Quasi-stationary Motion Research Articles

Curvilinear motion control laws for a semi-trailer caterpillar train for off-road cargo transportation

BACKGROUND: For transport accessibility in areas with an undeveloped road network, the use of tracked trains that provide low ground pressure is a rational solution. To ensure the mobility of a semi-trailed, unmanned caterpillar train, which can be controlled remotely by a driver-operator or by an automatic unmanned driving system, traffic control laws are needed.
 AIMS: Ensuring energy efficiency in curve control of a unmanned semi-trailer tracked train for off-road freight transport.
 METHODS: The methods of simulation mathematical modelling and analytical methods based on the consideration of the quasi-stationary motion of the caterpillar train links are used to derive energy-efficient control laws and determine the mobility performance that can be achieved.
 RESULTS: Control laws are obtained for two variants of tracked trains: a tracked train with independent drive control of driving wheels and a tracked train with a differential drive scheme of a semi-trailer link. The control laws are designed to improve the energy efficiency of travel which is achieved by rational distribution of traction forces on the driving wheels of the tracked train and use of the regulator which ensures adjustment of the traction on the semi-trailer driving wheels accord-ing to the sign and magnitude of force in the fifth-wheel coupling of the tractor.
 A block diagram of a governing system of a caterpillar train and a mathematical description of its basic structural components (blocks) are given. Using the developed control laws the theoretical research of curvilinear movement by simulation mathematical modelling is carried out; the comparative analysis of the considered control laws of the semitrailer caterpillar train movement with two transmission variants is given.
 CONCLUSIONS: The application of the developed caterpillar train motion control laws will enable the vehicle to move unmanned or follow the lead vehicle along a set path with high accuracy of turning manoeuvres and, consequently, will improve the safety of freight transportation.

Квазистационарное турбулентное течение в цилиндрическом канале с неровными стенками

A simple asymptotic model of a stationary rotationally symmetric flow in an infinite cylindrical channel with irregular walls is constructed and investigated. We assume that kinematic viscosity is depends on the radial and axial coordinates. The kinematic condition corresponding to the impermeability of the boundary for the liquid is chosen. It is assumed that the classical non-slip condition is completed only in straight segments of the boundary. For parts of the boundary that are not straight, any additional terms, in addition to the kinematic conditions, not required. It is shown that at any fluid flow rate in domains where the curvature of the cylinder boundary is negative, there are toroidal vortices in the stationary flow. The solution of the problem is constructed in analytical form. This solution is valid in any domain with sufficiently smooth cylinder boundaries. As an example, we consider the case of turbulent kinematic viscosity vanishing at the cylinder boundary. To prevent the velocity singularities the roughness of the wall is introduced. The proposed model can simulate the blood flow through the vessels and, in particular, be used to study the quasi-stationary motion of impurities, for example, erythrocytes, in the flow with the known structure.

Two-phase flows in the formed tornado funnel

At present, it is obvious that the problem of the tornado is important not only for our planetЮ to determine the conditions for the formation of a tornado, it is required to take into account a number of hydrodynamic and plasma processes [1 - 6]. Along to prediction of a tornado generation conditions [1 - 3] it is necessary to evaluate the characteristics of its quasi-stationary motion in a formed funnel: the mass of the moving moist air involved in the funnel and the size and form of the funnel. For a complete description of the phenomena, it is necessary to involve numerical calculations. We note that even for numerical calculations using powerful computers, the problem is very difficult because of the need to calculate multiphase turbulent flows with free, self-organizing boundaries [1, 6]. However, “strict” numerical calculations, it is impossible to do without the use of many, often mutually exclusive, models. For example, how to choice an adequate model of turbulence (algebraic, k-ε model, etc.) or the use of additional, often not accepted, hypotheses about certain processes used in calculations (mechanisms on the nature of moisture condensation, etc.). Therefore, along with numerical calculations of such flows, modeling problems that allow an exact solution and allow to determine the most important and observed characteristics of a tornado.

