Thick Vortex Research Articles

Center vortices on SU(2) lattices

We show that gauge invariant definition of thin, thick and hybrid center vortices, defined by Kovacs and Tomboulis on SO(3) x Z(2) configurations, can also be defined in SU(2). We make this connection using the freedom of choosing a particular SU(2) representative of SO(3). We further show that in another representative the Tomboulis \sigma - \eta thin vortices are P (projection) vortices. The projection approximation corresponds to dropping the perimeter factor of a Wilson loop after appropriate gauge fixing. We present results for static quark potentials based on these vortex counters and compare pojection vortex counters with gauge invariant ones on the same configuration.

Topological susceptibility of Yang-Mills center projection vortices

The topological susceptibility induced by center projection vortices extracted from SU(2) lattice Yang-Mills configurations via the maximal center gauge is measured. Two different smoothing procedures, designed to eliminate spurious ultraviolet fluctuations of these vortices before evaluating the topological charge, are explored. They result in consistent estimates of the topological susceptibility carried by the physical thick vortices characterizing the Yang-Mills vacuum in the vortex picture. This susceptibility is comparable to the one obtained from the full lattice Yang-Mills configurations. The topological properties of the SU(2) Yang-Mills vacuum can thus be accounted for in terms of its vortex content.

Vortex structure of the vacuum and confinement

We discuss the recently published numerical computations of the vortex free energy. They dramatically demonstrate that the excitation probability for a sufficiently thick vortex approaches unity at large beta, i.e. that thick vortices ‘condense’ in the vacuum. This is known to imply confinement. An analytical approach for exploring this phenomenon is also outlined.

Vortices in SU(2) lattice gauge theory

We investigate some properties of thick vortices and thick monopoles in the SU(2) lattice gauge theory by inserting operators that create these excitations. We measure the derivative of the free energy of the vortex with respect to the coupling and we find that it falls exponentially with the cross sectional area of the vortex. We also study the monopole-monopole potential energy of thick and thin monopoles. Our results suggest that vortices and monopoles of increasing thickness will play an important role in the large β limit.

Computation of the vortex free energy in SU(2) gauge theory

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.

Bound on the string tension by the excitation probability for a vortex

A lower bound on the string tension for large beta in SU(2) LGT is derived. The derivation is from first principles and bounds the string tension from below by the expectation for the excitation of a single ‘tagged’ thick vortex winding around the lattice. Thus confinement follows if this expectation remains nonvanishing at large beta. Numerical simulations are presented to show that this is indeed the case.

Energy and velocity of a forming vortex ring

It is known that vortex rings formed by large stroke ratios (in a piston/cylinder arrangement) pinch off from their generating jets at a fairly constant universal time scale. In this paper we show that the hypothesis that at the pinch off the translational velocity of the ring equals the jet flow velocity near the ring is equivalent to the recently proposed idea based on a variational principle by Kelvin and Benjamin that the pinch off occurs when the apparatus is no longer able to deliver energy at a rate required for steady vortex ring existence. A formula for the propagation velocity of a thick vortex ring is also proposed and compared with available experimental data and empirical relations.

Vortices and black holes in dilatonic gravity

We study analytically black holes pierced by a thin vortex in dilatonic gravity for an arbitrary coupling of the vortex to the dilaton in an arbitrary frame. We show that the horizon of the charged black hole supports the long-range fields of the Nielsen-Olesen vortex that can be considered as black hole hair for both massive and massless dilatons. We also prove that extremal black holes exhibit a flux expulsion phenomenon for a sufficiently thick vortex. We consider the gravitational back reaction of the thin vortex on the spacetime geometry and dilaton, and discuss under what circumstances the vortex can be used to smooth out the singularities in the dilatonic C metrics. The effect of the vortex on the massless dilaton is to generate an additional dilaton flux across the horizon.

Absence of confinement in the absence of vortices

We consider the Wilson loop expectation in SU(2) lattice gauge theory in the presence of constraints. The constraints eliminate gauge field configurations, which, in physical terms, allow the presence of thick center vortices linking with the loop. We prove that, for dimension d⩾3, the so-constrained Wilson loop follows perimeter law, i.e., nonconfining behavior, at weak coupling (low temperature).

SU(3) string tension and the presence of vortices

Lattice simulations are presented showing the expectation of the fluctuation of the Wilson loop solely by elements of the center to fully reproduce the SU(3) heavy quark potential. The results are stable under smoothing, and point to thick vortices as being responsible for the full SU(3) tension. An analytic result on the necessary presence of thick vortices for confinement at weak coupling is also presented.

Wilson loop distributions, higher representations and centre dominance in SU(2)

To help understand the centre dominance picture of confinement, we look at Wilson loop distributions in pure SU(2) lattice gauge theory. A strong coupling approximation for the distribution is developed to use for comparisons. We perform a Fourier expansion of the distribution: centre dominance here corresponds to suppression of odd terms beyond the first. The Fourier terms correspond to SU(2) representations; hence Casimir scaling behaviour leads to centre dominance. We examine the positive plaquette model, where only thick vortices are present. We show that a simple picture of random, non-interacting centre vortices gives a string tension about 3 4 of the measured value. Finally, we attempt to limit confusion about the adjoint representation.

