On the two-component Benard problem a numerical solution

A numerical solution for the two-component Bénard problem is presented, taking into account the contribution of thermal diffusion to the total density gradient. The results are compared with the approximate solution obtained by the variational technique of the local potential introduced some years ago by Glansdorff and Prigogine. The results calculated by the two methods are in agreement when the Soret coefficient is not too large. But when the gradients become important, the exact numerical solution presented here shows a small divergence from the variational method.The critical Rayleigh number is also compared with the one extrapolated from the analytical solution obtained for free boundary conditions.     

Simulation of water potential for the electronic structureof serine

First-principles, all-electron, \textit{ab initio} calculations have been performed to construct an equivalent water potential for the electronic structure of serine (Ser) in solution. The calculation is composed of three steps. The first step is to search for the configuration of the Ser + NH₂O system with a minimum energy. The second step is to calculate the electronic structure of Ser with the water molecule potential via the self-consistent cluster-embedding method (SCCE), based on the result obtained in the first step. The last step is to calculate the electronic structure of Ser with the dipole potential after replacing the water molecules with dipoles. The results show that the occupied states of Ser are raised by about 0.017~Ry on average due to the effect of water. The water effect can be successfully simulated by using the dipole potential. The obtained equivalent potential can be applied directly to the electronic structure calculation of protein in solution by using the SCCE method.     

离散修正KdV方程的解析近似解

将同伦分析法进行了推广,使之适用于求解离散修正KdV方程.获得了由指数函数表达的亮孤子解,该解析近似解与精确解符合很好.数值模拟结果说明了同伦分析法对求解复杂非线性问题的有效性和潜力.     

Solution of the schrödinger equation for a particle moving in a two-well potential

A solution to the Schrödinger equation for a particle moving in a two-well potential is obtained based on a variational method. This potential represents the sum of the harmonic and Gauss components. An analytical expression for the wave function of the ground state of the particle is derived. The dependence of the solution obtained on the potential barrier height and width is investigated. It is shown that the stronger the potential barrier, the higher the accuracy of calculations. The parameters of the two-well potential are indicated at which good agreement between the results of calculations and the exact numerical solution of the Schrödinger equation are expected.     

幂函数叠加势的径向薛定谔方程的解析解(英文)

当薛定谔方程中出现高次非谐振子势,电偶极矩势,分子晶体势,极化等效势等高次正幂与逆幂势函数以及它们的叠加时,薛定谔方程的求解变得非常复杂,本文采用奇点邻域附近的级数解法与求解渐近解相结合并且通过系数比较法,得到势函数为V(r)=a1r6 a2r2 a3r-4 a4r-6的径向薛定谔方程的一系列定态波函数解析解以及能级结构,并作了适当讨论与结论.     

New considerations of the Poisson–Boltzmann equation

A generalization of the Poisson–Boltzmann equation solution has been obtained as a function of a single parameter that is only temperature and concentration dependent. This new solution improves the analytical expressions for the surface charge density/surface potential relationship stated by other authors and shows excellent agreement with the exact numerical values obtained by Loeb, Overbeek and Wiersema [The Electrical Double Layer Around a Spherical Colloidal Particle, MIT Press, Cambridge, MA, 1961].     

超短沟道MOSFET电势的二维半解析模型

本文根据超短沟道MOSFET的工作原理, 在绝缘栅和空间电荷区引入两个矩形源, 提出了亚阈值下电势二维分布的定解问题. 通过半解析法和谱方法相结合, 首次得到了该定解问题的二维半解析解, 解的结果是一个特殊函数, 为无穷级数表达式. 该模型的优点是避免了数值分析时的方程离散化, 表达式不含适配参数、运算量小、精度与数值解的精度相同, 可直接用于电路模拟程序. 文中计算了沟道长度是45—22 nm的MOSFET电势、表面势和阈值电压. 结果表明, 新模型与Medici数值分析结果相同. 关键词： 半解析法 电势 阈值电压 MOSFET     

Wilsonian Renormalization Group and the Lippmann-Schwinger Equation with a Multitude of Cutoff Parameters

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced.A system of integro-differential equations for the cutoff-dependent potential is obtained.As an illustration,a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained.The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.     

The unitary pole expansion of the off-shell t-matrix elements for local potentials with hard cores

A convenient separable expansion of the t-matrix, similar to the one developed recently by Harms for local potentials with soft cores, has been obtained in the case of a hard-core potential as well. The unitary pole expansion (UPE), as it is called, is found to be strongly convergent. The UPE values of the off-shell t-matrix elements for a hard-core potential with an exponential shape agree fairly well with those obtained by Laughlin and Scott from the direct solution of the inhomogeneous Lippman-Schwinger equation.     

The jost function and bound state solution for the hulthén potential

The parameters of the attractive Hulthén potential are obtained in terms of the parameters of effective range theory by using the Jost function for the potential. The bound state solution for 1 + 0 is found from the corresponding Jost solution. The possibility of extending the present treatment to higher angular momentum states is discussed.     

