Solving two-dimensional coupled Burgers equations via a stable hybridized discontinuous Galerkin method

The purpose of this paper is to design a fully discrete hybridized discon-tinuous Galerkin (HDG) method for solving a system of two-dimensional (2D) coupled Burgers equations over a specified spatial domain. The semi-discrete HDG method is designed for a nonlinear variational formulation on the spatial domain. By exploiting broken Sobolev approximation spaces in the HDG scheme, numerical fluxes are defined properly. It is shown that the proposed method is stable under specific mild conditions on the stabi-lization parameters to solve a well-posed (in the sense of energy method) 2D coupled Burgers equations, which is imposed by Dirichlet boundary conditions. The fully discrete HDG scheme is designed by exploiting the Crank–Nicolson method for time discretization. Also, the Newton–Raphson method that has the order of at least two is nominated for solving the obtained nonlinear system of coupled Burgers equations over the rect-angular domain. To reduce the complexity of the proposed method and the size of the linear system, we exploit the Schur complement idea. Numerical results declare that the best possible rates of convergence are achieved for approximate solutions of the 2D coupled Burgers equations and their first-order derivatives. Moreover, the proposed HDG method is examined for two other types of systems, that is, a system with high Reynolds numbers and a system with an unavailable exact solution. The acceptable results of examples show the flexibility of the proposed method in solving various problems

Foot and ankle biomechanics during walking in older adults : a systematic review and meta-analysis of observational studies

The foot and ankle complex undergoes significant structural and functional changes with advancing age. The objective of this systematic review and meta-analysis was to synthesize and critique the research literature pertaining to foot and ankle biomechanics while walking in young and older adults. Electronic databases (Web of Science, PubMed, Scopus and Embase) were searched from inception to April 2019 for cross-sectional studies which compared kinematics, kinetics and plantar pressure differences between young and older adults. Screening and data extraction were performed by two independent assessors, with disagreements resolved by consensus. A total of 39 articles underwent full-text screening, and 19 articles met the inclusion criteria and were included. Meta-analysis showed that older adults had less ankle joint plantar flexion (5 studies; weighted mean difference [WMD]: -5.15; 95 %CI: -6.47 to -3.83; P < 0.001) and less ankle joint power generation (6 studies; standardized mean difference [SMD]: -0.62; 95 %CI: -0.82 to -0.41; P < 0.001) during propulsion compared to young adults. These differences persisted in subgroup analyses comparing different walking speeds. Plantar pressure findings were highly variable due to differences in data collection protocols and meta-analysis was not possible. Older adults have unique foot and ankle kinematics and kinetics during walking characterized by reduced ankle joint plantarflexion and power generation during propulsion. [Abstract copyright: Copyright © 2021 Elsevier B.V. All rights reserved.

Design for Ukraine’s heritage: engaging international students during times of war through design activism

The Russian invasion of Ukraine - which began in February 2022 - has caused, and continues to inflict, a substantial number of deaths and destruction of buildings, including museums, cultural institutions, and heritage. Despite the instruments of international law put in place to protect cultural heritage, alarming reports of the removal and displacement of museums’ collections from occupied areas continue to emerge. In the amid of this complex context, how can design researchers and educators prompt students towards the development of contributions for emergencies such as war? Can digital platforms be used to support such development? And how can these technologies be employed to safeguard and raise awareness about at-risk heritage? Drawing from the legacy of design activism and socially responsible design, the research aims to provide an answer to these questions, presenting the results of the Design for Ukraine’s Heritage (D4UH) experience. D4UH is an educational project, the first step of a broader strategy that has the goal of creating a network of European institutions and NGOs to envision and develop possible solutions to safeguard the Ukrainian museums’ heritage during and after times of war. D4UH pairs 20 Ukrainian museums with 20 international students from architecture and design schools, united by the desire to give support to the Ukrainian heritage. Partners, students and museums are asked to collaborate in the collection of videos, pictures and interviews to design the Virtual Museum of Ukrainian Museums, which acts as a statement of Ukrainian museums’ current situation. Offering the chance of engaging, researching, curating and designing the virtual exhibition’s narrative space, students and design educators can directly experience how the action of designing can tackle intricate cultural, social and political issues. The expected results of the project are, in fact, not merely to exhibit Ukrainian cultural heritage, but also to consider the relevance of museum institutions themselves as guardians of temporality to be interpreted and protected, especially in times of war, because of their contribution to the community’s progress