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International audience; This work validates a posteriori the use of the theory developed ca. 40 years ago by Amatore and Savéant for regular arrays of electroactive band or disk electrodes. This theory has been profitably used and widely applied in more than 900 research papers for the treatment of the voltammetric responses of arrays of nanoelectroactive objects that were necessarily random by construction. In this work we show that competitive diffusion interaction between the active sites enforce redistribution of individual diffusion layer which homogenize dimensions of the solution volumes 'feeding' each active site. For arrays of nanodisk electrodes, it also validates the corresponding approximation assuming that its voltammetric behavior is to that afforded by identical independent cylindrical unit cells performing in parallel.

During the past 60 min, oil companies have extracted 6 trillion liters of oil from the ground, thereby giving a striking illustration of the impact of multiphase flows on the world economy. From a fundamental perspective, we largely understand the dynamics of interfaces separating immiscible fluids driven through heterogeneous environments. In stark contrast, the basic mechanisms ruling the transport of fragmented fluids, such as foams and emulsions, remain elusive with studies mostly limited to isolated droplets and bubbles. Here, we demonstrate that the mobilization of emulsion driven through model disordered media is a critical plastic depinning transition. To elucidate this collective dynamics, we track the trajectories of hundreds of thousands of microfluidic droplets advected through random lattices of pinning sites. Their dynamics reveals that macroscopic mobilization only requires the coordinated motion of small groups of particles and does not involve any large-scale avalanches. Criticality arises from the interplay between contact and hydrodynamic interaction, which channel seemingly erratic depinning events along smectic river networks correlated over system spanning scales. Beyond the specifics of emulsion transport, we close our article discussing the similarities and profound differences with the plastic depinning transitions of driven flux lines in high- T c superconductors, charged colloids, and grain transport in eroded sand beds.

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced., Comment: 7 pages, 5 figures

We classify the sectors of configurations that result from the dynamics of 2d crossing flux lines, which are the simplest degrees of freedom of the 3-coloring lattice model. We show that the dynamical obstruction is the consequence of two effects: (i) conservation laws described by a set of invariants that are polynomials of the winding numbers of the loop configuration, (ii) steric obstruction that prevents paths between configurations, for lack of free space. We argue that the invariants fully classify the configurations in five, chiral and achiral, sectors and no further obstruction in the limit of low-winding numbers., 25 pages, 12 figures, Submission to SciPost

This paper analyzes the impact of the flux barriers shape and parametrization on the optimization of synchronous reluctance machines. Four different shapes are considered, rectangular flux barriers, round flux barriers, hyperbolic flux barriers, and finally Joukowski flux barriers, which follow the natural flux lines in a solid rotor. A novel parametrization that simplifies the non-overlapping constraints is described, and, for each of these shapes, the number of parameters is discussed. A multi-objective optimization algorithm is run to maximize the mean torque while minimizing the torque ripple. The evaluations are made by a nonlinear finite element magnetic model. The obtained Pareto fronts show that the optimization is able to reduce the torque ripple down to about 3% for all the shapes, with a little impact on the mean torque. The different shapes, however, are shown to have similar performances.

One of the most common faults experienced by the permanent magnet synchronous motor (PMSM) is stator interturn fault which account for 35-40% of the machine failure. This paper focuses on the stator inter-turn fault analysis in the stator winding of Permanent Magnet Synchronous Motor (PMSM) using Finite Element Method. The analysis is carried out for 12.5% and 25% inter-turn short in stator winding of PMSM. The analytical parameters of the motor which includes torque, winding current, induced voltage, speed and electromagnetic parameters like flux density, flux lines and radial flux density were obtained for the faulty machine and compared with the healthy machine. The simulation is done using the ANSYS Maxwell finite element analysis tool.

International audience; In order to assess the precision of simulations of diffusion at arrays based on the Voronoi tessellation approach we investigated two representative types of random arrays involving bands or disk electroactive sites [J. Electroanal. Chem. 147 (1983) 39] and modelled their diffusional patterns when the solution contains only one electroactive species undergoing a simple electron transfer reaction at the active sites under chronoamperometric conditions. On the one hand, the ensuing results establish that in both cases the Voronoi approach produces reasonably good predictions of the total current intensities flowing through the elementary cells of each array. Indeed, the relative error introduced by the Voronoi-based approach, being less than 5% in each case, is acceptable from an experimental point of view owing to many other sources of uncertainties involved for random arrays. On the other hand, this work demonstrates that the current intensities predicted for the individual sites within an elementary cell based on simulations using Voronoi approaches are excessively wrong since they totally neglect the excessive redistributions of flux lines that happen when the diffusion layers expand with time. This hints to possible severe complication when Voronoi approaches are applied to encompass complex kinetics or to predict the outcome of electroanalytical methods that rely on a fine coupling between local concentrations and local fluxes.

