Integrals on a moving manifold and geometrical probability

1977 ◽  
Vol 9 (3) ◽  
pp. 588-603 ◽  
Author(s):  
Adrian Baddeley
Keyword(s):  
Fluid Mechanics ◽  
General Expression ◽  
Rate Of Change ◽  
Time Rate ◽  
Geometrical Probability ◽  
Interface Displacement ◽  
Numerical Property

For a manifold which is moving and changing with time, consider some numerical property which at each instant is equal to an integral over the manifold. We derive a general expression for the time rate of change of this integral. Corollaries include a precise general form of Crofton's boundary theorem, de Hoff's interface displacement equations (with some new extensions) and a theorem in fluid mechanics.

Integrals on a moving manifold and geometrical probability

1977 ◽  
Vol 9 (03) ◽  
pp. 588-603 ◽  
Author(s):  
Adrian Baddeley
Keyword(s):  
Fluid Mechanics ◽  
General Expression ◽  
Rate Of Change ◽  
Time Rate ◽  
Geometrical Probability ◽  
Interface Displacement ◽  
Numerical Property

For a manifold which is moving and changing with time, consider some numerical property which at each instant is equal to an integral over the manifold. We derive a general expression for the time rate of change of this integral. Corollaries include a precise general form of Crofton's boundary theorem, de Hoff's interface displacement equations (with some new extensions) and a theorem in fluid mechanics.

STUDY OF PHASE PROPAGATION IN SUPERCONDUCTING ALUMINUM BY ULTRASONIC ATTENUATION MEASUREMENTS

1959 ◽  
Vol 37 (5) ◽  
pp. 614-618 ◽  
Author(s):  
K. L. Chopra ◽  
T. S. Hutchison
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Ultrasonic Attenuation ◽  
Cylindrical Specimen ◽  
Current Theory ◽  
Superconducting Phase ◽  
Rate Of Change ◽  
Time Rate ◽  
Phase Propagation ◽  
The Magnetic Field

The phase propagation in superconducting aluminum has been studied by measuring the time rate of change of ultrasonic attenuation. The time taken for the destruction of the superconducting phase in a cylindrical specimen, by means of a magnetic field, H, greater than the critical field, Hc, is approximately proportional to{H/(H–Hc)} in agreement with eddy-current theory. In the converse case, where the superconducting phase is restored by switching off the magnetic field H (>Hc), the total time taken is nearly independent of the temperature (or Hc) as well as H. The superconducting phase grows at a non-uniform volume rate which is considerably less than the uniform rate of collapse.

Cosmic-Ray Energy Changes

1974 ◽  
Vol 2 (5) ◽  
pp. 297-299 ◽  
Author(s):  
L. J. Gleeson ◽  
G. M. Webb
Keyword(s):  
Cosmic Rays ◽  
Current Density ◽  
Cosmic Ray ◽  
Rate Of Change ◽  
Time Rate ◽  
Differential Current

The purpose of this paper is to provide a new expression for < ṗ > the average time-rate-of-change of momentum of cosmic-ray particles propagating in the interplanetary region. The expression derived replaces the previously used adiabatic deceleration formula and it is arrived at by a rearrangement and reinterpretation of the well known equation of transport for cosmic-rays. Thus, although we provide a new expression for < ṗ > we maintain the equation of transport and do not render invalid results for differential intensity and differential current density of cosmic-ray particles obtained by its solution (Jokipii 1971; Gleeson 1972).

Sound and turbulence modulation by particles in high-speed shear flows

2019 ◽  
Vol 875 ◽  
pp. 254-285 ◽  
Author(s):  
David A. Buchta ◽  
Gregory Shallcross ◽  
Jesse Capecelatro
Keyword(s):  
Gas Phase ◽  
High Speed ◽  
Pressure Fluctuations ◽  
Sound Radiation ◽  
Rate Of Change ◽  
Intensity Increase ◽  
Mass Loading ◽  
Local Pressure ◽  
Time Rate ◽  
Particle Laden Flows

High-speed free-shear-flow turbulence, laden with droplets or particles, can radiate weaker pressure fluctuations than its unladen counterpart. In this study, Eulerian–Lagrangian simulations of high-speed temporally evolving shear layers laden with monodisperse, adiabatic, inertial particles are used to examine particle–turbulence interactions and their effect on radiated pressure fluctuations. An evolution equation for gas-phase pressure intensity is formulated for particle-laden flows, and local mechanisms of pressure changes are quantified over a range of Mach numbers and particle mass loadings. Particle–turbulence interactions alter the local pressure intensity directly via volume displacement (due to the flow of finite-size particles) and drag coupling (due to local slip velocity between phases), and indirectly through significant turbulence changes. The sound radiation intensity near subsonic mixing layers increases with mass loading, consistent with existing low Mach number theory. For supersonic flows, sound levels decrease with mass loading, consistent with trends observed in previous experiments. Particle-laden cases exhibit reduced turbulent kinetic energy compared to single-phase flow, providing one source of their sound changes; however, the subsonic flow does not support such an obvious source-to-sound decomposition to explain its sound intensity increase. Despite its decrease in turbulence intensity, the louder particle-laden subsonic flows show an increase in the magnitude and time-rate-of-change of fluid dilatation, providing a mechanism for its increased sound radiation. Contrasting this, the quieter supersonic particle-laden flows exhibit decreased gas-phase dilatation yet its time-rate-of-change is relatively insensitive to mass loading, supporting such a connection.