Rigorous Derivation of the Cubic NLS in Dimension One

We derive rigorously the one-dimensional cubic nonlinear Schrödinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weak-coupling limit together with a short-range one. We start from a factorized initial state, and prove propagation of chaos with the usual two-step procedure: in the former step, convergence of the solution of the BBGKY hierarchy associated to the many-body quantum system to a solution of the BBGKY hierarchy obtained from the cubic NLS by factorization is proven; in the latter, we show the uniqueness for the solution of the infinite BBGKY hierarchy.     

A continuous analytic channel potential solution to doped symmetric double-gate MOSFETs from the accumulation to the strong-inversion region

A continuous yet analytic channel potential solution is proposed for doped symmetric double-gate (DG) MOSFETs from the accumulation to the strong-inversion region. Analytical channel potential relationship is derived from the complete 1-D Poisson equation physically, and the channel potential solution of the DG MOSFET is obtained analytically. The extensive comparisons between the presented solution and the numerical simulation illustrate that the solution is not only accurate and continuous in the whole operation regime of DG MOSFETs, but also valid to wide doping concentration and various geometrical sizes, without employing any fitting parameter.     

Solution of the Energy Level of Hydrogen-Like Atom for the Debye Shielding Potential

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-likeatoms under the condition of Debye shielding potential are achieved by means of the Rayleigh-Schrodinger perturbationtheory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Basedon the above solutions and with the use of energy consistent method the equivalent value of second-order reversion underthe condition of Debye shielding potential is produced as well and the result is compared with the data obtained by thenumerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.     

Solution of the System of Electrodiffusion Equations

The solution of the electrodiffusion equations together with the Poisson equation is examined. It is demonstrated that in the main approximation in a small parameter, the solution is reduced to that of two first-order differential equations. The obtained equations allow the transition processes in systems of charged particles to be examined for an arbitrary time dependence of the external potential.     

The bound state solution for the Morse potential with a localized mass profile

We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.     

Derivation of collective potential and mass from the generator coordinate method

The Hill-Wheeler equation of the generator coordinate method is approximated by a local collective Schrödinger equation. General expressions for the potential and the mass parameter are obtained by a symmetrized moment expansion. The validity of the approximation is tested for several examples where the exact solution is known. These include the Gaussian overlap with harmonic and anharmonic interaction, the Lipkin model, and monopole resonances of spherical light nuclei. In all cases, surprisingly close agreement with the exact solution is found. Other possible applications of the formalism are indicated.     

Invariants of the dynamics of molecular vibrational wave packets in phase modulation

An exact analytic solution was obtained for the correlation function of the motion of a phase-modulated Gauss wave packet in an anharmonic potential. The solution is expressed through the theta-function with the parameters depending on both the potential and phase modulation of the initial wave packet. Changes in both linear and quadratic chirps result in an invariant correlation function time shift in a weakly anharmonic potential with the conservation of all the total and fractional revivals. At a strong potential anharmonicity, translational invariance with respect to a quadratic chirp is preserved in certain instances, whereas the dynamics of packets experiences qualitative changes depending on linear phase modulation. This approach can be used to qualitatively analyze intramolecular dynamics if the potential energy surface is not known exactly, which is especially useful for quantum control of large molecules, in particular, photochromes.     

Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem

Generating functions for a complete collection of symmetries of the multiphased averaged KdV equation are constructed. The isospectral generating function has a potential form with one of the canonical basis holomorphic differentials as a potential and possesses some remarkable properties at double points of the hyperelliptic Riemann surface. A new representation for the characteristic speeds of the Whitham-KdV hierarchy is obtained. A global solution to the Whitham system is constructed in an effective form for the case of smooth decreasing initial data with a finite number of inflection points. The large time asymptotics of this solution implies the single-phase limiting behaviour of the oscillations to correlate with the asymptotic predictions of the Lax-Levermore theory.     

Constructing effective nucleon-nucleon interaction on the basis of the Idaho potential

An effective nucleon-nucleon interaction at an energy of 200 MeV is constructed for the Idaho nucleon-nucleon potential obtained on the basis of the theory of spontaneous chiral-symmetry breaking. This interaction approximates the nonlocal t matrix obtained for free nucleon-nucleon scattering from a solution to the Lippmann-Schwinger equation for the Idaho potential. The exact and approximated t matrices for the Paris potential, Idaho potential, and the von Geramb Hamburg potential are compared. The effective potential obtained in the way outlined above is used to calculate the inelastic scattering of 200-MeV polarized protons that is accompanied by the excitation of the 2⁺ level at 4.44 MeV and the 1⁺ level at 15.11 MeV in the ¹²C nucleus and the 6^? level at 14.1 MeV in the ²⁸Si nucleus. The results are compared with the results of the calculations on the basis of the Paris potential.     

Precise value for the three-bond 13C-1H coupling constant in acetone

A method based on the utilization of continuous space-filling curves is applied to a two-dimensional elastic scattering problem involving a central Yukawa potential. The Lippmann-Schwinger equation is brought into the form of a one-dimensional inhomogeneous integral equation and solved numerically. The results agree to within about 5 per cent with those obtained by a recent direct numerical solution based on two-dimensional quadratures.