Ellipsoidal Distribution Research Articles

Static in-situ curing characteristics of CFRP based on near infrared laser

Study on static in-situ curing characteristics of CFRP based on near infrared laserThe quick curing method of carbon fibre reinforced plastics (CFRP) is one of the hotspots in current research. A static in-situ curing method for CFRP prepreg based on near-infrared laser was put forward in this study. The in-situ curing structural characteristics and the mechanism of CFRP were investigated through real-time surface temperature measurement, COMSOL temperature field simulation, 3D measurement of curing morphology and resin curing degree test. The thermal conductivity of the CFRP along the fiber direction is considerably higher than that along the perpendicular fiber direction. As a result, the temperature profile in the plane takes on an elliptical shape. During the transfer, the temperature field gradually decreases, resulting in an ellipsoidal 3D high-temperature distribution. The different shrinkage phenomena in the different curing regions between the layers lead to an irregular ellipsoidal solidification morphology of the unidirectional CFRP. The temperature in the center of the heat affected zone increases as a power exponential function with time. The area and depth of the heat-affected zone increases with the laser power, and the curing area is positively correlated with the degree of curing. As a result, curing temperature governing equations based on laser power and layer thickness have been proposed, while relationship equations based on laser power, curing depth and curing morphology have been developed. In addition, prediction equations based on curing morphology have been developed for curing degree, in order to achieve precise curing of CFRP.

Generation of UV Ellipsoidal Pulses by 3D Amplitude Shaping for Application in High-Brightness Photoinjectors

Photocathode laser pulse shaping is a crucial technology for enhancing the performance of X-ray free-electron lasers by optimizing the quality of electron beams generated from photocathodes within high-gradient radio frequency guns. By precisely shaping these laser pulses, it is possible to significantly reduce the transverse emittance of produced electron bunches. The optimal pulse shape is an ellipsoidal distribution, commonly referred to as the Kapchinskij–Vladimirskij profile. A pulse-shaping scheme utilizing a commercial Yb:KGW laser operating at 514 nm with a repetition rate of 1 MHz and duration of 260 fs has been developed for generating electron bunches with high peak and average power. This study presents the experimental realization of ellipsoidal pulses via three-dimensional amplitude shaping using spatial light modulators at 514 nm, followed by conversion to UV (257 nm) suitable for Cs 2Te photocathodes. The preservation of pulse shape and a high conversion efficiency during this process are investigated and our experiments pave the way for future emittance minimization for X-ray free-electron lasers.

A Gaussian Process-Based extended Goldak heat source model for finite element simulation of laser powder bed fusion additive manufacturing process

Laser powder bed fusion (L-PBF) additive manufacturing (AM) is a key enabling technology to manufacture highly complex and integrated metallic structures. In L-PBF AM process, the melting of the metal powders and the layers underneath can be governed by either “conduction mode” or “keyhole mode”, with the keyhole mode reportedly leading to porosity and decreased strength and ductility by many studies. In part scale simulations, finite element (FE) model is often used to study the temperature distribution during printing and to predict the residual stress, where a volumetric heat flux with a Gaussian or a double ellipsoidal (Goldak) distribution is often applied as the laser heat source. However, the above heat source models can only capture the melt pool shape in the conduction mode, and fail to capture the transition to keyhole melting mode when the process parameters change. To overcome this inaccuracy, an extended Goldak heat source model is proposed by introducing a laser penetration term as a function of laser parameters obtained from a Gaussian-Process (GP) model. The model is validated by “2D pad” AlSi10Mg L-PBF experiments under a wide range of laser power, scan speed, and laser focus offset, and the results show the model successfully captures the measured melt pool shape in all conditions.

