Stationary Stream Research Articles

Flow separation structure in a nonstationary viscous gas flowing over a body

This paper studies the structure of the nonstationary pulsating flow of a viscous compressible heat-conducting gas flowing over a cylinder with a cylindrical step projection on its front end. In a stationary incident stream, a projecting step usually produces a separated vortex flow. In a pulsating incident stream, the overall flow structure, and the structure of the separated flow in particular, changes depending on the frequency and the amplitude of pulsations, and this change substantially affects the aerodynamic characteristics of the immersed body. Such nonstationary processes have been studied by numerical solution of two-dimensional nonstationary Navier-Stokes equations using an implicit iterative difference scheme [1], which approximates the original systems of equations with second-order accuracy in space and in time.

Energy principles for self-gravitating barotropic flows - II. The stability of Maclaurin discs

We analyze stability conditions of "Maclaurin flows" (self-gravitating, barotropic, two dimensional, stationary streams moving in closed loops around a point) by minimizing their energy, subject to fixing all the constants of the motion including mass and circulations. Necessary and sufficient conditions of stability are obtained when gyroscopic terms in the perturbed Lagrangian are zero. To illustrate and check the properties of this new energy principle, we have calculated the stability limits of an ordinary Maclaurin disk whose dynamical stability limits are known. Perturbations are in the plane of the disk. We find all necessary and sufficient conditions of stability for single mode symmetrical or antisymmetrical perturbations. The limits of stability are identical with those given by a dynamical analysis. Regarding mixed types of perturbations the maximally constrained energy principle give for some the necessary and sufficient condition of stability, for others only sufficient conditions of stability. The application of the new energy principle to Maclaurin disks shows the method to be as powerful as the method of dynamical perturbations.

The mean waiting time in a G/G/m/∞ queue with the LCFS-P service discipline

A single- or multiserver queue with work-conserving service discipline and a stationary and ergodic input stream with bounded service times and arbitrarily light traffic intensity may have infinite mean waiting time. We give an example of this paradox and we also give a mixing condition which, in the case of the preemptive-resume LCFS discipline, excludes this phenomenon. Furthermore, the same methods allow to estimate the durations of the first busy period and cycle and the number of customers served in the first busy cycle of a work-conserving queue.

The mean waiting time in a G/G/m/∞ queue with the LCFS-P service discipline

A single- or multiserver queue with work-conserving service discipline and a stationary and ergodic input stream with bounded service times and arbitrarily light traffic intensity may have infinite mean waiting time. We give an example of this paradox and we also give a mixing condition which, in the case of the preemptive-resume LCFS discipline, excludes this phenomenon. Furthermore, the same methods allow to estimate the durations of the first busy period and cycle and the number of customers served in the first busy cycle of a work-conserving queue.

Inviscid spatial stability of a compressible mixing layer. Part 2. The flame sheet model

We report the results of an inviscid spatial stability calculation for a compressible reacting mixing layer. The limit of infinite Damkohler number is taken and the diffusion flame is approximated by a flame sheet. Results are reported for the phase speeds of the neutral waves and maximum growth rates of the unstable waves as a function of the parameters of the problem: the ratio of the temperature of the stationary stream to that of the fast stream, the Mach number of the fast stream, the heat release per unit mass fraction of the reactant, the equivalence ratio of the reaction, and the frequency of the disturbance. These results are compared to the phase speeds and growth rates of the corresponding non-reacting mixing layer. We show that the addition of combustion has important, and complex, effects on the flow stability. In particular, we show that the flow can become absolutely unstable with a sufficient amount of heat release.

First passage problem of the beam under a random stream of moving forces

The problem of first crossing of the dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes is considered. Force arrivals at the beam are assumed to constitute a Poisson process of events. Thus, the excitation process idealizes vehicular traffic loads on the bridge. It is assumed that the parameters of the beam can be random. In order to obtain a crossing rate n + for the given threshold, the solution for the joint characteristic function and the joint probability density function of response (deflection and speed of the deflection) of the beam are determined. As an example, the response of a beam to stationary stream of forces is determined for some practical situations and discussed. The solutions and results presented can be used in estimations of the reliability of bridge structures.

