Lipschitz stability of impulsive systems of differential equations

In the present paper notions of Lipschitz stability of the zero solution of impulsive systems of differential equations with fixed moments of impulse effect arc introduced. Sufficient conditions for various types of uniform Lipschitz stability are obtained and the relations between these options are investigated The results obtained are used for the investigation of the uniform Lipschitz stability of the zero solution of linear impulsive systems of differential equations.     

动静圆柱坐标系下Navier-Stokes方程的分区算法

通过耦合相对和绝对圆柱坐标系下的三维Navier-Stokes方程,本文采用高精度高分辨率的三阶ENN格式及LU-SGS隐式解法进行子域求解;提出了动静子域干涉面的重合处理与重叠处理,并最终发展了一种新的分区算法。通过对某带进口导叶的三级轴流压气机的数值实验,验证了该分区算法的有效性,计算结果与实验数据吻合较好。     

Accurate analysis of power coupling between two arbitrarily ended dielectric slab waveguides by the boundary-element method

The boundary integral equations that are called guided-mode extracted integral equations are applied to the investigation of the power-coupling-properties between two arbitrarily ended dielectric slab waveguides. The integral equations derived in this paper can be solved by the conventional boundary-element method. The reflection and coupling coefficients of the guided wave, as well as the scattering power, are calculated numerically for the case of incident TE guided-mode waves. The results presented are checked by the energy conservation law and the reciprocity theorem. Numerical results are presented for several geometries of coupling, including systems with three-layered symmetrical and asymmetrical slab waveguides.     

Decoupling joint and elastic accelerations in deformable mechanical systems using non‐linear recursive formulations

The aim of this paper is to develop non‐linear recursive formulations for decoupling joint and elastic accelerations, while maintaining the non‐linear inertia coupling between rigid body motion and elastic deformation in deformable mechanical systems. The inertia projection schemes used in most existing recursive formulations for the dynamic analysis of deformable mechanisms lead to dense coefficient matrices in the equations of motion. Consequently, there are strong dynamic couplings between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the equations of motion becomes large. Consequently, the use of these recursive formulations for solving the joint and elastic accelerations becomes less efficient. In this paper, the non‐linear recursive formulations have been used to decouple the elastic and joint accelerations in deformable mechanical systems. The relationships between the absolute, elastic and joint variables and generalized Newton–Euler equations are used to develop systems of loosely coupled equations that have sparse matrix structure. By using the inertia matrix structure of deformable mechanical systems and the fact that joint reaction forces associated with elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent of the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as for the joint reaction forces. The use of the approaches developed in this investigation is illustrated using deformable open‐loop serial robot and closed‐loop four‐bar mechanical systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Potential systems for PDEs having several conservation laws

A generalization of the usual procedure for constructing potential systems for systems of partial differential equations with multidimensional spaces of conservation laws is considered. More precisely, for the construction of potential systems with a multi-dimensional space of local conservation laws, instead of using only basis conservation laws, their arbitrary linear combinations are used that are inequivalent with respect to the equivalence group of the class of systems or symmetry group of the fixed system. It appears that the basis conservation laws can be equivalent with respect to groups of symmetry or equivalence transformations, or vice versa; in this sense the number of independent linear combinations of conservation laws can be grater than the dimension of the space of conservation laws. The first possibility leads to an unnecessary, often cumbersome, investigation of equivalent systems, the second one makes possible that a great number of inequivalent potential systems are missed. Examples of all these possibilities are given.     

Equations in stresses for the three-, two-, and one- dimensional dynamic problems of thermoelasticity

Source systems of differential equations for the six components of the tensor of dynamic stresses are presented in Cartesian and cylindrical coordinates by using the equations of motion, Hooke’s law, Cauchy formulas, and the Saint-Venant compatibility conditions for strains. Without introducing auxiliary potential functions, these systems of interrelated equations are reduced to systems of hierarchically connected wave equations for the key function, i.e., the first invariant and unknown components of the stress tensor. We also present the systems of key equations for the solution of two-dimensional dynamic problems in stresses (the plane problem in Cartesian coordinates and the plane and axially symmetric problems in cylindrical coordinates) and the wave equations for the one-dimensional problems of evaluation of the normal and tangential components of stresses in the same coordinate systems. This enables us to use standard methods of mathematical physics for the solution of the equations obtained as a result. If, in the quasistatic problem, the influence of temperature and bulk forces is absent, then the proposed equations coincide with the equations known from the literature. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 2, pp. 20–26, March-April, 2000.     

