A Windows bitmap-based numerically controlled sculpture method and its application

Bitmap （BMP） is a widely used format in image processing. With the combination of the digital image processing and computer numerically controlled （NC） techniques, we developed a bitmap-based NC single-step and multi-dot method. An example was provided to illustrate the application and principle of this bitmap-based method in our newly innovated sandblasting glass NC sculpture system.

Three-Variable Shifted Jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients

In this paper,the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of threedimensional multi-term fractional-order PDEs with variable coefficients.The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem.The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by threevariable shifted Jacobi polynomials are compared with the exact solutions.Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm.Lastly,several numerical examples are presented to test the superiority and efficiency of the proposed method.

Predicting numerically the large increases in extra pressure drop when boger fluids flow through

Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional vis-cosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Max- well (UCM) models to represent the behavior of so-called Boger fluids in axisymmetric contrac-tion flows, in (unsuccessful) attempts to predict the very large enhancements that were ob-served experimentally. In more recent studies, other constitutive models have been employed to interpret observed behavior and some pro-gress has been made, although finding a (re-spectable) model to describe observed contrac-tion-flow behavior, even qualitatively, has been frustratingly difficult. With this in mind, the present study discusses the ability of a well- known FENE type model (the so-called FENE- CR model) to describe observed behavior. For various reasons, an axisymmetric (4:1:4) con-traction/expansion geometry, with rounded corners, is singled out for special attention, and a new hybrid finite element/volume algo-rithm is utilized to conduct the modeling, which reflects an incremental pressure-correction time-stepping structure. New to this algo-rithmic formulation are techniques in time discretization, discrete treatment of pressure terms, and compatible stress/velocity-gradient representation. We shall argue that the current simulations for the FENE-CR model have re-sulted in a major improvement in the sort-for agreement between theory and experiment in this important bench-mark problem.

Workflow to numerically reproduce laboratory ultrasonic datasets

The risks and uncertainties related to the storage of high-level radioactive waste （HLRW） can be reducedthanks to focused studies and investigations. HLRWs are going to be placed in deep geological repositories,enveloped in an engineered bentonite barrier, whose physical conditions are subjected tochange throughout the lifespan of the infrastructure. Seismic tomography can be employed to monitor itsphysical state and integrity. The design of the seismic monitoring system can be optimized via conductingand analyzing numerical simulations of wave propagation in representative repository geometry.However, the quality of the numerical results relies on their initial calibration. The main aim of this paperis to provide a workflow to calibrate numerical tools employing laboratory ultrasonic datasets. The finitedifference code SOFI2D was employed to model ultrasonic waves propagating through a laboratorysample. Specifically, the input velocity model was calibrated to achieve a best match between experimentaland numerical ultrasonic traces. Likely due to the imperfections of the contact surfaces, theresultant velocities of P- and S-wave propagation tend to be noticeably lower than those a prioriassigned. Then, the calibrated model was employed to estimate the attenuation in a montmorillonitesample. The obtained low quality factors （Q） suggest that pronounced inelastic behavior of the clay has tobe taken into account in geophysical modeling and analysis. Consequently, this contribution should beconsidered as a first step towards the creation of a numerical tool to evaluate wave propagation innuclear waste repositories. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Numerically investigating the crushing of sandstone by a tooth hob

To investigate the mechanical process that occurs between rocks and tooth hobs,the crushing of sandstone with a tooth hob was simulated using reconstructed multi-mineral mesoscopic numerical models of various grain-sized sandstone samples.When a piece of sandstone is crushed by the tooth of a hob rolling at a constant speed,the resultant reaction forces of the sandstone on the tooth first hinder and then contribute to the rolling of the hob.The absolute value of the longitudinal reaction force is significantly higher than that of the lateral reaction force.Because the tooth was subjected to reaction forces from the sandstone,forces and moments were applied to the hob in order to keep the hob rolling.The applied forces were equal in value and opposite in direction to the reaction forces of the sandstone on the tooth.Three typical curves of the work done by the applied forces and moment were obtained,and the contribution of the applied lateral force and moment to the total work done for crushing sandstones was variable;however,no work was done by the applied longitudinal force.Moreover,the applied longitudinal force and total work were positively correlated with the strength of sandstone samples.The total work,applied forces,and moment increased with the maximum penetration depth of the tooth in the sandstone.

