Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model

Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19

In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.

Application of shifted lattice model to 3D compressible lattice Boltzmann method

An additional potential energy distribution function is introduced on the basis of previous D3Q25 model,and the equilibrium distribution function of D3Q25 is obtained by spherical function.A novel three-dimensional(3D)shifted lattice model is proposed,therefore a shifted lattice model is introduced into D3Q25.Under the finite volume scheme,several typical compressible calculation examples are used to verify whether the numerical stability of the D3Q25 model can be improved by adding the shifted lattice model.The simulation results show that the numerical stability is indeed improved after adding the shifted lattice model.

Multi-Objective Optimization of Fused Deposition Modeling for Mechanical Properties of Biopolymer Parts Using the Grey-Taguchi Method

The urgent need to develop customized functional products only possible by 3D printing had realized when faced with the unavailability of medical devices like surgical instruments during the coronavirus-19 disease and the ondemand necessity to perform surgery during space missions.Biopolymers have recently been the most appropriate option for fabricating surgical instruments via 3D printing in terms of cheaper and faster processing.Among all 3D printing techniques,fused deposition modelling(FDM)is a low-cost and more rapid printing technique.This article proposes the fabrication of surgical instruments,namely,forceps and hemostat using the fused deposition modeling(FDM)process.Excellent mechanical properties are the only indicator to judge the quality of the functional parts.The mechanical properties of FDM-processed parts depend on various process parameters.These parameters are layer height,infill pattern,top/bottom pattern,number of top/bottom layers,infill density,flow,number of shells,printing temperature,build plate temperature,printing speed,and fan speed.Tensile strength and modulus of elasticity are chosen as evaluation indexes to ascertain the mechanical properties of polylactic acid(PLA)parts printed by FDM.The experiments have performed through Taguchi’s L27orthogonal array(OA).Variance analysis(ANOVA)ascertains the significance of the process parameters and their percent contributions to the evaluation indexes.Finally,as a multiobjective optimization technique,grey relational analysis(GRA)obtains an optimal set of FDM process parameters to fabricate the best parts with comprehensive mechanical properties.Scanning electron microscopy(SEM)examines the types of defects and strong bonding between rasters.The proposed research ensures the successful fabrication of functional surgical tools with substantial ultimate tensile strength(42.6 MPa)and modulus of elasticity(3274 MPa).

Modeling footing resting on anisotropic sand using material point method

Sand typically exhibits anisotropic internal structure which may significantly influence its mechanical behavior. The material point method (MPM) can eliminate mesh distortion and thus is suitable for investigating geotechnical problems with large deformation. In this study, an advanced anisotropic critical state theory (ACST)-based soil model is implemented in MPM to study the response of strip footing resting on anisotropic sand. The capability of the model is verified by simulating several element tests and strip footing tests with different soil densities and fabric bedding plane orientations. For the footing problem with a vertical load, as the fabric bedding plane orientation increases, the bearing capacity decreases and its corresponding settlement increases. The failure pattern becomes asymmetrical when the bedding plane orientation or the loading direction is inclined. A comparison between the simulation results predicted by the anisotropic and isotropic models is made, which demonstrates that neglecting the fabric anisotropy may lead to the overestimation of the bearing capacity.

Modeling One Dimensional Two-Cell Model with Tumor Interaction Using Krylov Subspace Methods

A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.

3D forward modeling and response characteristics of low-resistivity overburden of the CFS-PML absorbing boundary for ground-well transient electromagnetic method

This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field.The absorption boundary condition of complex frequency-shifted perfectly matched layer(CFS-PML)was used for truncation so that the low-frequency electromagnetic wave can be better absorbed at the model boundary.A typical three-dimensional(3D)homogeneous half-space model was established and a low-resistivity cube model was analyzed under the half-space condition.The response patterns and drivers of the low-resistivity cube model were discussed under the influence of a low-resistivity overburden.The absorption boundary conditions of CFS-PML significantly affected the low-frequency electromagnetic waves.For a low-resistivity cube around the borehole,its response curve exhibited a single-peak,and the extreme point of the curve corresponded to the center of the low-resistivity body.When the low-resistivity cube was directly below the borehole,the response curve showed three extreme values(two high and one low),with the low corresponding to the center of the low-resistivity body.The total field response of the low-resistivity overburden was stronger than that of the uniform half-space model due to the low-resistivity shielding effect of electromagnetic waves.When the receiving-transmitting distance gradually increased,the effect of the low-resistivity overburden was gradually weakened,and the response of the low-resistivity cube was strengthened.It was affected by the ratio of the overburden resistivity to the resistivity of the low-resistivity body.

