---
_id: '14884'
abstract:
- lang: eng
text: We perform a stochastic homogenization analysis for composite materials exhibiting
a random microstructure. Under the assumptions of stationarity and ergodicity,
we characterize the Gamma-limit of a micromagnetic energy functional defined on
magnetizations taking value in the unit sphere and including both symmetric and
antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic
energy functional with homogeneous coefficients. We provide explicit formulas
for the effective magnetic properties of the composite material in terms of homogenization
correctors. Additionally, the variational analysis of the two exchange energy
terms is performed in the more general setting of functionals defined on manifold-valued
maps with Sobolev regularity, in the case in which the target manifold is a bounded,
orientable smooth surface with tubular neighborhood of uniform thickness. Eventually,
we present an explicit characterization of minimizers of the effective exchange
in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s
predictions on the emergence of helical structures in composite ferromagnetic
materials with stochastic microstructure.
acknowledgement: All authors acknowledge support of the Austrian Science Fund (FWF)
through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally
been supported by the FWF through grants V662, Y1292, and P35359, as well as from
OeAD through the WTZ grant CZ09/2023.
article_number: '30'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Elisa
full_name: Davoli, Elisa
last_name: Davoli
- first_name: Lorenza
full_name: D’Elia, Lorenza
last_name: D’Elia
- first_name: Jonas
full_name: Ingmanns, Jonas
id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
last_name: Ingmanns
citation:
ama: Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions. Journal of Nonlinear Science.
2024;34(2). doi:10.1007/s00332-023-10005-3
apa: Davoli, E., D’Elia, L., & Ingmanns, J. (2024). Stochastic homogenization
of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear
Science. Springer Nature. https://doi.org/10.1007/s00332-023-10005-3
chicago: Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization
of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of
Nonlinear Science. Springer Nature, 2024. https://doi.org/10.1007/s00332-023-10005-3.
ieee: E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions,” Journal of Nonlinear Science,
vol. 34, no. 2. Springer Nature, 2024.
ista: Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2),
30.
mla: Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies
and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science, vol.
34, no. 2, 30, Springer Nature, 2024, doi:10.1007/s00332-023-10005-3.
short: E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).
date_created: 2024-01-28T23:01:42Z
date_published: 2024-01-23T00:00:00Z
date_updated: 2024-02-05T08:54:44Z
day: '23'
department:
- _id: JuFi
doi: 10.1007/s00332-023-10005-3
external_id:
arxiv:
- '2306.05151'
intvolume: ' 34'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2306.05151
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Journal of Nonlinear Science
publication_identifier:
eissn:
- 1432-1467
issn:
- 0938-8974
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stochastic homogenization of micromagnetic energies and emergence of magnetic
skyrmions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2024'
...
---
_id: '14934'
abstract:
- lang: eng
text: "We study random perturbations of a Riemannian manifold (M, g) by means of
so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the
given manifold. The fields\r\nh• : ω \x02→ hω will act on the manifold via the
conformal transformation g \x02→ gω := e2hω g.\r\nOur focus will be on the regular
case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated
Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric
and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion,
spectral bound, or spectral gap change under the influence of the noise. And if
so, is\r\nit possible to quantify these dependencies in terms of key parameters
of the noise? Another\r\ngoal is to define and analyze in detail the Fractional
Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent
interest."
acknowledgement: "The authors would like to thank Matthias Erbar and Ronan Herry for
valuable discussions on this project. They are also grateful to Nathanaël Berestycki,
and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24],
and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous
version of the proof of Proposition 3.10. The authors feel very much indebted to
an anonymous reviewer for his/her careful reading and the many valuable suggestions
that have significantly contributed to the improvement of the paper. L.D.S. gratefully
acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC
1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65
at Institute of Science and Technology Austria. This research was funded in whole
or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open
access, the authors have applied a CC BY public copyright licence to any Author
Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff
Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian
geometry. Potential Analysis. 2024. doi:10.1007/s11118-023-10118-0
apa: Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour
in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0
chicago: Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery
Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature,
2024. https://doi.org/10.1007/s11118-023-10118-0.
ieee: L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random
Riemannian geometry,” Potential Analysis. Springer Nature, 2024.
ista: Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian
geometry. Potential Analysis.
mla: Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.”
Potential Analysis, Springer Nature, 2024, doi:10.1007/s11118-023-10118-0.
short: L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024).
date_created: 2024-02-04T23:00:54Z
date_published: 2024-01-26T00:00:00Z
date_updated: 2024-02-05T13:04:23Z
day: '26'
department:
- _id: JaMa
doi: 10.1007/s11118-023-10118-0
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s11118-023-10118-0
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A discovery tour in random Riemannian geometry
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '14451'
abstract:
- lang: eng
text: 'We investigate the potential of Multi-Objective, Deep Reinforcement Learning
for stock and cryptocurrency single-asset trading: in particular, we consider
a Multi-Objective algorithm which generalizes the reward functions and discount
factor (i.e., these components are not specified a priori, but incorporated in
the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT,
XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of
the proposed Multi-Objective algorithm, and provide preliminary statistical evidence
showing increased predictive stability over the corresponding Single-Objective
strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge
over the corresponding Single-Objective strategy when the reward mechanism is
sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss
the generalization properties with respect to the discount factor. The entirety
of our code is provided in open-source format.'
acknowledgement: Open access funding provided by Università degli Studi di Trieste
within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant
No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Constantin
full_name: Disselkamp, Constantin
last_name: Disselkamp
- first_name: Davide
full_name: Scassola, Davide
last_name: Scassola
- first_name: Christopher
full_name: Helf, Christopher
last_name: Helf
citation:
ama: 'Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization:
improving performance of Deep Reinforcement Learning for applications in single-asset
trading. Neural Computing and Applications. 2023. doi:10.1007/s00521-023-09033-7'
apa: 'Cornalba, F., Disselkamp, C., Scassola, D., & Helf, C. (2023). Multi-objective
reward generalization: improving performance of Deep Reinforcement Learning for
applications in single-asset trading. Neural Computing and Applications.
Springer Nature. https://doi.org/10.1007/s00521-023-09033-7'
chicago: 'Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher
Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement
Learning for Applications in Single-Asset Trading.” Neural Computing and Applications.
