On an atom with a magnetic quadrupole moment in a rotating frame

The quantum description of an atom with a magnetic quadrupole moment in the presence of a uniform effective magnetic field is analysed. The atom is also subject to rotation and a scalar potential proportional to the inverse of the radial distance. It is shown that the spectrum of energy is modified, in contrast to the Landau-type levels, and there is a restriction on the possible values of the cyclotron frequency which stems from the influence of the rotation and scalar potential proportional to the inverse of the radial distance.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1705.0819

Multiobjective analysis for the design and control of an electromagnetic valve actuator

The electromagnetic valve actuator can deliver much improved fuel efficiency and reduced emissions in spark ignition (SI) engines owing to the potential for variable valve timing when compared with cam-operated, or conventional, variable valve strategies. The possibility exists to reduce pumping losses by throttle-free operation, along with closed-valve engine braking. However, further development is required to make the technology suitable for accept- ance into the mass production market. This paper investigates the application of multiobjective optimization techniques to the conflicting objective functions inherent in the operation of such a device. The techniques are utilized to derive the optimal force–displacement characteristic for the solenoid actuator, along with its controllability and dynamic/steady state performance

Young Measures Generated by Ideal Incompressible Fluid Flows

In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech. Ana

Improved thermal isolation of silicon suspended platforms for an all-silicon thermoelectric microgenerator based on large scale integration of Si nanowires as thermoelectric material

Special suspended micro-platforms have been designed as a part of silicon compatible planar thermoelectric microgenerators. Bottom-up grown silicon nanowires are going to bridge in the future such platforms to the surrounding silicon bulk rim. They will act as thermoelectric material thus configuring an all-silicon thermoelectric device. In the new platform design other additional bridging elements (usually auxiliary support silicon beams) are substituted by low conductance thin film dielectric membranes in order to maximize the temperature difference developed between both areas. These membranes follow a sieve-like design that allows fabricating them with a short additional wet anisotropic etch step. © Published under licence by IOP Publishing Ltd.Peer ReviewedPostprint (published version

Mathematical model for the assessment of fracture risk associated with osteoporosis

Osteoporosis is a skeletal disease characterized by low bone mass. It is considered a worldwide public health problem that affects a large number of people, in particularly for women with more than 50 years old. The occurrence pattern of osteoporosis in a population may be related to several factors, including socio-economic factors such as income, educational attainment, and factors related to lifestyle such as diet and physical activity. These and other aspects have increasingly been identified as determining the occurrence of various diseases, including osteoporosis. This work proposes a mathematical model that provides the level of osteoporosis in the patient. Preliminary numerical results are presented.The authors would like to thank the financial support from FEDER COMPETE and FCT Project FCOMP-01-0124-FEDER-022674

Una propuesta para la enseñanza y el aprendizaje de los sistemas de numeración

En este artículo se exponen algunas reflexiones sobre la enseñanza y el aprendizaje de las matemáticas escolares de grado sexto. Dichas reflexiones se refieren específicamente a la experiencia vivida al planear, diseñar y desarrollar una unidad temática sobre los sistemas de numeración, para estudiantes de grado sexto del colegio

Quantitative Evaluation of Particle Morphology

In geomechanics research shape is most often qualitatively assessed. Various definitions on how to quantify shape have been applied in the literature. This paper assesses the feasibility of applying these definitions to digital images of sand grains. Firstly the way in which size can be calculated from these digital images is discussed, then the sphericity and convexity definitions proposed by Sympatec (2008) are considered. These definitions of sphericity and convexity (SQP, Cx) are relatively easy to apply. By relating SQP and Cx to the qualitative measures of particle shape that are most often used in geotechnical sample description, we argue that there is significant scope to introduce these measures to engineering practice (Altuhafi et al., 2012). We show that distributions of convexity and sphericity obtained in 2D and 3D analyses differ