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To address the environmental impact of air travel, the industry has introduced various solutions, including sustainable fuels and new aircraft configurations. The Flying V is one such concept that promises a 20% reduction in fuel consumption compared to its most advanced competitor. Unlike traditional commercial airplanes, the Flying V is a tailless flying-wing design without a tubular fuselage, horizontal, and vertical tailplane, using elevons and winglets featuring rudders for control. This study aimed to optimize the wing geometry of the Flying V aircraft to minimize induced drag under specific subsonic conditions (M = 0.6) and a given lift coefficient of 0.26. The approach combined a Vortex Lattice Method (VLM) with an optimization algorithm, specifically using the Athena Vortex Lattice (AVL) software for aerodynamics calculations. A low-fidelity method, such as a VLM, allows a faster and deeper exploration of the design space than a high-fidelity method like Computational Fluid Dynamics (CFD). To improve the Flying V's design, a simpler parameterization was introduced to represent the complex model of the Outer Mold Line (OML) of the aircraft. It involved eight sections along half the wingspan. The inboard wing sections were parameterized in a wire-frame style, with the front part representing the location of the passengers' cabin, requiring fixed dimensions and inclination to accommodate a suitable cabin floor, and the aft part allowed to be rotated. The other sections' geometry was mainly described by the total inclination angle. The design vector included the aft angles of the first three sections, the total incidence angle of the last four sections, and the dihedral of the outboard wing, which is useful to ensure a straight hinge line for control power. A total of 8 design variables were utilized during the optimization process. Two aerodynamic constraints were implemented to ensure feasible optimized results. The first constraint was related to th, Aerospace Engineering | Flight Performance and Propulsion

We study an effective field theory of a vortex lattice in a two-dimensional neutral rotating superfluid. Utilizing particle-vortex dualities, we explore its formulation in terms of a $U(1)$ gauge theory coupled to elasticity, that at low energies reduces to a compact Lifshitz theory augmented with a Berry phase term encoding the vortex dynamics in the presence of a superflow. Utilizing elasticity- and Lifshitz-gauge theory dualities, we derive dual formulations of the vortex lattice in terms of a traceless symmetric scalar-charge theory and demonstrate low-energy equivalence of our dual gauge theory to its elasticity-gauge theory dual. We further discuss a multipole symmetry of the vortex lattice and its dual gauge theory's multipole one-form symmetries. We also study its topological crystalline defects, where the multipole one-form symmetry plays a prominent role. It classifies the defects, explains their restricted mobility, and characterizes descendant vortex phases, which includes a novel vortex supersolid phase. Using the dual gauge theory, we also develop a mean-field theory for the quantum melting transition from a vortex crystal to a vortex supersolid., Comment: 19 pages, 1 figure. v2: published version

In the present work, a low-fidelity three-dimensional approach has been developed for the prediction of the flow around shrouded rotors. This method is to be used in the initial steps of design, for a wide exploration of the design space, including disruptive geometries, at minimal cost. The present approach is based on the vortex lattice method. First, the formulation on rotating geometries is validated by comparison with experiments. The Prandtl-Glauert correction is introduced to account for mild compressibility effects. A discretized approach is proposed to model the casing and simulate the tip-leakage flow. The results are discussed for different tip-gap sizes. A periodic boundary condition is also proposed and validated. This condition, together with programming techniques, decreases the computational and memory costs of the method. On average, a computation takes approximately one second to execute in real time. Finally, the method is applied to a shrouded fan configuration and the influence of the tip-gap size is analyzed., QC 20240704

In the present work, a low-fidelity three-dimensional approach has been developed for the prediction of the flow around shrouded rotors. This method is to be used in the initial steps of design, for a wide exploration of the design space, including disruptive geometries, at minimal cost. The present approach is based on the vortex lattice method. First, the formulation on rotating geometries is validated by comparison with experiments. The Prandtl-Glauert correction is introduced to account for mild compressibility effects. A discretized approach is proposed to model the casing and simulate the tip-leakage flow. The results are discussed for different tip-gap sizes. A periodic boundary condition is also proposed and validated. This condition, together with programming techniques, decreases the computational and memory costs of the method. On average, a computation takes approximately one second to execute in real time. Finally, the method is applied to a shrouded fan configuration and the influence of the tip-gap size is analyzed., Duplicate record in Scopus 2-s2.0-85177693029QC 20230822

© 2003 The American Physical Society. The authors thank R. Markiewicz, F. Nori, F. Guinea, R. Mulet, and E. Altshuler for valuable discussions. C.E.C. acknowledges support from the EU TMR programme. J.P.R. acknowledges the hospitality of the Instituto de Ciencia de Materiales de Madrid, where this work was initiated., The two-dimensional (2D) vortex lattice in the extreme type-II limit is studied by Monte Carlo simulation of the corresponding 2D Coulomb gas, with identical pins placed at sites coinciding with the zero-temperature triangular vortex lattice. At weak pinning we find evidence for 2D melting into an intermediate hexatic phase. The strong pinning regime shows a Kosterlitz-Thouless transition, driven by interstitial vortex/antivortex excitations. A stack of such identical layers with a weak Josephson coupling models a layered superconductor with a triangular arrangement of columnar pins at the matching field. A partial duality analysis finds that layer decoupling of the flux-line lattice does not occur at weak pinning for temperatures below 2D melting., EU TMR programme., Depto. de Física de Materiales, Fac. de Ciencias Físicas, TRUE, pub

