Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems

We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverge is the same as the value given by the frequency map analysis for the break-up of invariant tori. Furthermore, we obtain by these methods numerical values of the threshold of the break-up of the last invariant torus.Comment: 18 pages, 4 figure

Low Dose of Bisphosphonate Enhances Sclerostin Antibody‐Induced Trabecular Bone Mass Gains in Brtl/+ Osteogenesis Imperfecta Mouse Model

Osteogenesis imperfecta (OI) is a genetic disorder characterized by altered bone quality and imbalanced bone remodeling, leading to skeletal fractures that are most prominent during childhood. Treatments for OI have focused on restoring pediatric bone density and architecture to recover functional strength and consequently reduce fragility. Though antiresorptive agents like bisphosphonates (BPs) are currently the most common intervention for the treatment of OI, a number of studies have shown efficacy of sclerostin antibody (SclAb) in inducing gains in bone mass and reducing fragility in OI mouse models. In this study, the effects of the concurrent use of BP and SclAb were evaluated during bone growth in a mouse harboring an OI‐causing Gly→Cys mutation on col1a1. A single dose of antiresorptive BP facilitated the anabolic action of SclAb by increasing availability of surfaces for new bone formation via retention of primary trabeculae that would otherwise be remodeled. Chronic effects of concurrent administration of BP and SclAb revealed that accumulating cycles conferred synergistic gains in trabecular mass and vertebral stiffness, suggesting a distinct advantage of both therapies combined. Cortical gains in mass and strength occurred through SclAb alone, independent of presence of BP. In conclusion, these preclinical results support the scientific hypothesis that minimal antiresorptive treatment can amplify the effects of SclAb during early stages of skeletal growth to further improve bone structure and rigidity, a beneficial outcome for children with OI. © 2018 American Society for Bone and Mineral Research.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144688/1/jbmr3421.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144688/2/jbmr3421_am.pd

Comparative analysis of the sustainability and seismic performance of a social interest house using RC moment frames and bahareque as structural systems

This study compares the seismic performance and environmental impact of a social housing structure designed with reinforced concrete with a structure using Guadua angustifolia “Kunth” cane. The aim is to contrast the implementation of an ecological material such as the Guadua cane, which is an accessible alternative due to its cost and construction time, versus the traditional reinforced concrete (RC) construction method. Both applied to social housing structures. The seismic performance of both methods is analyzed through nonlinear static analysis (pushover) with the objective of establishing the performance; structural and nonstructural damage, performance point, maximum displacements, and structural elements that induce structural failure; and acting forces, against a design earthquake (established by the NEC DS 2015 Standard), with a return period of 475 years. The environmental impact is evaluated through a life cycle assessment of the structure (LCA). Thus, the embodied carbon obtained from each structural element (foundations, beams, columns, floors, and roof support elements) was determined, considering material manufacturing, transportation, and construction. The results obtained demonstrated a higher seismic performance, with 70% less environmental impact on the Guadua cane structure