Computational schemes for non‐linear elasto‐dynamics

This paper deals with the development of computational schemes for the dynamic analysis of non‐linear elastic systems. The focus of the investigation is on the derivation of unconditionally stable time‐integration schemes presenting high‐frequency numerical dissipation for these types of problem. At first, schemes based on Galerkin and time‐discontinuous Galerkin approximations applied to the equations of motion written in the symmetric hyperbolic form are proposed. Though useful, these schemes require casting the equations of motion in the symmetric hyperbolic form, which is not always possible. Furthermore, this approaches to unacceptably high computational costs. Next, unconditionally stable schemes are proposed that do not rely on the symmetric hyperbolic form. Both energy‐preserving and energy‐decaying schemes are derived. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed schemes. Copyright © 1999 John Wiley & Sons, Ltd.     

The numerical solution of radiative heat transfer for grey bodies in an absorbing medium

A new approximate analytical method for solving the integral radiation equations [1, 2] is used for the numerical calculation and investigation of the local and average characteristics of radiative heat transfer in systems of grey bodies separated by an isothermal absorbing medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 3, pp 520–525, September, 1969.     

Use of incomplete decomposition of the coefficient matrix in solving linear equations

Matrix incomplete decompositions are widely and successfully used in iterative methods for solving systems of linear equations. We have found that one can also solve systems of linear equations directly by using an incomplete LU decomposition of the coefficient matrix. In some special cases, the proposed method not only leads to great savings in storage space but also improves the computational efficiency; for example, when solving large systems of linear equations with banded shifted coefficient matrices. Some interesting tested subroutines are also given.     

Linear systems with polynomials of filtered Poisson processes

Moment equations are calculated exactly for the response of linear systems subjected polynomials of filtered Poisson processes. The Itô formula for stochastic differential equations driven by Poisson white noise is applied to derive moment equations. It is shown that the set of moment equations is closed. The proposed method is used to calculate moments up to the fourth order for the response of two linear systems subjected to quadratic forms of filtered Poisson processes. Results by Monte Carlo simulations are also presented for comparison.     

Electrical Properties and Kinetics of Electrode Reactions

A common basis for investigations of the properties of electrode reactions is provided. The basic equations of electrostatics and electrodynamics and the assumption that electrode reactions are relaxation processes, are used to develop the equations for the electrical behavior of electrode systems. Thus electrode reaction processes are characterized as two states separated by an energy barrier. The application of static and alternating fields to electrode systems is interpreted in terms of the kinetic parameters of the electrode reactions. The equations for impedance are applied to silver and cadium electrode systems reported in the literature. The agreement of experiment and theoretical expectation is excellent. The equations are also applied to the interpretation of the impedance of LeClanché cells. The kinetic analysis of a simple unimolecular reaction is used to illustrate the kinetic interpretation of experimental information. This simple analysis may be extended to more complex reactions.     

Application of an analog of the δc-model to the analysis of strength of elastoplastic cracked shellsto the analysis of strength of elastoplastic cracked shells

We propose a method for the investigation of the limiting equilibrium of elastoplastic shells with systems of interacting cracks. It can be described as follows: By using an analog of the δ_c-model, the elastoplastic problem is reduced to an elastic problem of the limiting equilibrium of a shell with cracks of unknown length whose lips are subjected to the action of unknown forces and moments satisfying the conditions of plasticity for thin shells. By using equations of the general moment theory of shells and the theory of generalized functions, we reduce the problem to the solution of a system of singular integral equations with unknown limits of integration and singular right-hand sides. We construct an algorithm for the numerical solution of systems of this sort supplemented by the conditions of boundedness of stresses and conditions of plasticity. We investigate crack tip opening displacements in a closed cylindrical shell with a regular system of longitudinal cracks or two transverse cracks. For a cylindrical shell with a single crack, we present an approximate relation for the determination of the critical load or crack length. Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 5–15, May–June, 1996.     

The generalized scaling laws based on some deductions from the van der Waals equation

Some thermodynamic relations that follow from the van der Waals equation are considered. It is shown that they are applicable to real substances and model systems described by absolutely different equations of state. These relations are associated with definite geometric lines on the density–temperature plane. The data for the model systems that substantiate the derived regularities were calculated by numerical simulation methods. For real substances, the relevant databases constructed according to experiments were used. It has also been established by numerical simulation that the limitations of the regularities under investigation are related to the nature of attraction in the interparticle interaction potential.     

Energy and exergy analysis of single effect and series flow double effect water–lithium bromide absorption refrigeration systems

In this paper, the energy and exergy analysis of single effect and series flow double effect water–lithium bromide absorption systems is presented. A computational model has been developed for the parametric investigation of these systems. Newly developed computationally efficient property equations of water–lithium bromide solution have been used in the computer code. The analysis involves the determination of effects of generator, absorber and evaporator temperatures on the energetic and exergetic performance of these systems. The effects of pressure drop between evaporator and absorber, and effectiveness of heat exchangers are also investigated. The performance parameters computed are coefficient of performance, exergy destruction, efficiency defects and exergetic efficiency. The results indicate that coefficient of performance of the single effect system lies in range of 0.6–0.75 and the corresponding value of coefficient of performance for the series flow double effect system lies in the range of 1–1.28. The effect of parameters such as temperature difference between heat source and generator and evaporator and cold room have also been investigated. Irreversibility is highest in the absorber in both systems when compared to other system components.     

