Power-law Resistivity Research Articles

Model of a non-Fermi liquid with power-law resistivity: Strange metal with a not-so-strange origin

Model of a non-Fermi liquid with power-law resistivity: Strange metal with a not-so-strange origin

Numerical studies on resistance of concrete target under rigid projectile impact using Perzyna-type visco-damage model

In this paper, a whole process resistance analysis of the concrete target impacted by the high-speed rigid projectile is presented. Combining the SPH method with the established rate-dependent Perzyna-type visco-damage constitutive relationship, the behaviors of concrete targets under rigid bullet impact are simulated, which is validated by test data. The investigation into the relationship between the acceleration and the velocity of rigid bullets reveals that the resistance of concrete under impact is composed of two parts: a velocity-independent static term provided by the solid component and a velocity power function term provided by the component that is converted into pseudoplastic fluid due to high-speed striking. Finally, the analytic formulae are built using the power-law resistance model, which can predict penetration depths at different initial velocities as well as the movement of the bullet.

Effect of Gaussian Disorder on Power-Law Contact Resistance and Mobility in Organic Field-Effect Transistors

We study the effect of Gaussian energetic disorder on the organic field-effect transistors (OFETs) with surprisingly high field-effect mobility and the low contact resistance. The numerical device simulation assumes the thermally assisted hopping transport and injection in disordered semiconductors. The results are analyzed with the power-law field-effect mobility and the asymptotic power-law contact resistance model. Transistor parameters extracted by the models reveal that a higher Gaussian disorder, which leads to a lower injection barrier and a larger mobility enhancement, is the origin of the high field-effect mobility and the low contact resistance.

Resistivity of REBCO tapes in overcritical current regime: impact on superconducting fault current limiter modeling

A detailed knowledge of the resistivity of high-temperature superconductors in the overcritical current regime is important to achieve reliable numerical simulations of applications such as superconducting fault current limiters. We have previously shown that the combination of fast pulsed current measurements and finite element analysis allows accounting for heating effects occurring during the current pulses. We demonstrated that it is possible to retrieve the correct current and temperature dependence of the resistivity data points of the superconductor material. In this contribution, we apply this method to characterize the resistivity vs. current and temperature of commercial REBCO tapes in the overcritical current regime, between 77 and 90 K and in self-field conditions. The self-consistency of the overcritical resistivity model is verified by comparing DC fault measurements with the results of numerical simulations using this model as input. We then analyze by numerical simulation to what extent using the model instead of the widely used power-law model affects the thermal and electrical performance of the tapes in the practical case of a superconducting fault current limiter. A remarkable difference is observed between the measured overcritical current resistivity model and the power-law resistivity model . In particular, the simulations using the power-law model show that the device quenches faster than with the overcritical resistivity model. This information can be used to optimize the architecture of the stabilizer in superconducting fault current limiters.

Electromagnetic Modeling of Superconductors With Commercial Software: Possibilities With Two Vector Potential-Based Formulations

In recent years, the $H$ formulation of Maxwell's equation has become the de facto standard for simulating the time-dependent electromagnetic behavior of superconducting applications with commercial software. However, there are cases where other formulations are desirable, for example for modeling superconducting turns in electrical machines or situations where the superconductor is better described by the critical state than by a power-law resistivity. In order to accurately and efficiently handle those situations, here we consider two published approaches based on the magnetic vector potential: the $T$-$A$ formulation of Maxwell's equations (with power-law resistivity) and Campbell's implementation of the critical state model. In this contribution, we extend the $T$-$A$ formulation to thick conductors so that large coils with different coupling scenarios between the turns can be considered. We also revise Campbell's model and discuss it in terms of its ability to calculate AC losses: in particular, we investigate the dependence of the calculated AC losses on the frequency of the AC excitation and the possibility of using quick one-step (instead of full cycle) simulations to calculate the AC losses.

Coherent vs incoherent transport in holographic strange insulators

Holographic strange metals are known to have a power law resistivity rising with temperature, which is reminiscent of the strange metal phases in condensed matter systems. In some holographic models, however, the exponent of the power law in the resistivity can be negative. In this case one encounters phases with diverging resistivity at zero temperature: holographic strange insulators.These states arise as a result of translational symmetry breaking in the system, which can either be strong explicit and relevant in the IR, or spontaneous, but pinned by a small explicit source. In some regards, one can associate these two classes to the normal band insulators due to the strong ionic potential, and Mott insulator due to the commensurate lock in of the charge density wave.We study different features of these classes on the explicit example of a holographic helical model with homogeneous Bianchy VII type translational symmetry breaking, and uncover the main mechanisms underlying transport in these two cases. We find that while transport in the explicit relevant case is governed by the incoherent conductivity, in the pinned spontaneous case the leading contribution comes from the coherent part.

