scholarly journals Kinematics of a Fluid Ellipse in a Linear Flow

2018 ◽  
Author(s):  
Jonathan M. Lilly
Keyword(s):  
Velocity Gradient ◽  
Kinematic Model ◽  
Rate Of Change ◽  
Gradient Tensor ◽  
Rates Of Change ◽  
Elliptical Ring ◽  
Flow Equivalence ◽  
Linear Velocity Field ◽  
Two Dimensional Flow ◽  
The Moment

A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, the rates of change of the ellipse parameters are uniquely determined by the four parameters of the velocity gradient matrix, and vice-versa. This result, termed ellipse/flow equivalence, provides a stronger version of the well-known result that a linear velocity field maps an ellipse into another ellipse. Moreover, ellipse/flow equivalence is shown to be a manifestation of Stokes' theorem. This is done by deriving a matrix-valued relationship, called the geometric Stokes' theorem, that involves a spatial integral over the velocity gradient tensor, thus accounting for the two strain terms in addition to the divergence and vorticity. General expressions for various physical properties of an elliptical ring of fluid are also derived. The ellipse kinetic energy is found to be composed of three portions, associated respectively with the circulation, the rate of change of the moment of inertia, and the variance of parcel angular velocity around the ellipse. A particular innovation is the use of four matrices, termed the IJKL basis, that greatly facilitate the required calculations.

scholarly journals Disease-related disability burden: a comparison of seven chronic conditions in middle-aged and older adults

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Chieh-Ying Chou ◽  
Ching-Ju Chiu ◽  
Chia-Ming Chang ◽  
Chih-Hsing Wu ◽  
Feng-Hwa Lu ◽  
...  
Keyword(s):  
Older Adults ◽  
Physical Disability ◽  
Chronic Conditions ◽  
Chronic Condition ◽  
Disease Diagnosis ◽  
Rate Of Change ◽  
Middle Aged ◽  
Rates Of Change ◽  
Depression Status ◽  
Stage Disease

Abstract Background Although previous studies have explored the effect of chronic conditions on physical disability, little is known about the levels and rates of change in physical disability after a chronic condition diagnosis in middle-aged and older adults in the Asian population. The aim of this study is to ascertain the average levels and rates of change in the development of disability after disease diagnosis, as well as to determine the influences of sociodemographic and health-related correlates in the development of disability. Methods This is a retrospective cohort study analyzing data of nationally representative participants aged 50 and over with a chronic condition or having developed one during follow-ups based on data from the 1996–2011 Taiwan Longitudinal Study on Aging (TLSA) (n = 5131). Seven chronic conditions were examined. Covariates included age at initial diagnosis, gender, education level, number of comorbidities, and depression status. Physical disability was measured by combining self-reported ADL, IADL, and strength and mobility activities with 17 total possible points, further analyzed with multilevel modeling. Results The results showed that (1) physical disability was highest for stroke, followed by cancer and diabetes at the time of the initial disease diagnosis. (2) The linear rate of change was highest for stroke, followed by lung disease and heart disease, indicating that these diseases led to higher steady increases in physical disability after the disease diagnosis. (3) The quadratic rate of change was highest in diabetes, followed by cancer and hypertension, indicating that these diseases had led to higher increments of physical disability in later stage disease. After controlling for sociodemographic and comorbidity, depression status accounted for 39.9–73.6% and 37.9–100% of the variances in the physical disability intercept and change over time, respectively. Conclusions Despite the fact that a comparison across conditions was not statistically tested, an accelerated increase in physical disabilities was found as chronic conditions progressed. While stroke and cancer lead to disability immediately, conditions such as diabetes, cancer, and hypertension give rise to higher increments of physical disability in later stage disease. Mitigating depressive symptoms may be beneficial in terms of preventing disability development in this population.

Comparison of Transient Modeling Techniques for a Micro Turbine Engine

2006 ◽  
Author(s):  
Craig R. Davison ◽  
A. M. Birk
Keyword(s):  
Gas Turbines ◽  
Relative Size ◽  
Rate Of Change ◽  
Single Stage ◽  
Radial Compression ◽  
Shaft Speed ◽  
Transient Effects ◽  
Rates Of Change ◽  
Experimental Apparatus ◽  
Transient Modeling

A large number of papers have been published on transient modeling of large industrial and military gas turbines. Few, however, have examined micro turbines. The decrease in size affects the relative rates of change of shaft speed, gas dynamics and heat soak. This paper compares the modeled transient effects of a micro turbojet engine comprised of a single stage of radial compression and a single stage of axial expansion, with a diameter of 12cm. The model was validated with experimental data. Several forms of the model were produced starting with the shaft and fuel transients. Conservation of mass, and then energy, was subsequently added for the compressor, combustor and turbine, and a large inlet plenum that was part of the experimental apparatus. Heat soak to the engine body was incorporated into both the shaft and energy models. Heat soak was considered in the compressor, combustor and turbine. Since the engine diameter appears in the differential equations to different powers, the relative rates of change vary with diameter. The rate of change of shaft speed is very strongly influenced. The responses of the different transient effects are compared. The relative solution times are also discussed, since the relative size of the required time steps changes when compared to a large engine.

scholarly journals Doppler Shift of Radio Signals Transmitted between Orbiting Satellites

