Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

Numerical Simulation of the 2D Non-Parabolic MEP Energy-Transport Model with a Mixed Finite Elements Scheme

In the Mixed Finite Element approximation scheme has been used to simulate a consistent hydrodynamical model for electron transport in semiconductors, free of any fitting parameters , based on the Maximum Entropy Principle (MEP) and assuming the Parabolic Band approximation. In this paper we describe an application of the above numerical method in the case of the two dimensional Non-Parabolic MEP energy-transport model. We can consider this paper as a generalization of what has been done in . As done in results of the simulation of 2D-MESFET and 2D-MOSFET Silicon devices are presented

Interactions between Bio-Based Compounds and Cyclodextrins

Bio-based compounds, such as “green” surfactants and phytochemicals, are regarded as future sustainable resources for a vast range of applications in a modern society increasingly demanding economical, social, and environmental awareness. Natural compounds from plants (phytochemicals) are very sought by the pharmaceutical, cosmetic, and food industries. On the other hand, the growing interest in “green” surfactants (e.g., carbohydrate-based) is due to, inter alia, their preparation from renewable raw materials, ready biodegradability, and biocompatibility, among other reasons of fundamental, practical, economical, and environmental orders. Despite the wide range of potential applications of these bio-based compounds, their practical use is still limited due to many reasons such as poor aqueous solubility, volatility, reactivity, etc. Generally, when complexed with cyclodextrins, these bio-based compounds enhance considerably their performance and potential applications. Thus, this chapter aims at recalling some general fundamental aspects of phytochemicals and “green” surfactants, such as structure, function, and applications. In addition, their interactions with cyclodextrins are discussed from a physicochemical point of view with special focus on the techniques, mathematic modeling, and thermodynamic parameters (e.g., interactions, stoichiometries, association constants, etc.)

Evidence for two disparate spin dynamic regimes within Fe-substituted La0.7 Pb0.3 (Mn1-x Fex) O3 (0≤x≤0.2) colossal magnetoresistive manganites: Neutron spin-echo measurements

10 págs.; 7 figs.; 1 tab. ; PACS number s : 75.25. z, 75.30.Ds, 75.40.Gb, 75.47.GkThe spin dynamics of substituted colossal magnetoresistive (CMR) manganites of general formula La0.7 Pb0.3 (Mn1-x Fex) O3, 0≤x≤0.2 is investigated by means of neutron spin-echo measurements. Substitution of Mn by Fe leads to a strong decrease of the temperature of macroscopic magnetic long-range ordering with a concomitant enhancement of the CMR effect. For x=0.2, a long-range-ordered state is not achieved as a result of the increase in antiferromagnetic interactions brought forward by Fe+3 -Mn couplings. The results display two relaxations having well separated decay constants. A fast process with a relaxation time of about 10 ps within the paramagnetic phase is found for all compositions. It shows a remarkably strong dependence with temperature and sample composition as the apparent activation energy for spin diffusion as well as the preexponential term exemplify. The physical origin of such a fast relaxation is assigned to heavily damped or overdamped spin waves (spin diffusion) on the basis of some signatures of excitations having finite frequencies found for the parent compound La0.7 Pb0.3 Mn O3 at temperatures just below Tc, together with preliminary data on the effect of Fe doping on the stiffness constant. A slower relaxation is present for all compositions. Its temperature dependence follows the behavior of the macroscopic magnetization, and its intensity grows within the ordered ferromagnetic state. Its physical origin is ascribed to collective reorientation of nanoscale ferromagnetic domains on the basis of the wave-vector dependence of its relaxation rate and amplitude. © 2007 The American Physical Society.J.G. and J.M.B. thank the Spanish Ministerio de Educacion y Ciencia for financial support under research Grant No. MAT2005-0686-C04-03. F.J.B. and P.R. acknowledge financial support from the European Commission through NMI3 to carry out preliminary measurements at the FZJ facilities.Peer Reviewe

Experimental evidence of a cluster-glass transition on the colossal magnetoresistance manganite La0.7Pb0.3(Mn0.9Fe0.1)O3

4 págs.; 3 figs. ; PACS numberssd: 75.40.2s, 75.47.2m, 61.12.Ex, 61.46.1wNeutron small angle scattering on a colossal magnetoresistance material shows clear signatures of a rise in characteristic length of paramagnetic fluctuations as the maximum of dc susceptibility is approached from high temperatures. The phenomenon is accompanied by a rise in intensity of a broad peak that appears at wave vectors of ≈ 0.025-1, and this is interpreted as a fingerprint of the onset of ferromagnetic ordering due to intercluster magnetic interactions. © 2005 The American Physical Society.Peer Reviewe

A cluster theory for a Janus fluid

Recent Monte Carlo simulations on the Kern and Frenkel model of a Janus fluid have revealed that in the vapour phase there is the formation of preferred clusters made up of a well-defined number of particles: the micelles and the vesicles. A cluster theory is developed to approximate the exact clustering properties stemming from the simulations. It is shown that the theory is able to reproduce the micellisation phenomenon.Comment: 27 pages, 8 figures, 6 table

Numerical simulation of 2D Silicon MESFET and MOSFET described by the MEP based energy-transport model with a mixed finite elements scheme

The Mixed Finite Element approximation scheme presented in is used to simulate a consistent hydrodynamical model for electron transport in semiconductors, free of any fitting parameters, formulated on the basis of the maximum entropy principle (MEP) in \cite{AnRo,Ro1,Ro2}.. 2D-MESFET and 2D-MOSFET Silicon devices are simulated in the parabolic band approximation. Comparison with the results obtained by the Stratton model are presented for completeness

Numerical simulation of 2D Silicon MESFET and MOSFET described by the MEP based energy-transport model with a mixed finite elements scheme

The Mixed Finite Element approximation scheme presented in is used to simulate a consistent hydrodynamical model for electron transport in semiconductors, free of any fitting parameters, formulated on the basis of the maximum entropy principle (MEP) in \cite{AnRo,Ro1,Ro2}.. 2D-MESFET and 2D-MOSFET Silicon devices are simulated in the parabolic band approximation. Comparison with the results obtained by the Stratton model are presented for completeness

Avvio e gestione di attività estrattive: un approccio in "Prevention Through Design"

Una efficace analisi e gestione dei rischi presso le unità estrattive, su cui fondare l’attività in coerenza con le norme vigenti in materia di sicurezza del lavoro, implica un approccio pro-attivo, tenuto conto dei diversi fattori coinvolti. In tale contesto un approccio pro-attivo richiede una approfondita analisi di rischio, fondata sulla valutazione delle possibili opzioni progettuali e la conoscenza del sito e del programma di coltivazione; nel presente lavoro viene esposta una metodologia basata su un sistema di registrazione dei dati tecnici supportata da un apposito software interattivo, in grado di aiutare la valutazione degli aspetti generali e specifici della sicurezza di comparto e di singole unità estrattive. Il lavoro è stato svolto dal Dipartimento di Ingegneria del Territorio, dell’Ambiente e delle Geotecnologie del Politecnico di Torino (già Autore di Linee Guida in materia di sicurezza per il comparto estrattivo) con il supporto dell’Ufficio Tutela Ambientale della Provincia di Torino