Investigations on Transient Temperature Distribution and Distortion in Shielded Metal Arc Welding of SA 516 Gr. 70 Steel

Efforts are made in this article to investigate the thermal and mechanical phenomena by presenting a coupled thermal and structural analysis of SA516 Grade-70 steel. This material has wide applicability in the fabrication of pressure vessels, boilers, etc., due to its excellent weldability and formability. An actual ongoing problem from a reputed industry, related to distortion during the shielded metal arc welding process, is considered and experiments are carried out on the chosen steel. Results are evaluated employing a two- step methodology, involving simulation. The first step encompasses thermal analysis, providing insights into transient temperature distribution, while the subsequent mechanical analysis offers data on residual stresses and distortion. In the case of heat input, a volumetric heat source with double ellipsoidal heat distribution is used whereas a plasticity material model with rate-independent bilinear kinematic hardening is adopted for the structural analysis. Additionally, temperature-dependent material properties are factored into both scenarios. The data derived from numerical analysis align closely with experimental findings, presenting valuable insights for fabricating industries.

The worst-case scenario: robust portfolio optimization with discrete distributions and transaction costs

This research introduces min-max portfolio optimization models that incorporating transaction costs and focus on robust Entropic value-at-risk. This study offers a unified approach to handl the distribution of random parameters that affect the reward and risk aspects. Utilizing the duality theorem, the study transforms the optimization models into manageable forms, thereby accommodating the underlying random variables' discrete box and ellipsoidal distributions. The impact of transaction costs on optimal portfolio selection is examined through numerical examples under a robust return-risk framework. The results underscore the importance of the proposed model in safeguarding capital and reducing exposure to extreme risks, thus outperforming other strategies documented in the literature. This demonstrates the model's effectiveness in balancing maximizing returns and minimizing potential losses, making it a valuable tool for investors that seek to navigate uncertain financial markets.

Quantification in shooting precision for preferred and non-preferred foot in college soccer players using the 95% equal confidence ellipse.

Shooting precision is a fundamental characteristic in soccer, yet the probabilistic structure and magnitude of precision in soccer shooting remain quantitatively unexplored. This study aimed to quantify shooting precision using measures derived from the bivariate normal distribution for both preferred and non-preferred feet. Sixteen right-footed collegiate soccer players participated by performing instep kicks aiming at targets which are placed close to the left and right top corners of the soccer goal. We used bivariate normal distribution modeled the ball positions, revealing an ellipsoidal distribution, and the area of the 95% confidence ellipses served as an index of precision. Repeated measures ANOVAs revealed a significant main effect of the kicking foot. For shots aimed at the same side as the kicking foot, the area of the 95% confidence ellipse was 6.17 ± 1.93 m2 (mean ± SD) for the preferred foot and 10.22 ± 3.53 m2 for the non-preferred foot. Similar results were observed for shots aimed at the opposite side of the kicking foot. These quantitative findings hold promise for advancing soccer research and enhancing practical applications in soccer skill assessment.

Восстановление пространственной функции распределения неоднородностей покрытия по функции распределения на шлифе

In the experimental studies of the structure of the special coating layer overlaid on metal applying gas-thermal spraying technique, one of the main methods is the study of polished specimen micrography. According to the computer analysis of microphotographs, it is possible to obtain the distribution function of inhomogeneities in the sample. However, since micrography is a flat image, the resulting function will be two-dimensional, whereas in a real sample, the distribution of defects is described by a three-dimensional function. In this paper, the problem of the space function recovery for the distribution of defects in a gas-thermal coating is viewed on the basis of the analysis of polished specimen micrography. The actual inclusion of an irregular shape is replaced by an effective three-axis ellipsoid. The problem is solved in the general form of reduction of the space function f of inhomogeneities distribution according to their distribution function f P on the cross - sectional plane P, which includes some integral transformation I. It is shown that in the special case of spherical particles, the inversion I^(-1) exists and is an integral transformation of the same type as I. The space distribution of spherical particles is also viewed, which does not depend on the longitudinal coordinate z, where particle sizes are limited at each point by a function R(x,y), depending on the coordinates. This distribution is suitable in its essense to the stationary spraying technology, when in deep layers near the substrate, the coating material melts completely and forms a single melt, while closer to the surface and edges, the parts that are not completely melted form inclusions of noticeable sizes. The reduction of the Fuller distribution law, used to optimize the granulometric composition of powder materials, is viewed as a second example. It is found that the reduction of the density of the ellipsoid distribution function to the section of a flat strip transfers the density of the distribution of centers as original, and the product of Fuller distributions times independent parameters is transformed into the product of distributions times the opposite degree parameters and also the previous values of the parameters of the ellipsoid

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis.

