One-velocity model of a heterogeneous medium with a hyperbolic adiabatic kernel

The one-velocity model equations for a heterogeneous medium are presented that take into account the internal forces of interfractional interactions and heat and mass exchange. The shock adiabat obtained for the mixture agrees with the one-velocity model equations. For one-dimensional unsteady adiabatic flows, the characteristic equations are found and relations along characteristic directions are determined. It is shown that the model equations with allowance for interfractional interaction forces are hyperbolic. Several finite-difference and finite-volume schemes designed for integrating the model equations are discussed.     

A large-eddy-based lattice Boltzmann model for turbulent flow simulation

In this paper a novel and simple large-eddy-based lattice Boltzmann model is proposed to simulate two-dimensional turbulence. Unlike existing lattice Boltzmann models for turbulent flow simulation, which were based on primitive-variables Navier–Stokes equations, the target macroscopic equations of the present model are vorticity-streamfunction equations. Thanks to the intrinsic features of vorticity-streamfunction equations, the present model is efficient, stable and simple for two-dimensional turbulence simulation. The advantages of the present model are validated by numerical experiments.     

On a new 3D model for incompressible euler and navier-stokes equations

In this paper, we investigate some new properties of the incompressible Euler and Navier-Stokes equations by studying a 3D model for axisymmetric 3D incompressible Euler and Navier-Stokes equations with swirl. The 3D model is derived by reformulating the axisymmetric 3D incompressible Euler and Navier-Stokes equations and then neglecting the convection term of the resulting equations. Some properties of this 3D model are reviewed. Finally, some potential features of the incompressible Euler and Navier-Stokes equations such as the stabilizing effect of the convection are presented.     

一个药物作用肿瘤生长自由边界问题整体解的存在唯一性

该文研究一个描述药物作用下肿瘤生长的数学模型,这个肿瘤模型是对Jackson模型的一个改进,其数学形式是由一个二阶非线性抛物型方程与两个一阶非线性偏微分方程组耦合而成的自由边界问题.通过运用抛物型方程的L~P理论与一阶偏微分方程的特征方法,并利用Banach不动点定理,证明了该问题存在唯一的整体经典解.     

Parameter estimation in moving boundary problems

We describe an approximation scheme which can be used to estimate unknown parameters in moving boundary problems. The model equations we consider are fairly general nonlinear diffusion/reaction equations of one spatial variable. Here we give conditions on the parameter sets and model equations under which we can prove that the estimates obtained using the approximations will converge to best-fit parameters for the original model equations. We conclude with a numerical example.     

高温作用下混凝土热-水-力耦合损伤分析模型

以混合物理论为基础建立了高温作用下混凝土的热-水-力耦合损伤分析模型．将混凝土视为由固体骨架、液态水、水蒸气、干燥气体和溶解气体共5种组分构成的混合物,模型的宏观平衡方程包括各组分的质量守恒方程、整体的能量守恒方程及动量守恒方程,模型所需的状态方程及本构关系全部给出,最后给出基于4个主要参数（固体骨架位移、气压力、毛细压力和温度）的控制方程．模型考虑了混凝土在高温作用下,水分的蒸发与冷凝、胶结材料的水化及脱水、溶解气的溶解与挥发等相变过程;从材料变形破坏过程中能量耗散特征入手,基于Lemaitre应变等价性假说和能量守恒原理得到力学损伤演化方程,并考虑了高温引起的热损伤对材料力学性能及力学损伤演化规律的影响,建立了热-力耦合损伤本构模型．     

An existence result for elliptic partial differential-algebraic equations arising in semiconductor modeling

We consider a system of partial differential-algebraic equations which model an electric network containing semiconductor devices. The zero-dimensional differential-algebraic network equations are coupled with multi-dimensional elliptic partial differential equations which model the devices. For this coupled system we prove an existence result.     

On Some Model Equations of Euler and Navier-Stokes Equations

The author proposes a two-dimensional generalization of Constantin-Lax-Majda model. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line(vorticity formulation), the author presents some further model equations. He possibly models various aspects of difficulties related with the singular solutions of the Euler and Navier-Stokes equations. Some discussions on the possible connection between tur...     

