Zobrazeno 1 - 10
of 197
pro vyhledávání: '"Dondl, Patrick"'
This work examines a discrete elastic energy system with local interactions described by a discrete second-order functional in the symmetric gradient and additional non-local random long-range interactions. We analyze the asymptotic behavior of this
Externí odkaz:
http://arxiv.org/abs/2411.08623
This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove $\Gamma$-convergence to the continuous model. This disc
Externí odkaz:
http://arxiv.org/abs/2306.10936
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry perturbations on the effective mechanical properties of elastic rods. T
Externí odkaz:
http://arxiv.org/abs/2304.08785
We provide the convergence analysis for a sinc-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of an earlier article by the same authors, where the authors presented a sinc-function based method to sol
Externí odkaz:
http://arxiv.org/abs/2212.11581
Publikováno v:
ESAIM Control Optim. Calc. Var. (2024)
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both rigidities as obje
Externí odkaz:
http://arxiv.org/abs/2209.04538
Autor:
Dondl, Patrick, Zeinhofer, Marius
We consider the scaffold design optimization problem associated to the three dimensional, time dependent model for scaffold mediated bone regeneration considered in Dondl et al. (2021). We prove existence of optimal scaffold designs and present numer
Externí odkaz:
http://arxiv.org/abs/2112.11530
Autor:
Dondl, Patrick, Zeinhofer, Marius
We prove an $L^p(I,C^\alpha(\Omega))$ regularity result for a reaction-diffusion equation with mixed boundary conditions, symmetric $L^\infty$ coefficients and an $L^\infty$ initial condition. We provide explicit control of the $L^p(I,C^\alpha(\Omega
Externí odkaz:
http://arxiv.org/abs/2112.09500
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the $p$-Laplace equation or the Modica-Mortola energy with essential or natural boundary condition
Externí odkaz:
http://arxiv.org/abs/2111.05637
Time-discrete numerical minimization schemes for simple viscoelastic materials in the large strain Kelvin-Voigt rheology are not well-posed due to non-quasiconvexity of the dissipation functional. A possible solution is to resort into non-simple mate
Externí odkaz:
http://arxiv.org/abs/2110.13728
Autor:
Dondl, Patrick, Straughan, Brian
A bidisperse porous medium is one with two porosity scales. There are the usual pores known as macro pores but also cracks or fissures in the skeleton which give rise to micro pores. In this article we develop and analyse a model for thermal convecti
Externí odkaz:
http://arxiv.org/abs/2110.12291