Wire rope isolator (WRI) devices are widely used in vibration reduction industrial equipment, and stiffness is the key parameter that determines isolation effectiveness. WRI devices show slight nonlinearity under small loads, and the manufacturers generally only provide the initial parameters. To investigate the mechanical behavior changes in the WRI devices under repeated loads, five types of WRI specimens were tested under various amplitudes, loading speeds, and preloads. The test results of large symmetrical compression and tension loads showed that the WRI devices demonstrated stable hysteresis curves under repeated loads, while the hysteresis curves were independent of the loading speed. The test results of small cyclic loads with large preloads show that the stiffness of the WRI specimen follows the logarithmic law, with the cycle number under various loading conditions. Particularly, the stiffness of the specimen increases by about 10–30% after 50 cycles. The initial stiffness Ka decreases linearly with the preloads, while the decrease is quadratic in relation to the cyclic load. The hardening coefficient Ca shows a positive correlation with the loading capacity of the WRI devices, while it shows a negative correlation with the preload and cyclic load amplitudes. It is recommended to consider the stiffness increase in the WRI devices during the evaluation of isolation effectiveness.

Manufacturing and aging behavior of CuCr1Zr powder: Analysis and modelling of close-coupled gas atomization of CuCr1Zr and its impact on the melt beam disintegration and analysis powder oxidation kinetics

Powder bed-based additive manufacturing methods represent an increasingly vital role in industrial applications. Specifically, there has been considerable focus on highly reflective metals, such as CuCr1Zr, in recent years. However, current research primarily revolves around developing appropriate manufacturing parameters e.g. laser powder bed fusion (PBF/LB-M) and assessing the corresponding mechanical and electrical properties of CuCr1Zr. The impact of manufacturing routines and oxidation behavior of CuCr1Zr powder are seldom discussed in additive manufacturing. Therefore, the present study addresses the analysis of powder production and the oxidation behavior of CuCr1Zr powder via close-coupled gas atomization to analyze the disintegration of a CuCr1Zr melting jet during gas atomization of CuCr1Zr by using a high-speed camera. Critical conditions for secondary disintegration were calculated as a function of the initial gas pressure. Additionally, calorimetric measurements and isothermal oxidation experiments were conducted to quantify oxide formation and growth. According to the results, initial oxide formation occurs after 42 days with CuCr1Zr powder at room temperature in a nitrogen atmosphere. Subsequently, oxide growth follows a logarithmic law, associated with the formation and conversion of Cu2O to CuO.

The Anomalous Behavior of Stock Prices on the Canadian Securities Exchange

This paper examines the conformity of the distribution of stock prices on the Canadian Securities Exchange (CSE) to that theorized by Benford’s Law (BL). BL follows a logarithm law such that the leading digits have a higher probability of lower numbers such as 1, 2, or 3 versus higher numbers like 7, 8, or 9. This analysis can be used to detect fraudulent manipulation of stock prices. Previous research has applied BL to a broad range of data such as cost data, atomic weights, river areas, and populations, as well as stock prices. After collecting stock prices on the CSE, the number count for each digit was compared to the expected number given the frequencies posited by BL. A chi-square test was employed to determine statistical significance. The first digit was found to adhere to BL; however, the second digit was not congruent with that predicted by BL. There is an indication of possible manipulation on this stock exchange. These mixed results are consistent with the empirical evidence of other researchers. This evidence is relevant to auditors, shareholders, financial analysts, investment managers, government, and the CSE.

