Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom

The ways for improving on techniques for finding new solvable potentials based on supersymmetry and shape invariance has been discussed by Morales et al. [1] In doing so they address the peculiar system known as the one-dimensional hydrogen atom. In this paper we show that their remarks on such problem are mistaken. We do this by explicitly constructing both the one-dimensional Coulomb potential and the superpotential associated with the problem, objects whose existence are denied in the mentioned paper.

Simulation of three-dimensional tension-induced cracks based on cracking potential function-incorporated extended finite element method

In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously.

Theoretical Research on Scattering Resonance States of Reaction I＋HI（v=O）→IH（v＇=0）＋I： Partial Potential Energy Surface and One-dimensional Quantum Reactive Scattering Calculation

Based on the vibrational potential curves coupled with the minimum energy reaction path, the partial potential energy surface of the reaction I＋HI→IH＋I was constructed at the QCISD（T）//MP4SDQ level with pseudo potential method. And the formation mechanism of the scattering resonance states of this reaction was well interpreted with the partial potential energy surface. The scattering resonance states of this reaction should belong to Feshbach resonance because of the coupling of the vibrational mode and the translational mode. With the one-dimensional square potential well model, the resonance width and lifetime of the I＋HI（v=0）→IH（v＇=0）＋I state-to-state reaction were calculated, which preferably explained the high-resolved threshold photodetachment spectroscopy of the IHI- anion performed by Neumark et al..

Analytic Method to Study Influence of Finite Chemical Potential in QED_3~*

Adopting the approximation to the first order of chemical potential μ, we resolve rigidly the influence on fermion condensate from μ in QED3. We show that this condensate does not respond linear expression to μ. Moreover, the influence on fermion chiral condensate from chemieal potential is investigated.

Fermion-Boson Vertex at Finite Chemical Potential

Based on the Ward-Takahashi identity at finite chemical potential and Lorentz structure analyms, we generalize the Ball-Chiu vertex to the case of nonzero chemical potential and obtain the general form of the frmionboson vertex in QED at finite chemical potential.

3-D Marine CSEM Modeling in General Anisotropic Media by Using an Adaptive Finite Element Approach Based on the Vector-Scalar Potential

We present three-dimensional(3-D)modeling method of marine controlled-source electromagnetic(CSEM)fields in general anisotropic media using an adaptive finite element approach based on the vector-scalar potential.The modeling is based on the governing Helmholtz equations in the vector-scalar potential system.Unstructured tetrahedral grids are employed,which can exactly simulate the terrain relief and complex electrical structures.Moreover,based on the gradient recovery technology,the adaptive finite element approach is used to drive the mesh refinement,and make the finite element solutions converge gradually to the exact solutions.The primary-secondary field approach is used to improve the numerical accuracy of CSEM fields near the source point,where the primary field is calculated by using the quasi-analytical formula.The accuracy of this approach is verified by a one-dimensional model.Two 3-D models are used to demonstrate the effectiveness of the adaptive mesh refinement and the influences of dipping anisotropy layer on the marine CSEM responses for both inline and broadside geometries.The complex synthetic model is simulated to show the capability and flexibility of the approach for geometrically complex situations.

Potential Symmetries, One-Dimensional Optimal System and Invariant Solutions of the Coupled Burgers’ Equations

In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.

Subdiffusion of Dipolar Gas in One-Dimensional Quasiperiodic Potentials

Considering the discrete nonlinear Schrodinger model with dipole-dipole interactions （DDIs）, we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found： both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction （λ1） and DDI （A2） satisfy λ1 ≥ 2λ2, the property of the subdiffusion depends only on contact interaction; when λ1 ≤ 2λ2, the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v＊ for different values of contact interaction and DDI. When the disorder strength v ≥ v＊, the wave packet is localized. On the contrary, when the disorder strength v ≤ v＊, the wave packet is subdiffusive.

A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary

Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.

Scaled Boundary Finite Element Analysis of Wave Passing A Submerged Breakwater

The scaled boundary finite element method （SBFEM） is a novel semi-analytical technique combining the advantage of the finite element method （FEM） and the boundary element method （BEM） with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coeffcient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method （DBEM）, it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coeffcient and the transmission coefficient are given in the current study.

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.

The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method

A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.

