Energy states of colored particle in a chromomagnetic field

The unitary transformation which diagonalizes the squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of the diagonalized Hamiltonian, that describes the states with a definite value of energy, and we call them energy states. It is pointed out that the energy states are determined by the color interaction term of the particle with the background chromofield, and this term is responsible for the splitting of the energy spectrum. We construct supercharge operators for the diagonal Hamiltonian that ensure the superpartner property of the energy states. PACS 03.65.-w An erratum to this article can be found at     

Asymptotics and zeros of the imaginary part of the elastic scattering amplitude

The s-channel unitarity condition for the imaginary part of the hadronic elastic scattering amplitude outside the diffraction peak is studied within different assumptions about the behavior of its real part. The integral equation for the imaginary part is derived with the asymptotical expression for the real part inserted in the unitarity condition. The conclusions about the asymptotical approach to the black disk limit and possible zeros of the imaginary part of the amplitude are obtained. Their relation to the present day experiments is discussed.     

基于线性矩阵不等式的一类新羽翼倍增混沌分析与控制

在对已有的混沌系统分析和研究的基础上,将一个二次混沌系统第三个方程关于x的线性项引入到第二个方程中,通过对该系统第二个等式中的线性项x作绝对值运算,提出了一类新的二次非线性系统.采用非线性动力学方法分析了系统参数变化时所经历的稳定、准周期、混沌的过渡过程,模拟电路实验结果与Matlab数值仿真结果相一致.分析发现混沌态时绝对值运算后的系统比原系统的Lyapunov指数更大,并可将原系统的混沌吸引子由两个翼的拓扑结构变为四翼的拓扑结构,从而实现羽翼倍增.针对该混沌特性更强的羽翼倍增混沌系统,基于Takagi-Sugeno(T-S)模糊模型和线性矩阵不等式(LMI),设计出使该羽翼倍增混沌系统渐近稳定的鲁棒模糊控制器.仿真结果证实了所提出定理和设计控制器的有效性.     

Bad behavior of Godunov mixed methods for strongly anisotropic advection–dispersion equations

We study the performance of Godunov mixed methods, which combine a mixed-hybrid finite element solver and a Godunov-like shock-capturing solver, for the numerical treatment of the advection–dispersion equation with strong anisotropic tensor coefficients. It turns out that a mesh locking phenomenon may cause ill-conditioning and reduce the accuracy of the numerical approximation especially on coarse meshes. This problem may be partially alleviated by substituting the mixed-hybrid finite element solver used in the discretization of the dispersive (diffusive) term with a linear Galerkin finite element solver, which does not display such a strong ill conditioning. To illustrate the different mechanisms that come into play, we investigate the spectral properties of such numerical discretizations when applied to a strongly anisotropic diffusive term on a small regular mesh. A thorough comparison of the stiffness matrix eigenvalues reveals that the accuracy loss of the Godunov mixed method is a structural feature of the mixed-hybrid method. In fact, the varied response of the two methods is due to the different way the smallest and largest eigenvalues of the dispersion (diffusion) tensor influence the diagonal and off-diagonal terms of the final stiffness matrix. One and two dimensional test cases support our findings.     

The phase diagram and hidden order for generalized spin ladders

We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the [Formula: see text] chain with competing nn and nnn interactions, the [Formula: see text] chain with alternating exchange and the antiferromagnetic (AF) S = 1 chain. The Majumdar - Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the AF S = 1 chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar - Ghosh points are in the same phase as the AF S = 1 chain.     

带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊同步控制

针对带有非对称控制增益的不确定分数阶混沌系统的同步问题设计了模糊自适应控制器. 模糊逻辑系统用来逼近未知的非线性函数, 非对称的控制增益矩阵被分解为一个未知的正定矩阵、一个对角线上元素为+1或-1的已知对角矩阵和 一个未知的上三角矩阵的乘积. 基于分数阶Lyapunov稳定性理论构造了模糊控制器以及分数阶的参数自适应律, 在保证所有变量有界的情况下实现驱动系统和响应系统的同步. 在分数阶系统稳定性分析中给出了一种平方Lyapunov函数的使用方法, 根据此方法很多针对整数阶系统的控制方法可以推广到分数阶系统中. 最后数值仿真结果验证了所提控制方法的可行性.     

