---
_id: '8697'
abstract:
- lang: eng
text: In the computation of the material properties of random alloys, the method
of 'special quasirandom structures' attempts to approximate the properties of
the alloy on a finite volume with higher accuracy by replicating certain statistics
of the random atomic lattice in the finite volume as accurately as possible. In
the present work, we provide a rigorous justification for a variant of this method
in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach
is based on a recent analysis of a related variance reduction method in stochastic
homogenization of linear elliptic PDEs and the locality properties of the TFW
model. Concerning the latter, we extend an exponential locality result by Nazar
and Ortner to include point charges, a result that may be of independent interest.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
citation:
ama: Fischer JL, Kniely M. Variance reduction for effective energies of random lattices
in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772.
doi:10.1088/1361-6544/ab9728
apa: Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies
of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity.
IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728
chicago: Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective
Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity.
IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728.
ieee: J. L. Fischer and M. Kniely, “Variance reduction for effective energies of
random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity,
vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.
ista: Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random
lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772.
mla: Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies
of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity,
vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728.
short: J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.
date_created: 2020-10-25T23:01:16Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-08-22T10:38:38Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab9728
external_id:
arxiv:
- '1906.12245'
isi:
- '000576492700001'
file:
- access_level: open_access
checksum: ed90bc6eb5f32ee6157fef7f3aabc057
content_type: application/pdf
creator: cziletti
date_created: 2020-10-27T12:09:57Z
date_updated: 2020-10-27T12:09:57Z
file_id: '8710'
file_name: 2020_Nonlinearity_Fischer.pdf
file_size: 1223899
relation: main_file
success: 1
file_date_updated: 2020-10-27T12:09:57Z
has_accepted_license: '1'
intvolume: ' 33'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 5733-5772
publication: Nonlinearity
publication_identifier:
eissn:
- '13616544'
issn:
- '09517715'
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Variance reduction for effective energies of random lattices in the Thomas-Fermi-von
Weizsäcker model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2020'
...
---
_id: '7489'
abstract:
- lang: eng
text: 'In the present work, we consider the evolution of two fluids separated by
a sharp interface in the presence of surface tension—like, for example, the evolution
of oil bubbles in water. Our main result is a weak–strong uniqueness principle
for the corresponding free boundary problem for the incompressible Navier–Stokes
equation: as long as a strong solution exists, any varifold solution must coincide
with it. In particular, in the absence of physical singularities, the concept
of varifold solutions—whose global in time existence has been shown by Abels (Interfaces
Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism
for non-uniqueness. The key ingredient of our approach is the construction of
a relative entropy functional capable of controlling the interface error. If the
viscosities of the two fluids do not coincide, even for classical (strong) solutions
the gradient of the velocity field becomes discontinuous at the interface, introducing
the need for a careful additional adaption of the relative entropy.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: Fischer JL, Hensel S. Weak–strong uniqueness for the Navier–Stokes equation
for two fluids with surface tension. Archive for Rational Mechanics and Analysis.
2020;236:967-1087. doi:10.1007/s00205-019-01486-2
apa: Fischer, J. L., & Hensel, S. (2020). Weak–strong uniqueness for the Navier–Stokes
equation for two fluids with surface tension. Archive for Rational Mechanics
and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01486-2
chicago: Fischer, Julian L, and Sebastian Hensel. “Weak–Strong Uniqueness for the
Navier–Stokes Equation for Two Fluids with Surface Tension.” Archive for Rational
Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-019-01486-2.
ieee: J. L. Fischer and S. Hensel, “Weak–strong uniqueness for the Navier–Stokes
equation for two fluids with surface tension,” Archive for Rational Mechanics
and Analysis, vol. 236. Springer Nature, pp. 967–1087, 2020.
ista: Fischer JL, Hensel S. 2020. Weak–strong uniqueness for the Navier–Stokes equation
for two fluids with surface tension. Archive for Rational Mechanics and Analysis.
