initial spatial distribution
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2021 ◽  
Vol 84 (1) ◽  
Author(s):  
Yifei Li ◽  
Stuart T. Johnston ◽  
Pascal R. Buenzli ◽  
Peter van Heijster ◽  
Matthew J. Simpson

2020 ◽  
Vol 8 (1) ◽  
pp. 102-113
Author(s):  
Youcef Mammeri

AbstractWe wondered that if a reaction-diffusion model considering only the mean daily movement of susceptible, exposed and asymptomatic individuals was enough to describe the spread of the COVID-19 virus. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, 𝒭0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of unlockdown are compared according to variation of distancing, or partially spatial lockdown.


1990 ◽  
Vol 68 (9) ◽  
pp. 858-871 ◽  
Author(s):  
A. Hummel

High-energy charged particles, when slowing down in a molecular medium, lose their energy by electronic excitations and ionizations of molecules along their paths. If the secondary electrons that are formed as a result of the ionizations have sufficient energy, they give rise to further excitations and ionizations. In this way tracks of excited states, positive ions, and electrons are formed. The spatial distribution of the species initially formed in the track will change in time owing to diffusion; the charged species will also drift in each other's Coulomb field. In nonpolar systems the range of the Coulomb forces is very large (30 nm) and neutralization of the oppositely charged species in the track is a dominant process, which in turn leads to formation of excited molecules that generally decompose into reactive fragments. In polar liquids, like water, neutralization is less prevalent and a relatively large fraction of the charged species escapes from the Coulombic attraction. The transient species formed may react with one another and with molecules of the medium, either solvent molecules or solute molecules. The probability of the occurrence of these reactions depends on the initial spatial distribution of the reactive species in the track. The present state of the theory of the kinetics of the nonhomogeneous processes in tracks of high-energy charged particles, which relates the initial spatial distribution of the transient species in the track to the various experimental observables, will be discussed.


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