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BackgroundBased on the growing number of families and young children with a refugee background in Germany, day-care teachers face enormous challenges regarding culturally informed practice. The project “Gemeinsam stark durch den Start” (Stronger together by starting together) addresses these challenges on various levels. At the level of day-care teachers, training in culturally informed and sensitive education is combined with reflection sessions about their own attitudes and prevailing intercultural norms, thus contributing to the professionalization of day-care teachers.AimThis paper focuses on mechanisms of action that contributed to the effectiveness of the training from two perspectives: the day-care teachers’ perspective and the trainers’ perspective.MethodsStaff members of 11 German day-care centers underwent graded online training sessions (team and in-depths trainings) addressing intercultural topics. All participants were presented with a questionnaire for their training evaluation before and after the training sessions. Also, participants of the in-depths trainings participated in semi-structured interviews on the training. Furthermore, qualitative interviews were conducted with all trainers (N = 4) of the workshops.ResultsDay-care teachers evaluated the online training positively, especially the improvement of professionalization and the implementation of training elements. Results reveal that (work-related) reflexive sessions as well as sessions dealing with the implementation of exercise tools into daily practice were rated as fundamental parts in the training. Teachers from high-risk day-care centers estimated the trainings’ effectiveness lower than those working in low-risk day-care centers. Qualitative data shows that the day-care teachers are in need of (theoretical) knowledge about all training elements and hands-on advice for dealing with specific situations. Especially day-care teachers within a high-risk environment, who already report having an elevated level of intercultural knowledge and skills, may need a higher dose training while low-risk day-care teachers may profit more from a low threshold training.ConclusionThe introduced training sessions focusing on intercultural sensitivity and competence present an important contribution to the professionalization of day-care teachers in working with children from different cultural backgrounds. Trainings should focus on reflexive elements as well as exercises in perspective taking and provide hands on materials for daily work.

The third-body particle-involved sliding contact between two rough rubbers with wavy surfaces is experimentally studied. The experiment is designed to isolate the direct contact between the first bodies so that friction resistance is induced completely by the interactions between the third-body particle and the surfaces of the rubbers. In dry contact of a single particle, it is found that the particle exhibits pure rolling during the sliding of the first bodies, and the macroscopic friction resistance for overcoming sliding does not depend on the particle size, but it is significantly influenced by the initial position of the surface waviness relative to the particle’s position. The behavior of the particle under lubricated conditions exhibited significant differences. Due to the low local friction at the interface, the particle rapidly glided down to the valley of the waviness during compression. This abrupt motion of the particle resulted in it coming to rest in a stable position, awaiting a substantial force to push it forward. The friction resistance in the case with lubrication was found to be independent of the initial position of the waviness, and its value consistently remained at the maximum found in dry contact. Therefore, lubrication actually increases the macroscopic friction resistance. An approximate solution for the specific case of dry contact is proposed to understand the friction behavior.

The complex physics behind electroadhesion-based tactile displays poses an enormous modeling challenge since not only the fingerpad structure with multiple non-linear layers, but also the roughness at the microscopic scale play a decisive role. To investigate tactile perception, a potential model should also offer the possibility to extract mechanical stimuli at the sites of the relevant mechanoreceptors. In this paper, we present a two-scale approach that involves a finite element model (FEM) at the macroscopic scale and a simple bearing area model (BAM) that accounts for the measured roughness on the papillary ridges. Both separate scales couple in an iterative way using the concept of an equivalent air gap. We show that the electroadhesion-induced changes in friction and contact area predicted by the proposed model are in qualitative agreement with recent experimental studies. In a simple example, we demonstrate that the model can readily be extended by a neural dynamics model to investigate the tactile perception of electroadhesion.

A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein–Uhlenbeck processes such that the related bond prices possess affine representations. Also the dynamics of the associated instantaneous forward rate is provided and a condition is derived under which the model can be market-consistently calibrated. The analytical tractability of this model is illustrated by the derivation of an explicit plain vanilla option price formula. With view on practical applications, suitable probability distributions are proposed for the driving jump processes. The paper is concluded by presenting a post-crisis extension of the proposed short and forward rate model.

