二阶动力学方程数值积分的一种新格式

许多动力学问题归结为求解一个二阶常微分方程组.本文提出了适用于二阶方程组的一种包含不同阶次公式的自动调节步长数值积分格式,对方法的稳定性进行了分析,并给出了数值计算例子,说明了在同样的精度要求下,与传统的Runge-Kutta 法相比,这种新格式可以节省计算机时.

Numerical and experimental analysis of quenching process for cam manufacturing

In order to obtain satisfactory mechanical properties for the cam used in high-power ship diesel engines, a new quenching technology was proposed by designing a two-stage quenching process with an alkaline bath as the quenching medium. To demonstrate the effectiveness of the proposed new quenching technology, both numerical analysis and experimental study were performed. The new quenching technology was analyzed using finite element method. The combined effects of the temperature, stress and microstructure fields were investigated considering nonlinear material properties. Finally, an experimental study was performed to verify the effectiveness of the proposed new quenching technology. The numerical results show that internal stress is affected by both thermal stress and transformation stress. In addition, the direction of the internal stress is changed several times due to thermal interaction and microstructure evolution during the quenching process. The experimental results show that the proposed new quenching technology significantly improves the mechanical properties and microstructures of the cam. The tensile strength, the impact resistance and the hardness value of the cam by the proposed new quenching technology are improved by 4.3%, 8.9% and 3.5% compared with those by the traditional quenching technology. Moreover, the residual stress and cam shape deformation are reduced by 40.0% and 48.9% respectively for the cam manufactured by the new quenching technology.

General Modified Split-Step Balanced Methods for Stiff Stochastic Differential Equations

A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already reported split-step balanced methods, the drift increment function of the methods can be taken from any chosen ane-step ordinary differential equations （ODEs） solver. The schemes is proved to be strong convergent with order one. For the mean-square stability analysis, the investigation is confined to two cases. Some numerical experiments are reported to testify the performance and the effectiveness of the methods.

Numerical analysis on coal-breaking process under high pressure water jet

Based on the theory of nonlinear dynamic finite element,the control equation ofcoal and water jet was acquired in the coal breaking process under a water jet.The calculationmodel of coal breaking under a water jet was established;the fluid-structure couplingof water jet and coal was implemented by penalty function and convection calculation.The dynamic process of coal breaking under a water jet was simulated and analyzed bycombining the united fracture criteria of the maximum tensile strain and the maximal shearstrain in the two cases of damage to coal and damage failure to coal.

Stability control of underground construction

This paper presents the reason for instability of underground construction. In order to know failure mechanism during the whole construction process, a research framework of multi-scale based on experiments and numerical analysis is established. Some promising aspects in the topics of stability control are also given in the paper.

A Power Penalty Approach to Numerical Solutions of Two-Asset American Options

This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant λ〉 1 and a power parameter k 〉 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O（λ^-k/2）. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.

Non-complete relief method for measuring surface stresses in surrounding rocks

The measurement of surface stresses in surrounding rocks with the use of a relief method of annular hole-drilling was studied by numerical analysis. The stress relief process by hole-drilling was then simulated with the use of finite element method. The influences of the borehole diameter(d), the initial stresses and the ratio of the initial principle stresses on the variations of the remained stress and the released stress in function of the relief depth(h) were discussed. The relation between the non-dimensional ratio of the released principle strains and that of the initial principle stresses, and the effect of the elastic modulus and the Poisson ratio of the rock mass on the stress relief curves were studied. The results show that the stress relief behavior formulated with the non-dimensional ratio of the released stress and the ratio of h/d is only sensitive to the ratio of the initial principle stresses and the Poisson ratio. The stresses are completely released when h equals 1.6d, and the tensile stresses take place on the bore core surface in the relief measurement process. Finally, a non-complete relief method of annular hole-drilling for measuring surface stress in surrounding rocks is proposed and the procedure is presented.

A Scheme for Spin Manipulation in a Quantum Dot with Both Charge and Spin Bias

We propose a scheme for the effective polarization and manipulation of electron spin by using a quantum dot with both charge and spin bias. Using the equation of motion for Keldysh nonequilibrium Green function, we study the spin accumulation and polarization for the system. Through analytical analysis and a few numerical examples, it is demonstrated that fairly large spin accumulation and polarization can be produced due to the breaking symmetry of the chemical potential for different electron spin in the leads. Moreover, the direction and the strength of the spin polarization can be conveniently controlled and tuned by varying the charge bias or the gate voltage.