236, 967–1087.
mla: Fischer, Julian L., and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes
Equation for Two Fluids with Surface Tension.” Archive for Rational Mechanics
and Analysis, vol. 236, Springer Nature, 2020, pp. 967–1087, doi:10.1007/s00205-019-01486-2.
short: J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236
(2020) 967–1087.
date_created: 2020-02-16T23:00:50Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '01'
ddc:
- '530'
- '532'
department:
- _id: JuFi
doi: 10.1007/s00205-019-01486-2
ec_funded: 1
external_id:
isi:
- '000511060200001'
file:
- access_level: open_access
checksum: f107e21b58f5930876f47144be37cf6c
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T09:14:22Z
date_updated: 2020-11-20T09:14:22Z
file_id: '8779'
file_name: 2020_ArchRatMechAn_Fischer.pdf
file_size: 1897571
relation: main_file
success: 1
file_date_updated: 2020-11-20T09:14:22Z
has_accepted_license: '1'
intvolume: ' 236'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 967-1087
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- '14320673'
issn:
- '00039527'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '10007'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface
tension
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: 236
year: '2020'
...
---
_id: '7637'
abstract:
- lang: eng
text: The evolution of finitely many particles obeying Langevin dynamics is described
by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz
multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki
model based on second order Langevin dynamics by analysing a system of particles
interacting via a pairwise potential. Key tools of our analysis are the propagation
of chaos and Simon's compactness criterion. The model we obtain is a small-noise
stochastic perturbation of the undamped McKean–Vlasov equation. We also provide
a high-probability result for existence and uniqueness for our model.
article_processing_charge: No
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: Tony
full_name: Shardlow, Tony
last_name: Shardlow
- first_name: Johannes
full_name: Zimmer, Johannes
last_name: Zimmer
citation:
ama: Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised
Dean-Kawasaki model. Nonlinearity. 2020;33(2):864-891. doi:10.1088/1361-6544/ab5174
apa: Cornalba, F., Shardlow, T., & Zimmer, J. (2020). From weakly interacting
particles to a regularised Dean-Kawasaki model. Nonlinearity. IOP Publishing.
https://doi.org/10.1088/1361-6544/ab5174
chicago: Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting
Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity. IOP Publishing,
2020. https://doi.org/10.1088/1361-6544/ab5174.
ieee: F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles
to a regularised Dean-Kawasaki model,” Nonlinearity, vol. 33, no. 2. IOP
Publishing, pp. 864–891, 2020.
ista: Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles
to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.
mla: Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised
Dean-Kawasaki Model.” Nonlinearity, vol. 33, no. 2, IOP Publishing, 2020,
pp. 864–91, doi:10.1088/1361-6544/ab5174.
short: F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.
date_created: 2020-04-05T22:00:49Z
date_published: 2020-01-10T00:00:00Z
date_updated: 2023-08-18T10:26:07Z
day: '10'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab5174
external_id:
arxiv:
- '1811.06448'
isi:
- '000508175400001'
intvolume: ' 33'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.06448
month: '01'
oa: 1
oa_version: Preprint
page: 864-891
publication: Nonlinearity
publication_identifier:
eissn:
- '13616544'
issn:
- '09517715'
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: From weakly interacting particles to a regularised Dean-Kawasaki model
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2020'
...
---
_id: '9039'
abstract:
- lang: eng
text: We give a short and self-contained proof for rates of convergence of the Allen--Cahn
equation towards mean curvature flow, assuming that a classical (smooth) solution
to the latter exists and starting from well-prepared initial data. Our approach
is based on a relative entropy technique. In particular, it does not require a
stability analysis for the linearized Allen--Cahn operator. As our analysis also
does not rely on the comparison principle, we expect it to be applicable to more
complex equations and systems.
acknowledgement: "This work was supported by the European Union's Horizon 2020 Research
and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385
and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation)
under Germany's Excellence Strategy, EXC-2047/1--390685813."