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

A New Modified Helmholtz Equation for the Expression of the Gravity Gradient and the Intensity of an Electrostatic Field in Spherical Harmonics

In this work, it is shown that the geometry of a gravity field generated by a spheroid with low eccentricity can be described with the help of a newly modified Helmholtz equation. To distinguish this equation from the modified Helmholtz equation, we refer to it as the G-modified Helmholtz equation. The use of this new equation to study the spheroid’s gravity field is advantageous in expressing the gravity vector as a vector series of spherical harmonics. The solution of the G-modified Helmholtz equation involves both the gravity intensity g (or simply gravity g) and the intensity E of an electrostatic field as shown in sequel. An electrostatic field generated by an oblate spheroid charged with l electrons (uniform ellipsoidal charge distribution) is demonstrated to be a special case. Both gravity intensity g and intensity E are governed by the same law and can be expressed as a series of spherical harmonics, and thus the G-modified Helmholtz equation is useful for describing the gravity and electrostatic fields.

High-security automatic path planning of radiofrequency ablation for liver tumors

Background and objectiveRadiofrequency ablation (RFA) is an effective method for the treatment of liver tumors. Preoperative path planning, which plays a crucial role in RFA treatment, requires doctors to have significant experience and ability. Specifically, correct and highly active preoperative path planning should ensure the safety of the whole puncturing process, complete ablation of tumors and minimal damage to healthy tissues. MethodsIn this paper, a high-security automatic multiple puncture path planning method for liver tumors is proposed, in which the optimization of the ablation number, puncture number, target positions and puncture point positions subject to comprehensive clinical constraints are studied. In particular, both the safety of the puncture path and the distribution of ablation ellipsoids are taken into consideration.The influence of each constraint on the safety of the whole puncturing process is discussed in detail. On this basis, the efficiency of the planning method is obviously improved by simplifying the computational data and optimized variables. In addition, the performance and adaptability of the proposed method to large and small tumors are compared and summarized. ResultsThe proposed method is evaluated on 10 liver tumors of various geometric characteristics from 7 cases. The test results show that the average path planning time and average ablation efficiency are 41.4 s and 60.19%, respectively. For tumors of different sizes, the planning results obtained from the proposed method have similar healthy tissue coverage. Through the clinical evaluation of doctors, the planning results meet the needs of RFA for liver tumors. ConclusionsThe proposed method can provide reasonable puncture paths in RFA planning, which is beneficial to ensure the safety and efficiency of liver tumor ablation.

Estimation of heat source model parameters for partial penetration of TIG welding using numerical optimization method

Heat source parameters have a greater influence on the accuracy of numerical modelling for predicting residual stress and temperature field. Experimental measurements of stress and temperature during arc welding are cumbersome due to dynamic transfer of heat happening in a very short span of time. So, for modelling such a high temperature process, determining the heat source model parameters are critical. In this article, a novel method for figuring out the double ellipsoid heat distribution model’s heat source parameters is demonstrated. Here, finite element analysis (FEA) is done to predict the weld bead dimensions, thermal and structural cycles of tungsten inert gas (TIG) welding of AISI S304 stainless steel plates. 25 different sets of heat source parameters are generated for 100 and 120 A input power separately. Using this generated values, weld bead dimensions are determined from the simulation. The optimization is done with the Taguchi technique taking root mean square error (RMSE) value of heat source parameters and measured weld bead dimensions as response parameters. The model is validated using experimental data and the effects of each parameter on weld pool formation during TIG welding are also studied. Optimum values of heat source parameters for stainless steel AISI 304 at 100 A welding current are 2.3283, 2.3687 and 2.667, respectively, and that for 120 A weld current are 2.5909, 2.613 and 3.4949, respectively. The prediction of temperature and welding residual stress (WRS) distribution using optimizing heat source model parameters shows closer approximation with experimental results. The demonstrated model is very much reliable and simple to predict the heat source parameters for TIG welding with partial penetration with a very lesser number of operations and minimum error.