Springer Nature, 2023. https://doi.org/10.1007/s00521-023-09033-7.'
ieee: 'F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward
generalization: improving performance of Deep Reinforcement Learning for applications
in single-asset trading,” Neural Computing and Applications. Springer Nature,
2023.'
ista: 'Cornalba F, Disselkamp C, Scassola D, Helf C. 2023. Multi-objective reward
generalization: improving performance of Deep Reinforcement Learning for applications
in single-asset trading. Neural Computing and Applications.'
mla: 'Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving
Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.”
Neural Computing and Applications, Springer Nature, 2023, doi:10.1007/s00521-023-09033-7.'
short: F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications
(2023).
date_created: 2023-10-22T22:01:16Z
date_published: 2023-10-05T00:00:00Z
date_updated: 2023-10-31T10:58:28Z
day: '05'
department:
- _id: JuFi
doi: 10.1007/s00521-023-09033-7
ec_funded: 1
external_id:
arxiv:
- '2203.04579'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00521-023-09033-7
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Neural Computing and Applications
publication_identifier:
eissn:
- 1433-3058
issn:
- 0941-0643
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multi-objective reward generalization: improving performance of Deep Reinforcement
Learning for applications in single-asset trading'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14554'
abstract:
- lang: eng
text: 'The Regularised Inertial Dean–Kawasaki model (RIDK) – introduced by the authors
and J. Zimmer in earlier works – is a nonlinear stochastic PDE capturing fluctuations
around the meanfield limit for large-scale particle systems in both particle density
and momentum density. We focus on the following two aspects. Firstly, we set up
a Discontinuous Galerkin (DG) discretisation scheme for the RIDK model: we provide
suitable definitions of numerical fluxes at the interface of the mesh elements
which are consistent with the wave-type nature of the RIDK model and grant stability
of the simulations, and we quantify the rate of convergence in mean square to
the continuous RIDK model. Secondly, we introduce modifications of the RIDK model
in order to preserve positivity of the density (such a feature only holds in a
“high-probability sense” for the original RIDK model). By means of numerical simulations,
we show that the modifications lead to physically realistic and positive density
profiles. In one case, subject to additional regularity constraints, we also prove
positivity. Finally, we present an application of our methodology to a system
of diffusing and reacting particles. Our Python code is available in open-source
format.'
acknowledgement: "The authors thank the anonymous referees for their careful reading
of the manuscript and their\r\nvaluable suggestions. FC gratefully acknowledges
funding from the Austrian Science Fund (FWF) through the project F65, and from the
European Union’s Horizon 2020 research and innovation programme under the Marie
Sk lodowska-Curie grant agreement No. 754411 (the latter funding source covered
the first part of this project)."
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Tony
full_name: Shardlow, Tony
last_name: Shardlow
citation:
ama: 'Cornalba F, Shardlow T. The regularised inertial Dean’ Kawasaki equation:
Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM:
Mathematical Modelling and Numerical Analysis. 2023;57(5):3061-3090. doi:10.1051/m2an/2023077'
apa: 'Cornalba, F., & Shardlow, T. (2023). The regularised inertial Dean’ Kawasaki
equation: Discontinuous Galerkin approximation and modelling for low-density regime.
ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. https://doi.org/10.1051/m2an/2023077'
chicago: 'Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’
Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density
Regime.” ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences,
2023. https://doi.org/10.1051/m2an/2023077.'
ieee: 'F. Cornalba and T. Shardlow, “The regularised inertial Dean’ Kawasaki equation:
Discontinuous Galerkin approximation and modelling for low-density regime,” ESAIM:
Mathematical Modelling and Numerical Analysis, vol. 57, no. 5. EDP Sciences,
pp. 3061–3090, 2023.'
ista: 'Cornalba F, Shardlow T. 2023. The regularised inertial Dean’ Kawasaki equation:
Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM:
Mathematical Modelling and Numerical Analysis. 57(5), 3061–3090.'
mla: 'Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki
Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.”
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5, EDP
Sciences, 2023, pp. 3061–90, doi:10.1051/m2an/2023077.'
short: 'F. Cornalba, T. Shardlow, ESAIM: Mathematical Modelling and Numerical Analysis
57 (2023) 3061–3090.'
date_created: 2023-11-19T23:00:55Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2023-11-20T08:38:47Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1051/m2an/2023077
ec_funded: 1
file:
- access_level: open_access
checksum: 3aef1475b1882c8dec112df9a5167c39
content_type: application/pdf
creator: dernst
date_created: 2023-11-20T08:34:57Z
date_updated: 2023-11-20T08:34:57Z
file_id: '14560'
file_name: 2023_ESAIM_Cornalba.pdf
file_size: 1508534
relation: main_file
success: 1
file_date_updated: 2023-11-20T08:34:57Z
has_accepted_license: '1'
intvolume: ' 57'
issue: '5'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 3061-3090
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 'ESAIM: Mathematical Modelling and Numerical Analysis'
publication_identifier:
eissn:
- 2804-7214
issn:
- 2822-7840
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/tonyshardlow/RIDK-FD
scopus_import: '1'
status: public
title: 'The regularised inertial Dean'' Kawasaki equation: Discontinuous Galerkin
approximation and modelling for low-density regime'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 57
year: '2023'
...
---
_id: '10145'
abstract:
- lang: eng
text: We study direct integrals of quadratic and Dirichlet forms. We show that each
quasi-regular Dirichlet space over a probability space admits a unique representation
as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same
underlying topology. The same holds for each quasi-regular strongly local Dirichlet
space over a metrizable Luzin σ-finite Radon measure space, and admitting carré
du champ operator. In this case, the representation is only projectively unique.
acknowledgement: The author is grateful to Professors Sergio Albeverio and Andreas
Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the
present work, and for respectively pointing out the references [1, 13], and [3,
20]. Finally, he is especially grateful to an anonymous Reviewer for their very
careful reading and their suggestions which improved the readability of the paper.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals
and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y
apa: Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y
chicago: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis. Springer Nature, 2023.
https://doi.org/10.1007/s11118-021-09951-y.
ieee: L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals
and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615,
2023.
ista: Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. 58, 573–615.
mla: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature,
2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.
short: L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.
date_created: 2021-10-17T22:01:17Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-10-04T09:19:12Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-021-09951-y
ec_funded: 1
external_id:
arxiv:
- '2003.01366'
isi:
- '000704213400001'
file:
- access_level: open_access
checksum: 625526482be300ca7281c91c30d41725
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T09:18:59Z
date_updated: 2023-10-04T09:18:59Z
file_id: '14387'
file_name: 2023_PotentialAnalysis_DelloSchiavo.pdf
file_size: 806391
relation: main_file
success: 1
file_date_updated: 2023-10-04T09:18:59Z
has_accepted_license: '1'
intvolume: ' 58'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 573-615
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decomposition of Dirichlet forms via direct integrals and applications
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2023'
...