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Theresa M.
full_name: Simon, Theresa M.
last_name: Simon
citation:
ama: 'Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 2020;52(6):6222-6233. doi:10.1137/20M1322182'
apa: 'Fischer, J. L., Laux, T., & Simon, T. M. (2020). Convergence rates of
the Allen-Cahn equation to mean curvature flow: A short proof based on relative
entropies. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/20M1322182'
chicago: 'Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates
of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative
Entropies.” SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics, 2020. https://doi.org/10.1137/20M1322182.'
ieee: 'J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn
equation to mean curvature flow: A short proof based on relative entropies,” SIAM
Journal on Mathematical Analysis, vol. 52, no. 6. Society for Industrial and
Applied Mathematics, pp. 6222–6233, 2020.'
ista: 'Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 52(6), 6222–6233.'
mla: 'Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to
Mean Curvature Flow: A Short Proof Based on Relative Entropies.” SIAM Journal
on Mathematical Analysis, vol. 52, no. 6, Society for Industrial and Applied
Mathematics, 2020, pp. 6222–33, doi:10.1137/20M1322182.'
short: J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis
52 (2020) 6222–6233.
date_created: 2021-01-24T23:01:09Z
date_published: 2020-12-15T00:00:00Z
date_updated: 2023-08-24T11:15:16Z
day: '15'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/20M1322182
ec_funded: 1
external_id:
isi:
- '000600695200027'
file:
- access_level: open_access
checksum: 21aa1cf4c30a86a00cae15a984819b5d
content_type: application/pdf
creator: dernst
date_created: 2021-01-25T07:48:39Z
date_updated: 2021-01-25T07:48:39Z
file_id: '9041'
file_name: 2020_SIAM_Fischer.pdf
file_size: 310655
relation: main_file
success: 1
file_date_updated: 2021-01-25T07:48:39Z
has_accepted_license: '1'
intvolume: ' 52'
isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 6222-6233
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- '10957154'
issn:
- '00361410'
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence rates of the Allen-Cahn equation to mean curvature flow: A short
proof based on relative entropies'
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: 52
year: '2020'
...
---
_id: '9196'
abstract:
- lang: eng
text: In order to provide a local description of a regular function in a small neighbourhood
of a point x, it is sufficient by Taylor’s theorem to know the value of the function
as well as all of its derivatives up to the required order at the point x itself.
In other words, one could say that a regular function is locally modelled by the
set of polynomials. The theory of regularity structures due to Hairer generalizes
this observation and provides an abstract setup, which in the application to singular
SPDE extends the set of polynomials by functionals constructed from, e.g., white
noise. In this context, the notion of Taylor polynomials is lifted to the notion
of so-called modelled distributions. The celebrated reconstruction theorem, which
in turn was inspired by Gubinelli’s \textit {sewing lemma}, is of paramount importance
for the theory. It enables one to reconstruct a modelled distribution as a true
distribution on Rd which is locally approximated by this extended set of models
or “monomials”. In the original work of Hairer, the error is measured by means
of Hölder norms. This was then generalized to the whole scale of Besov spaces
by Hairer and Labbé. It is the aim of this work to adapt the analytic part of
the theory of regularity structures to the scale of Triebel–Lizorkin spaces.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tommaso
full_name: Rosati, Tommaso
last_name: Rosati
citation:
ama: Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. Studia
Mathematica. 2020;252(3):251-297. doi:10.4064/sm180411-11-2
apa: Hensel, S., & Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin
type. Studia Mathematica. Instytut Matematyczny. https://doi.org/10.4064/sm180411-11-2
chicago: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin
Type.” Studia Mathematica. Instytut Matematyczny, 2020. https://doi.org/10.4064/sm180411-11-2.
ieee: S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,”
Studia Mathematica, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297,
2020.
ista: Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type.
Studia Mathematica. 252(3), 251–297.
mla: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin
Type.” Studia Mathematica, vol. 252, no. 3, Instytut Matematyczny, 2020,
pp. 251–97, doi:10.4064/sm180411-11-2.
short: S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.
date_created: 2021-02-25T08:55:03Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-10-17T09:15:53Z
day: '01'
department:
- _id: JuFi
- _id: GradSch
doi: 10.4064/sm180411-11-2
external_id:
arxiv:
- '1709.05202'
isi:
- '000558100500002'
intvolume: ' 252'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
month: '03'
oa_version: Preprint
page: 251-297
publication: Studia Mathematica
publication_identifier:
eissn:
- 1730-6337
issn:
- 0039-3223
publication_status: published
publisher: Instytut Matematyczny
quality_controlled: '1'
scopus_import: '1'
status: public
title: Modelled distributions of Triebel–Lizorkin type
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 252
year: '2020'
...
