Vortex Lines Research Articles

Exploring the free-energy landscape of a rotating superfluid.

The equilibrium state of a superfluid in a rotating cylindrical vessel is a vortex crystal-an array of vortex lines, which is stationary in the rotating frame. Experimental realizations of this behavior typically show a sequence of transient states before the free-energy-minimizing configuration is reached. Motivated by these observations, we construct a new method for a systematic exploration of the free-energy landscape via gradient-based optimization of a scalar loss function. Our approach is inspired by the pioneering numerical work of Campbell and Ziff [Phys. Rev. B. 20, 1886 (1979)] and makes use of automatic differentiation, which crucially allows us to include entire solution trajectories in the loss. We first use the method to converge thousands of low free-energy relative equilibria in the unbounded domain for vortex numbers in the range 10≤N≤30, which reveals an extremely dense set of mostly saddle-like solutions. As part of this search, we discover new continuous families of relative equilibria, which are often global minimizers of free energy. These continuous families all consist of crystals arranged in a double-ring configuration, and we assess which state from the family is most likely to be observed experimentally by computing energy-minimizing pathways from nearby local minima-identifying a common entry point into the family. The continuous families become discrete sets of equal-energy solutions when the wall is introduced in the problem. Finally, we develop an approach to compute homoclinic orbits and use it to examine the dynamics in the vicinity of the minimizing state by converging connections for low-energy saddles.

Model of the photon made up of lines of elementary waves. Realistic explanation of obtaining interferences by emitting photons one by one through two Young’s slits

The theory of the dynamic medium of reference (DMR) has already been presented in several articles, in particular, by Olivier Pignard [Phys. Essays 32, 422 (2019)]. The objective of this article is to present a model of the photon within the framework of the DMR theory. A concept of elementary wave on the subatomic level is introduced. An elementary wave is always identical to itself while being constantly renewed by new gravitons (entities that make up the medium of propagation of the wave). This elementary wave propagates in its medium (DMR) at the speed of light whatever its trajectory. A possible model of the elementary wave called light-vortex is presented in Appendix B. Then the concept of line of vortices is introduced. The vortices constituting a line all have their axis parallel to each other and perpendicular to the direction of propagation are separated by half a wavelength and rotate alternately in one direction and the other. The model of the proposed photon is then a set of lines of vortices parallel to each other (the number of lines of vortices as well as the length of the photon are constants whatever the frequency of the photon.) This model makes it possible to attribute to the photon, the speed c, a frequency ν, a period T = 1/ν, a wavelength λ = c/ν, the energy E = hν, the momentum p = E/c =h · ν/c, and even a polarization (rectilinear, circular, or elliptical). It allows above all to explain that the photon has at the same time a wave aspect (because composed only of elementary waves) and a corpuscular aspect (since the elementary waves remain identical to themselves and the photon remains delimited by the same volume). It also explains the phenomenon of diffraction by emitting photons, even one by one, through a slit and that of interferences by emitting photons, even one by one, through two Young’s slits.

Weather system classification and water vapor transport characteristics of extreme value rainstorm in northwestern Hunan

Abstract Using meteorological analysis, composite analysis and water vapor trajectory analysis, the extreme value rainstorm process in northwest Hunan was analyzed. The results show that three types are summarized: the Southwest Vortex and Warm Shear Line Pattern (SVWSLP), the Subtropical High Edge Pattern (SHEP) and the Cold Trough and Shear Line Pattern (CTSLP). The main influence systems are upper trough, southwest vortex, shear line, low-level jet and subtropical high edge. For SVWSLP, the water vapor transport channels are only from the low-latitude ocean whether it is affected by long-distance typhoons. For SHEP, the main water vapor channel comes from the long-distance ocean and is finally transported to northwestern Hunan around 650 hPa in the form of warm and wet airflow, whether it is affected by long-distance typhoons. The CTSLP appears a significant water vapor confrontation between the north and the south and the baroclinicity of the atmosphere in the rainstorm area. The southern and western boundaries are the input boundary, while the eastern and northern boundaries are the outflow boundary. Therefore, one of the three types of weather systems appears in northwestern Hunan in May–August, with strong water vapor transport from the ocean surface, which is likely to cause extreme rainstorm.

Vortex rings in paraxial laser beams.

Interference of a fundamental vortex-free Gaussian beam with a co-propagating plane wave leads to nucleation of a series of vortex rings in the planes transverse to the optical axis; the number of rings grows with vanishing amplitude of the plane wave. In contrast, such interference with a beam carrying on-axis vortex with winding number l results in the formation of |l| rings elongated and gently twisted in propagation direction. The twist handedness of the vortex lines is determined by the interplay between dynamic and geometric phases of the Gaussian beam and the twist angle grows with vanishing amplitude of the plane wave. In the counter-propagating geometry the vortex rings nucleate and twist with half-wavelength period dominated by the interference grating in propagation direction.