---
_id: '10551'
abstract:
- lang: eng
text: 'The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of
fluctuating hydrodynamics; it has been proposed in the physics literature to describe
the fluctuations of the density of N independent diffusing particles in the regime
of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation
presents a substantial challenge for both its analysis and its rigorous mathematical
justification. Besides being non-renormalisable by the theory of regularity structures
by Hairer et al., it has recently been shown to not even admit nontrivial martingale
solutions. In the present work, we give a rigorous and fully quantitative justification
of the Dean–Kawasaki equation by considering the natural regularisation provided
by standard numerical discretisations: We show that structure-preserving discretisations
of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting
diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In
other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate
and efficient numerical simulations of the density fluctuations of independent
diffusing particles.'
acknowledgement: "We thank the anonymous referee for his/her careful reading of the
manuscript and valuable suggestions. FC gratefully acknowledges funding from the
Austrian Science Fund (FWF) through the project F65, and from the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science
Fund (FWF)."
article_number: '76'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density
fluctuations in systems of diffusing particles. Archive for Rational Mechanics
and Analysis. 2023;247(5). doi:10.1007/s00205-023-01903-7
apa: Cornalba, F., & Fischer, J. L. (2023). The Dean-Kawasaki equation and the
structure of density fluctuations in systems of diffusing particles. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01903-7
chicago: Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and
the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive
for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01903-7.
ieee: F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure
of density fluctuations in systems of diffusing particles,” Archive for Rational
Mechanics and Analysis, vol. 247, no. 5. Springer Nature, 2023.
ista: Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure
of density fluctuations in systems of diffusing particles. Archive for Rational
Mechanics and Analysis. 247(5), 76.
mla: Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and
the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive
for Rational Mechanics and Analysis, vol. 247, no. 5, 76, Springer Nature,
2023, doi:10.1007/s00205-023-01903-7.
short: F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247
(2023).
date_created: 2021-12-16T12:16:03Z
date_published: 2023-08-04T00:00:00Z
date_updated: 2024-01-30T12:10:10Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00205-023-01903-7
ec_funded: 1
external_id:
arxiv:
- '2109.06500'
isi:
- '001043086800001'
file:
- access_level: open_access
checksum: 4529eeff170b6745a461d397ee611b5a
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:09:34Z
date_updated: 2024-01-30T12:09:34Z
file_id: '14904'
file_name: 2023_ArchiveRationalMech_Cornalba.pdf
file_size: 1851185
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:09:34Z
has_accepted_license: '1'
intvolume: ' 247'
isi: 1
issue: '5'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dean-Kawasaki equation and the structure of density fluctuations in systems
of diffusing particles
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 247
year: '2023'
...
---
_id: '12087'
abstract:
- lang: eng
text: Following up on the recent work on lower Ricci curvature bounds for quantum
systems, we introduce two noncommutative versions of curvature-dimension bounds
for symmetric quantum Markov semigroups over matrix algebras. Under suitable such
curvature-dimension conditions, we prove a family of dimension-dependent functional
inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power
in the noncommutative setting. We also provide examples satisfying certain curvature-dimension
conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers
over group algebras and generalized depolarizing semigroups.
acknowledgement: H.Z. is supported by the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411
and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges
support from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (Grant Agreement No. 716117) and from the
Austrian Science Fund (FWF) through grant number F65. Both authors would like to
thank Jan Maas for fruitful discussions and helpful comments. Open access funding
provided by Austrian Science Fund (FWF).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov
semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x
apa: Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric
quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x
chicago: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for
Symmetric Quantum Markov Semigroups.” Annales Henri Poincare. Springer
Nature, 2023. https://doi.org/10.1007/s00023-022-01220-x.
ieee: M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum
Markov semigroups,” Annales Henri Poincare, vol. 24. Springer Nature, pp.
717–750, 2023.
ista: Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum
Markov semigroups. Annales Henri Poincare. 24, 717–750.
mla: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric
Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature,
2023, pp. 717–50, doi:10.1007/s00023-022-01220-x.
short: M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.
date_created: 2022-09-11T22:01:57Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-08-14T11:39:28Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00023-022-01220-x
ec_funded: 1
external_id:
arxiv:
- '2105.08303'
isi:
- '000837499800002'
file:
- access_level: open_access
checksum: 8c7b185eba5ccd92ef55c120f654222c
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T11:38:28Z
date_updated: 2023-08-14T11:38:28Z
file_id: '14051'
file_name: 2023_AnnalesHenriPoincare_Wirth.pdf
file_size: 554871
relation: main_file
success: 1
file_date_updated: 2023-08-14T11:38:28Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 717-750
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Curvature-dimension conditions for symmetric quantum Markov semigroups
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '12104'
abstract:
- lang: eng
text: We study ergodic decompositions of Dirichlet spaces under intertwining via
unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular
Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore,
every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces
is decomposable over their ergodic decompositions up to conjugation via an isomorphism
of the corresponding indexing spaces.
acknowledgement: Research supported by the Austrian Science Fund (FWF) grant F65 at
the Institute of Science and Technology Austria and by the European Research Council
(ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully
acknowledges funding of his current position by the Austrian Science Fund (FWF)
through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding
of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme
(Grant No. 156).
article_number: '9'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order
isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7
apa: Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet
forms under order isomorphisms. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00859-7
chicago: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of
Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations.
Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.
ieee: L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms
under order isomorphisms,” Journal of Evolution Equations, vol. 23, no.
1. Springer Nature, 2023.
ista: Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms
under order isomorphisms. Journal of Evolution Equations. 23(1), 9.
mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet
Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23,
no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.
short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).
date_created: 2023-01-08T23:00:53Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-06-28T11:54:35Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00028-022-00859-7
ec_funded: 1
external_id:
isi:
- '000906214600004'
file:
- access_level: open_access
checksum: 1f34f3e2cb521033de6154f274ea3a4e
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T10:45:06Z
date_updated: 2023-01-20T10:45:06Z
file_id: '12325'
file_name: 2023_JourEvolutionEquations_DelloSchiavo.pdf
file_size: 422612
relation: main_file
success: 1
file_date_updated: 2023-01-20T10:45:06Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decompositions of Dirichlet forms under order isomorphisms
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2023'
...