---
_id: '10012'
abstract:
- lang: eng
text: We prove that in the absence of topological changes, the notion of BV solutions
to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical)
non-uniqueness. Our approach is based on the local structure of the energy landscape
near a classical evolution by mean curvature. Mean curvature flow being the gradient
flow of the surface energy functional, we develop a gradient-flow analogue of
the notion of calibrations. Just like the existence of a calibration guarantees
that one has reached a global minimum in the energy landscape, the existence of
a "gradient flow calibration" ensures that the route of steepest descent in the
energy landscape is unique and stable.
acknowledgement: Parts of the paper were written during the visit of the authors to
the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, in the
framework of the trimester program “Evolution of Interfaces”. The support and the
hospitality of HIM are gratefully acknowledged. This project has received funding
from the European Union’s Horizon 2020 research and innovation programme under the
Marie Sklodowska-Curie Grant Agreement No. 665385.
article_number: '2003.05478'
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Thilo
full_name: Simon, Thilo
last_name: Simon
citation:
ama: 'Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape
in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions.
arXiv.'
apa: 'Fischer, J. L., Hensel, S., Laux, T., & Simon, T. (n.d.). The local structure
of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness
and stability of evolutions. arXiv.'
chicago: 'Fischer, Julian L, Sebastian Hensel, Tim Laux, and Thilo Simon. “The Local
Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong
Uniqueness and Stability of Evolutions.” ArXiv, n.d.'
ieee: 'J. L. Fischer, S. Hensel, T. Laux, and T. Simon, “The local structure of
the energy landscape in multiphase mean curvature flow: weak-strong uniqueness
and stability of evolutions,” arXiv. .'
ista: 'Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy
landscape in multiphase mean curvature flow: weak-strong uniqueness and stability
of evolutions. arXiv, 2003.05478.'
mla: 'Fischer, Julian L., et al. “The Local Structure of the Energy Landscape in
Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.”
ArXiv, 2003.05478.'
short: J.L. Fischer, S. Hensel, T. Laux, T. Simon, ArXiv (n.d.).
date_created: 2021-09-13T12:17:11Z
date_published: 2020-03-11T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '11'
department:
- _id: JuFi
ec_funded: 1
external_id:
arxiv:
- '2003.05478'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2003.05478
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '10007'
relation: dissertation_contains
status: public
status: public
title: 'The local structure of the energy landscape in multiphase mean curvature flow:
weak-strong uniqueness and stability of evolutions'
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...
---
_id: '6617'
abstract:
- lang: eng
text: 'The effective large-scale properties of materials with random heterogeneities
on a small scale are typically determined by the method of representative volumes:
a sample of the random material is chosen—the representative volume—and its effective
properties are computed by the cell formula. Intuitively, for a fixed sample size
it should be possible to increase the accuracy of the method by choosing a material
sample which captures the statistical properties of the material particularly
well; for example, for a composite material consisting of two constituents, one
would select a representative volume in which the volume fraction of the constituents
matches closely with their volume fraction in the overall material. Inspired by
similar attempts in materials science, Le Bris, Legoll and Minvielle have designed
a selection approach for representative volumes which performs remarkably well
in numerical examples of linear materials with moderate contrast. In the present
work, we provide a rigorous analysis of this selection approach for representative
volumes in the context of stochastic homogenization of linear elliptic equations.
In particular, we prove that the method essentially never performs worse than
a random selection of the material sample and may perform much better if the selection
criterion for the material samples is chosen suitably.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- 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: Fischer JL. The choice of representative volumes in the approximation of effective
properties of random materials. Archive for Rational Mechanics and Analysis.
