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Conditions for formation and trapping of the two-ion Coulomb cluster in the dissipative optical superlattice

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Chinese Physics B 2015年第6期24卷 305-313页

作者： I.V.Krasnov Institute of computational Modeling Siberian DivisionRussian Academy of Sciences

Conditions have been studied under which a polychromatic optical superlattice can form and trap the Coulomb cluster of two strongly interacting ions. In our previous work （Krasnov I V and Kamenshchikov L P 2014 Opt. Comm. 312 192） this new all-optical method of obtaining and confining the Coulomb clusters was demonstrated by numerical simulations for special values of the optical superlattice parameters and in the case of Yb ions. In the present paper the conditions are explicitly formulated, under which the long-lived two-ion cluster in the superlattice cell is formed. The peculiarity of these conditions is the renormalization of the ion-ion Coulomb interaction. Notably, the renormalized Coulomb force is determined by the effective charge which depends on the light field parameters and can strongly differ from the ＂bare＂ ion charge. This result can be accounted for by the combined manifestation of the quantum fluctuations of optical forces, nonlinear dependence of these forces on the velocity, and non-Maxwellian （Tsallis type） velocity distribution of the ions in the optical superlattice. Explicit analytical formulas are also obtained for the parameters of the optical two-ion cluster.

关键词： optical trap ion trap rectified gradient force Coulomb clusters

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

A WEAK GALERKIN MIXED FINITE ELEMENT METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

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Journal of computational Mathematics 2016年第5期34卷 532-548页

作者： Qian Zhang Ran Zhang Department of Mathematics Jilin University Changchun China Applied and computational Mathematics division Beijing Computational Science Research Center Beijing China

In this paper, we present a weak Galerkin （WG） mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the L^2 for the flux and H1 for the scalar function. Also an optimal order error estimate in L^2 is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.

关键词： Second-order elliptic equations Robin boundary conditions Weak Galerkin,Weak divergence.

A combination of damage locating vector method （DLV） and differential evolution algorithm （DE） for structural damage assessment

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Frontiers of Structural and Civil Engineering 2018年第1期12卷 92-108页

作者： T. NGUYEN-THOI A. TRAN-VIET N. NGUYEN-MINH T. VO-DUY V. HO-HUU division of computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Hochiminh City Vietnam division of Construction Computation Institute for Computational Science Ton Duc Thang University Hochiminh City Vietnam Faculty of Civil Engineering Ton Duc Thang University Hochiminh City Vietnam

In this study, a two-stage method is presented for identifying multiple damage scenarios. In the first stage, the damage locating vector （DLV） method using normalized cumulative energy （nce） is employed for damage localization in structures. In the second stage, the differential evolution algorithm （DE） is used for damage severity of the structures. In addition, in the second stage, a modification of an available objective function is made for handing the issue of symmetric structures. To verify the effectiveness of the present technique, numerical examples of a 72-bar space truss and a one-span steel portal frame are considered. In addition, the effect of noise on the performance of the identification results is also investigated. The numerical results show that the proposed combination gives good assessment of damage location and extent for multiple structural damage cases.

关键词： damage assessment damage locating vector method (DLV) differential evolution (DE) multiple damagelocation assurance criterion (MDLAC) mode shape error function

Damage assessment of laminated composite beam structures using damage locating vector （DLV） method

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Frontiers of Structural and Civil Engineering 2015年第4期9卷 457-465页

作者： T. VO-DUY division of computational Mathematics and Engineering (CME) Institute for Computational Science (INCOS) Ton Duc ThangUniversity Hochiminh City Vietnam division of Construction Computation (DCC) Institute for Computational Science (INCOS) Ton Duc Thang University HochiminhCity vietnam Faculty of Civil Engineering Ton Duc Thang University Hochiminh City Vietnam

In this paper, the damage locating vector (DLV) method using normalized cumulative energy (nce) is employed to locate multiple damage sites in laminated composite beam structures. Numerical simulations of two laminated composite beams are employed to investigate several damage scenarios in which the degradation of elements is modeled by the reduction in the longitudinal Young’s modulus and transverse Young’s modulus of beam layers. The results show that the DLV method gives good performance for this kind of structure.

关键词： damage locating vector method (DLV) laminated composite beam structure normalized cumulative energy structural health monitoring (SHM)

PRESSURE-VELOCITY EQUILIBRIUM HYDRODYNAMIC MODELS

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Acta Mathematica Scientia 2010年第2期30卷 563-594页

作者： John W.Grove computational Physics Group Computer Computationaland Statistical Sciences DivisionCCS-2 MS D413Los Alamos National Laboratory

This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive model... 详细信息

关键词： Euler equations multiple phase mixtures non-equilibrium temperature mixtures

Thermo-field Dynamics of the Casimir Effect and Its Quantum Deformation

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Chinese Physics Letters 2001年第6期18卷 740-742页

作者： JING Hui XIE Bing-Hao CHEN Jing-Ling Theoretical Physics division Nankai Institute of MathematicsNankai UniversityTianjin 300071 Laboratory of computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088

The Casimir effect of the deformed cavity field at finite temperature is investigated by generalizing the thermo field dynamics formalism into q-deformed *** has been shown that the impact of q-deformation on the Casimir force only manifests in the finite temperature case and the expression for the ideal pure vacuum remains unchanged,which just coincides with the suggestions of Man’ko et al.[***.A 176(1993)173]about the nature of q-oscillators as the nonlinear vibrations of electromagnetic field.

关键词： field deformed Casimir

Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions

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Applied Mathematics and Mechanics(English Edition) 2008年第3期29卷 311-331页

作者：徐承龙郭本瑜 Department of Mathematics Tongji University division of computational Science of E-institute of Shanghai Universities

The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.

关键词： modified Laguerre orthogonal approximation and interpolation multiple dimensions spectral and pseudospectral methods nonlinear partial differential equations

Simulation of buoyancy-induced turbulent flow from a hot horizontal jet

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Journal of Hydrodynamics 2014年第1期26卷 104-113页

作者： El-AMIN M.F. SUN Shuyu SALAM Amgad computational Transport Phenomena Laboratory (CTPL) Division of Physical Sciences and EngineeringKing Abdullah University of Science and Technology

Experimental visualizations and numerical simulations of a horizontal hot water jet entering cold water into a rectangular storage tank are described. Three different temperature differences and their corresponding Reynolds numbers are considered. Both experimental visualization and numerical computations are carried out for the same flow and thermal conditions. The realizable k-e model is used for modeling the turbulent flow while the buoyancy is modeled using the Boussinesq approximation. Polynomial approximations of the water properties are used to compare with the Boussinesq approximation. Numerical solutions are obtained for unsteady flow while pressure, velocity, temperature and turbulence distributions inside the water tank as well as the Froude number are analyzed. The experimental visualizations are performed at intervals of five seconds for all different cases. The simulated results are compared with the visualized results, and both of them show the stratification phenomena and buoyancy force effects due to temperature difference and density variation. After certain times, depending on the case condition, the flow tends to reach a steady state.

关键词： turbulent flow realizablc k - e turbulence model heat transfer jet heat storage