Inviscid spatial stability of a compressible mixing layer

We present the results of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency, and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than ½ and is supersonic with respect to the stationary stream. The other is slow with phase speeds less than ½ and supersonic with respect to the moving stream. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. Finally, we show that three-dimensional modes have the same general behaviour as the two-dimensional modes but with higher growth rates over some range of propagation direction.

Random vibration of a suspension bridge due to highway traffic

The problem of dynamic non-linear response of a suspension bridge to the passage of a train of concentrated forces with random weight is considered. Force arrivals at the bridge are assumed to constitute a Poisson process of events. Thus, the excitation process idealizes vehicular traffic loads on a bridge. By use of both iterative and linearization methods the solution for the expected value and variance of the bridge's deflections is determined. As an example, the response of a bridge to a stationary stream of forces is obtained. A numerical technique is developed to compute the solution for a particular bridge and some practical cases of the loading.

Controlled-dispersion flow analysis : Flow-injection analysis applied to clinical chemistry

Mechanisation came early to clinical chemistry and has passed through a number of phases. Selective multichannel machines, usually discrete analysers with their associated mechanical complexities, have become popular; the simplicity and reliability of flow analysers has been lost. Flow injection offers new opportunities to develop simple selective machines. Sample waste is avoided in the controlled-dispersion flow analyser; the slug of sample is picked up by a probe, the volume being metered by the peristaltic pump driven by a stepping motor under computer control. Reagent waste is avoided by a similar system and use of merging zones. Very economical operation is thus possible and acceptable precision is attained. Various features of the technique, including prolonged incubation, use of kinetic methods to minimise the need for blanks, and application of different detectors are discussed in the context of clinical assays. Anomalous behaviour of particulate matter in flow streams and the changing shape of sample slugs in stationary streams are described. The application of flow-injection systems in clinical chemistry is extremely promising.

On some properties of Poisson processes

The Poisson process, i.e., the simple stream, is defined by Khintchine as a stationary, orderly and finite stream without after-effects. A necessary and sufficient condition for a stream to be a simple stream is that the interarrival times are independent random variables with identical exponential distributions. This paper gives a simple and rigorous proof of the necessary and sufficient condition, and discusses the other necessary and sufficient conditions for a renewal process to be a Poisson process.

Vibration of a beam due to a random stream of moving forces with random velocity

The problem of dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes and velocities is considered. Force arrivals at the beam are assumed to constitute the point stochastic process of events. Thus, the excitation process is an idealization of vehicular traffic loads on a bridge. An analytical technique is developed to determine the response of the beam. Explicit expressions for the expected value and the variance of the beam deflection are provided. As an example, the response of a beam to a stationary stream of forces is determined for some practical situations, and discussed.

Vibration of a Beam under a Random Stream of Moving Forces*

ABSTRACT The problem of dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes is considered. Force arrivals at the beam are assumed to constitute a Poisson process of events. Thus, the excitation process idealizes vehicular traffic loads on a bridge. An analytical technique is developed to determine the response of the beam. This technique is based on the introduction of two influence functions, one of which satisfies nonhomogeneous, the other homogeneous differential equations for beam response. Explicit expressions for expected value and variance of the beam deflection are provided. As an example, the response of a beam to a stationary stream of forces is determined for some practical situations and discussed. The extension of the approach presented to the case of two-axle vehicles is also outlined

On the asymptotic behavior of velocity and on forces acting on a body in a stationary stream of viscous fluid: PMM vol. 38, n≗ 1, 1974, pp. 84–91

It is shown that if the direction of the force acting on a body differs from that of the velocity of the oncoming stream, logarithmic factors appear in the asymptotic formula for velocity. A formula is derived for the force, which can be taken as the extension of the known Joukowsky theorem to the case of three-dimensional flow of viscous fluid past a body.

On the Distributions of the Times between Events in a Stationary Stream of Events

Summary In this paper, series expressions are obtained for the distributions of times between events in a stationary stream of events. The terms in the series involve factorial moments of the number of events in the interval (0, t). Similar results are obtained for a “mixture” of two stationary streams.

