The use of the constructive method in systems with static friction

The problem of determining the accelerations in a mechanical system with friction at zero initial velocities is discussed. To approximate the solutions, an auxiliary system is constructed in which non-ideal geometrical constraints are produced by elastic forces, the structure of which complies with the static-friction law. It is proved that the auxiliary system is always solvable for the accelerations (possibly, non-uniquely) and hence a solution of the initial system also exists and can be constructed by taking a certain limit.     

The design and implementation of a prototype structured modeling environment

This paper describes the design and implementation of the prototype structured modeling environment FW/SM. The underlying design principles provide the central focus. Other points of interest include discussions of FW/SM's delivery platform, its interface to external packages, and its optimization interfaces. The intended audience is all modeling system evaluators, designers, and implementors, including those who do not happen to take a structured modeling approach.     

Studies of the dynamics of space motion of a class of parachute systems

A mathematical model of space motion of a mechanical system that consists of a load and a parachute is presented. With the help of the apparatus of the Lyapunov functions, a particular case of the model is studied when the load can be considered as a mass point that does not have resistance. A sufficient condition of stability is obtained. The results can be applied to the model/ing and construction of parachute systems.Translated from Dinamicheskie Sistemy, No. 9, pp. 99–102, 1990.     

A simplified method of computing the process of opening of a parachute

We propose a simplified method of determining the integral characteristics of the opening of a parachute which makes it possible to compute the maximal stress on a parachute and the trajectory parameters of the motion of the load in the region of the opening of the parachute, and to determine the size of the portion of the canopy at the time of maximal stress.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 38–41.     

The large-particle method in arbitrary nets and its application to the solution of problems in the aeroelasticity of a parachute

Modifications are introduced into the large-particle method to make it possible to use the method in arbitrary nonrectangular computing nets in the study of the flow of an ideal compressible gas over mobile thin permeable membranes. A problem in the aeroelasticity of a parachute is stated. An example is given of the solution of a problem in the stationary formulation for an axially symmetric parachute in the wake of a cylindrical leading body for supersonic flow.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 16–22     

Detecting unstable periodic orbits embedded in chaotic systems using the simplex method

This paper proposes an approach for detecting unstable periodic orbits embedded in chaotic systems by using the simplex method. The simplex algorithm is easily implemented and does not require the derivatives of the function to be optimized. As a result, it is also applicable to chaotic systems with discontinuities or in which functions contain noise.     

Implementing the simplex method as a cutting-plane method, with a view to regularization

We show that the simplex method can be interpreted as a cutting-plane method, assuming that a special pricing rule is used. This approach is motivated by the recent success of the cutting-plane method in the solution of special stochastic programming problems. We focus on the special linear programming problem of finding the largest ball that fits into a given polyhedron. In a computational study we demonstrate that ball-fitting problems have such special characteristics which indicate their utility in regularization schemes.     

The double pivot simplex method

The simplex method, created by George Dantzig, optimally solves a linear program by pivoting. Dantzig’s pivots move from a basic feasible solution to a different basic feasible solution by exchanging exactly one basic variable with a nonbasic variable. This paper introduces the double pivot simplex method, which can transition between basic feasible solutions using two variables instead of one. Double pivots are performed by identifying the optimal basis in a two variable linear program using a new method called the slope algorithm. The slope algorithm is fast and allows an iteration of DPSM to have the same theoretical running time as an iteration of the simplex method. Computational experiments demonstrate that DPSM decreases the average number of pivots by approximately 41% on a small set of benchmark instances.     

Towards a practical parallelisation of the simplex method

The simplex method is frequently the most efficient method of solving linear programming (LP) problems. This paper reviews previous attempts to parallelise the simplex method in relation to efficient serial simplex techniques and the nature of practical LP problems. For the major challenge of solving general large sparse LP problems, there has been no parallelisation of the simplex method that offers significantly improved performance over a good serial implementation. However, there has been some success in developing parallel solvers for LPs that are dense or have particular structural properties. As an outcome of the review, this paper identifies scope for future work towards the goal of developing parallel implementations of the simplex method that are of practical value.     

Set systems without a simplex or a cluster

A d-dimensional simplex is a collection of d+1 sets with empty intersection, every d of which have nonempty intersection. A k-uniform d-cluster is a collection of d+1 sets of size k with empty intersection and union of size at most 2k.     