Displacement Field Variable Modeling Method for Heterogeneous Materials in Wind Power Blade Core Plates

In order to study the mechanical properties of the heterogeneous core plate of the wind turbine blade,a modeling method of the core plate based on displacement field variables is proposed.Firstly,the wind turbine blade core plate was modeled according to the theory of modeling heterogeneous material characteristics.Secondly,the three-point bending finite element model of the wind turbine blade core plate was solved by the display dynamic equation to obtain the deformation pattern and force-deformation relationship of the core plate.Finally,the three-point bending static test was conducted to compare with the finite element analysis.The test results show that:the damage form of the wind turbine blade core plate includes elasticity,yield,and failure stages.The main failure modes are plastic deformation,core material collapse,and panel-core delamination.The failure load measured by the test is 1.59 kN,which is basically consistent with the load-displacement result obtained by the simulation,with a difference of only 1.9%,which verifies the validity and reliability of the model.It provides data references for wind turbine blade structure design.

Design of N-11-Azaartemisinins Potentially Active against Plasmodium falciparum by Combined Molecular Electrostatic Potential, Ligand-Receptor Interaction and Models Built with Supervised Machine Learning Methods

N-11-azaartemisinins potentially active against Plasmodium falciparum are designed by combining molecular electrostatic potential (MEP), ligand-receptor interaction, and models built with supervised machine learning methods (PCA, HCA, KNN, SIMCA, and SDA). The optimization of molecular structures was performed using the B3LYP/6-31G* approach. MEP maps and ligand-receptor interactions were used to investigate key structural features required for biological activities and likely interactions between N-11-azaartemisinins and heme, respectively. The supervised machine learning methods allowed the separation of the investigated compounds into two classes: cha and cla, with the properties εLUMO+1 (one level above lowest unoccupied molecular orbital energy), d(C6-C5) (distance between C6 and C5 atoms in ligands), and TSA (total surface area) responsible for the classification. The insights extracted from the investigation developed and the chemical intuition enabled the design of sixteen new N-11-azaartemisinins (prediction set), moreover, models built with supervised machine learning methods were applied to this prediction set. The result of this application showed twelve new promising N-11-azaartemisinins for synthesis and biological evaluation.

Model test of negative Poisson’s ratio cable for supporting super-largespan tunnel using excavation compensation method

In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。

Hydrodynamic Performance of a Newly-Designed Pelagic and Demersal Trawls Using Physical Modeling and Analytical Methods for Cameroonian Industrial Fisheries

This study proposed the newly-designed Pelagic and demersal trawls for the fishing vessels operating in Cameroonian waters in pelagic and demersal fishing grounds. The engineering performances of both trawls were investigated using physical modelling method and analytical method based on the predicted equations. In a flume tank, a series of physical model tests based on Tauti’s law were performed to investigate the hydrodynamic and geometrical performances of both trawls and to assess the applicability of the analytical methods based on predicted equations. The results showed that in model scale, the working towing speed and door spread for the pelagic trawl were 3.5 knots and 1.85 m, respectively, and for the bottom trawl net they were 4.0 knots and 1.8 m. At that speed and door spread, the drag force, net opening height, and wing-end spread of the pelagic model trawl were 36.73 N, 0.89 m, and 0.86 m, respectively, and the swept area was 0.76 m2. Bottom trawl speed and door spread were 30.43 N, 0.38 m, and 0.45 m, respectively, and the swept area was 0.25 m2. The maximum difference between the experimental and analytical results of hydrodynamic performances was less than 56.22% and 41.45%, respectively, for pelagic and bottom trawls, the results of the geometrical performances obtained using predicted equations were close to the experimental results in the flume tank with a maximum relative error less than 12.85%. The newly developed pelagic and bottom trawls had advanced engineering performance for high catch efficiency and selectivity and could be used in commercial fishing operations in Cameroonian waters.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

A new liquid membrane diffusion model for characterizing the adsorption kinetics of europium by using a continuous measurement of adsorption platform