Wireless power transfer using magnetic resonance requires cutting flux lines generated from the transmitter coil by the receiver coil. This letter shows that an exact one to one coil area ratio or CAR (i.e. primary relative to secondary) is not a pre-condition to obtain high efficiency. It is also shown that high efficiency can be achieved for relatively small CARs by adjustment of the turns ratio. We go on to show that it is possible to achieve a higher energy efficiency than the coil area ratio and the associated flux cut would dictate.

In general, Light Electric Vehicle applications mostly prefer Permanent Magnet Synchronous Motors (PMSM) with nominal power up to 2kW. With the objective of to explore the feasibility of non-permanent magnet solution in this category, present paper considers the design and analysis of 1.5kW Synchronous Reluctance Motor (SynRM) with concentrated type winding. Design has been carried out to determine the dimension of the stator and rotor structure, and calculation of winding parameters. The designed data is verified and optimized through Finite Element Method (FEM) analysis. The distribution of flux lines and flux density on stator and rotor periphery is also presented. Rotor structure has been optimized with respect to the variation in flux barriers per pole to ensure improved torque performance specially torque ripple and average torque.

To investigate the effect of discontinuity of 1-D pinning centers on the flux pinning in a wide range of magnetic field directions, discontinuous columnar defects (CDs) and continuous CDs were formed in GdBCO coated conductors using Xe-ion irradiations with 80 and 270 MeV, respectively. An overall shift upward in J c , for the 80-MeV-irradiated sample compared to the 270-MeV-irradiated one, can be observed in every direction of magnetic field, which is more remarkable as temperature decreases. This implies a synergetic effect of the pinning interaction between the linearity and the discontinuity for the discontinuous CDs. When the density of CDs is lower, however, the difference in Jc between the discontinuous and the continuous CDs becomes less at lower temperature, even in the magnetic field parallel to the c-axis. At lower density of CDs, the average spacing between CDs is wider, which would hardly lead to automatic entanglement of flux lines in the discontinuous CDs, i.e., to the synergetic effect.

The influence of rare earth (RE – Ce, Gd) doping at the Nd site in the NdFeAsO0.7F0.3 superconductor wherein Ce and Gd have ionic radii in the order Ce > Nd > Gd is investigated. The structural and superconductivity characterization of the pure and doped samples show that Ce doping enhances the TC of Nd1−xRExFeAsO0.7F0.3 to a maximum of 53.6 K at x = 0.1 while Gd doping attains a TC of 55.1 K at x = 0.15. Interestingly, both Ce and Gd doping create neither secondary phases nor precipitates within the detection limit of XRD. However, the lattice defects due to Ce and Gd doping modifies NdFeAsO0.7F0.3 and assists in pinning the flux lines on these defects thereby exhibiting an enhanced JC(H) performance especially at high fields. It is also observed that the relatively small ionic size of Gd is more effective in TC enhancement, while the lattice defects due to larger ionic size of Ce favor the remarkable enhancement of JC(H).

An analysis of the interrelated changes in the material composition and the pinning strength in nanostructured Nb (1 1 0) thin films is presented. The nanopatterns were prepared by focused ion beam milling of an array of uniaxial grooves. They induce a washboard-like pinning potential landscape for vortices in the mixed state. By applying different magnetic fields, the most likely pinning sites along which the flux lines move through the samples have been selected. By this, either the background isotropic pinning of the pristine film or the enhanced isotropic pinning originating from the nanoprocessing has been probed. The enhanced pinning strength in the processed films has been found to correlate with the content of Ga implanted into the films during the nanopatterning.

The magnetic anisotropy in grain oriented FeSi alloys (FeSi GO) is very important nowadays, because these steels are usually used for their very good magnetic properties along the rolling direction (RD). In electrical devices the steel magnetic core is subjected to flux lines that are making an angle, different from 0° to the RD and to 2D magnetic flux densities. In the paper there were analyzed samples of a commercial FeSi GO M0H steel industrial grade cut through mechanical punching and electro-erosion technologies. The investigated samples have a thickness of 0.3 mm and an area of 300 mm × 30 mm and were cut at angles θ ranging between 0° and 90° at 15° intervals with respect to the RD. The magnetic characterization was performed with a standardized unidirectional Single Strip Tester (IEC 60404-7) and a frequency analysis from 10 Hz to 100 Hz was done, in order to investigate the energy loss behavior. The loss separation concept was applied, to determine the influence of the cutting technology on the m...

