Fakultät für Mathematik und Physik
https://www.repo.uni-hannover.de/handle/123456789/7
Frei zugängliche Publikationen aus der Fakultät für Mathematik und Physik2019-09-16T22:17:22ZA phase-field description for mixed-mode fracture propagation
https://www.repo.uni-hannover.de/handle/123456789/5416
A phase-field description for mixed-mode fracture propagation
Meng, Fan; Yan, Jin; Thomas, Wick
The goal of this work is to develop a phase-field fracture model capable of capturing mixed-
mode fracture propagation behavior. In nature, failure of rocks and rock-like materials is usually
accompanied by the propagation of mixed-mode fractures. To address this problem, some recent
studies have incorporated mixed-mode fracture propagation criteria to the classic phase-field frac-
ture model and proposed new energy splitting methods to split the total crack driving energy into
mode-I and mode-II parts. But these new models have sometimes the shortcomings of being not
numerically-robust or not physically sound. From a numerical viewpoint, they are all solved with
staggered solution schemes. In this work, an existing energy splitting method for masonry-like
materials is modified and incorporated into the phase-field model for mixed-mode fractures. A
fully-monolithic scheme is used to solve the model. Therein, a primal-dual active set method is
employed for treating the fracture irreversibility. Moreover, our computational framework uses
adaptive mesh refinement of a predictor-corrector type and parallel computing to reduce the com-
putation time. Three numerical tests are carried out, and the results of the new model are compared
to those of existing models, demonstrating the numerical robustness and physical soundness of the
new model. In total, six splitting methods are compared and computationally analyzed.
2019-01-01T00:00:00ZNull vectors in logarithmic conformal field theory
https://www.repo.uni-hannover.de/handle/123456789/5400
Null vectors in logarithmic conformal field theory
Flohr, Michael
The representation theory of the Virasoro algebra in the case of a logarithmic conformal field theory is considered. Here, indecomposable representations have to be taken into account, which has many interesting consequences. We study the generalization of null vectors towards the case of indecomposable representation modules and, in particular, how such logarithmic null vectors can be used to derive differential equations for correlation functions. We show that differential equations for correlation functions with logarithmic fields become inhomogeneous.
2000-01-01T00:00:00ZPure Yang–Mills solutions on dS 4
https://www.repo.uni-hannover.de/handle/123456789/5402
Pure Yang–Mills solutions on dS 4
Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.
We consider pure SU(2) Yang–Mills theory on four-dimensional de Sitter space dS 4 and construct smooth and spatially homogeneous classical Yang–Mills fields. Slicing dS 4 as ℝ×S 3 , via an SU(2)-equivariant ansatz we reduce the Yang–Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a particular three-dimensional potential. Its classical trajectories yield spatially homogeneous Yang–Mills solutions in a very simple explicit form, depending only on de Sitter time with an exponential decay in the past and future. These configurations have not only finite energy, but their action is also finite and bounded from below. We present explicit coordinate representations of the simplest examples (for the fundamental SU(2) representation). Instantons (Yang–Mills solutions on the Wick-rotated S 4 ) and solutions on AdS 4 are also briefly discussed.
2017-01-01T00:00:00ZNoncommutative instantons and solitons
https://www.repo.uni-hannover.de/handle/123456789/5398
Noncommutative instantons and solitons
Lechtenfeld, Olaf
I explain how to construct noncommutative BPS configurations in four and lower dimensions by solving linear matrix equations. Examples are instantons in D=4 Yang-Mills, monopoles in D=3 Yang-Mills-Higgs, and (moving) solitons in D=2+1 Yang-Mills-Higgs. Some emphasis is on the latter as a showcase for the dressing method.
2003-01-01T00:00:00Z