Vortex Strings Research Articles

Flow field analysis of newtonian fluid flow induced by planetary and radial motion of drill string

Abstract At present, in the process of oil drilling, the drill string is an essential downhole drilling tool. It is immersed in the hole filled with drilling fluid for a long time, and it is driven by the rotation of the rotary table to drill down. In this process, the drill string will not only rotate around its axis but also may rotate around the axis of the hole and produce radial motion. It is important to study the flow law of Newtonian fluid flow induced by drill string movement, which can effectively reduce drilling accidents caused by drill string vortex and buckling, thus reducing economic losses. After research and analysis, the finite volume method, which has good applicability and obvious advantages, is used to discretize the established mathematical model, and the mathematical equation after discretization is obtained. By using MATLAB software, the flow field of Newtonian fluid induced by drill string rotation motion is analyzed, the axial velocity distribution diagram and tangential velocity distribution diagram are obtained, and the velocity flow diagram under different eccentricity conditions is drawn. It is found that secondary flow occurs only when the eccentricity reaches a certain distance requirement.

Flowing between string vacua for the critical non-Abelian vortex with a deformation of N=2 Liouville theory

It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N=2 supersymmetric QCD (SQCD) with the U(2) gauge group and Nf=4 quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact threefold, namely, the conifold. The spectrum of low-lying closed string states was found and interpreted as a spectrum of hadrons in 4D N=2 SQCD. In particular, the lowest string state appears to be a massless Bogomol’nyi-Prasad-Sommerfield (BPS) baryon associated with the deformation of the complex structure modulus b of the conifold. It was recently shown that the Coulomb branch of the associated string sigma model which opens up at strong coupling can be described by N=2 Liouville theory. Building on these results we switch on quark masses in 4D N=2 SQCD and study the interpolation of the initial U(2) SQCD with Nf=4 quarks to the final SQCD with the U(4) gauge group and Nf=8 quarks. To find the true string vacuum which arises due to the mass deformation we solve the effective supergravity equations of motion associated with the deformed world sheet Liouville theory. We show that the massless BPS baryon b survives the deformation and that finding of the spectrum of low-lying massive hadrons in the final SQCD is linked to the Calogero problem. Published by the American Physical Society 2024

Spatiotemporal vortex strings.

Light carrying orbital angular momentum (OAM) holds unique properties and boosts myriad applications in diverse fields. However, the generation of an ultrafast wave packet carrying numerous vortices with various transverse OAM modes, i.e., vortex string, remains challenging, and the corresponding detection method is lacking. Here, we demonstrate that a vortex string with 28 spatiotemporal optical vortices (STOVs) with customizable topological charge (TC) arrangements can be generated in one wave packet. The diffraction rules of STOV strings are revealed theoretically and experimentally. Following these rules, the TC values and positions of all STOVs in a vortex string can be simultaneously recognized from the diffraction pattern. Such STOV strings facilitate STOV-based optical communication. As a proof-of-principle demonstration, the transmission of an image is realized with 16-STOV strings. This work provides guidance for revealing the underlying properties of the transverse OAM light and opens up opportunities for applications of the structured light in optical communication, quantum information processing, etc.

Ground state of two-species spin–orbit-coupled in mass-imbalanced Bose condensates

In this paper, we study the ground state of two-component spin–orbit-coupled (SOC) Bose–Einstein condensates with mass imbalance. Our results are based on the framework of mean-field Gross–Pitaevskii theory. The effects of unequal atomic mass and SOC strength are studied. Different density structures such as heliciform stripes, linear stripes and string vortex chains are found. Different density structures such as heliciform stripes, linear stripes and string vortex chains are found. With the increase of SOC strength, the azimuthal phase separation is kept while radial phase separation is broken. In addition, increasing the mass ratio is unfavorable to vortex formation, whereas more vortices can be generated by increasing the SOC strength. We also discuss the physical quantities such as angular momentum per atom and spin polarisation, for a larger mass ratio, showing that angular momentum gets a little bigger as the SOC strength increases and the first-order phase transition does not exist.

