Viscous flow around three-dimensional macroscopic cavities in a granular material

2021 ◽  
Vol 931 ◽  
Author(s):  
Osamu Sano ◽  
Timir Karmakar ◽  
G.P. Raja Sekhar
Keyword(s):  
Granular Material ◽  
Viscous Flow ◽  
Stokes Equation ◽  
Three Dimensional ◽  
Volume Flow ◽  
The Other ◽  
Brinkman Equation ◽  
Local Enhancement ◽  
Reasonable Estimate ◽  
The Stokes Equation

Viscous flow around spherical macroscopic cavities in a granular material is investigated. The Stokes equation inside and the Darcy–Brinkman equation outside the cavities are considered. In particular, the interaction of two equally sized cavities positioned in tandem is examined in detail, where the asymptotic effect of the other cavity is taken into account. The present analysis gives a reasonable estimate on the volume flow into the cavity and the local enhancement of stresses. This is applicable to predict the microscale waterway formation in that material, onset of landslides, collapse of cliffs and river banks, etc.

scholarly journals XXVI.—On a Group of Linear Differential Equations of the 2nd Order, including Professor Chrystal's Seiche-equations

1906 ◽  
Vol 41 (3) ◽  
pp. 651-676 ◽  
Author(s):  
J. Halm
Keyword(s):  
Differential Equations ◽  
Stokes Equation ◽  
Mathematical Theory ◽  
General Type ◽  
The Other ◽  
Special Cases ◽  
Linear Differential ◽  
Image Position ◽  
Special Case ◽  
The Stokes Equation

It is readily seen that the two differential equationswhich play an important rôle in Professor Chrystal's mathematical theory of the Seiches, are special cases of the more general typeWith regard to the first, the Seiche-equation, this becomes at once apparent by writing a= − ½. Equation (2), on the other hand, which we may briefly call the Stokes equation [see Professor Chrystal's paper on “Some further Results in the Mathematical Theory of Seiches,” Proc. Roy. Soc. Edin., vol. xxv.] will be recognised as a special case (a = + 1) of the equationwhich is transformed into (3) by the substitution .

scholarly journals The Use of a Distributed Body Force to Simulate Viscous Effects in 3D Flow Calculations

1986 ◽  
Author(s):  
J. D. Denton
Keyword(s):  
Simple Model ◽  
Viscous Flow ◽  
Body Force ◽  
Computational Cost ◽  
Three Dimensional ◽  
Secondary Flows ◽  
The Other ◽  
Simple Extension ◽  
Viscous Effects ◽  
3D Flow

Three dimensional viscous flow calculations methods for turbomachinery are starting to become available but are not yet sufficiently well developed to be used for design purposes. Three dimensional inviscid calculations on the other hand are now well developed and are widely used for design purposes. This paper describes a method intermediate between fully viscous methods and inviscid methods. The viscous effects are approximated by a very simple model which can be tuned empirically to get the correct overall level of loss and which reproduces many of the details of real viscous flow, such as boundary layers and secondary flows. The method is a simple extension to a widely used inviscid method and enables viscous effects to be simulated with little extra computational cost compared to a 3D inviscid calculation.

scholarly journals A tridimensional model for the motion of nanobots at high viscosity coeflcient environment based on Navier-Stokes’ Equation, by applying Oseen’s approximation

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Alireza Jorkesh ◽  
Amir Hossein Ghaffari ◽  
Amir Abolfazleh Suratgar ◽  
Mahmoud Dehghan Afify
Keyword(s):  
Stokes Equation ◽  
Three Dimensional ◽  
High Viscosity ◽  
Navier Stokes ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Navier Stokes Equation ◽  
The Stokes Equation

Abstract Till now, various models of the motion of nanobots have been submitted; the pioneer models, in spite of being exact in mathematics, had their own kind of problems. The most recent challenge is to describe a model whose attitude can be practical so that these motions can be estimated. Considering the massive uses of nanobots, the kinds of motions and velocities of these very small robots need to be studied in a more accurate way. In this essay, we tried to develop a three-dimensional model. The three dimensional model is based on 7 spheres and 6 arms and describes a kind of movement requiring 2 spheres at each arm. The velocity of each kind has also been evaluated. Furthermore, two kinds of three-dimensional movements have been issued and compared as well. That will result in the simplicity of the equations. By applying Oseen’s approximation in the Stokes’ equation, the velocity in various media has been calculated and modulated.

Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

1990 ◽  
Vol 48 (1) ◽  
pp. 258-259
Author(s):  
J.L. Carrascosa ◽  
G. Abella ◽  
S. Marco ◽  
M. Muyal ◽  
J.M. Carazo
Keyword(s):  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Series Method ◽  
Three Dimensional Reconstruction ◽  
Structural Components ◽  
E Coli ◽  
Dimensional Reconstruction ◽  
Morphogenetic Factors ◽  
Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

An Efficient Multiple Description Coding for Multi-View Video Based on the Correlation of Spatial Polyphase Transformed Subsequences

2019 ◽  
Vol 63 (5) ◽  
pp. 50401-1-50401-7 ◽  
Author(s):  
Jing Chen ◽  
Jie Liao ◽  
Huanqiang Zeng ◽  
Canhui Cai ◽  
Kai-Kuang Ma
Keyword(s):  
Video Transmission ◽  
Video Sequence ◽  
Three Dimensional ◽  
The Other ◽  
Multiple Description Coding ◽  
Multiple Description ◽  
Prediction Mode ◽  
Gradient Based ◽  
Directional Interpolation ◽  
Description Coding

Abstract For a robust three-dimensional video transmission through error prone channels, an efficient multiple description coding for multi-view video based on the correlation of spatial polyphase transformed subsequences (CSPT_MDC_MVC) is proposed in this article. The input multi-view video sequence is first separated into four subsequences by spatial polyphase transform and then grouped into two descriptions. With the correlation of macroblocks in corresponding subsequence positions, these subsequences should not be coded in completely the same way. In each description, one subsequence is directly coded by the Joint Multi-view Video Coding (JMVC) encoder and the other subsequence is classified into four sets. According to the classification, the indirectly coding subsequence selectively employed the prediction mode and the prediction vector of the counter directly coding subsequence, which reduces the bitrate consumption and the coding complexity of multiple description coding for multi-view video. On the decoder side, the gradient-based directional interpolation is employed to improve the side reconstructed quality. The effectiveness and robustness of the proposed algorithm is verified by experiments in the JMVC coding platform.

Three-dimensional thermochemical nonequilibrium viscous flow over blunt bodies with catalytic surface

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 626-636
Author(s):  
S. Peigin ◽  
V. Kazakov ◽  
M.-C. Druguet ◽  
S. Seror ◽  
D. E. Zeitoun
Keyword(s):  
Viscous Flow ◽  
Three Dimensional ◽  
Catalytic Surface ◽  
Blunt Bodies
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