This paper is about an intriguing property of the continuous Newton-Raphson method for the minimization of a continuous objective function f: if x is a point in the domain of attraction of a strict local minimizer x* then the flux line of the Newton-Raphson flow that starts in x approaches x* from a direction that depends only on the behavior of f in arbitrarily small neighborhoods around x and x*. In fact, if F is a sufficiently benign perturbation of f on an open region D not containing x, then the two flux lines through x defined by the Newton-Raphson vector fields that correspond to f and F differ from one another only within D. The work was supported by EPSRC grant GR/S34472 (R. Hauser) and by the Clarendon Fund, Oxford University Press and ORS Award, Universities UK (J Nedic)

A simple one dimensional model to simulate the establishment of the Bean critical state is introduced. It is shown that the dynamics of the flux lines as they enter the superconductor are dominated by ’avalanches‘. The distribution of distances moved by vortices in the avalanches obeys a power law with an exponent of −1. This suggests that the Bean state is a self-organised critical state. The density of flux lines is parabolic.

This paper deals with electromagnetic actions that allow one to control the shaped-charge effect at different stages of shaped-charge operation. A decrease in penetration of the shaped-charge jet is attained by production of an axial magnetic field in the shaped-charge liner immediately before shot, and production of a magnetic field in the conducting target material that is transverse to the direction of jet propagation. The considerable decrease in the penetration capability of the charge observed in the experiments is attributed to a sharp amplification of the magnetic field in the jet formation region upon liner collapse. The effects accompanying the “field pumping” prevent the normal formation of a shaped-charge jet. A model of magnetic field generation in a conducting medium subjected to high-velocity deformation with particle elongation along the magnetic flux lines is considered. X-ray photographs of shaped-charge jets formed from a “magnetized liner” are given. Theoretical calculations have shown that deformation conditions that can provide for intense magnetic field generation also arise during high-velocity jet penetration into a conducting target across the flux lines of the initial magnetic field previously produced in the target.

Flux-reversal machine (FRM) is a new doubly salient stator-permanent magnet (PM) machine with flux linkage reversal in the stator concentrated windings. It can operate in both motoring and generating modes. Its simple structure makes it cost effective and suitable for mass production. However, there is notable permanent magnet flux leakage which deteriorates the torque ability of the FRM. In this paper, a novel design to improve the performance of an FRM is proposed. The proposed FRM has permanent magnets parallel to the stator magnet flux lines and thus is much more difficult to demagnetize. To analyze the characteristics of the proposed FRM, a two-dimensional finite-element method (2-D FEM) is used. The prototype FRM is also built to prove the advantage of the new design method. From the analysis and experimental results, it is shown that the proposed FRM has an improved performance.

We present a Hamiltonian for the boson–boson interaction, based on elastic coupling through flux lines. This Hamiltonian may be used to study polaritons and plasmons and likewise the cohesive energy in crystals of noble gases. The presented results for crystals of noble gases are in a good agreement with experimental data.

The saturation and non-saturation phenomena for pinning force density are described. Models for these phenomena are introduced and compared experimentally. It can be concluded that the non-saturation phenomenon observed in commercial Nb-Ti belongs to the pinning regime of higher pinning performance than the saturation phenomenon observed in Nb3Sn. Such classification is determined by the number density and elementary pinning force of the pinning centers. The peculiar behavior of flux lines in the saturation phenomenon can be clarified by a small AC ripple field measurement called Campbell's method. An avalanching flux flow model based on this experimental result explains the saturation and non-saturation properties well.

Current–voltage ( I – V ) measurements were carried out for different current sweep rates (d I /d t ) of transport current at zero magnetic field ( H = 0) and H ≠ 0 in a polycrystalline sample of Bi 1.7 Pb 0.3 Sr 2 Ca 2 Cu 3 O x (BSCCO) with a macroscopic cylindrical hole (CH) drilled. Similar measurements were also performed in the same BSCCO sample without CH for a comparison before drilling CH. For the same values of H , T , and d I /d t taken for both samples, it was observed that hysteresis effects appear in I – V curves upon cycling of transport current in upward and downward directions which contain the increasing and decreasing current values, respectively. However these effects which are seen in I – V curves of BSCCO sample with CH is more prominent than that of the BSCCO sample without CH. Further, the irreversibility effects in I – V curves of the BSCCO sample without CH disappears for H ≠ 0 exhibiting nearly a linear behaviour, whereas the hysteretic behaviour in I – V curves of the BSCCO sample with CH is still observed. This interesting behaviour could be evaluated that macroscopic cylindrical hole improves pinning properties of sample acting as a macroscopic flux pinning center for flux lines.