Observation of vortex-string chiral modes in metamaterials

As hypothetical topological defects in the geometry of spacetime, vortex strings could have played many roles in cosmology, and their distinct features can provide observable clues about the early universe’s evolution. A key feature of vortex strings is that they can interact with Weyl fermionic modes and support massless chiral-anomaly states along strings. To date, despite many attempts to detect vortex strings in astrophysics or to emulate them in artificially created systems, observation of these vortex-string chiral modes remains experimentally elusive. Here we report experimental observations of vortex-string chiral modes using a metamaterial system. This is implemented by inhomogeneous perturbation of Yang-monopole phononic metamaterials. The measured linear dispersion and modal profiles confirm the existence of topological modes bound to and propagating along the string with the chiral anomaly. Our work provides a platform for studying diverse cosmic topological defects in astrophysics and offers applications as topological fibres in communication techniques.

Chirality coupling in topological magnetic textures with multiple magnetochiral parameters

Chiral effects originate from the lack of inversion symmetry within the lattice unit cell or sample’s shape. Being mapped onto magnetic ordering, chirality enables topologically non-trivial textures with a given handedness. Here, we demonstrate the existence of a static 3D texture characterized by two magnetochiral parameters being magnetic helicity of the vortex and geometrical chirality of the core string itself in geometrically curved asymmetric permalloy cap with a size of 80 nm and a vortex ground state. We experimentally validate the nonlocal chiral symmetry breaking effect in this object, which leads to the geometric deformation of the vortex string into a helix with curvature 3 μm−1 and torsion 11 μm−1. The geometric chirality of the vortex string is determined by the magnetic helicity of the vortex texture, constituting coupling of two chiral parameters within the same texture. Beyond the vortex state, we anticipate that complex curvilinear objects hosting 3D magnetic textures like curved skyrmion tubes and hopfions can be characterized by multiple coupled magnetochiral parameters, that influence their statics and field- or current-driven dynamics for spin-orbitronics and magnonics.

Hall Droplet Sheets in Holographic QCD

In single-flavor QCD, the low energy description of baryons as Skyrmions is not available. In this case, it has been proposed by Komargodski that baryons can be viewed as kinds of charged quantum Hall droplets, or “sheets”. In this paper we propose a string theory description of the sheets in single-flavor holographic QCD, focusing on the Witten-Sakai-Sugimoto model. The sheets have a “hard” gluonic core, described by D6-branes, and a “soft” mesonic shell, dual to non-trivial D8-brane gauge field configurations. We first provide the description of an infinitely extended sheet with massless or moderately massive quarks. Then, we construct a semi-infinite sheet ending on a one-dimensional boundary, a “vortex string”. The holographic description allows for the precise calculation of sheet observables. In particular, we compute the tension and thickness of the sheet and the vortex string, and provide their four dimensional effective actions.

Critical behavior and the Kibble-Zurek mechanism in a musical phase transition.

We investigate the critical phenomena emerging from a statistical mechanics model of musical harmony on a three-dimensional (3D) lattice, and the resulting structure of the ordered phase. In this model, each lattice site represents a tone, with nearest neighbors interacting via the perception of dissonance between them. With dissonance assumed to be an octave-wise periodic function of pitch difference, this model is a 3D XY system with the same symmetry and dimensionality as superfluid helium and models of the cosmological axion field. We use numerical simulation to observe a phase transition from disordered sound to ordered arrangements of musical pitches as a parameter analogous to the temperature is quenched towards zero. We observe the divergence of correlation length and relaxation time at the phase boundary, consistent with the critical exponents in similar systems. Furthermore, the quenched low-temperature phase of these systems displays topological defects in the form of vortex strings that thread throughout the system volume. We observe the formation of these vortex strings in accordance with the Kibble-Zurek mechanism, and discuss the structure of these vortex strings in the context of the theory of musical harmony, finding both similarities to established music theory, and uncovering new avenues to explore.

