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In this study, the motion of a charged spin-1/2 fermion is found out. It is assumed, in the system, that the free fermion is subjected to a linearly space-dependent magnetic field that can be supposed to be a focusing magnetic field of a quadrupole magnet in beam dynamics in the accelerator physics. In such an examination, two-component Dirac equation is solved via perturbation approximation of the asymptotic iteration method (AIM), which has been widely used for the last decades. The results show that the fermion is bounded to the magnetic field for a certain condition of the strength of the field. For such a system, the analytical form of the energy eigenvalues are obtained. Moreover, to see whether this analytical expression works properly, the numerical eigenvalues are compared with the ones obtained by direct use of the AIM. We have an inspiration that the studies on beam dynamics and magnet design in particle accelerator physics may gain from this work. Key words: Dirac equation, asymptotic iteration method, perturbation theory, quadrupole magnet field, exact solutions, 1. Introduction According to our knowledge of basic quantum mechanics, if one wants to get information about a quantum mechanical system, it is needed to achieve the energy spectrum of [...]

This article is designed to inspect the thermal effects of an unsteady compressible flow of a viscous fluid through a symmetric channel. Combined effects of convective heat transfer, magnetic field, and radiation are also given special attention in this article. Basic laws of mass, momentum, and energy for compressible flow are employed in the modeling of the current problem. In addition, slip boundary conditions are also implemented in the analysis of the above thermal flow problem. Coupled nonlinear differential equations are solved numerically using explicit finite difference technique. Finally, the influence of different sundry parameters on the axial velocity, flow rate, and heat transfer are visualized through graphs. Time variant behavior of flow rate is calculated. Outcomes of the results reveal that the increment of the flow rate is related to the increase of compressibility parameters. Enhancement in the temperature profiles in the presence of radiation number is also reported. This model is the most general version of peristalsis of compressible flow in view of natural convection and radiation impact with extensive applications in aircraft industry, geophysics, and other industrial situations (cooling of electronic equipment, heat exchangers, and so forth). Key words: magneto-hydrodynamics, natural convection, compressible flow, radiation, Mach number, 1. Introduction Peristalsis is the mechanism in which traveling waves are responsible for fluid flow. It is the natural process that causes the motion of a fluid in human. One [...]

We studied the two-dimensional trajectories of a charged particle that was subjected to the simultaneous effect of a restoring force and a force perpendicular to its speed, which could thus be a magnetic force. Several results have been provided and compared with other modern works relative to this topic. In particular, using a classical method based on the introduction of complex variables, we showed that these trajectories are, when the force is attractive, a part of the centered trochoid curves. When force was repulsive, we obtained a second family of trajectories, this time entirely original. In the two cases, several possible trajectories are detailed and limiting cases are studied. Possible applications are discussed, especially about the normal Zeeman effect and Paschen-Back effect. Key words: central force, magnetic field, harmonic oscillator, trochoid curves, Zeeman effect Nous etudions en 2 dimensions les trajectoires d'une particule chargee qui est soumise simultanement a une force de rappel et a une force perpendiculaire a sa vitesse qui pourrait donc etre une force magnetique. Plusieurs resultats sont presentes et compares a d'autres travaux recents portant sur ce probleme. En particulier, en utilisant la methode classique basee sur l'introduction de variables complexes, nous montrons que ces trajectoires sont, lorsque la force est attractive, une partie de courbes trochoides centrees. Quand la force est repulsive, nous obtenons une seconde famille de courbes, cette fois entierement originales. Dans les deux cas, plusieurs varietes de trajectoires possibles sont detailles et les cas limites sont etudies. Nous discutons certaines applications possibles, specialement touchant l'effet Zeeman normal et l'effet Paschen-Bach. [Traduit par la Redaction] Mots-cles : force centrale, champ magnetique, oscillateur harmonique, courbes trochoides, effet Zeeman, 1. Introduction The study of the trajectories of particles that move under the influence of restoring forces is an important topic in physics, considering the many physical applications in almost [...]

