Oscillatory Growth Research Articles

An historical analysis of engineering college research and degree programs as dynamic systems

An analysis is made to illuminate and interpret the recent history of engineering education. The production of engineering degrees and research is modeled as a dynamic process using parameters derived for that purpose. The dominant fact in the production of bachelors degrees is the damped oscillatory growth which characterized the two decades after World War II. Short-term fluctuations exist, but over the long term the growth rate matches U.S. population growth rate. Graduate degree production increased at a constant 12 percent per year between 1956 and 1968, resulting in the ratio of graduate degrees to B.S. degrees increasing from 1:6 to the current 1:2. Methods are developed to classify colleges of engineering according to their dominant characteristic as graduate or undergraduate institutions. Growth in Ph.D. production is shown to have been influenced by a "geographical potential" as well as other factors. Application is made to a method for planning graduate research centers in developing countries. Cost effectiveness in graduate research is shown to correlate with size. The largest colleges are shown to have maintained their productivity while smaller ones declined during periods of decreasing national production. Methods for critical comparison of colleges, departments, and even professors, are discussed and illustrated.

Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flows

The bursting process in turbulent boundary layers provides new insight on turbulence phenomena, mechanics of sedimentation, and genesis of bedforms in natural geophysical flows. Recent visualization experiments suggest that the turbulent boundary layer can be divided into an inner zone, whose essential characteristics scale with inner (wall) variables, and an outer zone, whose properties scale with the fluid-dynamic variables of the entire flow. The inner zone is distinguished by (i) a viscous sublayer displaying spanwise alternations of high-and low-speed streaks and (ii) episodic disruption by lift-ups of low-speed streaks. Oscillatory growth and breakup stages of the Stanford model of bursting characterize the turbulent structure of the outer zone. The burst cycle exists in turbulent boundary layers of all natural flows except perhaps (i) open-channel flows in the upper part of the upper flow regime and (ii) wind-generated surface waves.Fluid motions described as kolks and boils in incompressible open-channel flows correspond to the oscillatory growth stage andthe late oscillatory growthand breakup stages, respectively, of the Stanford model of bursting. Supporting evidence includes (i) close similarity of gross fluid motions, (ii) equivalent scaling of boils and bursts, and (iii) intensification of boils and bursts in adverse pressure gradients and over rough beds. McQuivey's (1973) turbulence measurements show that the Eulerian integral time scaleTEscales with the same outer variables asboilperiodicity and burst periodicity. It is hypothesized thatTEequals the mean duration of bursts at a point in the flow.Bedforms governed by the turbulent structure of the inner zone (microforms) cannot form if the sublayer is disrupted by bed roughness. The conditions for the existence of two common microforms and their spacings scale with the inner variables. Grain roughness increases the vertical intensity of the turbulence (by enhancing lift-ups) within the inner zone, thereby explaining textural differences between the coarse ripple and fine ripple bed stages of Moss (1972).Mesoforms respond to the fluid-dynamical regime in the outer zone and scale with the outer variables. The mean spacing of dunelike large-scale ripples in equilibrium open-channel flows is proportional to the boundary-layer thickness and equals the length scale formed by the product of the free-stream velocity and the boil period.Strong upward flow in a burst provides the vertical anisotropy in the turbulence which is needed to suspend sediment. Bursting promotes the entrain-ment of more and coarser sediment than tractive forces alone can accomplish.

A proposed model of the bursting process in turbulent boundary layers

A model is proposed which attempts to explain the complete ‘burst cycle’. This model views the wall streak as a sub-boundary layer, within the conventionally defined boundary layer, and the lift-up stage of bursting either as an upwelling motion of this sub-boundary layer which is similar to a local, convected separation or, equivalently, as the consequence of a vortex roll-up. ‘Sweeps’ are thought to represent the passage of a previous burst from further upstream. They appear either to impress on the wall streak the temporary adverse pressure gradient required to bring about its lifting or, alternatively, to provide the outer vortex which rolls up with the vortex associated with the wall streak. The model is also used to explain how the interactions between a burst and a sweep bring about (i) breakup, as well as (ii) new wall streaks further downstream.Arguments are presented to demonstrate that the three kinds of oscillatory growth reported by Kim, Kline & Reynolds (1971) may be associated with just one type of flow structure: the stretched and lifted vortex described by Klineet al.(1967).

Gravitational Stimulations Inhibit Oscillatory Growth Movements of Plants

Abstract Spontaneous oscillatory growth movements around (or across) the plumb line occur in young sunflower seedlings. The period is about 2.5 h. When such plants are tilted 90° and continuously rotated around their axis with a speed of 0.5 rpm, the oscillatory spontaneous movements cease. The findings are interpreted as supporting a previously published model for gravitationally induced plant movements.

Oscillatory Growth in Three Nations

Abstract Both the definition of economic activity and the definition of periodicity seem to determine whether there are long tides in economic affairs. Spectral analysis of growth rates finds no long waves in the U.S., U.K., and Sweden, but this is consistent with the appearance of long classical (upcross) swings in the deviations from trend of several raw data series. These upcross oscillations may not be independent components of economic evolution but merely distorted reflections of trend growth processes.

Oscillatory Growth in Three Nations

Oscillatory Growth in Three Nations

Computer model studies of dendritic growth

A computer model (simulation) approach to the study of the dendritic growth phenomenon is reviewed, and related to prior analytic work. Results are presented for the simulation of idealised tin crystals in the form of single fibers and in the form of arrays. The quantities generated by a long-term simulation are fitted within a theoretical framework. Tip shape is related to the temperature gradient in liquid near the tip using a stability argument. An independent relationship between tip radius and the adjacent gradient (a measure of growth velocity) is proposed as a replacement for the “maximum velocity criterion” used in prior studies to define a unique crystal. The possibility of oscillatory growth is discussed.

