Potential method of integration for solving the equations of mechanical systems

This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.

EVOLUTION OF CREEP-FATIGUE DAMAGE IN TYPE 304STAINLESS STEEL AND ITS DETECTION BY ELECTRICALPOTENTIAL METHOD

Creep-fatigue test was carried out using smooth round bar specimens of Type 304 stainless steel. Cavities and small cracks on the cross-section of the specimen were carefully observed by a scanning laser microscope. Moreover, direct current electrical potential method (DC-EPM) was applied in order to evaluate non-destructively the distribution of internal cracks. The distribution evaluated by DC-EPM agrees well with the actual one. (Edited author abstract) 9 Refs.

Probing the electric double layer structure at nitrogen-doped graphite electrodes by constant-potential molecular dynamics simulations

Electric double layer(EDL)is a critical topic in electrochemistry and largely determines the working performance of lithium batteries.However,atomic insights into the EDL structures on heteroatom-modified graphite anodes and EDL evolution with electrode potential are very lacking.Herein,a constant-potential molecular dynamics(CPMD)method is proposed to probe the EDL structure under working conditions,taking N-doped graphite electrodes and carbonate electrolytes as an example.An interface model was developed,incorporating the electrode potential and atom electronegativities.As a result,an insightful atomic scenario for the EDL structure under varied electrode potentials has been established,which unveils the important role of doping sites in regulating both the EDL structures and the following electrochemical reactions at the atomic level.Specifically,the negatively charged N atoms repel the anions and adsorb Li~+at high and low potentials,respectively.Such preferential adsorption suggests that Ndoped graphite can promote Li~+desolvation and regulate the location of Li~+deposition.This CPMD method not only unveils the mysterious function of N-doping from the viewpoint of EDL at the atomic level but also applies to probe the interfacial structure on other complicated electrodes.

A potential integration method for Birkhoffian system

This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewritten as 2n first-order differential equations. Secondly, the corresponding partial differential equations are obtained by potential integration method and the solution is expressed as a complete integral. Finally, the integral of the system is obtained.

The dimension split element-free Galerkin method for three-dimensional potential problems

This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

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.

Fast Measurement of Dielectric Conductivity for Space Application by Surface Potential Decay Method

Surface potential decay of polymers for electrical insulation can help to determine the dark conductivity for spacecraft charging analysis. Due to the existence of radiation-induced conductivity, it decays fast in the first few hours after irradiation and exponentially slowly for the remaining time. The measurement of dark conductivity with this method usually takes the slow part and needs a couple of days. Integrating the Fowler formula into the deep dielectric charging equations, we obtain a new expression for the fast decay part. The experimental data of different materials, dose rates and temperatures are fitted by the new expression. Both the dark conductivity and the radiation-induced conductivity are derived and compared with other methods. The result shows a good estimation of dark conductivity and radiation-induced conductivity in high-resistivity polymers, which enables a fast measurement of dielectric conductivity within about 600 rain after irradiation.

Energy Spectrum for a Short-Range 1/r Singular Potential with a Non-Orbital Barrier Using the Asymptotic Iteration Method

Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.

Examination of Potential Energy Curves of CFCl by Multi-reference Configuration Interaction Method

We give a detailed examination of potential energy curves of the singlet and triplet states of CFC1 correlated with the lowest three dissociation limits. The calculations are carried out at the internally contracted multi- reference configuration interaction/cc-pV（T＋d）Z level with the other two geometric parameters fixed at the state equilibrium conformation. The vertical transition energy, the oscillator strength, the main configuration and the electron transition are also investigated at the same level.

Identification and evaluation of shale oil micromigration and its petroleum geological significance