This work is to elaborate the Jeffery stagnation point flow towards a cylindrical surface with the homogenous- heterogeneous reactions, magnetic field, and heat generation effects. The heat transport process is delineated by the Cattaneo- Christov heat flux model in concert with the thermal stratification. The consequential PDEs are reduced to ODEs by carrying out a set of similarity transformations. These equations are solved numerically using the Runge-Kutta-Fehlberg technique along with the shooting proficiency. The involved parameters are analysed and provided by means of graphs. It is concluded that the Jeffery fluid velocity reflects inciting values for curvature parameter but the opposite aspects are recorded for the magnetic field parameter. Further, the Jeffery fluid concentration shows higher values via both the homogenous and heterogeneous reaction parameters. The obtained outcomes are validated with an existing work. Key words: Jeffery fluid model, heat generation, Cattaneo-Christov heat flux model, stretching cylinder, stagnation point. Nous etudions ici le deplacement du point de stagnation d'un fluide de Jeffrey vers une surface cylindrique, avec reactions homogenes-heterogenes, champ magnetique et effets de generation de chaleur. Le mecanisme de transfert se chaleur est decrit par le modele de flux de chaleur de Cattaneo-Christov dans un cas de stratification thermique. Le systeme est decrit par des equations differentielles aux derivees partielles, qui sont transformees en equations differentielles ordinaires par transformation de similarite. Ces dernieres sont alors solutionnees numeriquement par technique de Runge-Kutta-Fehlberg et methode de tir. Les parametres impliques sont analyses et presentes graphiquement. Nous concluons que la vitesse du fluide de Jeffrey a un effet positif sur le parametre de courbure, mais l'inverse est vrai du champ magnetique. De plus, la concentration du fluide de Jeffrey montre des valeurs maximale a la fois pour les reactions homogenes et heterogenes. Les resultats sont valides par comparaison avec ceux d'un travail existant. [Traduit par la Redaction] Mots-cles: MHD, generation de chaleur, cylindre en etirement, reactions homogenes-heterogenes, modele du flux de chaleur de Catteneo-Christov., 1. Literature survey Magnetohydrodynamics (MHD) is the studyof fluids with electric conduction and magnetic features. This type of fluids is of great interest for industrial and technological aspects, such as [...]

Magnetization relaxation and the steady state response of the S = 1 Ising model with random crystal field to a time varying magnetic field with a frequency [omega] is modelled and studied here by a method that combines the statistical equilibrium theory with the theory of irreversible thermodynamics. The method offers information on the relaxation time ([tau]) of the system as well as the temperature ([theta]) and [omega] dependencies of the complex (AC or dynamical) susceptibility (i.e., [chi]([omega]) = [chi]'([omega]) - i[chi]'([omega])). The so-called low- and high-frequency regions are separated by [tau] because [[tau].sup.-1] [right arrow] 0 as [theta] approaches the critical temperatures ([[theta].sub.c]). One can choose to keep the frequency m fixed and observe the low-frequency behaviors followed by the high-frequency behaviors when [theta] [right arrow] [[theta].sub.c]. It is shown that [chi]([omega]) exhibits different behaviors in low- and high-frequency regimes that are separated by the quantity [omega][tau]: [chi]'([omega]) converges to static susceptibility and [chi]'([omega]) [right arrow] 0 for [omega][tau] << 1. However, in the high-frequency region where [omega][tau] >> 1, [chi]'(m) vanishes and [chi]'(m) displays a peak at the critical temperature ([[theta].sub.c]). Besides the above, the logarithm of the susceptibility components versus log(m) is also plotted. From these plots, one plateau (a step-like) region and a shifted peak with rising temperature is observed for the real and imaginary parts, respectively.Key words: Blume-Capel model, random crystal field, AC susceptibility, critical exponents.Utilisant une methode qui combine la theorie de l'equilibre statistique et la theorie de la thermodynamique irreversible, nous modelisons et etudions ici la relaxation magnetique et la reponse stationnaire du modele de Ising S = 1 avec champ cristallin aleatoire sous un champ magnetique variant dans le temps a la frequence [omega]. La methode nous renseigne sur le temps de relaxation (t) du systeme, ainsi que sur sa temperature ([tau]) et la dependance en [omega] de la susceptibilite complexe (AC ou dynamique) (i.e., [chi]([omega]) = [chi]'([omega])- i[chi]'([omega])). Les regions dites de basse et de haute frequence sont separees par t, puisque [[tau].sup.-1] [right arrow] 0 lorsque 0 approche la temperature critique ([[theta].sub.c]). On peut choisir de garder la frequence m fixe et observer le regime de basse frequence, suivi par le regime haute frequence lorsque [theta] [right arrow] [[theta].sub.c]. On peut montrer que x(m) a des comportements differents dans les regimes de basse frequence et de haute frequence, qui sont separes par la valeur de [omega][tau]: [chi]'([omega]) converge vers la susceptibilite statique et [chi]'([omega]) [right arrow] 0 lorsque [omega][tau] <> 1, alors [chi]'(m) [right arrow] 0 et [chi]'(m) aun pic a la temperature critique ([[theta].sub.c]). De plus, nous presentons les graphiques du logarithme des composantes de la susceptibilite en fonction de log(m). Sur ces graphiques, nous observons un plateau et un pic deplace par l'augmentation de la temperature, pour les parties reelle et imaginaire respectivement. [Traduit par la Redaction.]Mots-cles: modele de Blume-Capel, champ cristallin aleatoire, susceptibilite AC, exposants critiques, dispersion magnetique., 1. IntroductionIf a small AC drive magnetic field is superimposed on a DC field, a time-dependent magnetic moment is induced. The induced magnetization is proportional to the external field for [...]