A Finite-Element Method Framework for Modeling Rotating Machines With Superconducting Windings

Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic modeling of superconductors by finite-element method (FEM) is usually based on a power-law resistivity for their electrical behavior. The implementation of such constitutive law in conventional models of electrical machines is quite problematic: the magnetic vector potential directly gives the electric field and requires using a power-law depending on it. This power-law is a non-bounded function that can generate enormous uneven values in low electric field regions that can destroy the reliability of solutions. The method proposed here consists in separating the model of an electrical machine in two parts, where the magnetic field is calculated with the most appropriate formulation: the H-formulation in the part containing the superconductors and the A-formulation in the part containing conventional conductors (and possibly permanent magnets). The main goal of this work is to determine and to correctly apply the continuity conditions on the boundary separating the two regions. Depending on the location of such boundary -- in the fixed or rotating part of the machine -- the conditions that one needs to apply are different. In addition, the application of those conditions requires the use of Lagrange multipliers satisfying the field transforms of the electromagnetic quantities in the two reference systems, the fixed and the rotating one. In this article, several exemplary cases for the possible configurations are presented. In order to emphasize and capture the essential point of this modeling strategy, the discussed examples are rather simple. Nevertheless, they constitute a solid starting point for modeling more complex and realistic devices.

Roughness height of submerged vegetation in flow based on spatial structure

The classic hydraulic resistance formulas, such as those in the Darcy-Weisbach methods, perform well in the hydraulic design with the characteristic roughness height ks smaller than the flow depth, which can be linked with the momentum roughness height based on the turbulent boundary-layer theory with the log-law formulation. However, when the roughness scale is of the same order as the flow depth, the traditional log-law formulation cannot provide satisfactory results because the flow structure is complicated and the vortices in different layers are dominated by various principles, such as the Karman streets near the channel bed, the mixing layer near the vegetation top, and a canonical turbulent boundary layer above the vegetation layer. Thus, the distribution of the streamwise velocity in the vegetated flow is a combination of the velocity profile linked with the dominant vortex and shows significant differences as compared with the traditional log-law distribution. This paper proposes a new characteristic roughness height of vegetation kv by linking vegetation attributes, especially the characteristics of the cross section in the flow within the vegetation. The power law resistance formula is derived based on a large amount of experimental data. Results show that the new formula is applicable to shallow flows with vegetation.

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

The electrons in the edge channels of two-dimensional topological insulators can be described as a helical Tomonaga-Luttinger liquid. They couple to nuclear spins embedded in the host materials through the hyperfine interaction, and are therefore subject to elastic spin-flip backscattering on the nuclear spins. We investigate the nuclear-spin-induced edge resistance due to such backscattering by performing a renormalization-group analysis. Remarkably, the effect of this backscattering mechanism is stronger in a helical edge than in nonhelical channels, which are believed to be present in the trivial regime of InAs/GaSb quantum wells. In a system with sufficiently long edges, the disordered nuclear spins lead to an edge resistance which grows exponentially upon lowering the temperature. On the other hand, electrons from the edge states mediate an anisotropic Ruderman-Kittel-Kasuya-Yosida nuclear spin-spin interaction, which induces a spiral nuclear spin order below the transition temperature. We discuss the features of the spiral order, as well as its experimental signatures. In the ordered phase, we identify two backscattering mechanisms, due to charge impurities and magnons. The backscattering on charge impurities is allowed by the internally generated magnetic field, and leads to an Anderson-type localization of the edge states. The magnon-mediated backscattering results in a power-law resistance, which is suppressed at zero temperature. Overall, we find that in a sufficiently long edge the nuclear spins, whether ordered or not, suppress the edge conductance to zero as the temperature approaches zero.

Cd2Re2O7under high pressure: Pyrochlore lattice distortion-driven metal-to-nonmetal transition

Pyrochlore ${\mathrm{Cd}}_{2}{\mathrm{Re}}_{2}{\mathrm{O}}_{7}$ has been investigated under high pressure by x-ray diffraction, resistivity and, mid-IR reflectance measurements. At $\ensuremath{\sim}14$ GPa, the high-temperature cubic pyrochlore phase [space group (SG): $Fd\overline{3}m$] undergoes a second-order transition to a rhombohedral structure (SG: $R\overline{3}m$) with trigonal distortion in its pyrochlore lattice. Temperature-dependent resistivity $\ensuremath{\rho}(T)$ reveals a large number of exotic electronic phases (including superconducting and unconventional metallic phases) in its $P\text{\ensuremath{-}}T$ phase diagram. At the metal-nonmetal boundary (at 21 GPa) the resistivity displays quadratic power-law behavior over a wide $T$ range with possible formation of heavy mass coherent quasiparticles. In the nonmetallic state $(d\ensuremath{\rho}/dTl0)$, the nondivergent and quadratic power-law resistivity as $T\ensuremath{\rightarrow}0$ reveals the novel character of the ground state. High-pressure optical conductivity measurement evidences electronic correlation playing the vital role in the emergence of the nonmetallic state as the electron-lattice coupling exceeds spin-orbit interaction due to large structural distortion.