Interaction Forces Between Two Ships During Underway Replenishment

Knowledge of forces and yaw moments which exist between a pair of vessels moving parallel to each other is crucial to the design of their automatic motion control system. Studies involving measurements of forces and moments occurring between a pair of ships were undertaken. The research was carried out on the basis of two real floating training ship models made at 1:24 scale in real conditions on the Silm Lake in Ilawa Kamionka. As a result, suction forces and yaw moments occurring between the pair of vessels calculated according to semi-empirical formula were verified. It was found that the process of overtaking and parallel motion (which is a quasi-stationary motion) could not be modelled in the same way. Nevertheless, the results confirmed the presence of forces and moments with values similar to those in the catch-up and parallel motion phases during the ships’ overtaking manoeuvre. Thanks to this confirmation, it was possible to use the results of the analytical calculation for the catch-up phase during design of the ships' parallel motion automatic control system.

Analytical study of microsatellite attitude determination algorithms

An analytical approach to study of attitude determination algorithms is considered. The approach is applicable for quasi-stationary motion determination. It is based on filter post-convergence computation of the Kalman filter covariance matrix and allows one to estimate the influence of unaccounted perturbations on motion determination accuracy. The dependence of attitude determination accuracy on filter parameters and perturbations is obtained. The proposed method of improving the Kalman filter performance is applied on board a microsatellite of the TabletSat series.

Numerical Investigation on Mechanism for Inertial Lift on Particles in Micro-channel

Based on the ‘Galileo Principle of Relativity', a numerical model is proposed to describe the quasi-stationary motion of a particle in a straight pipe, by which the inertial lift is numerically obtained on the spherical particle inside a straight micro-channel with squared section, combined by computational fluid dynamics(CFD) technique. The spatial distribution of the inertial lift is numerically investigated and the influence on the inertial force is also obtained by the particle's diameter. Results indicate, the inertial lift shows an obvious regularity in spatial distribution: it is towards the channel wall in the vicinity of the channel axis with its magnitude increasing firstly to the maximum and then gradually decreasing to zero in radial direction while it is towards the channel axis in the vicinity of the channel wall with its magnitude increasing sharply close to the channel wall. There is a unique position with zero inertial lift in radial direction, which is just the position of ‘Inertial Focus of Particles'. The inertial force consists of two components, one is the viscous stress, the other is the pressure stress, but the latter is the determinant to ‘Inertial Focus of Particles'. These results help to perfect the mechanical mechanism on the solid-liquid flow field with low Reynolds number and enhance the further commercial applications of the ‘Inertial Focus of Particles'.

The optimal quasi-stationary motion of a vibration-driven robot in a viscous medium

We consider a rectilinear quasi-stationary motion of a two-mass system in a viscous medium. The motion of the system as a whole occurs due to periodic movements of the internal mass relatively to the shell. The problem is to describe the law of motion of the internal mass that provides the minimum energy consumption with a specified average velocity of the shell. We propose an algorithm for solving the problem with any law of the resistance of the medium. We obtain the energy-optimal law of motion of a spherical shell in a viscous liquid.

Aerodynamics of a Heaving Airfoil in Ground Effect

The aerodynamic behavior of an inverted airfoil in ground effect under heaving motion was investigated numerically. A sinusoidal vertical movement perpendicular to a uniform freestream was imposed on the airfoil. The response showed a periodic pattern that repeated with the same frequency as the heaving motion. The effect of reduced frequency at several mean distances from the ground was examined. By analyzing the lag of the aerodynamic coefficients with respect to the vertical motion, the flow can be classified into different regimes. Three fundamental features that define these regimes have been identified: 1) ground effect, 2) incidence effect, and 3) added mass effect. At low frequencies, the airfoil can be assumed to be in a quasi-stationary motion and the ground effect governs the flow. The contribution of incidence effects becomes apparent at medium frequencies and can be explained by defining an effective angle of attack. The maximum downforce is obtained at high effective angles of attack. As the frequency is increased even further, the only apparent effect is that of added mass. In this regime, downforce is shown to be related to the vertical acceleration of the airfoil. These mechanisms are independent of Reynolds number.