High-frequency vortex dynamics and losses in the mixed state of nanostructured superconductors with columnar defects

We suggest a theoretical model for the microwave response of Abrikosov vortices in nanostructured superconductors with columnar defects, which serve as effective pinning sites for vortices that are considered elastic strings. For this case, we suppose that microwave losses related to the vortex oscillations in a microwave field arise caused by viscous oscillations of vortex kinks, which connect different parts of the vortex line pinned on adjacent columnar defects and vortex segments pinned on these defects. We consider the case of inclined magnetic field H, which creates vortex staircases consisting of pinned vortex segments and vortex kinks inside the superconductor. In this case, rf losses due to viscous kinks oscillations under the microwave current action arise even at T = 0 if the inclination angle of the magnetic field θΗ, concerning the columnar pinning site axis (z axis), exceeds some locking angle value θL.

Hybrid wave/current energy harvesting with a flexible piezoelectric plate

We investigate the dynamics and energy production capability of a flexible piezoelectric plate submerged close to the free surface and exposed to incident head gravity waves and current. A theoretical model is derived in which the flag and its wake are represented with a vortex line while the body of the fluid is considered to be inviscid. The model is employed to describe the hydrodynamic interactions between a flexible plate, its wake, gravity incident waves and the current. The model reveals two distinct vibration states of a piezoelectric device corresponding to almost similar optimal energy production levels. The first is associated with the cantilever fluttering mode of the plate, with limited dependency on the plate's flexibility across different Froude numbers and incoming wave frequencies. The other resembles the flow-induced flapping mode in more flexible plates, with the energy output showing a higher dependency on plate flexibility. The concurrent existence of these two energetic modes allows adjustment of the plate length to consistently achieve the maximum energy production level across different flow conditions. The role of the Froude number of the system's responses is explored and correlated to the appearance of gravity wave groups on the surface, each propagating with a different wavenumber. It is shown that a submergence depth of less than half of the body length is required to reach a high energetic condition in subcritical and critical flows. Finally, the optimal inductive and resistive values are related to proper matching between flow, mechanical and electrical time scales.

Quantum vortices of strongly interacting photons

Vortices are topologically nontrivial defects that generally originate from nonlinear field dynamics. All-optical generation of photonic vortices—phase singularities of the electromagnetic field—requires sufficiently strong nonlinearity that is typically achieved in the classical optics regime. We report on the realization of quantum vortices of photons that result from a strong photon-photon interaction in a quantum nonlinear optical medium. The interaction causes faster phase accumulation for copropagating photons, producing a quantum vortex-antivortex pair within the two-photon wave function. For three photons, the formation of vortex lines and a central vortex ring confirms the existence of a genuine three-photon interaction. The wave function topology, governed by two- and three-photon bound states, imposes a conditional phase shift of π per photon, a potential resource for deterministic quantum logic operations.

Numerical analysis of reverse wake-induced vibration at low Reynolds number

Reverse wake-induced vibration (RWIV) of two tandem cylinders with the downstream one fixed is numerically studied in this paper; Reynolds number is set as 150 (Re = 150). The effect of different spacing ratios (α) ranging from 3 to 6 with a gap of 0.5 is simulated to investigate the vibration characteristics of RWIV, where the spacing ratio (α) is defined as the nondimensional ratio of the center-to-center separation between the cylinders. As the spacing ratio increases from 3 to 6, RWIV shows a transition from galloping to vortex-induced vibration (VIV), which is also a reverse phenomenon compared to wake-induced vibration (WIV). As to the wake mode, two different types of vortex motion (2S - 2P - 2S and 2S - 2P) are observed within the given range of spacing ratio. Empirical modal decomposition is also applied to further analyze the vibration characteristics of galloping and VIV in RWIV. When the system shows galloping, the number of decomposed modes is larger with the increasing reduced velocity, and different vibration modes show evident mutual anisotropy. In addition, the vortex line diagram is used to analyze the wake vortex characteristics of the RWIV and to supplement the above findings.

