Exact solutions of the Dirac equation with Pschl-Teller double-ring-shaped Coulomb potential via the Nikiforov-Uvarov method

Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov method,and the exact bound-state energy eigenvalues and corresponding two-component spinor wavefunctions are reported.

Method of Images to Study the Charge Distribution in Cases of Potentials Deviating from Coulomb’s Law

The method of images is used to study the charge distribution for cases where Coulomb’s law deviates from the inverse square law. This method shows that in these cases some of the charge goes to the surface, while the remainder charge distributed over the volume of the conductor. In accord with the experimental work, we show that the charge distribution will depend on the photon rest mass and is very sensitive to it;a very small value of the rest of mass of the photon will create deviation from Coulomb’s law.

Coulomb规范下地电磁场的自适应有限元模拟的理论分析

地电磁场的直接求解法存在伪解现象,且电磁场分量在界面上的不连续性与节点型有限元的基本要求矛盾.本文将Coulomb规范下磁矢量势-电标量势与自适应有限元相结合,提出了地球物理电磁场计算的快速、高精度方法.首先从地电磁场一般边值问题出发,给出了Coulomb规范下磁矢量势-电标量势的公式系统,分析了求解域内势的连续性.采用Galerkin加权余值法推导出积分弱解形式和Delaunay非结构化四面体单元时Hierarchal基函数的有限元方程.基于超收敛恢复技术,提出了适用于电磁场的后验误差估计方法,阐述了地电磁场自适应计算的策略及迭代算法,分析了计算时间消耗和误差收敛性质,表明本文方法可以用最优的计算资源得到呈拟指数收敛到准确解的数值结果,从而为后续的数值计算奠定了理论基础.

Coulomb土压力理论的两种解法

采用极限平衡变分法和Culmann分析方法,对土压力问题进行了研究。在极限平衡变分法中,以滑动体静力平衡的2个力的平衡方程为基础,引入Lagrange乘子,将以变分学观点来描述的主动土压力和被动土压力问题,转化为确定含有2个函数自变量的泛函极值问题。依据泛函取极值时,必须满足Euler方程,得出了主动土压力和被动土压力取极值时墙后土体沿平面滑动破坏的结论。在Culmann分析方法中,沿用了Coulomb土压力理论关于平面滑动破坏的假定,而在推导土压力计算公式的过程中,仅利用了滑动体沿某一特定方向的一个力的平衡方程。与目前通行的Coulomb土压力公式的证明过程相比,Culmann分析方法更为简洁。

纤维拔出时Coulomb摩擦界面应力传递

假设纤维/基体界面分离区域内的摩擦剪切应力遵循Coulomb摩擦律,包括泊松效应的影响,建立了纤维拔出时的摩擦界面应力传递模型,获得了包含摩擦滑移和由纤维/基体热失配引起的法向残余热应力效应的纤维轴向应力和界面剪切应力的表达式.对纤维增强复合材料SCS-6/Ti-6Al-4V作参数化的数值计算,且和有限元结果进行比较.结果表明,随纤维轴向位置的增加,纤维轴向应力和界面剪切应力均减小;法向残余热应力、高纤维体积分数和短纤维延缓纤维失效.

Triaxial strength behaviour of rockmass satisfying Modified Mohr-Coulomb and Generalized Hoek-Brown criteria

The triaxial strength of twenty rockmass types was predicted using two non-linear triaxial strength criteria for rockmass i.e. Modified Mohr-Coulomb(MMC) criterion and Generalized Hoek-Brown(GHB)criterion. Four different rockmass classification systems were used for the calculation of MMC criterion parameters while only GSI classification system has been used for calculation of GHB parameters. The representative value of the uniaxial compressive strength and elastic modulus of rockmass have been estimated using probabilistic approach. A hypothetical case of an unsupported tunnel has been analyzed considering both MMC and GHB criteria. The analysis was done using the convergence-confinement method with two different approaches. The first approach predicts the tunnel response using GHB criterion directly. The second approach predicts the tunnel response using equivalent Mohr-Coulomb parameters obtained by linearization of triaxial data points obtained from MMC and GHB criteria. The tunnel response has been estimated in terms of radius of plastic zone, tunnel convergence and tunnel convergence strain. For very poor rockmasses the tunnel response predicted by MMC criterion is less than that predicted by GHB criterion. For poor and fair rockmass, the tunnel response estimated considering both the criteria are comparable except for few cases. Squeezing condition in rockmass has been also evaluated.