On Three Basic Results in the Theory of Stationary Point Processes

A simple, unified treatment is given for three basic results in the theory of stationary streams of events (point processes). These results are the basic theorem of Khintchine concerning the existence of a stream intensity, Korolyuk’s theorem, and a fundamental lemma of Dobrushin giving sufficient conditions for a stationary stream to be orderly in the sense of Khintchine [2].

On three basic results in the theory of stationary point processes

A simple, unified treatment is given for three basic results in the theory of stationary streams of events (point processes). These results are the basic theorem of Khintchine concerning the existence of a stream intensity, Korolyuk’s theorem, and a fundamental lemma of Dobrushin giving sufficient conditions for a stationary stream to be orderly in the sense of Khintchine [2].

Adaptive Bayes Classification Model with Incompletely Specified Experiment

A 2-stage classification model is presented in which the first stage is a quick, computerized Bayes rule decision device, and the second a slow, but perfectly accurate, classifier. A stationary stream of elements or objects to be classified into one of several mutually exclusive categories is fed into the model. The conditional probabilities associated with the Bayes device are assumed unknown at the outset, except up to an initial probability distribution. The a posteriori probabilities from the first stage are treated as information that can speed up or slow down the processing time in the second stage. The latter, after a delay time, feeds back accurate classification information to the first stage to update the conditional probabilities. It is shown that, as the classification process unfolds, any updating scheme that causes the Bayes classifier ultimately to learn the true values of the conditional probabilities also minimizes the expected processing time in the second stage. The learning rate of the system is discussed as a function of the updating scheme. An example of a simple system is presented and the learning rate is derived specifically for that case.

On a characteristic property of stationary streams without aftereffect

Let us consider a stream of homogeneous random events which we call signals and let us denote by the probability that exactly k signals will appear in the time interval . We assume that the stream is not empty, i.e. the probability P0 (a, t) is not identically equal to 1.

On a characteristic property of stationary streams without aftereffect

Let us consider a stream of homogeneous random events which we call signals and let us denote by the probability that exactly k signals will appear in the time interval . We assume that the stream is not empty, i.e. the probability P0(a, t) is not identically equal to 1.

Lectures on Electricity and Light

IN a book of 370 pages it is quite impossible thatuthe subjects of magnetism, electricity and light could be treated in anything but a scrappy manner, so that we cannot expect from Prof. Jaumann anything more than a general view of the subjects treated. The book under review arose from a course of lectures at Prague for beginners at the University and teachers in the secondary schools, and is therefore of the nature of an outline to be used as a guide in study supplemented by other more technical reading. For this purpose, if there had been a good selection of references to standard treatises, the book would have been admirable; but, unfortunately, references are almost entirely absent. The author has undoubtedly made a most interesting volume and has treated the subject in a very original manner, dealing with the phenomena of magnetism, electricity and light from a physical point of view, using throughout the Faraday conception of tubes of force. The first eighty-four pages consist of an introduction dealing with stationary stream lines in the motion of a liquid to lead on to the conceptions of magnetic and electric lines of force. The analogies between liquid stream lines due to sources and sinks and vortices and lines of force due to charges and electric currents are well brought out, and considerable ingenuity is exercised in constructing cases of fluid motion to be analogous to the behaviour of lines of electric force when more, than one dielectric is present in the field. It seems, however, curious to introduce, for the benefit of readers who cannot be supposed to understand lines of force, the lines of flow for a vortex filament in a steady stream as the first case of stream lines discussed. However, later on the author deals with the resultant of two sets of stream lines and shows how complicated cases can be built up out of simple cases. This might have been done at first and have led up to the more complicated and confusing cases which he presents to the reader at the very beginning. By means of a hot or cold region in the centre of a stream, he constructs stream lines which are analogous to the lines of force for a dielectric cylinder in a steady uniform electric field. The hot region is supposed to be produced by the sun shining on this part of the stream, the rest being in shadow. Asa limiting case he has a region of vapour in the middle of the stream, and states in a footnote:—