CABARET scheme in vorticity-velocity variables for the numerical modeling of ideal fluid motion in a two-dimensional domain

A modification of the CABARET scheme is proposed for the numerical solution of equations of ideal fluid motion in vorticity-velocity variables. The dissipative and dispersive properties of the obtained numerical algorithm were investigated for the problem of an isolated vortex. Calculations were performed for decaying homogeneous isotropic turbulence on grids of varying density. In all investigated grids, the spectral density of the kinetic energy was found to obey the ??-3?? law, which conforms to the Kraichnan-Batchelor theory. The structural functions of the obtained vortex flow conform to the law derived using the dimension theory.     

CABARET scheme’s modification ensuring its high accuracy on local extrema

It is demonstrated that the standard flow-variables’ correction required for the monotonicity of the CABARET scheme reduces its accuracy near local extrema. A modified correction of the flows is proposed; it retains the strong monotonicity of the CABARET scheme for Courant numbers r ∈ (0,0.5], and thus ensures its high accuracy near local extrema. The results of the test computations of discontinuous solutions of a nonlinear transport equation are presented; these results illustrate the advantages of the modified scheme.     

On the powerof second-order accurate numerical methods for model problems of gas- and hydrodynamics

The paper provides an overview on the use of high-resolution methods based on the CABARET scheme. The results are provided for several test problems including gas dynamics, computational aeroacoustics, and geophysical fluid dynamics for a classical double-gyre quasi-geostrophic model of ocean dynamics.     

CABARET: rule interpretation in a hybrid architecture

Rules often contain terms that are ambiguous, poorly defined or not defined at all. In order to interpret and apply rules containing such terms, appeal must be made to their previous constructions, as in the interpretation of legal statutes through relevant legal cases. We describe a system CABARET (CAse-BAsed REasoning Tool) that provides a domain-independent shell that integrates reasoning with rules and reasoning with previous cases in order to apply rules containing ill-defined terms. The integration of these two reasoning paradigms is performed via a collection of control heuristics, which suggest how to interleave case-based methods and rule-based methods to construct an argument to support a particular interpretation. CABARET is currently instantiated with cases and rules from an area of income tax law, the so-called “home office deduction”. An example of CABARET's processing of an actual tax case is provided in some detail. The advantages of CABARET's hybrid approach to interpretation stem from the synergy derived from interleaving case-based and rule-based tasks.     

Direct modeling of the interaction between vortex pairs

This work is devoted to the numerical modeling of the conjugate problem on the dynamics of two vortex pairs and calculation of the acoustic field generation at Reynolds numbers Re = 5000–10 000 on a fixed Eulerian grid. The computation was based on the CABARET scheme. For the main characteristics of integrated solutions, such as the slip period of vortex pairs and the velocity of their center of mass, a comparison is presented with the analytical solution obtained for the case of point vortices in an ideal fluid. The sensitivity of the obtained numerical solutions to the grid refinement was studied including both the hydrodynamic near field and instantaneous and root-mean-square acoustic pulsations.     

Arguments and cases: An inevitable intertwining

We discuss several aspects of legal arguments, primarily arguments about the meaning of statutes. First, we discuss how the requirements of argument guide the specification and selection of supporting cases and how an existing case base influences argument formation. Second, we present,our evolving taxonomy of patterns of actual legal argument. This taxonomy builds upon our much earlier work on argument moves and also on our more recent analysis of how cases are used to support arguments for the interpretation of legal statutes. Third, we show how the theory of argument used by CABARET, a hybrid case-based/rule-based reasoner, can support many of the argument patterns in our taxonomy.This work was supported in part by the National Science Foundation, contract IRI-890841, the Air Force Office of Sponsored Research under contract 90-0359, the Office of Naval Research under a University Research Initiative Grant, contract N00014-87-K-0238, and a grant from GTE Laboratories, Inc., Waltham, Mass.     

The IKBALS project: Multi-modal reasoning in legal knowledge based systems

In attempting to build intelligent litigation support tools, we have moved beyond first generation, production rule legal expert systems. Our work integrates rule based and case based reasoning with intelligent information retrieval.When using the case based reasoning methodology, or in our case the specialisation of case based retrieval, we need to be aware of how to retrieve relevant experience. Our research, in the legal domain, specifies an approach to the retrieval problem which relies heavily on an extended object oriented/rule based system architecture that is supplemented with causal background information. We use a distributed agent architecture to help support the reasoning process of lawyers.Our approach to integrating rule based reasoning, case based reasoning and case based retrieval is contrasted to the CABARET and PROLEXS architectures which rely on a centralised blackboard architecture. We discuss in detail how our various cooperating agents interact, and provide examples of the system at work. The IKBALS system uses a specialised induction algorithm to induce rules from cases. These rules are then used as indices during the case based retrieval process.Because we aim to build legal support tools which can be modified to suit various domains rather than single purpose legal expert systems, we focus on principles behind developing legal knowledge based systems. The original domain chosen was theAccident Compensation Act 1989 (Victoria, Australia), which relates to the provision of benefits for employees injured at work. For various reasons, which are indicated in the paper, we changed our domain to that ofCredit Act 1984 (Victoria, Australia). This Act regulates the provision of loans by financial institutions.The rule based part of our system which provides advice on the Credit Act has been commercially developed in conjunction with a legal firm. We indicate how this work has lead to the development of a methodology for constructing rule based legal knowledge based systems. We explain the process of integrating this existing commercial rule based system with the case base reasoning and retrieval architecture.     