Efficient stochastic model for the point kinetics equations

A new stochastic model for the point kinetics equations with I-delayed neutron precursor groups is presented. In this stochastic model, the point kinetics equations are separated into three terms: prompt neutrons, delayed neutrons and external neutrons source. The matrix form of the efficient stochastic model is solved by a semi-analytical method. The semi-analytical method is based on the exponential function of the coefficient matrix. The eigenvalues of the coefficient matrix and Gaussian elimination are used to calculate this exponential function. The mean and standard deviation of neutron and precursor populations of the efficient stochastic model with step, ramp, and sinusoidal reactivities are computed. The results of the efficient stochastic model are compared with the results of Allen's stochastic model for the point kinetics equations. This comparison confirms that the efficient stochastic model is an accurate model compared with the deterministic point kinetics equations. This stochastic model is efficient to study the natural behavior of neutron and precursor populations in the nuclear reactor dynamics.     

Fluid dynamics and thermodynamics as a unified field theory

We study the problem of consistency of equations of continuum dynamics (using the Euler equations and the continuity equation as examples) and thermodynamic equations of state (for the specific free energy, entropy, and volume). We propose a variant of the Hamiltonian formulation of a model that combines the fluid dynamics of a potential flow of a compressible fluid or gas and local equilibrium thermodynamics into a unified field theory. Thermodynamic equations of state appear in this model as second-class constraint equations. As a consistency condition, there arises another second-class constraint requiring that the product of density and temperature should be independent of time. The model provides an in-principle possibility of finding the time dependence of the specific entropy of the arising dynamical system.     

A nonlinear truck model and its treatment as a multibody system

A planar vertical truck model with nonlinear suspension and its multibody system formulation are presented. The equations of motion of the model form a system of differential-algebraic equations (DAEs). All equations are given explicitly, including a complete set of parameter values, consistent initial values, and a sample road excitation. Thus the truck model allows various investigations of the specific DAE effects and represents a test problem for algorithms in control theory, mechanics of multibody systems, and numerical analysis. Several numerical tests show the properties of the model.     

Model Equations for Gravity-Capillary Waves in Deep Water

The Euler equations for water waves in any depth have been shown to have solitary wave solutions when the effect of surface tension is included. This paper proposes three quadratic model equations for these types of waves in infinite depth with a two-dimensional fluid domain. One model is derived directly from the Euler equations. Two further simpler models are proposed, both having the full gravity-capillary dispersion relation, but preserving exactly either a quadratic energy or a momentum. Solitary wavepacket waves are calculated for each model. Each model supports the elevation and depression waves known to exist in the Euler equations. The stability of these waves is discussed, as is the dynamics resulting from instabilities and solitary wave collisions.     

Numerical resolution for a compressible two-phase flow model based on the theory of thermodynamically compatible systems

This paper is concerned with the numerical solution of the equations governing two-phase gas-solid mixture in the framework of thermodynamically compatible systems theory. The equations constitute a non-homogeneous system of nonlinear hyperbolic conservation laws. A total variation diminishing (TVD) slope limiter centre (SLIC) numerical scheme, based on the splitting approach, is presented and applied for the solution of the initial-boundary value problem for the equations. The model equations and the numerical methods are systematically assessed through a series of numerical test cases. Strong numerical evidence shows that the model and the methods are accurate, robust and conservative. The model correctly describes the formations of shocks and rarefactions in two-phase gas-solid flow.     

Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach

We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset.     