Oxidation behavior of Fe-Ni Invar alloy under high pressure: A ReaxFF molecular dynamics study

The Fe-Ni Invar alloy is often employed under extreme conditions such as high temperatures, high pressures, and corrosive environments, making it susceptible to oxidation and subsequent failure. Hence, a thorough understanding of its oxidation behavior is crucial. We performed ReaxFF-based molecular dynamics (MD) simulations to study the oxidation behaviour of Fe-Ni Invar alloy at the atomic scale under extreme conditions. The initial stage of oxidation involves the preferential adsorption and dissociation of O2, demonstrating its surface-site selectivity. The initial oxidation kinetics follows a logarithmic law, and the whole oxidation process results in dominant low-coordinated clusters configurations in the oxide film. Simultaneously, Fe atoms tend to donate more electrons to O atoms than Ni atoms. Moreover, the O2 consumption rate were found to increase with pressure and amorphous oxides formed more readily under high pressure. Our results indicate that adjusting the pressure may enhance the oxidation resistance of the Fe-Ni alloy, which is significant for the design and application of alloys in extreme conditions.

Estimation of ground vibration emission increase with respect to velocity in high-speed railways

During the design of a new line, it is often necessary to estimate railway vibration emissions at a given future speed from experimental data in similar circumstances, but at a different speed. Future levels are usually estimated according to a logarithmic evolution law with respect to speed, a typical one being that in USA FTA Report nº0123 "Transit Noise and Vibration Impact Assessment Manual", a de facto standard in the sector. Also, it is known that for high-speed lines a drastic increase in vibrations is observed when railway speed is higher than the propagation speed of surface Rayleigh waves. This phenomenon, known as trans-Rayleigh boom, produces a sharp discontinuity in the evolution of vibration emissions. However, vibration levels observed in the vicinity of a high-speed line have shown values well above the prediction rule suggested in FTA Manual, which could not be explained by a trans-Rayleigh boom. A more accurate extrapolation method based on local rail roughness measurements is capable of producing improved predictions compared to FTA rule of thumb. This contribution shows the details of the method suggested, and the improvement in the prediction (with respect to FTA extrapolation law) obtained in the specific case of a high-speed railway.

Prediction and Visualization of 3D Wake Field of a Rectangular High-rise Building in Tropical Island Cities Based on UAV Measurements

It is especially crucial to utilize measured data as samples to increase the accuracy of wind field prediction. However, scarce wake field measured data of high-rise buildings leads to the deviation between prediction results and the actual wake distribution. In this study, a six-rotor unmanned aerial vehicle wind measurement system (UAVWMS) equipped with an anemometer is used to measure the wake field of a rectangular high-rise building in a tropical island city, and the characteristics of fluctuating wind velocity spectra and distribution patterns of the wind velocity and turbulence intensity in the wake region are analyzed; the Kriging method is adopted to predict and visualize the three-dimensional (3D) wake field based on the measured data from UAVWMS. The results show that the exponential law is better than the logarithmic law in fitting the incoming wind velocity profile in the tropical island city. The measured points in the wake region, located near the central axis of the building, exhibit a pronounced reduction in wind velocity and an increase in turbulence intensity compared to those in the incoming region. Compared to the incoming wind velocity spectra and empirical spectra, the peak frequencies of wake wind velocity spectra shift to the high-frequency band. In addition, the wake wind velocity spectra are lower in the low-frequency band and higher in the high-frequency band. When designing a measured scheme based on UAVWMS, it's crucial to place measured points surrounding the target spatial wake field as much as possible. It helps enhance the accuracy of predicting wind parameters within the 3D spatial wake field. The research results provide a theoretical reference for the measurement, prediction and visualization of the wake field of high-rise buildings in dense urban buildings.

Multi-Objective Optimization based decision-making process using Dombi Logarithmic aggregation operator in CNN environment and its application to optimally select suitable greenhouse site for tomato crops

