Asymptotic Expansions and Extrapolations of $H^1$-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation

In this paper, a high-accuracy $H^1$-Galerkin mixed finite element method (MFEM) for strongly damped wave equation is studied by linear triangular finite element. By constructing a suitable extrapolation scheme, the convergence rates can be improved from $\mathcal{O}(h)$ to $\mathcal{O}(h^3)$ both for the original variable $u$ in $H^1(Ω)$ norm and for the actual stress variable $\boldsymbol{P}=∇u_t$ in $H$(div;$Ω$) norm, respectively. Finally, numerical results are presented to confirm the validity of the theoretical analysis and excellent performance of the proposed method.     

Finite Element $θ$-Schemes for the Acoustic Wave Equation

In this paper, we investigate the stability and convergence of a family of implicit finite difference schemes in time and Galerkin finite element methods in space for the numerical solution of the acoustic wave equation. The schemes cover the classical explicit second-order leapfrog scheme and the fourth-order accurate scheme in time obtained by the modified equation method. We derive general stability conditions for the family of implicit schemes covering some well-known CFL conditions. Optimal error estimates are obtained. For sufficiently smooth solutions, we demonstrate that the maximal error in the $L^2$-norm error over a finite time interval converges optimally as $\mathcal{O}(h^{p+1}+∆t^s)$, where $p$ denotes the polynomial degree, $s$=2 or 4, $h$ the mesh size, and $∆t$ the time step.     

Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

In this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal$\mathcal{O}(h^3)$ convergence rate in $H^1$ norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.     

A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems

In this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent order $\mathcal{O}(h^2+k^2)$ is obtained for the numerical solution in a discrete $L^2$-norm. A numerical experiment is presented to test the theoretical result.     

Implicit DG Method for Time Domain Maxwell's Equations Involving Metamaterials

An implicit discontinuous Galerkin method is introduced to solve the time-domain Maxwell's equations in metamaterials. The Maxwell's equations in metamaterials are represented by integral-differential equations. Our scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal domain. The fully discrete numerical scheme is proved to be unconditionally stable. When polynomial of degree at most $p$ is used for spatial approximation, our scheme is verified to converge at a rate of $\mathcal{O}(τ^2+h^{p+1/2})$. Numerical results in both 2D and 3D are provided to validate our theoretical prediction.     

一维准周期晶格中玻色子对的迁移率边

研究了一维非公度的准周期晶格中的玻色子对的迁移率边.通过微扰方法,解析推导出强相互作用极限下准周期晶格中玻色子对迁移率边的解析表达式,通过数值证明在系统参数b较小时,迁移率边的解析结果符合得较好,而当b→1时,解析结果将发生偏离.     

Negative refraction in ferromagnetic materials under external magnetic field: a theoretical analysis

We present a detailed theoretical analysis on the possibilities and conditions for negative permeability and negative refraction occuring in the magnetic materials with both pronounced magnetic and dielectric responses to electromagnetic waves. The results indicate that the permeability is always positive for $\de=(2q+0.5)\pi$ ($\de$ is the initial phase difference of magnetic components $h_{x}$ and $h_{y }$ of incident electromagnetic wave, $q$ is integer), which means that it is difficult to realize negative refraction. However, for $\de=2q\pi, \de=(2q+1)\pi$, or $\de=(2q-0.5)\pi$, the negative permeability occurs at some range of free procession frequency, which means that the refraction can become negative under certain conditions. Further analysis reveals that for general positive permittivity there are various opportunities for realizing the negative refraction provided that some requirements are met. One concludes also that the refractive index for $\de=2q\pi$ case is similar to $\de=(2q+1)\pi$. The only difference between two cases of $\de=2q\pi$ and $\de=(2q+1)\pi$ is that the $x$-direction for $\de=2q\pi$ corresponds to the $y$-direction for $\de=(2q+1)\pi$, and the $y$-direction for $\de=2q\pi$ corresponds to the $x$-direction for $\de=(2q+1)\pi$. The results are valuable for designing and analysing the complex negative refraction of magnetic materials.     

Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods

In this paper, we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods. We mainly concern the case when pressure coefficients and source terms are nonlinear. To linearize the nonlinear mixed equations, we use the two-grid algorithm. We first solve the nonlinear equations on the coarse grid, then, on the fine mesh, we solve a linearized problem using Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy $H =\mathcal{O}(h^{\frac{1}{2}})$. As a result, solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.     