Inertial considerations in peristaltically activated MHD blood flow model in an asymmetric channel using Galerkin finite element simulation for moderate Reynolds number

Numerically investigated analysis occupying considerations free from long wavelength and creeping flow regime has been addressed in this paper for non-Newtonian Casson fluid induced by peristaltic activity. Rheological measurements have been exposed by fluid progression in the asymmetric conduit influenced by a normally settled magnetic field. The analysis is made without implementation of the lubrication theory which allows the role of inertial forces in the flow model not addresses before. Galerkin formulated finite element method is practiced by simplifying full Navier-Stokes equations to assure the appearance of non-trivial Reynolds number and wave independence in an ongoing study. The solution hinged based on code formulated in MATLAB for velocity distribution, pressure profiles, vorticity lines, and stream function is graphically plotted. It has been deduced that inflating the Casson fluid parameter (0.1≤β≤0.5) drives an inappreciable reduction in velocity close to the central region and vorticity lines to remain unaffected. An appreciable increase in bolus formation is inspected by rising time mean flow (1.1≤Q≤1.6) with the diffusion of streamlines in the provision of a progressive phase in waves.

Turbine vane endwall aerothermal and film cooling performance considering realistic swirling inflow conditions

The turbine vane inlet downstream of the lean premixed combustor presents nonuniform distributions of velocity and temperature. For obtaining swirling inflow profiles close to reality, the simulated non-reacting combustor is designed firstly. Applying these profiles as inflow boundary conditions, the effects of realistic swirling inflow on the turbine vane endwall aerothermal characteristics and film cooling performance are numerically investigated through solving the three-dimensional Reynolds-Averaged Navier-Stokes equations coupled with the shear stress transfer ([Formula: see text]) turbulence model. Two swirling orientations (anticlockwise and clockwise) and five swirling core pitch-wise positions (aligned with vane 1 to vane 2) are considered in the current work. The results indicate that the residual vortices in the vane passage are strengthened and move with the swirling core along the pitch-wise direction. The migration of the horseshoe vortex is controlled by this movement. The shrinkage or expansion of the separation line of the horseshoe vortex can be observed under the anticlockwise and clockwise swirling inflow conditions respectively. The anticlockwise swirling inflow results in a larger aerodynamic loss by a 10%–35% increase of the laterally [Formula: see text]. The high Nu region near the pressure side surface enlarges and the area-averaged Nu at [Formula: see text] increases from 2337.9 to 2878.3. For the cases with clockwise swirling inflow, the area of the hot ring is enlarged and the Nu downstream of the row 3 film holes is decreased. As for the film cooling performance, the endwall coverage area shrinks and the phantom cooling area enlarges when the anticlockwise swirling core is aligned with vane 2. The endwall loses the protection from the row 3 film holes and the cooling failure ([Formula: see text]) occurs at [Formula: see text] when the swirling core is aligned with the vane passage. This is an extremely bad phenomenon that should be avoided. Among all cases, the highest endwall area-averaged [Formula: see text] (0.122) is obtained when the clockwise swirling core is aligned with vane 1. The largest endwall coverage area is achieved when the clockwise swirling core is aligned with vane 2.

On the electric charge of quantized vortices and the dipole moment of vortex pairs and rings in a magnetic field

It is shown that, in the presence of a magnetic field, a quantized vortex line in a superfluid liquid acquires a linear polarization charge, which is localized near the vortex axis over a length on the order of the coherence length. It is found that the total charge of a rectilinear vortex is nonzero, while the vortex pair and vortex ring have a nonzero dipole moment. The electric fields of rectilinear vortices near the end surface of a cylindrical vessel filled with a superfluid liquid are calculated. The electric polarization of superfluid systems in the presence of thermally activated vortex pairs and vortex rings has been studied. It is shown that such a polarization arises in the presence of relative motion of the normal and superfluid components.

Anomalous coherence length of Majorana zero modes at vortices in superconducting topological insulators

The coherence length of two Majorana zero-energy modes in a $p$-wave topological superconductor is inversely proportional to the superconducting order parameter. We studied the finite size effect of the Majorana zero modes at vortices in a topological insulator/superconductor heterostructure in the presence of a vortex and found that the coherence length of the two zero-energy modes at the terminals of a vortex line is independent of the superconducting order parameter and determined by the intrinsic properties of the topological insulator. This anomalous property illustrates that the superconducting topological insulator is topologically distinct, contrary to a $p$-wave topological superconductor.

