Exterior Magnetic Field Research Articles

Técnicas de simulación y filtrado de ruido en señales de espectroscopía RMN mediante transformadas wavelets

In this article is shown the development of simulation programs for studying the techniques of noise filter in NMR (Nuclear Magnetic Resonance) signals, known as FID (Free induction decay). This signals are generated by exciting resonant nucleus with radio frequency pulses in an exterior magnetic field, presenting a complex exponential wave with gaussian noise. The computed programs may generate FID arameters signals definable by the user, add gaussian oise with a SNR determined.The signals with a low SNR may be treated by the traditional method of accumulations. Another considered alternative is the noise suppression through wavelets. This innovated technique promises to be quick and efficient. The created programs areused for the study and further development of these techniques, making more easy the results evaluation through the MonteCarlo method. The calculus is easier in different cases of the relation signal to noise residual in dB, establishing the difference signal without noise and with noise,also for the filtered method using accumulations so WT and WPT. From these programs and the associated methodology the investigations of better filtration variables for noise suppression in the FID signals is easier.

Convergence of Meissner minimisers of the Ginzburg–Landau energy as κ→+∞

We consider Meissner solutions, critical points of the Ginzburg–Landau energy E κ for an infinite cylinder of smooth bounded section Ω⊂ R 2 . These Meissner solutions do not contain vortices, satisfy a convexity condition, and are local minimisers. For an exterior magnetic field H 0 less than a critical field H 0 ∗ , we prove the existence and uniqueness of such a Meissner solution u κ H 0 for κ large enough. Moreover, we prove the convergence of u κ H 0 towards u ∞ H 0 as κ→+∞, where u ∞ H 0 is a local minimiser of some energy E ∞ , and can be understood as a Meissner solution for κ=+∞. On another hand we prove that E ∞ has no global minimisers.

Dynamo action and the nearly axisymmetric magnetic field of Saturn

We examine kinematic dynamo action in an electrically conducting spherical body of fluid with an overlying shell of differential rotation. It is thought that such flow types could explain the nearly axisymmetric magnetic field of Saturn. Although we find that an outer layer of differential rotation can ‘axisymmetrize’ the exterior magnetic field, surprisingly, sometimes it does not, giving magnetic fields that have no axisymmetric ingredients.

On the exterior magnetic field and silent sources inmagnetoencephalography

Two main results are included in this paper. The first one deals with the leading asymptotic term of the magnetic field outside any conductive medium. In accord with physical reality, it is proved mathematically that the leading approximation is a quadrupole term which means that the conductive brain tissue weakens the intensity of the magnetic field outside the head. The second one concerns the orientation of the silent sources when the geometry of the brain model is not a sphere but an ellipsoid which provides the best possible mathematical approximation of the human brain. It is shown that what characterizes a dipole source as “silent” is not the collinearity of the dipole moment with its position vector, but the fact that the dipole moment lives in the Gaussian image space at the point where the position vector meets the surface of the ellipsoid. The appropriate representation for the spheroidal case is also included.

Effect on the groundstate threshold pc by different boundary conditions in 2 D ± J Ising models

In the so-called uniform classes HC z , SQ z , TR z of random honeycomb, square and triangular ± J Ising models without exterior magnetic field, we investigate the effect of periodic and mixed lattice boundary conditions (b.c.) on the groundstate threshold p c of the spontaneous absolute magnetization per spin; z is a fixed number of PAF-bonds on the plaquette perimeter where these bonds have the same positive probability p to be antiferromagnetic and the probability 1− p to be ferromagnetic, the remaining bonds are ferromagnetic. For the models in the uniform classes it turns out that periodic b.c. ensure the existence of a critical concentration p c, p. b. c. (at zero temperature). Whereas for mixed b.c. (periodic b.c. in one direction, and in the orthogonal direction only couplings +1 on opposite boundaries) there are, in the classes SQ 1 and TR 1, models for which p c, m. b. c. does not exist. The emphasis is on models in classes SQ 1, TR 1, HC 1, as a counterpart to isotropic models. For z=1, by means of simulations of exact groundstates, we have strong support that there is a first-order phase transition in the magnetization, in several models. For p c in the three regular isotropic models we give a simple formula based on the lattice node degree.

