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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

A hybrid subcell-remapping algorithm for staggered multi-material arbitrary Lagrangian-Eulerian methods

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applied mathematics and Mechanics(English Edition) 2019年第10期40卷 1487-1508页

作者： Haihua YANG Ping ZHANG institute of applied Physics and Computational mathematics

A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.

关键词： multi-material arbitrary Lagrangian-Eulerian (MMALE) subcell remapping method hybrid remapping method

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

REMARKS ON THE CONTRIBUTIONS OF CONSTANTINE *** TO THE SUBJECT OF CONSERVATION LAWS

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Acta Mathematica Scientia 2012年第1期32卷 3-14页

作者： Athanasios E.Tzavaras Department of applied mathematics University of Crete and Institute for Applied and Computational Mathematics

Constantine M. Dafermos has done extensive research at the interface of partial differential equations and continuum physics. He is a world leader in nonlinear hyperbolic conservation laws, where he introduced several fundamental methods in the subject including the methods of relative entropy, generalized characteristics, and wave-front tracking, as well as the entropy rate criterion for the selection of admissible wave fans. He has also made fundamental contributions on the mathematical theory of the equations of thermomechanics as it pertains in modeling and analysis of materials with memory, thermoelasticity, and thermoviscoelasticity. His work is distinctly characterized by an understanding of the fundamental issues of continuum physics and their role in developing new techniques of mathematical analysis.

关键词： REMARKS ON THE CONTRIBUTIONS OF CONSTANTINE M.DAFERMOS TO THE SUBJECT OF CONSERVATION LAWS

Analytic solutions to a finite width strip with a single edge crack of two-dimensional quasicrystals

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Chinese Physics B 2011年第11期20卷 404-408页

作者：李梧 institute of applied mathematics Xuchang University

In this paper, we investigate the well-known problem of a finite width strip with a single edge crack, which is useful in basic engineering and material science. By extending the configuration to a two-dimensional decagonal quasicrystal, we obtain the analytic solutions of modesⅠand Ⅱ using the transcendental function conformal mapping technique. Our calculation results provide an accurate estimate of the stress intensity factors K_Ⅰ and K_Ⅱ, which can be expressed in a quite simple form and are essential in the fracture theory of quasicrystals. Meanwhile, we suggest a generalized cohesive force model for the configuration to a two-dimensional decagonal quasicrystal. The results may provide theoretical guidance for the fracture theory of two-dimensional decagonal quasicrystals.

关键词： transcendental function conformal mapping quasicrystal stress intensity factor

Optical nuclear spin polarization in quantum dots

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Chinese Physics B 2016年第10期25卷 535-539页

作者：李爱仙段素青张伟 institute of applied Physics and Computational mathematics

Hyperfine interaction between electron spin and randomly oriented nuclear spins is a key issue of electron coherence for quantum information/computation. We propose an efficient way to establish high polarization of nuclear spins and reduce the intrinsic nuclear spin fluctuations. Here, we polarize the nuclear spins in semiconductor quantum dot(QD) by the coherent population trapping(CPT) and the electric dipole spin resonance(EDSR) induced by optical fields and ac electric fields. By tuning the optical fields, we can obtain a powerful cooling background based on CPT for nuclear spin polarization. The EDSR can enhance the spin flip–flop rate which may increase the cooling efficiency. With the help of CPT and EDSR, an enhancement of 1300 times of the electron coherence time can be obtained after a 10-ns preparation time.

关键词： nuclear spin polarization coherent population trapping electron dipole spin resonance

Molecular dynamics simulations of jet breakup and ejecta production from a grooved Cu surface under shock loading

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Chinese Physics B 2014年第4期23卷 504-507页

作者：何安民王裴邵建立段素青 institute of applied Physics and Computational mathematics

Large-scale non-equilibrium molecular dynamics simulations are performed to explore the jet breakup and ejecta production of single crystal Cu with a triangular grooved surface defect under shock loading. The morphology of the jet breakup and ejecta formation is obtained where the ejecta clusters remain spherical after a long simulation time. The effects of shock strength as well as groove size on the steady size distribution of ejecta clusters are investigated. It is shown that the size distribution of ejecta exhibits a scaling power law independent of the simulated shock strengths and groove sizes. This distribution, which has been observed in many fragmentation processes, can be well described by percolation theory.

关键词： molecular dynamics ejection

Uncertainty Quantification of Numerical Simulation of Flows around a Cylinder Using Non-intrusive Polynomial Chaos

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Chinese Physics Letters 2016年第9期33卷 17-21页

作者：王言金张树道 institute of applied Physics and Computational mathematics

The uncertainty quantification of flows around a cylinder is studied by the non-intrusive polynomial chaos method. Based on the validation with benchmark results, discussions are mainly focused on the statistic properties of the peak lift and drag coefficients and base pressure drop over the cylinder with the uncertainties of viscosity coefficient and inflow boundary velocity. As for the numerical results of flows around a cylinder, influence of the inflow boundary velocity uncertainty is larger than that of viscosity. The results indeed demonstrate that a five-order degree of polynomial chaos expansion is enough to represent the solution of flow in this study.

关键词： of in on is it Uncertainty Quantification of Numerical Simulation of Flows around a Cylinder Using Non-intrusive Polynomial Chaos for

Bandgap characteristics analysis and graded design of a novel metamaterial for flexural wave suppression

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applied mathematics and Mechanics(English Edition) 2025年第01期 1-24页

作者： Fan YANG Zhaoyang MA Xingming GUO Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Institute of Applied Mathematics and Mechanics School of Mechanics and Engineering ScienceShanghai University Shanghai institute of Aircraft Mechanics and Control

A novel elastic metamaterial is proposed with the aim of achieving lowfrequency broad bandgaps and bandgap regulation. The band structure of the proposed metamaterial is calculated based on the Floquet-Bloch theorem, and the boundary modes of each bandgap are analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the metamaterials with a low elastic modulus of ligaments can generate flexural wave bandgaps below 300 Hz. Multi-frequency vibrations can be suppressed through the selective manipulation of bandgaps. The dual-graded design of metamaterials that can significantly improve the bandgap width is proposed based on parametric studies. A new way that can regulate the bandgap is revealed by studying the graded elastic modulus in the substrate. The results demonstrate that the nonlinear gradient of the elastic modulus in the substrate offers better bandgap performance. Based on these analyses, the proposed elastic metamaterials can pave the way for multi-frequency vibration control, low-frequency bandgap broadening, and bandgap tuning.

关键词：

Mixedness of the N-qubit states with exchange symmetry

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Chinese Physics B 2008年第10期17卷 3559-3564页

作者：胡明亮惠小强 Department of applied mathematics and applied Physics Xi’an Institute of Posts and Telecommunications

The mixedness of the N-qubit quantum states with exchange symmetry has been studied, and the results show that the linear entropy of the single qubit reduced density matrix （RDM）, which can describe the mixedness, is completely determined by the expectation values 〈Sz〉 and 〈S±〉 for both the pure and the mixed states. The mixedness of the pure states can be used to describe the bipartite entanglement, as an example we have calculated the mixedness of the Dicke state and the spin squeezed Kitagawa-Ueda state. For the mixed states, we determine the mixedness properties of both the ground states and the thermal states in mean-field clusters of spin-1/2 particles interacting via the anisotropy Heisenberg XXZ interaction, and found for the ferromagnetic case （J 〈 0）, the mixedness will approximate to the pairwise entanglement when the anisotropic parameter △ 〉 △c.

关键词： mixedness linear entropy symmetric quantum state