In a two-dimensional superconducting vortex lattice, the melting from the solid to the isotropic liquid can occur via an intermediate phase that retains orientational correlations. The effect of such correlations on transport and their interplay with the quenched disorder remain open questions. We perform magnetotransport measurements in a wide range of temperatures and magnetic fields on a weakly pinned two-dimensional vortex system in amorphous MoGe films. While at high fields, where quenched disorder dominates, we recover the typical strong-glass behavior of a vortex liquid, at low fields the resistivity shows a clear crossover to a fragile vortex glass. Our findings, supported by numerical simulations, suggest that this is a signature of heterogeneous dynamics that arises from the presence of orientational correlations.

Using sound velocity and attenuation measurements in high magnetic fields, we identify a new transition in the vortex lattice state of La$_{2−x}$Sr$_{x}$CuO$_4$. The transition, observed in magnetic fields exceeding 35 T and temperatures far below zero field T$_c$, is detected in the compression modulus of the vortex lattice, at a doping level of x=p=0.17. Our theoretical analysis based on Eilenberger’s theory of the vortex lattice shows that the transition corresponds to the long-sought 45° rotation of the square vortex lattice, predicted to occur in d-wave superconductors near a van Hove singularity.

Topologically protected polar textures have provided a rich playground for the exploration of novel, emergent phenomena. Recent discoveries indicate that ferroelectric vortices and skyrmions not only host properties markedly different from traditional ferroelectrics, but also that these properties can be harnessed for unique memory devices. Using a combination of capacitor-based capacitance measurements and computational models, it is demonstrated that polar vortices in dielectric-ferroelectric-dielectric trilayers exhibit classical ferroelectric bi-stability together with the existence of low-field metastable polarization states. This behavior is directly tied to the in-plane vortex ordering, and it is shown that it can be used as a new method of non-destructive readout-out of the poled state.

Recent experiments on the iron-based superconductor FeSe in a high magnetic field have suggested the presence of both the fluctuation-induced vortex liquid regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a general picture of the magnetic phase diagram in type II superconductors with strong superconducting (SC) fluctuation and strong paramagnetic pair breaking (PPB) such as FeSe, the vortex lattice melting curve Hm(T) is theoretically investigated in situations where a FFLO state is expected to occur. In general, PPB tends to narrow the vortex liquid regime intervening between Hc₂(T) and Hm(T). In particular, the vortex liquid regime is found to rapidly shrink upon entering; by cooling, the temperature range in which the FFLO state with a periodic modulation parallel to the magnetic field is stable in mean-field theory. Based on the present results, the high-field SC phase diagrams of FeSe in the parallel and perpendicular field configurations are discussed.

We investigate the thermodynamics of two-flavor quark matter in presence of nonzero isospin chemical potential and external magnetic field. It is known that at sufficiently high isospin chemical potential, charged pions undergo Bose-Einstein condensation (BEC). The condensate behaves as a superconductor, exhibiting Meissner effect in weak external magnetic fields. Stronger fields stress the superconducting state, turning it first into an Abrikosov lattice of vortices, and eventually destroying the condensate altogether. On the other hand, for sufficiently strong magnetic fields and low-to-moderate isospin chemical potential, the ground state of quantum chromodynamics (QCD) is expected to be a spatially modulated condensate of neutral pions, induced by the chiral anomaly: the chiral soliton lattice (CSL). We map the phase diagram of QCD as a function of isospin chemical potential and magnetic field in the part of the parameter space accessible to a low-energy effective field theory description of QCD. Our main result is an explicit account of the competition between the CSL and the Abrikosov vortex lattice. This is accomplished by adopting a fast numerical algorithm for finding the vortex lattice solution of the equation of motion and the corresponding Gibbs energy. We find that the Abrikosov vortex lattice phase persists in the phase diagram, separating the uniform charged pion BEC phase from the CSL phase. The precise layout of the phase diagram depends sensitively on the choice of the vacuum pion mass., Comment: 13 pages, 5 figures

In superconducting films, the role of intrinsic disorder is typically to compete with superconductivity by fragmenting the global phase coherence and lowering the superfluid density. Nonetheless, when a transverse magnetic field is applied to the system and an Abrikosov vortex lattice form, the presence of disorder can actually strengthen the superconducting state against thermal fluctuations. By means of Monte Carlo simulations on the uniformly frustrated XY model in two dimensions, we show that while for weak pinning the superconducting critical temperature Tc increases with the applied field H, for strong enough pinning, the experimental decreasing dependence between Tc and H is recovered with a resulting more robust vortex lattice.

We study the magnetic-field dependence of the vortex-core charge in the Abrikosov lattice of an s-wave superconductor based on the augmented quasiclassical equations, where we incorporate the pair-potential gradient (PPG) terms characteristic of charging in superconductors besides the well-known Lorentz force. Our numerical results at T = 0.2T(c) and 0.5T(c) reveal that periodic charge redistribution is superimposed on the magnetic flux-line lattice with different spatial patterns at different fields. The PPG terms are dominant at weak fields over the Lorentz force for accumulating charge in the vortex cores, whereas the Lorentz force prevails at higher fields to give rise to a peak structure in the core charge around H similar to 1/2 H-c2. We estimate the peak value of the core charge at T = 0.2T(c) using parameters appropriate for cuprates to obtain a large value of Q similar to 10(-2) vertical bar e vertical bar in the core region of radius 0.2 xi(0) in the ab plane and length 1 nm along the c axis.