Stable Configurations in Superconductivity: Uniqueness, Multiplicity, and Vortex-Nucleation

. We find new stable solutions of the Ginzburg‐Landau equation for high κ superconductors with exterior magnetic field h ex. First, we prove the uniqueness of the Meissner‐type solution. Then, we prove, in the case of a disc domain, the coexistence of branches of solutions with n vortices of degree one, for any n not too high and for a certain range of h ex; and describe these branches. Finally, we give an estimate on the nucleation energy barrier, to pass continuously from a vortexless configuration to a configuration with a centered vortex.

On the solutions of the one-dimensional Ginzburg–Landau equations for superconductivity

This paper gives a complete description of the solutions of the one-dimensional Ginzburg–Landau equations which model superconductivity phenomena in infinite slabs. We investigate this problem over the entire range of physically important parameters: a the size of the slab, κ the Ginzburg–Landau parameter, and h 0, the exterior magnetic field. We do extensive numerical computations using the software AUTO, and determine the number, symmetry and stability of solutions for all values of the parameters. In particular, our experiments reveal the existence of two key-points in parameter space which play a central role in the formation of the complicated patterns by means of bifurcation phenomena. Our global description also allows us to separate the various physically important regimes, to classify previous results in each regime according to the values of the parameters and to derive new open problems. In addition, our investigation provides new insight into the problem of differentiating between the types of superconductors in terms of the parameters.

Magnetic fluid brake

The paper presents a series of theoretical and experimental results concerning the influence of an exterior magnetic field of various configurations and intensities over a power dissipated by a disk brake in magnetic liquid. The formula of the dissipated power and the influence of magnetic field over this for regimes of laminar and turbulent flow of the liquid has been determined. The conclusions resulted from the interpretation of the experimental results confirm the theoretical aspects explained in the paper.

LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART I

We find local minimizers of the two-dimensional Ginzburg–Landau functionals depending on a large parameter κ, which describe the behavior of a superconductor in a prescribed exterior magnetic field hex. We prove an estimate on the critical value Hc1 of hex(κ), corresponding to the first phase-transition in which vortices appear in the superconductor; and we locate these vortices.

THE SEPARATION OF FIELD AND FLUID IN THE SUN

The magnetic field at the surface of the Sun is confined to widely separated small, intense magnetic flux bundles or fibrils with most of the gas in a relatively field free state in the interstices. There is evidently a systematic field and fluid separation effect in operation, overriding the tendency for turbulent mixing of the two phases. It is well known that a constantly rotating volume of fluid soon excludes any exterior magnetic field. To take the next theoretical step, this paper examines the exclusion of magnetic field from a circular cylinder with oscillating angular velocity. The result is that the field is effectively excluded from any oscillating or tumbling body of fluid that maintains coherence over a sufficiently long time. However, there is no expectation of such long term coherence in turbulent convection in the Sun, suggesting that the observed separation of field and fluid does not come about by the exclusion of field from convective cells. This leads to the conclusion that the separation of fluid and field is a consequence of extraction of fluid from the field through buoyancy and reconnection.

On minimal/maximal ground-state thresholds in uniform classes of 2D ± J Ising models

We start from the so-called uniform classes HC z , SQ z , TR z of honeycomb, square and triangular ± J Ising models without exterior magnetic field; z is a fixed number of PAF-bonds on the plaquette perimeter where these bonds have the same positive probability p to be antiferromagnetic and the probability 1− p to be ferromagnetic, the other bonds are always ferromagnetic. For each of these classes we investigate the minimal/maximal ground-state threshold l z, type , u z, type of spontaneous magnetization ( type= hc, sq, tr). Based on the notion of PAF-bond node-degree distribution (with respect to a fixed model) we derive special models for which we have strong indications that they just produce the l z, type , u z, type . Estimates for the critical concentrations p c , from simulations with these models, are in good agreement with presumably exact values for the l z, type , u z, type (e.g., in the isotropic cases l 6,hc=u 6,hc= 1 15 , l 4,sq=u 4,sq= 1 10 , l 3,tr=u 3,tr= 3 20 ).

