{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T19:47:31Z","timestamp":1779392851968,"version":"3.53.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2022,7,5]],"date-time":"2022-07-05T00:00:00Z","timestamp":1656979200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,7,5]],"date-time":"2022-07-05T00:00:00Z","timestamp":1656979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s40314-022-01929-9","type":"journal-article","created":{"date-parts":[[2022,7,5]],"date-time":"2022-07-05T11:09:06Z","timestamp":1657019346000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["An advection\u2013diffusion\u2013reaction model for coffee percolation"],"prefix":"10.1007","volume":"41","author":[{"given":"Nadaniela","family":"Egidi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7772-569X","authenticated-orcid":false,"given":"Josephin","family":"Giacomini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierluigi","family":"Maponi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessia","family":"Perticarini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luca","family":"Cognigni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lauro","family":"Fioretti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,7,5]]},"reference":[{"issue":"8","key":"1929_CR1","doi-asserted-by":"publisher","first-page":"1320","DOI":"10.1134\/S0965542506080057","volume":"46","author":"AB Al\u2019shin","year":"2006","unstructured":"Al\u2019shin AB, Al\u2019shina EA, Kalitkin NN, Koryagina A (2006) Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems. Comput Math Math Phys 46(8):1320\u20131340","journal-title":"Comput Math Math Phys"},{"issue":"1","key":"1929_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-020-02580-6","volume":"2020","author":"S Bu","year":"2020","unstructured":"Bu S, Bak S (2020) Simulation of advection\u2013diffusion\u2013dispersion equations based on a composite time discretization scheme. Adv Differ Equ 2020(1):1\u201319","journal-title":"Adv Differ Equ"},{"issue":"6","key":"1929_CR3","doi-asserted-by":"publisher","first-page":"1034","DOI":"10.3390\/math8061034","volume":"8","author":"R B\u00fcrger","year":"2020","unstructured":"B\u00fcrger R, Gavil\u00e1n E, Inzunza D, Mulet P, Villada LM (2020a) Implicit\u2013explicit methods for a convection\u2013diffusion\u2013reaction model of the propagation of forest fires. Mathematics 8(6):1034","journal-title":"Mathematics"},{"issue":"10","key":"1929_CR4","doi-asserted-by":"publisher","first-page":"1674","DOI":"10.3390\/math8101674","volume":"8","author":"R B\u00fcrger","year":"2020","unstructured":"B\u00fcrger R, Gavil\u00e1n E, Inzunza D, Mulet P, Villada LM (2020b) Exploring a convection\u2013diffusion\u2013reaction model of the propagation of forest fires: computation of risk maps for heterogeneous environments. Mathematics 8(10):1674","journal-title":"Mathematics"},{"key":"1929_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.matt.2019.12.019","author":"MI Cameron","year":"2020","unstructured":"Cameron MI, Morisco D, Hofstetter D, Uman E, Wilkinson J, Kennedy ZC, Fontenot SA, Lee WT, Hendon CH, Foster JM (2020) Systematically improving espresso: insights from mathematical modeling and experiment. Matter. https:\/\/doi.org\/10.1016\/j.matt.2019.12.019","journal-title":"Matter"},{"issue":"9\u201310","key":"1929_CR6","doi-asserted-by":"publisher","first-page":"2177","DOI":"10.1016\/j.mcm.2011.05.005","volume":"57","author":"BM Chen-Charpentier","year":"2013","unstructured":"Chen-Charpentier BM, Kojouharov HV (2013) An unconditionally positivity preserving scheme for advection\u2013diffusion reaction equations. Math Comput Model 57(9\u201310):2177\u20132185","journal-title":"Math Comput Model"},{"key":"1929_CR7","doi-asserted-by":"publisher","unstructured":"Clairambault J (2013) Reaction\u2013diffusion\u2013advection equation. In: Dubitzky, W., Wolkenhauer, O., Cho, K.