Nonminimal Kane's Equations of Motion for Multibody Dynamical Systems Subject to Nonlinear Nonholonomic Constraints

Nonholonomic constraint equations that are nonlinear in velocities are incorporated with Kane's dynamical equations by utilizing the acceleration form of constraints, resulting in Kane's nonminimal equations of motion, i.e. the equations that involve the full set of generalized accelerations. Together with the kinematical differential equations, these equations form a state-space model that is full-order, separated in the derivatives of the states, and involves no Lagrange multipliers. The method is illustrated by using it to obtain nonminimal equations of motion for the classical Appell–Hamel problem when the constraints are modeled as nonlinear in the velocities. It is shown that this fictitious nonlinearity has a predominant effect on the numerical stability of the dynamical equations, and hence it is possible to use it for improving the accuracy of simulations. Another issue is the dynamics of constraint violations caused by integration errors due to enforcing a differentiated form of the constraint equations. To solve this problem, the acceleration form of the constraint equations is augmented with constraint stabilization terms before using it with the dynamical equations. The procedure is illustrated by stabilizing the constraint equations for a holonomically constrained particle in the gravitational field.     

Dynamic equations in descriptor form

This paper studies a general form of sets of equations that is often the product of problem formulation in large-scale systems, especially when the equations are expressed in terms of the natural describing variables of the system. Such equations represent a broad class of time-evolutionary phenomena, and include as special cases ordinary static equations of arbitrary dimension, ordinary state-space equations, combinations of static and dynamic equations, and noncausal systems. The main thrust of the paper is to show (for sets of linear equations) that familiar concepts of dynamic system theory can be extended to this more general class, although sometimes with significant modification. Two new (and essentially dual) concepts, that of solvable and conditionable sets of equations, are found to be fundamental to the study of equations of this form. The notion of initial conditions, although not directly related to a state, is used as a general solution method for equations of this type. In addition a set of necessary and sufficient conditions for a set of dynamic equations to contain an embedded state-space representation is derived.     

On the modelling of actuator dynamics and the computation of prescribed trajectories

The dynamics of actuator mechanisms is presented using a multibody modelling approach to concisely express the structure of the system equations. The Lagrange equations are used to obtain the Newton–Euler equations to which constraint equations are augmented to form a system of differential algebraic equations. The differential algebraic equations are cast as ordinary differential equations and computed using the numerical integrator LSODAR of Petzold and Hindmarsh. Constraint compliance is investigated to ensure the accuracy of the results. Animation of an excavator and wheel loader system is presented and graphs of constraint forces show the nature of the actuator dynamics involved in maintaining specified bucket trajectories. The model is general in nature and caters for arbitrary mechanism connectivity and physical properties.     

Nonlinear generalized equations of motion for multi-link inverted pendulum systems

In this paper, the equations of motion for a general multi-link inverted pendulum system are derived. Assumptions previously employed to simplify such formulation are removed. The pendulum system is more general and includes nonlinear friction terms to suit various engineering applications. The generalized equations are first developed in the absolute coordinate system using Lagrange's technique, then a simple linear transformation is proposed to obtain the set of nonlinear equations in the DevanitHartenberg coordinate system. The equations of motion for double and triple link inverted pendulum systems are given as examples for such dynamics equations.     

粒子群算法在求解方程组中的应用

提出了采用粒子群算法求解线性方程组和非线性方程组的智能算法。采用粒子群算法求解方程组具有形式简单、收敛迅速和容易理解等特点,且能在一次计算中多次发现方程组的解,可以解决非线性方程组多解的求解问题,为线性方程组和非线性方程组的求解提供了一种新的方法。     

Boundary value problems for a class of impulsive functional equations

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differential equations with maximum and integro-differential equations. In this paper, we also prove that the Lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval. The corresponding results are established for the impulsive case. The general formulation includes several types of functional dependence (delay equations, equations with maxima, integro-differential equations). Finally, we consider the case of functional dependence which is given by nonincreasing and bounded functions.     

