scholarly journals The formation of vortices from a surface of discontinuity

1931 ◽  
Vol 134 (823) ◽  
pp. 170-192 ◽  
Keyword(s):  
Steady State ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Small Oscillations ◽  
Approximate Form ◽  
History Of ◽  
State Increase ◽  
Liquid Surfaces

Helmholtz was the first to remark on the instability of those “liquid surfaces” which separate portions of fluid moving with different velocities, and Kelvin, in investigating the influence of wind on waves in water, supposed frictionless, has discussed the conditions under which a plane surface of water becomes unstable. Adopting Kelvin’s method, Rayleigh investigated the instability of a surface of discontinuity. A clear and easily accessible rendering of the discussion is given by Lamb. The above investigations are conducted upon the well-known principle of “small oscillations”—there is a basic steady motion, upon which is superposed a flow, the squares of whose components of velocity can be neglected. This method has the advantage of making the equations of motion linear. If by this method the flow is found to be stable, the equations of motion give the subsequent history of the system, for the small oscillations about the steady state always remain “small.” If, however, the method indicates that the system is unstable, that is, if the deviations from the steady state increase exponentially with the time, the assumption of small motions cannot, after an appropriate interval of time, be applied to the case under consideration, and the equations of motion, in their approximate form, no longer give a picture of the flow. For this reason, which is well known, the investigations of Rayleigh only prove the existence of instability during the initial stages of the motion. It is the object of this note to investigate the form assumed by the surface of discontinuity when the displacements and velocities are no longer small.

The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations

1972 ◽  
Vol 52 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Robert Y. S. Lai ◽  
Lyle F. Mockros
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Equations Of Motion ◽  
Mass Effect ◽  
Added Mass ◽  
Fluid Forces ◽  
Fluid Resistance ◽  
Oblate Spheroids ◽  
History Of ◽  
Flow Drag

Stokes's linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.

Sensitivity Analysis for the Steady-State Response of Damped Linear Elastodynamic Systems Subject to Periodic Loads

1990 ◽  
Author(s):  
Daniel A. Tortorelli
Keyword(s):  
Steady State ◽  
Vibration Amplitude ◽  
Equations Of Motion ◽  
Steady State Response ◽  
Analysis Techniques ◽  
Direct Differentiation ◽  
State Response ◽  
Need To Evaluate ◽  
The Time Domain ◽  
General Response

Abstract Adjoint and direct differentiation methods are used to formulate design sensitivities for the steady-state response of damped linear elastodynamic systems that are subject to periodic loads. Variations of a general response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple the equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity expressions. This eliminates the need to evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over time, thus they are quickly computed. The methodology is valid for problems with proportional as well as non-proportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crankshaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. Both the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are also calculated to validate the explicit sensitivity results.

A System for Individualized Dosing of Intravenous Aminophylline Using a Programmable Calculator

PEDIATRICS ◽  
1984 ◽  
Vol 73 (1) ◽  
pp. 64-67
Author(s):  
J. Chris Mitsuoka ◽  
Richard J. Fleck
Keyword(s):  
Steady State ◽  
Serum Sample ◽  
Drug Exposure ◽  
Plasma Concentrations ◽  
Dose Administration ◽  
Programmable Calculator ◽  
Concentration Determination ◽  
A Value ◽  
Individualized Dosing ◽  
History Of

A program that calculates a value of clearance for an individual patient prior to reaching steady state in the early stages of aminophylline therapy is presented. The program is written for the Texas Instruments TI-59 programmable calculator and may be used with or without the PC-100C printer. The program can provide clinically useful information concerning projected plasma concentrations prior to reaching steady state with an accurate history of the dose administration and serum concentration determination. If the patient has not received xanthene therapy prior to admission, only one serum sample is required. If there has been prior drug exposure, a second serum sample is required. An iterative technique, which would be impractical to use without calculator assistance, is employed to make these determinations.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

Acute hypoxia increases cytosolic calcium in cultured pulmonary arterial myocytes

1993 ◽  
Vol 264 (3) ◽  
pp. L323-L328 ◽  
Author(s):  
C. G. Salvaterra ◽  
W. F. Goldman
Keyword(s):  
Smooth Muscle ◽  
Steady State ◽  
Sarcoplasmic Reticulum ◽  
Acute Hypoxia ◽  
Cytosolic Calcium ◽  
Pulmonary Arterial ◽  
Pulmonary Arterial Smooth Muscle ◽  
Early Rise ◽  
Ca2 Channels ◽  
State Increase

The effects of hypoxia on the cytosolic Ca2+ concentration, [Ca2+]i, were characterized in cultured pulmonary arterial smooth muscle (PASM) cells. Reducing O2 tension (PO2) from 150 to < 25 Torr induced a reversible 100-200% increase in [Ca2+]i that was characterized by two components: an early rise in [Ca2+]i that was dependent on the rate, as well as the magnitude, of decline in PO2 and a later, steady-state increase that was independent of the rate at which PO2 changed. Caffeine lowered [Ca2+]i during normoxia and blocked the early component of the response to hypoxia, whereas the steady-state hypoxic response was only partially inhibited. Like hypoxia, thapsigargin (TG) elevated [Ca2+]i, and there was no additional hypoxia-induced elevation in [Ca2+]i at any time after exposure to TG. At steady state, the hypoxic responses were completely reversed by removal of extracellular Ca2+, whereas, on average, verapamil and nifedipine attenuated the hypoxia-induced increases in [Ca2+]i by only 44 and 35%, respectively. These results suggest that hypoxia-induced elevation of [Ca2+]i in PASM cells consists of an early release of Ca2+ from the sarcoplasmic reticulum and a later influx of extracellular Ca2+, in part, through nifedipine- and verapamil-insensitive Ca2+ channels. The results are consistent with the idea that hypoxia and thapsigargin may share common mechanisms for tonically increasing [Ca2+]i.