Order–disorder transitions are widely explored in various vortex structures in condensed matter physics, that is, in the type-II superconductors and Bose–Einstein condensates. In this study, the ordering of the polar vortex phase in [Pb(Zr0.4Ti0.6)O3]n/(SrTiO3)n (PZT/STO) superlattices is investigated through phase-field simulations. With a large tensile substrate strain, an antiorder vortex state (where the rotation direction of the vortex arrays in the neighboring ferroelectric layers are flipped) is discovered for short-period PZT/STO superlattice. The driving force is the induced in-plane polarization in the STO layers due to the large tensile epitaxial strain. Increasing the periodicity leads to antiorder to disorder transition, resulting from the high energy of the head-to-head/tail-to-tail domain structure in the STO layer. On the other hand, when the periodicity is kept constant in short-period superlattices, the order–disorder–antiorder transition can be engineered by mediating the substrate strain, due to the competition between the induction of out-of-plane (due to interfacial depolarization effect) and in-plane (due to strain) polarization in the STO layer. The 3D ordering of such polar vortices is still a topic of significant current interest and it is envisioned that this study will spur further interest toward the understanding of order–disorder transitions in ferroelectric topological structures.

We study the magnetic-field dependence of the vortex-core charge in the Abrikosov lattice of an s-wave superconductor based on the augmented quasiclassical equations, where we incorporate the pair-potential gradient (PPG) terms characteristic of charging in superconductors besides the well-known Lorentz force. Our numerical results at T = 0.2T(c) and 0.5T(c) reveal that periodic charge redistribution is superimposed on the magnetic flux-line lattice with different spatial patterns at different fields. The PPG terms are dominant at weak fields over the Lorentz force for accumulating charge in the vortex cores, whereas the Lorentz force prevails at higher fields to give rise to a peak structure in the core charge around H similar to 1/2 H-c2. We estimate the peak value of the core charge at T = 0.2T(c) using parameters appropriate for cuprates to obtain a large value of Q similar to 10(-2) vertical bar e vertical bar in the core region of radius 0.2 xi(0) in the ab plane and length 1 nm along the c axis.

We estimate the conjectured interaction between the Earth gravitational field and a superconductor immersed in external, static electric and magnetic field. The latter is close to the sample upper critical field and generates the presence of a vortex lattice. The proposed interaction could lead to multiple, measurable effects. First of all, a local affection of the gravitational field inside the superconductor could take place. Second, a new component of a generalized electric field parallel to the superconductor surface is generated inside the sample. The analysis is performed by using the time-dependent Ginzburg-Landau theory combined with the gravito-Maxwell formalism. This approach leads us to analytic solutions of the problem, also providing the average values of the generated fields and corrections inside the sample. We will also study which are the physical parameters to optimize and, in turn, the most suitable materials to maximize the effect., Comment: 17 pages, 2 figures, 1 table (corrected figure scales)

We estimate the conjectured interaction between the Earth gravitational field and a superconductor immersed in external, static electric and magnetic field. The latter is close to the sample upper critical field and generates the presence of a vortex lattice. The proposed interaction could lead to multiple, measurable effects. First of all, a local affection of the gravitational field inside the superconductor could take place. Second, a new component of a generalized electric field parallel to the superconductor surface is generated inside the sample. The analysis is performed by using the time-dependent Ginzburg-Landau theory combined with the gravito-Maxwell formalism. This approach leads us to analytic solutions of the problem, also providing the average values of the generated fields and corrections inside the sample. We will also study which are the physical parameters to optimize and, in turn, the most suitable materials to maximize the effect., Comment: 17 pages, 2 figures, 1 table (corrected figure scales)

[ES] En el presente Trabajo de Fin de Máster se realiza un estudio aerodinámico de un perfil alar a través de diversas metodologías tales como un estudio experimental, el uso de métodos numéricos que pretenden aproximarse a la solución real o la resolución analítica proveniente de distintos métodos teóricos. El principal método utilizado para el desarrollo del proyecto es el modelo denominado Vortex Lattice que consiste en la discretización de la geometría real para obtener velocidades a partir de un tipo de singularidades. Estas se relacionan con la teoría potencial, por lo que se imponen sus hipótesis tales como flujo incompresible y estacionario. Con el fin de poder contrastar los resultados de coeficiente de sustentación y momento, se ha realizado de manera paralela un estudio experimental de un modelo alar y un estudio analítico mediante la teoría de perfiles delgados y la teoría del ala larga de Prandtl. Como resultado se obtiene que el método numérico Vortex Lattice se ajusta adecuadamente con un bajo porcentaje de error a los resultados experimentales, mientras que la teoría de perfiles delgados sobreestima el coeficiente de sustentación y la teoría de alas largas lo subestima, debido a las hipótesis que asumen., [EN] In this Final Master Thesis, an aerodynamic study of an airfoil is adressed throughout different methodologies such as an experimental study, an analytical study and the use of numerical methods that pretend to obtain an approximation of the real solution. The main method used for the development of the project is the Vortex Lattice method which consists in the discretization of the real geometry in order to derive speeds from a specific type of singularities. These are related to the potential theory, so that their hypotheses such as incompressible and stationary flow are also imposed. With the purpose of comparing the results of the lift and moment coefficient, an experimental study of an airfoil and an analytical study have been carried out in parallel with the thin airfoil theory and the Prandtl¿s lifting-line theory. As a result, it is obtained that the Vortex Lattice method fits properly with a low percentage of error to the experimental results, whereas the theory of thin airfoils overestimates the lift coefficient and the Prandtl¿s theory underestimates it.

