Publications Prof. Trunk

Publications of the employees

Publications of the Group

Results: 170
Created on: Wed, 27 Mar 2024 23:22:32 +0100 in 0.0771 sec


Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl
Prevention of solidification cracking during pulsed laser beam welding. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (7 Seiten). - (Preprint ; M17,09)

We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coeff cients depend on the temperature, this leads to a quasi-linear parabolic partial differential equation. It is our goal to prevent solidif cation cracking. We address this problem by means of optimal control. It is the intensity prof le of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidif cation interface need to be properly penalized in order to deal with and avoid cracking phenomena.



https://www.db-thueringen.de/receive/dbt_mods_00032771
Gernandt, Hannes; Krauße, Dominik; Sommer, Ralf; Trunk, Carsten
A new method for network redesign via rank one updates. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (5 Seiten). - (Preprint ; M17,08)

We present a method to place the eigenvalues of an electrical network towards a prescribed set of complex numbers by inserting an additional capacitance into the network. We use recent results on rank one perturbations of regular matrix pencils and provide an upper bound on the approximation error of the eigenvalues in the chordal distance.



https://www.db-thueringen.de/receive/dbt_mods_00032770
Gernandt, Hannes; Trunk, Carsten
Eigenvalue placement for regular matrix pencils with rank one perturbations. - In: SIAM journal on matrix analysis and applications, ISSN 1095-7162, Bd. 38 (2017), 1, S. 134-154

http://dx.doi.org/10.1137/16M1066877
Jacob, Birgit; Tretter, Christiane; Trunk, Carsten; Vogt, Hendrik
Numerical range and quadratic numerical range for damped systems. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (27 Seiten). - (Preprint ; M17,05)

We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations z'' (t) + D z' (t) + A_0 z(t) = 0 in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved; in particular, the damping operator only needs to be accretive and may have the same strength as A_0. By means of the quadratic numerical range, we establish tight spectral estimates in terms of the unbounded operator coefficients A_0 and D which improve earlier results for sectorial and selfadjoint D; in contrast to numerical range bounds, our enclosures may even provide bounded imaginary part of the spectrum or a spectral free vertical strip. An application to small transverse oscillations of a horizontal pipe carrying a steady-state flow of an ideal incompressible fluid illustrates that our new bounds are explicit.



https://www.db-thueringen.de/receive/dbt_mods_00031984
Derkach, Volodymyr; Trunk, Carsten
Coupling of definitizable operators in Krein spaces. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (18 Seiten). - (Preprint ; M17,03)

Indefinite Sturm-Liouville operators defined on the real line are often considered as a coupling of two semibounded symmetric operators defined on the positive and the negative half axis. In many situations, those two semibounded symmetric operators have in a special sense good properties like a Hilbert space self-adjoint extension. In this paper we present an abstract approach to the coupling of two (definitizable) self-adjoint operators. We obtain a characterization for the definitizability and the regularity of the critical points. Finally we study a typical class of indefinite Sturm-Liouville problems on the real line.



https://www.db-thueringen.de/receive/dbt_mods_00031469
Giribet, Juan; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra; Martínez Pería, Francisco; Trunk, Carsten
Spectrum of J-frame operators. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (20 Seiten). - (Preprint ; M17,01)

A J-frame is a frame F for a Krein space which is compatible with the indefinite inner product in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H . With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2X2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2X2 block representation. Moreover, this 2X2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.



https://www.db-thueringen.de/receive/dbt_mods_00031058
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
Eigenvalue estimates for operators with finitely many negative squares. - In: Opuscula mathematica, ISSN 2300-6919, Bd. 36 (2016), 6, S. 717-734

https://doi.org/10.7494/OpMath.2016.36.6.717
Shkalikov, A. A.; Trunk, Carsten
On stability of closedness and self-adjointness for 2 x 2 operator matrices. - In: Mathematical notes, ISSN 1573-8876, Bd. 100 (2016), 5, S. 870-875

http://dx.doi.org/10.1134/S0001434616110274
Jacob, Birgit; Langer, Matthias; Trunk, Carsten
Variational principles for self-adjoint operator functions arising from second-order systems. - In: Operators and matrices, Bd. 10 (2016), 3, S. 501-531

http://dx.doi.org/10.7153/oam-10-29
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten
Bounds on the non-real spectrum of a singular indefinite Sturm-Liouville operator on R. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 16 (2016), 1, S. 881-882

http://dx.doi.org/10.1002/pamm.201610429