2019;234(2):635–726. doi:10.1007/s00205-019-01400-w
apa: Fischer, J. L. (2019). The choice of representative volumes in the approximation
of effective properties of random materials. Archive for Rational Mechanics
and Analysis. Springer. https://doi.org/10.1007/s00205-019-01400-w
chicago: Fischer, Julian L. “The Choice of Representative Volumes in the Approximation
of Effective Properties of Random Materials.” Archive for Rational Mechanics
and Analysis. Springer, 2019. https://doi.org/10.1007/s00205-019-01400-w.
ieee: J. L. Fischer, “The choice of representative volumes in the approximation
of effective properties of random materials,” Archive for Rational Mechanics
and Analysis, vol. 234, no. 2. Springer, pp. 635–726, 2019.
ista: Fischer JL. 2019. The choice of representative volumes in the approximation
of effective properties of random materials. Archive for Rational Mechanics and
Analysis. 234(2), 635–726.
mla: Fischer, Julian L. “The Choice of Representative Volumes in the Approximation
of Effective Properties of Random Materials.” Archive for Rational Mechanics
and Analysis, vol. 234, no. 2, Springer, 2019, pp. 635–726, doi:10.1007/s00205-019-01400-w.
short: J.L. Fischer, Archive for Rational Mechanics and Analysis 234 (2019) 635–726.
date_created: 2019-07-07T21:59:23Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-08-28T12:31:21Z
day: '01'
ddc:
- '500'
department:
- _id: JuFi
doi: 10.1007/s00205-019-01400-w
external_id:
arxiv:
- '1807.00834'
isi:
- '000482386000006'
file:
- access_level: open_access
checksum: 4cff75fa6addb0770991ad9c474ab404
content_type: application/pdf
creator: kschuh
date_created: 2019-07-08T15:56:47Z
date_updated: 2020-07-14T12:47:34Z
file_id: '6626'
file_name: Springer_2019_Fischer.pdf
file_size: 1377659
relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: ' 234'
isi: 1
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 635–726
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: The choice of representative volumes in the approximation of effective properties
of random materials
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: 234
year: '2019'
...
---
_id: '6762'
abstract:
- lang: eng
text: "We present and study novel optimal control problems motivated by the search
for photovoltaic materials with high power-conversion efficiency. The material
must perform the first step: convert light (photons) into electronic excitations.
We formulate various desirable properties of the excitations as mathematical control
goals at the Kohn-Sham-DFT level\r\nof theory, with the control being given by
the nuclear charge distribution. We prove that nuclear distributions exist which
give rise to optimal HOMO-LUMO excitations, and present illustrative numerical
simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features
such as large electron-hole separation, and a hierarchy of length scales: internal
HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the
doping profiles < system size."
article_processing_charge: No
arxiv: 1
author:
- first_name: Gero
full_name: Friesecke, Gero
last_name: Friesecke
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
citation:
ama: Friesecke G, Kniely M. New optimal control problems in density functional theory
motivated by photovoltaics. Multiscale Modeling and Simulation. 2019;17(3):926-947.
doi:10.1137/18M1207272
apa: Friesecke, G., & Kniely, M. (2019). New optimal control problems in density
functional theory motivated by photovoltaics. Multiscale Modeling and Simulation.
SIAM. https://doi.org/10.1137/18M1207272
chicago: Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density
Functional Theory Motivated by Photovoltaics.” Multiscale Modeling and Simulation.
SIAM, 2019. https://doi.org/10.1137/18M1207272.
ieee: G. Friesecke and M. Kniely, “New optimal control problems in density functional
theory motivated by photovoltaics,” Multiscale Modeling and Simulation,
vol. 17, no. 3. SIAM, pp. 926–947, 2019.
ista: Friesecke G, Kniely M. 2019. New optimal control problems in density functional
theory motivated by photovoltaics. Multiscale Modeling and Simulation. 17(3),
926–947.
mla: Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density
Functional Theory Motivated by Photovoltaics.” Multiscale Modeling and Simulation,
vol. 17, no. 3, SIAM, 2019, pp. 926–47, doi:10.1137/18M1207272.
short: G. Friesecke, M. Kniely, Multiscale Modeling and Simulation 17 (2019) 926–947.
date_created: 2019-08-04T21:59:21Z
date_published: 2019-07-16T00:00:00Z
date_updated: 2023-09-05T15:05:45Z
day: '16'
department:
- _id: JuFi
doi: 10.1137/18M1207272
external_id:
arxiv:
- '1808.04200'
isi:
- '000487931800002'
intvolume: ' 17'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1808.04200
month: '07'
oa: 1
oa_version: Preprint
page: 926-947
publication: Multiscale Modeling and Simulation
publication_identifier:
eissn:
- '15403467'
issn:
- '15403459'
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: New optimal control problems in density functional theory motivated by photovoltaics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 17
year: '2019'
...