---
_id: '12959'
abstract:
- lang: eng
text: "This paper deals with the large-scale behaviour of dynamical optimal transport
on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy
densities. Our main contribution is a homogenisation result that describes the
effective behaviour of the discrete problems in terms of a continuous optimal
transport problem. The effective energy density can be explicitly expressed in
terms of a cell formula, which is a finite-dimensional convex programming problem
that depends non-trivially on the local geometry of the discrete graph and the
discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence
result for action functionals on curves of measures, which we prove under very
mild growth conditions on the energy density. We investigate the cell formula
in several cases of interest, including finite-volume discretisations of the Wasserstein
distance, where non-trivial limiting behaviour occurs."
acknowledgement: J.M. gratefully acknowledges support by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian
Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support
by the German Research Foundation through the Hausdorff Center for Mathematics and
the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the
anonymous reviewer for the careful reading and for useful suggestions. Open access
funding provided by Austrian Science Fund (FWF).
article_number: '143'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Gladbach, Peter
last_name: Gladbach
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal
transport on periodic graphs. Calculus of Variations and Partial Differential
Equations. 2023;62(5). doi:10.1007/s00526-023-02472-z
apa: Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2023). Homogenisation
of dynamical optimal transport on periodic graphs. Calculus of Variations and
Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-023-02472-z
chicago: Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation
of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations
and Partial Differential Equations. Springer Nature, 2023. https://doi.org/10.1007/s00526-023-02472-z.
ieee: P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical
optimal transport on periodic graphs,” Calculus of Variations and Partial Differential
Equations, vol. 62, no. 5. Springer Nature, 2023.
ista: Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical
optimal transport on periodic graphs. Calculus of Variations and Partial Differential
Equations. 62(5), 143.
mla: Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic
Graphs.” Calculus of Variations and Partial Differential Equations, vol.
62, no. 5, 143, Springer Nature, 2023, doi:10.1007/s00526-023-02472-z.
short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and
Partial Differential Equations 62 (2023).
date_created: 2023-05-14T22:01:00Z
date_published: 2023-04-28T00:00:00Z
date_updated: 2023-10-04T11:34:49Z
day: '28'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-023-02472-z
ec_funded: 1
external_id:
arxiv:
- '2110.15321'
isi:
- '000980588900001'
file:
- access_level: open_access
checksum: 359bee38d94b7e0aa73925063cb8884d
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T11:34:10Z
date_updated: 2023-10-04T11:34:10Z
file_id: '14393'
file_name: 2023_CalculusEquations_Gladbach.pdf
file_size: 1240995
relation: main_file
success: 1
file_date_updated: 2023-10-04T11:34:10Z
has_accepted_license: '1'
intvolume: ' 62'
isi: 1
issue: '5'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
- 0944-2669
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homogenisation of dynamical optimal transport on periodic graphs
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 62
year: '2023'
...
---
_id: '11330'
abstract:
- lang: eng
text: In this article we study the noncommutative transport distance introduced
by Carlen and Maas and its entropic regularization defined by Becker and Li. We
prove a duality formula that can be understood as a quantum version of the dual
Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions
of a Hamilton–Jacobi–Bellmann equation.
acknowledgement: "The author wants to thank Jan Maas for helpful comments. He also
acknowledges financial support from the Austrian Science Fund (FWF) through Grant
Number F65 and from the European Research Council (ERC) under the European Union’s
Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. A dual formula for the noncommutative transport distance. Journal
of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9
apa: Wirth, M. (2022). A dual formula for the noncommutative transport distance.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9
chicago: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.”
Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9.
ieee: M. Wirth, “A dual formula for the noncommutative transport distance,” Journal
of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022.
ista: Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal
of Statistical Physics. 187(2), 19.
mla: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.”
Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022,
doi:10.1007/s10955-022-02911-9.
short: M. Wirth, Journal of Statistical Physics 187 (2022).
date_created: 2022-04-24T22:01:43Z
date_published: 2022-04-08T00:00:00Z
date_updated: 2023-08-03T06:37:49Z
day: '08'
ddc:
- '510'
- '530'
department:
- _id: JaMa
doi: 10.1007/s10955-022-02911-9
ec_funded: 1
external_id:
isi:
- '000780305000001'
file:
- access_level: open_access
checksum: f3e0b00884b7dde31347a3756788b473
content_type: application/pdf
creator: dernst
date_created: 2022-04-29T11:24:23Z
date_updated: 2022-04-29T11:24:23Z
file_id: '11338'
file_name: 2022_JourStatisticalPhysics_Wirth.pdf
file_size: 362119
relation: main_file
success: 1
file_date_updated: 2022-04-29T11:24:23Z
has_accepted_license: '1'
intvolume: ' 187'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- '15729613'
issn:
- '00224715'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A dual formula for the noncommutative transport distance
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: 187
year: '2022'
...
---
_id: '11354'
abstract:
- lang: eng
text: We construct a recurrent diffusion process with values in the space of probability
measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process
is associated with the Dirichlet form defined by integration of the Wasserstein
gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional
base spaces to the modified massive Arratia flow over the unit interval described
in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800).
Together with two different constructions of the process, we discuss its ergodicity,
invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.
acknowledgement: Research supported by the Sonderforschungsbereich 1060 and the Hausdorff
Center for Mathematics. The author gratefully acknowledges funding of his current
position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the
European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr.
Jan Maas).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648.
doi:10.1214/21-AOP1541
apa: Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of
probability measures over a closed Riemannian manifold. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541
chicago: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space
of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability.
Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.
ieee: L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold,” Annals of Probability, vol.
50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.
ista: Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.
mla: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability
Measures over a Closed Riemannian Manifold.” Annals of Probability, vol.
50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.
short: L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.
date_created: 2022-05-08T22:01:44Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2023-10-17T12:50:24Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AOP1541
ec_funded: 1
external_id:
arxiv:
- '1811.11598'
isi:
- '000773518500005'
intvolume: ' 50'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1811.11598'
month: '03'
oa: 1
oa_version: Preprint
page: 591-648
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dirichlet–Ferguson diffusion on the space of probability measures over
a closed Riemannian manifold
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2022'
...
---
_id: '11700'
abstract:
- lang: eng
text: This paper contains two contributions in the study of optimal transport on
metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein
distance, which establishes the equivalence of static and dynamical optimal transport.
Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov
equations can be formulated as gradient flow of the free energy in the Wasserstein
space of probability measures. The proofs of these results are based on careful
regularisation arguments to circumvent some of the difficulties arising in metric
graphs, namely, branching of geodesics and the failure of semi-convexity of entropy
functionals in the Wasserstein space.
acknowledgement: "ME acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG),
Grant SFB 1283/2 2021 – 317210226. DF and JM were supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 716117). JM also acknowledges support by the Austrian Science
Fund (FWF), Project SFB F65. The work of DM was partially supported by the Deutsche
Forschungsgemeinschaft\r\n(DFG), Grant 397230547. This article is based upon work
from COST Action\r\n18232 MAT-DYN-NET, supported by COST (European Cooperation in
Science\r\nand Technology), www.cost.eu. We wish to thank Martin Burger and Jan-Frederik\r\nPietschmann
for useful discussions. We are grateful to the anonymous referees for\r\ntheir careful
reading and useful suggestions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Dominik L
full_name: Forkert, Dominik L
id: 35C79D68-F248-11E8-B48F-1D18A9856A87
last_name: Forkert
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Delio
full_name: Mugnolo, Delio
last_name: Mugnolo
citation:
ama: Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion
equations in the Wasserstein space over a metric graph. Networks and Heterogeneous
Media. 2022;17(5):687-717. doi:10.3934/nhm.2022023
apa: Erbar, M., Forkert, D. L., Maas, J., & Mugnolo, D. (2022). Gradient flow
formulation of diffusion equations in the Wasserstein space over a metric graph.
Networks and Heterogeneous Media. American Institute of Mathematical Sciences.
https://doi.org/10.3934/nhm.2022023
chicago: Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient
Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric
Graph.” Networks and Heterogeneous Media. American Institute of Mathematical
Sciences, 2022. https://doi.org/10.3934/nhm.2022023.
ieee: M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation
of diffusion equations in the Wasserstein space over a metric graph,” Networks
and Heterogeneous Media, vol. 17, no. 5. American Institute of Mathematical
Sciences, pp. 687–717, 2022.
ista: Erbar M, Forkert DL, Maas J, Mugnolo D. 2022. Gradient flow formulation of
diffusion equations in the Wasserstein space over a metric graph. Networks and
Heterogeneous Media. 17(5), 687–717.
mla: Erbar, Matthias, et al. “Gradient Flow Formulation of Diffusion Equations in
the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media,
vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717,
doi:10.3934/nhm.2022023.
short: M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media
17 (2022) 687–717.
date_created: 2022-07-31T22:01:46Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2023-08-03T12:25:49Z
day: '01'
department:
- _id: JaMa
doi: 10.3934/nhm.2022023
ec_funded: 1
external_id:
arxiv:
- '2105.05677'
isi:
- '000812422100001'
intvolume: ' 17'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.05677
month: '10'
oa: 1
oa_version: Preprint
page: 687-717
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Networks and Heterogeneous Media
publication_identifier:
eissn:
- 1556-181X
issn:
- 1556-1801
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gradient flow formulation of diffusion equations in the Wasserstein space over
a metric graph
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 17
year: '2022'
...
---
_id: '11739'
abstract:
- lang: eng
text: We consider finite-volume approximations of Fokker--Planck equations on bounded
convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures.
We reprove the convergence of the discrete to continuous Fokker--Planck equation
via the method of evolutionary $\Gamma$-convergence, i.e., we pass to the limit
at the level of the gradient flow structures, generalizing the one-dimensional
result obtained by Disser and Liero. The proof is of variational nature and relies
on a Mosco convergence result for functionals in the discrete-to-continuum limit
that is of independent interest. Our results apply to arbitrary regular meshes,
even though the associated discrete transport distances may fail to converge to
the Wasserstein distance in this generality.
acknowledgement: This work was supported by the European Research Council (ERC) under
the European Union's Horizon 2020 Research and Innovation Programme grant 716117
and by the AustrianScience Fund (FWF) through grants F65 and W1245.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dominik L
full_name: Forkert, Dominik L
id: 35C79D68-F248-11E8-B48F-1D18A9856A87
last_name: Forkert
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Forkert DL, Maas J, Portinale L. Evolutionary $\Gamma$-convergence of entropic
gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM
Journal on Mathematical Analysis. 2022;54(4):4297-4333. doi:10.1137/21M1410968
apa: Forkert, D. L., Maas, J., & Portinale, L. (2022). Evolutionary $\Gamma$-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
SIAM Journal on Mathematical Analysis. Society for Industrial and Applied
Mathematics. https://doi.org/10.1137/21M1410968
chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\Gamma$-Convergence
of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
SIAM Journal on Mathematical Analysis. Society for Industrial and Applied
Mathematics, 2022. https://doi.org/10.1137/21M1410968.
ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\Gamma$-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,”
SIAM Journal on Mathematical Analysis, vol. 54, no. 4. Society for Industrial
and Applied Mathematics, pp. 4297–4333, 2022.
ista: Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\Gamma$-convergence of
entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.
mla: Forkert, Dominik L., et al. “Evolutionary $\Gamma$-Convergence of Entropic
Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
SIAM Journal on Mathematical Analysis, vol. 54, no. 4, Society for Industrial
and Applied Mathematics, 2022, pp. 4297–333, doi:10.1137/21M1410968.
short: D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis
54 (2022) 4297–4333.
date_created: 2022-08-07T22:01:59Z
date_published: 2022-07-18T00:00:00Z
date_updated: 2023-08-03T12:37:21Z
day: '18'
department:
- _id: JaMa
doi: 10.1137/21M1410968
ec_funded: 1
external_id:
arxiv:
- '2008.10962'
isi:
- '000889274600001'
intvolume: ' 54'
isi: 1
issue: '4'
keyword:
- Fokker--Planck equation
- gradient flow
- evolutionary $\Gamma$-convergence
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2008.10962'
month: '07'
oa: 1
oa_version: Preprint
page: 4297-4333
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
record:
- id: '10022'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Evolutionary $\Gamma$-convergence of entropic gradient flow structures for
Fokker-Planck equations in multiple dimensions
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '10588'
abstract:
- lang: eng
text: We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying
the quasi curvature-dimension condition recently introduced in Milman (Commun
Pure Appl Math, to appear). We provide several applications to properties of the
corresponding heat semigroup. In particular, under the additional assumption of
infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the
heat semigroup with respect to the distance, and prove the irreducibility of the
heat semigroup. These results apply in particular to large classes of (ideal)
sub-Riemannian manifolds.
acknowledgement: "The authors are grateful to Dr. Bang-Xian Han for helpful discussions
on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor
Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino
Antonelli for reading a preliminary version of this work and for their valuable
comments and suggestions. Finally, they wish to express their gratitude to two anonymous
Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S.
gratefully acknowledges funding of his position by the Austrian Science Fund (FWF)
grant F65, and by the European Research Council (ERC, grant No. 716117, awarded
to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS
Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research
Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research
on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number
17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and
applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2
apa: Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on
QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property
on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature,
2022. https://doi.org/10.1007/s00208-021-02331-2.
ieee: L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces
and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp.