present problem is concerned with two-phase fluid flow through a horizontal porous channel in the presence of uniform inclined magnetic field. The micropolar fluid or Eringen fluid and Newtonian viscous fluid are flowing in the upper and lower regions of the horizontal porous channel, respectively. In this paper, the permeability of each region of the horizontal porous channel has been taken to be different. The effects of various physical parameters like angles of inclination of magnetic field, viscosity ratio, micropolarity parameter, etc., on the velocities, micro- rotational velocity of two immiscible fluids in horizontal porous channel, wall-shear stress, and flow rate have been discussed. The result obtained for immiscible micropolar-Newtonian fluids are compared with the results of two immiscible Newtonian fluids. The obtained result may be used in production of oil from oil reservoirs, purification of contaminated ground water, etc. Key words: Immiscible fluids, porous medium, micropolar fluid, Newtonian fluid, Hartmann number, Brinkman equation. Le probleme qui nous interesse concerne l'ecoulement de fluide a deux phases a travers un canal horizontal poreux en presence d'un champ magnetique uniforme incline. Le fluide micro-polaire ou fluide d'Eringen et le fluide visqueux newtonien circulent respectivement dans la partie superieure et inferieure du canal. Dans notre etude, la permeabilite est tenue comme differente dans les deux regions du canal. Nous discutons les effets de differents parametres physiques, comme l'angle d'inclinaison du champ magnetique, le rapport de viscosite, le parametre de micro-polarite, etc. sur les vitesses, la vitesse micro-rotationnelle des deux fluides non miscibles dans le canal horizontal poreux, la contrainte de cisaillement au mur et le taux d'ecoulement. Le resultat obtenu avec deux fluides micro-polaires- newtoniens non miscibles est compare avec le resultat de deux fluides newtoniens non miscibles. Le resultat obtenu peut etre utilise dans la production d'huile a partir de reservoirs d'huile, la purification d'eau de surface contaminee, etc. [Traduit par la Redaction] Mots-cles: fluide micro-polaire, fluide newtonien, equation de Brinkman, nombre de Hartmann, milieu poreux., 1. Introduction The numerous applications of fluid flow problems in bioengineering, climatology, fluid control system, oceanography, etc., are motivating many researchers, engineers, and scientists to move forward in the field [...]

Author(s): Zhe Wang (corresponding author) [1, 2]; Jianda Wu [3]; Wang Yang [3]; Anup Kumar Bera [4, 5]; Dmytro Kamenskyi [6]; A. T. M. Nazmul Islam [4]; Shenglong Xu [3]; [...]

A numerical investigation has been done to study the impact of nonlinear magnetic field, nonlinear thermal radiation, variable thickness, and Brownian motion on flow and heat transfer characteristics (i.e., skin friction and surface heat flux) as a physical application. Moreover, the impact of these forces on the rate of cooling and the mechanical properties (i.e., hardness, ductility, ...) of a surface that is cooled using nanofluid as a coolant is explored. The governing boundary layer equations describing the problem are transformed to ordinary differential equations using the similarity transformation method and are then solved numerically using the fourth-order Runge-Kutta method with shooting technique with the assistance of Mathematica program. Key words: nanofluids, variable thickness, nonlinear thermal radiation, magnetic field. Nous presentons une etude numerique de l'impact d'un champ magnetique non lineaire, de la radiation thermique non lineaire, de l'epaisseur variable et du mouvement brownien sur les caracteristiques d'ecoulement et de transfert de chaleur (i.e. le frottement superficiel et le flux de chaleur de surface) en tant que un systeme physique. Nous etudions aussi l'impact de ces forces sur le taux de refroidissement et les proprietes mecaniques (i.e., la durete, la ductilite, ...) des surfaces refroidies en utilisant un nanofluide comme refroidisseur. Les equations directrices de la couche limite sont transformees en en equations differentielles ordinaires par la methode des transformations de similarite, qui sont ensuite solutionnees par methode de Runge-Kutta du quatrieme ordre avec une technique de tir en utilisant un programme de Mathematica. [Traduit par la Redaction] Mots-cles: nanofluide, epaisseur variable, radiation thermique non lineaire, champ magnetique., 1. Introduction Study of boundary layer behavior over a moving surface is an important problem because of its importance to industry processes, such as paper production, plastic extrusion, and fibers. [...]