[ES] En el presente Trabajo de Fin de Máster se realiza un estudio aerodinámico de un perfil alar a través de diversas metodologías tales como un estudio experimental, el uso de métodos numéricos que pretenden aproximarse a la solución real o la resolución analítica proveniente de distintos métodos teóricos. El principal método utilizado para el desarrollo del proyecto es el modelo denominado Vortex Lattice que consiste en la discretización de la geometría real para obtener velocidades a partir de un tipo de singularidades. Estas se relacionan con la teoría potencial, por lo que se imponen sus hipótesis tales como flujo incompresible y estacionario. Con el fin de poder contrastar los resultados de coeficiente de sustentación y momento, se ha realizado de manera paralela un estudio experimental de un modelo alar y un estudio analítico mediante la teoría de perfiles delgados y la teoría del ala larga de Prandtl. Como resultado se obtiene que el método numérico Vortex Lattice se ajusta adecuadamente con un bajo porcentaje de error a los resultados experimentales, mientras que la teoría de perfiles delgados sobreestima el coeficiente de sustentación y la teoría de alas largas lo subestima, debido a las hipótesis que asumen., [EN] In this Final Master Thesis, an aerodynamic study of an airfoil is adressed throughout different methodologies such as an experimental study, an analytical study and the use of numerical methods that pretend to obtain an approximation of the real solution. The main method used for the development of the project is the Vortex Lattice method which consists in the discretization of the real geometry in order to derive speeds from a specific type of singularities. These are related to the potential theory, so that their hypotheses such as incompressible and stationary flow are also imposed. With the purpose of comparing the results of the lift and moment coefficient, an experimental study of an airfoil and an analytical study have been carried out in parallel with the thin airfoil theory and the Prandtl¿s lifting-line theory. As a result, it is obtained that the Vortex Lattice method fits properly with a low percentage of error to the experimental results, whereas the theory of thin airfoils overestimates the lift coefficient and the Prandtl¿s theory underestimates it.

Calculating the unsteady convective heat transfer on helicopter blades is the first step in the prediction of ice accretion and the design of ice-protection systems. Simulations using Computational Fluid Dynamics (CFD) successfully model the complex aerodynamics of rotors as well as the heat transfer on blade surfaces, but for a conceptual design, faster calculation methods may be favorable. In the recent literature, classical methods such as the blade element momentum theory (BEMT) and the unsteady vortex lattice method (UVLM) were used to produce higher fidelity aerodynamic results by coupling them to viscous CFD databases. The novelty of this research originates from the introduction of an added layer of the coupling technique to predict rotor blade heat transfer using the BEMT and UVLM. The new approach implements the viscous coupling of the two methods from one hand and introduces a link to a new airfoil CFD-determined heat transfer correlation. This way, the convective heat transfer on ice-clean rotor blades is estimated while benefiting from the viscous extension of the BEMT and UVLM. The CFD heat transfer prediction is verified using existing correlations for a flat plate test case. Thrust predictions by the implemented UVLM and BEMT agree within 2% and 80% compared to experimental data. Tip vortex locations by the UVLM are predicted within 90% but fail in extreme ground effect. The end results present as an estimate of the heat transfer for a typical lightweight helicopter tail rotor for four test cases in hover, ground effect, axial, and forward flight.

We investigate vortex lattice solutions in a holographic superconductor model in asymptotically AdS4 spacetime which includes the gravitational backreaction of the vortex. The circular cell approximation, which is known to give a good result for several physical quantities in the Ginzburg-Landau model, is used. The critical magnetic fields and the magnetization curve are computed. The vortex lattice profiles are compared to expectations from the Abrikosov solution in the regime nearby the upper critical magnetic field H2c for which superconductivity is lost.

Low-temperature scanning tunneling microscopy and spectroscopy has been used to image the vortex core and the vortex lattice in FeSe single crystals. The local tunneling spectra acquired at the center of elliptical vortex cores display a strong particle-hole asymmetry with spatial oscillation, characteristic of the quantum-limit vortex core. Furthermore, a quasihexagonal vortex lattice at low magnetic field undergoes noticeable rhombic distortions above a certain field ∼1.5 T. This field H∗ also reveals itself as a kink in the magnetic field dependence of the specific heat. The observation of a nearly hexagonal vortex lattice at low field is very surprising for materials with an orthorhombic crystal structure and it is in apparent contradiction with the elliptical shape of the vortex cores. These observations can be directly connected to the multiband nature of superconductivity in this material, provided we attribute them to the suppression of superconducting order parameter in one of the energy bands. Above the field H∗ the superconducting coherence length for this band can well exceed the intervortex distance which strengthens the nonlocal effects. Therefore, in addition to multiple-band effects, other possible sources that can contribute to the observed evolution of the vortex-lattice structure include nonlocal effects which cause the field-dependent interplay between the symmetry of the crystal and vortex lattice or the magnetoelastic interactions due to the strain field generated by vortices. © 2019 American Physical Society.