Due to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, because of the varying material properties, especially the type of in-depth grading of Young’s modulus, the solution of contact problems including the frequently encountered tangential fretting becomes significantly more difficult. The present work is intended to contribute to this context. The partial-slip contact of axisymmetric, power-law graded elastic solids under classical loading by a constant normal force and an oscillating tangential force is investigated both numerically and analytically. For this purpose, a fictitious equivalent contact model in the mathematical space of the Abel transform is used since it simplifies the solution procedure considerably without being an approximation. For different axisymmetric shaped solids and various elastic inhomogeneities (types of in-depth grading), the hysteresis loops are numerically generated and the corresponding dissipated frictional energies per cycle are determined. Moreover, a closed-form analytical solution for the dissipated energy is derived, which is applicable for a breadth class of axisymmetric shapes and elastic inhomogeneities. The famous solution of Mindlin et al. emerges as a special case.

For the steady wear state of two contact problems involving power-law graded materials, closed-form solutions are derived in terms of pressure distribution and limiting shapes of profile. Both gross slip of an initially flat-ended cylindrical punch on a power-law graded half-space and the load-controlled fretting wear under partial slip of an initially parabolic indenter are studied. In the case of gross slip at fixed penetration depth there exists a certain exponent of elastic inhomogeneity, for which the effective volume change takes its maximum value. To minimize wear due to fretting under partial slip, an amplitude dependent design of the material gradient is necessary. For large amplitudes of the tangential force a gradient ranged from a soft surface to a hard ground is beneficial, small amplitudes require a reverse gradient characterized by a hard surface and a soft ground. However, the choice of the material gradient also has a decisive influence on the strength of stress singularities at the contact edge and thus the initiation of fretting fatigue cracks, which is why it is discussed in more detail.

Electrovibration is one of the key technologies in surface haptics. By inducing controlled electrostatic forces, the friction within a sliding contact between the human finger and a capacitive screen is modulated, which in turn gives effective tactile feedback to the user. Such powerful haptic displays can be built into mobile phones, tablets, navigation devices, games consoles and many other devices of consumer electronics. However, due to the layered structure and complex material of human skin, the underlying contact mechanical processes have not yet been fully understood. This work provides new continuum-based approaches to macroscopic modeling of the electro-adhesive frictional contact. A solution of pure normal contact between a human finger and a rigid, smooth plane under electroadhesion is derived by applying Shull's compliance method in the extended regime of large deformations. Based on these results and assuming pressure-controlled friction, a model for the sliding electro-adhesive contact is developed, which adequately predicts the friction force and coefficient of friction over the whole range of relevant voltages and applied normal forces. The experimentally observed area reduction caused by the tangential force is incorporated in a more empirical than profound contact mechanical way. This effect is studied with the help of a two-dimensional finite element model of the fingertip, assuming non-linear elastic material for the skin tissue. Although the simulations are restricted to non-adhesive tangential contacts, they show a significant reduction of the contact area, which is caused by large deformations of the non-linear elastic material around the distal phalanx. This result indicates that adhesion is only of secondary importance for the area reduction.

Until recently the analysis of contacts in tribological systems usually required the solution of complicated boundary value problems of three-dimensional elasticity and was thus mathematically and numerically costly. With the development of the so-called Method of Dimensionality Reduction (MDR) large groups of contact problems have been, by sets of specific rules, exactly led back to the elementary systems whose study requires only simple algebraic operations and elementary calculus. The mapping rules for axisymmetric contact problems of elastic bodies have been presented and illustrated in the previously published parts of The User's Manual, I and II, in Facta Universitatis series Mechanical Engineering [5, 9]. The present paper is dedicated to axisymmetric contacts of viscoelastic materials. All the mapping rules of the method are given and illustrated by examples.

We investigate the pricing of cliquet options in a jump-diffusion model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a drifted Lévy process entailing a Brownian diffusion component as well as compound Poisson jumps. We also derive representations for the density and distribution function of the emerging Lévy process. In this setting, we infer semi-analytic expressions for the cliquet option price by two different approaches. The first one involves the probability distribution function of the driving Lévy process whereas the second draws upon Fourier transform techniques. With view on sensitivity analysis and hedging purposes, we eventually deduce representations for several Greeks while putting emphasis on the Vega.

We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner–Lévy process yielding Meixner distributed log-returns. In this setting, we infer semi-analytic expressions for the cliquet option price by using the probability distribution function of the driving Meixner–Lévy process and by an application of Fourier transform techniques. In an introductory section, we compile various facts on the Meixner distribution and the related class of Meixner–Lévy processes. We also propose a customized measure change preserving the Meixner distribution of any Meixner process.

