Core states and spectral flow in vortex dynamics

I review the semi-classical picture of how states bound in the core of a vortex in an S-wave superconductor respond to relative motion between the vortex and the condensate. I show how the momentum absorbed as a result of the Magnus force acting on the core leads to a change in the distribution of occupied states (“spectral flow”). In the simplest relaxation time approximation this modified distribution gives rise to the Kopnin–Kravtsov force on the vortex.     

Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg–Landau equation

The transition from phase chaos to defect chaos in the complex Ginzburg–Landau equation (CGLE) is related to saddle-node bifurcations of modulated amplitude waves (MAWs). First, the spatial period P of MAWs is shown to be limited by a maximum P_SN which depends on the CGLE coefficients; MAW-like structures with period larger than P_SN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients ν≈0 and various periods occur naturally in phase chaotic states of the CGLE. As a measure for these periods, we study the distributions of spacings p between neighbouring peaks of the phase gradient. A systematic comparison of p and P_SN as a function of coefficients of the CGLE shows that defects are generated at locations where p becomes larger than P_SN. In other words, MAWs with period P_SN represent “critical nuclei” for the formation of defects in phase chaos and may trigger the transition to defect chaos. Since rare events where p becomes sufficiently large to lead to defect formation may only occur after a long transient, the coefficients where the transition to defect chaos seems to occur depend on system size and integration time. We conjecture that in the regime where the maximum period P_SN has diverged, phase chaos persists in the thermodynamic limit.     

A Study of premixed propagating flame vortex interaction

Experimental data is presented for the interaction between a propagating flame and a simple vortex flow field structure generated in the wake of solid obstacles. The interaction between gas movement and obstacles creates vortex shedding forming a simple flow field recirculation. The presence of the simple turbulent structure within the gas mixture curls the flame front increasing curvature and enhancing burning rate. A novel twin camera Particle Image Velocimetry, PIV, was employed to characterise the flow field recirculation and the interaction with the flame front. The technique allowed the quantification of the flame/vortex interaction. The twin camera technique provides data to define the spatial variation of both the velocity of the flow field and flame front. Experimentally obtained values of local flame displacement speed and flame stretch rate are presented for simple flame/vortex interactions.     

Abrikosov vortex escape from a columnar defect as a topological electronic transition in a vortex core

The microscopic scenario of vortex escape from a columnar defect under the influence of a transport current has been studied. For defect radii smaller than the superconducting coherence length the depinning process is shown to be a consequence of two subsequent topological electronic transitions in a trapped vortex core. The first transition at a critical current j _L is associated with the opening of Fermi surface segments corresponding to the creation of a vortex-antivortex pair bound to the defect. The second transition at a certain current j _d > j _L is caused by merging of different Fermi surface segments, which accompanies the formation of a freely moving vortex.     

Superfluid vortex front at T→0: decoupling from the reference frame

Steady-state turbulent motion is created in superfluid (3)He-B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of (3)He-B and replaces vortex-free flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2T(c) during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e., the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.     

Numerical study on three-dimensional C-J detonation waves: detailed propagating mechanism and existence of OH radical

An unsteady three-dimensional simulation is performed for a hydrogen/air C–J detonation in a rectangular tube, where a detailed chemical reaction model is used to reveal the C–J detonation structure. In this simulation, detailed propagating detonation structures for a diagonal mode are described in three-dimensions. The detonation front structures, the line of triple points, and the strong explosions at the corners of the rectangular tube are revealed by using a three-dimensional numerical visualization. From the spatial isosurface profiles of H₂ mass fraction, it is confirmed that the triple point lines have a role of “shutter” to generate unburned gas pockets and become of a ring shape behind the detonation front due to its explosion. The explosion process and its influence on an induction delay are observed by visualizing the spatial isosurface profiles of OH mass fraction. Moreover, a high “peninsula-shaped” OH mass fraction area, which has been experimentally reported, is reproduced on the side wall of the rectangular tube.     

Quantum turbulence in a propagating superfluid vortex front

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.     

Two-phase regime in the magnetic field–temperature phase diagram of a type-II superconductor

The magnetic field and temperature dependencies of the magnetic moments of superconducting crystals of V₃Si have been studied. In a constant magnetic field and at temperatures somewhat below the superconducting transition temperature, the moments are hysteretic in temperature. However, the magnetic moment–magnetic field isotherms are reversible and exhibit features that formally resemble the pressure–volume isotherms of the liquid–gas transition. This suggests the existence of a first-order phase transition, a two-phase regime, and a critical point in the superconducting phase diagram. The two phases are disordered vortex configurations with the same magnetization, but with different vortex densities. The entropy change, determined from the data using the Clausius–Clapeyron equation, is consistent with estimates based on the difference in the vortex densities of the two phases.     

Noise-induced dynamic bistability of front propagation

We study noise-induced front propagation in a bistable system of the activator–inhibitor type. By varying the intensity of the multiplicative noise, the velocity of the front exhibits a transition to a bistable regime, where the actual velocity and direction of front motion depends mainly on the (random) initial conditions.     

