Dyson–Schwinger equations and N=4 SYM in Landau gauge - Maas, Axel; Zitz, Stefan (European Physical Journal C: Particles and Fields, 2016)
N=4 Super Yang–Mills theory is a highly constrained theory, and therefore a valuable tool to test the understanding of less constrained Yang–Mills theories. Our aim is to use it to test our understanding of both the Landau gauge beyond perturbation theory and the truncations of Dyson–Schwinger equations in ordinary Yang–Mills theories. We derive the corresponding equations within the usual one-loop truncation for the propagators after imposing the Landau gauge. We find a conformal solution in this approximation, which surprisingly resembles many aspects of ordinary Yang–Mills theories. We furthermore discuss which role the Gribov–Singer ambiguity in this context could play, should it exist in this theory.
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Lattice Boltzmann method for thin-liquid-film hydrodynamics - Zitz, Stefan; Scagliarini, A.; Maddu, S.; Darhuber, A. A.; Harting, Jens (Physical Review E, 2019)
We propose an approach to the numerical simulation of thin-film flows based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin-film equations are recovered, and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop toward its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.
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Lattice Boltzmann simulations of stochastic thin film dewetting - Zitz, Stefan; Scagliarini, A.; Harting, Jens (Physical Review E, 2021)
We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film flows, equipped with a properly devised stochastic term. While it is known that thermal fluctuations yield shorter rupture times, we show that this is a general feature of hydrophilic substrates, irrespective of the contact angle θ. The ratio between deterministic and stochastic rupture times, though, decreases with θ. Finally, we discuss the case of fluctuating thin film dewetting on chemically patterned substrates and its dependence on the form of the wettability gradients.
CRIS-Team Scopus Importer:2021-09-17