2020 ◽  
Author(s):  
Miftachul Hadi

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.


1993 ◽  
Vol 28 (2) ◽  
pp. 135-144 ◽  
Author(s):  
S. Matsui ◽  
R. Ikemoto Yamamoto ◽  
Y. Tsuchiya ◽  
B. Inanc

Using a fluidized bed reactor, experiments on glucose decomposition with and without sulfate reduction were conducted. Glucose in the reactor was mainly decomposed into lactate and ethanol. Lactate was mainly decomposed into propionate and acetate, while ethanol was decomposed into propionate, acetate, and hydrogen. Sulfate reduction was not involved in the decomposition of glucose, lactate, and ethanol, but was related to propionate and acetate decomposition. The stepwise reactions were modeled using either a Monod expression or first order reaction kinetics in respect to the reactions. The coefficients of the kinetic equations were determined experimentally. The modified Monod and first order reaction equations were effective at predicting concentrations of glucose, lactate, ethanol, propionate, acetate, and sulfate along the beight of the reactor. With sulfate reduction, propionate was decomposed into acetate, while without sulfate reduction, accumulation of propionate was observed in the reactor. Sulfate reduction accelerated propionate conversion into acetate by decreasing the hydrogen concentration.


Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 113
Author(s):  
Stephan Daniel Schwoebel ◽  
Thomas Mehner ◽  
Thomas Lampke

Three-component systems of diffusion–reaction equations play a central role in the modelling and simulation of chemical processes in engineering, electro-chemistry, physical chemistry, biology, population dynamics, etc. A major question in the simulation of three-component systems is how to guarantee non-negative species distributions in the model and how to calculate them effectively. Current numerical methods to enforce non-negative species distributions tend to be cost-intensive in terms of computation time and they are not robust for big rate constants of the considered reaction. In this article, a method, as a combination of homotopy methods, modern augmented Lagrangian methods, and adaptive FEMs is outlined to obtain a robust and efficient method to simulate diffusion–reaction models with non-negative concentrations. Although in this paper the convergence analysis is not described rigorously, multiple numerical examples as well as an application to elctro-deposition from an aqueous Cu2+-(β-alanine) electrolyte are presented.


1994 ◽  
Vol 23 (2) ◽  
pp. 125-139 ◽  
Author(s):  
Ronald W. Cotterill

This paper reviews prior research by agricultural economists on the demand for food products using scanner data. Thereafter, a differentiated product's oligopoly model with Bertrand price competition is developed and used to specify brand level demand and oligopoly price reaction equations. The model has sufficient detail to estimate brand level price elasticities and price response elasticities which in turn can be used to estimate three indices of market power. The first index estimated is the familiar Rothschild Index. The paper develops estimates two new indexes, the observed index and the Chamberlin quotient for tacit collusion. It concludes with comments on how the proposed method for the measurement of market power in a differentiated oligopoly can be improved.


2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Christian Engwer ◽  
Michael Wenske

AbstractGlioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection–diffusion–reaction equations. The patient-wise parametrization of these models, and their validation via experimental data has been found to be difficult, as time sequence measurements are mostly missing. Also the clinical interest lies in the actual (invisible) tumor extent for a particular MRI/DTI scan and not in a predictive estimate. Therefore we propose a stationalized approach to estimate the extent of glioblastoma (GBM) invasion at the time of a given MRI/DTI scan. The underlying dynamics can be derived from an instationary GBM model, falling into the wide class of advection-diffusion-reaction equations. The stationalization is introduced via an analytic solution of the Fisher-KPP equation, the simplest model in the considered model class. We investigate the applicability in 1D and 2D, in the presence of inhomogeneous diffusion coefficients and on a real 3D DTI-dataset.


1991 ◽  
Vol 113 (4) ◽  
pp. 388-394 ◽  
Author(s):  
O. B. Fedoseev ◽  
S. Malkin

An analysis is presented to predict the hardness distribution in the subsurface of hardened steel due to tempering and rehardening associated with high temperatures generated in grinding. The grinding temperatures are modeled with a triangular heat source at the grinding zone and temperature-dependent thermal properties. The temperature history, including the effect of multiple grinding passes, is coupled with thermally activated reaction equations for tempering and for reaustenitization which is the rate controlling step in rehardening. Experimental results from the literature are found to be in good agreement with the analytical predictions.


2008 ◽  
Vol 9 (2) ◽  
pp. 83-104 ◽  
Author(s):  
T. Bodnár ◽  
A. Sequeira

The process of platelet activation and blood coagulation is quite complex and not yet completely understood. Recently, a phenomenological meaningful model of blood coagulation and clot formation in flowing blood that extends existing models to integrate biochemical, physiological and rheological factors, has been developed. The aim of this paper is to present results from a computational study of a simplified version of this coupled fluid-biochemistry model. A generalized Newtonian model with shear-thinning viscosity has been adopted to describe the flow of blood. To simulate the biochemical changes and transport of various enzymes, proteins and platelets involved in the coagulation process, a set of coupled advection–diffusion–reaction equations is used. Three-dimensional numerical simulations are carried out for the whole model in a straight vessel with circular cross-section, using a finite volume semi-discretization in space, on structured grids, and a multistage scheme for time integration. Clot formation and growth are investigated in the vicinity of an injured region of the vessel wall. These are preliminary results aimed at showing the validation of the model and of the numerical code.


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