In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave so...In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.展开更多
This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that...This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.展开更多
In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asympt...In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.展开更多
The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were...The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were investigated using in-situ neutron diffraction and the EVPSC-TDT model.Neutron diffraction was used to quantitatively track grain-level lattice strains and diffraction intensity changes(related to mechanical twinning)in differently oriented grains of each alloy during cyclic tensile/compressive loadings.These measurements were accurately captured by the model.The stress-strain curves of Mg-1 wt%Zn and Mg-2 wt%Zn alloys show as-expected solid solution strengthening from the addition of Zn compared to pure Mg.The macroscopic yielding and hardening behaviors are explained by alternating slip and twinning modes as calculated by the model.The solid solution's influence on individual deformation modes,including basal〈a〉slip,prismatic〈a〉slip,and extension twinning,was then quantitatively assessed in terms of activity,yielding behavior,and hardening response by combining neutron diffraction results with crystal plasticity predictions.The Mg-1 wt%Zn alloy displays distinct yielding and hardening behavior due to solid solution softening of prismatic〈a〉slip.Additionally,the dependence of extension twinning,in terms of the twinning volume fraction,on Zn content exhibits opposite trends under tensile and compressive loadings.展开更多
This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution ...This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.展开更多
Solid solution hinders the extraction of bromine resources from bittern.To separate chlorine-brominebased solid solution in bittern tail solution,the solubilities of the quaternary system KCl-KBr-NaCl-NaBr-H_(2)O and ...Solid solution hinders the extraction of bromine resources from bittern.To separate chlorine-brominebased solid solution in bittern tail solution,the solubilities of the quaternary system KCl-KBr-NaCl-NaBr-H_(2)O and its ternary subsystem NaBr-KBr-H_(2)O at 333.15 K were determined by the isothermal dissolution method,and the corresponding phase diagrams were conducted.An improved model was employed to predict the solubilities of the quaternary system KCl-KBr-NaCl-NaBr-H_(2)O at 333.15 K.The calculated results coincide with the experimental values,implying that the prediction method is feasible.A closed loop crystallization process for the separation of chlorine-bromine-based solid solution in bittern tail solution was proposed and NaBr was obtained with a purity of 98.23%.展开更多
The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of...The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.展开更多
In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs...In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.展开更多
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifur...The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.展开更多
In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system fo...In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.展开更多
The focal mechanism solution is one of the important focal parameters for exploring fault activity and studying regional stress distribution and it has a wide range of applications. The geological structure of the Sic...The focal mechanism solution is one of the important focal parameters for exploring fault activity and studying regional stress distribution and it has a wide range of applications. The geological structure of the SichuanYunnan region in China is complex, with frequent earthquakes and abundant historical observation data, making it one of the popular areas of concern for scholars. This study utilizes the high-precision community velocity model v2.0 of southwest China, obtained through joint inversion based on multiple data methods. The Cut-AndPaste(CAP) method was employed to fit and invert the observed waveforms of 1475 events with M_(L)≥ 3.5 in the Sichuan-Yunnan region from January 2012 to December 2022, thereby constructing a catalog of double-couple focal mechanisms. By comparing the focal mechanism inversion results of small earthquakes with those from multiple one-dimensional velocity models and conducting comparative statistical analysis on events below magnitude 4, it has been demonstrated that the model used in this study provides a better fit than onedimensional models. This contributes to establishing the lower magnitude limit for producing deeper focal mechanism solutions. This study compares the results of larger magnitude earthquakes in the catalog with those published by the Global Centroid-Moment Tensor(GCMT) project and smaller magnitude earthquakes with the catalog released by the Institute of Earthquake Forecasting, China Earthquake Administration. These comparisons serve to validate the accuracy of the catalog results. Leveraging the high-resolution velocity model, this catalog has re-examined the historical earthquake focal mechanism catalog of the Sichuan-Yunnan region. The inversion has yielded reliable results for smaller magnitudes and a greater number of events, providing additional data and support for understanding the regional stress field, active faults, the mechanisms of large earthquake genesis, and earthquake prediction efforts. Consequently, this enhances the depth of scientific research in the Sichuan-Yunnan region.展开更多
