Multiscale modeling for ferroelectric materials: a transition from the atomic level to phase-field modeling

To link the atomic level and the mesoscale within a knowledge-based multiscale modeling approach for ferroelectric materials, a method is suggested to transfer results from first-principles calculations into a phase-field model. DFT calculations and atomistic simulations are applied and provide a set of intrinsic and extrinsic material properties for PbTiO₃ and tetragonal Pb(Zr_0.5Ti_0.5)O₃. The Helmholtz free energy of the phase-field model that contains all crystallographic and domain wall information is discussed in detail, and a sensitivity analysis is performed to identify the coefficients of the energy function. Then, a method is developed to adjust the coefficients of the Helmholtz free energy solely based on results from first-principles calculations. Full sets of adjusted energy coefficients for PbTiO₃ and Pb(Zr_0.5Ti_0.5)O₃ are presented and discussed, as well the limits of the suggested adjustment method.     

一般运动刚体角速度向量引入的一种新方法

通过向量运算给出了角速度向量引入的一种较简单的方法. 利用刚体上的固连向量的导数与其自身垂直的特点,得出反映刚体整体运动特性的角速度向量,并对这样的导出方法与刚体角速度向量物理意义之间的联系进行了讨论.     

The distribution function of atomic level populations in a plasma

An analytic form is obtained for the population distribution function in an atomic plasma as a series in successive time derivatives of the population of the first level. The first approximation includes the well-known method of a stationary sink. The quasistationary distribution obtained for hydrogen agrees well with numerical calculations of recombination and ionization, and for lithium, helium, and argon the quasistationary distribution gives qualitative agreement with numerical calculations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 18–26, July–August, 1972.We should like to thank B. F. Gordiets for a helpful discussion.     

Hierarchical motion planning at the acceleration level based on task priority matrix for space robot

Nonlinear Dynamics - A capacitive micromachined ultrasonic transducer (CMUT) due to many benefits is being considered as an imaging and therapeutic technology recently. The critical challenge is to...     

Two-dimensional approach to the motion of a red blood cell in a plane couette flow of plasma

In relation to microrheology of blood, a theoretical approach to the motion of a red blood cell in a plane Couette flow between two parallel plates is made with emphasis on effects of wall. The red blood cell is assumed to be an elliptic cylindrical particle with a thin, inextensible membrane moving like a tank-tread along its perimeter and to contain a Newtonian fluid inside. Fluid motions are analysed numerically both inside and outside the particle on the basis of the Stokes equations, using the finite element method.A quasi-static equilibrium condition leads to the solution for the motion of the particle. It is shown that two types of motion exist (a stationary orientation motion and a flipping motion), depending on the viscosity ratio of inner to outer fluid, the axis ratio of the elliptic cylinder and the ratio of particle size to channel width. The results are applied to capillary blood flow.     

一种引出一般运动刚体角速度概念的新方法

在刚体一般运动的教学中,角速度是学生接受起来比较困难的一个概念,通过矢量运算引入这一概念,为角速度的教学提供了一种新的简单方法.     

The transient motion of a dislocation in a solid of general anisotropy

The transient motion of a dislocation starting from rest and moving in an arbitrary rectilinear motion in an anisotropic solid is analyzed by transform techniques and inversion according to the Cagniard-de Hoop technique.     

A nilpotent algebra approach to Lagrangian mechanics and constrained motion

Lagrangian mechanics is extended to the so-called nilpotent Taylor algebra \({\mathbb {T}}\). It is shown that this extension yields a practical computational technique for the evaluation and analysis of the equations of motion of general constrained dynamical systems. The underlying \({\mathbb {T}}\)-algebra utilized herein permits the analysis of constrained dynamical systems without the need for analytical or symbolic differentiations. Instead, the algebra produces the necessary exact derivatives inherently through binary operations, thus permitting the numerical analysis of constrained dynamical systems using only the defining scalar functions (the Lagrangian \({\mathcal {L}}\) and the imposed constraints). The extension of the Lagrangian framework to the \({\mathbb {T}}\)-algebra is demonstrated analytically for a problem of constrained motion in a central field and numerically for the calculation of Lyapunov exponents of N-pendulum systems.     

Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion

In the presented paper, a problem of non-holonomic constrained mechanical systems is treated. New methods in non-holonomic mechanics are applied to a problem of a general coupled rolling motion. Two goals are stressed.The first of them lies in the solution of an originally formulated problem of rolling motion of two rigid cylindrical bodies in the homogeneous gravitational field leading typically to non-linear equations of motion. A solid cylinder can roll inside a ring under the static frictional force assuring rolling without slipping, the ring rolls again without slipping along a generally shaped terrain formed by hills and valleys. “Surprising behaviour” of the mechanical system which permits interesting applications is studied and discussed.The second purpose of the paper is to show that the geometrical theory of non-holonomic constrained systems on fibered manifolds proposed and developed in the last decade by Krupková and others is an effective tool for solving non-holonomic mechanical problems. A comparison of this method to alternative methods is given and the benefits of coordinate-free formulation are mentioned.In this paper, the geometrical theory is applied to the abovementioned mechanical problem. Both types of equations of motion resulting from the theory—deformed equations with the so-called Chetaev-type constraint forces containing Lagrange multipliers, and reduced equations free from multipliers—are found and discussed. Numerical solutions for two particular cases of the motion of the cylindrical system along a cylindrical surface are presented.     

Using the Dirac approach to model the motion of a railway vehicle when its wheel flange climbs the rail

A mathematical model is proposed to analytically estimate the derailment conditions for a railway vehicle when its wheel flange climbs the rail. The structural parameters of the railway vehicle and the conditions of its motion are taken into account. This model is based on the primary Dirac constraints between the generalized coordinates and momenta and is quite different from the classical no-slip model in the general case. The primary Dirac constraints appear because of the fact that the Lagrangian becomes degenerate when the stiffness of the creep forces tends to infinity at the wheel-rail contact points and the ratio of the wheelset mass to the vehicle mass tends to zero.     

Long time behavior for one-dimensional motion of a general barotropic viscous fluid

Communicated byJ. Serrin     

A multi level approach to synthesis of planar mechanisms

A multi level approach to synthesis of planar mechanisms is presented. The approach covers both structural and dimensional synthesis of planar rigid body mechanisms containing revolute and translational joints. The synthesis is based on four different criteria. Firstly the type of mechanism is chosen with a view to get the simplest mechanism that satisfactorily fulfills the remaining three criteria. Two of these criteria are formulated as constraints on the kinematic behavior and the total area occupied by the mechanism, respectively. The fourth criteria is simply the desired minimization of the reactive forces/moments that appear in the mechanism. The desired kinematic behavior is based on a finite number, typically 1, ..., 6, of points in time (positions of the mechanism) where the position and orientation of up to two output bodies may be prescribed. The constraints on occupied areas are labelled territory constraints and formulated as a number of restricted areas (boxes). A synthesis is automatically performed at five levels. At the first level the structure of the mechanism is decided. At the second level initial dimensions for the given type of mechanism are found by random checking. At the third level the constraints on the kinematic behavior is fulfilled. At the fourth level the territory constraints are taken into account and, finally, at the fifth level the minimization of reactions is carried out. The entire approach has been implemented in a software package SYNMEC that runs on PCs and constitutes a way of performing the synthesis of a mechanism that is general and flexible with respect to both the type of mechanism that may be synthesized as well as the desired behavior upon which the synthesis is based.     

Transient motion of a liquid in a fissured porous stratum subject to periodic pressure variation at the boundary

To determine the physical parameters in a fissured porous stratum, it is necessary to produce periodic pressure variations. This requirement is met by adjusting the rate of flow of liquid into a out of the well. A discussion is given concerning one-dimensional periodic motion of a homogeneous liquid with reference to parameter determination.     

Equations of motion for mechanical systems: A unified approach

This paper presents a unified framework from which emerge the Lagrange equations, the Gibbs-Appell Equations and the Generalized Inverse Equations for describing the motion of constrained mechanical systems. The unified approach extends the applicability of the first two approaches to systems where the constraints are non-linear functions of the generalized velocities and are not necessarily independent. Furthermore, the approach leads to the Explicit Gibbs-Appell Equations.     

单壁碳纳米管屈曲的原子/连续介质混合模型

用数学和力学研究所，上海 200072)//力学学报.--2004,36(6).--744～748 提供了一种运用原子/连续介质混合(hybrid atomic/continuum,HAC)方法解决纳米力学问题的思路. 通过在连续介质力学模型中引入利用分子力学方法获得物性参数，建立了预测单壁碳纳米管临界屈曲参数的HAC模型. 结果表明, HAC模型具有与连续介质力学模型可比拟的简洁性, 同时可表征纳米管微观结构特征对屈曲参数的影响. 计算结果表明，Zigzag纳米管的抗屈曲性能优于Armchair纳米管. 基于Tersoff-Brenner作用势的分子动力学结果证实了这一结论.     

Effective boundary conditions at a rough wall: a high-order homogenization approach

Meccanica - Effective boundary conditions, correct to third order in a small parameter $$epsilon$$ , are derived by homogenization theory for the motion of an incompressible fluid over a rough...