TY  - JOUR
A1  - Kleefeld, Andreas
T1  - The hot spots conjecture can be false: some numerical examples
JF  - Advances in Computational Mathematics
N2  - The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10− 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.
KW  - Numerics
KW  - Boundary integral equations
KW  - Potential theory
KW  - Helmholtz equation
KW  - Interior Neumann eigenvalues
Y1  - 2021
U6  - https://doi.org/10.1007/s10444-021-09911-5
SN  - 1019-7168
VL  - 47
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Hugenroth, Kristin
A1  - Neidlin, Michael
A1  - Engelmann, Ulrich M.
A1  - Kaufmann, Tim A. S.
A1  - Steinseifer, Ulrich
A1  - Heilmann, Torsten
T1  - Tipless Transseptal Cannula Concept Combines Improved Hemodynamic Properties and Risk‐Reduced Placement: an In Silico Proof‐of‐Concept
JF  - Artificial Organs
Y1  - 2021
U6  - https://doi.org/10.1111/aor.13964
SN  - 1525-1594
IS  - Accepted Article
PB  - Wiley
CY  - Weinheim
ER  - 
TY  - JOUR
A1  - Molinnus, Denise
A1  - Drinic, Aleksander
A1  - Iken, Heiko
A1  - Kröger, Nadja
A1  - Zinser, Max
A1  - Smeets, Ralf
A1  - Köpf, Marius
A1  - Kopp, Alexander
A1  - Schöning, Michael Josef
T1  - Towards a flexible electrochemical biosensor fabricated from biocompatible Bombyx mori silk
JF  - Biosensors and Bioelectronics
Y1  - 2021
U6  - https://doi.org/10.1016/j.bios.2021.113204
SN  - 0956-5663
VL  - 183
IS  - Art. 113204
PB  - Elsevier
CY  - Amsterdam
ER  -