Scaling Law for Hysteresis Losses in Round Superconductors Magnetized by Alternating, Rotating or Elliptical Magnetic Fields

AC losses in an isolated superconducting round wire with a power-law electrical behavior produced by the combined effect of transverse alternating and rotating fields, i.e., an elliptical field, are investigated. The goal is to provide semianalytical expressions of the magnetization losses with a high enough reliability to be used in sizing code development or optimization methods. The fit expressions are based on data generated by means of a 2-D numerical model using the well-known and proved H-formulation. In the meantime, data processing allows for revealing a universal variable cn of utmost importance in magnetization loss calculation. This variable depends on the n-value of the power-law resistivity, and both the dimensionless magnetic field b* and frequency f*.

Solving the critical state using flux line properties

A method of solving the critical state in superconductors using the vector potential and commercial software (FlexPDE) is described. It avoids both time dependence and power law resistivity. It uses a material parameter which describes how far flux lines move before most become unpinned. This allows small oscillations and minor hysteresis loops to be modelled. The theory is applied to the problem of demagnetisation in bulks due to crossed fields. It may explain why experimental results do not agree with theory. The theory can be extended to coils, and two and three dimensions. This requires the introduction of a scalar potential Vo. This is not the usual scalar potential, which is due to electrostatic charges as the field is run up, but the integral of this value at the final field after charges have dissipated.

A Time-Harmonic Approach to Numerically Model Losses in the Metal Matrix in Twisted Superconductors in External Magnetic Field

The first NbTi superconductor was developed in 1962 at Westinghouse. During 50 years, the manufacturing process of NbTi wires became highly optimized, and complex wire structures, which are needed in reducing ac losses, can be produced these days. Twisted multifilamentary structures generate many challenges from the modeler's point of view. Considering numerical modeling, NbTi wires are too complicated to model with filament-level details. This is due to the high number and very nonlinear resistivity of filaments. Consequently, simplified approaches are needed for wire modeling. In this paper, a time-harmonic approach to model losses in the metal matrix is introduced. It is based on the linear approximation of filaments. The method to determine the linear resistivity of filaments is based on the definition of the skin depth and the radius of filaments. This can be done in advance without solving a nonlinear problem in 3-D. The suitability of the time-harmonic approach is benchmarked against the H-formulated 3-D eddy current model (ECM) with power-law resistivity. According to simulations, the losses in the metal matrix predicted by the time-harmonic approach agreed well with the nonlinear ECM when the filaments were uncoupled. The results achieved with the proposed approach similarly followed the effects of geometrical changes in the wire structure on losses as the nonlinear ECM and predicted the circumstances where the filaments became partially coupled. The simulation times were considerably lower with the new approach. From the manufacturer's perspective, it is important to design conductors where the filaments stay uncoupled and have low ac losses in such a situation. Thus, the new approach can provide an effective design tool in developing new superconductors.

Ripple field losses in direct current biased superconductors: Simulations and comparison with measurements

In several superconducting applications, as, for example, in some supercondcuting generators, motors, and power transmission cables, the superconductor experiences a changing magnetic field in a DC background. Simulating the losses caused by this AC ripple field is an important task from the application design point of view. In this work, we compare two formulations, the H-formulation and the minimum magnetic energy variation-formulation, based on the eddy current model (ECM) and the critical state model (CSM), respectively, for simulating ripple field losses in a DC biased coated conductor tape. Furthermore, we compare our simulation results with measurements. We investigate the frequency-dependence of the hysteresis loss predictions of the power law based ECM and verify by measurements, that in DC use, ECM clearly over-estimates the homogenization of the current density profile in the coated conductor tape: the relaxation of the local current density is not nearly as prominent in the measurement as it is in the simulation. Hence, we suggest that the power law resistivity, used as the local relation between the electric field intensity E and current density J in ECM, is not an intrinsic property of high-temperature superconductors. The difference between the models manifests itself as discrepancies in ripple field loss simulations in very low AC fields with significant DC fields or currents involved. The results also show, however, that for many practical situations, CSM and ECM are both eligible models for ripple field loss simulations.

