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Transport mechanism in chemically reactive hybrid nanofluid flow containing gyrotactic micro-organisms over a curved oscillatory surface

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applied mathematics and Mechanics(English Edition) 2025年第1期46卷 177-192页

作者： M.NAVEED M.IMRAN T.ASGHAR Z.ABBAS Department of mathematics Division of Science and TechnologyUniversity of Education Department of mathematics The Islamia University of Bahawalpur

This paper examines the transport analysis, including both heat transfer and mass transfer, in hybrid nanofluid flow containing gyrotactic microorganisms towards a curved oscillatory surface. The influence of magnetic fields is also inspected in terms of their physical characteristics. To depict the phenomena of transport, modified versions of both Fick's and Fourier's laws are used. Additionally, the characteristics of both heterogeneous and homogeneous chemical reactions are also incorporated. Utilizing a curvilinear coordinate system, the flow problem is formulated as partial differential equations(PDEs)for momentum, concentration, microorganism field, and energy. An analytical solution to the obtained flow equations is achieved utilizing the homotopy analysis method(HAM).The effects of significant flow parameters on the pressure and microorganism fields, velocity, oscillation velocity, concentration, and temperature distributions are shown via graphs. Furthermore, the variations in skin friction, mass transfer rate, heat transfer rate, and local motile number due to different involved parameters are presented in tables and are analyzed in detail. Graphical results indicate that the curves of velocity and temperature fields are enhanced as the values of the solid volume fraction variables *** is also verified that the concentration rate field decreases as the values of the homogeneous reaction strength parameter and the radius of curvature parameter increase, and it increases with the Schmidt number and the heterogeneous reaction strength *** outcomes show a favorable response of the motile number to advanced values of the Peclet number, the Schmidt number, the microorganism difference parameter, and the bio-convective Lewis number.

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A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems

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Numerical mathematics(Theory,Methods and Applications) 2022年第4期15卷 1173-1192页

作者： Martin Stynes applied and computational mathematics division Beijing Computational Science Research CenterBeijing 100193China

A survey is given of convergence results that have been proved when the L1 scheme is used to approximate the Caputo time derivative D_(t)^(α)(where 0<α<1)in initial-boundary value problems governed by D_(t)^(α)u−△u=f and similar equations,while taking into account the weak singularity that is present in typical solutions of such *** aspects of these analyses are outlined,such as global and local convergence bounds and the techniques used to derive them,fast implementation of the L1 scheme,semilinear problems,multi-term time derivatives,α-robustness,a posteriori error analysis,and two modified L1 schemes that achieve better *** fifty references are provided in the bibliography,more than half of which are from the period 2019-2022.

关键词： L1 scheme fractional derivative survey

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Modelling of spall damage in ductile materials and its application to the simulation of the plate impact on copper

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Chinese Physics B 2012年第9期21卷 378-384页

作者：张凤国周洪强胡军邵建立张广财洪滔何斌 Institute of applied Physics and computational mathematics

A statistical model of dynamic spall damage due to void nucleation and growth is proposed for ductile materials under intense loading, which takes into account inertia, the elastic-plastic effect, and initial void size. To some extent, void interaction could be accounted for in this approach. Based on this model, the simulation of spall experiments for copper is performed by using the Lagrangian finite element method. The simulation results are in good agreement with experimental data for the free surface velocity profile, stress record behind copper target, final porosity, and void concentrations across the target. The influence of elastic-plastic effect upon the damage evolution is explored. The correlation between the damage evolution and the history of the stress near the spall plane is also analyzed.

关键词： spall damage ductile materials free surface velocity plate impact

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Coherent spectroscopy of a strongly driven triple quantum dot molecule

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Chinese Physics B 2010年第11期19卷 576-583页

作者：解研段素青楚卫东杨宁 Institute of applied Physics and computational mathematics

Based on a calculation model, we study the interference phenomena of serially coupled ∨-type and ∧-type triple quantum dots （CTQDs） driven simultaneously by a strong driving field and a weak probe field. Strongly depending on the configuration of the three-level CTQD, the probe absorption spectra, which are shown in the tunneling current, exhibit various quantum coherence properties. In the case where the two pairs of transitions of the CTQD have a small eigenfrequency difference △ω, the double-coupling effect of the driving field results in two Autler Townes doublets and one weak Mollow triplet in one spectrum. With the value of △ω increasing, only one Autler-Townes splitting remains due to the single-coupling of the field. We also find that the effect of spontaneous emission of phonons may lead to an obvious background current, which can be used to distinguish which transition is driven by the driving field in experiment. The interesting quantum property of a CTQD revealed in our results suggests its potential applications in quantum modulators and quantum logic devices.

关键词： coherent spectroscopy coupled quantum dots quantum transport photon assistance

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Transport diffuse interface model for simulation of solid-fluid interaction

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applied mathematics and Mechanics(English Edition) 2019年第3期40卷 321-330页

作者： Li LI Qian CHEN Baolin TIAN Institute of applied Physics and computational mathematics

For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phasedensity equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves,such as shear waves in fluids, are introduced by the artificial treatment. In this paper,a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.

