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Raveendran, Vishnu
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Raveendran, Vishnu
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Department of Mathematics and Computer Science (from 2013)
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Mathematics
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GoogleGoogle Scholar$(function(){PrimeFaces.cw('Chart','widget_formSmash_j_idt1307_0_downloads',{id:'formSmash:j_idt1307:0:downloads',type:'bar',responsive:true,data:[[14,27]],title:"Downloads of File (FULLTEXT02)",axes:{xaxis: {label:"",renderer:$.jqplot.CategoryAxisRenderer,tickOptions:{angle:-90}},yaxis: {label:"",min:0,max:30,renderer:$.jqplot.LinearAxisRenderer,tickOptions:{angle:0}}},series:[{label:'diva2:1841801'}],ticks:["Mar -24","Apr -24"],orientation:"vertical",barMargin:50,datatip:true,datatipFormat:"<span style=\"display:none;\">%2$d</span><span>%2$d</span>"},'charts');}); Total: 41 downloads$(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_j_idt1311",{id:"formSmash:j_idt1311",widgetVar:"widget_formSmash_j_idt1311",target:"formSmash:downloadLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade"});}); findCitings = function() {PrimeFaces.ab({s:"formSmash:j_idt1313",f:"formSmash",u:"formSmash:citings",pa:arguments[0]});};$(function() {findCitings();}); $(function(){PrimeFaces.cw('Chart','widget_formSmash_visits',{id:'formSmash:visits',type:'bar',responsive:true,data:[[91,236]],title:"Visits for this publication",axes:{xaxis: {label:"",renderer:$.jqplot.CategoryAxisRenderer,tickOptions:{angle:-90}},yaxis: {label:"",min:0,max:240,renderer:$.jqplot.LinearAxisRenderer,tickOptions:{angle:0}}},series:[{label:'diva2:1841801'}],ticks:["Mar -24","Apr -24"],orientation:"vertical",barMargin:50,datatip:true,datatipFormat:"<span style=\"display:none;\">%2$d</span><span>%2$d</span>"},'charts');}); Total: 327 hits
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Scaling effects and homogenization of reaction-diffusion problems with nonlinear driftPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2024 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Abstract [en]

##### Place, publisher, year, edition, pages

Karlstads universitet, 2024. , p. 24
##### Series

Karlstad University Studies, ISSN 1403-8099 ; 2024:7
##### Keywords [en]

homogenization, asymptotic expansion with drift, two-scale convergence with drift, effective transmission condition, dimension reduction, two-scale system, nonlinear dispersion
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kau:diva-98720DOI: 10.59217/fjww2863ISBN: 978-91-7867-440-4 (print)ISBN: 978-91-7867-441-1 (electronic)OAI: oai:DiVA.org:kau-98720DiVA, id: diva2:1841801
##### Public defence

2024-04-18, Sjöström lecture hall, 1B309, Karlstads universitet, Karlstad, 13:15 (English)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt540",{id:"formSmash:j_idt540",widgetVar:"widget_formSmash_j_idt540",multiple:true}); Available from: 2024-03-28 Created: 2024-02-29 Last updated: 2024-03-28Bibliographically approved
##### List of papers

We study the periodic homogenization of reaction-diffusion problems with nonlinear drift describing the transport of interacting particles in composite materials. The microscopic model is derived as the hydrodynamic limit of a totally asymmetric simple exclusion process for a population of interacting particles crossing a domain with obstacles. We are particularly interested in exploring how the scalings of the drift affect the structure of the upscaled model.

We first look into a situation when the interacting particles cross a thin layer that has a periodic microstructure. To understand the effective transmission condition, we perform homogenization together with the dimension reduction of the aforementioned reaction-diffusion-drift problem with variable scalings.

One particular physically interesting scaling that we look at separately is when the drift is very large compared to both the diffusion and reaction rate. In this case, we consider the overall process taking place in an unbounded porous media. Since we have the presence of a large nonlinear drift in the microscopic problem, we first upscale the model using the formal asymptotic expansions with drift. Then, with the help of two-scale convergence with drift, we rigorously derive the homogenization limit for a similar microscopic problem with a nonlinear Robin-type boundary condition. Additionally, we show the strong convergence of the corrector function.

In the large drift case, the resulting upscaled equation is a nonlinear reaction-dispersion equation that is strongly coupled with a system of nonlinear elliptic cell problems. We study the solvability of a similar strongly coupled two-scale system with nonlinear dispersion by constructing an iterative scheme. Finally, we illustrate the behavior of the solution using the iterative scheme.

We study the homogenization of reaction-diffusion problems with nonlinear drift. The microscopic model is derived as the hydrodynamic limit of a totally asymmetric simple exclusion process of interacting particles. We first look into a situation when the interacting particles cross a thin composite layer. To understand the effective transmission condition, we perform the homogenization and dimension reduction of the model with variable scalings. One physically interesting scaling that we look at separately is when the drift is large. In this case, we consider the overall process taking place in an unbounded porous media. We first upscale the model using the asymptotic expansions with drift. Then, using two-scale convergence with drift, we rigorously derive the homogenization limit for a similar microscopic problem with a nonlinear boundary condition. Additionally, we show the strong convergence of the corrector function. In the large drift case, the resulting upscaled model is a nonlinear reaction-dispersion equation strongly coupled with a system of nonlinear elliptic cell problems. We study the solvability of a similar strongly coupled two-scale system with nonlinear dispersion by constructing an iterative scheme. Finally, we illustrate the behavior of the solution using the iterative scheme.

1. Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer$(function(){PrimeFaces.cw("OverlayPanel","overlay1607228",{id:"formSmash:j_idt594:0:j_idt598",widgetVar:"overlay1607228",target:"formSmash:j_idt594:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Upscaling of a reaction-diffusion-convection problem with exploding non-linear drift$(function(){PrimeFaces.cw("OverlayPanel","overlay1650978",{id:"formSmash:j_idt594:1:j_idt598",widgetVar:"overlay1650978",target:"formSmash:j_idt594:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data$(function(){PrimeFaces.cw("OverlayPanel","overlay1827526",{id:"formSmash:j_idt594:2:j_idt598",widgetVar:"overlay1827526",target:"formSmash:j_idt594:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Strongly Coupled Two-scale System with Nonlinear Dispersion: Weak Solvability and Numerical Simulation$(function(){PrimeFaces.cw("OverlayPanel","overlay1841799",{id:"formSmash:j_idt594:3:j_idt598",widgetVar:"overlay1841799",target:"formSmash:j_idt594:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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