Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof

In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with the XXZ spin-$\frac12$ chain on the segment with two generic integrable boundaries acting on the Bethe vector. The essential step is to prove that the expression of the action of a modified creation operator on the Bethe vector has an off-shell structure which results in an inhomogeneous term in the eigenvalues and Bethe equations of the corresponding transfer matrix.Comment: V2 published version, 16 page

Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators

Increasing damage tolerance in composites using hierarchical brick-and-mortar microstructures

Composites are attractive materials because of their high specific stiffness and specific strength, but their application in industry is restricted by their inherent lack of damage tolerance and stable energy dissipation mechanisms, due to the brittleness of the fibres. Nature overcomes a similar issue by arranging natural composites, made of mostly brittle constituents, in discontinuous and hierarchical microstructures. This work aims at evaluating the potential of hierarchical discontinuous carbon-fibre reinforced polymers to achieve damage tolerance, by a combination of modelling and experiments. Two different models (one analytical and the other numerical) are developed to predict the tensile response of hierarchical brick-and-mortar microstructures with two levels of hierarchies, and to design specimens with a non-linear response. Such specimens are then manufactured using laser micro-milled carbon/epoxy thin-plies, and tested under tension. The results show that the presence of discontinuities and hierarchies promotes stable energy dissipation before failure, ensures damage diffusion throughout the specimen, and delays damage localisation in otherwise brittle composites

Duration of Low Wage Employment: A Study Based on a Survival Model

This paper includes a survival analysis which attempts to explain the duration, as in the number of years a worker remains in a low wage situation. Explanatory variables take into account the characteristics of the employee, such as education, age, tenure with the company, gender and nationality, and the characteristics of the job and the company such as industry affiliation, number of employees, age of the company and location.low wage, survival, Portugal

Disc mechanical characteristics : construction of a finite element mathematical model, first results

Computational mechanics is an invaluable tool to analyze biomechanical systems, either in healthy or degenerative conditions, and to improve our understanding on the events that can trigger trauma or diseases, to design new medical devices to restore working conditions, or even to point out treatment techniques. Numerical methods in general, and the Finite Elements Analysis (FEA) in particular, if properly built and used, can allow an inside view, a rigorous analysis and a qualitative study of any assumption, frequently too much difficult or even impossible to achieve with any in-vivo or in-vitro experimental technique. An Intervertebral Disc (IVD) is a functionally-oriented construction of several soft tissues, supporting a wide range of dynamic and static loads that generate complex stress fields, which experimental study and understanding of its biomechanical behavior is of an enormous complexity. On the one hand, human’s in-vivo study is almost impossible – due to the high degree of uncertainty in applied loads, geometric variability of individuals, complex surrounding musculoskeletal interactions, the role played by electro-chemical phenomena like osmolarity, etc – and post-mortem studies hardly provides accurate information to allow a clear and precise characterization and transposition to in-vivo biomechanics. On the other hand, due to that intrinsic complexity of the IVD, an accurate biomechanical model cannot easily be achieved. It is rather a step-by-step task where, although there are still many open questions, an important effort is being done to bring to the FEA the multi-physics behavior, and the complex interactions between them, in order to accurately model the IVD’s constitutive performance. This work is focused in the most relevant issues and phenomena that shall be taken into account in the development of an accurate biomechanical FEA model of the IVD, either in healthy or degenerated states