---
_id: '151'
abstract:
- lang: eng
text: We construct planar bi-Sobolev mappings whose local volume distortion is bounded
from below by a given function f∈Lp with p>1. More precisely, for any 1<q<(p+1)/2
we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞,
we provide bi-Lipschitz maps. The basic building block of our construction are
bi-Lipschitz maps which stretch a given compact subset of the unit square by a
given factor while preserving the boundary. The construction of these stretching
maps relies on a slight strengthening of the celebrated covering result of Alberti,
Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We
apply our result to a model functional in nonlinear elasticity, the integrand
of which features fast blowup as the Jacobian determinant of the deformation becomes
small. For such functionals, the derivation of the equilibrium equations for minimizers
requires an additional regularization of test functions, which our maps provide.
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Olivier
full_name: Kneuss, Olivier
last_name: Kneuss
citation:
ama: Fischer JL, Kneuss O. Bi-Sobolev solutions to the prescribed Jacobian inequality
in the plane with L p data and applications to nonlinear elasticity. Journal
of Differential Equations. 2019;266(1):257-311. doi:10.1016/j.jde.2018.07.045
apa: Fischer, J. L., & Kneuss, O. (2019). Bi-Sobolev solutions to the prescribed
Jacobian inequality in the plane with L p data and applications to nonlinear elasticity.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2018.07.045
chicago: Fischer, Julian L, and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed
Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.”
Journal of Differential Equations. Elsevier, 2019. https://doi.org/10.1016/j.jde.2018.07.045.
ieee: J. L. Fischer and O. Kneuss, “Bi-Sobolev solutions to the prescribed Jacobian
inequality in the plane with L p data and applications to nonlinear elasticity,”
Journal of Differential Equations, vol. 266, no. 1. Elsevier, pp. 257–311,
2019.
ista: Fischer JL, Kneuss O. 2019. Bi-Sobolev solutions to the prescribed Jacobian
inequality in the plane with L p data and applications to nonlinear elasticity.
Journal of Differential Equations. 266(1), 257–311.
mla: Fischer, Julian L., and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed
Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.”
Journal of Differential Equations, vol. 266, no. 1, Elsevier, 2019, pp.
257–311, doi:10.1016/j.jde.2018.07.045.
short: J.L. Fischer, O. Kneuss, Journal of Differential Equations 266 (2019) 257–311.
date_created: 2018-12-11T11:44:54Z
date_published: 2019-01-05T00:00:00Z
date_updated: 2023-09-08T13:25:35Z
day: '05'
department:
- _id: JuFi
doi: 10.1016/j.jde.2018.07.045
external_id:
arxiv:
- '1408.1587'
isi:
- '000449108500010'
intvolume: ' 266'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1408.1587
month: '01'
oa: 1
oa_version: Preprint
page: 257 - 311
publication: Journal of Differential Equations
publication_status: published
publisher: Elsevier
publist_id: '7770'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with
L p data and applications to nonlinear elasticity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 266
year: '2019'
...
---
_id: '606'
abstract:
- lang: eng
text: We establish the existence of a global solution for a new family of fluid-like
equations, which are obtained in certain regimes in as the mean-field evolution
of the supercurrent density in a (2D section of a) type-II superconductor with
pinning and with imposed electric current. We also consider general vortex-sheet
initial data, and investigate the uniqueness and regularity properties of the
solution. For some choice of parameters, the equation under investigation coincides
with the so-called lake equation from 2D shallow water fluid dynamics, and our
analysis then leads to a new existence result for rough initial data.
acknowledgement: "The work of the author is supported by F.R.S.-FNRS ( Fonds de la
Recherche Scientifique - FNRS ) through a Research Fellowship.\r\n\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Mitia
full_name: Duerinckx, Mitia
last_name: Duerinckx
- 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: Duerinckx M, Fischer JL. Well-posedness for mean-field evolutions arising in
superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis.