Dark photon vortex formation and dynamics

We study the formation and evolution of vortices in U(1) dark photon dark matter and dark photon clouds that arise through black hole superradiance. We show how the production of both longitudinal mode and transverse mode dark photon dark matter can lead to the formation of vortices. After vortex formation, the energy stored in the dark photon dark matter will be transformed into a large number of vortex strings, eradicating the coherent dark photon dark matter field. In the case where a dark photon magnetic field is produced, bundles of vortex strings are formed in a superheated phase transition, and evolve towards a configuration consisting of many string loops that are uncorrelated on large scales, analogous to a melting phase transition in condensed matter. In the process, they dissipate via dark photon and gravitational wave emission, offering a target for experimental searches. Vortex strings were also recently shown to form in dark photon superradiance clouds around black holes, and we discuss the dynamics and observational consequences of this phenomenon with phenomenologically motivated parameters. In that case, the string loops ejected from the superradiance cloud, apart from producing gravitational waves, are also quantised magnetic flux lines and can be looked for with magnetometers. We discuss the connection between the dynamics in these scenarios and similar vortex dynamics found in type II superconductors.

NS three-form flux deformation for the critical non-Abelian vortex string

It has been shown that the non-Abelian solitonic vortex string supported in four-dimensional (4D) $\mathcal{N}=2$ supersymmetric QCD (SQCD) with the U(2) gauge group and ${N}_{f}=4$ quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact threefold, namely, the conifold. The spectrum of low-lying closed string states in the associated type-IIA string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N}=2$ SQCD. In particular, the lowest string state appears to be a massless BPS baryon associated with the deformation of the complex structure modulus $b$ of the conifold. In the previous work the deformation of the ten-dimensional background with nonzero Neveu-Schwarz 3-form flux was considered and interpreted as a switching on a particular choice of quark masses in 4D SQCD. This deformation was studied to leading order at small 3-form flux. In this paper we study the back reaction of the nonzero 3-form flux on the metric and the dilaton introducing the ansatz with several warp factors and solving the gravity equations of motion. We show that 3-form flux produces a potential for the conifold complex structure modulus $b$, which leads to the runaway vacuum. At the runaway vacuum warp factors disappear, while the conifold degenerates. In 4D SQCD we relate this to the flow to the U(1) gauge theory upon switching on quark masses and decoupling of two flavors.

Vortex String Formation in Black Hole Superradiance of a Dark Photon with the Higgs Mechanism.

Black hole superradiance, which only relies on gravitational interactions, can provide a powerful probe of the existence of ultralight bosons that are weakly coupled to ordinary matter. However, as a boson cloud grows through superradiance, nonlinear effects from interactions with itself or other fields may become important. As a representative example of this, we use nonlinear evolutions to study black hole superradiance of a vector boson that attains a mass, via a coupling to a complex scalar, through the Higgs mechanism. For the cases considered, we find that the superradiant instability can lead to a transient period where the scalar field reaches its symmetry restoration value, leading to the formation of closed vortex strings, the temporary disruption of the exponential growth of the cloud, and an explosive outburst of energy. After the cloud loses sufficient mass, the superradiant growth resumes, and the cycle repeats. Thus, the black hole will be spun down but, potentially, at a much lower rate compared to when nonlinear effects are unimportant and with the liberated energy going primarily into bosonic radiation instead of gravitational waves.

Critical non-Abelian vortices and holography for little string theory

It has been shown that non-Abelian vortex string supported in four dimensional (4D) ${\mathcal N}=2$ supersymmetric QCD (SQCD) with the U(2) gauge group and $N_f = 4$ quark flavors becomes a critical superstring. This string propagates in the ten dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau non-compact threefold, namely, the conifold. The spectrum of closed string states of the associated string theory was obtained using the equivalence between the critical string on the conifold and the non-critical string on the semi-infinite cigar described by SL($2, \mathbb{R}$)/U(1) Wess-Zumino-Novikov-Witten model. This spectrum was identified with the spectrum of hadrons in 4D ${\mathcal N}=2$ SQCD. In order to describe effective interactions of these 4D hadrons in this paper we study correlation functions of normalizable vertex operators localized near the tip of the SL($2, \mathbb{R}$)/U(1) cigar. We also compare our solitonic string approach to the gauge-string duality to the AdS/CFT-type holography for little string theories (LSTs). The latter relates off mass-shell correlation functions on the field theory side to correlation functions of non-normalizable vertex operators on the cigar. We show that in most channels holographic approach works in our theory because normalizable and non-normalizable vertex operators with the same conformal dimension are related due to the reflection from the tip of the cigar. However, we find that holography does not work for lightest hadrons with given baryonic charge.