关键词： solid-fluid interaction diffuse interface model phase-density equation Mie-Gruneisen equation of state(EOS) Eulerian method

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Numerical simulations of instabilities in the implosion process of inertial confined fusion in 2D cylindrical coordinates

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Science China(Physics,Mechanics & Astronomy) 2016年第1期59卷 75-85页

作者： Heng Yong ChuanLei Zhai Song Jiang Peng Song ZhenSheng Dai JianFa Gu Institute of applied Physics and computational mathematics

In this paper, we introduce a multi-material arbitrary Lagrangian and Eulerian method for the hydrodynamic radiative multi-group diffusion model in 2D cylindrical coordinates. The basic idea in the construction of the method is the following： In the Lagrangian step, a closure model of radiation-hydrodynamics is used to give the states of equations for materials in mixed cells. In the mesh rezoning step, we couple the rezoning principle with the Lagrangian interface tracking method and an Eulerian interface capturing scheme to compute interfaces sharply according to their deformation and to keep cells in good geometric quality. In the interface reconstruction step, a dual-material Moment-of-Fluid method is introduced to obtain the unique interface in mixed ceils. In the remapping step, a conservative remapping algorithm of conserved quantities is presented. A munber of numerical tests are carried out and the numerical results show that the new method can simulate instabilities in complex fluid field under large deformation, and are accurate and robust.

关键词： material interfaces Rayleigh-Taylor instability Richtmyer-Meshkov instability arbitrary Lagrangian and Eulerian frame-work Moment-of-Fluid method

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Mechanical, electronic, and thermodynamic properties of zirconium carbide from first-principles calculations

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Chinese Physics B 2015年第11期24卷 352-357页

作者：杨晓勇鲁勇郑法伟张平 Institute of applied Physics and computational mathematics

Mechanical, electronic, and thermodynamic properties of zirconium carbide have been systematically studied using the ab initio calculations. The calculated equilibrium lattice parameter, bulk modulus, and elastic constants are all well consistent with the experimental data. The electronic band structure indicates that the mixture of C 2p and Zr 4d and 4p orbitals around the Fermi level makes a large covalent contribution to the chemical bonds between the C and Zr atoms. The Bader charge analysis suggests that there are about 1.71 electrons transferred from each Zr atom to its nearest C atom. Therefore, the Zr-C bond displays a mixed ionic/covalent character. The calculated phonon dispersions of ZrC are stable, coinciding with the experimental measurement. A drastic expansion in the volume of ZrC is seen with increasing temperature, while the bulk modulus decreases linearly. Based on the calculated phonon dispersion curves and within the quasi-harmonic approximation, the temperature dependence of the heat capacities is obtained, which gives a good description compared with the available experimental data.

关键词： first-principles calculations mechanical properties electronic properties thermodynamic properties

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Global sensitivity analysis based on high-dimensional sparse surrogate construction

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applied mathematics and Mechanics(English Edition) 2017年第6期38卷 797-814页

作者： Jun HU Shudao ZHANG Institute of applied Physics and computational mathematics

Surrogate models are usually used to perform global sensitivity analysis （GSA） by avoiding a large ensemble of deterministic simulations of the Monte Carlo method to provide a reliable estimate of GSA indices. However, most surrogate models such as polynomial chaos （PC） expansions suffer from the curse of dimensionality due to the high-dimensional input space. Thus, sparse surrogate models have been proposed to alleviate the curse of dimensionality. In this paper, three techniques of sparse reconstruc- tion are used to construct sparse PC expansions that are easily applicable to computing variance-based sensitivity indices （Sobol indices）. These are orthogonal matching pursuit （OMP）, spectral projected gradient for L1 minimization （SPGL1）, and Bayesian compressive sensing with Laplace priors. By computing Sobol indices for several benchmark response models including the Sobol function, the Morris function, and the Sod shock tube problem, effective implementations of high-dimensional sparse surrogate construction are exhibited for GSA.

关键词： global sensitivity analysis (GSA) curse of dimensionality sparse surrogate construction polynomial chaos (PC) compressive sensing

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First-principles local density approximation (LDA) + U and generalized gradient approximation(GGA) + U studies of plutonium oxides

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Chinese Physics B 2008年第4期17卷 1364-1370页

作者：孙博张平 Institute of applied Physics and computational mathematics

The electronic structures and properties of PuO2 and Pu2O3 have been studied according to the first principles by using the all-electron projector-augmented-wave （PAW） method. The local density approximation （LDA）＋U and the generalized gradient approximation （GGA）＋U formalisms have been used to account for the strong on-site Coulomb repulsion among the localized Pu 5f electrons. We discuss how the properties of PuO2 and Pu2O3 are affected by choosing the values of U and exchange-correlation potential. Also, the oxidation reaction of Pu2O3, leading to the formation of PuO2, and its dependence on U and exchange-correlation potential have been studied. Our results show that by choosing an appropriate U it is possible to consistently describe structural, electronic, and thermodynamic properties of PuO2 and Pu2O3, which enable the modelling of the redox process involving Pu-based materials.

关键词： the first-principles calculation LDA + U GGA + U plutonium oxides

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Monte Carlo simulation for bremsstrahlung and photoneutron yields in high-energy x-ray radiography

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Chinese Physics B 2010年第6期19卷 213-220页

作者：许海波彭现科陈朝斌 Institute of applied Physics and computational mathematics

This paper reports on the results of calculations using a Monte Carlo code （MCNP5） to study the properties of photons, electrons and photoneutrons obtained in the converted target and their transportations in x-ray radiography. A comparison between measurements and calculations for bremsstrahlung and photoneutrons is presented. The radiographic rule and the effect of the collimator on the image are studied with the experimental model. The results provide exact parameters for the optimal design of radiographic layout and shielding systems.

关键词： x-ray radiography bremsstrahlung photoneutron energy spectrum angular distribution

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