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The modeling of magnetostrictive effects is a topic of intensive research. The authors' goal is the precise modeling and numerical simulation of the magnetic field and resulting mechanical vibrations caused by magnetostriction along the joint regions of electric transformers.

The authors apply the finite element (FE) method to efficiently solve the arising coupled system of partial differential equations describing magnetostriction. Hereby, they fully take the anisotropic behavior of the material into account, both in the computation of the nonlinear electromagnetic field as well as the induced magnetostrictive strains. To support their material models, the authors measure the magnetic as well as the mechanical hysteresis curves of the grain-oriented electrical steel sheets with different orientations (w.r.t the rolling direction). From these curves they then extract for each orientation the corresponding commutation curve, so that the hysteretic behavior is simplified to a nonlinear one.

The numerical simulations show strong differences both in the magnetic field as well as mechanical vibrations when comparing this newly developed anisotropic model to an isotropic one, which just uses measured curves in rolling direction of the steel sheets. Therefore, a realistic modeling of the magnetostrictive behavior, especially for grain-oriented electrical steel as used in transformers, needs to take into account the anisotropic material behavior.

The authors have developed an enhanced material model for describing magnetostrictive effects along the joint regions of electric transformers, which fully considers the anisotropic material behavior. This model has been integrated into a FE scheme to numerically simulate the mechanical vibrations in transformer cores caused by magnetostriction.

The fast and flexible development of fast switching electromagnetic valves as used in modern gasoline engine demands the availability of efficient and accurate simulation tools. The purpose of this paper is to provide an enhanced computational scheme of these actuators including all relevant physical effects of magneto‐mechanical systems and including contact mechanics.

The finite element (FE) method is applied to efficiently solve the arising coupled system of partial differential equations describing magneto‐mechanical systems. The algorithm for contact mechanics is based on the cross‐constraint method using an energy‐ and momentum‐conserving time‐discretisation scheme. Although solving separately for the electromagnetic and mechanical system, a strong coupling is ensured within each time step by an iterative process with stopping criterion.

The numerical simulations of the full switching cycle of an electromagnetic direct injection valve, including the bouncing during the closing state, are just feasible with an enhanced and robust mechanical contact algorithm. Furthermore, the solution of the nonlinear electromagnetic and mechanical equations needs a Newton scheme with a line search scheme for the relaxation of the step size.

The paper provides a numerical simulation scheme based on the FE method, which includes all relevant physical effects in magneto‐mechanical systems, and which is robust even for long‐term contact periods with multitude re‐opening phases.

Magnetostrictive alloys are widely used in actuator and sensor applications. The purpose of this paper is to developed a realistic physical model and a numerical computational scheme for their precise computation.

The main step in the physical modeling is the decomposition of the mechanical strain and the magnetic induction into a reversible and an irreversible part. For the efficient solution of the arising coupled nonlinear partial differential equations the authors apply the finite element method.

It can be demonstrated, that the hysteresis operators can be fitted by appropriate measurements. Therewith, the developed physical model and numerical simulation scheme is applicable for the design of magnetostrictive actuators and sensors.

The decomposition of the mechanical strain and the magnetic induction into a reversible and an irreversible part. The reversible part is described by the linear magnetostrictive constitutive equations, where the entries of the coupling tensor depend on the magnetization. The irreversible part of the magnetic induction is modeled by a Preisach hysteresis operator, and the irreversible part of the mechanical strain by a polynomial function depending on the magnetization.

Inhibitory control (IC) is a central executive function that shows significant development throughout the preschool years. IC is known as a factor that underlies the ability to self-regulate in daily situations. This ability is challenged when a child faces negative emotions; a challenge that is seen in children’s IC performance and brain activity. This chapter elaborates on the effects that negative emotional experiences have on children’s IC functioning. Moreover, previous studies regarding the way emotional experiences are reflected in brain activity are included. Additionally, this chapter will offer a comprehensive review of the factors affecting individual differences in IC, including the role of children’s temperamental effortful control and negative affectivity. Further, the role of parenting behaviors will be discussed, focusing on the way in which maternal self-regulation influences child inhibitory control, including related educational implications.

This paper presents a 2D nonlinear magnetomechanical analysis of an electromagnetic actuator based on finite elements. An impact mechanical problem with its inherent convergence problems has to be solved inside the magnetic field region. Beside material and geometric nonlinearities also dynamic effects like eddy currents are considered.

Psychotherapy and clinical supervision outcomes are influenced by client and supervisee factors, one of which is cultural identity. Those with diverse racial and ethnic minoritised identities often experience disparities in therapy outcomes. Therapists and supervisors need to be responsive to the identity of those they support. The multicultural orientation (MCO) framework is an emerging concept in psychotherapy and clinical supervision that may offer these practitioners a framework to be responsive.

A preferred reporting items for systematic reviews and meta-analyses extension for scoping reviews was conducted. Six databases, PubMed, Scopus, Embase, Academic Search Complete, Web of Science and PsychInfo, were searched for peer-reviewed literature published in English between the years 2000 and 2023.

A total of 1,553 sources were identified, of which (n = 42) are included in this review. Findings suggest that MCO is still in its infancy as applied to therapy and clinical supervision. Most of the research has been conducted in America, using quantitative methodologies with white western populations. Cultural humility is the most studied MCO pillar, and variables such as reductions in psychological stress, the working alliance and microaggressions are reported on as outcomes. MCO applied to the group therapy process is an emerging finding of interest. However, more research is needed, especially experiential designs across different and diverse populations and contexts.

MCO is an emerging therapy and clinical supervision process that has the potential to improve the outcomes for therapy clients and supervisees. Further research is needed to replicate current studies, and further research with diverse populations, countries and contexts should be undertaken as a priority.

The purpose of this paper is to propose a solution strategy for both accurate and efficient simulation of nonlinear magnetostatic problems in thin structures using higher order finite element methods. Special interest is put in the investigation of the step-lap joints of transformer cores, with a focus on the spatial resolution of the field quantities.

The usage of hierarchical finite elements of higher order makes it possible to adapt the local accuracy in different spatial directions in thin steel sheets. Due to explicit representation of gradients in the basis functions, a simple Schwarz-type block preconditioner with a conjugate gradient solver can efficiently solve the arising algebraic system. By adapting the block size automatically according to the aspect ratio, deterioration of convergence in case of thin elements can be prevented. The resulting Newton scheme is accelerated utilizing the hierarchical splitting in a two-level scheme, where an initial guess is computed on a coarse sub-space.

Compared to an isotropic choice of polynomial order for the basis functions, significant runtime and memory can be saved in the simulation of thin structures without losing accuracy. The iterative solution scheme proves to be robust with respect to the polynomial order, even for aspect ratios of 1:1000 and anisotropies in two directions. An additional saving in runtime and Newton iterations can be achieved by solving the nonlinear problem initially on the lowest order basis functions only and projecting the solution to the complete space as starting value, analogous to a full multigrid scheme.

Within the presented solution strategy, especially the anisotropic block preconditioner and the accelerated Newton scheme based on the two-level splitting constitute a novel contribution. They provide building blocks, which can be utilized for other types of magnetic field problems like transient nonlinear problems or hysteresis modeling as well.