Theoretical Distribution Models Research Articles

Reasonable layout range of lower mining roadways in the close and variable interval coal seams mining: a case study.

In the context of close-distance coal seam mining, the stress transfer mechanism following the extraction of the upper coal seam is crucial for the layout of roadways in the lower coal seam. This study utilizes ground-penetrating radar (GPR) to analyze the stability and plastic zone extent of residual coal pillars after upper seam extraction. A theoretical model for the stress distribution of multiple goaves and coal pillars was established. Based on a case study with variable inter-seam spacing, the stress distribution and transfer mechanisms of the floor were analyzed. The results indicate that during the transition from the center of the coal pillar to the goaf, stress concentration initially decreases significantly and then gradually returns to the original rock stress, forming a distinct stress gradient distribution. As the depth of the floor strata increases, the weight of the overlying strata is more evidently transferred through the coal pillars to the goaf. Finally, a reasonable layout range for the lower seam mining roadways under different inter-seam spacings is proposed, providing a reference for optimizing roadway layout in similar geological conditions.

Design and mechanical properties analysis of a novel CFRP tendons anchorage structure

To address the challenges of larger size, stress concentration at the loading end, and insufficient anchoring performance at the free end of traditional bonding-type anchors for Carbon Fiber Reinforced Polymer (CFRP) tendons, a novel anchor featuring a variable angle multi-stage cone is proposed. This solution is derived by analyzing the notch effect at the loading end caused by the wedging of the bonding medium in conventional cone-type anchors. A theoretical model for the stress distribution of the variable angle multi-stage conical anchor was developed using elastic deformation theory. The reliability of this model was validated through finite element analysis. Subsequently, a comparative analysis was conducted to evaluate the stress distribution and anchoring performance of the variable angle multi-stage conical anchor against several traditional anchor types. This analysis revealed the mechanical mechanisms and advantages of the variable angle multi-stage conical anchor in enhancing anchoring effectiveness. The study illustrates that the bonding medium between adjacent cone sections of the variable angle multi-stage conical anchor exhibits a specific gap under stress, leading to reduced stress in the tendon at the connection points. This ensures a smooth transition that prevents abrupt changes in stress due to sudden shape alterations, thereby guaranteeing uniform stress distribution within the anchor section. By incorporating a multi-stage cone structure and increasing the cone angle at the free end, compressive stress can be effectively transferred to the free end, mitigating the notch effect and enhancing anchoring performance. Compared to typical conical anchors, the maximum compressive stress of the variable angle multi-stage conical anchor is reduced by 53.5 %, the outer diameter of the anchor cylinder is decreased by 22.7 %, and the anchoring efficiency is improved by 12.2 %. These improvements result in a robust anchoring effect and significant size advantage. The anchor is suitable for multibar anchoring, providing a reliable solution for large tonnage and long-span cable-stayed bridges.

Circumferential multi-point corrosion status assessment of steel cables considering self-magnetic flux leakage superposition effect

With the advantages of convenient operation and efficient detection, the self-magnetic flux leakage (SMFL) has become an important technology for non-destructive testing of ferromagnetic materials. However, the multi-point corrosion status of steel cable structures is still difficult to precisely assess. In this study, the SMFL theoretical model for the circumferential distribution of steel cable corrosion was established, and the measurement experiment of circumferential multi-point corrosion status was carried out. The results show that the area of circumferential distribution region S, the accumulated magnetic field intensity A and ellipticity e are all positively and quadratically correlated with the corrosion ratio α and defect angle θ of steel cables. Moreover, the magnetic field superposition effect shows an exponential decay trend with the defect interval angle Δφ. The maximum deviation rate of A was less than 10 % under different multi-point corrosion distributions, verifying the principle of magnetic field superposition. Finally, the assessment method based on the effect was proposed, which could accurately and systematically diagnose the circumferential multi-point corrosion status in steel cables.