Influence of the Coulomb exchange term on nuclear single-proton resonances

Nuclear single-proton resonances are sensitive to the Coulomb field,while the exchange term of Coulomb field is usually neglected due to its nonlocality.By combining the complex scaling method with the relativistic mean-field model,the influence of the Coulomb exchange term on the single-proton resonances is investigated by taking Sn isotopes and N=82 isotones as examples.It is found that the Coulomb exchange term reduces the singleproton resonance energy within the range of 0.4-0.6 MeV and leads to similar isotopic and isotonic trends of the resonance energy as those without the Coulomb exchange term.Moreover,the single-proton resonance width is also reduced by the Coulomb exchange term,whose influence generally decreases with the increasing neutron number and increases with the increasing proton number.However,the influence of the Coulomb exchange term cannot change the trend of the resonance width with respect to the neutron number and proton number.Furthermore,the influence of the Coulomb exchange term on the resonance width is investigated for the doubly magic nuclei ^(40)Ca,^(56,78)Ni,^(100,132)Sn,and ^(208)Pb.It is found that the Coulomb exchange term reduces the proton resonance width within 0.2 MeV,whose magnitude depends on the specific nucleus and the quantum numbers of resonant states.

基于Sheorey岩体强度准则对等效Mohr-Coulomb强度参数的推导

引入基于RMR岩体分级指标的Sheorey岩体强度准则,根据σ1-σ3平面上用线性Mohr-Coulomb(M-C)强度准则对非线性准则进行拟合的原则,利用最小二乘法推导出相应的等效M-C强度参数,并给出等效强度参数的通用表达式,方便利用Sheorey准则评价岩体的强度及稳定性。之后,通过一个算例比较了Sheorey准则与HoekBrown准则的M-C等效强度参数。分析结果表明,两准则的等效强度参数具有良好的吻合度。

基于Mohr-Coulomb准则和二阶锥规划技术的轴对称自适应下限有限元法

轴对称Mohr-Coulomb准则屈服面的角点问题导致其在数值计算中存在困难,如何高效处理该屈服准则一直是极限分析下限有限元法的重要内容。首先,引入完全塑性假定将轴对称Mohr-Coulomb准则转化为1组不等式约束和3个线性等式约束;然后,将不等式约束直接转化为二阶锥约束,避免了对角点进行光滑近似处理;最后,将基于Mohr-Coulomb准则的轴对称极限分析下限有限元计算模型转化为具有较高计算效率的二阶锥规划数学优化模型。极限分析下限有限元法采用的线性应力单元难以精确模拟破坏区域的应力变化,单元的分布形式对计算精度存在较大影响。因此提出一种基于单元应力的网格自适应加密策略,通过判断单元内节点应力接近屈服的程度,自动识别破坏区域待加密的单元,实现对破坏区域应力分布的精确模拟,进而能够以较少单元获得高精度下限解。通过分析圆形基础承载力及竖向锚板极限抗拔力等典型轴对称岩土工程稳定性问题,表明了所提方法具有较高计算效率及计算精度,具有一定的理论价值和应用前景。

CNDO Studies on the Intermolecular Coulomb Interaction in TCNQ-Stack

The coulomb interaction among TCNQ- molecules in different stack structures was calculated by quantum chemistry CNDO method. The results of the calculation would be used to explain the change rule of the electricity property of the TCNQ complex very well.

Semiclassical investigation of Coulomb focusing effects in atomic above-threshold ionization with elliptically polarized laser fields

We investigate atomic above-threshold ionization in elliptically polarized strong laser fields with a semiclassical approach.With increasing laser intensity,the Coulomb focusing（CF） effects are found to become stronger in both parallel and perpendicular directions with respect to the polarization plane.The dependence of CF effects on tunnel exit,initial transverse momentum distribution and laser electric field is analyzed.It was revealed that the effects of tunnel exit are most prominent with variation of the laser intensity,and the other two factors both play non-negligible roles.Our results provide a deeper insight to the recent experiments of Coulomb asymmetry[Shafir D,et al.,2013 Phys.Rev.Lett.111 023005 and Li M,et al,2013 Phys.Rev.Lett.111 023006].