To explore the kinetic adsorption under continuous and nonequilibrium states, an integration of continuous measurement and adsorption platform kinetics method was proposed, which was initially called the ICM-AP kinetics method, and a corresponding kinetic adsorption experimental method was developed. Adsorption experiments of europium(Eu) on Ca-bentonite,Na-bentonite, and the D231 cation exchange resin were performed using the ICM-AP kinetics method and continuous measurements. Because the kinetic experimental results observed in this study were different from those of traditional batch adsorption data, pseudo-first-order or pseudo-second-order kinetic models were unsuitable for fitting the experimental data.Hence, a liquid membrane diffusion(LMD) model was developed based on the assumption of simultaneous adsorption/desorption to discuss the mechanism of kinetic adsorption. The kinetic adsorption mechanism was also studied by using XPS.The results indicated that the proposed adsorption model can fit the experimental data more suitably, and the adsorption/desorption behaviors of Eu on bentonite and the D231 resin were simultaneously observed, suggesting that the adsorption kinetics of Eu(Ⅲ) was mainly dominated by hydrated Eu(Ⅲ) ions on the liquid membrane.

Impacts of Aggregation Methods and Trophospecies Number on the Structure and Function of Marine Food Webs

Aggregation of species with similar ecological properties is one of the effective methods to simplify food web researches.However,species aggregation will affect not only the complexity of modeling process but also the accuracy of models’outputs.Selection of aggregation methods and the number of trophospecies are the keys to study the simplification of food web.In this study,three aggregation methods,including taxonomic aggregation(TA),structural equivalence aggregation(SEA),and self-organizing maps(SOM),were analyzed and compared with the linear inverse model–Markov Chain Monte Carlo(LIM-MCMC)model.Impacts of aggregation methods and trophospecies number on food webs were evaluated based on the robustness and unitless of ecological net-work indices.Results showed that aggregation method of SEA performed better than the other two methods in estimating food web structure and function indices.The effects of aggregation methods were driven by the differences in species aggregation principles,which will alter food web structure and function through the redistribution of energy flow.According to the results of mean absolute percentage error(MAPE)which can be applied to evaluate the accuracy of the model,we found that MAPE in food web indices will increase with the reducing trophospecies number,and MAPE in food web function indices were smaller and more stable than those in food web structure indices.Therefore,trade-off between simplifying food webs and reflecting the status of ecosystem should be con-sidered in food web studies.These findings highlight the importance of aggregation methods and trophospecies number in the analy-sis of food web simplification.This study provided a framework to explore the extent to which food web models are affected by dif-ferent species aggregation,and will provide scientific basis for the construction of food webs.

Data-driven casting defect prediction model for sand casting based on random forest classification algorithm

The complex sand-casting process combined with the interactions between process parameters makes it difficult to control the casting quality,resulting in a high scrap rate.A strategy based on a data-driven model was proposed to reduce casting defects and improve production efficiency,which includes the random forest(RF)classification model,the feature importance analysis,and the process parameters optimization with Monte Carlo simulation.The collected data includes four types of defects and corresponding process parameters were used to construct the RF model.Classification results show a recall rate above 90% for all categories.The Gini Index was used to assess the importance of the process parameters in the formation of various defects in the RF model.Finally,the classification model was applied to different production conditions for quality prediction.In the case of process parameters optimization for gas porosity defects,this model serves as an experimental process in the Monte Carlo method to estimate a better temperature distribution.The prediction model,when applied to the factory,greatly improved the efficiency of defect detection.Results show that the scrap rate decreased from 10.16% to 6.68%.

Discrete Element Modelling of Damage Evolution of Concrete Considering Meso-Structure of ITZ

The mechanical properties of interfacial transition zones(ITZs)have traditionally been simplified by reducing the stiffness of cement in previous simulation methods.A novel approach based on the discrete element method(DEM)has been developed for modeling concrete.This new approach efficiently simulates the meso-structure of ITZs,accurately capturing their heterogeneous properties.Validation against established uniaxial compression experiments confirms the precision of thismodel.The proposedmodel canmodel the process of damage evolution containing cracks initiation,propagation and penetration.Under increasing loads,cracks within ITZs progressively accumulate,culminating in macroscopic fractures that traverse themortarmatrix,forming the complex,serpentine path of cracks.This study reveals four distinct displacement patterns:tensile compliant,tensile opposite,mixed tensile-shear,and shear opposite patterns,each indicative of different stages in concrete’s damage evolution.The widening angle of these patterns delineates the progression of cracks,with the tensile compliant pattern signaling the initial crack appearance and the shear opposite pattern indicating the concrete model’s ultimate failure.