Theoretical probability distribution model and reduction techniques based on an interleaved DFT spread for PAPR in a digital sub-carrier multiplexing system

This paper presents a theoretical probability distribution model for peak-to-average power ratio (PAPR) in the digital sub-carrier multiplexing (DSCM) system, which has not previously been proposed in the literature. To reduce PAPR, an interleaved discrete Fourier transform spread DSCM (I-DFT-S-DSCM) scheme is proposed, which introduces reversible correlations between subcarriers. To investigate the effectiveness of the proposed schemes, a 64-GBaud 16 quadrature amplitude modulation (16-QAM) DSCM system with 4, 8, and 16 sub-carriers was constructed. In the digital domain, the results demonstrate that the proposed theoretical PAPR probability distribution model exhibits mean squared errors (MSE) below 10−5 for the observed and model-predicted complementary cumulative distribution functions (CCDF) in both DSCM and I-DFT-S-DSCM schemes. Regarding PAPR reduction, the I-DFT-S-DSCM scheme demonstrated a reduction in PAPR of up to 1.44 dB compared to the conventional DSCM scheme. To further investigate the impact of PAPR on the bit error rate (BER) performance of the DSCM system, the I-DFT-S-DSCM scheme is implemented with 8 subcarriers transmitted over a 100-km standard single-mode fiber (SSMF). A comparative analysis with DSCM indicates that I-DFT-S-DSCM achieves a PAPR reduction of approximately 1.1 dB and improves receiver sensitivity by approximately 0.7 dB at a 7% hard-decision forward error correction (HD-FEC) threshold, in 100-km single-mode fiber SSMF transmissions.

CFD–DEM method is used to study the multi-phase coupling slag discharge flow field of gas-lift reverse circulation in drilling shaft sinking

To elucidate the distribution law of the multiphase coupling slag discharge flow field in gas-lift reverse circulation during drilling shaft sinking, a numerical analysis model of gas–liquid–solid multiphase coupling slag discharge was established by CFD–DEM (Coupling of computational fluid dynamics and discrete element method) method, taking the drilling of North Wind well in Taohutu Coal Mine as an example. This model presented the distribution of the multiphase flow field in the slag discharge pipe and at the bottom hole, and was validated through experimentation and theoretical analysis. Finally, the impact of factors, including bit rotation speed, gas injection rate, air duct submergence ratio, and mud viscosity on the slag discharge flow field was clarified. The results indicated that the migration of rock slag at the bottom of the well was characterized by “slip, convergence, suspension, adsorption, and lifting”. The slag flow in the discharge pipe exhibited the states of “high density, low flow rate” and “low density, high flow rate”, respectively. The multiphase fluid flow patterns in the well bottom and slag discharge pipe were horizontal and axial flows, respectively. The model test of the gas lift reversed circulation slag discharge and the theoretical model of the bottom hole fluid velocity distribution confirmed the accuracy of the multiphase coupling slag discharge flow field distribution model. The rotation speed of the drill bit had the most significant impact on the bottom hole flow field. Increasing the rotation speed of the drill bit can significantly enhance the tangential velocity of the bottom hole fluid, increase the pressure difference between the bottom hole and annular mud column, and improve the adsorption capacity of the slag suction port. These findings can provide valuable insights for gas lift reverse circulation well washing in western drilling shaft sinking.

A quasi-exponential distribution of interfacial voids and its effect on the interlayer strength of 3D printed concrete

In this work, a novel theoretical model of the void length probability distribution in 3D printed concrete is established based on a zigzag analog of the layer interface. A quasi-exponential distribution of void length is predicted and subsequently validated on both the zigzag analog and the actual 3D printed concrete, with different void ratios that determine the descending rate and node intervals that decide the horizontal scaling of the distribution. Moreover, the relationships between the interlayer strength, void ratio, and quantity of voids are also studied based on the theoretical model. It is found that the quantity of voids is symmetric about a void ratio of 0.5, and the decrease in the interlayer strength against the void ratio is non-linear which is approximated well by combined exponential and linear functions. This work is believed to reveal the nature of the interfacial void distributions and significantly advance the understanding of the layer interface in 3D printed concrete. The code for the zigzag analog with the computation of its interlayer strength is publicly available at: https://github.com/Human-HLW/Layer-interface.