Comparison Between $\chi^2$ and Bayesian Statistics with Considering the Redshift Dependence of Stretch and Color from JLA Data

In this work, we compare the impacts given by $\chi^2$ statistics and Bayesian statistics. Bayesian statistics is a new statistical method proposed by [C. Ma, P. S. Corasaniti, and B. A. Bassett, arXiv:1603.08519[astro-ph.CO](2016)] recently, which gives a fully account for the standard-candle parameter dependence of the data covariance matrix. For this two statistical methods, we explore the possible redshift-dependence of stretch-luminosity parameter $\alpha$ and color-luminosity parameter $\beta$ by using redshift tomography. By constraining the $\Lambda$CDM model, we check the consistency of cosmology-fit results given by the SN sample of each redshift bin. We also adopt the linear parametrization to explore the possible evolution of $\alpha$ and $\beta$ and the deceleration parameter $q(z)$ for CPL, JBP, BA and Wang models. We find that: (i) Using the full JLA data, at high redshift $\alpha$ has a trend of decreasing at more than $1.5\sigma$ confidence level (CL), and $\beta$ has a significant trend of decreasing at more than $19\sigma$ CL. (ii) Compared with $\chi^2$ statistics (constant $\alpha$, $\beta$) and Bayesian statistics (constant $\alpha$, $\beta$), Bayesian statistics (linear $\alpha$ and $\beta$) yields a larger best-fit value of fractional matter density $\Omega_{m0}$ from JLA+CMB+GC data, which is much closer to slightly deviates from the best-fit result given by other cosmological observations. (iii) The figure of merit (FoM) given by JLA+CMB+GC data from Bayesian statistics is also larger than the FoM from $\chi^2$ statistics, which indicates that former statistics has a better accuracy. (iv) $q(z)$ given by both statistical methods favor an eternal cosmic acceleration at 1$\sigma$ CL.     

Multi-Symplectic Method for the Zakharov-Kuznetsov Equation

A new scheme for the Zakharov-Kuznetsov (ZK) equation with the accuracy order of $\mathcal{O}(∆t^2+∆x+∆y^2)$ is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new multi-symplectic scheme is also implemented. The solitary wave evolution behaviors of the Zakharov-Kunetsov equation are investigated by the new multi-symplectic scheme. The accuracy of the scheme is analyzed.     

Critical Number of Fermion Flavors at Finite Chemical Potential in QED3

We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dressed fermion propagator at finite chemical potential # has the form S（p） = iγ.p^-A（p^-2） ＋ B（ p^-2） with p^-μ= （p^-1p3 ＋ iμ）. Using this form of fermion propagator at nonzero chemical potential, we investigate the Dyson-Schwinger equation for the dressed fermion propagator at finite chemical potential and study the effects of the chemical potential on the critical number of the fermion flavors.     

Theory of nine elastic constants of biaxial nematics

In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average （Dmn^（l）） （Dm＇n＇^（l＇））, where Dmn^（l） is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ＇, λ, order parameters Q0 = Q0（D00^（2）） ＋Q2（D02^（2）＋D0-2^（2）） and Q2 = Q0（D20^（2）） ＋ Q2（D22^（2）＋D2-2^（2））. Here Γ and Γ＇ depend on the function form of molecular interaction energy vj′j″j （τ12） and probability function fk′k″k （τ12）, where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33.     

Thermal and mechanical characterizations of asubstrate-free focal plane array

We propose a substrate-free focal plane array (FPA) in this paper. The solid substrate is completely removed, and the microcantilevers extend from a supporting frame. Using finite element analysis, the thermal and mechanical characterizations of the substrate-free FPA are presented. Because of the large decrease in thermal conductance, the supporting frame is temperature dependent, which brings out a unique feature: the lower the thermal conductance of the supporting frame is, the higher the energy conversion efficiency in the substrate-free FPA will be. The results from the finite element analyses are consistent with our measurements: two types of substrate-free FPAs with pixel sizes of 200× 200 and 60× 60~μ m² are implemented in the proposed infrared detector. The noise equivalent temperature difference (NETD) values are experimentally measured to be 520 and 300~mK respectively. Further refinements are considered in various aspects, and the substrate-free FPA with a pixel size of 30× 30~μ m² has a potential of achieving an NETD value of 10~mK.     