We use large-scale Monte-Carlo simulations to study thermal fluctuations in chiral p-wave superconductors in an applied magnetic field in three dimensions. We consider the thermal stability of previously predicted unusual double-quanta flux-line lattice ground states in such superconductors. In previous works it was shown that, neglecting thermal fluctuations, a chiral p-wave superconductor forms a hexagonal lattice of doubly-quantized vortices, except extremely close to the vicinity of H-c2 where double-quanta vortices split apart. We find dissociation of double-quanta vortices driven by thermal fluctuations. However, our calculations also show that the previous predictions of hexagonal doubly-quantized vortices, where thermal fluctuations were ignored, are very robust in the considered model., QC 20230920

We investigate vortex lattice solutions in a holographic superconductor model in asymptotically $AdS_4$ spacetime which includes the gravitational backreaction of the vortex. The circular cell approximation, which is known to give a good result for several physical quantities in the Ginzburg-Landau model, is used. The critical magnetic fields and the magnetization curve are computed. The vortex lattice profiles are compared to expectations from the Abrikosov solution in the regime nearby the upper critical magnetic field $H_{2c}$ for which superconductivity is lost., Comment: 14 pages 4 figures, matches version published in JHEP

We investigate vortex lattice solutions in a holographic superconductor model in asymptotically $AdS_4$ spacetime which includes the gravitational backreaction of the vortex. The circular cell approximation, which is known to give a good result for several physical quantities in the Ginzburg-Landau model, is used. The critical magnetic fields and the magnetization curve are computed. The vortex lattice profiles are compared to expectations from the Abrikosov solution in the regime nearby the upper critical magnetic field $H_{2c}$ for which superconductivity is lost., Comment: 14 pages 4 figures, matches version published in JHEP

A new design procedure has been proposed for optimum marine propellers operating in uniform and radially non-uniform inflows based on a vortex lattice lifting-surface model (VLM). The procedure consists of two stages. In the first stage, the optimum circulation distribution along the radius is determined by using afixed camber line. Assuming that the local inflow is tangent to the camber line at the leading edge,the maximum camber at each radius is expressed as function of the pitch angle.Interactionsstart froma pitchangleprofile that the blade loading is zero.Before the thrust reaches design value, the pitch angle at each radius increases with anincrement proportionaltothe local gradient of efficiency to pitch.In the second stage, the optimum circulation distribution obtained in the first stage is used to design the pitch and camber with a prescribedchordwiseloading distribution. For a set of assumed pitch profileand camber surface geometry, the circulation distribution over the camber surface is computed by means of the VLM, and used to update the camber surface geometry by the Newton-Raphson iterative scheme according to the differences between the computed and the prescribed circulation distributions. The proposed method has been applied to the design of a highly skewed propeller in uniform and radially non-uniform inflows.

By utilizing the AdS/CFT correspondence, we explore the dynamics of strongly coupled superfluid vortices in a disk with constant angular velocity. Each vortex in the vortex lattice is quantized with vorticity one from the direct inspection of their phases. As the angular velocity of the disk is greater than a critical value, the first vortex will be excited as expected from theoretical predictions. The subsequent two and more vortices are also generated by increasingly rotating the disk, resulting in the remarkable step transitions for the angular velocity to excite each individual vortex. When the vortex number is large enough, the density of vortices is found to be linearly proportional to the angular velocity, which matches the Feynman relation very well., Comment: 5 pages, 5 figures; texts and figures improved; accepted by PRD Rapid Communication

By utilizing the AdS/CFT correspondence, we explore the dynamics of strongly coupled superfluid vortices in a disk with constant angular velocity. Each vortex in the vortex lattice is quantized with vorticity one from the direct inspection of their phases. As the angular velocity of the disk is greater than a critical value, the first vortex will be excited as expected from theoretical predictions. The subsequent two and more vortices are also generated by increasingly rotating the disk, resulting in the remarkable step transitions for the angular velocity to excite each individual vortex. When the vortex number is large enough, the density of vortices is found to be linearly proportional to the angular velocity, which matches the Feynman relation very well., Comment: 5 pages, 5 figures; texts and figures improved; accepted by PRD Rapid Communication

In this Letter we will show that, in the presence of a properly modulated Dzyaloshinskii-Moriya (DM) interaction, a $U(1)$ vortex-antivortex lattice appears at low temperatures for a wide range of the DM interaction. Even more, in the region dominated by the exchange interaction, a standard BKT transition occurs. In the opposite regime, the one dominated by the DM interaction, a kind of inverse BKT transition (iBKT) takes place. As temperature rises, the vortex-antivortex lattice starts melting by annihilation of pairs of vortex-antivortex, in a sort of "inverse" BKT transition., Comment: 6 pages, 5 figures