Characteristic function equations for the state of dynamic systems with Gaussian, Poisson, and Lévy white noise

The Itô formula for semimartingales is applied to develop equations for the characteristic function of the state of linear and non-linear dynamic systems with Gaussian, Poisson, and Lévy white noise, viewed as the formal derivatives of Brownian, compound Poisson, and Lévy processes, respectively. These equations can be obtained if the drift and diffusion coefficient of a dynamic system are polynomials of the system state and the driving noise is Gaussian or Poisson. It was not possible to derive equations for the characteristic function for the state of systems driven by Lévy white noise. Numerical results are presented for dynamic systems with real-valued states driven by Gaussian, Poisson, and Lévy white noise processes.     

Hamiltonian direct differentiation and adjoint approaches for multibody system sensitivity analysis

The design of multibody systems involves high fidelity and reliable techniques and formulations that should help the analyst to make reasonable decisions. Given that constrained equations of motion for the simplest of multibody systems are highly nonlinear, determining the sensitivity terms is a computationally intensive and complex process that requires the application of special procedures. In this article, two novel Hamiltonian-based approaches are presented for efficient sensitivity analysis of general multibody systems. The developed direct differentiation and the adjoint methods are based on constrained Hamilton's canonical equations of motion. This formulation provides solutions, which are more stable as compared to the results of direct integration of equations of motion expressed in terms of accelerations due to a reduced differential index of the underlying system of differential-algebraic equations and explicit constraint imposition at the velocity level.The proposed Hamiltonian based methods are both capable of calculating the sensitivity derivatives and keeping the growth of constraint violation errors at a reasonable rate. The Hamiltonian-based procedures derived herein appear to be good alternatives to existing methods for sensitivity analysis of general multibody systems.     

A simple set of equations of state for process calculations and its application to R134a and R152a

This paper reports a useful set of equations which enables the consistent and reliable calculation of thermodynamic properties. This set of equations consists of a vapour pressure equation, an equation for the gas phase p, v, T properties, an equation giving the saturated liquid densities and an equation for the specific heat capacity in the ideal gas domain. These equations are of a simple structure because the critical region is excluded. Therefore, for a preliminary investigation only few experimental data points are required for parameter regression, which makes this set of equations suitable for ‘new’ refrigerants. The relationships for enthalpy and entropy are derived from these equations and evaluation procedures are summarized. Examples are given for the refrigerants R134a and R152a.     

Analysis of a class of nonconservative systems reducible to pseudoconservative ones and their energy relations

This paper analyzes a class of nonconservative systems, whose Lagrangian equations can be reduced to Euler–Lagrangian equations by introducing a new Lagrangian, which is equal to a product of some function of time f(t) and the primary Lagrangian. These equations formally have the same form as for the systems with potential forces, while the influence of nonconservative forces is contained in the factor f(t), and such systems are called pseudoconservative. It is further shown that the requirement for a nonconservative system to be considered as a pseudoconservative is the existence of at least one particular solution of a system of differential equations with unknown function f(t), or their linear combination with suitably chosen multipliers. Further on, the energy relations and corresponding conservation laws of those systems are analyzed from two aspects: directly, on the basis of the corresponding Lagrangian equations and via modified Emmy Noether’s theorem. So, it has been shown, even in two different ways, that there are two types of the integrals of motion, in the form of the product of an exponential factor and the sum of the generalized energy (energy function) and an additional term. For the existence of these integrals of motion, it is necessary and sufficient that there exists at least one particular solution of a partial differential equation, which is in accordance with the Lagrangian equations for the observed problem. The obtained results are equivalent to so-called energy-like conservation laws, obtained via Vujanovi?-Djuki?’s generalized Noether’s theorem for nonconservative systems (Vujanovi? and Jones in: Variational Methods in Nonconservative Phenomena (monograph). Acad. Press, Boston, 1989).     

Averaging method and long-wave asymptotics in vibrational convection in layers with an interface

A scheme for applying an averaging method to the problem of convection in a two-layer system with an interface under the influence of high-frequency vibration is proposed. The derivation of the averaging equations is given, and the stability of the equilibrium of the averaged problem is considered. Long-wavelength asymptotics of steady and oscillatory instability are constructed. The results of numerical calculations for acetonitrile?Cn-hexane and silicone oil?Cfluorinert systems are given. The directions in which the investigation of thermovibrational convection in problems with free surfaces and interfaces can be continued, are indicated.