A PC-Based Modeling Tool for Creep, Fatigue, and Creep-Fatigue Interactions Using a Viscoplasticity Theory

1991 ◽  
Vol 113 (2) ◽  
pp. 174-179 ◽  
Author(s):  
J. T. Fong ◽  
B. Bernstein
Keyword(s):  
Elevated Temperatures ◽  
Helmholtz Free Energy ◽  
Thermodynamic Theory ◽  
Rate Of Change ◽  
Free Energy Function ◽  
Explicit Dependence ◽  
Time Rate ◽  
Modeling Tools ◽  
One Dimensional ◽  
Creep Fatigue

Computational results for modeling one-dimensional stress relaxation, creep, fatigue, and creep-fatigue interaction phenomena of metals at elevated temperatures using a unifying thermodynamic theory of viscoplasticity are presented. The theory incorporates in a nonequilibrium formulation the idea of a “concealed” parameter α, originally due to Bridgman (1950), where the constitutive equations are governed by 1) a thermodynamic potential such as the Helmholtz free energy function F with an explicit dependence on α, and 2) a prescription for α˙, the time rate of change of α, such that α˙ is proportional to −Fα, the negative of the partial derivative of F with respect to α. Significance of the results and a comparison with other modeling tools in the literature are discussed.

Dynamic Analysis of Flexible Multi-Body Mechanical Systems

1996 ◽  
Vol 210 (4) ◽  
pp. 309-316
Author(s):  
P Davison ◽  
D K Longmore ◽  
C R Burrows
Keyword(s):  
Rate Of Change ◽  
The Other ◽  
Structural Deformation ◽  
Euler Parameters ◽  
Time Rate ◽  
Constraint Equations ◽  
Rigid Body Modes ◽  
The Individual ◽  
Multi Body ◽  
Flexible Component

The use of only the free component modes as coordinates when computing the motion of mechanisms involving flexible component structures connected together by driven or undriven joints has been further developed, with the constraint errors being controlled by penalty parameters related to both the errors and their time rate of change. Symbolic computation is used to incorporate the constraint equations into the solution program. The degenerate rigid-body modes may be indefinitely large, with Euler parameters being used for rotation, but the other free modes of the individual components, which involve structural deformation, are assumed small. The approach is examined in two examples in which the computed results are compared with experimental measurements.

scholarly journals A Differential Equation for Mutation Rates in Environmental Coevolution

2021 ◽  
Author(s):  
C E Neal-Sturgess
Keyword(s):  
Population Level ◽  
Equation Of Motion ◽  
Rate Of Change ◽  
Mutation Rates ◽  
Time Base ◽  
Time Rate ◽  
Least Action ◽  
Principle Of Least Action ◽  
Selection For ◽  
Rate Frequency

AbstractIn their paper Natural selection for least action (Kaila and Annila 2008) they depict evolution as a process conforming to the Principle of Least Action (PLA). From this concept, together with the Coevolution model of Lewontin, an equation of motion for environmental coevolution is derived which shows that it is the time rate (frequency) of evolutionary change of the organism (mutations) that responds to changes in the environment. It is not possible to compare the theory with viral or bacterial mutation rates, as these are not measured on a time base. There is positive evidence from population level avian studies where the coefficient of additive evolvability (Cav) and its square (IA) change with environmental favourability in agreement with this model. Further analysis shows that the time rate of change of the coefficient of additive evolvability (Cav) and its square (IA) are linear with environmental favourability, which could help in defining the Lagrangian of the environmental effects.

scholarly journals Set up and Operation of a Recirculating Wetted Rigid Media Evaporative Cooler Installed in a Gas Turbine Combustion Inlet Air System

1994 ◽  
Author(s):  
R. S. Johnson
Keyword(s):  
Gas Turbine ◽  
Water Hardness ◽  
Rate Of Change ◽  
Time Rate ◽  
Blow Down ◽  
Inlet System ◽  
Elemental Concentrations ◽  
Air Inlet ◽  
Evaporative Cooler ◽  
Set Up

A procedure for setting up and operating a recirculating evaporative cooler installed in the combustion air inlet system of a gas turbine is described. The procedure includes a recommendation for selecting the ambient operating wet and dry bulb temperatures. A description of the parameters used in the procedure and calculation methods are shown. In response to frequent inquiries about the rate at which water hardness (and elemental concentrations) increases with time, an equation to evaluate this increase with time is introduced. The time rate of change of water hardness and elemental concentrations for various blow-down rates and operating times are also evaluated.

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