[{"publication_identifier":{"eissn":["22277390"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2020-04-01T00:00:00Z","file":[{"access_level":"open_access","relation":"main_file","file_id":"7887","creator":"dernst","date_created":"2020-05-25T14:42:22Z","file_size":990540,"checksum":"a05a7df724522203d079673a0d4de4bc","date_updated":"2020-07-14T12:48:04Z","content_type":"application/pdf","file_name":"2020_Mathematics_Armstrong.pdf"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"oa_version":"Published Version","article_number":"484","month":"04","has_accepted_license":"1","publication":"Mathematics","language":[{"iso":"eng"}],"day":"01","doi":"10.3390/math8040484","abstract":[{"lang":"eng","text":"A few-body cluster is a building block of a many-body system in a gas phase provided the temperature at most is of the order of the binding energy of this cluster. Here we illustrate this statement by considering a system of tubes filled with dipolar distinguishable particles. We calculate the partition function, which determines the probability to find a few-body cluster at a given temperature. The input for our calculations—the energies of few-body clusters—is estimated using the harmonic approximation. We first describe and demonstrate the validity of our numerical procedure. Then we discuss the results featuring melting of the zero-temperature many-body state into a gas of free particles and few-body clusters. For temperature higher than its binding energy threshold, the dimers overwhelmingly dominate the ensemble, where the remaining probability is in free particles. At very high temperatures free (harmonic oscillator trap-bound) particle dominance is eventually reached. This structure evolution appears both for one and two particles in each layer providing crucial information about the behavior of ultracold dipolar gases. The investigation addresses the transition region between few- and many-body physics as a function of temperature using a system of ten dipoles in five tubes."}],"year":"2020","citation":{"short":"J.R. Armstrong, A.S. Jensen, A. Volosniev, N.T. Zinner, Mathematics 8 (2020).","mla":"Armstrong, Jeremy R., et al. “Clusters in Separated Tubes of Tilted Dipoles.” <i>Mathematics</i>, vol. 8, no. 4, 484, MDPI, 2020, doi:<a href=\"https://doi.org/10.3390/math8040484\">10.3390/math8040484</a>.","ista":"Armstrong JR, Jensen AS, Volosniev A, Zinner NT. 2020. Clusters in separated tubes of tilted dipoles. Mathematics. 8(4), 484.","apa":"Armstrong, J. R., Jensen, A. S., Volosniev, A., &#38; Zinner, N. T. (2020). Clusters in separated tubes of tilted dipoles. <i>Mathematics</i>. MDPI. <a href=\"https://doi.org/10.3390/math8040484\">https://doi.org/10.3390/math8040484</a>","ama":"Armstrong JR, Jensen AS, Volosniev A, Zinner NT. Clusters in separated tubes of tilted dipoles. <i>Mathematics</i>. 2020;8(4). doi:<a href=\"https://doi.org/10.3390/math8040484\">10.3390/math8040484</a>","ieee":"J. R. Armstrong, A. S. Jensen, A. Volosniev, and N. T. Zinner, “Clusters in separated tubes of tilted dipoles,” <i>Mathematics</i>, vol. 8, no. 4. MDPI, 2020.","chicago":"Armstrong, Jeremy R., Aksel S. Jensen, Artem Volosniev, and Nikolaj T. Zinner. “Clusters in Separated Tubes of Tilted Dipoles.” <i>Mathematics</i>. MDPI, 2020. <a href=\"https://doi.org/10.3390/math8040484\">https://doi.org/10.3390/math8040484</a>."},"date_updated":"2023-08-21T06:23:36Z","external_id":{"isi":["000531824100024"]},"isi":1,"volume":8,"ddc":["510"],"date_created":"2020-05-24T22:01:00Z","department":[{"_id":"MiLe"}],"article_processing_charge":"No","publication_status":"published","intvolume":"         8","title":"Clusters in separated tubes of tilted dipoles","scopus_import":"1","_id":"7882","issue":"4","author":[{"first_name":"Jeremy R.","last_name":"Armstrong","full_name":"Armstrong, Jeremy R."},{"full_name":"Jensen, Aksel S.","last_name":"Jensen","first_name":"Aksel S."},{"id":"37D278BC-F248-11E8-B48F-1D18A9856A87","full_name":"Volosniev, Artem","orcid":"0000-0003-0393-5525","last_name":"Volosniev","first_name":"Artem"},{"full_name":"Zinner, Nikolaj T.","last_name":"Zinner","first_name":"Nikolaj T."