{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:15:17Z","timestamp":1774592117831,"version":"3.50.1"},"reference-count":10,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,10,7]],"date-time":"2015-10-07T00:00:00Z","timestamp":1444176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>New patterns of steady-state chemical kinetics for continuously stirred-tank reactors (CSTR) have been found, i.e., intersections, maxima and coincidences, for two-step mechanism A\u2194B\u2192C. There were found elegant analytical relationships for characteristics of these patterns (space times, values of concentrations and rates) allowing kinetic parameters to be easily determined. It was demonstrated that for the pair of species involved into the irreversible reaction (B and C), the space time of their corresponding concentration dependence intersection is invariant and does not depend on the initial conditions of the system. Maps of patterns are presented for visualization of their combinations and ranking in space time, and values of concentration and rates.<\/jats:p>","DOI":"10.3390\/e17106783","type":"journal-article","created":{"date-parts":[[2015,10,7]],"date-time":"2015-10-07T10:39:13Z","timestamp":1444214353000},"page":"6783-6800","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["New Patterns in Steady-State Chemical Kinetics: Intersections, Coincidences, Map of Events (Two-Step Mechanism)"],"prefix":"10.3390","volume":"17","author":[{"given":"Daniel","family":"Branco Pinto","sequence":"first","affiliation":[{"name":"Department of Mathematical Analysis, Gent University, Galglaan 2, Gent B-9000, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gregory","family":"Yablonsky","sequence":"additional","affiliation":[{"name":"Parks College of Engineering, Aviation and Technology, Saint Louis University, 3450 Lindell Blvd., Saint Louis, MO 63103, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guy","family":"Marin","sequence":"additional","affiliation":[{"name":"Laboratory for Chemical Technology, Ghent University, Technologiepark 914, Gent B-9052, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denis","family":"Constales","sequence":"additional","affiliation":[{"name":"Department of Mathematical Analysis, Gent University, Galglaan 2, Gent B-9000, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.ces.2010.10.014","article-title":"Equilibrium relationships for non-equilibrium chemical dependencies","volume":"66","author":"Yablonsky","year":"2011","journal-title":"Chem. Eng. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"20004","DOI":"10.1209\/0295-5075\/93\/20004","article-title":"Reciprocal relations between kinetic curves","volume":"66","author":"Yablonsky","year":"2011","journal-title":"EuroPhys. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6065","DOI":"10.1016\/j.ces.2010.04.007","article-title":"Coincidences in chemical kinetics: Surprising news about simple reactions","volume":"65","author":"Yablonsky","year":"2010","journal-title":"Chem. Eng. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.ces.2012.01.017","article-title":"Thermodynamic time invariances for dual kinetic experiments: Nonlinear single reactions and more","volume":"73","author":"Constales","year":"2012","journal-title":"Chem. Eng. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4683","DOI":"10.1016\/j.ces.2011.06.033","article-title":"Thermodynamic time invariances: Theory of TAP pulse-response experiments","volume":"66","author":"Constales","year":"2011","journal-title":"Chem. Eng. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.ces.2014.11.030","article-title":"Predicting kinetics dependences and closing the balance: Wei and Prater revisited","volume":"123","author":"Constales","year":"2015","journal-title":"Chem. Eng. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1614","DOI":"10.1016\/j.camwa.2012.11.005","article-title":"Intersections and coincidences in chemical kinetics: Linear two-step reversible-irreversible reaction mechanism","volume":"65","author":"Constales","year":"2013","journal-title":"Comp. Math. Appl."},{"key":"ref_8","first-page":"69","article-title":"New types of complexity in chemical kinetics: Intersections, coincidences and special symmetric relationships","volume":"157","author":"Yablonsky","year":"2014","journal-title":"Adv. Chem. Phys."},{"key":"ref_9","unstructured":"Marin, G.B., and Yablonsky, G.S. (2011). Kinetics of Chemical Reactions, Wiley-VCH. [1st ed.]."},{"key":"ref_10","unstructured":"Marin, G.B., and Yablonsky, G.S. (2011). Kinetics of Chemical Reactions, Wiley-VCH."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/6783\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:49:44Z","timestamp":1760215784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/6783"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,7]]},"references-count":10,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2015,10]]}},"alternative-id":["e17106783"],"URL":"https:\/\/doi.org\/10.3390\/e17106783","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,7]]}}}