In this research article, we have defined Dombi Logarithmic aggregation operational laws in the framework of Cylindrical Neutrosophic Numbers (CNN) and utilized these laws to establish a new aggregation operator namely Cylindrical Neutrosophic Dombi Weighted Logarithmic Aggregation Operator(C N DW L A ). The said aggregation operational laws & aggregation operator have been used to present a new and novel decision making process where Full Consistency Method (FUCOM) and Multi-Objective Optimization(MOO) have been inte- grated and embedded fruitfully. Here the objective functions were formulated using the concept of a single-layer neural network and the FUCOM method to assess criterion weights. We have resolved the most favorable Pareto optimal solution derived from Multi-Objective Optimization by employing simulation and the Technique for Or- der of Preference by Similarity to Ideal Solution (TOPSIS) approach. Finally, we have applied our proposed decision making method along with MARCOS and MOORA techniques to determine the best greenhouse site for cultivating tomato crops. An exhaustive sensitivity and comparative analysis has been conducted to assess the robustness and stability of our Multi Criteria Group Decision Making (MCGDM) techniques. It is observed that our proposed method has some advantages in cylindrical neutrosophic environment and it produces stable robust results with the variation of underlying model parameters.

Turbulence scale and strength analysis in the roughness and inertial sublayers over urban areas: A wind tunnel study

The dissimilarity of dynamics and turbulence structures between the roughness and inertial sublayers (RSL, ISL) over roughness elements show that ISL turbulence is much more homogeneous. Conventional logarithmic law of the wall is merely applicable for the RSL mean-wind-speed profiles. To characterize the turbulence scales and elucidate the mechanism, the flows in the atmospheric surface layer (ASL) over real urban morphology are measured in wind tunnel experiments fabricated by 3D-printing, reduced-scale model of downtown Kowloon Peninsula, Hong Kong. Elevated dispersive stress at urban canopy signifies the influence from individual buildings and inhomogeneous RSL flows. A positive momentum contribution appears in the low-frequency regime. The large-scale turbulence in RSL thus enhances the mixing and transport, resulting in inhomogeneous flows. The contribution from ejection Q2 and sweep Q4 increases and decreases, respectively, with increasing RSL motion strength. The conventional −5/3 law is observed by empirical mode decomposition (EMD) and the largest amplitude fluctuation occurs more often when the turbulence length scale is comparable to the turbulent boundary layer (TBL) thickness. The single-point amplitude modulation (AM) shows that the large- and small-scale turbulence correlates tightly at the bottom of RSL. Besides, the joint probability density function (JPDF) illustrates that accelerating large scales often occur with decelerating small scales, and they are intensified with increasing wall-normal distance. As a result, large-scale turbulence influences substantially the flow structures over urban areas and the small-scale turbulence (even) in RSLs in the vicinity of building obstacles.

High-temperature oxidation behaviour of additively manufactured and wrought HAYNES 282

Direct Metal Laser Sintered Haynes 282 specimens as well as wrought ones were subjected to high-temperature exposure at 1000 °C for 100h in air to compare their oxidation behaviour. The specimens were removed from the furnace after 1h, 5h, 25h, 50h and 100h to reveal and study oxidation mechanisms through morphological and cross-sectional examination by using scanning electron microscopy with energy dispersive spectroscopy attachment and X-ray diffraction. Microstructural studies revealed that the oxidation kinetics, determined by changes in thickness scale and depth of aluminium diffusion zone, were mainly driven by the formation of Cr2O3 for the wrought material, and TiO2 for DMLS one. The wrought material was characterized by the oxidation rate equal to 0.96 and followed the logarithmic law. On the other hand, DMLS-manufactured Haynes 282 exhibited oxidation rate of 0.90 and follows the linear law for the thickness scale considerations. However, when the depth of aluminium diffusion was investigated, it had an oxidation rate of 0.87 and followed cubic law.

Comparison of high temperature oxidation behaviour of high speed steel and Hi-Cr steel

Abstract High speed steel and Hi-Cr steel are widely used as one of the important materials for rolls. The oxide layer during rolling plays a key role in the service life of the rolls and the quality of the rolled material. Therefore, it is very important to study the oxidation behaviour of high speed steel and Hi-Cr steel. In this paper, the oxidation behaviour of HSS and Hi-Cr steel is compared in the range of 500-700°C. The oxidation kinetic curve of HSS is dominated by a parabolic law, while the oxidation kinetic curve of Hi-Cr steel is dominated by a logarithmic law. To analyse the effect of their oxidation products on the oxidation behaviour, V2O5 in high speed steel plays a destructive role in the oxide layer, while Cr2O3 in Hi-Cr steel can effectively reduce the thickness of the oxide layer.