Taking the Lower Permian Fengcheng Formation shale in Mahu Sag of Junggar Basin,NW China,as an example,core observation,test analysis,geological analysis and numerical simulation were applied to identify the shale oil micro-migration phenomenon.The hydrocarbon micro-migration in shale oil was quantitatively evaluated and verified by a self-created hydrocarbon expulsion potential method,and the petroleum geological significance of shale oil micro-migration evaluation was determined.Results show that significant micro-migration can be recognized between the organic-rich lamina and organic-poor lamina.The organic-rich lamina has strong hydrocarbon generation ability.The heavy components of hydrocarbon preferentially retained by kerogen swelling or adsorption,while the light components of hydrocarbon were migrated and accumulated to the interbedded felsic or carbonate organic-poor laminae as free oil.About 69% of the Fengcheng Formation shale samples in Well MY1 exhibit hydrocarbon charging phenomenon,while 31% of those exhibit hydrocarbon expulsion phenomenon.The reliability of the micro-migration evaluation results was verified by combining the group components based on the geochromatography effect,two-dimension nuclear magnetic resonance analysis,and the geochemical behavior of inorganic manganese elements in the process of hydrocarbon migration.Micro-migration is a bridge connecting the hydrocarbon accumulation elements in shale formations,which reflects the whole process of shale oil generation,expulsion and accumulation,and controls the content and composition of shale oil.The identification and evaluation of shale oil micro-migration will provide new perspectives for dynamically differential enrichment mechanism of shale oil and establishing a“multi-peak model in oil generation”of shale.

Analytical mechanics methods for solving Whittaker equations

The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral method.

Higher-Order Line Element Analysis of Potential Field with Slender Heterogeneities

Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induced due to close interaction with other objects.Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect.In the present work,we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities.In a benchmark example of two parallel rods,we compare the line element solution with the boundary element solution to show the accuracy as a function in terms of rods distance.Furthermore,we use more complicated examples to demonstrate the capability of the line element technique.

Electrochemical Method for Evaluating the Passivated State of Medical StainlessSteel 317L

The electrochemical behavior of the medical Stainless steel 317L which is used as in vivo fixation materials has been investigated at different passivated states in several candidate-testing solutions. The potentiodynamic scanning polarizaion technique was employed to measure the polarizaion curves of 317L in 0.9%NaCl solution at 37℃. The results showed that the electrochemical behaviorin 0.9% NaCl solution at 37℃ and in 2% NaCl solotion at 30℃ can be better used to detect and evaluate passivated states and corrosionresistance of 317L. In addition,the pitting potential Eb can be used as a criterion and itS lower limit could be 0.85 V(SEC) for this system.

Bound state solutions of d-dimensional Schrdinger equation with Eckart potential plus modified deformed Hylleraas potential

We study the d-dimensional Schrdinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method.We obtain energy eigenvalues and the corresponding wave function expressed in terms of a Jacobi polynomial.We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions.Numerical results are also computed for the energy spectrum and the potentials.

Spin and pseudospin symmetries of the Dirac equation with shifted Hulthe′n potential using supersymmetric quantum mechanics

In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.

The(1+1)-dimensional nonlinear ion acoustic waves in multicomponent plasma containing kappa electrons

Large amplitude (1+1)-dimensional nonlinear ion acoustic waves are theoretically studied in multicomponent plasma consisting of positively charged ions and negatively charged ions, ion beam, kappa-distributed electrons, and dust grains,respectively. By using the Sagdeev potential method, the dynamical system and the Sagdeev potential function are obtained.The important influences of system parameters on the phase diagram of this system are investigated. It is found that the linear waves, the nonlinear waves and the solitary waves are coexistent in the multicomponent plasma system. Meanwhile,the variations of Sagdeev potential with parameter can also be obtained. Finally, it seems that the propagating characteristics of (1+1)-dimensional nonlinear ion acoustic solitary waves and ion acoustic nonlinear shock wave can be influenced by different parameters of this system.

A SCREW DISLOCATION IN A THREE-PHASE COMPOSITE CYLINDER MODEL WITH INTERFACIAL RIGID LINES

The problem of the elastic interaction between a screw dislocation and a three-phase circular inclusion with interracial rigid lines （anti-cracks） is investigated. An efficient and concise method for the complex multiply connected region is developed, with which explicit series form solutions of the complex potentials in the matrix, and the interphase layer and inclusion regions are derived. Based on the complex potentials, the image force on the screw dislocation is then calculated by using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various rigid line geometries, interphase layer thicknesses and material property combinations. The main results show that the interracial rigid lines exert a significant perturbation effect on the motion of the screw dislocation near the circular inclusion surrounded by an interphase layer.

INTERACTION OF A SCREW DISLOCATION IN THE INTERPHASE LAYER WITH THE INCLUSION AND MATRIX

The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with . An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory, Schwatz symmetric principle and Cauchy integral technique. The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution . By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.