Numerical Simulation of a Suspension of Swimming Micro-Organisms

2007 ◽  
Author(s):  
Takuji Ishikawa ◽  
T. J. Pedley ◽  
Takami Yamaguchi
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Continuum Model ◽  
Diffusion Tensor ◽  
Continuum Models ◽  
Dilute Suspensions ◽  
Plankton Bloom ◽  
Cell Concentrations ◽  
Micro Organisms ◽  
The Continuum

The size of individual micro-organisms is often much smaller than that of the flow field of interest, in an oceanic plankton bloom for instance. In such cases, the suspension of micro-organisms is modelled as a continuum in which the variables are volume-averaged quantities. Continuum models for suspensions of swimming micro-organisms have been proposed for the analysis of phenomena such as bioconvection. However, the continuum models proposed so far are restricted to dilute suspensions, in which cell-cell interactions are negligible. If one wishes to analyze larger cell concentrations, it will be necessary to consider the interactions between micro-organisms. Then the particle stress tensor, the velocities of the micro-organisms and the diffusion tensor in the continuum model will need to be replaced by improved expressions. In this study, we compute the motion of interacting swimming model micro-organisms in periodic suspensions in a fluid otherwise at rest, and discuss the microstructure constructed by micro-organisms.

scholarly journals Murray’s law for discrete and continuum models of biological networks

2019 ◽  
Vol 29 (12) ◽  
pp. 2359-2376
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Giulia Pilli
Keyword(s):  
Biological Networks ◽  
Discrete Model ◽  
Continuum Model ◽  
Transportation Network ◽  
Continuum Models ◽  
Scaling Relation ◽  
Murray's Law ◽  
Murray’S Law ◽  
Rectangular Mesh ◽  
The Continuum

We demonstrate the validity of Murray’s law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray’s law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray’s law for its linearly stable steady states.

scholarly journals Development and stability of gyrotactic plumes in bioconvection

1999 ◽  
Vol 400 ◽  
pp. 1-31 ◽  
Author(s):  
S. GHORAI ◽  
N. A. HILL
Keyword(s):  
Continuum Model ◽  
Stokes Equations ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence And Stability ◽  
Conservative Finite Difference Scheme ◽  
Micro Organisms ◽  
Good Agreement ◽  
The Continuum

Using the continuum model of Pedley, Hill & Kessler (1988) for bioconvection in a suspension of swimming, gyrotactic micro-organisms, we investigate the existence and stability of a two-dimensional plume in tall, narrow chambers with stress-free sidewalls. The system is governed by the Navier–Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plume is always unstable to both varicose and meandering modes. A linear stability analysis for an infinitely long plume predicts the growth rates of these instabilities, explains the mechanisms, and is in good agreement with the numerical results.

Sinhala diglossia: Discrete or continuous variation?

1997 ◽  
Vol 26 (2) ◽  
pp. 269-296 ◽  
Author(s):  
John C. Paolillo
Keyword(s):  
Sri Lanka ◽  
South Asia ◽  
Continuum Model ◽  
Distinct Type ◽  
Continuous Variation ◽  
Discrete Models ◽  
Continuum Models ◽  
Naturally Occurring ◽  
The Continuum

ABSTRACTSociolinguists disagree on how to characterize diglossia with respect to the structural relatedness of the H(igh) and L(ow) varieties: Ferguson 1959, 1991 holds that H and L should be distinct but related varieties of language, while others maintain that a continuum model is more appropriate. Both discrete models (Gair 1968, 1992) and continuum models (De Silva 1974, 1979) have been proposed for Sinhala, as spoken in Sri Lanka. In this article, I employ a computer-generated multidimensional graph of relations between varieties of Sinhala to show that the distribution of H and L grammatical features in a sample of naturally occurring texts supports the discrete H and L model more than the continuum model. A rigorous characterization of diglossia as a distinct type of language situation is proposed, based on the notion “functional diasystem.” (Diglossia, Sinhala, Sri Lanka, diasystem, hybridization, continuum, South Asia, standardization)

scholarly journals Numerical Simulation of Characteristics of Spray Flow Field on the Conical Surface

2020 ◽  
Vol 1670 ◽  
pp. 012030
Author(s):  
Shiming Chen ◽  
GuichunYang ◽  
Shuang Zhou ◽  
Wenzhuo Chen ◽  
Jinfa Guan ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Conical Surface

scholarly journals Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yoshifumi Asakura ◽  
Yohei Kondo ◽  
Kazuhiro Aoki ◽  
Honda Naoki
Keyword(s):  
Wound Healing ◽  
Cell Migration ◽  
Continuum Model ◽  
Tissue Level ◽  
Chemical Signals ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Collective Cell Migration ◽  
The Continuum ◽  
Cell Cell

AbstractCollective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

scholarly journals Influence of Vortex Finder Structure on Separation Performance of Double-Overflow Three-Product Hydrocyclones

Separations ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 79
Author(s):  
Yuekan Zhang ◽  
Jiangbo Ge ◽  
Lanyue Jiang ◽  
Hui Wang ◽  
Junru Yang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Experimental Research ◽  
Separation Efficiency ◽  
Structural Parameters ◽  
Separation Performance ◽  
Insertion Depth ◽  
Flow Field Characteristics ◽  
Vortex Finder ◽  
Fine Classification

In view of the difficulty of traditional hydrocyclones to meet the requirements of fine classification, a double-overflow three-product (internal overflow, external overflow and underflow) hydrocyclone was designed in this study. Numerical simulation and experimental research methods were used to investigate the effects of double-overflow flow field characteristics and structural parameters (i.e., internal vortex finder diameter and insertion depth) on separation performance. The research results showed that the larger the diameter of the internal vortex finder, the greater the overflow yield and the larger the cut size. The finest internal overflow product can be obtained when the internal vortex finder is 30 mm longer than the external vortex finder. The separation efficiency is highest when the internal vortex finder is 30 mm shorter than the external vortex finder.

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