---
_id: '7882'
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.
article_number: '484'
article_processing_charge: No
article_type: original
author:
- first_name: Jeremy R.
  full_name: Armstrong, Jeremy R.
  last_name: Armstrong
- first_name: Aksel S.
  full_name: Jensen, Aksel S.
  last_name: Jensen
- first_name: Artem
  full_name: Volosniev, Artem
  id: 37D278BC-F248-11E8-B48F-1D18A9856A87
  last_name: Volosniev
  orcid: 0000-0003-0393-5525
- first_name: Nikolaj T.
  full_name: Zinner, Nikolaj T.
  last_name: Zinner
citation:
  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>
  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>
  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>.
  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.
  ista: Armstrong JR, Jensen AS, Volosniev A, Zinner NT. 2020. Clusters in separated
    tubes of tilted dipoles. Mathematics. 8(4), 484.
  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>.
  short: J.R. Armstrong, A.S. Jensen, A. Volosniev, N.T. Zinner, Mathematics 8 (2020).
date_created: 2020-05-24T22:01:00Z
date_published: 2020-04-01T00:00:00Z
date_updated: 2023-08-21T06:23:36Z
day: '01'
ddc:
- '510'
department:
- _id: MiLe
doi: 10.3390/math8040484
ec_funded: 1
external_id:
  isi:
  - '000531824100024'
file:
- access_level: open_access
  checksum: a05a7df724522203d079673a0d4de4bc
  content_type: application/pdf
  creator: dernst
  date_created: 2020-05-25T14:42:22Z
  date_updated: 2020-07-14T12:48:04Z
  file_id: '7887'
  file_name: 2020_Mathematics_Armstrong.pdf
  file_size: 990540
  relation: main_file
file_date_updated: 2020-07-14T12:48:04Z
has_accepted_license: '1'
intvolume: '         8'
isi: 1
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Mathematics
publication_identifier:
  eissn:
  - '22277390'
publication_status: published
publisher: MDPI
quality_controlled: '1'
scopus_import: '1'
status: public
title: Clusters in separated tubes of tilted dipoles
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: 8
year: '2020'
...
---
_id: '8789'
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.
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."
article_number: '1945'
article_processing_charge: No
article_type: original
author:
- first_name: Maria
  full_name: Kleshnina, Maria
  id: 4E21749C-F248-11E8-B48F-1D18A9856A87
  last_name: Kleshnina
- first_name: Sabrina
  full_name: Streipert, Sabrina
  last_name: Streipert
- first_name: Jerzy
  full_name: Filar, Jerzy
  last_name: Filar
- first_name: Krishnendu
  full_name: Chatterjee, Krishnendu
  id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
  last_name: Chatterjee
  orcid: 0000-0002-4561-241X
citation:
  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>
  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.
  ista: Kleshnina M, Streipert S, Filar J, Chatterjee K. 2020. Prioritised learning
    in snowdrift-type games. Mathematics. 8(11), 1945.
  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>.
  short: M. Kleshnina, S. Streipert, J. Filar, K. Chatterjee, Mathematics 8 (2020).
date_created: 2020-11-22T23:01:24Z
date_published: 2020-11-04T00:00:00Z
date_updated: 2025-07-14T09:09:49Z
day: '04'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.3390/math8111945
ec_funded: 1
external_id:
  isi:
  - '000593962100001'
file:
- access_level: open_access
  checksum: 61cfcc3b35760656ce7a9385a4ace5d2
  content_type: application/pdf
  creator: dernst
  date_created: 2020-11-23T13:06:30Z
  date_updated: 2020-11-23T13:06:30Z
  file_id: '8797'
  file_name: 2020_Mathematics_Kleshnina.pdf
  file_size: 565191
  relation: main_file
  success: 1
file_date_updated: 2020-11-23T13:06:30Z
has_accepted_license: '1'
intvolume: '         8'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
  call_identifier: H2020
  grant_number: '863818'
  name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: Mathematics
publication_identifier:
  eissn:
  - '22277390'
publication_status: published
publisher: MDPI
quality_controlled: '1'
scopus_import: '1'
status: public
title: Prioritised learning in snowdrift-type games
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: 8
year: '2020'
...