Numerical Simulation of Fluid Flow and Oil-Water Separation in Hydrocyclones

The fluid flow and oil-water separation were simulated using a Reynolds stress transport equation model of turbulence in water flow and a stochastic model of oil droplet motion. Simulation results give the axial and tangential velocity components, the pressure and turbulence intensity distribution and droplet trajectories for a hydrocyclone of F type and a hydrocyclone proposed by the present authors. The flow field predictions are in qualitative agreement with the LDV measurements. The results show that the proposed hydrocyclone has better performance than the hydrocyclone of F type due to creating stronger centrifugal force and lower axial velocity.

A fractal approximation algorithm for inverse initial-value problems of nonlinear differential equations

A fractal approximation algorithm is developed to obtain approximate solutions to an inverse initial-value problem IVP(inverse IVP) for the differential equation. Numerical computational results are presented to demonstrate the effectiveness of this algorithm for solving inverse IVP for a class of specific differential equations.

Numerical simulation of temperature distribution and heat transfer during solidification of titanium alloy ingots in vacuum arc remelting process

In order to get a better understanding of the vacuum consumable arc remelting(VAR) processes and thus to optimize them,a 3D finite element model was developed for the temperature fields and heat transfer of titanium alloy ingots during VAR process.The results show that the temperature fields obtained by the simulation are well validated through the experiment results.The temperature distribution is different during the whole VAR process and the steady-state molten pool forms at 329 s for d100 mm × 180 mm ingots.At the initial stage of remelting,the heat dissipation of crucible bottom plays an important role in the whole heat dissipation system.At the middle of remelting,the crucible wall becomes a major heat dissipation way.The effect of cooling velocity on the solidification structure of ingots was investigated based on the temperature fields and the results can well explain the macrostructure of titanium alloy ingots.

Numerical Analysis on Soil and Rock Formation of Ancient Gravel Strata Around Nanjing

Research samples were taken from an ancient gravel stratum which is not only a representative soil layer along the middle-lower reaches of the Yangtze River in East China, but also one of the primary Neozoic strata in Naming district. Located mostly on the second and third terraces, the ancient gravel strata formed the geomorphic landscapes of terrace and step. They were complex in constitution, varied widely in stability, of multiple sources, locally derived, and associated with braided streams in the deposition environment. A CIPW (Cross, Iddings, Pirsson and Washington) method modified by the author was used to analyze the soil-rock-forming materials of finer grains (less than 2 mm in size) of the ancient gravel stratum. Results of the analysis showed that the sandy grains were composed of apatite, ilmenite, potassium feldspar, plagioclase, enstatite and free quartz, the clay mainly of kaolinite, and the cement of a combination of silicon, aluminum and iron at a ratio of 46:44:10. In the soil-rock-forming processes, including compactional solidification, water-stable illuviation-cementation t homogeneous overgrowth and so on, the loose soil-rock-forming components gradually changed into consolidated soil and further to the early stage of lithification. Meanwhile, from the analysis, we found that the ancient gravel stratum had been protected by the overlying Xiashu loess or basalt and the overloading resulted in overconsolidated strata. The modified CIPW method was applicable and effective for semi-quantitative analysis.

Basic Numerical Computational Using Scilab Programming

Mathematics is very important for the engineering and scientist but to make understand the mathematics is very difficult if without proper tools and suitable measurement. A numerical method is one of the algorithms which involved with computer programming. In this paper, Scilab is used to carter the problems related the mathematical models such as Matrices, operation with ODE＇s and solving the Integration.