Formation of stalagmite structures in magnetic fluid during switching on orthogonal magnetic field

The results of experimental researches of dependence of the surface form of magnetic fluid on the velocity of increase of magnetic field affixed perpendicularly on its surface are reduced. The conclusion about correlation of stalagmite structures number, amount loops of normal mode of magnetic fluid and characteristic times of exterior magnetic field increase is made.

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

The essential spectrum of a linear magnetohydrodynamic model containing a vcuum region

The essential spectrum of the force operator of the ideal linear magnetohydrodynamics has been extensively studied in the mathematical literature. However, all the rigorous from mathematical point of view works on this topic concern the magnetohydrodynamic (MHD) model of a plasma confined in a bounded domain O{sub p} {contained_in} R{sup 3} with perfectly conducting boundary. On the other hand, there exists another MHD model which is more realistic from physical point of view. According to this model, the plasma region O{sub p} is surrounded by a vacuum region O{sub v} whose boundary consists of two disjoint surfaces S{sub p} and S{sub v}. The surface S{sub p} coincides with the plasma-vacuum Interface, while the outer surface S{sub v} is perfectly conducting. The interaction between the plasma filling O{sub p} and the exterior magnetic field is described by the MHD equations, while the dynamics of the electromagnetic field in the vacuum region O{sub v} is governed by the Maxwell equations. Usually the domains O{sub p} and O{sub v} are assumed to be axisymmetric. In other words, they are obtained by the rotation of two plane domains {Omega}{sub p} and {Omega}{sub v} ({Omega}{sub p} being surrounded by {Omega}{sub v}), around air axis situatedmore » at a positive distance from the closure of {Omega}{sub p} {union} {Omega}{sub v}. In the case where the ratio of the small and tire large characteristic radii of the toroidal domain O{sub v} {union} O{sub p} is sufficiently small, one may consider O{sub p} arid, respectively, O{sub v} as the cylindrical manifolds {Omega}{sub p} x S{sup 1} and, respectively, {Omega}{sub v} x S{sup 1} where S{sup 1} := R/2{pi}Z. This is the exact meaning of the notations O{sub p} and O{sub v} adopted in the present paper. We denote by {Lambda}p and {Lambda}{sub v} respectively the boundaries of {Omega}{sub p} and {Omega}{sub v}. Thus we have S{sub p} = {Lambda}{sub p} x S{sup 1} and S{sub v} = {Lambda}{sub v} x S{sup 1}.« less

Equation of state for exclusion statistics in a harmonic well

We consider the equations of state for systems of particles with exclusion statistics in a harmonic well. Paradygmatic examples are noninteracting particles obeying ideal fractional exclusion statistics placed in (i) a harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level (LLL) of an exterior magnetic field. We show their identity with (i) the Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in a harmonic well.

Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE Formulations

An efficient parallel algorithm for solving linear and nonlinear exterior boundary value problems arising, e.g., in magnetostatics is presented. It is based upon the domaindecomposition-(DD)-coupling of Finite Element and Galerkin Boundary Element Methods which results in a unified variational formulation. In this way, e.g., magnetic field problems in an unbounded domain with Sommerfeld's radiation condition can be modelled correctly. The problem of a nonsymmetric system matrix due to Galerkin-BEM is overcome by transforming it into a symmetric but indefinite matrix and applying Bramble/Pasciak's CG for indefinite systems. For preconditioning, the main ideas of recent DD research are being applied. Test computations on a multiprocessor system were performed for two problems of practical interest including a nonlinear example.