We show that the Landau vortex-free state in rotating container may give rise to the lattice of spin vortices. We consider this effect on example of spin vortices in magnon Bose-Einstein condensate (the phase coherent spin precession) in the B-phase of superfluid $^3$He, and on example of spin vortices in the polar phase of $^3$He., Comment: 4 pages, no figures

In the Ginzburg-Landau limit, a possible texture without singular cores in a rotating neutron spin-triplet superfluid is studied. It is constructed the lattice of non-singular vortices with a vorticity diffusely distributed over the entire unit cell. The upper limit of the free energy associated with this structure is estimated, and the result shows that non-singular vortices are more preferable in the core of rotating neutron stars than ordinary linear singular vortices. The order parameter of the studied neutron system belongs to the unitary class. This implies that the superfluid under consideration does not have spin polarization and the core-less $^{3}$P$_{2}$ vortices do not have magnetization, which makes electron scattering by vortices ineffective. For the same reason, pinning with flux tubes is also suppressed. This can affect the hydrodynamics of superfluid neutron stars., Comment: 7 pages, 5 figures

Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that the Hall viscosity at zero frequency and momentum vanishes in a vortex lattice., Comment: v3: resubmitted to SciPost

[ES] Se procede a elaborar e implementar el método Vortex Lattice mediante la herramienta Matlab que permita calcular de forma aproximada y orientativa la sustentación de las alas en función de los principales parámetros geométricos: envergadura, cuerda, flecha, torsión, diedro y separación entre las alas. El método implementado, permitirá calcular la fuerza de sustentación de la aeronave de forma sencilla y computacionalmente económica. En el primer apartado se comenzará con una introducción en la que se tratará la motivación del estudio además de una revisión bibliográfica y el análisis de trabajos anteriores similares. En el segundo apartado, se explicará el método implementado para el problema bidimensional, empezando con el caso más sencillo (placa plana sin ángulo de ataque) hasta el estudio de un perfil con espesor y curvatura. En el tercer apartado se explicará el programa implementado para el caso de superficies tridimensionales, el cual incluirá un generador de geometría que permitirá estudiar diferentes tipos de alas. Por último, se comparará los resultados obtenidos con los obtenidos mediante otros métodos y se expondrán las principales ventajas del método implementado frente a los otros.

[ES] Se procede a elaborar e implementar el método Vortex Lattice mediante la herramienta Matlab que permita calcular de forma aproximada y orientativa la sustentación de las alas en función de los principales parámetros geométricos: envergadura, cuerda, flecha, torsión, diedro y separación entre las alas. El método implementado, permitirá calcular la fuerza de sustentación de la aeronave de forma sencilla y computacionalmente económica. En el primer apartado se comenzará con una introducción en la que se tratará la motivación del estudio además de una revisión bibliográfica y el análisis de trabajos anteriores similares. En el segundo apartado, se explicará el método implementado para el problema bidimensional, empezando con el caso más sencillo (placa plana sin ángulo de ataque) hasta el estudio de un perfil con espesor y curvatura. En el tercer apartado se explicará el programa implementado para el caso de superficies tridimensionales, el cual incluirá un generador de geometría que permitirá estudiar diferentes tipos de alas. Por último, se comparará los resultados obtenidos con los obtenidos mediante otros métodos y se expondrán las principales ventajas del método implementado frente a los otros.

Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that the Hall viscosity at zero frequency and momentum vanishes in a vortex lattice., Comment: v3: resubmitted to SciPost

Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that the Hall viscosity at zero frequency and momentum vanishes in a vortex lattice. Copyright S. Moroz et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.

Both mixtures of atomic Bose-Einstein condensates and systems with atoms trapped in optical lattices have been intensely explored theoretically, mainly due to the exceptional developments on the experimental side. We investigate the properties of ultracold atomic impurities (bosons) immersed in a vortex lattice of a second Bose-condensed species. In contrast to the static optical-lattice configuration, the vortex lattice presents intrinsic dynamics given by its Tkachenko modes. These excitations induce additional correlations between the impurities, which consist of a long-range attractive potential and a density-dependent hopping, described here in the framework of an extended Bose-Hubbard model. We compute the quantum phase diagram of the impurity species through a Gutzwiller ansatz and through the mean-field approach, and separately identify the effects of the two additional terms, i.e. the shift and the deformation of the Mott-insulator lobes. The long-range attraction, in particular, induces the existence of a triple point in the phase diagram, in agreement with previous quantum Monte Carlo calculations [Chaviguri et al. Phys. Rev. A 95, 053639 (2017)2469-992610.1103/PhysRevA.95.053639]., SCOPUS: ar.j, info:eu-repo/semantics/published