This article presents a novel optimization approach called RSWTLBO for accurately identifying unknown parameters in photovoltaic(PV)models.The objective is to address challenges related to the detection and maintenanc...This article presents a novel optimization approach called RSWTLBO for accurately identifying unknown parameters in photovoltaic(PV)models.The objective is to address challenges related to the detection and maintenance of PV systems and the improvement of conversion efficiency.RSWTLBO combines adaptive parameter w,Single Solution Optimization Mechanism(SSOM),and Weight Probability Exploration Strategy(WPES)to enhance the optimization ability of TLBO.The algorithm achieves a balance between exploitation and exploration throughout the iteration process.The SSOM allows for local exploration around a single solution,improving solution quality and eliminating inferior solutions.The WPES enables comprehensive exploration of the solution space,avoiding the problem of getting trapped in local optima.The algo-rithm is evaluated by comparing it with 10 other competitive algorithms on various PV models.The results demonstrate that RSWTLBO consistently achieves the lowest Root Mean Square Errors on single diode models,double diode models,and PV module models.It also exhibits robust performance under varying irradiation and temperature conditions.The study concludes that RSWTLBO is a practical and effective algorithm for identifying unknown parameters in PV models.展开更多
[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a cont...[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a control group,a model group,and an experimental group.The experimental group was administered with 10%Shuanghuanglian oral solution at a dose of 0.1 mL/(10 g·d),while the control group and experimental group received an equivalent dosage of normal saline.All three groups were treated for a period of 28 d.The liver function of the mice in each group was examined after the treatment.[Results]The body mass,liver index,triacylglycerol(TG),total cholesterol(TC),aspartate aminotransferase(AST),and alanine aminotransferase(ALT)levels were all significantly reduced compared to the model group(P<0.05).[Conclusions]Shuanghuanglian oral solution has a beneficial effect on liver function in BABL/cJ mice.展开更多
It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analyt...It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.展开更多
In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of t...In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.展开更多
The thermodynamic properties of the most important NaOH-NaAI（OH）4-H20 system in Bayer process for alumina production were investigated. A theoretical model for calculating the equilibrium constant of gibbsite dissol...The thermodynamic properties of the most important NaOH-NaAI（OH）4-H20 system in Bayer process for alumina production were investigated. A theoretical model for calculating the equilibrium constant of gibbsite dissolved in sodium hydroxide solution was proposed. New Pitzer model parameters and mixing parameters for the system NaOH-NaAI（OH）4-H20 were yielded and tested in the temperature range of 298.15-373.15 K. The results show that the proposed model for calculating the equilibrium constant of gibbsite dissolution is applicable and accurate. The obtained Pitzer model parameters of β（0）（NaAl（OH）4）、β（1）（NaAl（OH）4）和CΦ（NaAl（OH）4）,Al（OH）4 for NaAI（OH）4, the binary mixing parameter of θ（OH-Al（OH）4-） with OH-, and the ternary mixing parameter of ψ（Na＋OH-Al（OH）4-） for AI（OH）4- with OH- and Na＋ are temperature-dependent. The prediction of the equilibrium solubility of gibbsite dissolved in sodium hydroxide solution was feasible in the temperature range of 298.15-373.15 K.展开更多
A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexi...A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexistence theory and verified in four kinds of binary aqueous solutions and two kinds of ternary aqueous solutions. The calculated mass action concentrations of structural units or ion couples in four binary aqueous solutions and two ternary solutions at 298.15 K have good agreement with the reported activity data from literatures after shifting the standard state and concentration unit. Therefore, the calculated mass action concentrations of structural units or ion couples from the developed universal thermodynamic model for ternary and binary aqueous solutions can be applied to predict reaction ability of components in ternary and binary strong electrolyte aqueous solutions. It is also proved that the assumptions applied in the developed thermodynamic model are correct and reasonable, i.e., strong electrolyte aqueous solution is composed of cations and anions as simple ions, H2O as simple molecule and other hydrous salt compounds as complex molecules. The calculated mass action concentrations of structural units or ion couples in ternary and binary strong electrolyte aqueous solutions strictly follow the mass action law.展开更多
The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution ...The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.展开更多
In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model w...In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.展开更多
The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, pe...The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.展开更多
基金Supported by the National Natural Science Foundation of China(12261050)Science and Technology Project of Department of Education of Jiangxi Province(GJJ2201612 and GJJ211027)Natural Science Foundation of Jiangxi Province of China(20212BAB202021)。
文摘In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.
文摘This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.
基金supported by the National Natural Science Foundation of China(Grant Nos.12475003 and11705284)by the Natural Science Foundation of Beijing Municipality(Grant Nos.1232022 and 1212007)。
文摘In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.
基金supported by the National Research Foundation grant funded by the Korean government(No,2023R1A2C2007190,RS-2024-00398068)partially funded by the Natural Science Foundation of Shandong Province,China(No.ZR2022QE206).