Characterization of the 60-Hz Magnetic Fields in Schools of the Carleton Board of Education

The aim of this study was to characterize 60-Hz magnetic field levels in 79 schools managed by the Carleton Board of Education. Using a Field StarTM 1000 magnetometer, 43,009 60-Hz magnetic field measurements were taken in June 1993. The average magnetic field levels in schools (AM =9 0.082 µT, GM = 0.033 µT) were lower than in many other occupational environments. Typing rooms exhibited the highest level with an AM of 0.226 µT. There was a trend for stronger fields in secondary schools, with a GM of 0.072 µT, than those in elementary and intermediate schools, whose fields had a GM of 0.065 and 0.061 µT, respectively. High energy consumption (more than 50,000 kW hr) correlated with the 1 percentile (L1%) of magnetic field levels (r = 0.615).The geometric mean (GM) of the average magnetic field levels of two-story buildings (0.080 µT) was found to be significantly higher than that for one-story buildings (GM = 0.056 µT, p = 0.024). The sources accounting for the largest number of hot spots were wires in the floor with a GM of 0.418 µT (n = 26) in the unmovable source category and electric typewriters with a magnetic field of 1.84 µT (n = 127) in the movable source category. The relationship between interior magnetic field levels and nearness to high voltage power lines (HVPL) did not reach the conventional statistical significance (p = 0.13), possibly because of the small sample size of schools near high voltage lines. Only 6 of the 350 identifiable hot spots above 0.2 µT were attributable to nearby HVPL. Attenuation of exterior magnetic fields from HVPL by building structures was found. The coefficient of attenuation ranged from 1.0 to 9.0. A high correlation (r = 0.922) was found between interior magnetic fields and exterior magnetic field levels within the group of schools near HVPL. The results show that magnetic fields in schools may be manageable to below 0.1µT.

Characterization of the 60-Hz Magnetic Fields in Schools of the Carleton Board of Education

The aim of this study was to characterize 60-Hz magnetic field levels in 79 schools managed by the Carleton Board of Education. Using a Field StarTM 1000 magnetometer, 43,009 60-Hz magnetic field measurements were taken in June 1993. The average magnetic field levels in schools (AM =9 0.082 µT, GM = 0.033 µT) were lower than in many other occupational environments. Typing rooms exhibited the highest level with an AM of 0.226 µT. There was a trend for stronger fields in secondary schools, with a GM of 0.072 µT, than those in elementary and intermediate schools, whose fields had a GM of 0.065 and 0.061 µT, respectively. High energy consumption (more than 50,000 kW hr) correlated with the 1 percentile (L1%) of magnetic field levels (r = 0.615).The geometric mean (GM) of the average magnetic field levels of two-story buildings (0.080 µT) was found to be significantly higher than that for one-story buildings (GM = 0.056 µT, p = 0.024). The sources accounting for the largest number of hot spots were wires in the floor with a GM of 0.418 µT (n = 26) in the unmovable source category and electric typewriters with a magnetic field of 1.84 µT (n = 127) in the movable source category. The relationship between interior magnetic field levels and nearness to high voltage power lines (HVPL) did not reach the conventional statistical significance (p = 0.13), possibly because of the small sample size of schools near high voltage lines. Only 6 of the 350 identifiable hot spots above 0.2 µT were attributable to nearby HVPL. Attenuation of exterior magnetic fields from HVPL by building structures was found. The coefficient of attenuation ranged from 1.0 to 9.0. A high correlation (r = 0.922) was found between interior magnetic fields and exterior magnetic field levels within the group of schools near HVPL. The results show that magnetic fields in schools may be manageable to below 0.1µT.

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

In this paper we study two-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100×100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20,000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other, more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determineda priori. Our ground-state energy estimation at zero field is −1.317.

Explicit Calculation of the Solution to Backus′ Problem with a Condition for Uniqueness

In this work a uniqueness result for Backus′ problem for the exterior magnetic or gravitational field of the earth is given. Once this condition is established, an explicit series solution for the magnetic problem is computed and the convergance proved.