Orthogonal-triangular decomposition ghost imaging

Ghost imaging (GI) offers great potential with respect to conventional imaging techniques. However, there are still some obstacles for reconstructing images with high quality, especially in the case that the orthogonal measurement matrix is impossible to construct. In this paper, we propose a new scheme based on the orthogonal-triangular (QR) decomposition, named QR decomposition ghost imaging (QRGI) to reconstruct a better image with good quality. In the scheme, we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases. (1) When the random measurement matrix is square, it can be firstly decomposed into an orthogonal matrix $\bm Q$ and an upper triangular matrix $\bm R$. Then let the off-diagonal values of $\bm R$ equal to 0.0, the diagonal elements of $\bm R$ equal to a constant $k$, where $k$ is the average of all values of the main diagonal, so the resulting measurement matrix can be obtained. (2) When the random measurement matrix is with full rank, we firstly compute its transpose, and followed with above QR operation. Finally, the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values. Both experimental and simulation results verify the feasibility of the proposed QRGI scheme. Moreover, the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI (TGI) and differential GI (DGI). Besides, in comparison with the singular value decomposition ghost imaging (SVDGI), the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI, while the computing time (the time consuming on the light patterns computation) is substantially shortened.     

Collective Dand Structures in Doubly Odd 136La Nucleus

Using heavy-ion nuclear reaction and in-beam γ-ray spectroscopy technique,high spin states of ¹³⁶La have been studied. The nuclear reaction used is ¹³⁰Te(¹¹B,5n) with a beam energy 60MeV. The level scheme with three collective band structures has been updated with spin up to 20h. The collective backbending has been observed in $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band. According to the TRS calculations,this backbending is due to the alignment of a pair of h_11/2 neutrons. The signature splitting and inversion for the $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band were also discussed. Other two bands based on $12^-$ and $16^+$ levels were proposed as oblate deformation with $\gamma\approx -60^\circ$. They most probably originate from four- and six- quasiparticle configurations, that is,$\uppi h_{11/2}\otimes\upnu g_{7/2} h_{11/2}^2$ and $\uppi g_{7/2}\otimes\upnu g_{7/2}^2 d_{5/2}h_{11/2}^2$ respectively.     

Dynamic scaling of migration-driven aggregate growth

We study the kinetic behaviour of the growth of aggregates driven by reversible migration between any two aggregates. For a simple model with the migration rate K(i;j)=K′(i;j)∝i^uj^v at which the monomers migrate from the aggregates of size i to those of size j, we find that the aggregate size distribution in the system with u+v≤3 and u<2 approaches a conventional scaling form, which reduces to the Smoluchovski form in the u=1 case. On the other hand, for the system with u<2, the average aggregate size S(t) grows exponentially in the u+v=3 case and as (tlnt)^{1/(5-2u)} in another special case of v=u-2. Moreover, this typical size S(t) grows as t^{1/(3-u-v)} in the general u-2相似文献   

激光冷却SH~–阴离子的理论研究

本文采用多组态相互作用及Davidson修正方法和全电子基组计算了SH~-阴离子的X~1∑~+,a~3∏和A~1∏态的势能曲线、电偶极矩和跃迁偶极矩.计算的光谱常数与实验值及已有的理论值符合得很好.在计算中考虑了自旋-轨道耦合效应.计算得到a~3∏_1(v'=0)?X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)?X~1Σ_(0+)~+(v"=0)跃迁具有高对角分布的弗兰克-康登因子,分别为0.9990和0.9999;计算得到a~3∏_1和A~1∏_1态的自发辐射寿命分别为1.472和0.188 ms.A~1∏_1?X~1∑_(0+)~+跃迁存在中间态a~3∏_(0+)和a~3∏_1,但中间态对激光冷却SH~-阴离子的影响可以忽略.分别利用a~3∏_1(v'=0)? X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)? X~1∑_(0+)~+(v"=0)跃迁构建了准闭合的能级系统,冷却所需的激光波长分别为492.27和478.57 nm.最后预测了激光冷却SH~-阴离子能达到的多普勒温度和反冲温度.这些结果为进一步实验提供了理论参数.     

Cluster-state preparation in thermal cavities without single-qubit operation

A potential scheme is proposed for generating cluster states of many atoms in cavity quantum electradynamics （QED）, in which an unorthodox encoding is employed with the ground state being qubit [0〉 while two closely spaced upper states being qubit ｜1〉. Throughout the scheme the cavities can be in thermal states but axe only virtually excited. We show how to create the cluster states by performing a two-step hut no single-qubit operation. Discussion is also carried out on the experimental feasibility of our scheme.     

Cluster-state preparation in thermal cavities without single-qubit operation

A potential scheme is proposed for generating cluster states of many atoms in cavity quantum electradynamics (QED), in which an unorthodox encoding is employed with the ground state being qubit $\left\vert 0\right\rangle $ while two closely spaced upper states being qubit $\left\vert 1\right\rangle $. Throughout the scheme the cavities can be in thermal states but are only virtually excited. We show how to create the cluster states by performing a two-step but no single-qubit operation. Discussion is also carried out on the experimental feasibility of our scheme.