El objetivo de este proyecto es la implementación del método Vortex-Lattice para el estudio de la Aerodinámica no estacionaria e incompresible de alas. Las ecuaciones que rigen el comportamiento de los fluidos no permiten la obtención de una solución analítica, por ello, deben ser resueltas numéricamente a partir de métodos como el expuesto en la presente memoria. La principal ventaja que presenta este método es que ofrece la posibilidad de entender la física del problema al mismo tiempo que se obtienen resultados para problemas reales, los cuales no serían abordables desde un punto de vista analítico; por esta razón, resulta idóneo para su uso didáctico en las escuelas de ingeniería. De hecho, el método Vortex-Lattice para el caso estacionario es ampliamente tratado en las clases de Aerodinámica II de la Escuela Superior de Ingeniería de Sevilla. En este proyecto, se propone extender el método desde el caso estacionario al no estacionario., The aim of this project is to program the Vortex-Lattice method in order to study the unsteady incompressible aerodynamics of wings. The analytical solution of the fluid equations is not possible and for this reason it is necessary to use a numerical method. The main advantage of this method is the chance of understanding the physical concepts of the problem and at the same time, it is possible to obtain solutions to real problems that have no analytical solution. For this reason, it is ideal to be used in engineering schools lessons. The steady Vortex-Lattice method is widely used in aerodynamics classes in the School of Engineering of Seville. In this project, it is proposed to extend the method from the steady flow to the unsteady flow.

The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.

A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO3/SrTiO3. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO3/SrTiO3. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

The leading edge inflated (LEI) surf-kite is a suitable wing design for airborne wind energy (AWE) power generation because the bridling and leading edge design allow the wing to be de-powered while retaining good steer-ability. Fluid-Structure Interaction (FSI) modelling is required to capture the flight behavior of an LEI kite, due to it's extreme flexibility. Unfortunately, the current kite aerodynamic models do not meet the requirements for LEI-kite FSI modelling: they are either fast but insufficiently accurate, or accurate but computationally expensive. In particular, the current fast aerodynamic models are not able to represent the effects of the multiple flow separation regions - such as behind the LEI tube and above the canopy’s trailing edge - inherent to a LEI kite flying at a large range of angles of attack. This master’s thesis is intended to evaluate the hypothesis that a quasi-steady multiple-wake vortex lattice method can quickly and accurately model surf-kite aerodynamics to generate aerodynamic surface load distributions. This model uses multiple vortex lattices to represent the separation stream-surfaces in the flow, as well as the geometric surface itself. The vortex model chosen is the Vatistas Core Model, with a combined free- and fixed-wake wake deformation model. The method is applied to an arc-shaped wing with a Clark Y profile, a unity aspect ratio flat plate, and a demonstration LEI kite in order to assess the model's strengths and limitations. It appears that the usefulness of a multiple-wake vortex lattice method is strongly limited for membrane-wing kites, by an inability to enforce the Kutta condition on a reattachment-line when this reattachment-line crosses a separation-line. However, in certain high angle of attack cases, a single-wake and pressure-surface-separation double-wake vortex lattice method have the same order of uncertainty with respect to RANS results as is generated by the geometric approximations made in the TU Delft A, Wind Energy, Aerodynamics, Wind Energy, Flight Performance and Propulsion, Aerospace Engineering

Os métodos de painéis têm sido amplamente utilizados na indústria e estabeleceram-se desde 1970 no cálculo e a análise aerodinâmica. Este artigo tem como objetivo apresentar uma introdução a um método numérico em aerodinâmica altamente usado em CFD (Computational Fluid Dynamics) para o cálculo dos coeficientes aerodinâmicos em uma superfície de asa. O artigo centra-se na apresentação de um resumo detalhado deste método conhecido como VLM ou Vortex Lattice Method. É importante notar que este estudo é apresentado como um artigo de reflexão e faz parte de um capítulo de uma tese de mestrado em Engenharia Aeroespacial. Portanto, nenhum teste ou derivação teórica se realiza. Seu foco principal é fazer um resumo analítico de um método computacional amplamente utilizado na aerodinâmica, a fim de apresentar ao leitor uma breve introdução matemática do método VLM e sua importância no campo aeronáutico., Los métodos de panel han sido ampliamente utilizados en la industria y se han establecido desde la década de 1970 en el cálculo y el análisis aerodinámico. Este artículo tiene como objetivo presentar una introducción a un método numérico en aerodinámica altamente utilizado en CFD (Computational Fluid Dynamics) para el cálculo de coeficientes aerodinámicos en una superficie alar. El artículo se enfoca en presentar un resumen detallado de este método conocido como VLM o Vortex Lattice Method. Es importante anotar, que este estudio se presenta como un artículo de reflexión y hace parte de un capítulo de una tesis de maestría en Ingenieria Aeroespacial. Por ende, no realiza ninguna prueba o derivación teórica, su enfoque primario es realizar una aproximación analítica de un método computacional utilizado ampliamente en aerodinámica con el fin de presentarle al lector una breve introducción matemática del método VLM y su importancia en el campo aeronáutico., Panel methods have been widely used in industry and are well established since the 1970s for aerodynamic analysis and computation. The Vortex Lattice Panel Method presented in this study comes across a sophisticated method that provides a quick solution time, allows rapid changes in geometry and suits well for aerodynamic analysis. The aerospace industry is highly competitive in design efficiency, and perhaps one of the most important factors on airplane design and engineering today is multidisciplinary optimization. Any cost reduction method in the design cycle of a product becomes vital in the success of its outcome. The subsequent sections of this article will further explain in depth the theory behind the vortex lattice method, and the reason behind its selection as the method for aerodynamic analysis during preliminary design work and computation within the aerospace industry. This article is analytic in nature, and its main objective is to present a mathematical summary of this widely used computational method in aerodynamics.