Finite-difference solution of the incompressible three-dimensional boundary layer equations for a blunt body

The governing equations for a laminar flow are solved in terms of an orthogonal surface coordinate system. One of the coordinate is determined by the intersection with the body surface of meridional planes which pass through an axis containing the stagnation point. The other coordinate is obtained numerically from the orthogonality condition. The momentum equations have been written in a standard from which allows additional equations of this form to be added with a small modification of the computer code. This equation is replaced with a nonlinear finite-difference equation which is solved as an iterative solution of linear tridiagonal equations. The special form of the governing equations at the stagnation point and the plane of symmetry is determined and the solution of these equations is obtained to provide a unified code. Numerical solutions have been obtained for several special cases and compared to results of other authors. New results are presented for an ellipsoid ar angle of attack and an elliptic-paraboloid at zero incidence.     

Singularities in motion and displacement functions for a 7 degree-of-freedom manipulator

The authors propose a method for the determination of singularities in motion and displacement functions for a seven degree-of-freedom manipulator. The manipulator is considered, hereby, as a set of six degree-of-freedom manipulators. It is proven that two types of singularities in motion can occur at link positions that are independent and dependent with respect to the trajectory to be executed. The relations between the structure of singularity equations and displacement equations are discussed. The derivation of displacement equations for a manipulator with singularities of the second type is based on the idea of modeling of a manipulator by two open kinematic chains and invariants that may be found for these chains. The inverse kinematic equations and the equations of singularities in motion have been derived using a symbolic computer program which can handle manipulators of general structure (with five, six, and seven degrees-of-freedom). This program is written in the Symbolic Computation Language REDUCE.     

An efficient algorithm for computation of manipulator inertia matrix

In this article an efficient algorithm for computation of the manipulator inertia matrix is presented. The algorithm is derived based on Newton's and Euler's laws governing the motion of rigid bodies. Using spatial notations, the algorithm leads to the definition of the composite rigid-body spatial inertia which is a spatial representation of the notion of augmented body. The equations resulting from this algorithm are derived in a coordinate-free form. The choice of the coordinate frame for projection of the coordinate-free equations, that is, the intrinsic equations, is discussed by analyzing the vectors and the tensors involved in the final equations. Previously proposed algorithms, the physical interpretations leading to their derivation, and the redundancy in their computations are analyzed. The developed algorithm achieves a greater efficiency by eliminating the redundancy in the intrinsic equations as well as by a suitable choice of coordinate frame for projection of the intrinsic equations.     

System decomposition technique for spray modelling in CFD codes

A new decomposition technique for a system of ordinary differential equations is suggested, based on the geometrical version of the integral manifold method. This is based on comparing the values of the right hand sides of these equations, leading to the separation of the equations into ‘fast’ and ‘slow’ variables. The hierarchy of the decomposition is allowed to vary with time. Equations for fast variables are solved by a stiff ODE system solver with the slow variables taken at the beginning of the time step. The solution of the equations for the slow variables is presented in a simplified form, assuming linearised variation of these variables for the known time evolution of the fast variables. This can be considered as the first order approximation for the fast manifold. This technique is applied to analyse the explosion of a polydisperse spray of diesel fuel. Clear advantages are demonstrated from the point of view of accuracy and CPU efficiency when compared with the conventional approach widely used in CFD codes. The difference between the solution of the full system of equations and the solution of the decomposed system of equations is shown to be negligibly small for practical applications. It is shown that in some cases the system of fast equations is reduced to a single equation.     

Driving simulator with double-wishbone suspension using efficient block-triangularized kinematic equations

When modeled with ideal joints, many vehicle suspensions contain closed kinematic chains, or kinematic loops, and are most conveniently modeled using a set of generalized coordinates of cardinality exceeding the degrees-of-freedom of the system. Dependent generalized coordinates add nonlinear algebraic constraint equations to the ordinary differential equations of motion, thereby producing a set of differential-algebraic equations that may be difficult to solve in an efficient yet precise manner. Several methods have been proposed for simulating such systems in real time, including index reduction, model simplification, and constraint stabilization techniques. In this work, the equations of motion for a double-wishbone suspension are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. Symbolic computation is then used to triangularize a subset of the kinematic constraint equations, thereby producing a recursively solvable system for calculating a subset of the dependent generalized coordinates. Thus, the kinematic equations are reduced to a block-triangular form, which results in a more computationally efficient solution strategy than that obtained by iterating over the original constraint equations. The efficiency of this block-triangular kinematic solution is exploited in the real-time simulation of a vehicle with double-wishbone suspensions on both axles, which is implemented in a hardware- and operator-in-the-loop driving simulator.     

Stopping Criteria for Anisotropic PDEs in Image Processing

A number of nonlinear diffusion-like equations have been proposed for filtering noise, removing blurring and other applications. These equations are usually developed as time independent equations. An artificial time is introduced to change these equations to parabolic type equations which are then marched to a steady state. In practice the time iteration is stopped before the steady state is reached. The time when to stop the iteration is usually determined manually for each case. In this study we develop a more automatic procedure for stopping the time integration.