Theory of Holomorphic Maps of Two-Dimensional Complex Manifolds to Toric Manifolds and Type-A Multi-String Theory

We study the field theory localizing to holomorphic maps from a complex manifold of complex dimension 2 to a toric target (a generalization of A model). Fields are realized as maps to {{(mathbb{C}text{*})}^{N}} where one includes special observables supported on (1,1)-dimensional submanifolds to produce maps to the toric compactification. We study the mirror of this model. It turns out to be a free theory interacting with {{N}_{{{text{comp}}}}} topological strings of type A. Here, {{N}_{{{text{comp}}}}} is the number of compactifying divisors of the toric target. Before the mirror transformation, these strings are vortex (actually, holomortex) strings.

Large eddy simulation of cough jet dynamics, droplet transport, and inhalability over a ten minute exposure.

High fidelity simulations of expiratory events such as coughing provide the opportunity to predict the fate of the droplets from the turbulent jet cloud produced from a cough. It is well established that droplets carrying infectious pathogens with diameters of remain suspended in the air for several hours and transported by the air currents over considerable distances (e.g., in meters). This study used a highly resolved mesh to capture the multiphase turbulent buoyant cloud with suspended droplets produced by a cough. The cough droplets' dispersion was subjected to thermal gradients and evaporation and allowed to disperse between two humans standing 2 m apart. A nasal cavity anatomy was included inside the second human to determine the inhaled droplets. Three diameter ranges characterized the droplet cloud, , which made up 93% of all droplets by number; 5 to 100 μm comprised 3%, and m comprising 4%. The results demonstrated the temporal evolution of the cough event, where a jet is first formed, followed by a thermally driven puff cloud with the latter primarily composed of droplets under 5 μm diameter, moving with a vortex string structure. After the initial cough, the data were interpolated onto a more coarse mesh to allow the simulation to cover ten minutes, equivalent to 150 breathing cycles. We observe that the critical diameter size susceptible to inhalation was , although most inhaled droplets after 10 min by the second human were approximately . These observations offer insight into the risk of airborne transmission and numerical metrics for modeling and risk assessment.

Flux compactification for the critical non-Abelian vortex and quark masses

It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D) ${\mathcal N}=2\;$ supersymmetric QCD (SQCD) with the U($N=2$) gauge group and $N_f=4$ quark flavors behave as critical superstrings. In addition to four translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space $\mathbb{R}^4$ and a Calabi-Yau non-compact threefold $Y_6$, namely, the conifold. The spectrum of low lying closed string states in the associated type IIA string theory was found and interpreted as a spectrum of hadrons in 4D ${\mathcal N}=2\;$ SQCD. In particular, the lowest string state appears to be a massless BPS baryon associated with the deformation of the complex structure modulus $b$ of the conifold. Here we address a problem of switching on quark masses in 4D SQCD, which classically breaks the world sheet conformal invariance in the string sigma model. To avoid this problem we follow a standard string theory approach and use a flux "compactification" to lift the complex structure modulus of the conifold. Namely, we find a solution of supergravity equations of motion with non-zero NS 3-form flux. It produces a potential for the baryon $b$, which leads to the run-away vacuum. Using field theory arguments we interpret 3-form flux in terms of a particular choice of quark masses in 4D SQCD. At the run-away vacuum the conifold degenerates to lower dimensions. We interpret this as a flow from a non-Abelian string to an Abelian one.

Shape and dynamics of nonrelativistic vortex strings in parity-breaking media

The shape and dynamics of the nonrelativistic gauge vortex string in the parity-broken media is considered, upon reducing the problem to finding the extremum of the Abelian Higgs model effective action with the fixed B-type helicity of the gauge field. It is shown that in contrast with the case of the fixed A-type helicity, the static solution of the Ginzburg-Landau energy functional in the London limit is the helix with the specific relation between the curvature and torsion of the vortex line depending on the strength of the space parity violating contribution of the Lifshitz invariant. A nonlinear dynamical equation is linearized in case of small oscillations around the helical contour, and the polarization and dispersion law of the propagated waves are obtained.