Effects of temperature on acid-base balance and ventilation in desert iguanas

1981 ◽  
Vol 51 (2) ◽  
pp. 452-460 ◽  
Author(s):  
P. E. Bickler
Keyword(s):  
Steady State ◽  
Pulmonary Ventilation ◽  
Respiratory Acidosis ◽  
Lung Ventilation ◽  
Acid Base Balance ◽  
Acid Base ◽  
Arterial Ph ◽  
Blood Relative ◽  
Base Balance ◽  
History Of

The effects of constant and changing temperatures on blood acid-base status and pulmonary ventilation were studied in the eurythermal lizard Dipsosaurus dorsalis. Constant temperatures between 18 and 42 degrees C maintained for 24 h or more produced arterial pH changes of -0.0145 U X degrees C-1. Arterial CO2 tension (PCO2) increased from 9.9 to 32 Torr plasma [HCO-3] and total CO2 contents remained constant at near 19 and 22 mM, respectively. Under constant temperature conditions, ventilation-gas exchange ratios (VE/MCO2 and VE/MO2) were inversely related to temperature and can adequately explain the changes in arterial PCO2 and pH. During warming and cooling between 25 and 42 degrees C arterial pH, PCO2 [HCO-3], and respiratory exchange ratios (MCO2/MO2) were similar to steady-state values. Warming and cooling each took about 2 h. During the temperature changes, rapid changes in lung ventilation following steady-state patterns were seen. Blood relative alkalinity changed slightly with steady-state or changing body temperatures, whereas calculated charge on protein histidine imidazole was closely conserved. Cooling to 17-18 degrees C resulted in a transient respiratory acidosis correlated with a decline in the ratio VE/MCO2. After 12-24 h at 17-18 degrees C, pH, PCO2, and VE returned to steady-state values. The importance of thermal history of patterns of acid-base regulation in reptiles is discussed.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

scholarly journals Nonviscous Oblique Stagnation Point Flow towards Riga Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sobia Akbar ◽  
Azad Hussain
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Stagnation Point ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Riga Plate ◽  
Mathematical Techniques

Purpose. The flow of nonviscous Casson fluid is examined in this study over an oscillating surface. The model of the fluid flow has been inspected in the presence of oblique stagnation point flow. The scrutiny is subsumed for the Riga plate by considering the effects of magnetohydrodynamics. The Riga plate is considered as an electromagnetic lever which carries eternal magnets and a stretching line up of alternating electrodes coupled on a plane surface. We have considered nonboundary layer two-dimensional incompressible flow of the fluid. The fluid flow model is analyzed in the fixed frame of reference. Motivation. The motivation of achieving more suitable results has always been a quest of life for scientists; the capability of determining the boundary layer of flow on aircraft which either stays laminar or turns turbulent has encouraged the researcher to study compressible flow in depth. The compressible fluid with boundary layer flow has been utilized by numerous researchers to reduce skin friction and enhance thermal and convectional heat exchange. Design/Approach/Methodology. The attained partial differential equations will be critically inspected by using suitable similarity transformation to transform these flows thrived equations into higher nonlinear ordinary differential equations (ODE). Then, these equations of motion are intercepted by mathematical techniques such as the bvp4c method in Maple and Matlab. The graphical and tabular representation of different parameters is also given. Findings. The behavior of β and modified Hartmann number M increases by positively increasing the values of both parameters for F η , while ω decreases with increasing the values of ω for F η . The graph of β shows upward behavior for distinct values for both G η and G ′ η for velocity portray. Prandtl number and β for the temperature profile of θ η and θ 1 η goes downward with increasing parameters.

scholarly journals On the possible ellipticity of Saturn's ring

1924 ◽  
Vol 106 (739) ◽  
pp. 526-552 ◽  
Keyword(s):  
Nineteenth Century ◽  
The Other ◽  
Gravitational Attraction ◽  
History Of Astronomy ◽  
Small Oscillations ◽  
First Approximation ◽  
Elliptical Ring ◽  
Single Ring ◽  
History Of ◽  
Concentric Circles

Clerk Maxwell’s investigation into the constitution and stability of Saturn’s Ring was based upon the fundamental supposition that the rings were composed of particles arranged in concentric circles. Although the particles could perform small oscillations about their mean positions, it is evident that the outline of the ring would be to all appearances circular. A line in Clerke’s ‘Popular History of Astronomy in the Nineteenth Century’ (page 299) suggests that some observers have regarded the outline of the ring as elliptical. It is therefore of interest to enquire under what conditions an elliptical ring could exist. The ellipse is a more general form than a circle. If, therefore, it can be shown that an elliptic ring is possible, any explanation of the origin of the rings must take account of this fact. In this paper a single ring of particles is examined. The actual Ring of Saturn probably consists of numerous rings, one within the other. By their gravitational attraction, each will affect the motions of the others. As a first approximation, however, it is sufficient to consider the case of a single ring.

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