Due to its high relevance for designing ball joints in mechanical engineering and (artificial) hip joints in biomechanics, the almost conformal elastic contact between a sphere and a spherical cup represents an important contact problem of current research. As no closed-form analytical solution to the problem has been found to date, full computational methods such as the finite element method are needed for analysis. However, they often require incredibly long, unacceptable calculation times, making parameter studies hardly practicable. For this reason, approximate analytical and semi-analytical models are applied, capable of predicting quantities of interest with sufficient accuracy. In the present work, a very simple model based on a radially directed Winkler foundation is presented, which provides (approximate) closed-form analytical solutions for both the pressure distribution and the dependencies between macroscopic contact quantities such as normal force and indentation depth. To ensure an optimal mapping of a specific contact problem, only the foundation modulus must be defined in a suitable way. As an example, the proposed model has been successfully adapted to adequately simulate the frictionless normal contact for hard-on-soft hip implants. For this purpose, the foundation modulus was approximated with the aid of a finite element analysis instead of adopting it from already well-established models, as the latter produce clearly erroneous results for large liner thicknesses and large Poisson’s ratios. By a comparison with extensive parameter studies of finite element simulations, it is demonstrated that the proposed model provides acceptable results for all commonly used hard-on-soft hip implants. On this basis, the influence of geometrical changes of the femoral head and the acetabular cup on the maximum pressure as well as the half-contact angle is discussed, and consequences on the wear behavior are deduced.

Until recently, the only way of solving contact problems was to applythree-dimensional contact theories. However, this presupposes higher mathematical and numerical knowledge, which usually only research groups possess. This has changed drastically with the development of the method of dimensionality reduction (MDR), which allows every practically oriented engineer an access to the solution of contact problems. The simple and contact-type dependent rules are summarized in the first part of the user manual; they require contacts between elastically homogeneous materials. The present paper forms the second part of the user handbook and is dedicated to the solution of contact problems between power-law graded materials. All the MDR-rules are listed with which normal, tangential and adhesive contacts between such high-performance materials can be calculated in a simple manner.

Foreword to the special issue in honor of Prof. Valentin L. Popov

The present analyses empirically explored the roles in cyberbullying by using Latent Class Analysis. Potential predictors of class membership were also examined using multinomial logistic regression analysis. Participants were 849 German students (52.7% girls, 45.6% boys, Mage = 13.4 years, SDage = 1.1 years). Observed indicators of latent class measured own involvement in cyberbullying, reactions to cyberbullying of classmates, and behavioral willingness as assistant and as defender. Indicators for the post-hoc regression analyses were proactive aggression, reactive aggression, self-esteem, cognitive, and affective empathy. Control variables were age and gender. A model with five classes was chosen. The classes were labeled prosocial defenders, communicating outsiders, aggressive defenders, bully-victims, and assistants. The results of the post-hoc regression analyses showed that students in the classes especially differed regarding types of aggression and social competencies. Based on answer patterns, cyberbullying roles beyond the bullying-triad can be found. Remarkably, three of the classes are bystanders, i.e. they are not directly involved in cyberbullying. Two of these classes showed helping behavior and made up almost two thirds of the sample. Knowledge about cyberbullying roles and their predictors is important to inform the planning and development of interventions. The results further indicate that interventions should especially take into account antisocial and passive behavioral patterns in the context of cyberbullying.

Recently the method of dimensionality reduction (MDR) has been introduced to solve axisymmetric contact problems easily and exactly. The list of tasks that this method can deal with comprises normal, tangential, adhesive and rolling contacts with simply connected contact areas between elastic or viscoelastic bodies. Due to its simplicity and easy applicability the MDR provides the possibility of fast and comprehensive studies of contact problems in technological or biological systems, for example bearings, artificial hip joints, wheel-rail systems or others. Within the complicated three-dimensional contact theory those studies, in most cases, cannot be done without a tremendous mathematical or numerical effort. In view of all this, the torsional contact problems have been disregarded until now, although it is known that torsion is a major reason of wear and possible failure of system components. Therefore, in the present paper, we extend the MDR to contacts of axisymmetric profiles under superimposed normal and torsional loading.

For the long-time monitoring of electrocardiograms, electrodes must be skin-friendly and non-irritating, but in addition they must deliver leads without artifacts even if the skin is dry and the body is moving. Today’s adhesive conducting gel electrodes are not suitable for such applications. We have developed an embroidered textile electrode from polyethylene terephthalate yarn which is plasma-coated with silver for electrical conductivity and with an ultra-thin titanium layer on top for passivation. Two of these electrodes are embedded into a breast belt. They are moisturized with a very low amount of water vapor from an integrated reservoir. The combination of silver, titanium and water vapor results in an excellent electrode chemistry. With this belt the long-time monitoring of electrocardiography (ECG) is possible at rest as well as when the patient is moving.

