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In the automotive industry, corrosion protected galvanized advanced high strength steels with high ductility (AHSS-HD) gain importance due to their good formability and their lightweight potential. Unfortunately, under specific thermomechanical loading conditions such as during resistance spot welding galvanized, AHSS-HD sheets tend to show liquid metal embrittlement (LME). LME is an intergranular decohesion phenomenon leading to a drastic loss of ductility of up to 95%. The occurrence of LME for a given galvanized material mainly depends on thermal and mechanical loading. These influences are investigated for a dual phase steel with an ultimate tensile strength of 1200 MPa, a fracture strain of 14% and high ductility (DP1200HD) by means of systematic isothermal hot tensile testing on a Gleeble® 3800 thermomechanical simulator. Based on the experimental findings, a machine learning procedure using symbolic regression is applied to calibrate an LME damage model that accounts for the governing quantities of temperature, plastic strain and strain rate. The finite element (FE) implementation of the damage model is validated based on the local damage distribution in the hot tensile tested samples and in an exemplary 2-sheet resistance spot weld. The developed LME damage model predicts the local position and the local intensity of liquid metal induced cracking in both cases very well.

The response of single SnO2 nanowire gas sensors with different diameters between 20 and 140 nm are evaluated by calculating the nanowire conductivity as a function of the surface charge density. The procedure involves the numerical solution of the Poisson-Boltzmann equation for the electrostatic potential in cylindrical geometry in order to model the depletion region and band bending at the SnO2 nanowire surface. In the model we take into account varying surface charge densities σ and bulk electron concentrations n0 to calculate the electrical conductivity. Considering the fact that the surface charge density depends on the nanowire surface interactions with ambient gas, the model allows us to simulate the sensor response when the nanowire is employed as gas sensing component. We report a saturation in depletion length λ versus surface charge density σ which is the principal reason for limiting the sensor responses. The results also show that the conductivity is decreasing by increasing surface charge density, the smaller the nanowire diameter the steeper the decrease. As a result the nanowire response is proportional to 1/d where d is the nanowire diameter. Furthermore, we argue about the validity of the modeling results and their relevance to experimental findings on SnO2 nanowire based gas sensors reported in literature.

Hybrid semiparametric models integrate physics-based (“white-box”, parametric) and data-driven (“black-box”, non-parametric) submodels. Black-box models are often implemented using artificial neural networks (ANNs). In this work, we investigate the fitness of symbolic regression (SR) for black-box modelling. The main advantage of this approach is that a trained hybrid model can be expressed in closed form as an algebraic equation. We examine and test the idea on a simple example, namely the v-shape bending of a metal sheet, where an analytical solution for the stamping force is readily available. We explore unconstrained and hybrid symbolic regression modelling to show that hybrid SR models, where the regression tree is partly fixed according to a-priori knowledge, perform much better than purely data-driven SR models based on unconstrained regression trees. Furthermore, the generation of algebraic equations by this method is much more repeatable, which makes the approach applicable to process knowledge discovery.

In this work, we present and test an approach based on an inverse model applicable to the control of induction heat treatments. The inverse model is comprised of a simplified analytical forward model trained with experiments to predict and control the temperature of a location in a cylindrical sample starting from any initial temperature. We solve the coupled nonlinear electromagnetic-thermal problem, which contains a temperature dependent parameter &alpha, to correct the electromagnetic field on the surface of a cylinder, and as a result effectively the modeled temperature elsewhere in the sample. A calibrated model to the measurement data applied with the process information such as the operating power level, current, frequency, and temperature provides the basic ingredients to construct an inverse model toolbox, which finally enables us to conduct experiments with more specific goals. The input set values of the power supply, i.e., the power levels in the test rig control system, are determined within an iterative framework to reach specific target temperatures in prescribed times. We verify the concept on an induction heating test rig and provide two examples to illustrate the approach. The advantages of the method lie in its simplicity, computationally cost effectiveness and independence of a prior knowledge of the internal structure of power supplies.

A simple hybrid model, integrating observation (black-box) and physical knowledge (white-box), is employed to model an induction heating process. A neural network is used to estimate the unknown physical process parameter in the physical model. Most relevant to induction hardening is the temperature evolution in a layer under the surface of a sample, in our case a cylindrical sample. We show that with a hybrid model, in which a simple ordinary differential equation describes the heating rate, the experimental data can be approximated better than using a black-box only. The hybrid model extrapolates better and it is easier to interpret. The hybrid model can be used as a prediction tool to operate and optimize induction heating processes.

We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the transverse magnetic field across the transition or within a phase. We treat both the one-dimensional case, for which an exact solution is available, as well the two-dimensional one, for which has to resort to numerical results. Comparison with exact results shows that the approach provides a quite accurate description of the real-time dynamics up to a characteristic time scale $\tau$ that increses with the size of the cluster used for CPT. In addition, and not surprisingly $\tau$ is small for quenches across the equilibrium phase transition, but can be quite larger for quenches within the ordered or disordered phases.

We find evidence that superconductivity intrudes into the paramagnetic-to-magnetic transition of the Kondo lattice model if magnetic frustration is added. Specifically, we study by variational method the model on a square lattice in the presence of both nearest- ($t$) and next-nearest-neighbor ($t^\prime$) hopping of the conduction electrons. We find that when $t^\prime/t$ is finite a $d$-wave superconducting dome emerges between the magnetic and paramagnetic metal phases and close to the compensated regime, i.e., the number of conduction electrons equal to the number of localized spin-1/2 moments. Superconductivity is further strengthened by a direct antiferromagnetic exchange between the localized moments, to such an extent that we even observe coexistence with magnetic order.

We study the phase diagram of the Kondo-lattice model with nearest-neighbor hopping in the square lattice by means of the variational Monte Carlo technique. Specifically, we analyze a wide class of variational wave functions that allow magnetic and superconducting order parameters, so to assess the possibility that superconductivity might emerge close to the magnetic instability, as often observed in heavy fermion systems. Indeed, we do find evidence of d-wave superconductivity in the paramagnetic sector, i.e., when magnetic order is not allowed in the variational wave function. However, when magnetism is allowed, it completely covers the superconducting region, which thus disappears from the phase diagram., Comment: 7 pages and 9 figures

We investigate the phase diagram of an anisotropic ferrimagnet spin-(1/2, 1) in the presence of a non-commuting (transverse) magnetic field. We find a magnetization plateau for the isotropic case while there is no plateau for the anisotropic ferrimagnet. The magnetization plateau can appear only when the Hamiltonian has the U(1) symmetry in the presence of the magnetic field. The anisotropic model is driven by the magnetic field from the N\'{e}el phase for low fields to the spin-flop phase for intermediate fields and then to the paramagnetic phase for high fields. We find the quantum critical points and their dependence on the anisotropy of the aforementioned field-induced quantum phase transitions. The spin-flop phase corresponds to the spontaneous breaking of Z2 symmetry. We use the numerical density matrix renormalization group and analytic spin wave theory to find the phase diagram of the model. The energy gap, sublattice magnetization, and total magnetization parallel and perpendicular to the magnetic field are also calculated. The elementary excitation spectrums of the model are obtained via the spin wave theory in the three different regimes depending on the strength of the magnetic field., Comment: 14 pages, 11 eps figures