2018;35(5):1267-1319. doi:10.1016/j.anihpc.2017.11.004
apa: Duerinckx, M., & Fischer, J. L. (2018). Well-posedness for mean-field evolutions
arising in superconductivity. Annales de l’Institut Henri Poincare (C) Non
Linear Analysis. Elsevier. https://doi.org/10.1016/j.anihpc.2017.11.004
chicago: Duerinckx, Mitia, and Julian L Fischer. “Well-Posedness for Mean-Field
Evolutions Arising in Superconductivity.” Annales de l’Institut Henri Poincare
(C) Non Linear Analysis. Elsevier, 2018. https://doi.org/10.1016/j.anihpc.2017.11.004.
ieee: M. Duerinckx and J. L. Fischer, “Well-posedness for mean-field evolutions
arising in superconductivity,” Annales de l’Institut Henri Poincare (C) Non
Linear Analysis, vol. 35, no. 5. Elsevier, pp. 1267–1319, 2018.
ista: Duerinckx M, Fischer JL. 2018. Well-posedness for mean-field evolutions arising
in superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis.
35(5), 1267–1319.
mla: Duerinckx, Mitia, and Julian L. Fischer. “Well-Posedness for Mean-Field Evolutions
Arising in Superconductivity.” Annales de l’Institut Henri Poincare (C) Non
Linear Analysis, vol. 35, no. 5, Elsevier, 2018, pp. 1267–319, doi:10.1016/j.anihpc.2017.11.004.
short: M. Duerinckx, J.L. Fischer, Annales de l’Institut Henri Poincare (C) Non
Linear Analysis 35 (2018) 1267–1319.
date_created: 2018-12-11T11:47:27Z
date_published: 2018-08-01T00:00:00Z
date_updated: 2023-09-19T10:39:09Z
day: '01'
department:
- _id: JuFi
doi: 10.1016/j.anihpc.2017.11.004
external_id:
arxiv:
- '1607.00268'
isi:
- '000437975500005'
intvolume: ' 35'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1607.00268
month: '08'
oa: 1
oa_version: Submitted Version
page: 1267-1319
publication: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
publication_status: published
publisher: Elsevier
publist_id: '7199'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Well-posedness for mean-field evolutions arising in superconductivity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 35
year: '2018'
...
---
_id: '404'
abstract:
- lang: eng
text: "We construct martingale solutions to stochastic thin-film equations by introducing
a (spatial) semidiscretization and establishing convergence. The discrete scheme
allows for variants of the energy and entropy estimates in the continuous setting
as long as the discrete energy does not exceed certain threshold values depending
on the spatial grid size $h$. Using a stopping time argument to prolongate high-energy
paths constant in time, arbitrary moments of coupled energy/entropy functionals
can be controlled. Having established Hölder regularity of approximate solutions,
the convergence proof is then based on compactness arguments---in particular on
Jakubowski's generalization of Skorokhod's theorem---weak convergence methods,
and recent tools on martingale convergence.\r\n\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Günther
full_name: Grün, Günther
last_name: Grün
citation:
ama: Fischer JL, Grün G. Existence of positive solutions to stochastic thin-film
equations. SIAM Journal on Mathematical Analysis. 2018;50(1):411-455. doi:10.1137/16M1098796
apa: Fischer, J. L., & Grün, G. (2018). Existence of positive solutions to stochastic
thin-film equations. SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics . https://doi.org/10.1137/16M1098796
chicago: Fischer, Julian L, and Günther Grün. “Existence of Positive Solutions to
Stochastic Thin-Film Equations.” SIAM Journal on Mathematical Analysis.
Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1098796.
ieee: J. L. Fischer and G. Grün, “Existence of positive solutions to stochastic
thin-film equations,” SIAM Journal on Mathematical Analysis, vol. 50, no.
1. Society for Industrial and Applied Mathematics , pp. 411–455, 2018.
ista: Fischer JL, Grün G. 2018. Existence of positive solutions to stochastic thin-film
equations. SIAM Journal on Mathematical Analysis. 50(1), 411–455.
mla: Fischer, Julian L., and Günther Grün. “Existence of Positive Solutions to Stochastic
Thin-Film Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no.