A locally rotationally symmetric (LRS) Bianchi type I massive string cosmological model with vacuum energy density ([LAMBDA]) and magnetic field is investigated. To get a deterministic model of the universe, we assume that shear ([sigma]) is proportional to expansion ([theta]) and [LAMBDA] ~1/[R.sup.2] as considered by Chen and Wu (Phys. Rev. D, 41, 695 (1990)) where R is a scale factor. We find that the total energy density ([rho]), the particle density [[rho].sub.p] decreases with time. The strong energy conditions as given by Hawking and Ellis (The large scale structure of space-time. Cambridge University Press, Cambridge, UK. p. 88. (1974)) are satisfied. The vacuum energy density decreases with time, which matches with astronomical observation. The model in general represents anisotropic space-time because of the presence of strings. The total energy density and string tension density decrease because of the presence of a magnetic field. Both the models have point-type singularities at T = 0 and [tau] = 0, respectively. The other physical aspects of the models are also discussed. Key words: LRS, Bianchi I, massive string, cosmological, vacuum energy, magnetic field. Nous analysons un modele cosmologique de Bianchi de type I avec corde massive, localement symetrique sous rotation (LRS) et possedant une densite d'energie du vide ([LAMBDA]) et un champ magnetique. Afin d'obtenir un modele deterministe de l'univers, nous supposons que le cisaillement ([sigma]) est proportionnel a l'expansion ([theta]) et que [LAMBDA] ~ 1/[R.sup.2], tel que considere par Chen et Wu (Phys. Rev. D, 41, 695 (1990)) ou R est le facteur d'echelle. Nous trouvons que la densite totale d'energie ([rho]) et la densite de particules [[rho].sub.p] decroissent avec le temps. Les fortes conditions d'energie de Hawking et Ellis (The large scale structure of space-time. Cambridge University Press, Cambridge, UK. p. 88. (1974)) sont satisfaites. La densite d'energie du vide diminue avec le temps, ce qui correspond aux observations astronomiques. La presence de la corde fait que le modele represente un espace-temps anisotrope. La densite totale d'energie et la densite de tension de corde diminuent a cause du champ magnetique. Les deux modeles ont des singularites ponctuelles a T = 0 et [tau] = 0 respectivement. Nous discutons les autres aspects du modele. [Traduit par la Redaction] Mots-cles : localement symetrique sous rotation, Bianchi de type I, corde massive, cosmologique, energie du vide, champ magnetique. PACS Nos.: 04.50.Gh, 98.80.Cq, 98.80.-k., 1. Introduction The cosmological problem within the framework of general relativity is to find a model of the physical universe that correctly predicts the result of astronomical observation. The simplest [...]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2010.07.013 Byline: J. Zendejas (a), A. Segura (b), A.C. Raga (b) Keywords: Astrobiology; Atmospheres, Evolution; Extrasolar planets; Solar wind Abstract: We present an analytic model for the interaction between planetary atmospheres and stellar winds from main sequence M stars, with the purpose of obtaining a quick test-model that estimates the timescale for total atmospheric mass loss due to this interaction. Planets in the habitable zone of M dwarfs may be tidally locked and may have weak magnetic fields, because of this we consider the extreme case of planets with no magnetic field. The model gives the planetary atmosphere mass loss rate as a function of the stellar wind and planetary properties (mass, atmospheric pressure and orbital distance) and an entrainment efficiency coefficient [alpha]. We use a mixing layer model to explore two different cases: a time-independent stellar mass loss and a stellar mass loss rate that decreases with time. For both cases we consider planetary masses within the range of 1[right arrow]10M.sub.[direct sum] and atmospheric pressures with values of 1, 5 and 10atm. We apply our model to Venus by estimating its atmospheric mass loss rate by the interaction with the solar wind and compare our model with more detailed simulations. We find a good agreement between our results and the atmospheric mass loss obtained by more detailed models, and it is therefore appropriate for carrying out an exploration of the broad parameter space of exoplanetary systems. For the time-dependent case, planets without magnetic field in the habitable zone of M dwarfs with initial stellar mass losses of M.sub.w Author Affiliation: (a) Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, A.P. 70-264, 04510 D.F., Mexico (b) Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 D.F., Mexico Article History: Received 3 November 2009; Revised 13 July 2010; Accepted 14 July 2010

