APPLICATION OF PARAMETRIC DERIVATION METHOD TO THE CALCULATION OF PEIERLS ENERGY AND PEIERLS STRESS IN LATTICE THEORY

Applying the parametric derivation method, Peierls energy and Peierls stress are calculated with a non-sinusoidal force law in the lattice theory, while the results obtained by the power-series expansion according to sinusoidal law can be deduced as a limiting case of non- sinusoidal law. The simplified expressions of Peierls energy and Peierls stress are obtained for the limit of wide and narrow. Peierls energy and Peierls stress decrease monotonically with the factor of modification of force law. Present results can be used expediently for prediction of the correct order of magnitude of Peierls stress for materials.

A COMBINED PARAMETRIC QUADRATIC PROGRAMMING AND PRECISE INTEGRATION METHOD BASED DYNAMIC ANALYSIS OF ELASTIC-PLASTIC HARDENING/SOFTENING PROBLEMS

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.

Optimal sagittal gait with ZMP stability during complete walking cycle for humanoid robots

A parametric method to generate low energy gait for both single and double support phases with zero moment point（ZMP） stability is presented. The ZMP stability condition is expressed as a limit to the actuating torque of the support ankle, and the inverse dynamics of both walking phases is investigated. A parametric optimization method is implemented which approximates joint trajectories by cubic spline functions connected at uniformly distributed time knots and makes optimization parameters only involve finite discrete states describing key postures. Thus, the gait optimization is transformed into an ordinary constrained nonlinear programming problem. The effectiveness of the method is verified through numerical simulations conducted on the humanoid robot THBIP-I model.

On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

Theoretical analysis on the deformation characteristics of coal wall in a longwall top coal caving face

Against the background of analyzing coal wall stability in 14101 fully mechanized longwall top coal caving face in Majialiang coal mine,based on the torque equilibrium of the coal wall,shield support and the roof strata,an elastic mechanics model was established to calculate the stress applied on the coal wall.The displacement method was used to obtain the stress and deformation distributions of the coal wall.This study also researched the influence of support resistance,protective pressure to the coal wall,fracture position of the main roof and mining height on the coal wall deformation.The following conclusions are drawn:(1) The shorter the distance from the longwall face,the greater the vertical compressive stress and horizontal tensile stress borne by the coal wall.The coal wall is prone to failure in the form of compressive-shear and tension;(2) With increasing support resistance,the revolution angle of the main roof decreases linearly.As the support resistance and protective force supplied by the face guard increases,the maximum deformation of the coal wall decreases linearly;(3) As the face approaches the fracture position of the main roof,coal wall horizontal deformation increases significantly,and the coal wall is prone to instability;and(4) The best mining height of 14101 longwall face is 3.0 m.

Binary Tomography Reconstruction with Limited-Data by a Convex Level-Set Method

This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions.In this technique,we derive generic evolution equations for shape reconstruction in terms of the underlying level-set parameters.We show that using the appropriate basis function to parameterize the level-set function results in an optimization problem with a small number of parameters,which overcomes many of the problems associated with the traditional level-set approach.More concretely,in this paper,we use Gaussian functions as a basis function placed at sparse grid points to represent the parametric level-set function and provide more flexibility in the binary representation of the reconstructed image.In addition,we suggest a convex optimization method that can overcome the problem of the local minimum of the cost function by successfully recovering the coefficients of the basis function.Finally,we illustrate the performance of the proposed method using synthetic images and real X-ray CT projection data.We show that the proposed reconstruction method compares favorably to various state-of-the-art reconstruction techniques for limited-data tomography,and it is also relatively stable in the presence of modest amounts of noise.Furthermore,the shape representation using a compact Gaussian radial basis function works well.

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.

Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification.Here we focus on Stefan problems,and their quasi-static variants,with applications to crystal growth.New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.

AN ENERGY-STABLE PARAMETRICFINITE ELEMENT METHOD FOR SIMULATING SOLID-STATE DEWETTING PROBLEMS INTHREE DIMENSIONS

We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space.The model describes the motion of the film/vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line.We present a weak formulation for the problem,in which the contact angle condition is weakly enforced.By using piecewise linear elements in space and backward Euler method in time,we then discretize the formulation to obtain a parametric finite element approximation,where the interface and its contact line are evolved simultaneously.The resulting numerical method is shown to be well-posed and unconditionally energystable.Furthermore,the numerical method is generalized to the case of anisotropic surface energies in the Riemannian metric form.Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.