Heat transfer characteristics of subsea long-distance pipeline subject to direct electrical heating

For deep-water pipelines with long tie-back distances, high external pressure, and low ambient temperature, it is a key issue to ensure flow safety by controlling the generation of hydrates and waxes through electric heating technology. In-detail analysis of the heat transfer performance of electric heating pipelines is of great engineering significance for developing the safety of pipeline flow in offshore oil-gas fields. This paper proposed an electrical heating analytical method applicable to long-distance submarine pipelines. Based on the thermal equilibrium theory and the differential equation of heat conduction, a mathematical model of heat-fluid coupling for electric heating pipes is established, involving the theoretical model of the steady-state distribution of the electric heating in the axial and radial directions. Then, the definition of the average temperature of the pipeline is introduced and combined with the two-point Hermite approximation interpolation method, and an improved lumped parameter model of the transient heat transfer of the electric heating pipeline is established. Meanwhile, the finite difference method is applied to solve the ordinary differential equation of the pipeline and the energy equation of the internal fluid. The steady-state calculation result is utilized as the initial value of the transient heat transfer process, and the model is applied to analyze the influence variation on the transient temperature response characteristics of the pipeline under different working conditions, finally determining the prediction formula of the average temperature of the fluid under normal transportation and shutdown conditions.

Theoretical model of random freight flow distribution in the conveyor transport line of the coal mine

Purpose. Increasing the efficiency of the conveyor transport system of the mine due to the application of rational parameters, which are calculated objectively on the basis of the reliable output data of random freight flow in the conveyor transport line, taking into account the velocity of minerals transportation, including a perfect theoretical model application of the freight flow distribution. Methodology. Complex research: - statistical studies on the actual distribution of random freight flow in the highly productive stages of the PSU Mine “n.a Heroiv Kosmosu” PJSC “DTEK Pavlohradvuhillia”; - description of histograms of the distribution of random freight flow by various indicative algebraic functions, normal and gamma distribution of a random variable and a specially constructed function with separately defined parameters of its branches; - analysis of research results regarding the correctness of the theoretical model of the distribution of random freight flow according to various criteria of genuineness, a center of grouping, amplitude, velocity of rise and fall, and deviation. Findings. A perfect theoretical model was built in the form of an indicative algebraic function, whose branches are described by the normal distribution law of a random variable with separately determined parameters. It describes well the distribution of random freight flow in the conveyor transport line of the mine and ensures the determination of its parameters by the methods of probability theory. Originality. A theoretical model of the distribution of random freight flow in the conveyor transport line of the mine has been obtained for the first time, which describes well various cases of its distribution, including symmetric and asymmetric ones, and provides the determination of the freight flow parameters by the methods of probability theory. Practical value. The actual value of the coefficient of nonuniformity of the freight flow in the conveyor transport line of the mine, which was determined by a perfect theoretical model, exceeds, by almost a quarter, the value inherent in the model accepted in practice, the normal law of the distribution of a random variable. The coefficient of nonuniformity of the freight flow in the highly productive longwalls of only the specified mine reaches a value of 2.012, which already exceeds the normative value limit for conveyor transport lines along horizontal and inclined preparatory workings of mining areas (2.0). Reliable initial data on the variation of the random freight flow in the conveyor transport line of the mine, which is substantiated by a perfect theoretical model of its distribution, have a positive effect on the calculation of its parameters and contribute to increasing the efficiency and reliability of the functioning of the conveyor transport system.

Trajectory planning of deep-cutting laser profiling of superabrasive profile grinding wheels

The low profiling efficiency is the key barrier to the industrial application of laser dressing technology for profile grinding wheels. In this paper, the trajectory planning method of deep-cutting laser profiling was proposed for the first time, the theoretical model of the energy distribution of the Gaussian laser beam on the surface of the profile grinding wheel was established, and the effect of this method on improving the profiling efficiency of superabrasive profile grinding wheel was systematically studied. Through comparative experiments, it was confirmed that the trajectory planning method could effectively improve the profiling efficiency of the V-shaped grinding wheel, and it was found that the smaller the tip angle, the greater the efficiency improvement. The change of grain size will lead to the change of grain removal method, which will affect the profiling efficiency of V-shaped grinding wheel, but it has little influence on the profiling accuracy. The V-tip arc radius of the diamond grinding wheel with a particle size of 20–180 μm after laser profiling could be controlled between 10 and 20 μm, which was difficult to achieve by mechanical or electrical dressing method. The trajectory planning method could also significantly improve the profiling efficiency of convex/concave arc-shaped grinding wheels, and the greater the arc radius or chord-to-diameter ratio of the grinding wheel, the greater the efficiency improvement. Even though convex/concave arc-shaped grinding wheels were the same size, their profiling efficiency and material removal efficiency were quite different. For grinding wheels with different arc radii or chord-to-diameter ratios, different process strategies should be selected during laser profiling to ensure a comprehensive balance between efficiency, accuracy and quality.

