| 2023Iulia Cristian and Juan J. L. Velázquez
Fast fusion in a two-dimensional coagulation model
2023
https://arxiv.org/abs/2303.09475
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| 2022Iulia Cristian and Juan J. L. Velázquez
Coagulation equations for non-spherical clusters
2022
https://arxiv.org/abs/2209.00644
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| Iulia Cristian, Marina A. Ferreira, Eugenia Franco and Juan J. L. Velázquez
Long-time asymptotics for coagulation equations with injection that do not have stationary solutions
2022
https://ui.adsabs.harvard.edu/abs/2022arXiv221116399C
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| 2020James Chapman, Jin Woo Jang and Robert M. Strain
On the Determinant Problem for the Relativistic Boltzmann Equation
2020
https://ui.adsabs.harvard.edu/abs/2020arXiv200602540C
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| 2019Sergio Conti, Matteo Focardi and Flaviana Iurlano
Existence of strong minimizers for the Griffith static fracture model in dimension two
Ann. Inst. Henri Poincaré C, Anal. Non Linéaire, 36: 455-474 2019
10.1016/j.anihpc.2018.06.003
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| Sergio Conti, Martin Lenz, Nora Lüthen, Martin Rumpf and Barbara Zwicknagl
Geometry of martensite needles in shape memory alloys
2019
https://arxiv.org/abs/1912.02274
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| 2018P. Ariza, S. Conti, A. Garroni and M. Ortiz
Variational modeling of dislocations in crystals in the line-tension limit
In V. Mehrmann and M. Skutella, editor, European Congress of Mathematics, Berlin, 2016
page 583-598.
Publisher: EMS
2018
10.4171/176-1/27
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| Anton Bovier, Loren Coquille and Charline Smadi
Crossing a fitness valley as a metastable transition in a stochastic population model
2018
https://arxiv.org/abs/1801.06473
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| Antonin Chambolle, Sergio Conti and Gilles A. Francfort
Approximation of a britte fracture energy with the constraint of non-interpenetration
Arch. Ration. Mech. Anal., 228: 867-889 2018
10.1007/s00205-017-1207-z
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| Sergio Conti, Martin Rumpf, Rüdiger Schultz and Sascha Tölkes
Stochastic Dominance Constraints in Elastic Shape Optimization
SIAM J. Control Optim., 56: 3021-3034 2018
10.1137/16M108313X
Abstract: This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from finite-dimensional stochastic programming to shape optimization. Rather than handling risk aversion in the objective, this enables risk aversion by including dominance constraints that single out subsets of nonanticipative shapes which compare favorably to a chosen stochastic benchmark. This new class of stochastic shape optimization problems arises by optimizing over such feasible sets. The analytical description is built on risk-averse cost measures. The underlying cost functional is of compliance type plus a perimeter term, in the implementation shapes are represented by a phase field which permits an easy estimate of a regularized perimeter. The analytical description and the numerical implementation of dominance constraints are built on risk-averse measures for the cost functional. A suitable numerical discretization is obtained using finite elements both for the displacement and the phase field function. Different numerical experiments demonstrate the potential of the proposed stochastic shape optimization model and in particular the impact of high variability of forces or probabilities in the different realizations. |
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| S. Conti and G. Dolzmann
An adaptive relaxation algorithm for multiscale problems and application to nematic elastomers
J. Mech. Phys. Solids, 113: 126-143 2018
10.1016/j.jmps.2018.02.001
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| Sergio Conti, Stefan Müller and Michael Ortiz
Data-driven problems in elasticity
Arch. Ration. Mech. Anal., 229: 79-123 2018
10.1007/s00205-017-1214-0
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| Sergio Conti, Matteo Focardi and Flaviana Iurlano
Which special functions of bounded deformation have bounded variation
Proc. Roy. Soc. Edinb. A, 148: 33-50 2018
10.1017/S030821051700004X
Abstract: Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation (BV), but are less well understood. We discuss here the relation to BV under additional regularity assumptions, which may require the regular part of the strain to have higher integrability or the jump set to have finite area or the Cantor part to vanish. On the positive side, we prove that BD functions which are piecewise affine on a Caccioppoli partition are in GSBV, and we prove that $SBD^p$ functions are approximately continuous $H^n-1$-a.e. away from the jump set. On the negative side, we construct a function which is $BD$ but not in BV and has distributional strain consisting only of a jump part, and one which has a distributional strain consisting of only a Cantor part. |
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| Sergio Conti, Martin Lenz, Matthäus Pawelczyk and Martin Rumpf
Homogenization in magnetic-shape-memory polymer composites
In Volker Schulz and Diaraf Seck, editor, Shape Optimization, Homogenization and Optimal Control, Volume 169 of International Series of Numerical Mathematics
page 1-17.
Publisher: Birkhäuser, Cham
2018
10.1007/978-3-319-90469-6_1
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| S. Conti, M. Goldman, F. Otto and S. Serfaty
A branched transport limit of the Ginzburg-Landau functional
Journal de l'École polytechnique -- Mathématiques, 5: 317-375 2018
10.5802/jep.72
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| Sergio Conti, Benedict Geihe, Martin Lenz and Martin Rumpf
A posteriori modeling error estimates in the optimization of two-scale elastic composite materials
ESAIM: Mathematical Modelling and Numerical Analysis, 52: 1457-1476 2018
10.1051/m2an/2017004
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| Celia Reina, Landry Fokoua Djodom, Michael Ortiz and Sergio Conti
Kinematics of elasto-plasticity: Validity and limits of applicability of $F=F_eF_p$ for general three-dimensional deformations
Journal of the Mechanics and Physics of Solids, 121: 99--113 2018
10.1016/j.jmps.2018.07.006
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| W. Schill, S. Heyden, S. Conti and M. Ortiz
The anomalous yield behavior of fused silica glass
Journal of the Mechanics and Physics of Solids, 113: 105 - 125 2018
10.1016/j.jmps.2018.01.004
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| 2017Mathias Beiglböck, Alexander M. G. Cox and Martin Huesmann
he geometry of multi-marginal Skorokhod embedding
arxiv e-print 1705.09505 2017
https://arxiv.org/abs/1705.09505
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| David Bourne, Sergio Conti and Stefan Müller
Energy bounds for a compressed elastic film on a substrate
J. Nonlinear Science, 27: 453-494 2017
10.1007/s00332-016-9339-0
Abstract: We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate theory. The second part represents the fracture or delamination energy, which is approximated using the Griffith model of fracture. A simpler model containing the first term alone was previously studied with similar methods by several authors, assuming that the delaminated region is fixed. We include the fracture term, transforming the elastic minimization into a free-boundary problem, and opening the way for patterns which result from the interplay of elasticity and delamination. After rescaling, the energy depends on only two parameters: the rescaled film thickness, $σ$, and a measure of the bonding strength between the film and substrate, $γ$. We prove upper bounds on the minimum energy of the form $σ^a γ^b$ and find that there are four different parameter regimes corresponding to different values of $a$ and $b$ and to different folding patterns of the film. In some cases the upper bounds are attained by self-similar folding patterns as observed in experiments. Moreover, for two of the four parameter regimes we prove matching, optimal lower bounds. |
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