International Schools as Models for Educators to Dismantle Oppression and Promote Social Justice

International-mindedness is a strategy employed by international schools (IS) to create environments successfully promoting social justice, cultural diversity, and tolerance. The composition of the student body forces accommodation and assimilation of multiple cultures, backgrounds, and languages into one location or contact zone. The purpose of the study is to understand how IS navigate, manage, and lead educators and students from different races, genders, religions, and socioeconomic statuses by promoting equity and creating an environment with zero tolerance for discrimination. However, social justice gaps in education in general still exist, and practical applications and strategies to embrace diversity and equalize the marginalized are lacking. This chapter provides strategies as to how educators worldwide can benefit from approaches used by IS for social justice and tangible strategies used by IS to promote ethical-international-mindedness and decrease discrimination.

Higher-order synchronization on the sphere

We construct a system of $N$ interacting particles on the unit sphere $S^{d-1}$ in $d$-dimensional space, which has $d$-body interactions only. The equations have a gradient formulation derived from a rotationally-invariant potential of a determinantal form summed over all nodes, with antisymmetric coefficients. For $d=3$, for example, all trajectories lie on the $2$-sphere and the potential is constructed from the triple scalar product summed over all oriented $2$-simplices. We investigate the cases $d=3,4,5$ in detail, and find that the system synchronizes from generic initial values, for both positive and negative coupling coefficients, to a static final configuration in which the particles lie equally spaced on $S^{d-1}$. Completely synchronized configurations also exist, but are unstable under the $d$-body interactions. We compare the relative effect of $2$-body and $d$-body forces by adding the well-studied $2$-body interactions to the potential, and find that higher-order interactions enhance the synchronization of the system, specifically, synchronization to a final configuration consisting of equally spaced particles occurs for all $d$-body and $2$-body coupling constants of any sign, unless the attractive $2$-body forces are sufficiently strong relative to the $d$-body forces. In this case the system completely synchronizes as the $2$-body coupling constant increases through a positive critical value, with either a continuous transition for $d=3$, or discontinuously for $d=5$. Synchronization also occurs if the nodes have distributed natural frequencies of oscillation, provided that the frequencies are not too large in amplitude, even in the presence of repulsive 2-body interactions which by themselves would result in asynchronous behaviour.

Interactions between Two Deformable Droplets in Tandem Fixed in a Gas Flow Field of a Gas Well

Knowing the droplet-deformation conditions, the droplet-breakup conditions, and the drag force in the interaction between two droplets with a high Reynolds number is of importance for tracking droplet movement in the annular flow field of a gas well. The interactions between two droplets with a high Reynolds number in a tandem arrangement fixed in flowing gas was investigated. The volume of fluid (VOF) method was used to model the droplets’ surface structure. Two different body forces were exerted on both droplets to hold them suspended at a fixed location, which eliminated the effect of droplet acceleration or deceleration on the drag and decreased the amount of computation required. The exerted body forces were calculated using the Newton iteration procedure. The interactions between the two droplets were analyzed by comparison with the simulation results of a single isolated droplet. The effect of the separation distance on the drag force was investigated by changing the separation spacing. The simulation results showed that for droplets with a small separating space between them, the dynamics of the downstream droplet were influenced significantly by the upstream droplet. The drag coefficient of the downstream droplet decreased considerably to a small, even negative, value, especially for droplets with higher Weber numbers and smaller initial separating spaces between them, while the drag force of the upstream droplet was influenced only slightly. In addition, a formula for predicting the final drag coefficient of the downstream droplet was devised.

Isogeometric shape optimization for design dependent loads

This paper presents a new isogeometric formulation for shape optimization of structures subjected to design dependent loads. This work considers two types of design dependent loads, namely surface loads like pressure where the direction and/or magnitude of force changes with the variation of boundary shape, and body forces that depend on the material layout. These problems have been mostly solved by topology optimization methods which are prone to difficulties in determination of the loading surface for pressure loads and problems associated with non-monotonous behaviour of compliance and low density regions for body forces. This work uses an isogeometric shape optimization approach where the geometry is defined using NURBS and the control point coordinates and control weights of the boundary are chosen as design variables. This approach accommodates the design dependent loads easily, in addition to its other advantages like exact geometry representation, local control, fewer design variables, excellent shape sensitivity, efficient mesh refinement strategies, and smooth results that can be integrated with CAD. Two classes of optimization problems have been discussed, they are minimum compliance problems subject to volume constraint and minimum weight problems subjected to local stress constraints. These problems are solved using convex optimization programs. Hence, expressions for full sensitivities are derived which is new for structural shape optimization problems with design dependent loads. Some representative engineering examples are solved and compared with existing literature to demonstrate the application of the proposed method.

The validity of using one force platform to quantify whole-body forces, velocities, and power during a plyometric push-up

Background Previous studies have typically measured velocity and power parameters during the push-up, either using one or two force platforms. The purpose of the study was to compare the force, velocity, and power parameters between the one-force-platform method and the two-force-platform method during plyometric push-ups. Methods Thirty-four physically active young adults participated in the study to perform the plyometric push-up. For the two-force-platform calculation method, the forces applied to the feet and hands were both measured. For the one-force-platform calculation method, the forces applied to the feet were assumed to be constant, while the forces applied to hands were measured by one force platform. Whole-body linear velocities were calculated based on the impulse and momentum theorem. Whole-body power was calculated as the product of the whole-body forces and velocities. Results The one-force-platform method overestimated the whole-body velocities and power compared with the two-force-platform method (1.39 ± 0.37 m/s vs. 0.90 ± 0.23 m/s, Cohen’s d = 1.59, p < 0.05; 1.63 ± 0.47 W/body weight vs. 1.03 ± 0.29 W/body weight, Cohen’s d = 1.49, p < 0.05). These differences were caused by the decreased forces applied to the feet compared to the initial value throughout most of the push-up phase. Large to perfect correlations (r = 0.55 – 0.99) were found for most variables between the two-force-platform and one-force-platform methods. Previous findings of push-up velocities and power using the two-force-platform and one-force-platform methods should be compared with caution. While the two-force-platform method is recommended, linear regression equations may be used to predict velocities and power parameters obtained from one force platform. Conclusions For those professionals who need to accurately quantify kinetic variables during the plyometric push-up, the two-force-platform method should be considered.