Cyberbullying is a ubiquitous topic when considering young people and internet and communication technologies (ICTs). For interventional purposes, it is essential to take into account the perspective of adolescents. This is the reason why our main focus is (1) investigating the role of different criteria in the perceived severity of cyberbullying incidents, and (2) examining the differences between countries in the perceived severity of cyberbullying. The sample consisted of 1,964 adolescents (48.2% girls) from middle and high schools of four different countries, i.e., Estonia, Italy, Germany, and Turkey. The participants' age ranged from 12 to 20 years old with a mean age of 14.49 (SD = 1.66) years. To assess perceived severity, participants rated a set of 128 scenarios, which systematically included one or more of five criteria (intentionality, repetition, imbalance of power, public vs. private, and anonymity) and represented four types of cyberbullying behaviors (Written—Verbal, Visual, Exclusion, Impersonation). The role of different criteria was analyzed using the Exploratory Structural Equation Modeling (ESEM). Results showed a similar structure across the four countries (invariant except for the latent factors' means). Further, criteria of imbalance of power and, to a lesser extent, intentionality, anonymity, and repetition always in combination, were found to be the most important criteria to define the severity of cyberbullying. Differences between countries highlighted specific features of Turkish students, who perceived all scenarios as more severe than adolescents from other countries and were more sensitive to imbalance of power. German and Italian students showed an opposite perception of anonymity combined with intentionality. For Italian participants, an anonymous attack was less threatening than for participants of other countries, whereas for German students anonymity caused more insecurity and fear. In addition, Italian adolescents were more perceptive of the criterion of intentionality. Finally, Estonian adolescents did not show strong differences in their factor scores compared to adolescents from the other countries.

The Method of Dimensionality Reduction (MDR) is a method of calculation and simulation of contacts of elastic and viscoelastic bodies. It consists essentially of two simple steps: (a) substitution of the three-dimensional continuum by a uniquely defined one-dimensional linearly elastic or viscoelastic foundation (Winkler foundation) and (b) transformation of the three-dimensional profile of the contacting bodies by means of the MDR-transformation. As soon as these two steps are completed, the contact problem can be considered to be solved. For axial symmetric contacts, only a small calculation by hand is required which does not exceed elementary calculus and will not be a barrier for any practically-oriented engineer. Alternatively, the MDR can be implemented numerically, which is almost trivial due to the independence of the foundation elements. In spite of their simplicity, all the results are exact. The present paper is a short practical guide to the MDR.

Due to the growing interest in robotic and haptic applications, voltage-induced friction has rapidly gained in importance in recent years. However, despite extensive experimental investigations, the underlying principles are still not sufficiently understood, which complicates reliable modeling. We present a macroscopic model for solving electroadhesive frictional contacts which exploits the close analogy to classical adhesion theories, like Johnson-Kendall-Roberts (JKR) and Maugis, valid for electrically neutral bodies. For this purpose, we recalculate the adhesion force per unit area and the relative surface energy from electrostatics. Under the assumption of Coulomb friction in the contact interface, a closed form equation for the friction force is derived. As an application, we consider the frictional contact between the fingertip and touchscreen under electrovibration in more detail. The results obtained with the new model agree well with available experimental data of the recent literature. The strengths and limitations of the model are clearly discussed.

Bystanders play a crucial role in aggressive behavior in group contexts. Cyberbystanders can react in proactive ways such as assisting a cyberbully or defending the victim. Since school relationships spill over to the online world, the school context is likely to influence students' online behavior. In the present study, we examine the influence of school climate on active cyberbystanding behavior beyond the influence of individual social competences. Participants were 726 students from a more comprehensive study, who were classified as non-victims and non-bullies (i.e., pure bystanders). They were from 36 classes in five schools in Germany (Grades 7-10; M[subscript age] = 13.37 years, SD[subscript age] = 1.01 years, 53.3% female). Two hypothetical scenarios were used to operationalize active bystanding: one for assisting in cyberbullying and one for defending the cybervictim. Separate multilevel analyses were conducted to predict assisting in cyberbullying and defending the victim on the individual level, respectively. Individual-level independent variables were affective and cognitive empathy. Class-level independent variables were assessed with six subscales of the Inventory of School Climate (ISC-S; Brand et al. 2003). Age, gender, class-level offline and online bullying, and offline and online victimization were controlled for. Results showed cognitive and affective empathy, lack of positive peer interactions, and offline bullying to predict assisting. Defending was predicted by cognitive and affective empathy, lack of safety problems, and teacher support. School plays a role in students' online bystander behavior and interventions should aim to foster a supportive school climate.