Influence of filler topology on the thermal transport of composite materials based on similarity principle modeling: A cross-scale simulation study

The thermal conductivity parameter of the materials is a fundamental parameter for thermal design and study of heat transfer processes. In our study, we combined the homogenization theory based on the finite element with the thermal conductivity order-of-magnitude analysis and similarity principle, to construct structural models of fibers, spheres, ellipsoids, sheets, and interfaces, and establish the topology of intermingling and encapsulation of different structures. Combined thermal conductivity calculations of mesoscopic composites and microscopic interface models using finite element and molecular dynamics methods. The anisotropy model of thermal conductivity was established by coordinate transformation. Based on the numerical verification of the reliability of the method, the mechanisms of the influence on the thermal transport of composites were analyzed for parameters such as volume fraction of different structural fillers, structural shape, thermal conductivity ratio, thickness of highly thermally conductive coatings, and spatial orientation distribution. The results showed that the effective thermal conductivity (ETC) of the continuous structural reinforced composite was mainly influenced by the volume fraction of the filler; the modulation of ETC with ellipsoidal particle structure form and distribution mode was comparable to the effect of changing the volume fraction modulation; the mutual fusion between ellipsoids randomly distributed in the plane could effectively enhance the heat transport effect of the composite, and as the volume fraction increased to more than 3%, the heat transport gain from mutual fusion was more obvious; spraying high thermally conductive copper coating on ellipsoidal particles could significantly enhance the ETC of the composites. The present work could provide reference for composites in terms of structural improvement and thermal performance enhancement.

Effect of Grain Sizes on Electrically Assisted Micro—Filling of SUS304 Stainless Steel: Experiment and Simulation

The filling quality of micro-feature structures has a significant impact on the forming quality of micro-channels. The electrical-assisted forming technology can effectively improve the formability of difficult-to-deform materials. In this research, the electrically driven micro-compression constitutive model of SUS304 stainless steels was established to assign grain boundary and grain interior with different material properties. An electrical–thermal–mechanical coupling model was constructed to simulate the filling process considering the effect of grain boundary and grain size. Compared to the experimental results, the simulation indicated a good agreement in microstructure characteristics and higher filling height for the fine-grained material. The increase in grain boundary density makes the resistivity of the fine grain material larger, causing the current destiny and temperature of the specimen to increase with the decrease in grain size. An ellipsoidal gradient temperature distribution is observed due to the uneven current density. Because of the high geometric dislocation density near the grain boundary, a significant dislocation pile-up causes stress to concentrate. It is observed that the deformation coordination is enhanced between the grain boundary and grain core with the decrease in grain size, thus improving the material formability and forming quality.

Comparative Analysis of Temperature Field and Stress Field of TC4 Ti-tanium Alloy Joint Between CMT and MIG Welding

A model was used for the cold metal transfer (CMT) welding based on the volume heat flux distribution of double ellipsoids loaded with time intervals. The temperature field and stress field of TC4 titanium alloy were numerically simulated by ANSYS software. The distribution laws of temperature, residual stress and post-weld deformation during CMT and MIG welding were studied and compared. It was found that the maximum temperature of the molten pool in CMT welding was fluctuating and rising during the loading process, while the temperature of the molten pool in MIG welding was rising smoothly and the maximum temperature was higher than that in CMT welding. The welding stress field was analyzed by thermal-stress coupling analysis. The stress distribution simulated based on the MIG welding heat source was similar to CMT welding, but the maximum von Mises stress was greater than that of CMT welding. Due to the cooling shrinkage, both of them would produce angular deformation after welding. And the maximum angular deformation simulated based on the MIG welding heat source was greater than that of CMT welding. It was proved by welding simulation that CMT welding could reduce welding heat input and residual stress and deformation after welding.