Transfer Functions and Statistical Analysis of FDLCP Systems Described by Higher-order Differential Equations

The paper considers the investigation of finitedimensional linear continuous-time periodic (FDLCP) systems, where the process is described by differential equations of higher than first order, and is influenced by a differentiated input signal. The concept of quasistationary motion mode for such systems is introduced, and closed formulae are derived for calculating statistical characteristics of the quasi-stationary output, when the process is excited by a stationary stochastic signal. Moreover, closed formulae for determining the H2- norm and associated H∞-norms are derived. The methods use a generalization of the parametric transfer matrix (PTM) concept for FDLCP systems of the considered class, and then apply the corresponding classical frequency-domain methods for statistical analysis of continuous-time LTI systems.

Characteristic Features of the Hydrodynamics of Disk-Type Rotary-Pulsation Apparatuses

Based on solution of the equation of quasi-stationary motion of liquid, the characteristic features of the hydrodynamics of flow in disk-type rotary-pulsation apparatuses have been investigated. Time dependences of velocity and acceleration have been obtained. The region of the optimal geometry of channels has been revealed and the influence of physical parameters on the level of pressure pulsations has been studied.

Mobility and interactions of weakly nonwetting droplets

Lubrication equations based on diffuse interface theory are applied to description of slow motion and interaction of droplets on solid support. For the case of quasistationary motion of a weakly nonwetting fluid, we derive integral relations reducing the problem to computation of ratios of applicable “thermodynamic forces” to a dissipative integral characterizing an individual droplet. This allows us to describe the droplet motion without computing explicitly the distortion of their shape. Explicit computations are carried out for a droplet sliding on an inclined plane, and for an ensemble of droplets interacting through the precursor layer.

Anisotropic shear viscosity in nematic liquid crystals: new optical measurement method

We propose a new optical method and the experimental set-up for measuring the anisotropic shear viscosities of nematic liquid crystals (LCs). LC shear viscosities can be optimized to improve liquid crystal display (LCD) response times, e.g. in vertical aligned nematic (VAN) or bistable nematic displays (BND). In this case a strong back-flow effect essentially determines the LCD dynamic characteristics. A number of shear viscosity coefficients defines the LCD response time. The proposed method is based on the special type of a shear flow, namely, the decay flow, in the LC cell with suitably treated substrates instead of magnetic or electric field application. A linear regime of a quasi-stationary director motion induced by a pressure difference and a proper configuration of a LC cell produces decay flow conditions in the LC cell. We determine three principal shear viscosity coefficients by measuring relative time variations of the intensity of the light passed through LC cells. The shear viscosity coefficient measurements provide a new opportunity for the development of new LC mixtures with fast response times in VAN, BND and other important LCD types.

Numerical Simulation of Two-Phase Flow in a Tornado Funnel

The model of flow in a tornado funnel previously suggested in [1] is updated. The updating of the flow model involves the inclusion of the processes of volume condensation of water vapor. The notation for the input equations is suggested, which is convenient from the standpoint of numerical simulation of processes of heat and mass transfer with due regard for the condensation of moisture within the tornado funnel. The results are given of numerical simulation of two-phase turbulent heat and mass transfer within a tornado funnel. The obtained numerical distributions enable one to identify the range of problem parameters in the case of which an upward flow of moist air may arise, which is sufficient to maintain a quasistationary motion of the tornado.

