Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals

We analyze the radially symmetric solution corresponding to the vortex defect (the so-called melting hedgehog) in the Landau–de Gennes theory for nematic liquid crystals. We prove the existence, uniqueness and stability results of the melting hedgehog.     

Partial regularity and smooth topology-preserving approximations of rough domains

For a bounded domain \(\Omega \subset {\mathbb R}^m, m\ge 2,\) of class \(C^0\), the properties are studied of fields of ‘good directions’, that is the directions with respect to which \(\partial \Omega \) can be locally represented as the graph of a continuous function. For any such domain there is a canonical smooth field of good directions defined in a suitable neighbourhood of \(\partial \Omega \), in terms of which a corresponding flow can be defined. Using this flow it is shown that \(\Omega \) can be approximated from the inside and the outside by diffeomorphic domains of class \(C^\infty \). Whether or not the image of a general continuous field of good directions (pseudonormals) defined on \(\partial \Omega \) is the whole of \(S^{m-1}\) is shown to depend on the topology of \(\Omega \). These considerations are used to prove that if \(m=2,3\), or if \(\Omega \) has nonzero Euler characteristic, there is a point \(P\in \partial \Omega \) in the neighbourhood of which \(\partial \Omega \) is Lipschitz. The results provide new information even for more regular domains, with Lipschitz or smooth boundaries.     

Orientability and Energy Minimization in Liquid Crystal Models

Uniaxial nematic liquid crystals are modelled in the Oseen–Frank theory through a unit vector field n. This theory has the apparent drawback that it does not respect the head-to-tail symmetry in which n should be equivalent to ?n. This symmetry is preserved in the constrained Landau–de Gennes theory that works with the tensor \({Q=s \left(n\otimes n-\frac{1}{3} Id\right)}\). We study the differences and the overlaps between the two theories. These depend on the regularity class used as well as on the topology of the underlying domain. We show that for simply-connected domains and in the natural energy class W^1,2 the two theories coincide, but otherwise there can be differences between the two theories, which we identify. In the case of planar domains with holes and various boundary conditions, for the simplest form of the energy functional, we completely characterise the instances in which the predictions of the constrained Landau–de Gennes theory differ from those of the Oseen–Frank theory.     

The benefits of training with vibration in stabilizers and postural human muscle strengthening

The mechanical vibrations have been perceived as unhealthy, although in some circunstances these may lead to a human body fortification. The trainings that use the vibrating stimulus have certain advantages to the classical trainings. Stabilizers and postural muscles are less visible, being hidden by large muscle groups and have little growth potential. For this reason most types of training does not focus on training and strengthening them. This article presents the advantages of training muscular groups of the vertebral column performed on vibrating plates. This type of training has the advantage that besides the requiring to all muscles in where the vibratory stimulus reaches, leads to an increase flexibility of joints. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Refined approximation for minimizers of a Landau-de Gennes energy functional

We study minimizers of a Landau-de Gennes energy functional in the asymptotic regime of small dimensionless elastic constant L > 0. The results on the convergence to a minimizer of the limit Oseen-Frank functional in Majumdar and Zarnescu (Arch Ration Mech Anal 196:227–280, 2010) are revisited and improved, which in effect lead to a sharp rate of convergence. The equation for the first-order correction term is derived: it has a “normal component” given by an algebraic relation and a “tangential component” given by a linear system.     

The frequency transfer function corresponding to hand-arm system

The paper presents a study regarding the frequency transfer function corresponding to hand-arm system. Theoretical the frequency transfer function obtains applying the Laplace function for the differential equations of moving system. This is a part of the study regarding the mechanical vibrations action over the hand-arm system. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Research about transmission of the mechanical vibration done by machine-tools on the group of bones shoulder-neck-head

Different researches have shown that long–term exposure to whole–body vibration can induce different injuries like back pain, injuries of the different part of the body, disturbing the physical and intellectual activities. The resulted diseases could be occasional or could be for ever. Bearing in mind that vibration is applied on the hand or feet, the health rick can be assessed if the forces transmitted in the shoulder during vibration are known. To estimate the forces a biomechanical model has been developed in which the shoulder, neck and head are represented by rigid bodies. The bodies are connected by visco–elastic joint elements. The applied forces are resulted from experimental measurements. To assess the health risk the forces must be divised in two components, an ascendant one and a descendent one. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Mechanical Stability for the Hand-Arm System

The present paper contains a study regarding importance stability in the mechanical systems, mechanical systems are emerging under mechanical vibrations action, it referring especially to the human hand–arm system. Mechanical systems stability is directly influenced of the dumper and the elasticity factors. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibrating Portable Machine-Tools Acting on Human Operator

This paper will be a short presentation of the specialized literature and international standards about the importance of vibration action of portable machine tools on human body and particularly on the hand-arm system. Exposure to harmful vibrations can lead to health problems and disorders, especially in the upper joints and dorsal region of the human body. A detailed understanding of the undesirable effects of vibration on the human body is essential to achieve administrative and technical prevention. In modern times, vibration studies become more frequent, decisive for the many machines, vehicles and construction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)