Effects of kinked linear defects on planar flux line arrays

In the hard core limit, interacting vortices in planar type II superconductors can be modeled as non-interacting one dimensional fermions propagating in imaginary time. We use this analogy to derive analytical expressions for the probability density and imaginary current of vortex lines interacting with an isolated bent line defect and to understand the pinning properties of such systems. When there is an abrupt change of the direction of the pinning defect, we find a sinusoidal modulation of the vortex density in directions both parallel and perpendicular to the defect.     

Spatiotemporal measurements of flame stretch and propagation rates for lean and rich CH4/air premixed flames interacting with a turbulent-wake

A 1.5 m long turbulent-wake combustion vessel with a 0.15 m × 0.15 m cross-sectional area is proposed for spatiotemporal measurements of curvature, strain, dilatation and burning rates along a freely downward-propagating premixed flame interacting with a parallel row of staggered vortex pairs having both compression (negative) and extension (positive) strains simultaneously. The wanted wake is generated by rapidly withdrawing an electrically-controlled, horizontally-oriented sliding plate of 5 mm thickness for flame–wake interactions. Both rich and lean CH₄/air flames at the equivalence ratios  = 1.4 and  = 0.7 with nearly the same laminar burning velocity are studied, where flame–wake interactions and their time-dependent velocity fields are obtained by high-speed, high-resolution DPIV and laser-tomography. Correlations among curvature, strain, stretch, and dilatation rates along wrinkled flame fronts at different times are measured and thus their influences on front propagation rates can be analyzed. It is found that strain-related effects have significant influence on front propagation rates of rich CH₄/air (diffusionally stable) flames even when the curvature weights more in the total stretch than the strain rate does. The local propagation rates along the wrinkled flame front are more intense at negative strain rates corresponding to positive peak dilatation rates but the global propagation rate averaged along the rich flame front remains constant during all period of flame–wake interaction. For lean CH₄/air (diffusionally unstable) flames, the curvature becomes a dominant parameter influencing the structure and propagation of the wrinkled flame front, where both local and global propagation rates increase significantly with time, showing unsteady flame propagation. These experimental results suggest that the theory of laminar flame stretch can be applicable to a more complex flame–wake interaction involving unsteadiness and multitudinous interactions between vortices.     

Symmetric behavior of vortex states of superconducting networks in a magnetic field

We present magnetic field dependence of phase transition temperature and vortex configuration of superconducting networks based on theoretical study. The applied magnetic field is called “filling field” that is defined by applied magnetic flux (in unit of the flux quantum) per unit loop of the superconducting network. If a superconducting network is composed of very thin wires whose thicknesses are less than coherence length, the de Gennes–Alexander (dGA) theory is applicable. We have already shown that field dependences of transition temperature curves have symmetric behavior about the filling field of 1/2 by solving the dGA equation numerically in square lattices, honeycomb lattices, cubic lattices and those with randomly lack of wires networks. Many experimental studies also show the symmetric behavior. In this paper, we make an explicit theoretical explanation of symmetric behaviors of superconducting network respect to the applied field.     

Propagation dynamics of optical vortices in Laguerre–Gaussian beams

We have calculated the propagation dynamics of an initial off-axis vortex with topological charge 1 in Laguerre–Gaussian background beams , which are examples of background beams with non-generic dislocation surfaces, on which the real and imaginary parts of the light field are zero. When initially a vortex with broad core (e.g., r-vortex) is embedded in the background beam, the dislocation surfaces are destroyed during propagation and two vortices with opposite charge are created per dislocation surface in planes perpendicular to the propagation direction. For a vortex with narrow core (e.g., point vortex) diffraction is important and leads to the birth of more than two vortices per dislocation surface. These results are also valid for other background beams with dislocation surfaces, e.g., Hermite–Gaussian and Ince–Gaussian beams. We investigated experimentally the spatial evolution of the intensity distribution of an initial off-axis vortex with narrow core and topological charge 1 in background beams. The experimental results are in good agreement with the calculated intensity distributions.     

Spiral cracks in drying precipitates

We investigate the formation of spiral crack patterns during the desiccation of thin layers of precipitates in contact with a substrate. This symmetry-breaking fracturing mode is found to arise naturally not from torsion forces but from a propagating stress front induced by the foldup of the fragments. We model their formation mechanism using a coarse-grain model for fragmentation and successfully reproduce the spiral cracks. Fittings of experimental and simulation data show that the spirals are logarithmic. Theoretical aspects of the logarithmic spirals are discussed. In particular we show that this occurs generally when the crack speed is proportional to the propagating speed of stress front.     

Electron–hole liquid formation by exciton and biexciton resonant excitation in CuCl

The dynamics of a cold photoexcited electron–hole system created by resonant excitation with picosecond optical pulses are studied by time-resolved emission and pump–probe measurements. A rapid build-up of strong metallic reflection in the mid-infrared region was observed, which indicates the creation of electron–hole plasma via the exciton or biexciton Mott transition. Transient reflection spectra clearly show the transformation of high-density electron–hole plasma into a metallic colloid-like state within 10 ps. In the meantime, broad plasma emission turns to a narrow emission band, in which the spectral profile does not change within several tens of picoseconds. These features in the emission spectra disappear when switched to the band-to-band excitation. An analysis of the reflection and emission spectra reveals that the density of metastable electron–hole liquid is as high as 10²⁰ cm⁻³. This indicates that the plasma formation via the Mott transition is crucial to eliminate excess heating for reaching the low-temperature states of an electron–hole ensemble.     