1815–1832, 2022.
ista: Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces
and applications. Mathematische Annalen. 384, 1815–1832.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on
QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer
Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.
short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.
date_created: 2022-01-02T23:01:35Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-02T13:39:05Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00208-021-02331-2
ec_funded: 1
external_id:
arxiv:
- '2110.05137'
isi:
- '000734150200001'
file:
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checksum: 2593abbf195e38efa93b6006b1e90eb1
content_type: application/pdf
creator: alisjak
date_created: 2022-01-03T11:08:31Z
date_updated: 2022-01-03T11:08:31Z
file_id: '10596'
file_name: 2021_MathAnn_DelloSchiavo.pdf
file_size: 410090
relation: main_file
success: 1
file_date_updated: 2022-01-03T11:08:31Z
has_accepted_license: '1'
intvolume: ' 384'
isi: 1
keyword:
- quasi curvature-dimension condition
- sub-riemannian geometry
- Sobolev-to-Lipschitz property
- Varadhan short-time asymptotics
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1815-1832
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev-to-Lipschitz property on QCD- spaces and applications
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: 384
year: '2022'
...
---
_id: '12177'
abstract:
- lang: eng
text: Using elementary hyperbolic geometry, we give an explicit formula for the
contraction constant of the skinning map over moduli spaces of relatively acylindrical
hyperbolic manifolds.
acknowledgement: "The first author was partially supported by the National Science
Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted
by the Mathematical Sciences Research Institute in Berkeley, California, during
the Fall 2020 semester. The second author gratefully acknowledges funding by the
Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research
Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche
Forschungsgemeinschaft through the SPP 2265."
article_processing_charge: No
article_type: original
author:
- first_name: Tommaso
full_name: Cremaschi, Tommaso
last_name: Cremaschi
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. Proceedings
of the American Mathematical Society, Series B. 2022;9(43):445-459. doi:10.1090/bproc/134
apa: Cremaschi, T., & Dello Schiavo, L. (2022). Effective contraction of Skinning
maps. Proceedings of the American Mathematical Society, Series B. American
Mathematical Society. https://doi.org/10.1090/bproc/134
chicago: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of
Skinning Maps.” Proceedings of the American Mathematical Society, Series B.
American Mathematical Society, 2022. https://doi.org/10.1090/bproc/134.
ieee: T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,”
Proceedings of the American Mathematical Society, Series B, vol. 9, no.
43. American Mathematical Society, pp. 445–459, 2022.
ista: Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps.
Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.
mla: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning
Maps.” Proceedings of the American Mathematical Society, Series B, vol.
9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134.
short: T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical
Society, Series B 9 (2022) 445–459.
date_created: 2023-01-12T12:12:17Z
date_published: 2022-11-02T00:00:00Z
date_updated: 2023-01-26T13:04:13Z
day: '02'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1090/bproc/134
ec_funded: 1
file:
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checksum: cb4a79937c1f60d4c329a10ee797f0d2
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creator: dernst
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date_updated: 2023-01-26T13:02:07Z
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file_name: 2022_ProceedingsAMS_Cremaschi.pdf
file_size: 326471
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success: 1
file_date_updated: 2023-01-26T13:02:07Z
has_accepted_license: '1'
intvolume: ' 9'
issue: '43'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 445-459
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Proceedings of the American Mathematical Society, Series B
publication_identifier:
issn:
- 2330-1511
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Effective contraction of Skinning maps
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2022'
...
---
_id: '10005'
abstract:
- lang: eng
text: We study systems of nonlinear partial differential equations of parabolic
type, in which the elliptic operator is replaced by the first-order divergence
operator acting on a flux function, which is related to the spatial gradient of
the unknown through an additional implicit equation. This setting, broad enough
in terms of applications, significantly expands the paradigm of nonlinear parabolic
problems. Formulating four conditions concerning the form of the implicit equation,
we first show that these conditions describe a maximal monotone p-coercive graph.
We then establish the global-in-time and large-data existence of a (weak) solution
and its uniqueness. To this end, we adopt and significantly generalize Minty’s
method of monotone mappings. A unified theory, containing several novel tools,
is developed in a way to be tractable from the point of view of numerical approximations.
acknowledgement: "M. Bulíček and J. Málek acknowledge the support of the project No.
18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges
support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583
by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian
Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers
of the Nečas Center for Mathematical Modelling.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miroslav
full_name: Bulíček, Miroslav
last_name: Bulíček
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
- first_name: Josef
full_name: Málek, Josef
last_name: Málek
citation:
ama: Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with
implicit constitutive equations involving flux. Mathematical Models and Methods
in Applied Sciences. 2021;31(09). doi:10.1142/S0218202521500457
apa: Bulíček, M., Maringová, E., & Málek, J. (2021). On nonlinear problems of
parabolic type with implicit constitutive equations involving flux. Mathematical
Models and Methods in Applied Sciences. World Scientific. https://doi.org/10.1142/S0218202521500457
chicago: Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems
of Parabolic Type with Implicit Constitutive Equations Involving Flux.” Mathematical
Models and Methods in Applied Sciences. World Scientific, 2021. https://doi.org/10.1142/S0218202521500457.
ieee: M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic
type with implicit constitutive equations involving flux,” Mathematical Models
and Methods in Applied Sciences, vol. 31, no. 09. World Scientific, 2021.
ista: Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic
type with implicit constitutive equations involving flux. Mathematical Models
and Methods in Applied Sciences. 31(09).
mla: Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit
Constitutive Equations Involving Flux.” Mathematical Models and Methods in
Applied Sciences, vol. 31, no. 09, World Scientific, 2021, doi:10.1142/S0218202521500457.
short: M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied
Sciences 31 (2021).
date_created: 2021-09-12T22:01:25Z
date_published: 2021-08-25T00:00:00Z
date_updated: 2023-09-04T11:43:45Z
day: '25'
department:
- _id: JuFi
doi: 10.1142/S0218202521500457
external_id:
arxiv:
- '2009.06917'
isi:
- '000722222900004'
intvolume: ' 31'
isi: 1
issue: '09'
keyword:
- Nonlinear parabolic systems
- implicit constitutive theory
- weak solutions
- existence
- uniqueness
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2009.06917
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: On nonlinear problems of parabolic type with implicit constitutive equations
involving flux
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2021'
...
