Time-Space Model of Business Fluctuations

An ideal drinking water distribution system (DWDS) must supply safe drinking water with free chlorine residual (FCR) in the form of HOCl and OCl- at a required concentration level. The FCR as a disinfectant decreases over time due to chemical reactions in the bulk phase and at the pipe wall in the DWDS. In order to supply drinking water with the FCR concentration within the safety range of 0.2-0.6 mg/l at the points of water consumption, it is important to develop a dynamic model of the FCR using a discrete time-space model (DTSM) that accounts for free chlorine transport in the axial direction by convection, diffusion and the decay kinetic. A DTSM has been developed using Finite Difference Method (FDM) to predict the FCR in single pipes in the DWDS. The DTSM has been computed using Matlab 7.0.1 and tested with step inputs and rectangular pulse inputs to estimate the FCR at any point in the pipes over time. Data found in the literature have been used to validate the DTSM. The modelling and simulation study shows that the water velocity significantly affects the FCR concentration distribution along the pipe. Due to the fluctuation of the drinking water demand, a model-based adaptive chlorine dosing scheme is proposed to control the proper injection of chlorine.

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What is the Shape of Geographical Time-Space? A Three Dimensional Model made of Curves and Cones

10.20944/preprints202103.0594.v1 ◽

2021 ◽

Author(s):

Alain L’Hostis ◽

Farouk Abdou

Keyword(s):

Transport System ◽

Three Dimensional ◽

Road Transport ◽

Air Transport ◽

Dimensional Model ◽

Three Dimensional Model ◽

Relative Difficulty ◽

Space Model ◽

The Earth ◽

Time Space

We propose a geographical time-space model extending time-space relief cartography introduced by Mathis and L’Hostis [,,,]. The novelty of the model resides in the use of cones to describe the terrestrial surface instead of graph faces, and in the use of curves instead of broken segments for edges. The approach lies a the intersection of two domains involving graphic representation: cartography, and three dimensional computer graphics. We implement the model on the Chinese space. The Chinese geographical time-space of the reference year 2006 is produced by the combination and the confrontation of the fast air transport system and of the 7.5 times slower road transport system. Slower, short range flights are represented as curved lines above the earth surface with longer length than the geodesic, in order to account for a slower speed. The very steep slope of cones expresses the relative difficulty of crossing terrestrial time-space, as well as the comparably extreme efficiency of long-range flights for moving between cities. Finally, the whole image proposes a coherent representation of the geographical time-space where fast city to city transport is combined with slow terrestrial systems that allow to reach any location.

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A time-space model for the growth of microalgae biofilms for biofuel production

Journal of Theoretical Biology ◽

10.1016/j.jtbi.2017.08.017 ◽

2017 ◽

Vol 432 ◽

pp. 55-79 ◽

Cited By ~ 9

Author(s):

B. Polizzi ◽

O. Bernard ◽

M. Ribot

Keyword(s):

Biofuel Production ◽

Space Model ◽

Time Space

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