Hybrid-Vlasov simulation of soft X-ray emissions at the Earth’s dayside magnetospheric boundaries

Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause,the magnetosheath and the polar cusps by remote sensing techniques.The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)and Lunar Environment heliospheric X-ray Imager(LEXI)missions aim to obtain soft Xray images of near-Earth space thanks to their Soft X-ray Imager(SXI)instruments.While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission,the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma.To investigate the possible signatures of ion-kinetic-scale processes in soft Xray images,we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model.The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field.We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations,providing meridional and equatorial views.We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirrormode wave structures in the magnetosheath and flux transfer events(FTEs)at the magnetopause.Our results suggest that,although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers,mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images.For instance,a local increase by 30%in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12%enhancement in the line-of-sight-and time-integrated soft X-ray emissivity originating from this region.Likewise,a proton density increase by 14%in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%.These are likely conservative estimates,given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind.These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale,transient phenomena occurring on the dayside.

Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

Magnetopause properties at the dusk magnetospheric flank from global magnetohydrodynamic simulations,the kinetic Vlasov equilibrium,and in situ observations--Potential implications for SMILE

We derived the properties of the terrestrial magnetopause(MP)from two modeling approaches,one global–fluid,the other local–kinetic,and compared the results with data collected in situ by the Magnetospheric Multiscale 2(MMS2)spacecraft.We used global magnetohydrodynamic(MHD)simulations of the Earth’s magnetosphere(publicly available from the NASA-CCMC[National Aeronautics and Space Administration–Community Coordinated Modeling Center])and local Vlasov equilibrium models(based on kinetic models for tangential discontinuities)to extract spatial profiles of the plasma and field variables at the Earth’s MP.The global MHD simulations used initial solar wind conditions extracted from the OMNI database at the time epoch when the MMS2 observes the MP.The kinetic Vlasov model used asymptotic boundary conditions derived from the same in situ MMS measurements upstream or downstream of the MP.The global MHD simulations provide a three-dimensional image of the magnetosphere at the time when the MMS2 crosses the MP.The Vlasov model provides a one-dimensional local view of the MP derived from first principles of kinetic theory.The MMS2 experimental data also serve as a reference for comparing and validating the numerical simulations and modeling.We found that the MP transition layer formed in global MHD simulations was generally localized closer to the Earth(roughly by one Earth radius)from the position of the real MP observed by the MMS.We also found that the global MHD simulations overestimated the thickness of the MP transition by one order of magnitude for three analyzed variables:magnetic field,density,and tangential speed.The MP thickness derived from the local Vlasov equilibrium was consistent with observations for all three of these variables.The overestimation of density in the Vlasov equilibrium was reduced compared with the global MHD solutions.We discuss our results in the context of future SMILE(Solar wind Magnetosphere Ionosphere Link Explorer)campaigns for observing the Earth’s MP.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Aircraft Flutter Modal Parameter Identification Using a Numerically Robust Least-squares Estimator in Frequency Domain

Recently, frequency-based least-squares （LS） estimators have found wide application in identifying aircraft flutter parameters. However, the frequency methods are often known to suffer from numerical difficulties when identifying a continuous-time model, especially, of broader frequency or higher order. In this article, a numerically robust LS estimator based on vector orthogonal polynomial is proposed to solve the numerical problem of multivariable systems and applied to the flutter testing. The key idea of this method is to represent the frequency response function （FRF） matrix by a right matrix fraction description （RMFD） model, and expand the numerator and denominator polynomial matrices on a vector orthogonal basis. As a result, a perfect numerical condition （numerical condition equals 1） can be obtained for linear LS estimator. Finally, this method is verified by flutter test of a wing model in a wind tunnel and real flight flutter test of an aircraft. The results are compared to those with notably LMS PolyMAX, which is not troubled by the numerical problem as it is established in z domain （e.g. derived from a discrete-time model）. The verification has evidenced that this method, apart from overcoming the numerical problem, yields the results comparable to those acquired with LMS PolyMAX, or even considerably better at some frequency bands.