Parametric study of a new HOS-CFD coupling method

This paper presents a developed new coupled method which combined our in-house CFD solver naoe-FOAM-SJTU and naoe-FOAM-os with a potential theory High Order Spectral method(HOS).A parametric study of nonlinear wave propagation in computational fluid dynamics(CFD)zone is considered.Mesh convergence,time step convergence,time discretization scheme and length of relaxation zone are all carried out.Those parametric studies verify the steady of this new combined method and give better choice for wave propagation.The dissipation in propagation of nonlinear regular wave can be lower than 3%in static mesh,and less than 2%in overset grid mesh.Meanwhile,a LNG FPSO is put into the viscous wave tank to study the suitable size of CFD zone.To achieve a better solution with least calculating resources and best numerical results,the length of CFD zone is discussed.These parametric studies can give reference upon employment of the potential-viscous coupled method and validation of the coupled method.

Shape optimization design of a heaving buoy of wave energy converter based on fully parametric modeling and CFD method

The hydrodynamic shape of the heaving buoy is an important factor of the motion response in waves and thus concerns the energy conversion efficiency for the point absorbers(PAs).The current experience-based designs are time consuming and not very efficient,hence,faster and smarter methods are desirable.An automated optimization method based on a fully parametric modeling method and computational fluid dynamics(CFD),is proposed in this paper.Using this method,a benchmark buoy is screen designed and then optimized by maximizing the heave motion response.The geometry is described parametrically and deformed by means of the free-form deformation(FFD)method.During the optimization process,the expansion factor of control points is the basis for the variations.A combination of the Sobol and the non-dominated sorting genetic algorithm II(NSGA-II)is used to search for the solutions.After several iterations,the heaving buoy shape with optimal heave motion response is obtained.The analyses show that the heave motion response has increased 55.3%after optimization.The developed methodology is valid and seems to be a promising way to design a novel buoy that can significantly improve the wave energy conversion efficiency of the PAs in future.

Correlation study between the square-coneenergy-absorbing structure and the frontal collisionbehaviour of leading vehicles

In order to study the influence of square-cone energy-absorbing structures on the mechanical behaviour of the ollision performance of the leading vehicle,a parameterization method for rapidly changing the performance of energy-absorbing structures was proposed.Firstly,a finite element simulation model of the collision of the leading vehicle with a square-cone energy-absorbing structure was constructed.Then,the platform force,the slope of the platform force and the initial peak force of the force-displacement curve derived from the energy-absorbing structure were studied for the collision performance of the leading vehicle.Finally,the correlation model of the square-cone energy-absorbing structure and the mechanical behaviour of the collision performance of the leading vehicle was established by the response surface method.The results showed that the increase of the platform force of the energy-absorbing structure can effectively buffer the longitudinal impact of the train and reduce the nodding attitude of the train.The increase of the platform force slope can not only effectively buffer the longitudinal impact and vertical nodding of the train,but also reduce the lateral swing of the train.An increase in the initial peak force to a certain extent may lead to a change in the deformation mode,thereby reducing the energy-absorption fficiency.The correlation model can guide the design of the square-cone energy-absorbing structure and predict the deformation attitude of the leading vehicle.

Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator

We consider numerical approximation of spectral fractional Laplace-Beltrami problems on closed surfaces.The proposed numerical algorithms rely on their Balakrishnan integral representation and consists a sinc quadrature coupled with standard finite element methods for parametric surfaces.Possibly up to a log term,optimal rate of convergence are observed and derived analytically when the discrepancies between the exact solution and its numerical approximations are measured in L^(2)and H^(1).The performances of the algorithms are illustrated on different settings including the approximation of Gaussian fields on surfaces.

Constraints of gravitational baryo/leptogenesis on Cardassian expansion

In this paper, proceeding from the relation between the Cardassian model and the accelerated expansion of the universe, adopting a parametric method which does not depend on a precise mechanism for gravitational baryo/leptogenesis and using the model parameter of CPT-violating interaction, we study the role of the modified Friedmann equation which plays a role in the matter asymmetry of the early epoch and the accelerated expansion of the present universe. Thus the appropriate Cardassian component in the radiatiomdominated era or in the matter-dominated universe can be obtained. The results indicate that early CPT-violation is included in the Cardassian term. In the same way, the present Cardassian term that belongs to a quintessence-like model can drive the universe towards a flat, matter-dominated and accelerating expansion.

Oscillating Disturbance Propagation in Passages of Multi-Stage Hydrogen Turbine

The propagation of oscillating disturbances with various frequencies in multi stage turbine passages in a rocket is analyzed using the oscillating fluid mechanics theorem and the parametric polynomial method. The results show that oscillating disturbances can be rapidly dissipated when the disturbance occurs at the inlet except for very high frequency oscillation such as 50 kHz. Dangerous low frequency oscillations occur at the outlet. The effects of the flow parameter variations on the oscillating disturbance propagation are also studied. The analysis will facilitate safe operation of the whole rocket system.