Some open problems in the design and use of modern production systems

During the past two decades, manufacturing systems have moved towards automation, integration and modularity. These trends will certainly continue in the future due to the constraints of the market and to evolution of resources and worker requirements. As a consequence, the design and use of manufacturing systems are increasingly expensive. Numerous methods and tools have been developed to face up to this situation, but some complementary aids could be provided for designers and manufacturing engineers. The goal of this paper is to present important open problems whose solutions could certainly significantly improve the design and use of modern production systems.     

The simplex method and unrestricted variables

Suppose that the simplex method is applied to a linear programming problem havingm equality constraints andr unrestricted variables. We give a method of performing the steps of the simplex method which reduces the arithmetic operation count byrm at each iteration. This savings in operations is achieved, since the method does not update the rows of the basis inverse associated with the unrestricted variables. Similar computational savings are achieved when the method is applied to the updating of anLU-factorization of the basis matrix.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. A8189 and by a postgraduate fellowship.     

Shape of the parachute canopy

The article presents new equations of equilibrium of an axisymmetric parachute canopy generalizing Kh. A. Rakhmatulin's well-known equations. The equations take the biaxial nature of the state of stress near the pole of the canopy into account, and this leads to a finite value of the tension of the tissue and to a finite value of the radius of curvature at the pole.Translated from Dinamicheskie Sistemy, No. 5, pp. 21–25, 1986.     

The influence of a supporting canopy on the dynamics of opening of a parachute

A mathematical model of the opening of a circular parachute under the action of a supporting canopy was executed on a computer. The proposed model is based on the simultaneous integration of the equations of nonlinear aerodynamics and the theory of soft membranes. It is shown that the supporting canopy may both improve the characteristics of the parachute system and make them worse. The numerical results are presented in the form of graphs. One figure.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 23–26.     

A design method for embedded software systems

A method for design of embedded real-time systems is described. We discuss how the method separates concerns and at what points theory is applied. We also report on our experience from teaching the method to engineers from several Danish companies and their experience in using the method in real development projects.Dedicated to Peter Naur on the occasion of his 60th birthdayThis work has been partially supported by the National Agency of Technology.     

Pulsations of the parachute canopy

The problem of pulsations of the canopy of a parachute is considered. Equations which are linearized in a neighborhood of the stationary state of motion are given, the algorithm of solution that is based on the composition of the methods of discrete curls and finite differences is described. The results of computations of the characteristics of frequency of the canopy are given in the form of graphs.Translated from Dinamicheskie Sistemy, No. 9, pp. 87–94, 1990.     

The simplex method as a global optimizer: A c-programming perspective

In this paper we give a brief account of the important role that the conventional simplex method of linear programming can play in global optimization, focusing on its collaboration with composite concave programming techniques. In particular, we demonstrate how rich and powerful the c-programming format is in cases where its parametric problem is a standard linear programming problem.     

The effect of turbulence on mixing in prototype reaction‐diffusion systems

The effect of turbulence on mixing in prototype reaction‐diffusion systems is analyzed here in the special situation where the turbulence is modeled ideally with two separated scales consisting of a large‐scale mean flow plus a small‐scale spatiotemporal periodic flow. In the limit of fast reaction and slow diffusion, it is rigorously proved that the turbulence does not contribute to the location of the mixing zone in the limit and that this mixing zone location is determined solely by advection of the large‐scale velocity field. This surprising result contrasts strongly with earlier work of the authors that always yields a large‐scale propagation speed enhanced by small‐scale turbulence for propagating fronts. The mathematical reasons for these differences are pointed out. This main theorem rigorously justifies the limit equilibrium approximations utilized in non‐premixed turbulent diffusion flames and condensation‐evaporation modeling in cloud physics in the fast reaction limit. The subtle nature of this result is emphasized by explicit examples presented in the fast reaction and zero‐diffusion limit with a nontrivial effect of turbulence on mixing in the limit. The situation with slow reaction and slow diffusion is also studied in the present work. Here the strong stirring by turbulence before significant reaction occurs necessarily leads to a homogenized limit with the strong mixing effects of turbulence expressed by a rigorous turbulent diffusivity modifying the reaction‐diffusion equations. Physical examples from non‐premixed turbulent combustion and cloud microphysics modeling are utilized throughout the paper to motivate and interpret the mathematical results. © 2000 John Wiley & Sons, Inc.