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2010.01.004 Byline: C. Moore (a), K. Miki (a), D.B. Goldstein (a), K. Stapelfeldt (a)(b), P.L. Varghese (a), L.M. Trafton (a), R.W. Evans (a)(b) Keywords: Io; Aurorae; Jupiter, Satellites; Satellites, Atmospheres; Collisional physics Abstract: We present a Monte Carlo (MC) model of [OI] 6300A and [SII] 6716A emission from Io entering eclipse. The simulation accounts for the 3-D distribution of SO.sub.2, O, SO, S, and O.sub.2 in Io's atmosphere, several volcanic plumes, and the magnetic field around Io. Thermal electrons from the jovian plasma torus are input along the simulation domain boundaries and move along the magnetic field lines distorted by Io, occasionally participating in collisions with neutrals. We find that the atmospheric asymmetry resulting from varying degrees of atmospheric collapse across Io (due to eclipse ingress) and the presence of volcanoes contributes significantly to the unique morphology of the [OI] 6300A emission. The [OI] radiation lifetime of [approximately equal to]134s limits the emission to regions that have a sufficiently low neutral density so that intermolecular collisions are rare. We find that at low altitudes (typically 4x10.sup.9 cm.sup.-3) to collisionally quench nearly all (>95%) of the excited oxygen for reasonable quenching efficiencies. Upstream (relative to the plasma flow), Io's perturbation of the jovian magnetic field mirrors electrons with high pitch angles, while downstream collisions can trap the electrons. This magnetic field perturbation is one of the main physical mechanisms that results in the upstream/downstream brightness asymmetry in [OI] emission seen in the observation by Trauger et al. (Trauger, J.T., Stapelfeldt, K.R., Ballester, G.E., Clarke, J.I., 1997. HST observations of [OI] emissions from Io in eclipse. AAS-DPS Abstract (1997DPS29.1802T)). There are two other main causes for the observed brightness asymmetry. First, the observation's viewing geometry of the wake spot crosses the dayside atmosphere and therefore the wake's observational field of view includes higher oxygen column density than the upstream side. Second, the phased entry into eclipse results in less atmospheric collapse and thus higher collisional quenching on the upstream side relative to the wake. We compute a location (both in altitude and latitude) for the intense wake emission feature that agrees reasonably well with this observation. Furthermore, the peak intensity of the simulated wake feature is less than that observed by a factor of [approximately equal to]3, most likely because our model does not include direct dissociation-excitation of SO.sub.2 and SO. We find that the latitudinal location of the emission feature depends not so much on the tilt of the magnetic field as on the relative north/south flux tube depletion that occurs due to Io's changing magnetic latitude in the plasma torus. From 1-D simulations, we also find that the intensity of [SII] 6716 and 6731A emission is much weaker than that of [OI] even if the [SII] excitation cross section is 10.sup.3 times larger than excitation to [OI]. This is because the density of S.sup.+ is much less than that of O and because the Einstein-A coefficient of the [SII] emission is a factor of [approximately equal to]10 smaller than that of [OI]. Author Affiliation: (a) The University of Texas at Austin, Austin, TX 78712, USA (b) JPL, Caltech, USA Article History: Received 28 July 2009; Revised 2 January 2010; Accepted 3 January 2010

We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) random field by using Schramm--Loewner Evolution clusters and associated renormalized area measures. The renormalized areas are from the scaling limit of the critical Fortuin--Kasteleyn clusters and the random field is a convergent sum of the area measures with random signs. Extensions to off-critical scaling limits, to d = 3, and to Potts models are also considered. continuum scaling limit | critical |sing model | FK clusters | SLE | CLE

This paper shows that two apparently independent models of hysteresis--the Jiles-Atherton model, developed by Jiles and Atherton, and the energetic model, developed by Hauser--are mathematically equivalent. These two hysteresis models are examined with respect to their capability to describe the dependence of the magnetization on magnetic field and mechanical stress. Comparisons have been made between the predictions of the two models and measured hysteresis curves. Through a mathematical analysis of the structure of the models, conditions have been found under which both models predict the same magnetization curves. This 'common ground' agreement between the models has allowed us to establish correspondence between the descriptors of the models so that a mathematical transformation between the model parameters becomes possible. The result allows improved interpretation of the physical mechanisms that contribute to ferromagnetic hysteresis at different stages in the magnetization curve in terms of the reversible and irreversible physical processes such as domain wall motion and domain rotation which form the basis of these models. Furthermore, consideration of the internal demagnetizing factor has also allowed it to be included in the models. Index Terms--Anisotropy, demagnetizing factor, energetic model, hysteresis modeling, Jiles-Atherton model, mechanical stress.