文摘The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were investigated using in-situ neutron diffraction and the EVPSC-TDT model.Neutron diffraction was used to quantitatively track grain-level lattice strains and diffraction intensity changes(related to mechanical twinning)in differently oriented grains of each alloy during cyclic tensile/compressive loadings.These measurements were accurately captured by the model.The stress-strain curves of Mg-1 wt%Zn and Mg-2 wt%Zn alloys show as-expected solid solution strengthening from the addition of Zn compared to pure Mg.The macroscopic yielding and hardening behaviors are explained by alternating slip and twinning modes as calculated by the model.The solid solution's influence on individual deformation modes,including basal〈a〉slip,prismatic〈a〉slip,and extension twinning,was then quantitatively assessed in terms of activity,yielding behavior,and hardening response by combining neutron diffraction results with crystal plasticity predictions.The Mg-1 wt%Zn alloy displays distinct yielding and hardening behavior due to solid solution softening of prismatic〈a〉slip.Additionally,the dependence of extension twinning,in terms of the twinning volume fraction,on Zn content exhibits opposite trends under tensile and compressive loadings.
基金supported by the Anhui Provincial Natural Science Foundation(2408085QA031)the third author's work was supported by the National Natural Science Foundation of China(12001033).
文摘This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.
基金supported by the National Natural Science Foundation of China(22478095 and 22008049)Hebei Provincial Key Research Projects(22374101D)+4 种基金Scientific Research Projects of Colleges and University in Hebei Province(QN2023007)Central Guidance Project for Local Science and Technology Development from S&T Program of Hebei(246Z1009G)Special Proof-of-concept Project on Basic Research from S&T Program of Hebei(E2024402143)Science and Technology Project of Hebei Education Department(CXY2023004)Hebei University of Engineering Doctoral Scientific Research Start-up Foundation(SJ2401002210).
文摘Solid solution hinders the extraction of bromine resources from bittern.To separate chlorine-brominebased solid solution in bittern tail solution,the solubilities of the quaternary system KCl-KBr-NaCl-NaBr-H_(2)O and its ternary subsystem NaBr-KBr-H_(2)O at 333.15 K were determined by the isothermal dissolution method,and the corresponding phase diagrams were conducted.An improved model was employed to predict the solubilities of the quaternary system KCl-KBr-NaCl-NaBr-H_(2)O at 333.15 K.The calculated results coincide with the experimental values,implying that the prediction method is feasible.A closed loop crystallization process for the separation of chlorine-bromine-based solid solution in bittern tail solution was proposed and NaBr was obtained with a purity of 98.23%.
基金supported by the National Natural Science Foundation of China under Grant No.12375006the Weimu Technology Company Limited of Hangzhou of China under Grant No.KYY-HX-20240495。
文摘The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.
基金financial support from the Young Scientist Project of the National Key Research and Development Program of China(Grant No.2021YFC2900600)the Beijing Nova Program(Grant No.20220484057)+1 种基金The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2018-06902)industrial partners of the Research Institute on Mines and the Environment(RIME UQAT-Polytechnique:https://irme.ca/en/).
文摘In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.
基金supported as part of the Computational Materials Sciences Program funded by the U.S.Department of Energy,Office of Science,Basic Energy Sciences,under Award No.DE-SC0020145Y.Z.would like to acknowledge support for his effort by the Simons Foundation through Grant No.357963 and NSF grant DMS-2142500.
文摘The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.
文摘In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.
基金the National Key Research and Development Program for supporting this study (Project No.: 2021YFC3000701-03, 2021YFC3000705)。
文摘The focal mechanism solution is one of the important focal parameters for exploring fault activity and studying regional stress distribution and it has a wide range of applications. The geological structure of the SichuanYunnan region in China is complex, with frequent earthquakes and abundant historical observation data, making it one of the popular areas of concern for scholars. This study utilizes the high-precision community velocity model v2.0 of southwest China, obtained through joint inversion based on multiple data methods. The Cut-AndPaste(CAP) method was employed to fit and invert the observed waveforms of 1475 events with M_(L)≥ 3.5 in the Sichuan-Yunnan region from January 2012 to December 2022, thereby constructing a catalog of double-couple focal mechanisms. By comparing the focal mechanism inversion results of small earthquakes with those from multiple one-dimensional velocity models and conducting comparative statistical analysis on events below magnitude 4, it has been demonstrated that the model used in this study provides a better fit than onedimensional models. This contributes to establishing the lower magnitude limit for producing deeper focal mechanism solutions. This study compares the results of larger magnitude earthquakes in the catalog with those published by the Global Centroid-Moment Tensor(GCMT) project and smaller magnitude earthquakes with the catalog released by the Institute of Earthquake Forecasting, China Earthquake Administration. These comparisons serve to validate the accuracy of the catalog results. Leveraging the high-resolution velocity model, this catalog has re-examined the historical earthquake focal mechanism catalog of the Sichuan-Yunnan region. The inversion has yielded reliable results for smaller magnitudes and a greater number of events, providing additional data and support for understanding the regional stress field, active faults, the mechanisms of large earthquake genesis, and earthquake prediction efforts. Consequently, this enhances the depth of scientific research in the Sichuan-Yunnan region.
