Varieties of solvable Lie rings of finite width

1998 ◽  
Vol 63 (5) ◽  
pp. 569-574
Author(s):  
D. S. Ananichev ◽  
M. V. Volkov
Keyword(s):  
Finite Width ◽  
Lie Rings

Dispersion Characteristics of Multi-Step Open Slow-Wave Systems of Finite Width: Analysis

1997 ◽  
Vol 51 (8) ◽  
pp. 77-84
Author(s):  
L. M. Buzik ◽  
O. F. Pishko ◽  
S.A. Churilova ◽  
O. I. Sheremet
Keyword(s):  
Slow Wave ◽  
Finite Width ◽  
Dispersion Characteristics

Quantum Tunneling

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Tunneling ◽  
Alpha Particles ◽  
Attractive Potential ◽  
Scanning Tunneling ◽  
Finite Width ◽  
Potential Well ◽  
Surface Molecules ◽  
Repulsive Coulomb ◽  
The Subject ◽  
The One

Quantum tunneling, wherein a quanject has a non-zero probability of tunneling into and then exiting a barrier of finite width and height, is the subject of Chapter 13. The description for the one-dimensional case is extended to the barrier being inverted, which forms an attractive potential well. The first application of this analysis is to the emission of alpha particles from the decay of radioactive nuclei, where the alpha-nucleus attraction is modeled by a potential well and the barrier is the repulsive Coulomb potential. Excellent results are obtained. Ditto for the similar analysis of proton burning in stars and yet a different analysis that explains tunneling through a Josephson junction, the connector between two superconductors. The final application is to the scanning tunneling microscope, a device that allows the microscopic surfaces of solids to be mapped via electrons from the surface molecules tunneling into the tip of the STM probe.

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals

2004 ◽  
Vol 85 (21) ◽  
pp. 4834-4836 ◽  
Author(s):  
Zhaofeng Li ◽  
Haibo Chen ◽  
Zhitang Song ◽  
Fuhua Yang ◽  
Songlin Feng
Keyword(s):  
Photonic Crystals ◽  
Finite Width

Automated Deburring with a Filamentary Brush: Prescribed Burr Geometry

1999 ◽  
Vol 121 (3) ◽  
pp. 385-392 ◽  
Author(s):  
Robert J. Stango ◽  
Lienjing Chen ◽  
Vikram Cariapa
Keyword(s):  
Penetration Depth ◽  
Dynamic Model ◽  
Control Strategy ◽  
Feed Rate ◽  
Material Removal ◽  
Vision System ◽  
Closed Form Solution ◽  
Straight Edge ◽  
Finite Width ◽  
Production Environment

In this paper, a dynamic model for removal of edge burrs with a compliant brushing tool is reported. Description of the burr geometry is assumed to be known through on-line measurement methods such as a computer vision system in the flexible manufacturing cell. Dynamic response of the brush/workpiece system is evaluated on the basis of experimentally obtained data. Master Curves are introduced as machining descriptors which characterize the incremental burr removal performance of the brush/workpiece system, leading to the development of an analytical dynamic model for orthogonal burr removal using a finite-width brushing tool. Based upon the dynamic model for material removal, a control strategy for automatic deburring is presented for burr configurations having constant height as well as variable height. A closed-form solution for transverse brush feed rate is obtained which is applicable for removal of burrs having variable height, as described by suitable geometry functions. For illustrative purposes, simulations are carried out for a straight-edge burr profile and sinusoidal burr geometry. Results are reported which identify important relationships among brush feed rate, brush penetration depth, and brush rotational speed. In order to help assess the validity of the proposed analytical model and control strategy, experimental results are reported for a combination ramp/straight-edge burr configuration. The results demonstrate generally good correlation between the predicted and actual profile for the edge burr that has been machined. In addition, some important observations include; (1) burr removal is most rapidly carried out by using the highest brush speed and deepest brush/workpiece penetration depth, subject to the condition that the brush fiber is not damaged, (2) Currently available polymer abrasive brushing tools exhibit very slow machining characteristics and must be improved in order to be used in a production environment where burr size is appreciable, (3) Material removal characteristics of the leading and trailing edge of brushes may be a source of error which merits further investigation.

A Simple Approach to Evaluate Non-Newtonian Viscosity Effects in a Lubricating System

1987 ◽  
Vol 109 (1) ◽  
pp. 177-182 ◽  
Author(s):  
Patrick Bourgin ◽  
Joseph-Marc Francois
Keyword(s):  
Computer Code ◽  
Simple Approach ◽  
Rheological Parameters ◽  
Finite Width ◽  
Slider Bearing ◽  
Empirical Formulas ◽  
Newtonian Viscosity ◽  
Pocket Calculator ◽  
Viscosity Effects ◽  
Analytical Formulas

The working characteristics of a finite width slider bearing lubricated by a non-Newtonian fluid are computed. The analysis proposed here allows its performances to be evaluated by means of a pocket calculator. For that purpose, a computer code based on a finite element method is used. The program runs for different values of pertinent kinematical, geometrical and rheological parameters. The corresponding results are fitted by means of adequate analytical formulas, which are very easy to handle. The accuracy of these empirical formulas is investigated in several typical cases. The agreement with the numerical solution is proven to be satisfactory.

Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

2013 ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Fatigue Crack ◽  
Condition Monitoring ◽  
Crack Depth ◽  
Forced Response ◽  
System Response ◽  
Contour Plot ◽  
Crack Model ◽  
Finite Width ◽  
Angular Response ◽  
Crack Location

The goal of this work is to establish a condition monitoring regimen capable of diagnosing the depth and location of a transverse fatigue crack in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model used. The model should account for the depth of the crack and the localization of the crack along the shaft. Negating the influence of crack location on system response ignores a crucial component of real cracks. Two gaping crack models are presented; the first simulates a finite-width manufactured notch, while the second models an open fatigue crack. An overhung rotordynamic system is modeled, imitating an available rotordynamic test rig. Four degree-of-freedom equations of motion for both crack models are presented and discussed, along with corresponding transfer matrix techniques. Free and forced response analyses are performed, with emphasis placed on results applicable to condition monitoring. It is demonstrated that two identifiers are necessary to diagnose the crack parameters: the 2X resonance frequency and the magnitude of the 2X component of the rotor angular response at resonance. First, a contour plot of the 2X resonant shaft speed versus crack depth and location is generated. The magnitude of the 2X component of the rotor’s angular response along the desired contour is obtained, narrowing the possible pairs of crack location/depth to either one or two possibilities. Practical aspects of the diagnosis procedure are then discussed.

Elasto-Plastic Fracture Analysis of Finite-Width Cracked Stiffened Plate

2014 ◽  
Vol 496-500 ◽  
pp. 1052-1057 ◽  
Author(s):  
Jun Lin Deng ◽  
Ping Yang ◽  
Qin Dong ◽  
Xiang Yan
Keyword(s):  
Field Method ◽  
Uniaxial Tensile ◽  
Small Scale ◽  
Finite Width ◽  
Stiffened Plate ◽  
Line Field ◽  
Strain Fields ◽  
Zone Length ◽  
Crack Line ◽  
Crack Tips

Thispaper adopts the crack line-field method to analyze finite-width stiffenedplates with central through I-type crack under uniaxial tensile loading. Themethod completely abandons the small scale yield hypothesis. The plastic stressand strain fields at crack tips and the plastic-zone length can be accurately determinedby combining with equivalent shear stress of Westergaard stress function in theposition of stiffener. It can be seen from the illustrative example that theresults of the paper agree well with those by finite element method.

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