NEMATIC LIQUID CRYSTALS UNDER DECAY POUSEUILLE FLOW: NEW POSSIBILITIES FOR MEASUREMENT OF SHEAR VISCOSITY

The results of the optical investigation of a decay shear flow of a nematic liquid crystal are presented. The flow was produced by the varying hydrostatic pressure difference applied to the rectangular capillary. In the described experiment a quasi-stationary director motion took place. It allowed to control a pressure difference due to a measurement of an intensity of light, passing through the cell. The proposed procedure can be used to determine the shear viscosity of nematic liquid crystals.

Observational Constraints on Models of the Solar Background Spectrum

We discuss the properties of the solar background signal as observed in high-quality, l-ν power and phase difference spectra of the continuum (C), velocity (V), and line intensity (I) fluctuations of the Ni I 6768 A line. These spectra were generated from high-resolution images acquired by the Michelson Doppler Imager on board SOHO. We confirm that the background signal in the velocity power spectra can be reproduced by a composite model with two quasi-stationary components, describing large-scale and small-scale convective motions, and a periodic component. The line and continuum intensity power spectra require additional quasi-stationary and periodic components. The extra quasi-stationary component dominates the intensity and continuum background signals over the spectral region where the I-V phase difference spectra show essentially constant negative phase difference: i.e., below and in between the p-mode ridges (called the plateau-interridge regime by Deubner et al.). Since the I-V phase between the p-mode ridges is not random, the solar background beneath the p-modes must be considered as coherent. We thus speculate that the negative phase regime may be the manifestation of a correlated background. Such a background has been proposed to explain the opposite sense of the asymmetries of the p-mode line profiles in velocity and brightness oscillations.

Existence Results for the Quasistationary Motion of a Free Capillary Liquid Drop

We consider instationary creeping flow of a viscous liquid drop with free boundary driven by surface tension. This yields a nonlocal surface motion law involving the solution of the Stokes equations with Neumann boundary conditions given by the curvature of the boundary. The surface motion law is locally reformulated as a fully nonlinear parabolic (pseudodifferential) equation on a smooth manifold. Using analytic expansions, invariance properties, and a priori estimates we give, under suitable presumptions, a short-time existence and uniqueness proof for the solution of this equation in Sobolev spaces of sufficiently high order. Moreover, it is shown that if the initial shape of the drop is near the ball, then the evolution problem has a solution for all positive times which exponentially decays to the ball.

Cellular Automaton experiments on local galactic structure. II. Numerical simulations

This paper is a step towards demonstrating that the multi{parameter Cellular Automaton framework designed for the simulation of local galactic structure, developed in a companion paper (Perdang & Lejeune 1996, Paper I), is capable of duplicating the local irregularities observed in the structure of flocculent spiral galaxies. The numerical simulations exhibit the development of fractured galactic arms and the formation of fractal geometries associated with the matter distribution (fractal structure of the arms, of bulk dimension 1.7 and border dimension 1.3; distribution of dierent stellar components on fractal supports, of dimension 1.6, for reasonable estimates of the free model parameters). The prediction of fractional values for the dierent dimensions specifying the simulated structures can be exploited as a qualitative test of adequacy of the proposed model. The precise quantitative values of the observed dimensions, in conjunction with the observable global mass fractions of the dierent galactic components, play the parts of constraints for the free model parameters. We show that the currently theoretically inaccessible values of the free parameters of the formulation can be recovered from observation. In this Paper we report on an extended series of nu- merical experiments carried out in the framework of a 2{dimensional Cellular Automaton (CA) model for local galactic structure described in the companion paper (Pa- per I). The model takes account of stellar evolutionary eects not dealt with in current CA models, as well as of quasi-stationary motions more complex than usual dier- ential rotation. Our results are indicative that the floc- cular character of galaxies can be simulated in the CA framework. For technical details of the implementation of the galactic physics we refer to Paper I. Our results are given in a relative reference frame F in uniform rotation with respect to the galaxy to be simulated.

