Invariant surfaces and phase space flux in three‐dimensional surface diffusion

1990 ◽  
Vol 93 (7) ◽  
pp. 5300-5314 ◽  
Author(s):  
Richard E. Gillilan
Keyword(s):  
Phase Space ◽  
Surface Diffusion ◽  
Three Dimensional ◽  
Invariant Surfaces ◽  
Dimensional Surface

BREAKDOWN OF LIBRATIONAL INVARIANT SURFACES

1999 ◽  
Vol 09 (05) ◽  
pp. 975-982
Author(s):  
MIQUEL ANGEL ANDREU ◽  
ALESSANDRA CELLETTI ◽  
CORRADO FALCOLINI
Keyword(s):  
Phase Space ◽  
Numerical Investigation ◽  
Invariant Tori ◽  
Three Dimensional ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
The Moon ◽  
Dimensional Phase Space ◽  
Invariant Surfaces ◽  
The Stability

A numerical investigation of the stability of invariant librational tori is presented. The method has been developed for a model describing the spin-orbit coupling in Celestial Mechanics. Periodic orbits approaching the librational torus are computed by means of Newton's method. According to Greene's criterion, their stability is strictly related to the survival of invariant tori. We consider librational tori around the main spin-orbit resonances (1:1, 3:2). Their existence provides the stability of the resonances, due to the confinement properties in the three-dimensional phase space associated to our model. The results are consistent with the actual observations of the eccentricity and of the oblateness parameter. A different behavior of the Moon and Mercury around the main resonances is evidenced, providing interesting suggestions about the different probabilities of capture in a resonance.

scholarly journals Integrability and bifurcation of a three-dimensional circuit differential system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Brigita Ferčec ◽  
Valery G. Romanovski ◽  
Yilei Tang ◽  
Ling Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Phase Space ◽  
Lyapunov Function ◽  
Differential System ◽  
Stable Equilibrium ◽  
Three Dimensional ◽  
Asymptotically Stable ◽  
Center Manifolds ◽  
Invariant Foliation ◽  
Invariant Surfaces

<p style='text-indent:20px;'>We study integrability and bifurcations of a three-dimensional circuit differential system. The emerging of periodic solutions under Hopf bifurcation and zero-Hopf bifurcation is investigated using the center manifolds and the averaging theory. The zero-Hopf equilibrium is non-isolated and lies on a line filled in with equilibria. A Lyapunov function is found and the global stability of the origin is proven in the case when it is a simple and locally asymptotically stable equilibrium. We also study the integrability of the model and the foliations of the phase space by invariant surfaces. It is shown that in an invariant foliation at most two limit cycles can bifurcate from a weak focus.</p>

Three Dimensional Surface Waviness of an Epitaxial Layer Due to Surface Diffusion Induced by Interface Misfit Dislocations

1994 ◽  
Vol 356 ◽  
Author(s):  
F. Jonsdottir
Keyword(s):  
Surface Diffusion ◽  
Epitaxial Layer ◽  
Thermodynamic Equilibrium ◽  
Three Dimensional ◽  
Misfit Dislocations ◽  
Surface Waviness ◽  
Mismatch Strain ◽  
Equilibrium Surface ◽  
Elastic Mismatch ◽  
Dimensional Surface

AbstractIt has been observed that, for some strained epitaxial layer systems, the surface of the layer develops roughness or waviness which correlates spatially with the positions of underlying interface misfit dislocations which partially relax the elastic mismatch strain. A model based on redistribution of mass by surface diffusion is analyzed to estimate the waviness of the three dimensional thermodynamic equilibrium surface due to intersecting arrays of interface misfit dislocations.

Enhancement of Heat Transfer Performance in Nuclear Fuel Rod Using Nanofluids and Surface Roughness Technique

2015 ◽  
Author(s):  
Kang Liu ◽  
Titan C. Paul ◽  
Leo A. Carrilho ◽  
Jamil A. Khan
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Nuclear Fuel ◽  
Three Dimensional ◽  
Pressurized Water ◽  
Bulk Fluid ◽  
Fuel Rod ◽  
Dimensional Surface

The experimental investigations were carried out of a pressurized water nuclear reactor (PWR) with enhanced surface using different concentration (0.5 and 2.0 vol%) of ZnO/DI-water based nanofluids as a coolant. The experimental setup consisted of a flow loop with a nuclear fuel rod section that was heated by electrical current. The fuel rod surfaces were termed as two-dimensional surface roughness (square transverse ribbed surface) and three-dimensional surface roughness (diamond shaped blocks). The variation in temperature of nuclear fuel rod was measured along the length of a specified section. Heat transfer coefficient was calculated by measuring heat flux and temperature differences between surface and bulk fluid. The experimental results of nanofluids were compared with the coolant as a DI-water data. The maximum heat transfer coefficient enhancement was achieved 33% at Re = 1.15 × 105 for fuel rod with three-dimensional surface roughness using 2.0 vol% nanofluids compared to DI-water.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

Three-dimensional surface reconstruction within noncontact diffuse optical tomography using structured light

2012 ◽  
Vol 17 (12) ◽  
pp. 126009 ◽  
Author(s):  
Kirstin Baum ◽  
Raimo Hartmann ◽  
Tobias Bischoff ◽  
Jan O. Oelerich ◽  
Stephan Finkensieper ◽  
...  
Keyword(s):  
Surface Reconstruction ◽  
Structured Light ◽  
Optical Tomography ◽  
Three Dimensional ◽  
Diffuse Optical Tomography ◽  
Dimensional Surface
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