Topological effects on vorticity evolution in confined stratified fluids

2015 ◽  
Vol 776 ◽  
pp. 109-136 ◽  
Author(s):  
R. Camassa ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni
Keyword(s):  
Thought Experiment ◽  
Interface Boundary ◽  
Homogeneous Fluid ◽  
Continuous Density ◽  
Domain Boundaries ◽  
Vorticity Generation ◽  
Intersection Curves ◽  
Boundary Intersections ◽  
Vorticity Evolution ◽  
Vorticity Balance

For a stratified incompressible Euler fluid under gravity confined by rigid boundaries, sources of vorticity are classified with the aim of isolating those which are sensitive to the topological configurations of density isopycnals, for both layered and continuous density variations. The simplest case of a two-layer fluid is studied first. This shows explicitly that topological sources of vorticity are present whenever the interface intersects horizontal boundaries. Accordingly, the topological separation of the fluid domain due to the interface–boundary intersections can contribute additional terms to the vorticity balance equation. This phenomenon is reminiscent of Klein’s ‘Kaffeelöffel’ thought-experiment for a homogeneous fluid (Klein, Z. Math. Phys., vol. 59, 1910, pp. 259–262), and it is essentially independent of the vorticity generation induced by the baroclinic term in the bulk of the fluid. In fact, the two-layer case is generalized to show that for the continuously stratified case topological vorticity sources are generically present whenever density varies along horizontal boundaries. The topological sources are expressed explicitly in terms of local contour integrals of the pressure along the intersection curves of isopycnals with domain boundaries, and their effects on vorticity evolution are encoded by an appropriate vector, termed here the ‘topological vorticity’.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

Nucleation of Disorder in Fe3Al Alloys

1967 ◽  
Vol 25 ◽  
pp. 312-313
Author(s):  
P. R. Swann ◽  
W. R. Duff ◽  
R. M. Fisher
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Annealing Temperature ◽  
Antiphase Domain ◽  
Effect Of Temperature ◽  
Domain Structures ◽  
Transmission Electron ◽  
Domain Boundaries ◽  
Higher Temperature ◽  
The One

Recently we have investigated the phase equilibria and antiphase domain structures of Fe-Al alloys containing from 18 to 50 at.% Al by transmission electron microscopy and Mössbauer techniques. This study has revealed that none of the published phase diagrams are correct, although the one proposed by Rimlinger agrees most closely with our results to be published separately. In this paper observations by transmission electron microscopy relating to the nucleation of disorder in Fe-24% Al will be described. Figure 1 shows the structure after heating this alloy to 776.6°C and quenching. The white areas are B2 micro-domains corresponding to regions of disorder which form at the annealing temperature and re-order during the quench. By examining specimens heated in a temperature gradient of 2°C/cm it is possible to determine the effect of temperature on the disordering reaction very precisely. It was found that disorder begins at existing antiphase domain boundaries but that at a slightly higher temperature (1°C) it also occurs by homogeneous nucleation within the domains. A small (∼ .01°C) further increase in temperature caused these micro-domains to completely fill the specimen.

Antiphase Boundaries in Ordered Ni3FE Crystals

1969 ◽  
Vol 27 ◽  
pp. 62-63
Author(s):  
Y. H. Liu
Keyword(s):  
Domain Size ◽  
Antiphase Domain ◽  
X Ray Diffraction ◽  
X Ray ◽  
Hardening Mechanism ◽  
Superlattice Structure ◽  
Disordered Phase ◽  
Domain Boundaries ◽  
Atomic Scattering ◽  
The Difference

Ordered Ni3Fe crystals possess a LI2 type superlattice similar to the Cu3Au structure. The difference in slip behavior of the superlattice as compared with that of a disordered phase has been well established. Cottrell first postulated that the increase in resistance for slip in the superlattice structure is attributed to the presence of antiphase domain boundaries. Following Cottrell's domain hardening mechanism, numerous workers have proposed other refined models also involving the presence of domain boundaries. Using the anomalous X-ray diffraction technique, Davies and Stoloff have shown that the hardness of the Ni3Fe superlattice varies with the domain size. So far, no direct observation of antiphase domain boundaries in Ni3Fe has been reported. Because the atomic scattering factors of the elements in NijFe are so close, the superlattice reflections are not easily detected. Furthermore, the domain configurations in NioFe are thought to be independent of the crystallographic orientations.