Evolution of the domain structure in a FeNiCo nanowire under the action of a magnetic field

Based on the experimentally discovered domain structure and its evolution in an external magnetic field in thin films of FeNiCo composition with uniaxial anisotropy, a theoretical model of the magnetization distribution is proposed. The analytical dependence of the domain size on the magnitude of the magnetic field is obtained. The change in magnetoresistance because of the evolution of the magnetic domain structure is calculated.

Comparative study on characteristics of typhoon gusts in the coastal and offshore areas of the South China Sea

Typhoon gusts are hazardous to buildings and structures in both coastal and offshore areas, but the gust characteristics in the two areas could be quite different. In this study, the observational data from two meteorological stations, one at Shenzhen (coastal) and the other in the offshore area of the South China Sea are used to analyze the typhoon gust-related variables and to find the theoretical distribution model that best describes them. The results show that in both coastal and offshore areas, the probability density distributions of all gust-related variables are non-Gaussian. When fitting the curve of the statistical data, the Gengamma model performs the best, followed by the Lognormal model, and the generalized extreme value (GEV) distribution model. Specifically, the gust factor and turbulence intensity are generally Gengamma- and GEV- distributed, respectively. The distributions exhibit certain differences in different gust variables in coastal and offshore areas. The theoretical probabilistic models perform better in the offshore area than in the coastal area. The gust factor increases linearly with the turbulence intensity, while previous empirical models tend to overestimate it. The gust factor and turbulence intensity are significantly higher in the offshore area than in the coastal area. Slower turbulent dissipation is found in the offshore area during typhoon process. A strong positive correlation is shown between the gust amplitude and the turbulent flux. In both coastal and offshore areas, the larger the gust amplitude is, the more the turbulent flux is transmitted.

Pressure Model Study on Synchronous Grouting in Shield Tunnels Considering the Temporal Variation in Grout Viscosity

The grout pressure in the shield tunnel tail void during synchronous grouting is the key to controlling ground settlement and restraining the segment. However, the circumferential, longitudinal, and radial distribution of grout pressure considering the temporal variation in grout viscosity has not been well explored yet. In this study, a theoretical model of grout pressure distribution and dissipation considering the temporal variation in Bingham grout viscosity was established. The simulation results of the pressure model were verified by field-measured data. The results showed that the radial and longitudinal distributions of grout pressure considering the temporal variation in grout viscosity were closer to the field-measured data. The impacts of the main parameters on the pressure distribution and dissipation were analyzed. Compared with the effect of the shield tail void thickness, tunnel radius and yield shear stress have greater effects on grout pressure during the circumferential filling phase. During the longitudinal and radial diffusion phases, the increase in soil porosity and permeability coefficient was conducive to grout diffusion. The increase in the grout viscosity reduces the pressure loss during the grout flow process. The results of this research can provide a theoretical basis for the grout design process in shield tunnels.

Can models for forest attributes based on airborne laser scanning be generalized for different silvicultural management systems?

In Finland, interest in continuous cover forestry (CCF) has increased rapidly in recent years. During those years CCF has been examined from various viewpoints but not from the perspective of forest inventories. This holds especially true for applications based on remote sensing. Conversely, airborne laser scanning (ALS) data have been widely used to predict forest characteristics such as size distribution and vertical forest structure, which are closely related to the forest information needs of CCF.In this study we used the area-based approach to predict a set of stand attributes from ALS data (5 pulses per m2) in a CCF forest management experiment in Katajamäki, eastern Finland. In addition to the CCF stands, the experiment included shelterwood stands and untreated stands. The predicted attributes included volume, biomass, basal area, number of stems, mean diameter, Lorey’s height, dominant height, standing dead wood volume, parameters of the theoretical stem diameter distribution model, understory height and number of understory stems. Our main aim was to test whether the same model could be used across different management systems. The accuracy of the attributes predicted for the CCF stands was compared with the predictions for the other management systems in the same experiment. We also compared and discussed our results in relation to the even-aged stand attribute predictions that were conducted by using separate operational forest data collected from sites surrounding Katajamäki.The results showed that forest data from the different management systems could be combined into a single model of a stand attribute, i.e., ALS metrics were found to be suitable for comparing different management systems in regard to differences in forest structure. The accuracy of the predicted attributes in the CCF plots was comparable to that of the other management alternatives in the experiment. The accuracy was also comparable to that of even-aged forests.The results of this study were promising; the stand attributes of CCF-managed forests could be predicted analogously to those of other management systems. This indicates that for the purposes of forest inventories there may not be a need to stratify forest lands by management system. It should be noted, however, that the study area was relatively small, that the forest stands were harvested in the 1980 s, and that the attributes may not have been completely exhaustive for CCF.

