Violation of magnetic flux conservation by superconducting nanorings

The behavior of magnetic flux in the ring-shaped finite-gap superconductors is explored from the view-point of the flux-conservation theorem which states that under the variation of external magnetic field "the magnetic flux through the ring remains constant" (see, e.g., [L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuos Media, vol. 8 (New York, Pergamon Press, 1960), Section 42]). Our results, based on the time-dependent Ginzburg-Landau equations and COMSOL modeling, made it clear that in the general case, this theorem is incorrect. While for rings of macroscopic sizes the corrections are small, for micro and nanorings they become rather substantial. The physical reasons behind the effect are discussed. The dependence of flux deviation on ring sizes, bias temperature, and the speed of external flux evolution are explored. The detailed structure of flux distribution inside of the ring opening, as well as the electric field distribution inside the ring's wire cross section are revealed. Our results and the developed finite element modeling approach can assist in elucidating various fundamental topics in superconducting nanophysics and in the advancement of nanosize superconducting circuits prior to time-consuming and costly experiments.

Shadow wave solutions for a scalar two-flux conservation law with Rankine–Hugoniot deficit

This paper deals with hyperbolic conservation laws exhibiting a flux discontinuity at the origin and which does not admit a weak solution satisfying the Rankine–Hugoniot jump condition. We therefore seek unbounded solutions in the form of shadow waves supported by at the origin. The shadow waves are defined as nets of piecewise constant functions approximating a shock wave to which we add a delta function and possibly another unbounded part.

On the Transmittance of Metallic Superlattices in the Optical Regime and the True Refraction Angle

Transmission of electromagnetic fields through (dielectric/metallic)n superlattices, for frequencies below the plasma frequency ωp, is a subtle and important topic that is reviewed and further developed here. Recently, an approach for metallic superlattices based on the theory of finite periodic systems was published. Unlike most, if not all, of the published approaches that are valid in the n→∞ limit, the finite periodic systems approach is valid for any value of n, allows one to determine analytical expressions for scattering amplitudes and dispersion relations. It was shown that, for frequencies below ωp, large metallic-layer thickness, and electromagnetic fields moving along the so-called “true” angle, anomalous results with an apparent parity effect appear. We show here that these results are related to the lack of unitarity and the underlying phenomena of absorption and loss of energy. To solve this problem we present two compatible approaches, both based on the theory of finite periodic systems, which is not only more accurate, but has also the ability to reveal and predict the intra-subband resonances. In the first approach we show that by keeping complex angles, above and below ωp, the principle of flux conservation is fully satisfied. The results above ωp remain the same as in Pereyra (2020). This approach, free of assumptions, where all the information of the scattering process is preserved, gives us insight to improve the formalism where the assumption of electromagnetic fields moving along the real angles is made. In fact, we show that by taking into account the induced currents and the requirement of flux conservation, we end up with an improved approach, with new Fresnel and transmission coefficients, fully compatible with those of the complex-angle approach. The improved approach also allows one to evaluate the magnitude of the induced currents and the absorbed energy, as functions of the frequency and the superlattice parameters. We show that the resonant frequencies of intra-subband plasmons, which may be of interest for applications, in particular for biosensors, can be accurately determined. We also apply the approach for the transmission of electromagnetic wave packets, defined in the optical domain, and show that the predicted space-time positions agree extremely well with the actual positions of the wave packet centroids.

Modified virial theorem for highly magnetized white dwarfs

ABSTRACT Generally the virial theorem provides a relation between various components of energy integrated over a system. This helps us to understand the underlying equilibrium. Based on the virial theorem we can estimate, for example, the maximum allowed magnetic field in a star. Recent studies have proposed the existence of highly magnetized white dwarfs (B-WDs), with masses significantly higher than the Chandrasekhar limit. Surface magnetic fields of such white dwarfs could be more than $10^{9}$ G with the central magnitude several orders higher. These white dwarfs could be significantly smaller in size than their ordinary counterparts (with surface fields restricted to about $10^9$ G). In this paper, we reformulate the virial theorem for non-rotating B-WDs in which, unlike in previous formulations, the contribution of the magnetic pressure to the magnetohydrostatic balance cannot be neglected. Along with the new equation of magnetohydrostatic equilibrium, we approach the problem by invoking magnetic flux conservation and by varying the internal magnetic field with the matter density as a power law. Either of these choices is supported by previous independent work and neither violates any important physics. They are useful while there is no prior knowledge of field profile within a white dwarf. We then compute the modified gravitational, thermal, and magnetic energies and examine how the magnetic pressure influences the properties of such white dwarfs. Based on our results we predict important properties of these B-WDs, which turn out to be independent of our chosen field profiles.

Study on the influence of dynamic/static interface processing methods on CFD simulation results of the axial-flow blood pump

Computational fluid dynamics is an essential tool for the flow field analysis of the blood pump. The interface processing method between the dynamic/static regions will affect the accuracy of simulation results, but its influence on the simulation results is still unclear. In this study, the axial-flow blood pump was taken as the research object, and the effects of the mixing plane, frozen rotor, and sliding mesh methods on the following results were compared: flux conservation at the interface, hydraulic characteristics, and velocity field distribution. In parallel, the particle image velocimetry experiment was carried out to measure the velocity field of the impeller, the inlet, and the outlet area of the blood pump. The results show that the above methods have significant differences in flux conservation between the impeller and the back vane. The average surface energy flux’s error of frozen rotor and sliding mesh are 0.7% and 0.72%, respectively, while the mixing plane method reaches 3.6%. This nonconservative transfer affects the distribution of the downstream velocity field, and the velocity field predicted by the mixing plane at the outlet is quite different. It is suggested to use the frozen rotor method and the sliding mesh method in the simulation of the blood pump.

Unified quaternionic description of charge and spin transport and intrinsic nonlinearity of spin currents

We present a unified theory of charge and spin transport using quaternionic formalism. It is shown that both charge and spin currents can be combined together to form a quaternionic current. The scalar and vector part of quaternionic currents correspond to charge and spin currents, respectively. We formulate a unitarity condition on the scattering matrix for quaternionic current conservation. It is shown that in the presence of spin flip interactions, a weaker quaternionic unitarity condition implying charge flux conservation but spin flux nonconservation is valid. Using this unified theory, we find that spin currents are intrinsically nonlinear. Its implication for recent experimental observation of spin generation far away from the boundaries are discussed.

Lorentz invariant ‘potential magnetic field’ and magnetic flux conservation in an ideal relativistic plasma

A family of Lorentz invariant scalar functions of the magnetic field is defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the potential magnetic field introduced by Hide in (Ann. Geophys., vol. 1, 1983, 59) along the lines of Ertel’s theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the mapping from Eulerian to Lagrangian variables. In addition, the adopted procedure allows us to formulate, in a Lorentz invariant form, the Alfvén theorem for the conservation of the magnetic flux through a surface comoving with the plasma.