We investigate well-accepted formulations describing charge transport in composite cathodes of batteries. Our upscaling of carefully selected microscopic equations shows three main features: (i) a novel set of six equations equipped with nine effective parameters which systematically couple the microscale to the macroscale; (ii) the coupling of transport and flow equations allows to account for three scales: pore scale, Darcy scale, and macroscale; (iii) the upscaled equations take phase separation during Li-intercalation into account as well as specific particle configurations. The wide range of applications and interest in energy storage devices make these results a promising tool to study the influence of the microstructure on current-voltage characteristics and to optimize cathode designs.
{"title":"Upscaling of Solid-electrolyte Composite Intercalation Cathodes for Energy Storage Systems","authors":"M. Schmuck","doi":"10.1093/AMRX/ABX003","DOIUrl":"https://doi.org/10.1093/AMRX/ABX003","url":null,"abstract":"We investigate well-accepted formulations describing charge transport in composite cathodes of batteries. Our upscaling of carefully selected microscopic equations shows three main features: (i) a novel set of six equations equipped with nine effective parameters which systematically couple the microscale to the macroscale; (ii) the coupling of transport and flow equations allows to account for three scales: pore scale, Darcy scale, and macroscale; (iii) the upscaled equations take phase separation during Li-intercalation into account as well as specific particle configurations. The wide range of applications and interest in energy storage devices make these results a promising tool to study the influence of the microstructure on current-voltage characteristics and to optimize cathode designs.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"32 1","pages":"402-430"},"PeriodicalIF":0.0,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86169599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We are concerned with the non-normal Schrodinger operator H=−Δ+VH=−Δ+V on L2(Rn)L2(Rn) , where V∈W1,∞loc(Rn)V∈Wloc1,∞(Rn) and ReV(x)≥c∣x∣2−dReV(x)≥c∣x∣2−d for some c,d>0c,d>0 . The spectrum of this operator is discrete and its real part is bounded below by −d−d . In general, the e-pseudospectrum of H will have an unbounded component for any e>0e>0 and thus will not approximate the spectrum in a global sense.By exploiting the fact that the semigroup e−tHe−tH is immediately compact, we show a complementary result, namely that for every δ>0δ>0 , R>0R>0 there exists an e>0e>0 such that the e-pseudospectrum σe(H)⊂{z:Rez≥R}∪⋃λ∈σ(H){z:∣∣z−λ∣∣<δ}.σe(H)⊂{z:Rez≥R}∪⋃λ∈σ(H){z:∣z−λ∣<δ}. In particular, the unbounded part of the pseudospectrum escapes towards +∞+∞ as e decreases. In addition, we give two examples of non-selfadjoint Schrodinger operators outside of our class and study their pseudospectra in more detail.
{"title":"A bound on the pseudospectrum for a class of non-normal Schrödinger operators.","authors":"P. Dondl, P. Dorey, F. Rösler","doi":"10.1093/amrx/abw011","DOIUrl":"https://doi.org/10.1093/amrx/abw011","url":null,"abstract":"We are concerned with the non-normal Schrodinger operator H=−Δ+VH=−Δ+V on L2(Rn)L2(Rn) , where V∈W1,∞loc(Rn)V∈Wloc1,∞(Rn) and ReV(x)≥c∣x∣2−dReV(x)≥c∣x∣2−d for some c,d>0c,d>0 . The spectrum of this operator is discrete and its real part is bounded below by −d−d . In general, the e-pseudospectrum of H will have an unbounded component for any e>0e>0 and thus will not approximate the spectrum in a global sense.By exploiting the fact that the semigroup e−tHe−tH is immediately compact, we show a complementary result, namely that for every δ>0δ>0 , R>0R>0 there exists an e>0e>0 such that the e-pseudospectrum σe(H)⊂{z:Rez≥R}∪⋃λ∈σ(H){z:∣∣z−λ∣∣<δ}.σe(H)⊂{z:Rez≥R}∪⋃λ∈σ(H){z:∣z−λ∣<δ}. In particular, the unbounded part of the pseudospectrum escapes towards +∞+∞ as e decreases. In addition, we give two examples of non-selfadjoint Schrodinger operators outside of our class and study their pseudospectra in more detail.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"12 1","pages":"271-296"},"PeriodicalIF":0.0,"publicationDate":"2016-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87812310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Aharonov–Bohm Effect in Resonances for Scattering by Three Solenoids at Large Separation","authors":"H. Tamura","doi":"10.1093/AMRX/ABW009","DOIUrl":"https://doi.org/10.1093/AMRX/ABW009","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"52 1","pages":"65-117"},"PeriodicalIF":0.0,"publicationDate":"2016-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81093635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Diffusion Limit for a Finite Capacity Storage Allocation Model","authors":"C. Knessl, E. Sohn","doi":"10.1093/AMRX/ABW008","DOIUrl":"https://doi.org/10.1093/AMRX/ABW008","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"15 1","pages":"118-141"},"PeriodicalIF":0.0,"publicationDate":"2016-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88634607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Expectation Dependence: The Banking Firm Under Risk","authors":"Udo Broll, P. Welzel, K. Wong","doi":"10.1093/AMRX/ABW005","DOIUrl":"https://doi.org/10.1093/AMRX/ABW005","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"184 1","pages":"281-288"},"PeriodicalIF":0.0,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86816865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data","authors":"G. Maso, I. Lucardesi","doi":"10.1093/AMRX/ABW006","DOIUrl":"https://doi.org/10.1093/AMRX/ABW006","url":null,"abstract":"MIUR Project ``Calculus of Variations\" (PRIN 2010-11), \u0000ERC Grant No. 290888 ``Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture''.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"68 1","pages":"184-241"},"PeriodicalIF":0.0,"publicationDate":"2016-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75873423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper concerns the asymptotic expansion of the solution of the Dirichlet-Laplace problem in a domain with small inclusions. This problem is well understood for the Neumann condition in dimension greater than two or Dirichlet condition in dimension greater than three. The case of two circular inclusions in a bidimensional domain was considered in [1]. In this paper, we generalize the previous result to any shape and relax the assumptions of regularity and support of the data. Our approach uses conformal mapping and suitable lifting of Dirichlet conditions. We also analyze configurations with several scales for the distance between the inclusions (when the number is larger than 2).