Derivation of an adjoint high-Reynolds number model for thermally driven flows

This paper presents a high-Reynolds number (high-Re) approach to the adjoint Navier-Stokes-Fourier equations based upon modified high-Re boundary conditions for buoyancy-driven flows. For reasons of efficiency, the computational framework adheres to the continuous adjoint method using a frozen-turbulence assumption. Opposed to the state of the art, the present model uses a high-Re model for the primal equations and a high-Re model for the adjoint equations. The adjoint high-Re model can easily be implemented and be used for flow problems where wall functions are needed. The impact of this approach is an improved consistency of primal and adjoint equations which leads to stable and realistic shape optimisation results for industrial flows. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A complete steady state model of solute and water transport in the kidney

The purpose of this paper is to incorporate a detailed model, along with an optimized set of parameters for the proximal tubule, into J. L. Stephenson's current central core model of the nephron. In this model a set of equations for the proximal tubule are combined with Stephenson's equations for the remaining four tubules and interstitium, to form a complete nonlinear system of 34 ordinary differential and algebraic equations governing fluid and solute flow in the kidney. These equations are then discretized by the Crank-Nicholson scheme to form an algebraic system of nonlinear equations for the unknown concentrations, flows, hydrostatic pressure, and potentials. The resulting system is solved via factored secant update with a finite-difference approximation to the Jacobian. Finally, numerical simulations performed on the model showed that the modeled behavior approximates, in a general way, the physiological mechanisms of solvent and solute flow in the kidney.     

Traveling waves in excitable media

We consider a two-component reaction-diffusion model that describes the oxygenation of CO molecules on the surface of platinum in the one-dimensional case. The partial differential equations of the model are reduced to a system of ordinary differential equations. We show that the system of partial differential equations with fixed parameter values has a family of autowave solutions running along the spatial axis at various velocities. These solutions are described by some singular attractors and limit cycles of the corresponding period in the system of ordinary differential equations.     

Model-based control strategies for systems with constraints of the program type

The paper presents a model-based tracking control strategy for constrained mechanical systems. Constraints we consider can be material and non-material ones referred to as program constraints. The program constraint equations represent tasks put upon system motions and they can be differential equations of orders higher than one or two, and be non-integrable. The tracking control strategy relies upon two dynamic models: a reference model, which is a dynamic model of a system with arbitrary order differential constraints and a dynamic control model. The reference model serves as a motion planner, which generates inputs to the dynamic control model. It is based upon a generalized program motion equations (GPME) method. The method enables to combine material and program constraints and merge them both into the motion equations. Lagrange’s equations with multipliers are the peculiar case of the GPME, since they can be applied to systems with constraints of first orders. Our tracking strategy referred to as a model reference program motion tracking control strategy enables tracking of any program motion predefined by the program constraints. It extends the “trajectory tracking” to the “program motion tracking”. We also demonstrate that our tracking strategy can be extended to a hybrid program motion/force tracking.     

Modelling of closed-chain manipulators on an excavator vehicle

The main focus of this paper is to develop a physics-based model for a closed-chain manipulator in an excavator vehicle. The derivation of closed-chain manipulator dynamic equations with a structure similar to open-chain manipulator equations is an important research problem, particularly with reference to controller design. In this paper, an approach for deriving closed-chain manipulator equations with an open-chain structure, based on trigonometric t-formulae, is presented. Holonomic loop closure constraints are employed in order to derive the closed-chain mechanism dynamics from the reduced system dynamics. The closed-chain equations, with a structure similar to serial link equations, are presented. The model incorporates the dynamic properties of the manipulator and bucket. The dynamic model for the excavation system is validated against measured data obtained from a full-scale closed-chain excavator vehicle. A dynamic model is important for the design of control strategies for trajectory tracking, a key requirement for automating the excavation task. It is noted that even though the results presented in this paper are focused on a particular excavator vehicle, the research is generic and can be adapted to any closed-chain manipulator.     

基于卷积神经网络模型数值求解双曲型偏微分方程的研究

人工神经网络近年来得到了快速发展,将此方法应用于数值求解偏微分方程是学者们关注的热点问题.相比于传统方法其具有应用范围广泛(即同一种模型可用于求解多种类型方程)、网格剖分条件要求低等优势,并且能够利用训练好的模型直接计算区域中任意点的数值.该文基于卷积神经网络模型,对传统有限体积法格式中的权重系数进行优化,以得到在粗粒...