Vortices and the SU(3) string tension

We present simulation results comparing the SU(3) heavy quark potential extracted from the full Wilson loop expectation to that extracted from the expectation of the Wilson loop fluctuation solely by elements of Z(3). The two potentials are found to coincide. This agreement is stable under multiple smoothings of the configurations which remove short distance fluctuations, and thus reflects long-distance physics. It strongly indicates that the asymptotic string tension arises from thick center vortices linking with the Wilson loop.

98/01864 Pilot-scale studies using a hydrocyclone and froth flotation for the production of beneficiated coal fractions for improved coal liquefaction : Cloke, M. et al. Fuel, 1997, 76, (13), 1217–1223

The air-sparged hydrocyclone (ASH), known as a new type of efficient flotation apparatus, was used in grinding-classification circuit to control the overgrinding of hydrophobic materials after some modifications by the authors. The overgrinding of hydrophobic materials, resulted from the fact that the hydrophobic materials have higher density than the hydrophilic materials, has been known as a knotty problem. The modified ASH is designed with a relatively small length/diameter ratio, and a thick vortex finder wall is introduced, and the annular underflow opening between a pedestal and the cylindrical wall is replaced by a wide angle cone apex opening and a horizontal baffle that is positioned above the apex opening. Concentration and classification exist simultaneously in the modified ASH. Sample ore from Hongtoushan Copper Mine was used to investigate the concentration and classification characteristics in the modified ASH. In particular, the effects of design and operation parameters on the copper recovery and enrichment ratio and the classification efficiency in different particle size fractions were considered for a ⊘75 mm modified ASH. From a variety of runs, it can be concluded as follows: (1) the copper enrichment ratio of the finest particle size fraction (−400 mesh) in overflow of the ASH is always larger than 1.0, while those of the other coarser particle size fractions are not all the same; (2) not only is the copper in overflow is enriched by the flotation in the ASH, but also the classification efficiency is improved to some extent by the flotation; and (3) to consider both the concentration and classification in the ASH, the optimum design and operation parameters are different from that in the case of an ASH being just used for flotation, e.g., the ratio of the overflow opening area to the underflow opening area of this modified ASH should be larger than that of the flotation ASH.

Vortices and confinement at weak coupling

We discuss the physical picture of thick vortices as the mechanism responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory. By introducing appropriate variables on the lattice we distinguish between thin, thick and `hybrid' vortices, the latter involving Z(2) monopole loop boundaries. We present numerical lattice simulation results that demonstrate that the full SU(2) string tension at weak coupling arises from the presence of vortices linked to the Wilson loop. Conversely, excluding linked vortices eliminates the confining potential. The numerical results are stable under alternate choice of lattice action as well as a smoothing procedure which removes short distance fluctuations while preserving long distance physics.

97/01594 Taxodioxylon gypsaceum as parent botanical species of two lignites of central Italy

The air-sparged hydrocyclone (ASH), known as a new type of efficient flotation apparatus, was used in grinding-classification circuit to control the overgrinding of hydrophobic materials after some modifications by the authors. The overgrinding of hydrophobic materials, resulted from the fact that the hydrophobic materials have higher density than the hydrophilic materials, has been known as a knotty problem. The modified ASH is designed with a relatively small length/diameter ratio, and a thick vortex finder wall is introduced, and the annular underflow opening between a pedestal and the cylindrical wall is replaced by a wide angle cone apex opening and a horizontal baffle that is positioned above the apex opening. Concentration and classification exist simultaneously in the modified ASH. Sample ore from Hongtoushan Copper Mine was used to investigate the concentration and classification characteristics in the modified ASH. In particular, the effects of design and operation parameters on the copper recovery and enrichment ratio and the classification efficiency in different particle size fractions were considered for a ⊘75 mm modified ASH. From a variety of runs, it can be concluded as follows: (1) the copper enrichment ratio of the finest particle size fraction (−400 mesh) in overflow of the ASH is always larger than 1.0, while those of the other coarser particle size fractions are not all the same; (2) not only is the copper in overflow is enriched by the flotation in the ASH, but also the classification efficiency is improved to some extent by the flotation; and (3) to consider both the concentration and classification in the ASH, the optimum design and operation parameters are different from that in the case of an ASH being just used for flotation, e.g., the ratio of the overflow opening area to the underflow opening area of this modified ASH should be larger than that of the flotation ASH.

