On the Numerical Behavior of a Chemotaxis Model with Linear Production Term

Author(s):  
F. Guillén-González ◽  
M. A. Rodríguez-Bellido ◽  
D. A. Rueda-Gómez
Author(s):  
Mariia Fomicheva ◽  
Elena N. Vilchevskaya ◽  
Nikolay Bessonov ◽  
Wolfgang H. Müller

AbstractIn this paper, the solution to a coupled flow problem for a micropolar medium undergoing structural changes is presented. The structural changes occur because of a grinding of the medium in a funnel-shaped crusher. The standard macroscopic equations for mass and linear momentum are solved in combination with a balance equation for the microinertia tensor containing a production term. The constitutive equations of the medium describe a linear viscous material with a viscosity coefficient depending on the characteristic particle moment of inertia, the so-called microinertia. A coupled system of equations is presented and solved numerically in order to determine the distribution of the fields for velocity, pressure, viscosity coefficient, and microinertia in all points of the continuum. The numerical solution to this problem is found by using the implicit finite difference method and the upwind scheme.


Author(s):  
Kuo-Ching Chen

This paper is concerned with the modelling of a magnetorheological (MR) fluid in the presence of an applied magnetic field as a twofolded mixture—a macroscopic fluid continuum and mesoscopic multi-solid continua. By assigning to each solid particle a vectorial mesoscopic variable, which is defined as the nearest relative position vector with respect to other particles, the solid medium of the MR fluid is further treated as a mixture consisting of different components, specified by these mesoscopic variables. The treatment of multi-solid continua is similar to that in the mesoscopic theory of liquid crystals. However, the key difference lies in the fact that the time-discontinuity of the defined vectorial mesoscopic variable will give rise to a ‘pseudo’ chemical reaction in the solid continuum. The equation of the phenomenological mesoscopic distribution function of the solid continuum then has an additional production term from the pseudo chemical reaction, analogous to the collision term appearing in the Boltzmann equation. The mesoscopic and macroscopic balance equations are then derived and by assuming the special constitutive relations the macroscopic equation for the second moment of the distribution function can be obtained.


2012 ◽  
Vol 391 (1-2) ◽  
pp. 107-112 ◽  
Author(s):  
Santo Banerjee ◽  
Amar P. Misra ◽  
L. Rondoni

2018 ◽  
Vol 115 (10) ◽  
pp. 2034-2043 ◽  
Author(s):  
Seongjin Lim ◽  
Hyeono Nam ◽  
Jessie S. Jeon

2014 ◽  
Vol 420 (1) ◽  
pp. 684-704 ◽  
Author(s):  
Yajing Zhang ◽  
Xinfu Chen ◽  
Jianghao Hao ◽  
Xin Lai ◽  
Cong Qin

Author(s):  
Jens Truemner ◽  
Christian Mundt

Comparisons with experiments have shown that RANS models tend to underpredict the mixing process in shear layers with strong temperature gradients. In the modeling of jet engine’s exhaust systems this leads to an overpredicted potential core length and underestimated turbulence intensity in the free jet. In addition, the calculated efficiency gain is lower than indicated by measurements in mixed turbofan engines. Based on the findings from scale-resolving simulations a correction to the turbulence production term is proposed and compared with two NASA-experiments on hot jets. This correction is implemented in a Reynolds-stress and a k-ε model. The results are in very good agreement with the experimental data.


2006 ◽  
Vol 29 (13) ◽  
pp. 1563-1583 ◽  
Author(s):  
Piotr Biler ◽  
Grzegorz Karch ◽  
Philippe Laurençot ◽  
Tadeusz Nadzieja

2007 ◽  
Vol 4 (4) ◽  
pp. 2593-2640 ◽  
Author(s):  
P. Harley ◽  
J. Greenberg ◽  
Ü. Niinemets ◽  
A. Guenther

Abstract. Methanol is found throughout the troposphere, with average concentrations second only to methane among atmospheric hydrocarbons. Proposed global methanol budgets are highly uncertain, but all agree that at least 60% of the total source arises from the terrestrial biosphere and primary emissions from plants. However, the magnitude of these emissions is also highly uncertain, and the environmental factors which control them require further elucidation. Using a temperature-controlled leaf enclosure, we measured methanol emissions from leaves of six plant species by proton transfer reaction mass spectrometry, with simultaneous measurements of leaf evapotranspiration and stomatal conductance. Rates of emission at 30°C varied from 0.3 to 38 μg g (dry mass)−1 h−1, with higher rates measured on young leaves, consistent with the production of methanol via pectin demethylation in expanding foliage. On average, emissions increased by a factor of 2.4 for each 10°C increase in leaf temperature. At constant temperature, emissions were also correlated with co-varying incident photosynthetic photon flux density and rates of stomatal conductance. The data were analyzed using the emission model developed by Niinemets and Reichstein (2003a, b), with the incorporation of a methanol production term that increased exponentially with temperature. It was concluded that control of emissions, during daytime, was shared by leaf temperature and stomatal conductance, although rates of production may also vary diurnally in response to variations in leaf growth rate in expanding leaves. The model, which generally provided reasonable simulations of the measured data during the day, significantly overestimated emissions on two sets of measurements made through the night, suggesting that production rates of methanol were reduced at night, perhaps because leaf growth was reduced or possibly through a direct effect of light on production. Although the short-term dynamics of methanol emissions can be successfully modeled only if stomatal conductance and compound solubility are taken into account, emissions on longer time scales will be determined by rates of methanol production, controls over which remain to be investigated.


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