An interface problem with a source and a sink in the heavy fluid

1969 ◽  
Vol 8 (2) ◽  
pp. 197-206 ◽  
Author(s):  
A. Verruijt
Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Helmut Abels ◽  
Johannes Kampmann

AbstractWe rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed in [H. Garcke, J. Kampmann, A. Rätz and M. Röger, A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes, Math. Models Methods Appl. Sci. 26 2016, 6, 1149–1189] to weak (varifold) solutions of the corresponding sharp-interface problem for a suitable subsequence. In the system a Cahn–Hilliard type equation on the boundary of a domain is coupled to a diffusion equation inside the domain. The proof builds on techniques developed in [X. Chen, Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Differential Geom. 44 1996, 2, 262–311] for the corresponding result for the Cahn–Hilliard equation.


2021 ◽  
Vol 288 ◽  
pp. 102337
Author(s):  
Shinji Kihara ◽  
Ingo Köper ◽  
Jitendra P. Mata ◽  
Duncan J. McGillivray
Keyword(s):  

1981 ◽  
Vol 102 ◽  
pp. 85-100 ◽  
Author(s):  
D. E. Fitzjarrald

Convection flows have been systematically observed in a layer of fluid between two isothermal horizontal boundaries. The working fluid was a nematic liquid crystal, which exhibits a liquid–liquid phase change at which latent heat is released and the density changed. In addition to ordinary Rayleigh–Bénard convection when either phase is present alone, there exist two distinct types of convective motions initiated by the unstable density difference. When a thin layer of heavy fluid is present near the top boundary, hexagons with downgoing centres exist with no imposed thermal gradient. When a thin layer of light fluid is brought on near the lower boundary, the hexagons have upshooting centres. In both cases, the motions are kept going once they are initiated by the instability due to release of latent heat. Relation of the results to applicable theories is discussed.


2021 ◽  
Vol 16 (11) ◽  
pp. C11013
Author(s):  
J.M. Santos ◽  
E. Ricardo ◽  
F.J. da Silva ◽  
T. Ribeiro ◽  
S. Heuraux ◽  
...  

Abstract The use of advanced simulation has become increasingly more important in the planning, design, and assessment phases of future fusion plasma diagnostics, and in the interpretation of experimental data from existing ones. The design cycle of complex reflectometry systems, such as the ones being planned for next generation machines (IDTT and DEMO), relies heavily on the results produced by synthetic diagnostics, used for system performance evaluation and prediction, both crucial in the design process decision making. These synthetic diagnostics need realistic representations of all system components to incorporate the main effects that shape their behavior. Some of the most important elements that are required to be well modelled and integrated in simulations are the wave launcher structures, such as the waveguides, tapers, and antennas, as well as the vessel wall structures and access to the plasma. The latter are of paramount importance and are often neglected in this type of studies. Faithfully modelling them is not an easy task, especially in 3D simulations. The procedure herein proposed consists in using CAD models of a given machine, together with parameterizable models of the launcher, to produce a description suited for Finite Difference Time Domain (FDTD) 3D simulation, combining the capabilities of real-world CAD design with the power of simulation. However, CAD model geometric descriptions are incompatible with the ones used by standard FDTD codes. CAD software usually outputs models in a tessellated mesh while FDTD simulators use Volumetric Pixel (VOXEL) descriptions. To solve this interface problem, we implemented a pipeline to automatically convert complex CAD models of tokamak vessel components and wave launcher structures to the VOXEL input required by REFMUL3, a full wave 3D Maxwell FDTD parallel code. To illustrate the full procedure, a complex reflectometry synthetic diagnostic for IDTT was setup, converted and simulated. This setup includes 3 antennas recessed into the vessel wall, for thermal protection, one for transmission and reception, and two just for reception.


2013 ◽  
Vol 15 (3) ◽  
pp. 323-357 ◽  
Author(s):  
Paolo Secchi ◽  
Yuri Trakhinin

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