1, Society for Industrial and Applied Mathematics , 2018, pp. 411–55, doi:10.1137/16M1098796.
short: J.L. Fischer, G. Grün, SIAM Journal on Mathematical Analysis 50 (2018) 411–455.
date_created: 2018-12-11T11:46:17Z
date_published: 2018-01-30T00:00:00Z
date_updated: 2023-09-11T13:59:22Z
day: '30'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/16M1098796
external_id:
isi:
- '000426630900015'
file:
- access_level: open_access
checksum: 89a8eae7c52bb356c04f52b44bff4b5a
content_type: application/pdf
creator: dernst
date_created: 2019-11-07T12:20:25Z
date_updated: 2020-07-14T12:46:22Z
file_id: '6992'
file_name: 2018_SIAM_Fischer.pdf
file_size: 557338
relation: main_file
file_date_updated: 2020-07-14T12:46:22Z
has_accepted_license: '1'
intvolume: ' 50'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 411 - 455
publication: SIAM Journal on Mathematical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7425'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Existence of positive solutions to stochastic thin-film equations
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 50
year: '2018'
...
---
_id: '712'
abstract:
- lang: eng
text: 'We establish a weak–strong uniqueness principle for solutions to entropy-dissipating
reaction–diffusion equations: As long as a strong solution to the reaction–diffusion
equation exists, any weak solution and even any renormalized solution must coincide
with this strong solution. Our assumptions on the reaction rates are just the
entropy condition and local Lipschitz continuity; in particular, we do not impose
any growth restrictions on the reaction rates. Therefore, our result applies to
any single reversible reaction with mass-action kinetics as well as to systems
of reversible reactions with mass-action kinetics satisfying the detailed balance
condition. Renormalized solutions are known to exist globally in time for reaction–diffusion
equations with entropy-dissipating reaction rates; in contrast, the global-in-time
existence of weak solutions is in general still an open problem–even for smooth
data–, thereby motivating the study of renormalized solutions. The key ingredient
of our result is a careful adjustment of the usual relative entropy functional,
whose evolution cannot be controlled properly for weak solutions or renormalized
solutions.'
author:
- 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: 'Fischer JL. Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion
equations. Nonlinear Analysis: Theory, Methods and Applications. 2017;159:181-207.
doi:10.1016/j.na.2017.03.001'
apa: 'Fischer, J. L. (2017). Weak–strong uniqueness of solutions to entropy dissipating
reaction–diffusion equations. Nonlinear Analysis: Theory, Methods and Applications.
Elsevier. https://doi.org/10.1016/j.na.2017.03.001'
chicago: 'Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating
Reaction–Diffusion Equations.” Nonlinear Analysis: Theory, Methods and Applications.
Elsevier, 2017. https://doi.org/10.1016/j.na.2017.03.001.'
ieee: 'J. L. Fischer, “Weak–strong uniqueness of solutions to entropy dissipating
reaction–diffusion equations,” Nonlinear Analysis: Theory, Methods and Applications,
vol. 159. Elsevier, pp. 181–207, 2017.'
ista: 'Fischer JL. 2017. Weak–strong uniqueness of solutions to entropy dissipating
reaction–diffusion equations. Nonlinear Analysis: Theory, Methods and Applications.
159, 181–207.'
mla: 'Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating
Reaction–Diffusion Equations.” Nonlinear Analysis: Theory, Methods and Applications,
vol. 159, Elsevier, 2017, pp. 181–207, doi:10.1016/j.na.2017.03.001.'
short: 'J.L. Fischer, Nonlinear Analysis: Theory, Methods and Applications 159 (2017)
181–207.'
date_created: 2018-12-11T11:48:05Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2021-01-12T08:11:55Z
day: '01'
department:
- _id: JuFi
doi: 10.1016/j.na.2017.03.001
intvolume: ' 159'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1703.00730
month: '08'
oa: 1
oa_version: Submitted Version
page: 181 - 207
publication: 'Nonlinear Analysis: Theory, Methods and Applications'
publication_identifier:
issn:
- 0362546X
publication_status: published
publisher: Elsevier
publist_id: '6975'
quality_controlled: '1'
scopus_import: 1
status: public
title: Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion
equations
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 159
year: '2017'
...