Bifurcation analysis of a two-neuron central pattern generator model for both oscillatory and convergent neuronal activities.

The neural oscillator model proposed by Matsuoka is a piecewise affine system that exhibits distinctive periodic solutions. Although such typical oscillation patterns have been widely studied, little is understood about the dynamics of convergence to certain fixed points and bifurcations between the periodic orbits and fixed points in this model. We performed fixed point analysis on a two-neuron version of the Matsuoka oscillator model, the result of which explains the mechanism of oscillation and the discontinuity-induced bifurcations such as subcritical/supercritical Hopf-like, homoclinic-like and grazing bifurcations. Furthermore, it provided theoretical predictions concerning a logarithmic oscillation-period scaling law and noise-induced oscillations observed around those bifurcations. These results are expected to underpin further investigations into oscillatory and transient neuronal activities concerning central pattern generators.

Experimental study on the interaction between particles and coherent structures in dilute liquid–solid two-phase turbulent boundary layer

In order to reveal the modulation of particles on turbulent coherent structures and particle concentration variations induced by turbulence, particle image velocimetry experiments were performed in a dilute liquid–solid two-phase turbulent boundary layer. Large-scale coherent structures, including streaks and hairpin vortices, were extracted in the liquid–solid two-phase turbulent boundary layer by using multiple methods, such as proper orthogonal decomposition and finite-time Lyapunov exponent. The results showed that the addition of particles thickened the buffer layer of the average velocity profile, weakened the streamwise turbulence intensity at y+ > 10, strengthened the wall-normal turbulence in the near wall region (y+ < 52), and weakened the Reynolds stress in the logarithmic law region. A more thorough study of the turbulent structure revealed that the particles caused the mean spacing of the near-wall streak structure to increase, hairpin vortex migration to slow down, the uplift of hairpin vortex to be suppressed, and the overall size of the hairpin vortex packet to be compressed. This demonstrated that particles could modulate turbulence by inhibiting the development of hairpin vortices.

Unorientable topological gravity and orthogonal random matrix universality

The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix integral has led to studies of the canonical spectral form factor (SFF) in the so called τ−scaled limit of large times, t → ∞, and fixed temperature, in order to demonstrate agreement with universal random matrix theory (RMT). Though this has been established for the unitary case, extensions to other symmetry classes requires the inclusion of unorientable manifolds in the sum over geometries, necessary to address time reversal invariance, and regularization of the corresponding prime geometrical objects, the Weil-Petersson (WP) volumes. We report here how universal signatures of quantum chaos, witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge for the low-energy limit of unorientable JT gravity, i.e. the unorientable Airy model/topological gravity. To this end, we implement the loop equations for the corresponding dual (double-scaled) matrix model and find the generic form of the unorientable Airy WP volumes, supported by calculations using unorientable Kontsevich graphs. In an apparent violation of the gravity/chaos duality, the τ−scaled SFF on the gravity side acquires both logarithmic and power law contributions in t, not manifestly present on the RMT side. We show the expressions can be made to agree by means of bootstrapping-like relations hidden in the asymptotic expansions of generalized hypergeometric functions. Thus, we are able to establish strong evidence of the quantum chaotic nature of unorientable topological gravity.