The cavitation flow and spray characteristics of gasoline-diesel blends in the nozzle of a high-pressure common-rail injector

In compression-ignition engines, gasoline-diesel blends have been widely concerned for its potential to reach 50% thermal efficiency and ultra-low emissions. Due to physical property difference between the two fuels, the spray atomization characteristics of the blended fuels are different from that of a single fuel, and the cavitation flow characteristics of the blends in the high-pressure nozzle and their impact on the spray are not well understood. In this paper, the visualization of cavitation flow and spray characteristics of five different proportion blended fuels (D100G0, D80G20, D60G40, D40G60, D20G80) was carried out. The influence of fuel properties corresponding to the gasoline-diesel mixing ratio on the initial generation of vortex-induced cavitation, the development of transient cavitation flow process and the injection rate and spray characteristics were studied respectively. For the tapered orifice nozzle, string cavitation is captured mainly concentrating in the needle opening initial period and closing end period, which is the main factor of spray instability and fluctuations. At the injection starting, the addition of gasoline into the diesel fuel resulted in a significant increase in string cavitation strength and larger injection rate compared to the pure diesel, even if the percentage of gasoline added is small. However, the different gasoline addition ratios have little effect on the maximum intensity of string cavitation and the duration of string cavitation in the nozzle. Accordingly, the addition of gasoline increased the overall spray cone angle and spray fluctuations throughout the injection process. Meanwhile, as the injection volume increased, the injection rate curve in the initial process is flat at first and then become steep which was precisely related to the cavitation of the vortex line in the nozzle. The findings of this paper are important guidelines for the determination of fuel injection strategies and spray analysis of gasoline-diesel blends for compression-ignition engines.

Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows

Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing quantum inviscid flows (or superfluids) in the zero temperature limit. In quantum flows, like liquid helium II at intermediate temperatures between zero and 2.17 K, a normal fluid and a superfluid coexist with independent velocity fields. The most advanced existing models for such systems use the Navier-Stokes equations for the normal fluid and a simplified description of the superfluid, based on the dynamics of quantized vortex filaments, with ad hoc reconnection rules. There was a single attempt (C. Coste, 1998 [22]) to couple Navier-Stokes and Gross-Pitaevskii equations in a global model intended to describe the compressible two-fluid liquid helium II. We present in this contribution a new numerical model to couple a Navier-Stokes incompressible fluid with a Gross-Pitaevskii superfluid. Coupling terms in the global system of equations involve new definitions of the following concepts: the regularized superfluid vorticity and velocity fields, the friction force exerted by quantized vortices to the normal fluid, the covariant gradient operator in the Gross-Pitaevskii model based on a slip velocity respecting the dynamics of vortex lines in the normal fluid. A numerical algorithm based on pseudo-spectral Fourier methods is presented for solving the coupled system of equations. Finally, we numerically test and validate the new numerical system against well-known benchmarks for the evolution in a normal fluid of different types or arrangements of quantized vortices (vortex crystal, vortex dipole and vortex rings). The new coupling model has the advantage to keep the full Gross-Pitaevskii model for the superfluid, and thus describe quantized vortex dynamics without any phenomenological approximation. This opens new possibilities to revisit and enrich existing numerical results for complex quantum fluids, such as quantum turbulent flows.

Cavitation generated by vibrating quartz tuning fork in concentrated 3He–4He mixture

The state of the problem of cavitation in superfluid helium and the content of previous works on this topic are analyzed. The transition between turbulent flow and cavitation under oscillations of a quartz tuning fork in a normal and superfluid isotopic mixture containing 15% of 3He in the temperature range of 0.5–3 K is studied experimentally. The temperature dependences of the critical velocity for the cavitation onset and the critical transition excitation force are obtained. We compare the results of our measurements with the data obtained by other groups. The results of measurements with tuning forks in restricted and unrestricted geometries suggest that the presence of acoustic emission facilitates the conditions for the onset of cavitation and indirectly confirms the role of vortex lines. A comparison of the temperature dependences of the critical velocity of cavitation onset in pure 4He and a concentrated 3He–4He mixture did not give an unambiguous answer to the reason for the sharp increase of this velocity, at the transition to the superfluid state, and the contributions of both thermal effects and the 3He impurities to the velocity increase.