激波冲击V形界面重气体导致的壁面与旋涡作用及其对湍流混合的影响

基于多组分混合物质量分数模型,采用色散最小耗散可控的高分辨率有限体积方法,数值模拟了弱激波冲击V形空气/SF_6界面后,界面不稳定性生成的旋涡与固体壁面作用问题.激波冲击V形界面之后,因斜压效应诱导涡量沉积在界面附近,形成沿界面规则排列的多个涡对结构.旋涡的诱导作用使界面不断变形和卷起,同时旋涡之间不断发生相互并对,诱导更多更小尺度的旋涡产生.旋涡诱导作用的叠加效应,使界面尖端处的初始涡对向上下壁面发展.随后,涡结构开始与壁面发生复杂的相互作用.旋涡与壁面作用后沿壁面加速,使得物质界面沿壁面伸展,随后,旋涡从壁面回弹,并诱导二次旋涡产生.旋涡与壁面相互作用的过程,能够明显加剧物质混合.本文从物质混合的角度研究了该过程的机理,分析了旋涡与壁面作用对物质混合的影响.     

Curvature and the evolution of fronts

The evolution of a front propagating along its normal vector field with speedF dependent on curvatureK is considered. The change in total variation of the propagating front is shown to depend only ondF/dK only whereK changes sign. Analysis of the caseF(K)=1–K, where is a constant, shows that curvature plays a role similar to that of viscosity in Burgers equation. For =0 and non-convex initial data, the curvature blows up, corners develop, and an entropy condition can be formulated to provide an explicit construction for a weak solution beyond the singularity. We then numerically show that the solution as goes to zero converges to the constructed weak solution. Numerical methods based on finite difference schemes for marker particles along the front are shown to be unstable in regions where the curvature builds. As a remedy, we show that front tracking based on volume of fluid techniques can be used together with the entropy condition to provide transition from the classical to weak solution.National Science Foundation Mathematical Sciences Post-Doctoral Fellow     

On Vortex Dynamics in the Self-Dual Chern–Simons–Higgs System

The dynamics of n vortices in the self-dual Chern–Simons–Higgs system defined on the infinite plane is investigated. In adiabatic approximation, the vortex dynamics is determined by considering a rigid motion of a vortex configuration and a motion around a fixed center of mass. A motion of two vortices is studied in detail.     

On the vortex formation at the moving front of lightweight granular particles

The formation of vortices at a moving front of lightweight granular particles is investigated experimentally. The particles used in this study are made of polystyrene foam with three different diameters of nearly uniform size. Pairs of vortices are found to emerge at the moving front at regular intervals, thereby forming a wavy pattern. Once the vortices are produced, the flow velocity tends to increase. A simple analysis suggests the existence of a velocity boundary layer at the moving front, whose thickness increases with increasing particle diameter. The frontal radius of each vortex pair is about the size of this boundary layer; when the radius exceeds this size, the front tends to bifurcate into a train of vortices with the size of the boundary layer. The formation of twin vortices leads to a reduction in the air drag force exerted on the system, and thereby the system attains a higher flow velocity, i.e., a higher conversion rate of gravitational potential energy to the kinetic energy of the particle motion. The higher conversion rate of potential energy thus feeds back to the development of the vortex motion, resulting in the twin vortex formation.     

Numerical Study of Axisymmetric Richtmyer–Meshkov Instability and Azimuthal Effect on Spherical Mixing

In this paper, we present a numerical study of the axisymmetric Richtmyer–Meshkov instability in converging spherical geometry by the front tracking method for the first time. The front tracking method has been successfully used in solving fluid instability problems in both rectangular and curved geometry.^(1–6) The central issue for axisymmetric flows is the absence of the rotational symmetry in the (r, z) plane, although the perturbed shape of the initial contact interface appears to have it. The cause of the asymmetry is somewhat obvious. The sinusoidal perturbations appear symmetric only in the cross-sectional view; in actuality they are not symmetric because they represent rings around the z-axis and hence the perturbed mass at the equator, for example, is different from the perturbed mass at the pole. The first purpose of this paper is to quantify the effect of this inherited asymmetry on the growth of the spherical mixing. We find this asymmetry drives the original structure to some degree so that the mixing radius at the north pole is noticeably larger than at the equator during the evolution of chaotic mixing. We also study quantitatively the azimuthal dependence of the mixing statistics, such as the mixing edges, the growth rate and volume fraction. Richtmyer–Meshkov (RM) instabilities in spherical geometry have been a challenge due to the inherent difficulty of their accurate simulation. Our second purpose is to demonstrate that our Front Tracking method can describe the Richtmyer–Meshkov instability growth in a complex flow involving multiple reshocks. We have successfully displayed the converging geometry, reshock process, asymmetry phenomenon through the density and pressure color plots. The quantitative growth rate analysis is also presented.