Comparison of inlet suppressor data with approximate theory based oncutoff ratio

1980 ◽  
Author(s):  
E. RICE ◽  
L. HEIDELBERG
Keyword(s):  
Approximate Theory

Line broadening in the electron resonance spectra of spin probes dissolved in anisotropic media: the effect of nuclear spin quantization

1977 ◽  
Vol 353 (1672) ◽  
pp. 87-102 ◽  
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Nuclear Spin ◽  
Dynamic Properties ◽  
Orientational Order ◽  
Anisotropic Media ◽  
Approximate Theory ◽  
Spin Probes ◽  
Line Broadening ◽  
Electron Resonance

The line broadening in the electron resonance spectra of monoradicals dissolved in anisotropic media, such as liquid crystals, provides a valuable probe of both the orientational order and the molecular dynamics. However, the fast-motion relaxation theory employed to extract this information from the linewidths assumes that the nuclear spin is quantized along the direction of the magnetic field. This approximation is only correct when the symmetry axis of a uniaxial liquid crystal is either parallel or perpendicular to the field. We have therefore removed this assumption and have developed a general theory of line broadening valid for all orientations of the liquid crystal. The theory is then used to evaluate the angular dependence of the linewidths and this is compared with the dependence predicted by the approximate theory, for two classes of nitroxide spin probes. These comparisons reveal that for steroidal spin probes the error, introduced by assuming the nuclear spin to be quantized along the field, is confined to the dynamic properties derived from the linewidths. In contrast, significant errors appear in both the dynamic and static properties obtained from an analysis of the linewidth variations for fatty acid spin probes based on the approximate theory. It would seem that the exact theory must be employed to obtain precise information from linewidth investigations of liquid crystals, except when the orientational order is extremely small.

Approximate theory of multiway block designs

1986 ◽  
Vol 14 (4) ◽  
pp. 339-346 ◽  
Author(s):  
Friedrich Pukelsheim
Keyword(s):  
Block Designs ◽  
Approximate Theory

A Stochastic Theory for Nonlinear Ship Rolling in irregular Seas

1982 ◽  
Vol 26 (04) ◽  
pp. 229-245 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
Markov Processes ◽  
Digital Simulation ◽  
Stochastic Theory ◽  
Simple Expression ◽  
Roll Angle ◽  
Rolling Motion ◽  
Approximate Theory ◽  
Averaging Techniques ◽  
Good Agreement ◽  
Ship Rolling

By a combination of averaging techniques with the theory of Markov processes, an approximate theory is developed for the rolling motion of a ship in beam waves. A simple expression is obtained for the distribution of the roll angle, and is tested by a comparison with a set of digital simulation estimates due to Dalzell. Good agreement is obtained over a realistic range of damping values.

An Approximate Theory of Lateral Impact on Beams

1955 ◽  
Vol 22 (1) ◽  
pp. 69-76
Author(s):  
B. A. Boley
Keyword(s):  
Sudden Change ◽  
Approximate Theory ◽  
Lateral Impact ◽  
Governing Equations ◽  
Transverse Impact ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Lateral Contraction ◽  
Velocity Of Propagation ◽  
Variation Technique

Abstract The approximate theory derived in this paper describes, by means of a “traveling-wave” approach, the behavior of beams under transverse impact. Lateral impact is considered in detail, namely, one in which a section of the beam undergoes a sudden change in velocity or shear force. The theory considers the effects of shear deformations and of rotatory inertia according to Timoshenko’s model, and that of lateral contraction as suggested by Love. The governing equations and the boundary conditions are developed with the aid of an energy-variation technique. Numerical examples are given in which the behavior of the boundary layer near the point of impact is examined. For one of these the exact solution is available and is in agreement with the present approximate results. Some general considerations concerning the velocity of propagation also are discussed.

A Basis for Automated Control of Steam Trap Subcool in SAGD

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 680-686 ◽  
Author(s):  
Dharmeshkumar R. Gotawala ◽  
Ian D. Gates
Keyword(s):  
Temperature Difference ◽  
Oil Sands ◽  
Dynamic Control ◽  
Recovery Process ◽  
Steam Injection ◽  
Liquid Pool ◽  
Gravity Drainage ◽  
Approximate Theory ◽  
Smart Wells ◽  
The Difference

Summary Full steam conformance along the well pair of the steam-assisted gravity-drainage (SAGD) oil-sands-recovery process is essential for high thermal efficiency. Conformance can be improved by controlling injection and production strategies to ensure that steam is delivered to target regions in the reservoir. Smart wells use interval-control valves (ICVs) that, conceptually, can be dynamically controlled to yield uniform steam injectivity along the well pair. Dynamic control algorithms, such as proportional-integral-derivative (PID) control and their associated controller parameters, have not yet been developed for the SAGD processes that use ICVs. One control strategy would be to control the interwell subcool temperature difference—that is, the difference between the steam-injection temperature and the produced-fluids temperature. If this temperature difference is small, then the liquid pool above the production well is small and there is a likelihood of live steam production from the chamber. On the other hand, if the difference is large, the pool may rise above the injection well and gravity drainage is hindered because the chamber is largely filled with liquid. Here, the focus is on developing a simple, approximate theory for the behavior of the liquid pool at the base of the steam chamber to determine the ranges of values of control parameters to achieve a targeted interwell subcool temperature difference.

The aerodynamic resistance to a rotating sphere in the transition régime between free molecule and continuum creep flow

1964 ◽  
Vol 279 (1376) ◽  
pp. 39-49 ◽  
Keyword(s):  
Rarefied Gas ◽  
Aerodynamic Drag ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Approximate Theory ◽  
Drag Torque ◽  
Free Molecule ◽  
Steel Sphere ◽  
Creep Flow ◽  
Wide Range

An experimental and theoretical study has been made of the aerodynamic drag torque on a sphere rotating in a rarefied gas. The drag torque on a magnetically suspended polished steel sphere rotating in air was measured over a wide range of Knudsen numbers from continuum to free molecule flow and for several different Mach numbers up to ca . 1. The drag under free molecule conditions was found to be consistent with the assumption of perfectly diffuse reflexion of molecules at the surface of the rotor. An approximate theory is derived which is analogous to Millikan’s solution to the problem of plane Couette flow and is valid for low Mach and Reynolds numbers. Theory and experiment are found to agree to within 10 % in the range investigated, for Reynolds numbers less than ca . 20.

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