Theory of Caroli–de Gennes–Matricon analogs in full-shell hybrid nanowires

Full-shell nanowires are hybrid nanostructures consisting of a semiconducting core encapsulated in an epitaxial superconducting shell. When subject to an external magnetic flux, they exhibit the Little-Parks (LP) phenomenon of flux-modulated superconductivity, an effect connected to the physics of Abrikosov vortex lines in type-II superconductors. We show theoretically that full-shell nanowires can host subgap states that are a variant of the Caroli-de Gennes-Matricon (CdGM) states in vortices. These CdGM analogs are shell-induced Van Hove singularities in core subbands. We elucidate their structure, parameter dependence and behavior in tunneling spectroscopy through a series of models of growing complexity. Using microscopic numerical simulations, we show that CdGM analogs exhibit a characteristic skewness towards higher flux values inside non-zero LP lobes resulting from the interplay of three ingredients. First, the orbital coupling to the field shifts the energy of the CdGM analogs proportionally to the flux and to their generalized angular momentum. Second, CdGM analogs coalesce into degeneracy points at flux values for which their corresponding radial wavefunctions are threaded by an integer multiple of the flux quantum. And third, the average radii of all CdGM-analog wavefunctions inside the core are approximately equal and are controlled by the electrostatic band bending at the core/shell interface. As the average radius moves away from the interface, the degeneracy points shift towards larger fluxes from the center of the LP lobes, causing the skewness. This analysis provides a transparent interpretation of the nanowire spectrum that allows to extract microscopic information by measuring the number and skewness of CdGM analogs. Moreover, it allows to derive an efficient Hamiltonian of the full-shell nanowire in terms of a modified hollow-core model at the average radius.

Large eddy simulation of flow field and particle dispersion in a ventilated model room using a parallel lattice Boltzmann method

The present paper addresses the use of a parallel lattice Boltzmann solver for large eddy simulation of particulate matter flow in a single ventilated model room. The formulation of lattice Boltzmann method (LBM), implementation of large eddy simulation (LES), description of finite volume method (FVM) and then integration of Lagrangian particle tracking in the present algorithm are outlined. A parallel processing method, known as decomposed domain method, for flow and particle phases is defined. Combined stream and collision step technique is employed to reduce CPU runtime and memory usage. The ultimate objective is validation and comparison of prediction accuracy and speed up between present LBM-LES results, FVM-LES results based on Navier–Stokes equations, and available experimental data. Results of flow field show acceptable accuracy for the present LBM-LES method when using high-resolution lattices. It is revealed that in order to achieve an accuracy almost equal to FVM, LBM requires twice the number of lattices but still provides a higher speed. Also, it is shown that the present model is well capable of predicting vortex core and vortex lines and it can capture the features and structure of the turbulence flow field reasonably well. In the particle field, it can capture concentration patterns and particle dispersion with an admissible discrepancy. The use of presently developed algorithm dramatically reduces computational time, such that speed can increase by up to four times in flow and eight times in particle simulations.Copyright © 2023 American Association for Aerosol Research

Anisotropic enhancement of lower critical field in ultraclean crystals of spin-triplet superconductor candidate UTe2

The paramagnetic spin-triplet superconductor UTe$_2$ has attracted significant attention because of its exotic superconducting properties including an extremely high upper critical field and possible chiral superconducting states. Recently, ultraclean single crystals of UTe$_2$ have become available, and thus measurements on these crystals are crucial to elucidate the intrinsic superconducting properties. Here, we report the thermodynamic critical field $H_{\rm c}$, the lower critical field $H_{\rm c1}$, and the upper critical field $H_{\rm c2}$ at low fields of these high-quality single crystals. From the comparison of the anisotropies in $H_{\rm c1}$ and $H_{\rm c2}$, we find that the experimental $H_{\rm c1}$ values with the magnetic field along $b$- and $c$-axes are anomalously enhanced, showing unusual low-temperature upturns. We propose an effect of the strong Ising-like ferromagnetic fluctuations on the vortex line energy as the origin of the anisotropic enhancement of $H_{\rm c1}$.

“Elastic” and “inelastic” twins and pinning of magnetic flux lines (vortices) in single crystals YBa2Cu3O7–x

In this work, we studied the fixation of magnetic vortices (pinning effect) on “inelastic” and “elastic” twins, whose wedge-shaped peaks in the direction of twinning do not reach the crystal surface. The effectiveness of the “elastic” twins effect as pinning centers was studied by measuring of the critical transport current Jc in single crystals YBa2Cu3O7–x. The presented experimental data indicate that the “elastic” twins boundaries are effective pinning centers of the magnetic flux lines in single crystals of the compound under study. The main pinning centers of the vortices are dislocation clusters forming at the vertices of the “elastic” twins. The dislocation lines are located in the twin plane and, if the orientation of the magnetic vortices and dislocation lines coincide, the energy of the vortices decreases, the pinning force appears, fixing their location, which ultimately leads to an increase in the critical density of the transport electric current.

Dissipation anomaly in a turbulent quantum fluid

In this work we show evidence for a superfluid analog to the classical dissipation anomaly: When the friction tends to zero, the dissipation does not vanish, but levels off to a constant non-zero value. This characteristic stems from the generation of smaller and smaller structures on the quantized vortex lines as the friction is lowered. This property of quantum turbulence is universal, not depending on the dynamics of the large scales.