}],"publisher":"MDPI","article_type":"original","quality_controlled":"1","ec_funded":1,"file_date_updated":"2020-07-14T12:48:04Z"},{"article_type":"original","publisher":"MDPI","file_date_updated":"2020-11-23T13:06:30Z","quality_controlled":"1","ec_funded":1,"intvolume":"         8","title":"Prioritised learning in snowdrift-type games","department":[{"_id":"KrCh"}],"date_created":"2020-11-22T23:01:24Z","article_processing_charge":"No","publication_status":"published","issue":"11","author":[{"id":"4E21749C-F248-11E8-B48F-1D18A9856A87","last_name":"Kleshnina","first_name":"Maria","full_name":"Kleshnina, Maria"},{"full_name":"Streipert, Sabrina","first_name":"Sabrina","last_name":"Streipert"},{"last_name":"Filar","first_name":"Jerzy","full_name":"Filar, Jerzy"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"}],"scopus_import":"1","_id":"8789","ddc":["000"],"acknowledgement":"This work was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement #754411, the Australian Research Council Discovery Grants DP160101236 and DP150100618, and the European Research Council Consolidator Grant 863818 (FoRM-SMArt).\r\nAuthors would like to thank Patrick McKinlay for his work on the preliminary results for this paper.","volume":8,"abstract":[{"lang":"eng","text":"Cooperation is a ubiquitous and beneficial behavioural trait despite being prone to exploitation by free-riders. Hence, cooperative populations are prone to invasions by selfish individuals. However, a population consisting of only free-riders typically does not survive. Thus, cooperators and free-riders often coexist in some proportion. An evolutionary version of a Snowdrift Game proved its efficiency in analysing this phenomenon. However, what if the system has already reached its stable state but was perturbed due to a change in environmental conditions? Then, individuals may have to re-learn their effective strategies. To address this, we consider behavioural mistakes in strategic choice execution, which we refer to as incompetence. Parametrising the propensity to make such mistakes allows for a mathematical description of learning. We compare strategies based on their relative strategic advantage relying on both fitness and learning factors. When strategies are learned at distinct rates, allowing learning according to a prescribed order is optimal. Interestingly, the strategy with the lowest strategic advantage should be learnt first if we are to optimise fitness over the learning path. Then, the differences between strategies are balanced out in order to minimise the effect of behavioural uncertainty."}],"day":"04","doi":"10.3390/math8111945","external_id":{"isi":["000593962100001"]},"isi":1,"year":"2020","citation":{"ista":"Kleshnina M, Streipert S, Filar J, Chatterjee K. 2020. Prioritised learning in snowdrift-type games. Mathematics. 8(11), 1945.","short":"M. Kleshnina, S. Streipert, J. Filar, K. Chatterjee, Mathematics 8 (2020).","mla":"Kleshnina, Maria, et al. “Prioritised Learning in Snowdrift-Type Games.” <i>Mathematics</i>, vol. 8, no. 11, 1945, MDPI, 2020, doi:<a href=\"https://doi.org/10.3390/math8111945\">10.3390/math8111945</a>.","chicago":"Kleshnina, Maria, Sabrina Streipert, Jerzy Filar, and Krishnendu Chatterjee. “Prioritised Learning in Snowdrift-Type Games.” <i>Mathematics</i>. MDPI, 2020. <a href=\"https://doi.org/10.3390/math8111945\">https://doi.org/10.3390/math8111945</a>.","ieee":"M. Kleshnina, S. Streipert, J. Filar, and K. Chatterjee, “Prioritised learning in snowdrift-type games,” <i>Mathematics</i>, vol. 8, no. 11. MDPI, 2020.","ama":"Kleshnina M, Streipert S, Filar J, Chatterjee K. Prioritised learning in snowdrift-type games. <i>Mathematics</i>. 2020;8(11). doi:<a href=\"https://doi.org/10.3390/math8111945\">10.3390/math8111945</a>","apa":"Kleshnina, M., Streipert, S., Filar, J., &#38; Chatterjee, K. (2020). Prioritised learning in snowdrift-type games. <i>Mathematics</i>. MDPI. <a href=\"https://doi.org/10.3390/math8111945\">https://doi.org/10.3390/math8111945</a>"},"date_updated":"2025-07-14T09:09:49Z","language":[{"iso":"eng"}],"article_number":"1945","month":"11","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Mathematics","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"content_type":"application/pdf","file_name":"2020_Mathematics_Kleshnina.pdf","date_updated":"2020-11-23T13:06:30Z","file_size":565191,"checksum":"61cfcc3b35760656ce7a9385a4ace5d2","date_created":"2020-11-23T13:06:30Z","creator":"dernst","file_id":"8797","access_level":"open_access","success":1,"relation":"main_file"}],"oa":1,"publication_identifier":{"eissn":["22277390"]},"type":"journal_article","date_published":"2020-11-04T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}}]