Based on the concept of using controllable mixed electric and magnetic coupling to design planar filters in our earlier work, we propose a novel inline coaxial filter, in which the electric and magnetic coupling can be separately controlled. Due to this controllable mixed coupling, the filter can operate with a quasi-elliptic characteristic. By modifying resonator structure and inserting additional coupling components, the filter size is substantially reduced and the coupling becomes more easily controllable, thus being able to produce a highly selective filter with a compact size. In addition, asymmetric response can be easily achieved. For the N-order filter, a maximum of N - 1 finite transmission zeros can be realized. Practical designs, concerning a global system for mobile communication specification, show the advantages of this filter. Index Terms--Coaxial, elliptic filtering characteristic, inline filter, mixed coupling.

In most finite element analysis, the numerical error range of the computed force must be specified. In this paper, an error estimation method for force computation using the virtual work method is presented. The merits of the proposed method include its simplicity and its applicability in force computation when the objects being studied are touching other objects. Index Terms--Error estimation, finite element method (FEM), force, magnetic field.

This paper presents a method for investigating, calculating, and optimizing back-bias magnets used in automotive sensor applications such as ABS/ESP. The performance of these applications crucially depends on the choice of magnet. Major parameters, such as shape and direction of magnetization, are investigated and optimized for different types of magnets. The calculations were performed using finite-element method simulations in 3-D. Index Terms--Magnetic fields, magnets, modeling, simulation software.

This paper discusses interface conditions used in a domain partitioning method and their approximation with a reduced number of degrees of freedom called hooks. In the electrostatic and magnetostatic cases, electric or magnetic hook-connectors are, respectively, used to describe interactions. Better numerical results are obtained in the full wave regime by using both electric and magnetic hooks. This paper proposes an efficient approximation of the interface conditions by using a coarser grid on this surface. We have shown that the interface tends to become transparent for the electromagnetic (EM) field, when the number of hooks is increased and consider this convergence property as the main result of the paper. The proposed domain partitioning (DP) method was successfully applied as a particular domain decomposition (DD) technique for the EM modeling with parallel algorithms of RF-IC components. Unlike DD which is an iterative approach, the new DP approach is a direct one. The sub-domain models being independently extracted, DP is more effective and suitable for parallelization. The open problem of hooks identification is reformulated as a discrete optimization problem. Index Terms--Domain decomposition (DD)/partitioning, electromagnetic (EM) analysis, electromagnetic (EM) circuit element, finite integration technique (FIT).

Hierarchic families of finite elements are widely used in higher order finite-element methods. Several hierarchic sets of basis functions for nodal, edge, and face elements are proposed by different authors in scientific literature. However, no general methodology exists for their construction. This paper presents an analysis of hierarchic families of finite elements which leads to the localization of their degrees of freedom. From this localization, we derive an algebraic approach for the construction of hierarchic families of nodal, edge, and face elements. The case of tetrahedral finite elements is discussed in detail. Index Terms--Basis functions, degrees of freedom, hierarchic families, higher order finite-element methods.

Graphics Processing Units (GPUs) for years have been dedicated mostly to real time rendering. Recently leading GPU manufactures have extended their research area and decided to support also graphics computing. In this paper, we describe an impact of new GPU features on development process of an efficient Finite Difference Time Domain (FDTD) implementation. Index Terms--FDTD, GPU, massively parallel computing.

The line-search technique was usually introduced to the Newton-Raphson (NR) method in order to improve the convergence characteristic of nonlinear magnetic field analysis with the toughness magnetic nonlinearlity. In this paper, we proposed the NR method combined with the optimal step size using exact functional minimization in every nonlinear iteration. The convergence process and computation time were investigated, and compared with the conventional line-search technique using the approximate functional minimization. Index Terms--Energy functional, exact minimization, line-search, Newton-Raphson (NR) method, nonlinear magnetic field analysis.