Static contact mechanism between serrated contact wheel and rail in rail grinding with abrasive belt

Rail grinding with abrasive belt essentially appears as the complex nonlinear contact interaction between contact wheel, abrasive belt, and rail surface to realize flexible and efficient rail grinding, and in the grinding process, the higher grinding efficiency can be achieved with a serrated contact wheel. However, the contact mechanism between serrated contact wheel and rail is obscure. In this paper, a parametric contact model between serrated contact wheel and rail is established by setting the non-structural (grinding pressure and rotation angle) and structural parameters (helix angle, cogging ratio, etc.) of the serrated contact wheel. Then, the finite element simulation of contact behaviors under the changing conditions of various parameters is carried out to reveal the influences of the above parameters on the maximum contact stress, contact area, and rubber layer indentation depth. On this basis of the extension of the traditional Hertz contact theory and the calculation of the geometric structures of serrated contact wheel and rail, the mathematical model of the contact area is obtained and the ellipsoidal pressure distribution area and the stress concentration area are calculated and combined together to obtain the contact area pressure distribution model. The contact static test platform was designed and the errors between the theoretical and experimental lengths of the long and short axes of the contact area under a rotation angle of 0° were respectively determined as 7.3 % and 9.9 %, thus verifying the correctness of the established mathematical model. In addition, the theoretical and experimental results of the same points on the characteristic lines of the pressure distribution were obtained separately for the comparison. The comparison results proved the correctness of the mathematical model of pressure distribution.

Numerical simulation of the fluid-solid coupling mechanism of water and mud inrush in a water-rich fault tunnel

This study developed a new model, a 3D coupled computational fluid dynamics (CFD)-discrete element method (DEM) model, by coupling two software programs, ABAQUS and PFC3D, to solve problems related to fluid-solid interaction systems. The complete governing equations and the two-way coupling process between the two software are presented herein. Via Transmission Control Protocol (TCP) socket communication with Python scripting, information between the two software is exchanged in real-time. Then, the classic example in the PFC5.0 documentation was used to verify the model. In the end, the ABAQUS-PFC3D model was employed to simulate the process of water and mud inrush in a water-rich fault tunnel, which could reflect the evolution process of water and mud inrush and track particle movement in a fault zone. The results show that the particles that collapsed inside the fault formed an ellipsoidal distribution during the water and mud inrush in a water-rich fault tunnel. With the continuous loss of particles in the fault into the tunnel, the migration of particles is discontinuous, and a large void appears inside the fault zone. The rapid change of the groundwater flow velocity caused the negative pore pressure. The pressure arch force structure is formed above the ellipsoidal collapse area inside the fault. The principal force field of the fault areas changes from close to the dip of the fault to close to the perpendicular to the fault.

Dilepton helical production in a vortical quark-gluon plasma

In this paper, we propose an observable counting a weighted difference between right-handed and left-handed lepton pairs, which is coined dilepton helical rate. The weight is the momentum difference of the lepton pairs projected onto an auxiliary vector. We derive the helical rate in a quark-gluon plasma with a vorticity in the limit when the quark and lepton masses are ignored. We find the helical rate is maximized when the auxiliary vector is parallel to the vorticity, in which case it has a nearly spherical oblate ellipsoidal distribution. We propose that it can be used as a vortical-meter for quark-gluon plasma.