Numerical analysis and geotechnical assessment of mine scale model

Various numerical methods are available to model,simulate,analyse and interpret the results;however a major task is to select a reliable and intended tool to perform a realistic assessment of any problem.For a model to be a representative of the realistic mining scenario,a verified tool must be chosen to perform an assessment of mine roof support requirement and address the geotechnical risks associated with longwall mining.The dependable tools provide a safe working environment,increased production,efficient management of resources and reduce environmental impacts of mining.Although various methods,for example,analytical,experimental and empirical are being adopted in mining,in recent days numerical tools are becoming popular due to the advancement in computer hardware and numerical methods.Empirical rules based on past experiences do provide a general guide,however due to the heterogeneous nature of mine geology(i.e.,none of the mine sites are identical),numerical simulations of mine site specific conditions would lend better insights into some underlying issues.The paper highlights the use of a continuum mechanics based tool in coal mining with a mine scale model.The continuum modelling can provide close to accurate stress fields and deformation.The paper describes the use of existing mine data to calibrate and validate the model parameters,which then are used to assess geotechnical issues related with installing a new high capacity longwall mine at the mine site.A variety of parameters,for example,chock convergences,caveability of overlying sandstones,abutment and vertical stresses have been estimated.

Boundary Value Problems for First Order Stochastic Differential Equations

In this paper,we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition(in the sense of expec- tation).Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value.Then by using the contraction mapping principle and Leray-Schauder fixed point theorem,we obtain the existence theorem.Finally,we explain our main results by an elementary example.

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.

H-stability of the Runge-Kutta methods with general variable stepsize for system of pantograph equations with two delay terms

This paper deals with H-stability of the Runge-Kutta methods with a general variable stepsize for the system of pantograph equations with two delay terms. It is shown that the Runge-Kutta methods with a regular matrix A are H-stable if and only if the modulus of the stability function at infinity is less than 1.

Homotopy Analysis Method for Solving Biological Population Model

In this paper,the homotopy analysis method (HAM) is applied to solve generalized biological populationmodels.The fractional derivatives are described by Caputo's sense.The method introduces a significant improvementin this field over existing techniques.Results obtained using the scheme presented here agree well with the analyticalsolutions and the numerical results presented in Ref.[6].However,the fundamental solutions of these equations stillexhibit useful scaling properties that make them attractive for applications.

Three-Dimensional Numerical Investigation of the Separation Process in a Vortex Tube at Different Operating Conditions

Air separators provide safe, clean, and appropriate air flow to engines and are widely used in vehicles with large engines such as ships and submarines. In this operational study, the separation process in a Ranque-Hilsch vortex tube cleaning （cooling） system is investigated to analyze the impact of the operating gas type on the vortex tube performance; the operating gases used are air, nitrogen, oxygen, carbon dioxide and nitrogen dioxide. The computational fluid dynamic model used is equipped with a three-dimensional structure, and the steady-state condition is applied during computations. The standard k-c turbulence model is employed to resolve nonlinear flow equations, and various key parameters, such as hot and cold exhaust thermal drops, and power separation rates, are described numerically. The results show that nitrogen dioxide creates the greatest separation power out of all gases tested, and the numerical results are validated by good agreement with available experimental data. In addition, a comparison is made between the use of two different boundary conditions, the pressure-far-field and the pressure-outlet, when analyzing complex turbulent flows in the air separators. Results present a comprehensive and practical solution for use in future numerical studies.

Dynamics and Thermodynamics of Porous HMX-like Material Under Shock

Strong shock may induce complex processes in porous materials. We use the newly developed materialpoint-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological characterization is used to treat with the temperature map. Via the Minkowski funetional analysis the dynamics and thermodynamics of the shock wave reaction on porous HMX-like material are studied. The geometrical and topological properties of the ＂hot-spots＂ are revealed. Numerical results indicate that, shocks in porous materials are not simple jump states as classically viewed, but rather are a complex sequence of compressions and rarefactions. They cover a broad spectrum of states. We can use coarse-grained description to the wave series. A threshold value of temperature presents a Turing pattern dynamical procedure. A higher porosity is generally preferred when the energetic material needs a higher temperature for initiation. The technique of data analysis can be used to other physical quantities, for example, density, particle velocity, some specific stress, etc. From a series of studies along the line, one may get a large quantity of information for desiring the fabrication of material and choosing shock strength according to what needed is scattered or connected ＂hot-spots＂. PACS numbers： 05.70.Ln, 05 Key words： porous material 70.-a, 05.40.-a, 62.50.Ef shock wave, Minkowski functionals