{"title":"Interactions Between Moderately Close Inclusions for the Two-Dimensional Dirichlet–Laplacian","authors":"V. Bonnaillie-Noël, M. Dambrine, C. Lacave","doi":"10.1093/AMRX/ABV008","DOIUrl":"https://doi.org/10.1093/AMRX/ABV008","url":null,"abstract":"This paper concerns the asymptotic expansion of the solution of the Dirichlet-Laplace problem in a domain with small inclusions. This problem is well understood for the Neumann condition in dimension greater than two or Dirichlet condition in dimension greater than three. The case of two circular inclusions in a bidimensional domain was considered in [1]. In this paper, we generalize the previous result to any shape and relax the assumptions of regularity and support of the data. Our approach uses conformal mapping and suitable lifting of Dirichlet conditions. We also analyze configurations with several scales for the distance between the inclusions (when the number is larger than 2).","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"2 1","pages":"1-23"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82047074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work we propose a new numerical procedure for the simulation of time-dependent problems based on the coupling between the finite element method and the lattice Boltzmann method. The procedure is based on the Parareal paradigm and allows to couple efficiently the two numerical methods, each one working with its own grid size and time-step size. The motivations behind this approach are manifold. Among others, we have that one technique may be more efficient, or physically more appropriate or less memory consuming than the other depending on the target of the simulation and/or on the sub-region of the computational domain. Furthermore, the coupling with finite element method may circumvent some difficulties inherent to lattice Boltzmann discretization, for some domains with complex boundaries, or for some boundary conditions. The theoretical and numerical framework is presented for parabolic equations, in order to describe and validate numerically the methodology in a simple situation.
{"title":"A Time-Parallel Framework for Coupling Finite Element and Lattice Boltzmann Methods","authors":"M. Astorino, F. Chouly, A. Quarteroni","doi":"10.1093/AMRX/ABV009","DOIUrl":"https://doi.org/10.1093/AMRX/ABV009","url":null,"abstract":"In this work we propose a new numerical procedure for the simulation of time-dependent problems based on the coupling between the finite element method and the lattice Boltzmann method. The procedure is based on the Parareal paradigm and allows to couple efficiently the two numerical methods, each one working with its own grid size and time-step size. The motivations behind this approach are manifold. Among others, we have that one technique may be more efficient, or physically more appropriate or less memory consuming than the other depending on the target of the simulation and/or on the sub-region of the computational domain. Furthermore, the coupling with finite element method may circumvent some difficulties inherent to lattice Boltzmann discretization, for some domains with complex boundaries, or for some boundary conditions. The theoretical and numerical framework is presented for parabolic equations, in order to describe and validate numerically the methodology in a simple situation.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"173 1","pages":"24-67"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79591561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
- The purpose of this article is to study possible concentrations of eigenfunc-tions of Laplace operators (or more generally quasi-modes) on product manifolds. We show that the approach of the first author and Zworski [10, 11] applies (modulo rescalling) and deduce new stabilization results for weakly damped wave equations which extend to product manifolds previous results by Leautaud-Lerner [12] obtained for products of tori.
{"title":"Laplace Eigenfunctions and Damped Wave Equation on Product Manifolds","authors":"N. Burq, C. Zuily","doi":"10.1093/AMRX/ABV005","DOIUrl":"https://doi.org/10.1093/AMRX/ABV005","url":null,"abstract":"- The purpose of this article is to study possible concentrations of eigenfunc-tions of Laplace operators (or more generally quasi-modes) on product manifolds. We show that the approach of the first author and Zworski [10, 11] applies (modulo rescalling) and deduce new stabilization results for weakly damped wave equations which extend to product manifolds previous results by Leautaud-Lerner [12] obtained for products of tori.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"19 1","pages":"296-310"},"PeriodicalIF":0.0,"publicationDate":"2015-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/AMRX/ABV005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72515719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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