Investigation of Coulomb force effects on ethylene glycol based nanofluid laminar flow in a porous enclosure

Forced convection heat transfer of ethylene glycol based nanofluid with FeOinside a porous medium is studied using the electric field. The control volume based finite element method(CVFEM) is selected for numerical simulation. The impact of the radiation parameter(R), the supplied voltage(?φ), the volume fraction of nanofluid(?), the Darcy number(Da), and the Reynolds number(Re) on nanofluid treatment is demonstrated. Results prove that thermal radiation increases the temperature gradient near the positive electrode. Distortion of isotherms increases with the enhance of the Darcy number and the Coulomb force.

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.

Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential

In this work, we modeled and simulated the electric potential generated by point charges in the region of grounded conductor planes for Yukawa potential (e−μ/r) and Coulomb potential (1/r). We show the symbolic expression for the electric potential and some graphs for it and for the electric field with different values of μ. We observe that the electric potential decreases as the value of μ increases and that does not allow all the charge to be distributed on the surface of the conductor.

Calculation of Neutron-Proton Mass Difference by the Monte Carlo Method

Calculation results of the Monte Carlo method of the average energy of the electrostatic interaction between the quarks are presented to the neutron and proton. The proposed model of the distribution of quarks in protons and neutrons is possible to assess the area which included a strong (gluon) interaction. Given the fact that the probability of finding a quark in the field with strong interaction is less than one, there is a good agreement between the experimental and calculated values of the mass difference between the neutron and the proton.

Point Charge between Two Grounded and Conducting Planes Forming a 60°Angle and for Yukawa’s Potential and Coulomb’s Potential

For a point charge between two grounded conductor planes forming a 60° angle, the potential and electric field generated by point charge for Yukawa’s potential (e-μr/r) and Coulomb’s potential (1/r) are modeled and simulated. The expression for the potential that generalizes the cases discussed in López-Mariño, M. and Trujillo Caballero, J. (2017) Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential. Journal of Electromagnetic Analysis and Applications, 9, 135-146. https://doi.org/10.4236/jemaa.2017.910012 is presented. Graphs for the potential and electric field for both cases are showed using Maple, that of Coulomb and that of Yukawa for different values of μ . The purpose of this work is to offer students a practical guide for problem analysis of electrostatics using Maple’s capabilities as a computational tool.

The Coulomb Resonances, the Quasi-Real Photons and Electro-Disintegration of Nuclei by High-Energy Electrons

Various aspects of the influence of the quasi-real photons and the Coulomb resonances on the formation of the crosssection of inelastic scattering of high energy electrons on atomic nuclei are investigated. Emiss is the energy that disappears in the processes of knocking-on of protons in the reactions . A new hypothesis that interprets the origin of the energy losses is proposed. Specific experiments that can confirm or refute this hypothesis are proposed as well. The “regularized” cross-sections of electro-disintegration of nuclei by high-energy electrons are calculated in the framework of the nuclear shell model. It is shown that for the experimental verification of the existence of Coulomb resonances, it is necessary to investigate the processes at relatively small angles of scattering. The peculiarities of numerical methods that are crucial in the investigation of inelastic scattering of high-energy electrons on nuclei in the framework of the nuclear shell model are analyzed in this work as well. The cross-sections of the scattering of high-energy electrons on the angle are calculated. It is shown that the orthogonality of the wave functions of a knocked-on proton in the initial and final states plays an important role in the interpretation of this process.

基于Mohr-Coulomb准则和强度折减法边坡稳定性数值分析

结合某隧道现场实测地质参数和地貌状况,建立了边坡的三维数值模型,基于Mohr-Coulomb准则和强度折减法,分析了渗透力作用下隧道边坡稳定性,并根据数值计算和分析结果,提出了合理的边坡加固措施。

等效Mohr-Coulomb屈服准则在岩质边坡稳定性分析中的应用

基于等效Mohr-Coulomb屈服准则原理,通过岩体材料参数的人工换算,实现其在有限元软件Ansys中的应用,并论证了转化后的材料参数与原参数的大小关系,即转化后参数恒比原参数小。结合算例分析,得知采用等效Mohr-Coulomb屈服准则计算得到的岩质边坡安全系数偏小、保守,可用来模拟岩体材料;同时,对不同位移及应力工程精度要求的岩质边坡工程,提出采用不同屈服准则的建议。

New Possibilities of Harmonic Oscillator Basis Application for Quantum System Description.Two Particles with Coulomb Interaction

This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310034003400340037003600360038000000 is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.