Concentration and classification characteristics in a modified air-sparged hydrocyclone (ASH)

Abstract The air-sparged hydrocyclone (ASH), known as a new type of efficient flotation apparatus, was used in grinding-classification circuit to control the overgrinding of hydrophobic materials after some modifications by the authors. The overgrinding of hydrophobic materials, resulted from the fact that the hydrophobic materials have higher density than the hydrophilic materials, has been known as a knotty problem. The modified ASH is designed with a relatively small length/diameter ratio, and a thick vortex finder wall is introduced, and the annular underflow opening between a pedestal and the cylindrical wall is replaced by a wide angle cone apex opening and a horizontal baffle that is positioned above the apex opening. Concentration and classification exist simultaneously in the modified ASH. Sample ore from Hongtoushan Copper Mine was used to investigate the concentration and classification characteristics in the modified ASH. In particular, the effects of design and operation parameters on the copper recovery and enrichment ratio and the classification efficiency in different particle size fractions were considered for a ⊘75 mm modified ASH. From a variety of runs, it can be concluded as follows: (1) the copper enrichment ratio of the finest particle size fraction (−400 mesh) in overflow of the ASH is always larger than 1.0, while those of the other coarser particle size fractions are not all the same; (2) not only is the copper in overflow is enriched by the flotation in the ASH, but also the classification efficiency is improved to some extent by the flotation; and (3) to consider both the concentration and classification in the ASH, the optimum design and operation parameters are different from that in the case of an ASH being just used for flotation, e.g., the ratio of the overflow opening area to the underflow opening area of this modified ASH should be larger than that of the flotation ASH.

A Localized Approximation Method for Vortical Flows

An approximation method of Moore for Kelvin–Helmholtz instability is formulated as a general method for two-dimensional, incompressible, inviscid flows generated by a vortex sheet. In this method the nonlocal equations describing evolution of the sheet are approximated by a system of (local) differential equations. These equations are useful for predicting singularity formation on the sheet and for analyzing the initial value problem before singularity formation. The general method is applied to a number of problems: Kelvin–Helmholtz instability for periodic vortex sheets, motion of an interface in Hele–Shaw flow, Rayleigh–Taylor instability for stratified flow, and Krasny’s desingularized vortex sheet equation. A new physically desingularized vortex sheet equation is proposed, which agrees with the finite thickness vortex layer equations in the localized approximation.

Determinants of the occurrence of vortex rings in the left ventricle during diastole

This study employs classical inviscid fluid dynamics theory to investigate whether LV diastolic inflow volume and the size of the LV play a role in vortex ring formation. Fluid injection across an orifice into a large container results in the generation of a vortex ring having a constant size and speed. Relations between the vortex size and speed and the injection were obtained by applying conservation laws regarding kinetic energy, impulse and vorticity; the initial state was computed using a bolus injection model, and the final state by using the Kelvin vortex model. An important parameter in the equations is the relative injection length, i.e., the ratio of the length of the injected bolus and the radius of the orifice ( L R ). Its estimated highest value in man, L R = 15 , produces a rather thick vortex ring (relative thickness 0.77). Comparable results following from the Hill vortex model convinced us that the Kelvin vortex model can be applied in the whole range of injection lengths in the human left ventricle. In an in vitro model it is shown experimentally that vortex rings can be generated for L R in the range from 2 to 16. The measured traveling speed of the vortex ring is in fair agreement with the theory, as well as the ring radius for large injections. A vortex ring located in a narrow channel cannot reach its proper traveling speed. The method of images is used to estimate the speed reduction of vortex rings within a cylinder. It turns out that propagation of vortex rings is possible when the ratio of orifice to cylinder radius is less than about 0.5. Further narrowing of the cylinder impedes propagation of the vortex ring. We conclude that the size of the left ventricle is an important factor for the generation of vortex rings in human ventricles, whereas the injection volume is not. Probably, vortex rings will not develop in the average normal ventricle, whereas they can be generated in dilated ventricles having a diameter which is more than twice as large as the mitral valve orifice diameter.

Transition process from one celled vortex to two celled vortex

Changes in the flow structure, the vorticity distribution and the stream function during the transition process from the one celled vortex to the two celled vortex following a rapid change in the radial Reynolds number have been examined. Starting from a thin filament-like structure corresponding to the one celled vortex. a thick vortex core first grew up from the outlet region and turned into a cylindrical structure corresponding to the two celled vortex. The vorticity distribution also changed from a single-summit type to a ring-summit type.

Idiopathic Serous Detachment of the Choroid, Ciliary Body, and Retina (Uveal Effusion Syndrome)

Nine patients with bilateral idiopathic serous detachment of the peripheral choroid, ciliary body, and retina (uveal effusion syndrome)are presented. The following features are emphasized: (1) dilationof episcleral vessels, (2) vitreous cells, (3) characteristic leopardspot pigment epithelial changes, and (4) ultrasonic and angiographic findings. One patient presented with recurrent serous macular detachment and was misdiagnosed as idiopathic central serous choroidopathy. Although the pathogenesis of this syndrome is uncertain, the available clinical and histopathologic findings suggest that obstruction of the venous outflow of the uveal tract occurring predominantly in nanophthalmic or normal size eyes with abnormally thick sclera and vortex vein anomalies may be the primary cause of the uveal and retinal detachment.