The observation of solutions in Ni3Nb

1988 ◽  
Vol 46 ◽  
pp. 540-541
Author(s):  
Z.M. Wang ◽  
J.P. Zhang
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Phase Modulation ◽  
High Resolution Electron Microscopy ◽  
Antiphase Domain ◽  
Boundary Area ◽  
Matrix Type ◽  
Resolution Electron ◽  
Domain Boundaries ◽  
Kontorova Model

High resolution electron microscopy reveals that antiphase domain boundaries in β-Ni3Nb have a hexagonal unit cell with lattice parameters ah=aβ and ch=bβ, where aβ and bβ are of the orthogonal β matrix. (See Figure 1.) Some of these boundaries can creep “upstairs” leaving an incoherent area, as shown in region P. When the stepped boundaries meet each other, they do not lose their own character. Our consideration in this work is to estimate the influnce of the natural misfit δ{(ab-aβ)/aβ≠0}. Defining the displacement field at the boundary as a phase modulation Φ(x), following the Frenkel-Kontorova model [2], we consider the boundary area to be made up of a two unit chain, the upper portion of which can move and the lower portion of the β matrix type, assumed to be fixed. (See the schematic pattern in Figure 2(a)).

Contrasts of planar defects in reflection electron microscopy

1993 ◽  
Vol 51 ◽  
pp. 1004-1005
Author(s):  
Feng Tsai ◽  
J. M. Cowley
Keyword(s):  
Electron Microscopy ◽  
Surface Defects ◽  
Practical Importance ◽  
Theoretical Treatment ◽  
Crystal Surfaces ◽  
Planar Defects ◽  
Surface Steps ◽  
Surface Reconstructions ◽  
Domain Boundaries ◽  
Reflection Electron Microscopy

Reflection electron microscopy (REM) has been used to study surface defects such as surface steps, dislocations emerging on crystal surfaces, and surface reconstructions. However, only a few REM studies have been reported about the planar defects emerging on surfaces. The interaction of planar defects with surfaces may be of considerable practical importance but so far there seems to be only one relatively simple theoretical treatment of the REM contrast and very little experimental evidence to support its predications. Recently, intersections of both 90° and 180° ferroelectric domain boundaries with BaTiO3 crystal surfaces have been investigated by Tsai and Cowley with REM.The REM observations of several planar defects, such as stacking faults and domain boundaries have been continued by the present authors. All REM observations are performed on a JEM-2000FX transmission electron microscope. The sample preparations may be seen somewhere else. In REM, the incident electron beam strikes the surface of a crystal with a small glancing angle.

Investigation of ferroelectrics using conventional and in situ electron microscopy

1994 ◽  
Vol 52 ◽  
pp. 586-587
Author(s):  
V. Saikumar ◽  
H. M. Chan ◽  
M. P. Harmer
Keyword(s):  
Nonvolatile Memory ◽  
Ferroelectric Materials ◽  
Gate Insulator ◽  
Sensors And Actuators ◽  
In Situ Electron Microscopy ◽  
Ferroelectric Domains ◽  
Domain Boundaries ◽  
Domain Interactions ◽  
Memory Applications

In recent years, there has been a growing interest in the application of ferroelectric thin films for nonvolatile memory applications and as a gate insulator in DRAM structures. In addition, bulk ferroelectric materials are also widely used as components in electronic circuits and find numerous applications in sensors and actuators. To a large extent, the performance of ferroelectric materials are governed by the ferroelectric domains (with dimensions in the micron to sub-micron range) and the switching of domains in the presence of an applied field. Conventional TEM studies of ferroelectric domains structures, in conjunction with in-situ studies of the domain interactions can aid in explaining the behavior of ferroelectric materials, while providing some answers to the mechanisms and processes that influence the performance of ferroelectric materials. A few examples from bulk and thin film ferroelectric materials studied using the TEM are discussed below.Figure 1 shows micrographs of ferroelectric domains obtained from undoped and Fe-doped BaTiO3 single crystals. The domain boundaries have been identified as 90° domains with the boundaries parallel to <011>.

Epistemological Status of Models and Thought Experiments in Economics

2015 ◽  
pp. 123-140 ◽  
Author(s):  
O. Koshovets ◽  
T. Varkhotov
Keyword(s):  
Natural Science ◽  
Thought Experiment ◽  
Thought Experiments ◽  
Theoretical Modeling ◽  
Epistemological Status ◽  
Epistemological Analysis ◽  
Field Of Inquiry

The paper considers the analogy of theoretical modeling and thought experiment in economics. The authors provide historical and epistemological analysis of thought experiments and their relations to the material experiments in natural science. They conclude that thought experiments as instruments are used both in physics and in economics, but in radically different ways. In the natural science, a thought experiment is tightly connected to the material experimentation, while in economics it is used in isolation. Material experiments serve as a means to demonstrate the reality, while thought experiments cannot be a full-fledged instrument of studying the reality. Rather, they constitute the instrument of structuring the field of inquiry.

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