Weak gravitational fields

This is the published version, also available here: http://dx.doi.org/10.1063/1.1666824.We consider the set of Ck bounded tensor fields of type (r,s) on R 4 in the topology of uniform Ck convergence. For each k≥2, the map sending a metric to its curvature tensor is shown to be analytic at the Minkowski metric. The same is true of the map sending a metric to its Einstein tensor. The well‐known linearized theory of gravitation amounts to studying the directional derivatives of these maps. An iterative method for solving the full field equations along an analytic curve of Einstein tensors passing through zero is proposed

From Foreign Text to Local Meaning: The Politics of Religious Exclusion in Transnational Constitutional Borrowing

Constitutional drafters often look to foreign constitutional models, ideas, and texts for inspiration; many are explicit about their foreign borrowing. However, when implemented domestically, the meaning of borrowed elements often changes. Political scientists and scholars of comparative constitutional law have analyzed the transnational movement of constitutional ideas and norms, but the political processes through which the meaning of foreign provisions might be refashioned remain understudied. Socio-legal scholars have examined the “transplantation” and “translation” of laws and legal institutions, but they rarely scrutinize this process in the context of constitutions. Drawing on an examination of borrowed constitutional elements in four cases (Pakistan, Morocco, Egypt, Israel), this article builds on research in comparative politics, comparative constitutional law, and socio-legal studies to provide a nuanced picture of deliberate efforts to import “inclusive” constitutional provisions regarding religion-state relations while, at the same time, refashioning the meaning of those provisions in ways that “exclude” specific forms of religious, sectarian, doctrinal, or ideological diversity. Building on socio-legal studies regarding the translation of law, we argue that foreign constitutional elements embraced by politically embedded actors are often treated as “empty signifiers” with meanings that are deliberately transformed. Tracing the processes that lead political actors to engage foreign constitutional elements, even if they have no intention of transplanting their prior meaning, we highlight the need for detailed case studies to reveal both the international and the national dynamics that shape and re-shape the meaning of constitutions today

Human knee joint finite element model using a two bundle anterior cruciate ligament: Validation and gait analysis

Anterior cruciate ligament (ACL) deficient individuals are at a much higher risk of developing osteoarthritis (OA) compared to those with intact ACLs, likely due to altered biomechanical loading [1]. Research indicates the ACL is comprised of two “bundles”, the anteromedial (AM) and posterolateral (PL) bundles [2]. Although the function of both bundles is to restrain anterior tibial translation (ATT), each bundle has their own distinct range of knee flexion where they are most effective [3]. Articular cartilage contact stress measurements are difficult to measure in vivo. An alternative approach is to use knee joint finite element models (FEMs) to predict soft tissue stresses and strains throughout the knee. Initial and boundary conditions for these FEMs may be determined from knee joint kinematics estimated from motion analysis experiments. However, there is a lack of knee joint FEMs which include both AM and PL bundles to predict changes to articular cartilage contact pressures resulting from ACL injuries. The purpose of this study is to develop and validate a knee joint FEM using both AM and PL bundles and subsequently perform a gait analysis of varying ACL injuries

Development of a human knee joint finite element model to investigate cartilage stress during walking in obese and normal weight adults

Osteoarthritis (OA) is a degenerative condition characterized by the breakdown and loss of joint articular cartilage. While the cause of OA is not precisely known, obesity is a known risk factor [1]. Particular effort has gone towards understanding the relationship between obesity and knee OA because obesity is more strongly linked to OA at the knee than at any other lower extremity joint [2]. Although the relationship between obesity and knee OA is well established, the mechanism of pathogenesis is less understood. Excess body weight generates greater joint contact forces at the knee. However, obese individuals alter their gait, resulting in increased joint contact forces that are not proportional to body mass [3]. In this study, a partially validated knee joint finite element (FE) model was developed to predict cartilage loading during walking across individuals of varying adiposity. The model was used with kinematic and kinetic gait data to address the following hypotheses: 1) increased loading due to obesity will produce greater cartilage stress compared to the normal weight control; and 2) altered gait kinematics of obese individuals will alter the distribution of stress on the surface of the tibial cartilage