Simulation of the SMILE Soft X-ray Imager response to a southward interplanetary magnetic field turning

The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)Soft X-ray Imager(SXI)will shine a spotlight on magnetopause dynamics during magnetic reconnection.We simulate an event with a southward interplanetary magnetic field turning and produce SXI count maps with a 5-minute integration time.By making assumptions about the magnetopause shape,we find the magnetopause standoff distance from the count maps and compare it with the one obtained directly from the magnetohydrodynamic(MHD)simulation.The root mean square deviations between the reconstructed and MHD standoff distances do not exceed 0.2 RE(Earth radius)and the maximal difference equals 0.24 RE during the 25-minute interval around the southward turning.

Numerical simulation of microwave-induced cracking and melting of granite based on mineral microscopic models

This study introduces a coupled electromagnetic–thermal–mechanical model to reveal the mechanisms of microcracking and mineral melting of polymineralic rocks under microwave radiation.Experimental tests validate the rationality of the proposed model.Embedding microscopic mineral sections into the granite model for simulation shows that uneven temperature gradients create distinct molten,porous,and nonmolten zones on the fracture surface.Moreover,the varying thermal expansion coefficients and Young's moduli among the minerals induce significant thermal stress at the mineral boundaries.Quartz and biotite with higher thermal expansion coefficients are subjected to compression,whereas plagioclase with smaller coefficients experiences tensile stress.In the molten zone,quartz undergoes transgranular cracking due to theα–βphase transition.The local high temperatures also induce melting phase transitions in biotite and feldspar.This numerical study provides new insights into the distribution of thermal stress and mineral phase changes in rocks under microwave irradiation.

Numerical analysis of geosynthetic-reinforced embankment performance under moving loads

The performance of geosynthetic-reinforced embankments under traffic moving loads is always a hotspot in the geotechnical engineering field.A three-dimensional(3D)model of a geosynthetic-reinforced embankment without drainage consolidation was established using the finite element software ABAQUS.In this model,the traffic loads were simulated by two moving loads of rectangular pattern,and their amplitude,range,and moving speed were realized by a Fortran subroutine.The embankment fill was simulated by an equivalent linear viscoelastic model,which can reflect its viscoelasticity.The geogrid was simulated by the truss element,and the geocell was simulated by the membrane element.Infinite elements were utilized to weaken the boundary effect caused by the model geometry at the boundaries.Validation of the established numerical model was conducted by comparing the predicted deformations in the cross-section of the geosynthetic-reinforced embankment with those from the existing literature.On this basis,the dynamic stress and strain distribution in the pavement structure layer of the geosynthetic-reinforced embankment under a moving load was also analyzed.Finally,a parametric study was conducted to examine the influences of the different types of reinforcement,overload,and the moving load velocity on the geosynthetic-reinforced embankment.

Numerical simulation on the multiphase flow and reoxidation of the molten steel in a two-strand tundish during ladle change

A 3D mathematical model was proposed to investigate the molten steel–slag–air multiphase flow in a two-strand slab continuous casting(CC)tundish during ladle change.The study focused on the exposure of the molten steel and the subsequent reoxidation occurrence.The exposure of the molten steel was calculated using the coupled realizable k–εmodel and volume of fluid(VOF)model.The diffusion of dissolved oxygen was determined by solving the user-defined scalar(UDS)equation.Moreover,the user-defined function(UDF)was used to describe the source term in the UDS equation and determine the oxidation rate and oxidation position.The effect of the refilling speed on the molten steel exposure and dissolved oxygen content was also discussed.Increasing the refilling speed during ladle change reduced the refilling time and the exposure duration of the molten steel.However,the elevated refilling speed enlarged the slag eyes and increased the average dissolved oxygen content within the tundish,thereby exacerbating the reoxidation phenomenon.In addition,the time required for the molten steel with a high dissolved oxygen content to exit the tundish varied with the refilling speed.When the inlet speed was 3.0 m·s^(-1)during ladle change,the molten steel with a high dissolved oxygen content exited the outlet in a short period,reaching a maximum dissolved oxygen content of 0.000525wt%.Conversely,when the inlet speed was 1.8 m·s^(-1),the maximum dissolved oxygen content was 0.000382wt%.The refilling speed during the ladle change process must be appropriately decreased to minimize reoxidation effects and enhance the steel product quality.