The solution of the diffusion equation with a sink term using the radiation boundary condition

The diffusion equation with an added sink term describing the energy transfer by a dipole-dipole mechanism was solved under steady state conditions using the radiation boundary condition. An equation for the non-radiative energy transfer rate constant between organic fluorescent molecules was obtained. This general equation contains the particular cases of a total reflecting boundary condition and the so-called Smoluchowski boundary condition already obtained by other authors.     

Dissipation-Managed Bright Soliton in a 1D Bose-Einstein Condensate in an Optical-Lattice Potential

We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross-Pitaevskii equation, trapped in a shallow optical-latticepotential. Based on the direct approach of perturbation theory for the nonlinear Schrödinger equation, we demonstrate that the height (as well as width) of bright soliton may have little change through selecting experimental parameters.     

Analogue of the Cole-Hopf transform for the incompressible Navier–Stokes equations and its application

We consider the Navier–Stokes equations written in the stream function in two dimensions and vector potentials in three dimensions, which are critical dependent variables. On this basis, we introduce an analogue of the Cole-Hopf transform, which exactly reduces the Navier–Stokes equations to the heat equations with a potential term (i.e. the nonlinear Schrödinger equation at imaginary times). The following results are obtained. (i) A regularity criterion immediately obtains as the boundedness of condition for the potential term when the equations are recast in a path-integral form by the Feynman-Kac formula. (ii) This in turn gives an additional characterisation of possible singularities for the Navier–Stokes equations. (iii) Some numerical results for the two-dimensional Navier–Stokes equations are presented to demonstrate how the potential term captures near-singular structures. Finally, we extend this formulation to higher dimensions, where the regularity issues are markedly open.     

基于截断奇异值分解的三维火焰温度场重建研究

利用CCD摄像机得到的火焰辐射能图像进行炉膛三维火焰温度场重建，但温度重建矩阵方程是一个不适定方程组，从而重建问题是一个不适定问题.应用截断奇异值分解(truncated singular value decomposition，TSVD)的正则化方法对该不适定方程组进行求解，并且采用了L曲线法对正则化参数进行选取.结合重建算例，采用奇异值分解(singular value decomposition，SVD)与离散Picard条件对这个不适定问题进行了分析.重建结果表明，在不同的模拟测量误差下，TSVD能够成功得到合理的解，重建温度场较好的再现了原始假设温度场的特征.     

Parametric Analysis of Complex Dispersion Curves for Flexural Lamb Waves in Layered Plates in the Low-Frequency Range

A combined asymptotical and iteration method is used to study dispersion curves for the case of dynamic bending of isotropically layered plates. Based on the explicit limit formulation of dispersion equation, asymptotics of roots are derived in closed form for large values of root moduli. The influence of elastic and geometric parameters of layers are analyzed. The existence of critical values of geometric parameters that correspond to change of the type of asymptotics is demonstrated. The errors of asymptotics are estimated, and an iterative method is proposed for calculating the exact values of roots in statics. A low-frequency long-wave asymptotics of complex dispersion curves is derived; its accuracy is the higher the lower the frequency and the greater the number of the curve are. It is also proved that each complex curve has a long flat segment, the length of which increases simultaneously with the number of curve. The dispersion curves themselves are also calculated by another specific iterative procedure. The fundamental bending mode is analyzed together with its purely imaginary sister. The existence of the additional purely imaginary curve at low frequency is proved. Examples of calculating the static roots and the dispersion curves for subcritical and supercritical values of geometrical parameters are presented, and the efficiency of the algorithm is estimated.     

Tensor coupling effect on relativistic symmetries

The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.     

Theoretical investigations of the optical properties of SrS

A computation of the band structure of SrS is performed self-consistently by the method of linear associated plane waves within the framework of the electron density functional. On the basis of the states density obtained, computations are made of the imaginary part of the dielectric permittivity function in a constant matrix element approximation and with its exact value taken into account. The strong energy dependence of the matrix element and the necessity to take it into account in computations of the optical characteristics of dielectrics are shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 79–81, March, 1990.     

Extended State to Localization in Random Aperiodic Chains

The electronic states in Thus-Morse chain （TMC） and generalized Fibonacci chain （GFC） are studied by solving eigenequation and using transfer matrix method. Two model Hamiltonians are studied. One contains the nearest neighbor （n.n.） hopping terms only and the other has additionally next nearest neighbor （n.n.n.） hopping terms. Based on the transfer matrix method, a criterion of transition from the extended to the localized states is suggested for CFC and TMC. The numerical calculation shows the existence of both extended and localized states in pure aperiodic system. A random potential is introduced to the diagonal term of the Hamiltonian and then the extended states are always changed to be localized. The exponents related to the localization length as a function of randomness are calculated. For different kinds of aperiodic chain, the critical value of randomness for the transition from extended to the localized states are found to be zero, consistent with the case of ordinary one-dimensional systems.     

