CAPACITIES AND DISPLACEMENT ENERGY IN CONTACT HOFER GEOMETRY

2011 ◽  
Vol 08 (04) ◽  
pp. 709-724
Author(s):  
GHEORGHE PITIŞ
Keyword(s):  
Contact Manifold ◽  
Displacement Energy ◽  
Contact Displacement ◽  
Symplectic Case

A contact version of a Laudenbach's engulfing theorem is proved. Some properties of the notions of contact displacement energy and contact Hofer–Zehnder capacities are presented and, under the condition of existence of a modified action selector on a contact manifold, we can prove some inequalities involving these invariants. These inequalities are similar to the ones obtained by Frauenfelder, Ginzburg and Schlenk, in the symplectic case.

scholarly journals Development of a Compound Speckle Interferometer for Precision Three-Degree-of-Freedom Displacement Measurement

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1828
Author(s):  
Hung-Lin Hsieh ◽  
Bo-Yen Sun
Keyword(s):  
Speckle Interferometry ◽  
Degree Of Freedom ◽  
Heterodyne Interferometry ◽  
Beam Splitting ◽  
Speckle Interferometer ◽  
Real World Applications ◽  
Three Degree Of Freedom ◽  
Contact Displacement ◽  
Displacement Measurements ◽  
Measurement Capabilities

In this study, a compound speckle interferometer for measuring three-degree-of-freedom (3-DOF) displacement is proposed. The system, which combines heterodyne interferometry, speckle interferometry and beam splitting techniques, can perform precision 3-DOF displacement measurements, while still having the advantages of high resolution and a relatively simple configuration. The incorporation of speckle interferometry allows for non-contact displacement measurements by detecting the phase of the speckle interference pattern formed from the convergence of laser beams on the measured rough surface. Experiments were conducted to verify the measurement capabilities of the system, and the results show that the proposed system has excellent measurement capabilities suitable for future real-world applications.

Paper 6: Electronic Instrumentation Techniques in the Development of Pistons and Rings

1965 ◽  
Vol 180 (7) ◽  
pp. 54-69 ◽  
Author(s):  
M. H. Westbrook ◽  
R. Munro
Keyword(s):  
Internal Combustion Engine ◽  
Combustion Engine ◽  
Extreme Conditions ◽  
Dynamic Measurements ◽  
Inductive Transducer ◽  
New Type ◽  
Electronic Instrumentation ◽  
Mechanical Linkage ◽  
Contact Displacement ◽  
Engine Development

Both general and particular aspects of the application of electronic instrumentation in internal combustion engine development are discussed, and the work which has been carried out in the authors' establishment on instrumentation for dynamic measurements on the piston assembly is described, in particular, measurements of engine noise and vibration, and of displacement and temperature during operation, using telemetry systems, and making use of both radio and mechanical linkage techniques. The development of a new type of sub-miniature inductive transducer for non-contact displacement measurement under the extreme conditions inside a working piston is described, and the reasons making its development necessary discussed. Results obtained from a working engine showing piston movements as measured by several inductive transducers and transmitted over the linkage system are shown and compared to block vibration recordings made simultaneously; an initial interpretation of the very recent results is made. Finally, electronic methods developed for the static measurement of piston and ring properties are described and the results obtained discussed.

On the lebesgue measure of the periodic points of a contact manifold

1995 ◽  
Vol 218 (1) ◽  
pp. 91-102 ◽  
Author(s):  
Vesselin Petkov ◽  
Georgi Popov
Keyword(s):  
Lebesgue Measure ◽  
Contact Manifold ◽  
Periodic Points

scholarly journals Effect of strain and temperature on the threshold displacement energy in body-centered cubic iron

2016 ◽  
Vol 474 ◽  
pp. 113-119 ◽  
Author(s):  
Benjamin Beeler ◽  
Mark Asta ◽  
Peter Hosemann ◽  
Niels Grønbech-Jensen
Keyword(s):  
Body Centered Cubic ◽  
Displacement Energy ◽  
Threshold Displacement

A TRANSIENT DYNAMIC CONTACT PROBLEM IN THREE DIMENSIONS

1994 ◽  
Vol 05 (02) ◽  
pp. 215-217
Author(s):  
T.Y. Fan ◽  
H.G. Hahn ◽  
A. Voigt
Keyword(s):  
Contact Problem ◽  
Contact Stress ◽  
Dynamic Stress ◽  
Three Dimensional ◽  
Dynamic Contact ◽  
Three Dimensions ◽  
Dynamic Contact Problem ◽  
Transient Dynamic ◽  
Elliptic Region ◽  
Contact Displacement

In this study a three-dimensional transient dynamic contact problem is solved, and a theorem relating the contact stress and displacement over an elliptic region is proved. Numerical results for the contact displacement-time variation clearly demonstrate the effect of inertia induced by the dynamic stress.

On Harmonic Theory in Flows

2003 ◽  
Vol 46 (4) ◽  
pp. 617-631 ◽  
Author(s):  
Hong Kyung Pak
Keyword(s):  
Contact Manifold ◽  
Natural Generalization ◽  
Basic Flow ◽  
Compact Manifolds ◽  
Cohomology Spaces ◽  
Special Case

AbstractRecently [8], a harmonic theory was developed for a compact contact manifold from the viewpoint of the transversal geometry of contact flow. A contact flow is a typical example of geodesible flow. As a natural generalization of the contact flow, the present paper develops a harmonic theory for various flows on compact manifolds. We introduce the notions of H-harmonic and H*-harmonic spaces associated to a Hörmander flow. We also introduce the notions of basic harmonic spaces associated to a weak basic flow. One of our main results is to show that in the special case of isometric flow these harmonic spaces are isomorphic to the cohomology spaces of certain complexes. Moreover, we find an obstruction for a geodesible flow to be isometric.

A Variational Characterization of Contact Metric Manifolds With Vanishing Torsion

1992 ◽  
Vol 35 (4) ◽  
pp. 455-462 ◽  
Author(s):  
D. E. Blair ◽  
D. Perrone
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Integral Functional ◽  
Riemannian Metrics ◽  
Contact Manifold ◽  
Contact Condition ◽  
Contact Metric Manifolds ◽  
Point Condition ◽  
Webster Scalar Curvature ◽  
Group Of Isometries

AbstractChern and Hamilton considered the integral of the Webster scalar curvature as a functional on the set of CR-structures on a compact 3-dimensional contact manifold. Critical points of this functional can be viewed as Riemannian metrics associated to the contact structure for which the characteristic vector field generates a 1-parameter group of isometries i.e. K-contact metrics. Tanno defined a higher dimensional generalization of the Webster scalar curvature, computed the critical point condition of the corresponding integral functional and found that it is not the K-contact condition. In this paper two other generalizations are given and the critical point conditions of the corresponding integral functionals are found. For the second of these, this is the K-contact condition, suggesting that it may be the proper generalization of the Webster scalar curvature.

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