---
_id: '10023'
abstract:
- lang: eng
text: We study the temporal dissipation of variance and relative entropy for ergodic
Markov Chains in continuous time, and compute explicitly the corresponding dissipation
rates. These are identified, as is well known, in the case of the variance in
terms of an appropriate Hilbertian norm; and in the case of the relative entropy,
in terms of a Dirichlet form which morphs into a version of the familiar Fisher
information under conditions of detailed balance. Here we obtain trajectorial
versions of these results, valid along almost every path of the random motion
and most transparent in the backwards direction of time. Martingale arguments
and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer
and Tschiderer for conservative diffusions. Extensions are developed to general
“convex divergences” and to countable state-spaces. The steepest descent and gradient
flow properties for the variance, the relative entropy, and appropriate generalizations,
are studied along with their respective geometries under conditions of detailed
balance, leading to a very direct proof for the HWI inequality of Otto and Villani
in the present context.
acknowledgement: I.K. acknowledges support from the U.S. National Science Foundation
under Grant NSF-DMS-20-04997. J.M. acknowledges support from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 716117) and from the Austrian Science Fund (FWF) through project
F65. W.S. acknowledges support from the Austrian Science Fund (FWF) under grant
P28861 and by the Vienna Science and Technology Fund (WWTF) through projects MA14-008
and MA16-021.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ioannis
full_name: Karatzas, Ioannis
last_name: Karatzas
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Walter
full_name: Schachermayer, Walter
last_name: Schachermayer
citation:
ama: Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient
flow for the relative entropy in Markov chains. Communications in Information
and Systems. 2021;21(4):481-536. doi:10.4310/CIS.2021.v21.n4.a1
apa: Karatzas, I., Maas, J., & Schachermayer, W. (2021). Trajectorial dissipation
and gradient flow for the relative entropy in Markov chains. Communications
in Information and Systems. International Press. https://doi.org/10.4310/CIS.2021.v21.n4.a1
chicago: Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation
and Gradient Flow for the Relative Entropy in Markov Chains.” Communications
in Information and Systems. International Press, 2021. https://doi.org/10.4310/CIS.2021.v21.n4.a1.
ieee: I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and
gradient flow for the relative entropy in Markov chains,” Communications in
Information and Systems, vol. 21, no. 4. International Press, pp. 481–536,
2021.
ista: Karatzas I, Maas J, Schachermayer W. 2021. Trajectorial dissipation and gradient
flow for the relative entropy in Markov chains. Communications in Information
and Systems. 21(4), 481–536.
mla: Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the
Relative Entropy in Markov Chains.” Communications in Information and Systems,
vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:10.4310/CIS.2021.v21.n4.a1.
short: I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and
Systems 21 (2021) 481–536.
date_created: 2021-09-19T08:53:19Z
date_published: 2021-06-04T00:00:00Z
date_updated: 2021-09-20T12:51:18Z
day: '04'
department:
- _id: JaMa
doi: 10.4310/CIS.2021.v21.n4.a1
ec_funded: 1
external_id:
arxiv:
- '2005.14177'
intvolume: ' 21'
issue: '4'
keyword:
- Markov Chain
- relative entropy
- time reversal
- steepest descent
- gradient flow
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2005.14177
month: '06'
oa: 1
oa_version: Preprint
page: 481-536
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Communications in Information and Systems
publication_identifier:
issn:
- 1526-7555
publication_status: published
publisher: International Press
quality_controlled: '1'
status: public
title: Trajectorial dissipation and gradient flow for the relative entropy in Markov
chains
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 21
year: '2021'
...
---
_id: '10030'
abstract:
- lang: eng
text: "This PhD thesis is primarily focused on the study of discrete transport problems,
introduced for the first time in the seminal works of Maas [Maa11] and Mielke
[Mie11] on finite state Markov chains and reaction-diffusion equations, respectively.
More in detail, my research focuses on the study of transport costs on graphs,
in particular the convergence and the stability of such problems in the discrete-to-continuum
limit. This thesis also includes some results concerning\r\nnon-commutative optimal
transport. The first chapter of this thesis consists of a general introduction
to the optimal transport problems, both in the discrete, the continuous, and the
non-commutative setting. Chapters 2 and 3 present the content of two works, obtained
in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have
been able to show the convergence of discrete transport costs on periodic graphs
to suitable continuous ones, which can be described by means of a homogenisation
result. We first focus on the particular case of quadratic costs on the real line
and then extending the result to more general costs in arbitrary dimension. Our
results are the first complete characterisation of limits of transport costs on
periodic graphs in arbitrary dimension which do not rely on any additional symmetry.
In Chapter 4 we turn our attention to one of the intriguing connection between
evolution equations and optimal transport, represented by the theory of gradient
flows. We show that discrete gradient flow structures associated to a finite volume
approximation of a certain class of diffusive equations (Fokker–Planck) is stable
in the limit of vanishing meshes, reproving the convergence of the scheme via
the method of evolutionary Γ-convergence and exploiting a more variational point
of view on the problem. This is based on a collaboration with Dominik Forkert
and Jan Maas. Chapter 5 represents a change of perspective, moving away from the
discrete world and reaching the non-commutative one. As in the discrete case,
we discuss how classical tools coming from the commutative optimal transport can
be translated into the setting of density matrices. In particular, in this final
chapter we present a non-commutative version of the Schrödinger problem (or entropic
regularised optimal transport problem) and discuss existence and characterisation
of minimisers, a duality result, and present a non-commutative version of the
well-known Sinkhorn algorithm to compute the above mentioned optimisers. This
is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally,
Appendix A and B contain some additional material and discussions, with particular
attention to Harnack inequalities and the regularity of flows on discrete spaces."
acknowledged_ssus:
- _id: M-Shop
- _id: NanoFab
acknowledgement: The author gratefully acknowledges support by the Austrian Science
Fund (FWF), grants No W1245.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Portinale L. Discrete-to-continuum limits of transport problems and gradient
flows in the space of measures. 2021. doi:10.15479/at:ista:10030
apa: Portinale, L. (2021). Discrete-to-continuum limits of transport problems
and gradient flows in the space of measures. Institute of Science and Technology
Austria. https://doi.org/10.15479/at:ista:10030
chicago: Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems
and Gradient Flows in the Space of Measures.” Institute of Science and Technology
Austria, 2021. https://doi.org/10.15479/at:ista:10030.