-H., Yokota, H. (eds.) Encyclopedia of Systems Biology. Springer, New York, pp 1817\u20131817. https:\/\/doi.org\/10.1007\/978-1-4419-9863-7_697","DOI":"10.1007\/978-1-4419-9863-7_697"},{"issue":"1","key":"1929_CR8","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0771-050X(80)90013-3","volume":"6","author":"JR Dormand","year":"1980","unstructured":"Dormand JR, Prince PJ (1980) A family of embedded Runge\u2013Kutta formulae. J Comput Appl Math 6(1):19\u201326","journal-title":"J Comput Appl Math"},{"key":"1929_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmultiphaseflow.2020.103252","author":"J Giacomini","year":"2020","unstructured":"Giacomini J, Khamitova G, Maponi P, Vittori S, Fioretti L (2020) Water flow and transport in porous media for in-silico espresso coffee. Int J Multiphase Flow. https:\/\/doi.org\/10.1016\/j.ijmultiphaseflow.2020.103252","journal-title":"Int J Multiphase Flow"},{"key":"1929_CR10","volume-title":"Espresso coffee: the science of quality","author":"A Illy","year":"2005","unstructured":"Illy A, Viani R (2005) Espresso coffee: the science of quality. Academic Press, London"},{"issue":"3","key":"1929_CR11","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1007\/s13668-019-0274-1","volume":"8","author":"M Inoue","year":"2019","unstructured":"Inoue M, Tsugane S (2019) Coffee drinking and reduced risk of liver cancer: update on epidemiological findings and potential mechanisms. Curr Nutr Rep 8(3):182\u2013186. https:\/\/doi.org\/10.1007\/s13668-019-0274-1","journal-title":"Curr Nutr Rep"},{"key":"1929_CR12","doi-asserted-by":"publisher","DOI":"10.1080\/23311908.2017.1392230","author":"CR Kennedy","year":"2017","unstructured":"Kennedy CR, Abraham S (2017) Association between coffee consumption and different types of cancers: a review of meta-analysis. Cogent Psychol. https:\/\/doi.org\/10.1080\/23311908.2017.1392230","journal-title":"Cogent Psychol"},{"key":"1929_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.foodchem.2020.126220","volume":"314","author":"G Khamitova","year":"2020","unstructured":"Khamitova G, Angeloni S, Borsetta G, Xiao J, Maggi F, Sagratini G, Vittori S, Caprioli G (2020) Optimization of espresso coffee extraction through variation of particle sizes, perforated disk height and filter basket aimed at lowering the amount of ground coffee used. Food Chem 314:126220","journal-title":"Food Chem"},{"key":"1929_CR14","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.jfoodeng.2017.03.002","volume":"206","author":"M Kuhn","year":"2017","unstructured":"Kuhn M, Lang S, Bezold F, Minceva M, Briesen H (2017) Time-resolved extraction of caffeine and trigonelline from finely-ground espresso coffee with varying particle sizes and tamping pressures. J Food Eng 206:37\u201347","journal-title":"J Food Eng"},{"key":"1929_CR15","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.apnum.2021.06.013","volume":"169","author":"H Liu","year":"2021","unstructured":"Liu H, L\u00fc S (2021) A high-order numerical scheme for solving nonlinear time fractional reaction-diffusion equations with initial singularity. Appl Numer Math 169:32\u201343","journal-title":"Appl Numer Math"},{"key":"1929_CR16","unstructured":"Mastersizer\u2014Malvern Panalytical. https:\/\/www.malvernpanalytical.com\/en\/products\/product-range\/mastersizer-range. Accessed 2021"},{"key":"1929_CR17","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.ces.2015.06.003","volume":"137","author":"K Moroney","year":"2015","unstructured":"Moroney K, Lee W, Suijver F, Marra J (2015) Modelling of coffee extraction during brewing using multiscale methods: an experimentally validated model. Chem Eng Sci 137:216\u2013234","journal-title":"Chem Eng Sci"},{"issue":"6","key":"1929_CR18","doi-asserted-by":"publisher","first-page":"2196","DOI":"10.1137\/15M1036658","volume":"76","author":"K Moroney","year":"2016","unstructured":"Moroney K, Lee W, Brien S, Suijver F, Marra J (2016a) Asymptotic analysis of the dominant mechanisms in the coffee extraction process. SIAM J Appl Math 76(6):2196\u20132217. https:\/\/doi.org\/10.1137\/15M1036658","journal-title":"SIAM J Appl Math"},{"issue":"1","key":"1929_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13362-016-0024-6","volume":"7","author":"KM Moroney","year":"2016","unstructured":"Moroney KM, Lee WT, O\u2019Brien SB, Suijver F, Marra J (2016b) Coffee extraction kinetics in a well mixed system. J Math Ind 7(1):1\u201319. https:\/\/doi.org\/10.1186\/s13362-016-0024-6","journal-title":"J Math Ind"},{"issue":"7","key":"1929_CR20","doi-asserted-by":"publisher","first-page":"0219906","DOI":"10.1371\/journal.pone.0219906","volume":"14","author":"KM Moroney","year":"2019","unstructured":"Moroney KM, O\u2019Connell K, Meikle-Janney P, O\u2019Brien SB, Walker G, Lee WT (2019) Analysing extraction uniformity from porous coffee beds using