Holographic Lattices Give the Graviton an Effective Mass

We discuss the dc conductivity of holographic theories with translational invariance broken by a background lattice. We show that the presence of the lattice induces an effective mass for the graviton via a gravitational version of the Higgs mechanism. This allows us to obtain, at leading order in the lattice strength, an analytic expression for the dc conductivity in terms of the size of the lattice at the horizon. In locally critical theories this leads to a power law resistivity that is in agreement with an earlier field theory analysis of Hartnoll and Hofman.

Current-Penetration Patterns in Twisted Superconductors in Self-Field

In a straight and untwisted superconducting wire, the current penetrates from the edges and flows along the wire's axis. The generated self-field is in the wire's cross-section plane and always perpendicular to the current. Bean's critical state model (CSM) describes the mesoscopic current and magnetic field penetration in such a configuration. Also, by using power-law resistivity, an eddy current problem can be formulated to simulate such a case. However, when a conductor is twisted, the self-field is no longer perpendicular to the helicoidal trajectories of the filaments. When this non-perpendicularity of the magnetic field occurs, the current does not flow along the helicoidal lines of the filaments. If that was the case, the central regions of the filaments would not be shielded from the magnetic field. In this paper we investigate current penetration in a twisted configuration by means of numerical simulations. We used the finite element method to solve eddy current formulations where the resistivity in the superconducting regions was described with an isotropic power-law model.

The Difficulty of Modeling Ripple Field Losses in Superconductors Using the Eddy Current Model

The eddy current (EC) model is a widely used tool for simulating hysteresis losses in superconductors. It is a reliable way to estimate losses in 50 Hz transport current, applied field or AC-AC cases. However, in some applications, such as synchronous electric motors with superconducting field windings, a small multifrequency external magnetic field is present while a superconducting coil carries a DC current. In such cases, the use of the EC model becomes challenging. In this paper, we investigate the challenges confronted in such cases by using the EC model in their simulation. It is observed that the EC model using the power law resistivity leads to current density profile homogenization even when no changes happen in the driving quantities. Also, modeling uncoupled cases in which a DC bias current flows in the conductor is troublesome.

Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films: II. Applications

A normal power-law distribution of local resistivity with a uniform dielectric constant was found to be consistent with the constant-phase element (CPE). An analytic expression, based on the power-law resistivity distribution, was found that relates CPE parameters to the physical properties of a film. This expression worked well for such diverse systems as aluminum oxides, oxides on stainless steel, and human skin. Good values for film thickness were obtained, even when previously proposed expressions could not be used or yielded incorrect results. The power-law model yields a CPE impedance behavior in an appropriate frequency range, defined by two characteristic frequencies. Ideal capacitive behavior is seen above the upper characteristic frequency and below the lower characteristic frequency. A symmetric CPE response between the characteristic frequencies can be obtained by adding a parallel resistive pathway.

Power-law resistivity, magnetic relaxation and ac susceptibility

The nonlinear diffusion of magnetic flux into a superconducting sample can be studied by measuring the relaxation of the magnetisation after application of a step field or by measuring the ac susceptibility, χ 1 and its third harmonic, χ 3, or preferably both methods covering different time scales. Each has been analysed recently for a field-cooled sample of a material whose creep activation energy depends logarithmically on current density, J corresponding to a power-law relation between electric field, E and J. Here, results are compared, using a universal scaling depth. Maximum χ 1″ and |χ 3| values occur, and also the magnetisation has relaxed to half its initial value when the scaling depth is comparable to the sample half-thickness.

Momentum and Energy Coefficients Based on Power‐Law Velocity Profile

The theoretical momentum coefficient (β\N) and energy coefficient (α\N for turbulent shear flow in circular pipes and wide channels are derived from the power law, then compared with their counterparts on the basis of the logarithmic law. For such undirectional flows, the exponent (\Im\N) of the power-law velocity distribution is the sole parameter that determines the values of β\N and α\N. A comparison of the corresponding expressions for β\N and α\N derived using both laws shows that their values differ only slightly within a valid range of small \Im\N’s. Use of a power-law–based β\N expression along with a power-law resistance formula in the cross-section–averaged equation of momentum can not only eliminate the theoretical incompatibility that results from mixing logarithmic and power laws in the equation but also remove the inconsistent assumption of β\N = 1 made in the equation. Improvement on the accuracy of the flow equation of momentum is demonstrated through an example in which a new stability limit for the Froude number for turbulent shear flow in wide channels can be accurately derived without assuming β\N = 1.