ieee: L. Portinale, “Discrete-to-continuum limits of transport problems and gradient
flows in the space of measures,” Institute of Science and Technology Austria,
2021.
ista: Portinale L. 2021. Discrete-to-continuum limits of transport problems and
gradient flows in the space of measures. Institute of Science and Technology Austria.
mla: Portinale, Lorenzo. Discrete-to-Continuum Limits of Transport Problems and
Gradient Flows in the Space of Measures. Institute of Science and Technology
Austria, 2021, doi:10.15479/at:ista:10030.
short: L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient
Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.
date_created: 2021-09-21T09:14:15Z
date_published: 2021-09-22T00:00:00Z
date_updated: 2023-09-07T13:31:06Z
day: '22'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JaMa
doi: 10.15479/at:ista:10030
file:
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checksum: 8cd60dcb8762e8f21867e21e8001e183
content_type: application/x-zip-compressed
creator: cchlebak
date_created: 2021-09-21T09:17:34Z
date_updated: 2022-03-10T12:14:42Z
file_id: '10032'
file_name: tex_and_pictures.zip
file_size: 3876668
relation: source_file
- access_level: open_access
checksum: 9789e9d967c853c1503ec7f307170279
content_type: application/pdf
creator: cchlebak
date_created: 2021-09-27T11:14:31Z
date_updated: 2021-09-27T11:14:31Z
file_id: '10047'
file_name: thesis_portinale_Final (1).pdf
file_size: 2532673
relation: main_file
file_date_updated: 2022-03-10T12:14:42Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10022'
relation: part_of_dissertation
status: public
- id: '9792'
relation: part_of_dissertation
status: public
- id: '7573'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: Discrete-to-continuum limits of transport problems and gradient flows in the
space of measures
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: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '10070'
abstract:
- lang: eng
text: We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties
for generalized intrinsic distances on strongly local Dirichlet spaces possibly
without square field operator. We present many non-smooth and infinite-dimensional
examples. As an application, we prove the integral Varadhan short-time asymptotic
with respect to a given distance function for a large class of strongly local
Dirichlet forms.
acknowledgement: 'The authors are grateful to Professor Kazuhiro Kuwae for kindly
providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful
discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They
wish to express their deepest gratitude to an anonymous Reviewer, whose punctual
remarks and comments greatly improved the accessibility and overall quality of the
initial submission. This work was completed while L.D.S. was a member of the Institut
für Angewandte Mathematik of the University of Bonn. He acknowledges funding of
his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center)
1060 - project number 211504053. He also acknowledges funding of his current position
by the Austrian Science Fund (FWF) grant F65, and by the European Research Council
(ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges
funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier
International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid
for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials
Design”, Grant Number 17H06465.'
article_number: '109234'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
2021;281(11). doi:10.1016/j.jfa.2021.109234
apa: Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2021.109234
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and
Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal
of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109234.
ieee: L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces,” Journal of Functional Analysis,
vol. 281, no. 11. Elsevier, 2021.
ista: Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
281(11), 109234.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz
Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis,
vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234.
short: L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).
date_created: 2021-10-03T22:01:21Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2023-08-14T07:05:44Z
day: '15'
department:
- _id: JaMa
doi: 10.1016/j.jfa.2021.109234
ec_funded: 1
external_id:
arxiv:
- '2008.01492'
isi:
- '000703896600005'
intvolume: ' 281'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2008.01492
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local
Dirichlet spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...
---
_id: '10575'
abstract:
- lang: eng
text: The choice of the boundary conditions in mechanical problems has to reflect
the interaction of the considered material with the surface. Still the assumption
of the no-slip condition is preferred in order to avoid boundary terms in the
analysis and slipping effects are usually overlooked. Besides the “static slip
models”, there are phenomena that are not accurately described by them, e.g. at
the moment when the slip changes rapidly, the wall shear stress and the slip can
exhibit a sudden overshoot and subsequent relaxation. When these effects become
significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical
analysis of Navier–Stokes-like problems with a dynamic slip boundary condition,
which requires a proper generalization of the Gelfand triplet and the corresponding
function space setting.
acknowledgement: The research of A. Abbatiello is supported by Einstein Foundation,
Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical
Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No.
20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the
Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support
from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583
by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian
Science Fund (FWF), grants P30000, W1245, and F65.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Anna
full_name: Abbatiello, Anna
last_name: Abbatiello
- first_name: Miroslav
full_name: Bulíček, Miroslav
last_name: Bulíček
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
citation:
ama: Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition
for Navier-Stokes-like problems. Mathematical Models and Methods in Applied
Sciences. 2021;31(11):2165-2212. doi:10.1142/S0218202521500470
apa: Abbatiello, A., Bulíček, M., & Maringová, E. (2021). On the dynamic slip
boundary condition for Navier-Stokes-like problems. Mathematical Models and
Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/S0218202521500470
chicago: Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic
Slip Boundary Condition for Navier-Stokes-like Problems.” Mathematical Models
and Methods in Applied Sciences. World Scientific Publishing, 2021. https://doi.org/10.1142/S0218202521500470.
ieee: A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary
condition for Navier-Stokes-like problems,” Mathematical Models and Methods
in Applied Sciences, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212,
2021.
ista: Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition
for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences.
31(11), 2165–2212.
mla: Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like
Problems.” Mathematical Models and Methods in Applied Sciences, vol. 31,
no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:10.1142/S0218202521500470.
short: A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods
in Applied Sciences 31 (2021) 2165–2212.
date_created: 2021-12-26T23:01:27Z
date_published: 2021-10-13T00:00:00Z
date_updated: 2023-08-17T06:29:01Z
day: '13'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1142/S0218202521500470
external_id:
arxiv:
- '2009.09057'
isi:
- '000722309400001'
file:
- access_level: open_access
checksum: 8c0a9396335f0b70e1f5cbfe450a987a
content_type: application/pdf
creator: dernst
date_created: 2022-05-16T10:55:45Z
date_updated: 2022-05-16T10:55:45Z
file_id: '11385'
file_name: 2021_MathModelsMethods_Abbatiello.pdf
file_size: 795483
relation: main_file
success: 1
file_date_updated: 2022-05-16T10:55:45Z
has_accepted_license: '1'
intvolume: ' 31'
isi: 1
issue: '11'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 2165-2212
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the dynamic slip boundary condition for Navier-Stokes-like problems
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 31
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...