基金supported in part by the Natural Science Foundation of Zhejiang Province(LTGS23E070001)National Natural Science Foundation of China(62076185,62301367).
文摘This article presents a novel optimization approach called RSWTLBO for accurately identifying unknown parameters in photovoltaic(PV)models.The objective is to address challenges related to the detection and maintenance of PV systems and the improvement of conversion efficiency.RSWTLBO combines adaptive parameter w,Single Solution Optimization Mechanism(SSOM),and Weight Probability Exploration Strategy(WPES)to enhance the optimization ability of TLBO.The algorithm achieves a balance between exploitation and exploration throughout the iteration process.The SSOM allows for local exploration around a single solution,improving solution quality and eliminating inferior solutions.The WPES enables comprehensive exploration of the solution space,avoiding the problem of getting trapped in local optima.The algo-rithm is evaluated by comparing it with 10 other competitive algorithms on various PV models.The results demonstrate that RSWTLBO consistently achieves the lowest Root Mean Square Errors on single diode models,double diode models,and PV module models.It also exhibits robust performance under varying irradiation and temperature conditions.The study concludes that RSWTLBO is a practical and effective algorithm for identifying unknown parameters in PV models.
文摘[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a control group,a model group,and an experimental group.The experimental group was administered with 10%Shuanghuanglian oral solution at a dose of 0.1 mL/(10 g·d),while the control group and experimental group received an equivalent dosage of normal saline.All three groups were treated for a period of 28 d.The liver function of the mice in each group was examined after the treatment.[Results]The body mass,liver index,triacylglycerol(TG),total cholesterol(TC),aspartate aminotransferase(AST),and alanine aminotransferase(ALT)levels were all significantly reduced compared to the model group(P<0.05).[Conclusions]Shuanghuanglian oral solution has a beneficial effect on liver function in BABL/cJ mice.
文摘It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.
文摘In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.
基金Project (2005CB6237) supported by the National Basic Research Program of China
文摘The thermodynamic properties of the most important NaOH-NaAI（OH）4-H20 system in Bayer process for alumina production were investigated. A theoretical model for calculating the equilibrium constant of gibbsite dissolved in sodium hydroxide solution was proposed. New Pitzer model parameters and mixing parameters for the system NaOH-NaAI（OH）4-H20 were yielded and tested in the temperature range of 298.15-373.15 K. The results show that the proposed model for calculating the equilibrium constant of gibbsite dissolution is applicable and accurate. The obtained Pitzer model parameters of β（0）（NaAl（OH）4）、β（1）（NaAl（OH）4）和CΦ（NaAl（OH）4）,Al（OH）4 for NaAI（OH）4, the binary mixing parameter of θ（OH-Al（OH）4-） with OH-, and the ternary mixing parameter of ψ（Na＋OH-Al（OH）4-） for AI（OH）4- with OH- and Na＋ are temperature-dependent. The prediction of the equilibrium solubility of gibbsite dissolved in sodium hydroxide solution was feasible in the temperature range of 298.15-373.15 K.
基金Project supported by Publication Foundation of National Science and Technology Academic Books of China
文摘A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexistence theory and verified in four kinds of binary aqueous solutions and two kinds of ternary aqueous solutions. The calculated mass action concentrations of structural units or ion couples in four binary aqueous solutions and two ternary solutions at 298.15 K have good agreement with the reported activity data from literatures after shifting the standard state and concentration unit. Therefore, the calculated mass action concentrations of structural units or ion couples from the developed universal thermodynamic model for ternary and binary aqueous solutions can be applied to predict reaction ability of components in ternary and binary strong electrolyte aqueous solutions. It is also proved that the assumptions applied in the developed thermodynamic model are correct and reasonable, i.e., strong electrolyte aqueous solution is composed of cations and anions as simple ions, H2O as simple molecule and other hydrous salt compounds as complex molecules. The calculated mass action concentrations of structural units or ion couples in ternary and binary strong electrolyte aqueous solutions strictly follow the mass action law.
文摘The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.
文摘In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.
基金supported by the National Outstanding Young Scientist Foundation of China (Grant 11225213)the Key Subject "Computational Solid Mechanics" of China Academy of Engineering Physics
文摘The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.
