--- _id: '10550' abstract: - lang: eng text: The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter. acknowledgement: "We thank the referees for their valuable comments and suggestions. A major part of this work was carried out when B. Q. Tang visited the Institute of Science and Technology Austria (ISTA). The hospitality of ISTA is greatly acknowledged. This work was partially supported by NAWI Graz.\r\nOpen access funding provided by University of Graz." article_number: '66' article_processing_charge: No article_type: original author: - first_name: Klemens full_name: Fellner, Klemens last_name: Fellner - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 - first_name: Bao Quoc full_name: Tang, Bao Quoc last_name: Tang citation: ama: Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-023-09926-w apa: Fellner, K., Fischer, J. L., Kniely, M., & Tang, B. Q. (2023). Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-09926-w chicago: Fellner, Klemens, Julian L Fischer, Michael Kniely, and Bao Quoc Tang. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science. Springer Nature, 2023. https://doi.org/10.1007/s00332-023-09926-w. ieee: K. Fellner, J. L. Fischer, M. Kniely, and B. Q. Tang, “Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion,” Journal of Nonlinear Science, vol. 33. Springer Nature, 2023. ista: Fellner K, Fischer JL, Kniely M, Tang BQ. 2023. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 33, 66. mla: Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science, vol. 33, 66, Springer Nature, 2023, doi:10.1007/s00332-023-09926-w. short: K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023). date_created: 2021-12-16T12:15:35Z date_published: 2023-06-07T00:00:00Z date_updated: 2023-08-01T14:40:33Z day: '07' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00332-023-09926-w external_id: arxiv: - '2109.12019' isi: - '001002343400002' file: - access_level: open_access checksum: f3f0f0886098e31c81116cff8183750b content_type: application/pdf creator: dernst date_created: 2023-06-19T07:33:53Z date_updated: 2023-06-19T07:33:53Z file_id: '13149' file_name: 2023_JourNonlinearScience_Fellner.pdf file_size: 742315 relation: main_file success: 1 file_date_updated: 2023-06-19T07:33:53Z has_accepted_license: '1' intvolume: ' 33' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: Journal of Nonlinear Science publication_identifier: eissn: - 1432-1467 issn: - 0938-8974 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 33 year: '2023' ... --- _id: '10547' abstract: - lang: eng text: "We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities,\r\nwhile at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear." acknowledgement: M.K. gratefully acknowledges the hospitality of WIAS Berlin, where a major part of the project was carried out. The research stay of M.K. at WIAS Berlin was funded by the Austrian Federal Ministry of Education, Science and Research through a research fellowship for graduates of a promotio sub auspiciis. The research of A.M. has been partially supported by Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center SFB 1114 “Scaling Cascades in Complex Systems” (Project no. 235221301), Subproject C05 “Effective models for materials and interfaces with multiple scales”. J.F. and A.M. are grateful for the hospitality of the Erwin Schrödinger Institute in Vienna, where some ideas for this work have been developed. The authors are grateful to two anonymous referees for several helpful comments, in particular for the short proof of estimate (2.7). article_processing_charge: No article_type: original author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Katharina full_name: Hopf, Katharina last_name: Hopf - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 - first_name: Alexander full_name: Mielke, Alexander last_name: Mielke citation: ama: Fischer JL, Hopf K, Kniely M, Mielke A. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 2022;54(1):220-267. doi:10.1137/20M1387237 apa: Fischer, J. L., Hopf, K., Kniely, M., & Mielke, A. (2022). Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1387237 chicago: Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/20M1387237. ieee: J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis of energy-reaction-diffusion systems,” SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022. ista: Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1), 220–267. mla: Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:10.1137/20M1387237. short: J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical Analysis 54 (2022) 220–267. date_created: 2021-12-16T12:08:56Z date_published: 2022-01-04T00:00:00Z date_updated: 2023-08-02T13:37:03Z day: '04' department: - _id: JuFi doi: 10.1137/20M1387237 external_id: arxiv: - '2012.03792 ' isi: - '000762768000006' intvolume: ' 54' isi: 1 issue: '1' keyword: - Energy-Reaction-Diffusion Systems - Cross Diffusion - Global-In-Time Existence of Weak/Renormalised Solutions - Entropy Method - Onsager System - Soret/Dufour Effect language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2012.03792 month: '01' oa: 1 oa_version: Preprint page: 220-267 publication: SIAM Journal on Mathematical Analysis publication_identifier: issn: - 0036-1410 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Global existence analysis of energy-reaction-diffusion systems type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 54 year: '2022' ... --- _id: '7866' abstract: - lang: eng text: In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation. acknowledgement: Open access funding provided by Austrian Science Fund (FWF). The second author has been supported by the International Research Training Group IGDK 1754 “Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian Science Fund (FWF) under grant number [W 1244-N18]. article_processing_charge: No article_type: original author: - first_name: Klemens full_name: Fellner, Klemens last_name: Fellner - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 citation: ama: Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 2020;6:529-598. doi:10.1007/s41808-020-00068-8 apa: Fellner, K., & Kniely, M. (2020). Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. Springer Nature. https://doi.org/10.1007/s41808-020-00068-8 chicago: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations. Springer Nature, 2020. https://doi.org/10.1007/s41808-020-00068-8. ieee: K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model,” Journal of Elliptic and Parabolic Equations, vol. 6. Springer Nature, pp. 529–598, 2020. ista: Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 6, 529–598. mla: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations, vol. 6, Springer Nature, 2020, pp. 529–98, doi:10.1007/s41808-020-00068-8. short: K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020) 529–598. date_created: 2020-05-17T22:00:45Z date_published: 2020-12-01T00:00:00Z date_updated: 2021-01-12T08:15:47Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1007/s41808-020-00068-8 file: - access_level: open_access checksum: 6bc6832caacddceee1471291e93dcf1d content_type: application/pdf creator: dernst date_created: 2020-11-25T08:59:59Z date_updated: 2020-11-25T08:59:59Z file_id: '8802' file_name: 2020_JourEllipticParabEquat_Fellner.pdf file_size: 8408694 relation: main_file success: 1 file_date_updated: 2020-11-25T08:59:59Z has_accepted_license: '1' intvolume: ' 6' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 529-598 project: - _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1 call_identifier: FWF name: FWF Open Access Fund publication: Journal of Elliptic and Parabolic Equations publication_identifier: eissn: - '22969039' issn: - '22969020' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 6 year: '2020' ... --- _id: '8697' abstract: - lang: eng text: In the computation of the material properties of random alloys, the method of 'special quasirandom structures' attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach is based on a recent analysis of a related variance reduction method in stochastic homogenization of linear elliptic PDEs and the locality properties of the TFW model. Concerning the latter, we extend an exponential locality result by Nazar and Ortner to include point charges, a result that may be of independent interest. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 citation: ama: Fischer JL, Kniely M. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772. doi:10.1088/1361-6544/ab9728 apa: Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728 chicago: Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity. IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728. ieee: J. L. Fischer and M. Kniely, “Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity, vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020. ista: Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772. mla: Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity, vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728. short: J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772. date_created: 2020-10-25T23:01:16Z date_published: 2020-11-01T00:00:00Z date_updated: 2023-08-22T10:38:38Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1088/1361-6544/ab9728 external_id: arxiv: - '1906.12245' isi: - '000576492700001' file: - access_level: open_access checksum: ed90bc6eb5f32ee6157fef7f3aabc057 content_type: application/pdf creator: cziletti date_created: 2020-10-27T12:09:57Z date_updated: 2020-10-27T12:09:57Z file_id: '8710' file_name: 2020_Nonlinearity_Fischer.pdf file_size: 1223899 relation: main_file success: 1 file_date_updated: 2020-10-27T12:09:57Z has_accepted_license: '1' intvolume: ' 33' isi: 1 issue: '11' language: - iso: eng license: https://creativecommons.org/licenses/by/3.0/ month: '11' oa: 1 oa_version: Published Version page: 5733-5772 publication: Nonlinearity publication_identifier: eissn: - '13616544' issn: - '09517715' publication_status: published publisher: IOP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 33 year: '2020' ... --- _id: '6762' abstract: - lang: eng text: "We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level\r\nof theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the doping profiles < system size." article_processing_charge: No author: - first_name: Gero full_name: Friesecke, Gero last_name: Friesecke - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 citation: ama: Friesecke G, Kniely M. New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. 2019;17(3):926-947. doi:10.1137/18M1207272 apa: Friesecke, G., & Kniely, M. (2019). New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. SIAM. https://doi.org/10.1137/18M1207272 chicago: Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” Multiscale Modeling and Simulation. SIAM, 2019. https://doi.org/10.1137/18M1207272. ieee: G. Friesecke and M. Kniely, “New optimal control problems in density functional theory motivated by photovoltaics,” Multiscale Modeling and Simulation, vol. 17, no. 3. SIAM, pp. 926–947, 2019. ista: Friesecke G, Kniely M. 2019. New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. 17(3), 926–947. mla: Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” Multiscale Modeling and Simulation, vol. 17, no. 3, SIAM, 2019, pp. 926–47, doi:10.1137/18M1207272. short: G. Friesecke, M. Kniely, Multiscale Modeling and Simulation 17 (2019) 926–947. date_created: 2019-08-04T21:59:21Z date_published: 2019-07-16T00:00:00Z date_updated: 2023-09-05T15:05:45Z day: '16' department: - _id: JuFi doi: 10.1137/18M1207272 external_id: arxiv: - '1808.04200' isi: - '000487931800002' intvolume: ' 17' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1808.04200 month: '07' oa: 1 oa_version: Preprint page: 926-947 publication: Multiscale Modeling and Simulation publication_identifier: eissn: - '15403467' issn: - '15403459' publication_status: published publisher: SIAM quality_controlled: '1' scopus_import: '1' status: public title: New optimal control problems in density functional theory motivated by photovoltaics type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 17 year: '2019' ...