In this paper, we suggest methods for calculating the magnetic conductivity of plane-paralle, planemeridian, and three-dimensional magnetic fields. The following assumptions are made: flux lines are replaced by straight lines and arcs or smooth lines constructed manually in scale pictures; a coil with current is considered to be an infinite thin wire or layer etc. Methods are recommended for use during the first steps of the design of a magnetic system.

This thesis is dedicated to the evaluation and the improvement of the synchronous reluctance machine’s performance for variable speed drive applications in general and for automotive applications in particular. The two axes of development are machine design and phase current harmonics injection. The rotor is an important element in the machine design and particular emphasis is placed to the design and evaluation of the rotor for enhancing the machine performance. An analytical procedure is proposed for the rotor design. The rotor elements like the ribs and the bridges that maintain the rotor mechanically strong as well as the q-axis insulation ratio (air-to-steel ratio) are studied. A computer-aided design study based on a parametric optimization problem is presented as well. The main three families of the optimization algorithms are evaluated for the optimization procedure: a gradient-based algorithm (Quasi Newton Algorithm), a non-gradient based non-evolutionary algorithm (Nelder Mead Simplex) and a non-gradient based evolutionary algorithm (Genetic Algorithm). The machine designs based on the analytical procedure and the optimization procedure are both manufactured and tested on a bench. The second axis of study of the thesis is the injection of harmonics in the phase currents of the synchronous reluctance machine. The interaction of current harmonics with the spatial inductance harmonics is studied and formalized for an m-phase machine. Then, the harmonics injection concept is evaluated in the particular case of a 2-phase machine. This study shows the benefi t of harmonics injection in the reduction of the machine torque ripple. A synchronous reluctance machine design is fi nally developed for an automotive application based on parametric optimization of the stator and rotor. This design is evaluated for the electromagnetic specifi cations imposed by a mid-power electric vehicle traction application

We report on the effects of neutron irradiation on the irreversible magnetic properties of MgB2 single crystals. The size of the newly created defects is comparable to the superconducting coherence length of MgB2, which makes these defects particularly suitable for pinning flux lines. Indeed, we observe significant quantitative and qualitative modifications of the critical current density. In particular, a second peak (fishtail effects) emerges in the field dependence and is accompanied by history effects. The fishtail effect is thoroughly studied with respect to different neutron fluences and good agreement with a recent theoretical explanation by an order-disorder transition is obtained.

Among the different methods of vortex study in superconductors, Scanning Tunneling Microscopy (STM) and Spectroscopy (STS), occupies a particular place. Due to its extraordinary spatial and energy resolution STS allows the study of vortices in real space on a nanometeric scale. In practice however, the success of the observation of vortices by STS depends strongly on the surface quality. Usually highly uniform surfaces are needed to distinguish vortices. As a result of this limitation, the vortex lattice has been successfully studied only in a limited number of superconductors. Here we suggest a simple method extending the vortex analysis to 'difficult cases' of 'bad' superconductors, thin films and even granular materials. In this method the STM tip is positioned in a chosen location of the sample and the local tunneling spectroscopy is continuously performed while the magnetic field is slowly swept. The vortices entering the sample move under the tip and are detected due to the change in the shape of tunneling spectra. We show that the method allows not only to follow the vortex penetration but also to estimate essential superconducting parameters such as the penetration and the coherence lengths. Moreover, it authorizes the study of the vortex cores in the cases where scanning is difficult or impossible. (c) 2005 Elsevier Ltd. All rights reserved.

The infinite square well potential in one dimension has a smooth supersymmetric partner potential which is shape invariant. In this paper, we study the generalization of this to two dimensions by constructing the supersymmetric partner of the disk billiard. We find that the property of shape invariance is lost in this case. Nevertheless, the WKB results are significantly improved when SWKB calculations are performed with the square of the superpotential. We also study the effect of inserting a singular flux line through the center of the disk.

A significant overestimation of the critical current density Jc was discovered in a measuring method that utilizes induced third harmonic voltage for thin superconductors with a thickness less than 1 μm. This is speculated to be caused by the reversible motion of flux lines in the pinning potential, which reduces nonlinear properties such as hysteresis loss or third harmonic voltage. It is known that the effect of reversible flux motion is prominent for superconductors comparable to or smaller than the pinning correlation length at the sub-micrometer order called Campbell's AC penetration depth. In this paper, the effect of reversible flux motion on the estimation of Jc utilizing this method is investigated using a simplified Campbell's model for the force-displacement characteristics of flux lines, and the factor of overestimation of Jc is discussed.