1982 ◽  
Vol 35 (2) ◽  
pp. 155 ◽  
Author(s):  
PL Dyson ◽  
JA Bennett
Keyword(s):  
Electron Concentration ◽  
Doppler Shift ◽  
Rate Of Change ◽  
Line Of Sight ◽  
Concentration Gradients ◽  
Mean Velocity ◽  
Radio Signals ◽  
The Mean ◽  
The Moment ◽  
The Individual

A general expression, applicable at VHF and above, is derived for the Doppler shift of radio signals transmitted between two satellites embedded in the ionosphere. The Doppler shift is made up of several contributions which depend on (a) the rate of change of the free space path between the satellites, (b) the components, perpendicular to the line of sight between the satellites, of both the mean velocity of the satellites and the electron concentration gradients, (c) the moment of the perpendicular electron concentration gradients and the deviations from the mean of the individual satellite perpendicular velocities, (d) the velocity components along the line of sight between the satellites, and the electron concentration values at each satellite, and (e) changes occurring in the ionosphere with time.

346. Measurements of the rate of change of temperature in high temperature-short time pasteurization plant

1947 ◽  
Vol 15 (1-2) ◽  
pp. 18-23
Author(s):  
F. Steghart
Keyword(s):  
High Temperature ◽  
Time Constant ◽  
Rate Of Change ◽  
Hot Water ◽  
Water Pipe ◽  
Temperature Changes ◽  
Rates Of Change ◽  
High Temperature Short Time ◽  
Short Time

It has recently been claimed that in modern high temperature-short time pasteurization plant fluctuations in temperature of the order of 1° F./sec. are unusual and probably artefacts, and that an instantaneous drop is certainly fictitious.It has, nevertheless, been shown that such rapid drops in temperature do in fact occur frequently in high temperature-short time plants of the type investigated. The plant investigated was not of the latest design incorporating devices for speeding up the control by injecting steam directly into the hot-water pipe.Temperature changes of the order of those in question were first observed by Mattick & Hiscox(1) of the National Institute for Research in Dairying, who carried out tests on pasteurization plant using a small mirror galvanometer with a very short time constant. The maximum rates of change were, however, not observed.

scholarly journals Eddy growth and mixing in mesoscale oceanographic flows

1997 ◽  
Vol 4 (4) ◽  
pp. 223-235 ◽  
Author(s):  
G. Haller ◽  
A. C. Poje
Keyword(s):  
Direct Relationship ◽  
Kinematic Model ◽  
Fluid Flows ◽  
Time Dependent ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Fluid Particles ◽  
Lagrangian Tracers ◽  
Particle Paths ◽  
General Time

Abstract. We study the relation between changes in the Eulerian topology of a two dimensional flow and the mixing of fluid particles between qualitatively different regions of the flow. In general time dependent flows, streamlines and particle paths are unrelated. However, for many mesoscale oceanographic features such as detaching rings and meandering jets, the rate at which the Euierian structures evolve is considerably slower than typical advection speeds of Lagrangian tracers. In this note we show that for two-dimensional, adiabatic fluid flows there is a direct relationship between observable changes in the topology of the Eulerian field and the rate of transport of fluid particles. We show that a certain class of flows is amenable to adiabatic or near adiabatic analysis, and, as an example, we use our results to study the chaotic mixing in the Dutkiewicz and Paldor (1994) kinematic model of the interaction of a meandering barotropic jet with a strong eddy.

A bladder contractility constant

1983 ◽  
Vol 245 (5) ◽  
pp. R673-R677
Author(s):  
J. C. Byrne ◽  
A. Tozeren
Keyword(s):  
Initial Velocity ◽  
Active Component ◽  
Isometric Force ◽  
Muscle Length ◽  
Rate Of Change ◽  
Contractile Element ◽  
Tetanic Contraction ◽  
Muscle Contractility ◽  
Maximum Isometric Force ◽  
The Moment

Muscle contractility can be characterized by two related properties: force and velocity. The initial velocity of a tetanic contraction is inversely related to preload. This was demonstrated experimentally by Hill and quantified in his well-known empiric equation. Subsequent investigators argued that a theoretical maximum contractile element velocity (V max) could be predicted from the rate of change of isometric force. V max has been applied clinically in heart studies, prompting others to use similar methods to evaluate bladder contractility. These attempts have so far been unsuccessful. The present study shows for whole canine bladders that the time to reach maximum isometric force from the moment of onset of active contraction is a constant independent of muscle length, preload, and maximum force. This can be expressed as a frequency constant (omega) whose calculation appears similar to that for V max. In contrast to V max, omega is obtained only from the active component of pressure.

The Anthropocene equation

2017 ◽  
Vol 4 (1) ◽  
pp. 53-61 ◽  
Author(s):  
Owen Gaffney ◽  
Will Steffen
Keyword(s):  
Limit Cycle ◽  
Late Quaternary ◽  
Rate Of Change ◽  
Earth System ◽  
Human Influence ◽  
Rates Of Change ◽  
The Earth ◽  
Uncertain Future ◽  
External Forces ◽  
Anthropogenic Forcings

The dominant external forces influencing the rate of change of the Earth System have been astronomical and geophysical during the planet’s 4.5-billion-year existence. In the last six decades, anthropogenic forcings have driven exceptionally rapid rates of change in the Earth System. This new regime can be represented by an ‘Anthropocene equation’, where other forcings tend to zero, and the rate of change under human influence can be estimated. Reducing the risk of leaving the glacial–interglacial limit cycle of the late Quaternary for an uncertain future will require, in the first instance, the rate of change of the Earth System to become approximately zero.

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