A model for predicting growth responses in plants to changes in external water potential: Zea mays primary roots

In response to osmotic step changes, three distinct phases have been noted in the growth response of Zea mays primary roots. They are cessation or slowing of growth over a period of 15–20 minutes, tissue contraction, and a damped oscillatory return to nearly normal growth rate, all within a period of about one hour. A system model of the tissue response is presented to explain such behavior and to serve in a predictive capacity to govern future experiments. It is supposed that for turgor pressure in excess of a cell wall yield threshold, plastic flow is the major component of wall deformation, and that when turgor falls below yield threshold, elastic deformation is dominant. The equations of the model describe growth rate as a function of time in terms of the following properties; plastic flow, elastic deformation, permeability to water, and solute uptake. They are derived from basic equations of feedback interactions between internal osmotic pressure and growth rate, and between wall softening, turgor and growth rate. The model predicts oscillatory growth rate regulation, and phase and amplitude relationships between turgor pressure and growth rate. The simplest model which accounts for all observations is that of biphasic deformation, two modes of wall softening, and a dual feedback system involving osmotic and yield threshold control of growth rate. It should be noted that to predict the time course of turgor pressure, osmotic pressure, yield pressure, and growth rate, two initial conditions and six system parameter values are sufficient. So far only the initial values of growth rate and its derivative can be obtained for Zea mays primary roots. However, values for wall softening and hardening coefficients (including the strain and turgor independent component), plastic extensibility, water permeability and dilution rate coefficients have not been obtained as yet for Zea roots. Values for some of these parameters have been obtained for other roots, coleoptiles, and giant algal cells. Lest the reader despair, it should be pointed out that experimental observations coupled with simulation studies will help establish restricted ranges of values that the system parameters might assume. These can then be compared with known values in the literature and values experimentally obtained in the future.

The Oscillatory Boundary Layer Growth Over the Top and Bottom Plates of a Rotating Channel

The behavior of the steady boundary layers formed over the top and bottom surfaces of a rotating channel is theoretically investigated. At the leading edge, not surprisingly, the flow behaves in accordance with the Blasius solution. Far downstream, the boundary layers are established as an Ekman layer. The transition from the Blasius layer to the Ekman layer is not monotonously smooth, but occurs in a spatially wave-like manner. This undulatory transition zone results from the Coriolis coupling between the motion in the main and cross flow directions. The length of the transition zone is relatively short, occuring within a few cycles of the aforementioned undulations.

Electrohydrodynamic stability: effects of charge relaxation at the interface of a liquid jet

The interactions between electrical tractions at the interface of a liquid jet and instability phenomena are studied with emphasis on effects due to interfacial charge relaxation. Charge relaxation causes the oscillatory growth of a perturbation. When viscous effects are small, small fields tend to decrease the growth rate of the axisymmetric mode, up to a point, and precipitate instability of the non-axisymmetric modes. Still larger field strengths increase the growth rates of asymmetric as well as axisymmetric modes. Instabilities characterized by highfrequency oscillations appear to persist even though the charge relaxation phenomena may be quite rapid. When, on the other hand, viscous effects predominate the only unstable disturbance form is the axisymmetric one, although the manner of growth may be oscillatory.

A study of T-burner behavior.

An experimental study is described in which detailed oscillatory-pressure measurements were made in a single-ended T-burner, i.e., a T-burner with propellant being burned in only one end. The acoustic behavior in this system was found to be greatly different from any previous description of the behavior. Most significantly, the oscillatory-pressure amplitude was found to be lower by a factor of 0.45 at the burning surface than at the opposite end of the motor. In addition, the oscillatory envelopes exhibited very unusual, but reproducible, behavior. These characteristics cannot be explained analytically if the normal assumptions are employed. They can be explained if the mean temperature varies along the length of the motor, but only if the temperature distribution has a specific character. The temperature distribution must approximate two regions of uniform temperature separated by a discontinuity, with the gas temperature in the nonburning end of the motor near ambient. Although the actual temperature distribution has not been determined, the existence of such a distribution is regarded as not unlikely. Calculations show that the oscillatory growth constant can be significantly altered by such a temperature distribution. The results of this work indicate important effects that must be considered in various kinds of T-burner measurements.

Oscillatory growth rate responses of S. Cerevisiae in continuous culture

AbstractThe yeast S. cerevisiae was grown on dilute, chemically defined media in continuous culture with either glucose or ammonium sulfate as the growth‐limiting ingredient. Changes in dilution rate or glucose concentration induced decaying oscillations in the numbers of yeast growing on ammonium sulfate‐limited media. Spot checks indicated that Cell dry weight and Kjeldahl nitrogen followed the cell numbers during these oscillations. With glucose‐limited media, there was no response to step changes in ammonium sulfate concentration, and dilution rate step changes gave non‐oscillatory transient responses.

A mathematical model of coagulation

A simplified mathematical model of floc growth in a stirred suspension is developed with the aid of the Smoluchowski equation for orthokinetic coagulation. Particles are assumed to be spherical and to conjoin into spheres of proportionate volume upon contact. Particle growth is restricted to different maximum sizes or multiple volumes, larger particles breaking up into smaller ones which are returned to the system. A smooth growth pattern asymptotically approaching a steady-state mean size results when a model parameter of gross contact opportunity is less than 0.04 in magnitude; as it approaches 0.10, the growth pattern becomes oscillatory. Oscillatory growth was observed also experimentally when a controlled shear gradient was imposed on a suspension of iron flocs.