Multi-physical fields distribution in billet during helical electromagnetic stirring:A numerical simulation research

Electromagnetic stirring is one of the widely applied techniques to modify the quality of casting billets.Different from conventional rotate stirring,the helical stirring is more professional in assisting multi-dimensional flow of molten metal and eliminating solidification defects.In this study,the single-winding helical stirring(SWHS)was introduced,offering advantages such as smaller volume and lower electromagnetic shielding compared to traditional helical stirring methods.Following a comprehensive numerical simulation,the stirring parameters of SWHS were adjusted to yoke inclination angle of 43°and frequency of 12 Hz.The higher electromagnetic force and flow velocity in drawing direction,as well as the lower temperature gradient induced by the SWHS,are positive factors for homogeneous solidification of billet.The experimental results on Al-8%Si alloy and 0.4%C-1.1%Mn steel demonstrate that compared to rotate stirring,the SWHS process can induce better billet quality and is more effective in accelerating the equiaxed expansion and reducing element segregation.The SWHS process can enhance the equiaxed ratio of the billet by 58.3%and reduce segregation degree of carbon element by 10.97%.Consequently,SWHS holds great promise as a potential approach for improving the quality of continuous casting billets.

Refiector Deformation Measurement and Correction Methodology of Large Antenna Based on Phased Array Feed

To solve the problem of time-consuming measurement and correction of large antennas’reflector deformation,a new microwave holography methodology based on a Phased Array Feed(PAF)is proposed.Starting from the known expression of receiving signals in microwave holography,the theory of PAF holography is derived through Geometrical Optics.Reflector deformation,as well as pointing deviation and subreflector offset,can be calculated out by applying the derived equations.A measurement and correction system based on PAF holography is depicted,and two kinds of measurement methods are illustrated.The proposed measurement methodology is verified by numerical simulation,and its measurement error is analyzed.The results indicate that our proposed methodology is feasible,especially for Cassegrain antennas.

Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

Applying Hybrid Clustering in Pulsar Candidate Sifting with Multi-modality for FAST Survey

Pulsar search is always the basis of pulsar navigation,gravitational wave detection and other research topics.Currently,the volume of pulsar candidates collected by the Five-hundred-meter Aperture Spherical radio Telescope(FAST)shows an explosive growth rate that has brought challenges for its pulsar candidate filtering system.Particularly,the multi-view heterogeneous data and class imbalance between true pulsars and non-pulsar candidates have negative effects on traditional single-modal supervised classification methods.In this study,a multi-modal and semi-supervised learning based on a pulsar candidate sifting algorithm is presented,which adopts a hybrid ensemble clustering scheme of density-based and partition-based methods combined with a feature-level fusion strategy for input data and a data partition strategy for parallelization.Experiments on both High Time Resolution Universe SurveyⅡ(HTRU2)and actual FAST observation data demonstrate that the proposed algorithm could excellently identify pulsars:On HTRU2,the precision and recall rates of its parallel mode reach0.981 and 0.988 respectively.On FAST data,those of its parallel mode reach 0.891 and 0.961,meanwhile,the running time also significantly decreases with the increment of parallel nodes within limits.Thus,we can conclude that our algorithm could be a feasible idea for large scale pulsar candidate sifting for FAST drift scan observation.

Overall Assessment of Heat Transfer for a Rarefied Flow in a Microchannel with Obstacles Using Lattice Boltzmann Method

The objective of this investigation is to assess the effect of obstacles on numerical heat transfer and fluid flow momentum in a rectangular microchannel(MC).Two distinct configurations were studied:one without obstacles and the other with alternating obstacles placed on the upper and lower walls.The research utilized the thermal lattice Boltzmann method(LBM),which solves the energy and momentum equations of fluids with the BGK approximation,implemented in a Python coding environment.Temperature jump and slip velocity conditions were utilized in the simulation for the MC and extended to all obstacle boundaries.The study aims to analyze the rarefaction effect,with Knudsen numbers(Kn)of 0.012,0.02,and 0.05.The outcomes indicate that rarefaction has a significant impact on the velocity and temperature distribution.The presence of nine obstacles led to slower fluid movement inside the microchannel MC,resulting in faster cooling at the outlet.In MCs with obstacles,the rarefaction effect plays a crucial role in decreasing the Nusselt number(Nu)and skin friction coefficient(Cf).Furthermore,the study demonstrated that the obstacles played a crucial role in boosting fluid flow and heat transfer in the MC.The findings suggest that the examined configurations could have potential applications as cooling technologies in micro-electro-mechanical systems and microdevice applications.