General formulation of Coulomb explosion dynamics of highly symmetric charge distributions

We present a theoretical approach to study the dynamics of spherical, cylindrical and ellipsoidal charge distributions under their self-Coulomb field and a stochastic force due to collisions and random motions of charged particles. The approach is based on finding the current density of the charge distribution from the charge-current continuity equation and determining the drift velocities of the particles. The latter can be used either to derive the Lagrangian of the system, or to write Newton’s equation of motion with the Lorentz force. We develop a kinetic theory to include the stochastic force due to random motions of electrons in our model. To demonstrate the efficacy of our method, we apply it to various charge distributions and compare our results to N-body simulations. We show that our method reproduces the well-known emittance term in the envelope equation of uniform spherical and cylindrical charge distributions with correct coefficients. We use our model for the gravitational collapse of an ideal gas as well as the cyclotron dynamics of a cylindrical charge distribution in a uniform magnetic field and propose a method to measure the emittance of electron beams.

Three-Dimensional Model of Soil Water and Heat Transfer in Orchard Root Zone under Water Storage Pit Irrigation

To reveal the water and heat transfer characteristics of the orchard soil under water storage pit irrigation and to regulate the distribution of soil water and heat for improving apple quality and increasing yield, a 3D soil water and heat transfer model of orchards under water storage pit irrigation was established. The model not only considered the influences of root water uptake, precipitation, evaporation, and irrigation, but also simulated the infiltration process of the variable water head in the pit according to the principle of mass conservation and introduced the pit coefficient to simulate the difference in radiation in the pit to describe the influence of the pit on the model. Verify and analyze the simulation results. Results showed that the variation trend of simulated soil moisture and heat was consistent with that of measured data. The mean absolute percentage error, root mean square error, and mean absolute deviation were 3.23%, 0.9460, and 0.6984 for soil temperature and 10.05%, 0.0269, and 0.0214 for water content after irrigation, respectively. The simulation results have high accuracy and show that the soil moisture content centers on the pit with an ellipsoid distribution and tends to be uniform over time. The soil temperature was higher in the 4–5 cm area near the soil surface and the wall of pit, and it remarkably changed with time. The intraday variation of soil temperature was mainly affected by atmospheric temperature, but a certain lag was observed compared with the change of atmospheric temperature. With the increase of the irrigation amount, the distribution range of soil moisture content and water high value area increased, while the average and maximum soil temperature decreased. With the increase of irrigation water temperature to 18–24 h after irrigation, the soil temperature in the ellipsoidal area around the pit remarkably increased. The model established in this paper can be used to simulate the hydrothermal status of the soil in the field under water storage pit irrigation. The results prove that the water storage pit irrigation can effectively improve the hydrothermal status of the middle-deep soil and promote the root system of fruit trees to absorb water.

A model-based clustering of expectation–maximization and K -means algorithms in crime hotspot analysis

Hotspot analysis of spatial attributes is a persistent research field in data mining, and applying a model-based clustering procedure is increasingly becoming popular in identifying trends and patterns in datasets on crime events occurring in space. The distributions of potential crime hotspots are parameterized as arising from Gaussian multivariate distributions, whose parameters are estimated by the expectation–maximization (E-M) algorithm, an iterative process with convergence very sensitive to initializations. In this study, a model-based clustering algorithm is explored from the E-M algorithm, initialized by K-means clustering using geodesic distance classification to estimate the model parameters and compared with the classical E-M algorithm, initialized with hierarchical clustering, to identify the distributional patterns of incidence of criminal activities. These model-based clustering algorithms were demonstrated on an open-source large dataset of violent crime activities, which occurred in West Midlands County. Training the data as a Gaussian process, the study identified 12 hotspots of Gaussian mixed models as clusters of an ellipsoidal distribution varying in shape, volume, and orientation, which are mostly found in central parts of boroughs of the study area. The proposed model-based clustering of the E-M algorithm combined with K-means clustering algorithm proved efficient as being fast and stable in convergence with low probability of uncertainty by classifications, producing same classification in some cases when compared to that of the classical E-M and K-means algorithms. The combined model-based clustering techniques applied in the hotspot analysis of criminal activities in space will not only provide insight into crime prediction and resource allocation in combating strategies but also guide researchers to adopt mechanisms for modeling large spatial attributes in data mining.