String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence

We study non-Abelian vortex strings in four-dimensional (4D) $\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has been recently shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N} = 2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless BPS "baryon." Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string -- the so called weighted $\mathcal{N} = (2,2)$ supersymmetric $\mathbb{CP}$ model. Its target space is given by the six-dimensional non-compact Calabi-Yau space $Y_6$, the conifold. We use mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a non-perturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS "baryon" previously found in string theory.

Ground-state phases and spin textures of spin–orbit-coupled dipolar Bose–Einstein condensates in a rotating toroidal trap* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11475144 and 11047033), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2019203049 and A2015203037), the University Science and Technology Foundation of Hebei Provincial Department of Education, China (Grant No. Z2017056), Science

We investigate the ground-state phases and spin textures of spin–orbit-coupled dipolar pseudo-spin-1/2 Bose–Einstein condensates in a rotating two-dimensional toroidal potential. The combined effects of dipole–dipole interaction (DDI), spin–orbit coupling (SOC), rotation, and interatomic interactions on the ground-state structures and topological defects of the system are analyzed systematically. For fixed SOC strength and rotation frequency, we provide a set of phase diagrams as a function of the DDI strength and the ratio between inter- and intra-species interactions. The system can show rich quantum phases including a half-quantum vortex, symmetrical (asymmetrical) phase with quantum droplets (QDs), asymmetrical segregated phase with hidden vortices (ASH phase), annular condensates with giant vortices, triangular (square) vortex lattice with QDs, and criss-cross vortex string lattice, depending on the competition between DDI and contact interaction. For given DDI strength and rotation frequency, the increase of the SOC strength leads to a structural phase transition from an ASH phase to a tetragonal vortex lattice then to a pentagonal vortex lattice and finally to a vortex necklace, which is also demonstrated by the momentum distributions. Without rotation, the interplay of DDI and SOC may result in the formation of a unique trumpet-shaped Bloch domain wall. In addition, the rotation effect is discussed. Furthermore, the system supports exotic topological excitations, such as a half-skyrmion (meron) string, triangular skyrmion lattice, skyrmion–half-skyrmion lattice, skyrmion–meron cluster, skyrmion–meron layered necklace, skyrmion–giant-skyrmion necklace lattice, and half-skyrmion–half-antiskyrmion necklace.

Topological defects in rotating spin–orbit-coupled dipolar spin-1 Bose–Einstein condensates

We consider the topological defects and spin structures of spin-1 Bose–Einstein condensates with spin–orbit coupling (SOC) and dipole–dipole interaction (DDI) in a rotating harmonic plus quartic trap. The combined effects of SOC, DDI and rotation on the ground-state phases of the system are analyzed. Our results show that for fixed rotation frequency structural phase transitions can be achieved by adjusting the magnitudes of the SOC and DDI. A ground-state phase diagram is given as a function of the SOC and DDI strengths. It is shown that the system exhibits rich quantum phases including vortex string phase with isolated density peaks (DPs), triangular (square) vortex lattice phase with DPs, checkerboard phase, and stripe phase with hidden vortices and antivortices. For given SOC and DDI strengths, the system can display pentagonal vortex lattice with DPs, vortex necklace with DPs, and exotic topological structure composed of multi-layer visible vortex necklaces, a hidden giant vortex and hidden vortex necklaces, depending on the rotation frequency. In addition, the system sustains fascinating novel spin textures and skyrmion excitations, such as an antiskyrmion pair, antiskyrmion-half-antiskyrmion (antiskyrmion–antimeron) cluster, skyrmion–antiskyrmion lattice, skyrmion–antiskyrmion cluster, skyrmion–antiskyrmion–meron–antimeron lattice, double-layer half-antiskyrmion necklaces, and composite giant-antiskyrmion–antimeron necklaces.

Linked vortices as baryons in the miscible BEC-Skyrme model

We introduce a variation of the Bose-Einstein condensate(BEC)-Skyrme model, with an altered potential for miscible BECs that gives rise to two physical vortex strings. In the ground state of each topological sector, the vortices are linked exactly $B$ times, due to a recently formulated theorem, with $B$ being the baryon number of the solution. The model also possesses metastable states, where the vortices are degenerate and do not lend the interpretation of the baryon number as the linking number of the vortices.