---
_id: '823'
abstract:
- lang: eng
  text: The resolution of a linear system with positive integer variables is a basic
    yet difficult computational problem with many applications. We consider sparse
    uncorrelated random systems parametrised by the density c and the ratio α=N/M
    between number of variables N and number of constraints M. By means of ensemble
    calculations we show that the space of feasible solutions endows a Van-Der-Waals
    phase diagram in the plane (c, α). We give numerical evidence that the associated
    computational problems become more difficult across the critical point and in
    particular in the coexistence region.
article_number: '093404'
article_processing_charge: No
author:
- first_name: Simona
  full_name: Colabrese, Simona
  last_name: Colabrese
- first_name: Daniele
  full_name: De Martino, Daniele
  id: 3FF5848A-F248-11E8-B48F-1D18A9856A87
  last_name: De Martino
  orcid: 0000-0002-5214-4706
- first_name: Luca
  full_name: Leuzzi, Luca
  last_name: Leuzzi
- first_name: Enzo
  full_name: Marinari, Enzo
  last_name: Marinari
citation:
  ama: 'Colabrese S, De Martino D, Leuzzi L, Marinari E. Phase transitions in integer
    linear problems. <i> Journal of Statistical Mechanics: Theory and Experiment</i>.
    2017;2017(9). doi:<a href="https://doi.org/10.1088/1742-5468/aa85c3">10.1088/1742-5468/aa85c3</a>'
  apa: 'Colabrese, S., De Martino, D., Leuzzi, L., &#38; Marinari, E. (2017). Phase
    transitions in integer linear problems. <i> Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOPscience. <a href="https://doi.org/10.1088/1742-5468/aa85c3">https://doi.org/10.1088/1742-5468/aa85c3</a>'
  chicago: 'Colabrese, Simona, Daniele De Martino, Luca Leuzzi, and Enzo Marinari.
    “Phase Transitions in Integer Linear Problems.” <i> Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOPscience, 2017. <a href="https://doi.org/10.1088/1742-5468/aa85c3">https://doi.org/10.1088/1742-5468/aa85c3</a>.'
  ieee: 'S. Colabrese, D. De Martino, L. Leuzzi, and E. Marinari, “Phase transitions
    in integer linear problems,” <i> Journal of Statistical Mechanics: Theory and
    Experiment</i>, vol. 2017, no. 9. IOPscience, 2017.'
  ista: 'Colabrese S, De Martino D, Leuzzi L, Marinari E. 2017. Phase transitions
    in integer linear problems.  Journal of Statistical Mechanics: Theory and Experiment.
    2017(9), 093404.'
  mla: 'Colabrese, Simona, et al. “Phase Transitions in Integer Linear Problems.”
    <i> Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2017, no.
    9, 093404, IOPscience, 2017, doi:<a href="https://doi.org/10.1088/1742-5468/aa85c3">10.1088/1742-5468/aa85c3</a>.'
  short: 'S. Colabrese, D. De Martino, L. Leuzzi, E. Marinari,  Journal of Statistical
    Mechanics: Theory and Experiment 2017 (2017).'
date_created: 2018-12-11T11:48:41Z
date_published: 2017-09-26T00:00:00Z
date_updated: 2023-09-26T16:18:12Z
day: '26'
department:
- _id: GaTk
doi: 10.1088/1742-5468/aa85c3
ec_funded: 1
external_id:
  isi:
  - '000411842900001'
intvolume: '      2017'
isi: 1
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1705.06303
month: '09'
oa: 1
oa_version: Submitted Version
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: ' Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
  issn:
  - '17425468'
publication_status: published
publisher: IOPscience
publist_id: '6826'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Phase transitions in integer linear problems
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 2017
year: '2017'
...
---
_id: '2232'
abstract:
- lang: eng
  text: The purpose of this contribution is to summarize and discuss recent advances
    regarding the onset of turbulence in shear flows. The absence of a clear-cut instability
    mechanism, the spatio-temporal intermittent character and extremely long lived
    transients are some of the major difficulties encountered in these flows and have
    hindered progress towards understanding the transition process. We will show for
    the case of pipe flow that concepts from nonlinear dynamics and statistical physics
    can help to explain the onset of turbulence. In particular, the turbulent structures
    (puffs) observed close to onset are spatially localized chaotic transients and
    their lifetimes increase super-exponentially with Reynolds number. At the same
    time fluctuations of individual turbulent puffs can (although very rarely) lead
    to the nucleation of new puffs. The competition between these two stochastic processes
    gives rise to a non-equilibrium phase transition where turbulence changes from
    a super-transient to a sustained state.
article_number: P02001
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Baofang
  full_name: Song, Baofang
  id: a79e57f5-e8a5-11ec-9dc9-83fb8c81cf72
  last_name: Song
- first_name: Björn
  full_name: Hof, Björn
  id: 3A374330-F248-11E8-B48F-1D18A9856A87
  last_name: Hof
  orcid: 0000-0003-2057-2754
citation:
  ama: Song B, Hof B. Deterministic and stochastic aspects of the transition to turbulence.
    <i>Journal of Statistical Mechanics Theory and Experiment</i>. 2014;2014(2). doi:<a
    href="https://doi.org/10.1088/1742-5468/2014/02/P02001">10.1088/1742-5468/2014/02/P02001</a>
  apa: Song, B., &#38; Hof, B. (2014). Deterministic and stochastic aspects of the
    transition to turbulence. <i>Journal of Statistical Mechanics Theory and Experiment</i>.
    IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/2014/02/P02001">https://doi.org/10.1088/1742-5468/2014/02/P02001</a>
  chicago: Song, Baofang, and Björn Hof. “Deterministic and Stochastic Aspects of
    the Transition to Turbulence.” <i>Journal of Statistical Mechanics Theory and
    Experiment</i>. IOP Publishing, 2014. <a href="https://doi.org/10.1088/1742-5468/2014/02/P02001">https://doi.org/10.1088/1742-5468/2014/02/P02001</a>.
  ieee: B. Song and B. Hof, “Deterministic and stochastic aspects of the transition
    to turbulence,” <i>Journal of Statistical Mechanics Theory and Experiment</i>,
    vol. 2014, no. 2. IOP Publishing, 2014.
  ista: Song B, Hof B. 2014. Deterministic and stochastic aspects of the transition
    to turbulence. Journal of Statistical Mechanics Theory and Experiment. 2014(2),
    P02001.
  mla: Song, Baofang, and Björn Hof. “Deterministic and Stochastic Aspects of the
    Transition to Turbulence.” <i>Journal of Statistical Mechanics Theory and Experiment</i>,
    vol. 2014, no. 2, P02001, IOP Publishing, 2014, doi:<a href="https://doi.org/10.1088/1742-5468/2014/02/P02001">10.1088/1742-5468/2014/02/P02001</a>.
  short: B. Song, B. Hof, Journal of Statistical Mechanics Theory and Experiment 2014
    (2014).
date_created: 2018-12-11T11:56:28Z
date_published: 2014-02-01T00:00:00Z
date_updated: 2022-06-10T10:13:15Z
day: '01'
department:
- _id: BjHo
doi: 10.1088/1742-5468/2014/02/P02001
external_id:
  arxiv:
  - '1403.4516'
intvolume: '      2014'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1403.4516
month: '02'
oa: 1
oa_version: Submitted Version
publication: Journal of Statistical Mechanics Theory and Experiment
publication_identifier:
  issn:
  - '17425468'
publication_status: published
publisher: IOP Publishing
publist_id: '4729'
quality_controlled: '1'
status: public
title: Deterministic and stochastic aspects of the transition to turbulence
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2014
year: '2014'
...