Fundamental Scaling of Adiabatic Compression of Field Reversed Configuration Thermonuclear Fusion Plasmas

Field Reversed Configuration (FRC) plasmas are plasma devices that have demonstrated that through magnetic compression they can be heated to thermonuclear fusion conditions in the parameter space of an energy-producing generator Kirtley et al. (IEEE Symposium on Fusion Engineering, 2021). Of particular interest, FRCs are high-beta, in that the plasma particle kinetic energy is in balance with an externally applied magnetic field at all stages of operation. The following work will show that a cylindrical approximation for the energy and particle distribution within an FRC can, within 11%, match the fusion performance results of both full Magnetohydrodynamic (MHD) simulations as well as all robust, modern theoretical spatial and energy distribution models. Further, by using the simplified cylindrical model, detailed fusion reaction, radiation, and energy transport equations are now numerically-tractable and can be modelled over a wide parameter space. In the second section of this work, a detailed numerical model will be presented with the key theoretical performance of the compression of high-beta fusion plasmas in both deuterium–tritium (D–T) and deuterium–helium-3 (D–He-3) fuels. As will be shown, a high-beta D–He-3 plasma outperforms a low-beta D–T fuel and can theoretically yield a net-positive fusion generator.

Variable viscous flow resistance based on rotational inertia

Viscous flow resistance is dominated by viscous friction between fluid and wall. The flow resistance characteristic curve (i.e., the relationship curve between pressure drop and flow rates, represented as the Δp–Q curve) depends on some inherent characteristic variables, such as structural size, fluid viscosity, density, and temperature. Usually, to change the Δp–Q curve, these inherent characteristic variables must be changed. This paper proposes a new design of variable viscous flow resistance. The new design uses two disks to construct a slit flow channel, and rotate one of the disks to drive the fluid in the slit flow channel to form a rotational inertia effect. Therefore, by changing the rotating speed of the disk, the rotational inertia effect can be changed, thereby achieving the purpose of changing the Δp–Q curve. This paper derives a theoretical model for the pressure distribution of the rotating slit flow field and conducted experimental verification. It was found that the rotational inertia gradient and viscous gradient terms play major roles in governing the radial pressure gradient. The sum of the other two inertial gradient terms accounts for a maximum of about 1.58% of the total pressure gradient. There is a coupling relationship between circumferential velocity, radial velocity, and flow rates. An increase in Q can increase the rotational inertial gradient term by up to 24.9%. The rotating disk causes additional radial velocity and thus weakens the viscous gradient term by at least 16.41%.

Theoretical and experimental research on a spatially modulated femtosecond bessel-like laser for microdrilling in silica glass

Beam shaping has been widely used in laser processing. Compared with Bessel beam, Bessel-like beam has unique advantages of fabricating high-aspect-ratio holes due to its tunable and longer non-diffraction length. However, the theoretical and experimental optimization of Bessel-like beams for laser manufacture has remained to be investigated. In this paper, we established a theoretical model of the intensity distribution and peak energy density of the Bessel-like beams based on a simplified phase of arc axicon. It was found that the longer propagation length and the lower peak energy density of the Bessel-like beams, contributed to the longer ablation length and higher ablation precision in the silica glass. The ablation length of the optimized Bessel-like beams was at least 1.6 times longer than that of the Bessel beam, which furtherly improved the fabrication efficiency of microdrilling.