mathematical modelling and computational fluid dynamics approaches. PLoS ONE 14(7):0219906. https:\/\/doi.org\/10.1371\/journal.pone.0219906","journal-title":"PLoS ONE"},{"key":"1929_CR21","unstructured":"Mythos 1 Grinder\u2014Victoria Arduino. https:\/\/www.victoriaarduino.com\/mythos-1\/. Accessed 2021"},{"key":"1929_CR22","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1016\/B978-0-12-384746-1.00014-8","volume-title":"Progress in filtration and separation","author":"M Naderi","year":"2015","unstructured":"Naderi M (2015) Surface area: Brunauer-Emmett-Teller (BET). In: Tarleton S (ed) Progress in filtration and separation. Academic Press, UK, pp 585\u2013608"},{"issue":"7","key":"1929_CR23","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1212\/WNL.0b013e318263570d","volume":"79","author":"RB Postuma","year":"2012","unstructured":"Postuma RB, Lang AE, Munhoz RP, Charland K, Pelletier A, Moscovich M, Filla L, Zanatta D, Rios Romenets S, Altman R, Chuang R, Shah B (2012) Caffeine for treatment of Parkinson disease. Neurology 79(7):651\u2013658. https:\/\/doi.org\/10.1212\/WNL.0b013e318263570d","journal-title":"Neurology"},{"key":"1929_CR24","unstructured":"PUQ PRESS M2 Tamper. https:\/\/www.puqpress.com\/products\/puq-m-line\/puqpress-m2-for-mythos\/. Accessed 2021"},{"issue":"1","key":"1929_CR25","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.envsoft.2007.05.009","volume":"23","author":"A Rubio","year":"2008","unstructured":"Rubio A, Zalts A, El Hasi C (2008) Numerical solution of the advection\u2013reaction\u2013diffusion equation at different scales. Environ Model Softw 23(1):90\u201395","journal-title":"Environ Model Softw"},{"issue":"19","key":"1929_CR26","doi-asserted-by":"publisher","first-page":"9853","DOI":"10.1016\/j.amc.2012.03.062","volume":"218","author":"SA Sarra","year":"2012","unstructured":"Sarra SA (2012) A local radial basis function method for advection\u2013diffusion\u2013reaction equations on complexly shaped domains. Appl Math Comput 218(19):9853\u20139865","journal-title":"Appl Math Comput"},{"issue":"1","key":"1929_CR27","doi-asserted-by":"publisher","first-page":"127","DOI":"10.15344\/2456-8171\/2018\/127","volume":"4","author":"C Severini","year":"2018","unstructured":"Severini C, Derossi A, Ricci I, Caporizzi R, Fiore A (2018) Roasting conditions, grinding level and brewing method highly affect the healthy benefits of a coffee cup. Int J Clin Nutr Diet 4(1):127","journal-title":"Int J Clin Nutr Diet"},{"issue":"1","key":"1929_CR28","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1515\/phys-2020-0011","volume":"18","author":"N Shahid","year":"2020","unstructured":"Shahid N, Ahmed N, Baleanu D, Alshomrani AS, Iqbal MS, Rehman MA-U, Shaikh TS, Rafiq M (2020) Novel numerical analysis for nonlinear advection\u2013reaction\u2013diffusion systems. Open Phys 18(1):112\u2013125","journal-title":"Open Phys"},{"issue":"1","key":"1929_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/S1064827594276424","volume":"18","author":"LF Shampine","year":"1997","unstructured":"Shampine LF, Reichelt MW (1997) The matlab ode suite. SIAM J Sci Comput 18(1):1\u201322","journal-title":"SIAM J Sci Comput"},{"issue":"9344","key":"1929_CR30","doi-asserted-by":"publisher","first-page":"1477","DOI":"10.1016\/S0140-6736(02)11436-X","volume":"360","author":"RM Van Dam","year":"2002","unstructured":"Van Dam RM, Feskens EJ (2002) Coffee consumption and risk of type 2 diabetes mellitus. Lancet 360(9344):1477\u20131478","journal-title":"Lancet"},{"key":"1929_CR31","unstructured":"Victoria Arduino VA388 Black Eagle. https:\/\/www.victoriaarduino.com\/black-eagle\/. Accessed 2021"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01929-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-01929-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01929-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T22:09:26Z","timestamp":1662761366000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-01929-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,5]]},"references-count":31,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["1929"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-01929-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,5]]},"assertion":[{"value":"17 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 May 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"229"}}