The pinning properties of vortices of four different compounds of the κ-(BEDT-TTF) 2 X family are presented. From the characteristic energies for pinning, we establish scaling laws for the evolution of the penetration depth and the anisotropy with respect to chemical pressure. These quantities are then deduced as unpinning in the liquid phase is attributed to disentanglement of the flux lines.

Size dependencies of the peak effect and irreversibility field in superconducting Sm-123 powder specimens were investigated. The peak effect was found to disappear in the two-dimensional pinning regime in which powder size is smaller than pinning correlation length. This shows that the peak effect does not originate directly from elementary pinning mechanisms, but from a cooperative phenomenon of flux lines, as proposed by the pinning-induced disorder transition model. In addition, when powder size is smaller than virtual pinning correlation length in the ideal creep-free case, irreversibility field decreases with powder size. This supports the hypothesis that longitudinal flux bundle size is given by this length, as predicted by flux creep theory. These findings indicate that pinning correlation length is a general parameter that determines various properties associated with flux pinning phenomena.

We present strong evidence observed in a YBCO superconducting tube that helical flux lines can concurrently enter and leave across the inner surface of the wall of a hollow cylinder of sintered high-Tc superconductors at 77 K, and hence cut and traverse each other. The evidence for flux line cutting and cross-flow is examined in the perspective of basic concepts. The traffic of the flux lines is also described mathematically. The penetration fields across the wall and into the grains of the sintered ceramic tube are seen to correlate with salient features (peaks and valleys) of the flux line cutting and cross-flow phenomena. This enables us to claim that we are witnessing flux line cutting and cross-flow in the weak links as well as in the interior of the grains in the YBCO tube. The Clem/Perez-Gonzalez phenomenological theory is exploited in a simplified framework to describe the crucial features of the data semi-quantitatively. This analysis confirms the above conclusions and provides estimates of jc||m and jc||g, the critical current densities for intergranular and intragranular flux line cutting and their dependence on the magnetic flux density.

Using the Lagrangian formalism we attempt to calculate the interaction energy between the two bodies, nonconnected and connected, in a linear lattice. The obtained results show that the interaction is dependent on the dispersion relation ω (q). On this basis we calculate the binding energy of an ionic lattice and we have found a good agreement with experimental data.

Current–voltage characteristics are investigated in Bi1.8Pb0.2Sr2CaCu2O8+δ single crystals irradiated by high-energy heavy-ions parallel and along the direction tilted by 45° from to the c-axis. The angular dependence of the resistance exhibits, in the vortex solid state and for T≥40 K, a usual unidirectional effect when a magnetic field is aligned to the columnar defects (CDs) for both samples. In the case of inclined defects two dips are available: one in the direction parallel to the tracks and the other perpendicularly. The melting transition for magnetic field applied parallely to the CDs and over a wide filling factor (f

We study the topologically protected Majorana zero modes induced by lattice dislocations in chiral topological superconductors. Dislocations provide a new way to realize Majorana modes at zero magnetic field. In particular, we study several different types of dislocations in the candidate material ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$ We also discuss the properties of linked dislocation lines and linked dislocation and flux lines. Various experimental consequences are predicted which provide an approach to determine the nature of the superconducting phase of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$

Microstructures of flux lines (FL) in Bi 2 Sr 2 CaCu 2 O 8 single crystals are observed by a high-resolution Bitter-decoration technique. Experiments were performed at low (4.2 K) and high (77 K) temperatures under a constant magnetic field of 20 G. We could observe the interaction between FL and defects of materials, such as growth steps and other planar crystal defects. FL near defects were remarkably different between low and high temperatures. We also found that planar crystal defects, which extended parallel to the a -axis, were only active at low temperatures.

The creep motions of flux lines in both Bragg glass (BrG) and vortex glass (VG) are studied. The power-law dependence of the creep activation barrier on the driving force is obtained. Two universal classes of creep motion are found with the exponent μ=0.5±0.02 for the BrG and μ=0.28±0.02 for the VG. The former is in good agreement with the prediction by the scaling theory and the functional-renormalization-group theory on creep, while the latter is a new estimate. The different dynamics of flux lines in the VG and in the BrG are investigated accordingly.

It is well known that the point charge, line charge and homogeneously charged plane of infinite extent are sources of electrostatic fields with straight flux lines. It is proved in this note that provided these flux lines occupy all of three-dimensional space, then these charge configurations and appropriate variants of them are the only sources of straight-line electrostatic fields in R 3.