Macroplastics in the Bottom of the Veracruz Reef System National Park

The presence of macroplastics in the marine ecosystem is one of the most serious types of pollution today. On the seabed of reef ecosystems, macroplastics are an indicator of contamination because they are easily observable due to their size greater than 2.5 cm. When these wastes sink, they cause serious damage, such as physical changes to the seabed, entanglement, ingestion and transport of invasive species, and can serve as vectors for other pollutants. The main types of macroplastics found in this research work correspond to 57% fishing gear, 14% plastic fragments and 9% textiles. Most of the macroplastics were located in the Veracruz reef subsystem, in the Gallega, Anegada de adentro, Ingenieros, Pájaros and Hornos reefs; In the Antón Li-zardo reef subsystem, macroplastics were found in the Anegadilla reef and in the middle. In reference to the concentration of macroplastics at the bottom of the PNSAV, it is possible to point out that the higher the density of the material with respect to seawater, the economic activities carried out near the reefs have a greater influence, both in the distribution and in the classification of macroplastics, compared to the hydrodynamics. Finally, with all these elements, a theoretical model of distribution and concentration of macroplastics in reef bottoms is proposed.

Normalized modeling of airflow-respirable dust migration and distribution in drilling construction tunnels with different cross-sections

Underground construction mainly relies on drilling work. A large amount of dust generated at the drilling location considerably increases the dust concentration in the worker's breathing area. To explore the distribution of respirable dust during the drilling construction, the virtual point source method was selected and extended to establish the theoretical distribution models for tunnels with curved edge cross-sections, and the assumed parameters in the theoretical models were determined via nonlinear fitting with Euler-Lagrange numerical dust migration field generated by drilling construction. The experimental data and theoretical results agree well based on dimensionless analysis, which verifies the validity of the built models. The respirable dust concentration prediction model curves show that the migration process of dust generated by drilling construction in tunnels encompasses free diffusion section phases, restricted diffusion section phases and full diffusion section phases along the tunnel airway, and the corresponding dimensionless distance ranges are 0–5, 5–20 and beyond 20. For the convenience of engineering application, a dimensionless normalization model is proposed based on the established theoretical models. When the ventilation velocity is between 0.4 m/s and 3 m/s, the recommended values of normalization parameters are 0.80, 0.77 and 1.81, respectively. The abovementioned research results reveal that the established effective theoretical prediction model provides a reliable theoretical basis to gain an in-depth understanding of dust migration behavior during drilling construction.

Study of the large scale structure through modified gravity theory using statistical mechanics

We discuss the galaxy clustering based on thermodynamics and statistical mechanics in the expanding universe in a modified theory of gravity. The modified general relativity (MGR) is developed using the regular line element field to construct a symmetric tensor that represents the energy momentum of the gravitational field. This in turn provides a modified gravitational potential with terms that represent dark matter and dark energy effects without actually invoking the two. Based on the modified gravitational potential we calculate the distribution function of the galaxies. We also calculate various thermodynamic equations of state. We make a data analysis of the data obtained through the SDSS-III survey and check the feasibility of the theoretical model of probability distribution of galaxies in the universe.

Probability distribution models for the ultimate strength of tubular T/Y-joints reinforced with collar plates at room and different fire conditions

In this research work, the simulation results of 360 T/Y-joints reinforced with collar plates have been used to propose theoretical probability distribution models for the ultimate capacity at ambient and fire conditions. So far, no study has been carried out on the probability distribution of ultimate strength in joints with collar plates at room or elevated temperature. Therefore, according to the reinforced T/Y-joint models, which were verified with 18 tests, a total of ultimate capacity data sets was produced. In the FE models, the welds along the collar/brace intersection and between the chord and collar have been generated. Also, the Augmented Lagrange method was applied as the contact algorithm for solving the contact between the collar and chord. In the next step, 13 theoretical probability density functions (PDFs) were fitted to the relative frequency histograms of the databases. For obtaining the parameters of each distribution, the maximum likelihood (ML) method was utilized. Assessing the goodness-of-fit based on the Kolmogorov-Smirnov and Anderson Darling tests indicated that the Johnson SB distribution is the best for the ultimate capacity values in the T/Y-joints reinforced with collar plates at 20, 400, 600, and 800 °C. But, for the reinforced joints at 200 °C, the Inverse Gaussian (3P) distribution is the best. In the next step, five fully defined theoretical PDFs were proposed for the collar plate reinforced T/Y-joints at room and different high temperatures. Probability difference and probability-probability graphs indicated that the proposed theoretical probability distributions are well near the given data sets.