Particle-two-particle interaction in configuration space

The problem of three identical particles with zero-range two-particle interaction is considered. An explicit expression for the effective potential between one particle and the remaining two-particle system is obtained in the coordinate representation. It is shown that for arbitrary energies, at small and, for zero energy, at large distances ρ between the one particle and centre of mass of the other two particles the diagonal matrix element of the effective potential is attractive and proportional to 1/ρ². This property of the effective potential explains both the Thomas singularity and the Efimov effect. In the case of zero total energy of the system the general form of the solution of the three-particle integral equation is found in configuration space.     

Extended State to Localization in Random Aperiodic Chains

The electronic states in Thus-Morse chain (TMC) and generalized Fibonacci chain (GFC) are studied by solving eigenequation and using transfer matrix method. Two model Hamiltonians are studied. One contains the nearest neighbor (n.n.) hopping terms only and the other has additionally next nearest neighbor (n.n.n.) hopping terms. Based on the transfer matrix method, a criterion of transition from the extended to the localized states is suggested for GFC and TMC. The numerical calculation shows the existence of both extended and localized states in pure aperiodic system. A random potential is introduced to the diagonal term of the Hamiltonian and then the extended states are always changed to be localized. The exponents related to the localization length as a function of randomness are calculated. For different kinds of aperiodic chain, the critical value of randomness for the transition from extended to the localized states are found to be zero, consistent with the case of ordinary one-dimensional systems.     

On the structure of the nucleon optical potential

The structure of the nucleon generalized optical potential (GOP) is investigated in the framework of Green's function (GF) theory. First an exact relation between its imaginary part and the total reaction cross section is derived. In the second part the GOP is decomposed using a kind of projection formalism which enables to couple in the continuum in successive steps. This is achieved by splitting up the one particle GF into a discrete and a continuous part and by summing up all contributions to the GOP containing a given numbern0 continuum propagators. Three expressions are extracted corresponding to different processes involving the scattering of at most two particles in the continuum in intermediate states. The remaining terms are argued to be small. Further support for retaining only the above three terms is given by evaluating the diagonal element of their imaginary part between the exact eigenstates of the GOP. This is shown to be approximately proportional to the sum of the total inelastic, charge exchange, pick-up and knockout cross sections. The corresponding matrix element of the exact potential is proportional to the total reaction cross section.     

Transverse magneto-optical Kerr effect of Fe at the 2p excitation threshold

The transverse magneto-optical Kerr effect (T-MOKE) was investigated for thin epitaxial Fe films grown on Ag(0 0 1) in the region of the 2p excitation threshold. The experimental reflectivity and asymmetry spectra are compared to those derived from the complex dielectric function tensor calculated by using the first-principles spin-polarized relativistic band theory. We found that the T-MOKE asymmetry in general is a mixture of both the real and imaginary parts of the off-diagonal element of the dielectric function tensor, depending sensitively on the relative magnitudes of real and imaginary parts of the diagonal element. For angles of incidence larger than about 5° the influence of the Ag-substrate is significant. The major features in experimental and calculated reflectivity and asymmetry spectra are in agreement.     

The Coriolis attenuation in the pairing plus recoil model

The attenuation factor of the Coriolis off diagonal matrix element has been found to be very sensitive to the pairing strength. About 10% extra reduction of the attenuation factor coming from the recoil term may be expected in the pairing plus recoil model for some Coriolis matrix elements, if a reasonable pairing gap parameter is taken.     

A Fokker–Planck Model of the Boltzmann Equation with Correct Prandtl Number for Polyatomic Gases

We propose an extension of the Fokker–Planck model of the Boltzmann equation to get a correct Prandtl number in the Compressible Navier–Stokes asymptotics for polyatomic gases. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperature tensor, like the Ellipsoidal-Statistical model is obtained from the Bathnagar–Gross–Krook model of the Boltzmann equation, and by adding a diffusion term for the internal energy. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman–Enskog analysis shows how to compute the transport coefficients of our model. Some numerical tests are performed to illustrate that a correct Prandtl number can be obtained.