3D Measurements of a Two-phase Flow inside an Optical Cylinder Based on Full-Field Cross-Interface Computed Tomography
0
Citation
28
Reference
10
Related Paper
Abstract:
Abstract Three-dimensional (3D) tomographic reconstruction in confined-space requires a mapping relationship which considers the refraction distortion caused by optical walls. In this work, a tomography method, namely full-field cross-interface computed tomography (FCICT), is proposed to solve confine-space problems. The FCICT method utilizes Snell’s law and reverse ray-tracing to analytically correct imaging distortion and establishes the mapping relationship from 3D measurement domain to 2D images. Numerical phantom study is first employed to validate the FCICT method. Afterwards, the FCICT is applied on the experimental reconstruction of an illuminated two-phase jet flow which is initially generated inside an optical cylinder and then gradually moves outside. The comparison between accurately reconstructed vapor by FCICT and coarse result by traditional open space tomography algorithm provides a practical validation of FCICT. Based on the 3D vapor reconstructions at different time sequences, the distributions of surface velocity and 3D curvatures are calculated, and their correspondences are systematically analyzed. It is found that the velocity of a surface point is positively correlated with the mean curvature at the same point, which indicates the concavity/convexity of vapor surface is possibly in accordance with the surface velocity. Moreover, the surface velocity presents monotonical increasing trend with larger Gaussian curvature for elliptic surface points only, due to the dominated Brownian motion as the vapor develops.Keywords:
Gaussian curvature
Surface reconstruction
Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet, thus, encodes a pattern of contraction on heating, which can morph the sheet into a curved shell, akin to how a pattern of growth sculpts a developing organism. Here, we consider theoretically, numerically, and experimentally patterns constructed from regions of radial and circular director, which, in isolation, would form cones and anticones. The resultant surfaces contain curved ridges with sharp V-shaped cross sections, associated with the boundaries between regions in the patterns. Such ridges may be created in positively and negatively curved variants and, since they bear Gauss curvature (quantified here via the Gauss–Bonnet theorem), they cannot be flattened without energetically prohibitive stretch. Our experiments and numerics highlight that, although such ridges cannot be flattened isometrically, they can deform isometrically by trading the (singular) curvature of the V angle against the (finite) curvature of the ridge line. Furthermore, in finite thickness sheets, the sharp ridges are inevitably non-isometrically blunted to relieve bend, resulting in a modest smearing out of the encoded singular Gauss curvature. We close by discussing the use of such features as actuating linear features, such as probes, tongues, and grippers. We speculate on similarities between these patterns of shape change and those found during the morphogenesis of several biological systems.
Gaussian curvature
Cite
Citations (4)
We calculate the Gaussian curvature of a curved, twisted crease in terms of the rate of change of solid angle along its length; we find that this depends on the fold angle across the crease and on the curvature along it but is independent of twist. We use this result to resolve a paradox concerning the geometry of a creased, twisted-prismatic tube; that there can be no Gaussian curvature overall despite the surface being doubly-curved.
Gaussian curvature
Cite
Citations (0)
Gaussian curvature
Willmore energy
Cite
Citations (20)
The applications of the differential geometry of sectional curvature plays a great role in the field of physics, mathematics and engineering because it paves to knowledge of curves, surfaces, curvature, radius of curvature and sectional curvature . The study aims to explain some applications of sectional curvature. We followed the analytical induction mathematical method. We found the following some result: The sectional curvature indicate to know the behavior of some the functions and also we found that the sectional curvature is the Gaussian curvature.
Gaussian curvature
Radius of curvature
Curvature form
Cite
Citations (0)
We calculate the Gaussian curvature of a curved, twisted crease in terms of the rate of change of solid angle along its length; we find that this depends on the fold angle across the crease and on the curvature along it but is independent of twist. We use this result to resolve a paradox concerning the geometry of a creased, twisted-prismatic tube; that there can be no Gaussian curvature overall despite the surface being doubly-curved.
Gaussian curvature
Cite
Citations (0)
Abstract Negative Gaussian curvature in deformed surface subjected to concentrated loads is a key weakening factor on the surface accuracy of umbrella antennas. The negative impacts can be mitigated by increasing the bending rigidity of the reflector surface. Thus, firstly, this paper is concerned with the effect of bending rigidity on Gaussian curvature based on the analysis of bending circular thin plate with large deflection. Exact expressions of Gaussian curvature for deformed circular thin plates are derived using the analytical solution of the von-Karman plate equation and the properties of positive and negative for Gaussian curvature is investigated. After solving the zeroes of Gaussian curvature using the Newton iteration method, Gaussian curvature distribution of the deformed surface is obtained.
Gaussian curvature
Flexural rigidity
Rigidity (electromagnetism)
Cite
Citations (1)
It is shown that the molecular surface and the accessible surface lead to exactly the same results when calculating solvation free energies and transfer free energies, from methods using the surface tension as a parameter if the exact geometric curvature is used with the accessible surface. However, the use of the exact curvature is not necessarily the best approach chemically. Other modifications, including an approximate curvature improves the approach. Such modifications are difficult to include in methods in which the molecular surface rather than the accessible surface is used to calculate solvent effects. A modification of a Gaussian curvature term is necessary if dissociation is to be accounted for properly. The inclusion of a Gaussian curvature term, in addition to the usual mean curvature term, reconciles the difference in magnitude of the microscopic and macroscopic surface tension in the case of the accessible surface area. © 1997 by John Wiley & Sons, Inc.
Gaussian curvature
Implicit solvation
Cite
Citations (20)
Gaussian curvature analysis (GCA) is a technique for identifying those portions of a geological structure that, on the basis of their geometrical attributes, are likely to be more fractured than surrounding regions. As simple paper folding experiments show, a layer which does not stretch or contract can be folded into a huge variety of shapes but these do not include those with double curvature, such as domes or saddles. The occurrence of geometries of the latter type, which have non-zero Gaussian curvature values, implies the presence of folding-related strains which could be expressed as fracturing. The new method involves the computation and display of Gaussian curvature values across a mapped structure, and serves to highlight those parts which are more likely to show a greater intensity of fracturing. Current developments of the GCA method concentrate on the quantification of local strains within a folded layer. A theoretical model of three-dimensional buckling is presented which allows the calculation of strain magnitudes from principal curvature values. Several examples of GCA will be discussed, including applications to structures associated with salt diapirs.
Gaussian curvature
Cite
Citations (0)
urvature quantity in Riamannian Space is a further use of Gaussian curvature in thesurface, This paper mainly Points out some properties of curvature quantity,concluding thatin Riemannian Space whose coordinate system is n-fold Ortiogonal System of hypersurfaces,Curvature quantity can be expressed by mean curvature of coordinate surfaces and first cur-vature of parametric curves,revealing the important characteristic of curvature quantity.
Gaussian curvature
Cite
Citations (0)
We calculate the Gaussian curvature of a curved, twisted crease in terms of the rate of change of solid angle along its length; we find that this depends on the fold angle across the crease and on the curvature along it but is independent of twist. We use this result to resolve a paradox concerning the geometry of a creased, twisted-prismatic tube; that there can be no Gaussian curvature overall despite the surface being doubly-curved.
Gaussian curvature
Cite
Citations (0)