Quisistationary spherically summetric flow of an intensively emitting plasma heated by laser radiation

Estimates and numerical computations show that under a sufficiently prolonged action of laser radiation on a target in a vacuum under plane geometry conditions of vapor transit, a significant part of the laser pulse energy is converted into thermal radiation emitted by the plasma. If the vapor layer thickness during the laser action becomes commensurate with the characteristic size of the spot being irradiated, r b, then the vapor density is reduced more rapidly in the lateral direction because of the jet broadening being initiated than in the case of transit in the form of a plane layer. The peripheral layers of the plasma torch become transparent and transmit the laser radiation practically totally, absorption is realized only near the target, and a quasistationary self-consistent heating and vapor transit mode is built up [5, 6]. The plasma parameters attained at the end of the plane transit stage later seem "to be frozen." Consequently, modes in which the thermal radiation becomes a dominant factor can be realized even in the stationary stage. Since the role of the thermal radiation grows as the pulse duration increases in the plane stage, as does the vapor layer thickness x, correspondingly, [1-4], then the radiation yield in the stationary stage grows as the spot size r b increases [6]. The quasistationary mode of intensively emitting plasma motion, in which the energy of an external source is liberated, is of considerable interest since its mass flow rate, pressure, density, temperature, and optical plasma thickness as well as emitted radiation flux density, are sustained at a constant level. This facilitates investigation of the optical properties of an emitting plasma and the practical utilization of the emitted radiation. In the quasistationary mode the plasma mass, pressure pulse, and emitted radiation pulse are proportional to the energy supplied, i.e., they can, in principle, grow to arbitrarily large values. Description of the radiation-gas dynamic processes occurring in a'two~dimensional nonstationary or quasistationary motion of a radiating vapor jet is a rather complex problem. We limit ourselves here just to the simpler case of radially symmetric steady motion of radiating vapors. We make certain additional assumptions about the nature of the radiation. i. We will describe the radiation transport in the quasivolume de-excitation approximation [7, 8]. Let us compute the radiation intensity I e being propagated in a uniformly heated volume of substance under different values of its temperature T, density p, and characteristic dimension L. We find the integrated spectral radiation intensity F r on the volume boundaries

Global Oscillations of the Sun

The topic of this Joint Discussion has received enormously increased interest in the last couple of years, owing to its potential for the investigation of the structure of the interior of the sun, including related topics like the structure of the convection zone, solar metal abundance, and the still unsettled neutrino problem.The first stimuli came from the startling observations of Hill et al. (1976) in Arizona, Severny et al. (1976) on Crimea, and Brookes et al. (1976) in Birmingham, accompanied by a large volume of theoretical papers, the details of analysis of which soon went beyond the actual status of the observational facts.We then witnessed, however, the success of considerable refinements of the techniques of observation, together with an obvious widespread temptation to push the interpretation of many of the new results to the limits of optimism. Yet, despite of the still increasing body of data suggesting the reality of the solar origin of the observed phenomena, much scepticism was prompted by the complicated statistics and the intricate numerical procedures involved in the data analysis, as well as by the great uncertainty about the significance and the amounts of “noise” contributed to the signal by electronics, changes of the conditions of the ray path within the telescope, terrestrial atmospheric inhomogeneities and solar quasi-stationary motions.

Some warnings concerning the Lorentz-Dirac equation

Different ways conducting to the Lorentz-Dirac equation are revised and some physical implications of it are examined. Attention is paid to the conditions justifying the correct manipulation of Maxwell equations in the problems connected with elementary charges. It follows that Lienard-Wiechert formulae can only be safely applied for quasi-uniform motion of the charges. Hence the Lorentz-Dirac equation is only valid when the acceleration to which the charge is subjected is very small. A new equation is proposed that automatically preserves energy conservation and does not imply runaways. The electron is considered to be a variable-mass system and the new formulae obtained are valid only for quasi-stationary motion. Therefore, any really significant modification of it must include a generalization of it for any value of the acceleration.