AN OVERVIEW OF THE DISTRIBUTIONS OF CLAIMS USED IN NON-LIFE INSURANCE THAT CONFORM TO BENFORD'S LAW

<p>Benford's law, known as the law of the first digit, is used as a basic method to identify possible manipulation, or errors dеtection, in a large data set. Namely, according to that law, the first digits of the corresponding data set appear with a frequency determined according to the decreasing logarithmic law, which is contrary to the intuition about their uniform appearance. Thus, the number 1 appears in approximately 30% of the cases as the first digit, while the number 9 appears in 4.58% of cases. The subject of the paper is an overview of  distributions that conform to Benford's law, which is confirmed both theoretically (by proving the theorems) and empirically (by conducting simulations). The goal of the paper is to determine the distribution that best fits the data on non-life insurance claims and then to examine the agreement with Benford's law using statistical tests applied in the literature. The main result of the paper is to determine the agreement or disagreement of the observed data set with Benford's law, thus providing an answer to the question about their possible manipulation and a possible proposal for a deeper analysis of individual numbers.</p>

A Comparative Study on Wind Profiles and Surface Aerodynamic Parameters of Typhoons Over Coastland and Coastal Sea

AbstractUnderstanding the aerodynamic characteristics of landfalling typhoons is of great importance for both wind engineering and meteorology. This study comparatively investigated the near‐surface wind profiles and aerodynamic parameters over coastland and coastal sea areas using typhoon observational data collected by Doppler wind lidars and wind tower anemometers during the passage of 15 typhoons that made landfall over China during 2009–2020. Specifically, the three surface aerodynamic parameters of roughness length, friction velocity, and drag coefficient (Cd) were obtained using the logarithmic law wind profile method. Results showed that the near‐surface wind profiles became much closer to the power law wind profile with increase in wind speed. The values of roughness length and friction velocity over the coastal sea were found to exceed those over coastland areas when the 10‐m wind speed (U(10)) was larger than 18 m s−1. The critical wind speed at which Cd peaks over the coastal sea was found to be 24 m s−1. There are two peaks in the variation of Cd with U(10) under the condition of onshore wind over the sea, which has never been reported in previous observational studies. Finally, a formula for Cd was proposed to describe the variation in Cd with U(10) under the condition of onshore wind over land, which is expected to be applied in the typhoon surface layer scheme to improve numerical simulation of landfalling typhoons.

Bimodal grain sized barium titanate dielectrics enabled under the cold sintering process

In barium titanate (BaTiO3) the relative permittivity varies as a function of grain size due to the influence of various sizes and scaling effects. The cold sintering process (CSP) has been applied to sinter nanocrystalline BaTiO3 (<200 nm), however in conventionally sintered BaTiO3 a maximum relative permittivity is achieved at average grain sizes around 0.8 μm. In this work the feasibility of cold sintering 1 μm BaTiO3 inclusions in ratios of fine-grained BaTiO3 matrixes from 50 to 200 nm is investigated. Occurrences of both conformal sintering of inclusions into the matrix and constrained sintering with residual porosity are observed. Subsequently, electrical resistivities increased from 1 × 108 Ω cm to approximately 1 × 1012 Ω cm by a post CSP heat treatment of 500 °C. Relative permittivity of annealed samples increases systematically following a logarithmic mixing law as a function of matrix grain size and increasing the ratio of inclusions to matrix.

A logarithmic law for the velocity- and retention-dependency of the eddy dispersion in chromatographic columns

Applying the recently introduced patchwork model for porous media, we present a new step forward in the modelling of eddy dispersion in chromatographic columns. The logarithmic law describing the velocity dependency emerging from this patchwork model is supplemented with a retention factor dependency via first principles modelling of the variations in flow resistance and retention capacity caused by the packing disorder. Furthermore, it is shown the derived expression is also able to fit the eddy dispersion originating from the wall effect on the packing. When applied to literature data of eddy dispersion, the newly introduced logarithmic law has a goodness of fit that is at least equal to that of Knox’ empirical power law (R2>0.98). The main difference is that, whereas Knox’ power law requires a separate fit for each component due to the retention factor dependency, the present model simultaneously fits all plate height curves measured on one chromatographic column, using only two parameters with a clear physical meaning.