Use of Finite Element Analysis for the Prediction of Driver Fatality Ratio Based on Vehicle Intrusion Ratio in Head-On Collisions

To estimate the aggressivity of vehicles in frontal crashes, national highway traffic safety administration (NHTSA) has introduced the driver fatality ratio, DFR, for different vehicle-to-vehicle categories. The DFR proposed by NHTSA is based on the actual crash statistical data, which makes it difficult to evaluate for other vehicle categories newly introduced to the market, as they do not have sufficient crash statistics. A finite element (FE) methodology is proposed in this study based on computational reconstruction of crashes and some objective measures to predict the relative risk of DFR associated with any vehicle-to-vehicle crash. The suggested objective measures include the ratios of maximum intrusion in the passenger compartments of the vehicles in crash, and the transmitted peak deceleration of the vehicles’ center of gravity, which are identified as the main influencing parameters on occupant injury. The suitability of the proposed method is established for a range of bullet light truck and van (LTV) categories against a small target passenger car with published data by NHTSA. A mathematical relation between the objective measures and DFR is then developed. The methodology is then extended to predict the relative risk of DFR for a crossover category vehicle, a light pick-up truck, and a mid-size car in crash against a small size passenger car. It is observed that the ratio of intrusions produces a reasonable estimate for the DFR, and that it can be utilized in predicting the relative risk of fatality ratios in head-on collisions. The FE methodology proposed in this study can be utilized in design process of a vehicle to reduce the aggressivity of the vehicle and to increase the on-road fleet compatibility in order to reduce the occupant injury out- come.

An easy way to controllably synthesize one-dimensional Sm B_6 topological insulator nanostructures and exploration of their field emission applications

A convenient fabrication technique for samarium hexaboride（SmB6） nanostructures（nanowires and nanopencils） is developed, combining magnetron-sputtering and chemical vapor deposition. Both nanostructures are proven to be single crystals with cubic structure, and they both grow along the [001] direction. Formation of both nanostructures is attributed to the vapor-liquid-solid（VLS） mechanism, and the content of boron vapor is proposed to be the reason for their different morphologies at various evaporation distances. Field emission（FE） measurements show that the maximum current density of both the as-grown nanowires and nanopencils can be several hundred μA/cm^2, and their FN plots deviate only slightly from a straight line. Moreover, we prefer the generalized Schottky-Nordheim（SN） model to comprehend the difference in FE properties between the nanowires and nanopencils. The results reveal that the nonlinearity of FN plots is attributable to the effect of image potential on the FE process, which is almost independent of the morphology of the nanostructures.All the research results suggest that the SmB6 nanostructures would have a more promising future in the FE area if their surface oxide layer was eliminated in advance.

A NEW HIGH-ORDER MULTI-JOINT FINITE ELEMENTFOR THIN-WALLED BAR

A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high accuracy and can be used in finite method analysis of bridge, tall mega-structure building.

NONLINEAR QUASI-CONFORMING FINITE ELEMENT METHOD

The nonlinear quasi-conforming FEM is presented based on the basic concept of the quasi- -conforming finite element. First, the incremental principle of stationary potential energy is discussed, Then, the formulation process of the nonlinear quasi-conforming FEM is given. Lastly, two computational examples of shells are given.

Investigation on ductile fracture in fine-blanking process by finite element method

In order to continuously analyze the whole fine-blanking process, from the beginning of the operation up to the total rupture of the sheet-metal, without computational divergence, a 3-D rigid visco-plastic finite-element method based on Gurson void model was developed. The void volume fraction was introduced into the finite element method to document the ductile fracture of the sheet-metal. A formulation of variation of the rigid visco-plastic material was presented according to the virtual work theory in which both the effects of equivalent stress and hydrostatic pressure in the deformation process were considered. The crack initiation of the sheet was predicted and the crack propagation was geometrically fulfilled in the simulation by separating the nodes according to the stress state. Furthermore, the influences of different state-variables on the deformation process were also studied.

Three－dimensional Global Scale Permanent－wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion

The three-dimensional nonlinear quasi-geostrophic potential vorticity equation is reduced to a linear form in the stream function in spherical coordinates for the permanent wave solutions consisting of zonal wavenumbers from 0 to n and rn vertical components with a given degree n.This equation is solved by treating the coefficient of the Coriolis parameter square in the equation as the eigenvalue both for sinusoidal and hyperbolic variations in vertical direction. It is found that these solutions can represent the observed long term flow patterns at the surface and aloft over the globe closely. In addition, the sinusoidal vertical solutions with large eigenvalue G are trapped in low latitude,and the scales of these trapped modes are longer than 10 deg. lat. even for the top layer of the ocean and hence they are much larger than that given by the equatorial β-plane solutions.Therefore such baroclinic disturbances in the ocean can easily interact with those in the atmosphere.Solutions of the shallow water potential vorticity equation are treated in a similar manner but with the effective depth H=RT/g taken as limited within a small range for the atmosphere.The propagation of the flow energy of the wave packet consisting of more than one degree is found to be along the great circle around the globe both for barotropic and for baroclinic flows in the atmosphere.