Convolutional-network models to predict wall-bounded turbulence from wall quantities

Two models based on convolutional neural networks are trained to predict the two-dimensional instantaneous velocity-fluctuation fields at different wall-normal locations in a turbulent open-channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), and is hence named FCN-POD. Both models are trained using data from direct numerical simulations at friction Reynolds numbers $Re_{\tau } = 180$ and 550. Being able to predict the nonlinear interactions in the flow, both models show better predictions than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between the input and output fields. The performance of the models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. FCN exhibits the best predictions closer to the wall, whereas FCN-POD provides better predictions at larger wall-normal distances. We also assessed the feasibility of transfer learning for the FCN model, using the model parameters learned from the $Re_{\tau }=180$ dataset to initialize those of the model that is trained on the $Re_{\tau }=550$ dataset. After training the initialized model at the new $Re_{\tau }$ , our results indicate the possibility of matching the reference-model performance up to $y^{+}=50$ , with $50\,\%$ and $25\,\%$ of the original training data. We expect that these non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.

The effect of Dzyaloshinskii–Moriya interaction on direct and backward transition between magnetic states of Pt/Co/Ir/Co/Pr synthetic ferrimagnet

In this paper, we present the study of domain structure accompanying interstate transitions in Pt/Co/Ir/Co/Pr synthetic ferrimagnet (SF) of 1.1 nm thick and 0.6 – 1.0 nm thin ferromagnetic Co layers. Variation in the thickness of the thin layer causes noticeable changes in the domain structure and mechanism of magnetization reversal revealed by MOKE (Magneto-Optical Kerr Effect) technique. Magnetization reversal includes coherent rotation of magnetization of the ferromagnetic layers, generation of magnetic nuclei, spreading of domain walls (DW), and development of areas similar with strip domains, dependently on thickness of the thin layer. Inequivalence of the direct and backward transitions between magnetic states of SF with parallel and antiparallel magnetizations was observed in sample with thin layer thicknesses 0.8 nm and 1.0 nm. Asymmetry of the transition between these states is expressed in difference fluctuation fields and shapes of reversal magnetization nucleus contributing to the correspondent forward and backward transitions. We proposed simple model based on asymmetry of Dzyaloshinskii–Moriya interaction. This model explains competition between nucleation and domain wall propagation due to increase/decrease of the DW energy dependently on direction of the spin rotation into the DW in respect to external field.

AdS backgrounds and induced gravity

In this paper, we look for AdS solutions to generalized gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein–Hilbert gravity is induced when the scalar acquires a nonzero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.

SYNTHESIZED ENRICHMENT FUNCTIONS FOR EXTENDED FINITE ELEMENT ANALYSES WITH FULLY RESOLVED MICROSTRUCTURE

Inspired by the first order numerical homogenization, we present a method for extracting continuous fluctuation fields from the Wang tile based compression of a material microstructure. The fluctuation fields are then used as enrichment basis in Extended Finite Element Method (XFEM) to reduce number of unknowns in problems with fully resolved microstructural geometry synthesized by means of the tiling concept. In addition, the XFEM basis functions are taken as reduced modes of a detailed discretization in order to circumvent the need for non-standard numerical quadratures. The methodology is illustrated with a scalar steady-state problem.