Dynamics of backfill compressive strength obtained from enrichment tails for the circular waste management

At the current stage of development, the transition to a circular economy is a single option to achieve sustainable mining. Purpose was to identify a direction for mining tailings usage based on the circular waste management. The novelty of the author's approach lies in regulation of mechanical treatment of slag to optimize the backfill composition. The methodology involved a study of mining waste (slag) obtained from major (eight) metallurgical plants in Russia. For mathematical processing primary data, smoothing and deterministic three-dimensional interpolation methods were used. As a result, for the first time it has been established that the ultimate uniaxial compressive strength after mechanical treatment of slag increases by logarithmic laws. As the curing time increases from 10 days to 90 days (with the addition of Ca or Si) the strength increases by 21 % (7 % and 23 %). The possibility of completely replacing the traditional cement binder with metallurgical slag in the backfill composite has been proven. It has been established that the use of activation treatment (both mechanical and chemical) makes it possible to increase the strength characteristics of backfill samples after their curing. The principle of organizing mining production has been implemented, which provides for the use of intermediate products (blast furnace granulated slag), previously classified as technogenic waste, in a closed production cycle. The introduction of this principle will eliminate (minimize) the formation of man-made waste. The scientific merit of replacing traditional cement binder with technogenic waste (blast furnace granulated slag) allows implementation of circular economy in mining.

Research on damage behavior of silicone rubber under dynamic impact

Viscoelastic rubber materials are widely used in various vibration reduction structures of military and construction machinery. The complex driving and working conditions make the mechanical structure suffer severe impact, which leading to the damage or lose efficacy of the important viscoelastic elements. In order to reveal the dynamic mechanical properties of silicone rubber after impact, the Uniaxial compression tests of silicone rubber under different high strain rates were carried out with the separated Hopkinson pressure bar (SHPB) dynamic impact experiment, and the original Zhu-Wang-Tang (ZWT) constitutive model was modified by combining logarithmic law and power function law. The dynamic impact simulation model of silicone rubber was established using the modified ZWT-rate-dependent constitutive model, and the dynamic impact damage behavior of silicone rubber was studied under the condition of high strain rate, and the microscopic damage analysis was carried out on the experimental silicone rubber samples by scanning electron microscopy (SEM). The results show that the silicone rubber has obvious strain rate effect and strong deformation resistance at high strain rate. The modified ZWT-rate-dependent constitutive model can be used to obtain the constitutive expression of unified parameters, which can better describe the dynamic mechanical properties of silicone rubber at high strain rates. After dynamic impact compression, a damage line zone appears in the silicone rubber sample. There is a certain rule between the position of the line zone and the loading strain rate and the friction coefficient of the end face, and the silicone rubber is significantly affected by the friction effect of the end face.

Vertical Distribution of Rip Currents Generated by Intersecting Waves in a Sandbar–Groin Systems

To analyze the impacts of groins, sandbars, and channels on the three-dimensional features of rip currents, we conducted experimental investigations on the vertical distribution of rip currents under intersecting waves along barred beaches with channels. This study employed ADV flow velocity measurements at two distinct locations: within channel and on a sandbar. The results indicate that in nodal sections within channel and on a sandbar, the rip head region manifests surface flow characteristics, characterized by high velocities near water surface. In a rip neck location, the vertical distribution of rip currents on a sandbar exhibits greater variability, whereas within channel, the distribution is more homogeneous. The vertical distribution of rip currents in nodal sections within channel aligns with the logarithmic distribution law. The vertical distributions of the alongshore velocity of rip currents display a consistent pattern of higher at the top and lower at the bottom. However, this pattern varies slightly depending on the wave period. The presence of groins influences the fluctuation characteristics of the alongshore velocity of rip currents by regulating the nearshore circulation system. This results in the alongshore velocity of rip currents in channel pointing towards the groin. In contrast, the alongshore velocity of rip currents on sandbar, situated farther away from groin, exerts a weaker effect on the alongshore velocity of a rip current.