Os métodos de painéis têm sido amplamente utilizados na indústria e estabeleceram-se desde 1970 no cálculo e a análise aerodinâmica. Este artigo tem como objetivo apresentar uma introdução a um método numérico em aerodinâmica altamente usado em CFD (Computational Fluid Dynamics) para o cálculo dos coeficientes aerodinâmicos em uma superfície de asa. O artigo centra-se na apresentação de um resumo detalhado deste método conhecido como VLM ou Vortex Lattice Method. É importante notar que este estudo é apresentado como um artigo de reflexão e faz parte de um capítulo de uma tese de mestrado em Engenharia Aeroespacial. Portanto, nenhum teste ou derivação teórica se realiza. Seu foco principal é fazer um resumo analítico de um método computacional amplamente utilizado na aerodinâmica, a fim de apresentar ao leitor uma breve introdução matemática do método VLM e sua importância no campo aeronáutico., Los métodos de panel han sido ampliamente utilizados en la industria y se han establecido desde la década de 1970 en el cálculo y el análisis aerodinámico. Este artículo tiene como objetivo presentar una introducción a un método numérico en aerodinámica altamente utilizado en CFD (Computational Fluid Dynamics) para el cálculo de coeficientes aerodinámicos en una superficie alar. El artículo se enfoca en presentar un resumen detallado de este método conocido como VLM o Vortex Lattice Method. Es importante anotar, que este estudio se presenta como un artículo de reflexión y hace parte de un capítulo de una tesis de maestría en Ingenieria Aeroespacial. Por ende, no realiza ninguna prueba o derivación teórica, su enfoque primario es realizar una aproximación analítica de un método computacional utilizado ampliamente en aerodinámica con el fin de presentarle al lector una breve introducción matemática del método VLM y su importancia en el campo aeronáutico., Panel methods have been widely used in industry and are well established since the 1970s for aerodynamic analysis and computation. The Vortex Lattice Panel Method presented in this study comes across a sophisticated method that provides a quick solution time, allows rapid changes in geometry and suits well for aerodynamic analysis. The aerospace industry is highly competitive in design efficiency, and perhaps one of the most important factors on airplane design and engineering today is multidisciplinary optimization. Any cost reduction method in the design cycle of a product becomes vital in the success of its outcome. The subsequent sections of this article will further explain in depth the theory behind the vortex lattice method, and the reason behind its selection as the method for aerodynamic analysis during preliminary design work and computation within the aerospace industry. This article is analytic in nature, and its main objective is to present a mathematical summary of this widely used computational method in aerodynamics.

The leading edge inflated (LEI) surf-kite is a suitable wing design for airborne wind energy (AWE) power generation because the bridling and leading edge design allow the wing to be de-powered while retaining good steer-ability. Fluid-Structure Interaction (FSI) modelling is required to capture the flight behavior of an LEI kite, due to it's extreme flexibility. Unfortunately, the current kite aerodynamic models do not meet the requirements for LEI-kite FSI modelling: they are either fast but insufficiently accurate, or accurate but computationally expensive. In particular, the current fast aerodynamic models are not able to represent the effects of the multiple flow separation regions - such as behind the LEI tube and above the canopy’s trailing edge - inherent to a LEI kite flying at a large range of angles of attack. This master’s thesis is intended to evaluate the hypothesis that a quasi-steady multiple-wake vortex lattice method can quickly and accurately model surf-kite aerodynamics to generate aerodynamic surface load distributions. This model uses multiple vortex lattices to represent the separation stream-surfaces in the flow, as well as the geometric surface itself. The vortex model chosen is the Vatistas Core Model, with a combined free- and fixed-wake wake deformation model. The method is applied to an arc-shaped wing with a Clark Y profile, a unity aspect ratio flat plate, and a demonstration LEI kite in order to assess the model's strengths and limitations. It appears that the usefulness of a multiple-wake vortex lattice method is strongly limited for membrane-wing kites, by an inability to enforce the Kutta condition on a reattachment-line when this reattachment-line crosses a separation-line. However, in certain high angle of attack cases, a single-wake and pressure-surface-separation double-wake vortex lattice method have the same order of uncertainty with respect to RANS results as is generated by the geometric approximations made in the TU Delft A, Wind Energy, Aerodynamics, Wind Energy, Flight Performance and Propulsion, Aerospace Engineering

High-resolution focused ion beam lithography has been used to fabricate YBa2Cu3O7-x (YBCO) wires with nanometric lateral dimensions. In the present work, we investigate Flux-flow instabilities in nanowires of different widths, showing sudden voltage switching jumps from the superconducting to the normal state. We present an extensive study on the temperature and field dependence of the switching characteristics which reveal that voltage jumps become less abrupt as the temperature increases, and disappear at the vortex-liquid state. On the contrary, the current distribution at the critical point becomes narrower at high temperatures. Sharp voltage switchings very close to the critical current density can be obtained by reducing the width of the nanowires, making them very appealing for practical applications.

We analytically consider the spontaneous formation of a fermionic crystalline geometry in a gravity background with Lifshitz scaling and/or hyperscaling violation. Fermionic vortex lattice solution sourced by the lowest Laundau level has been obtained. Thermodynamic analysis shows that the fermionic vortex lattice favors a triangular configuration, regardless of the values of the Lifshitz scaling $z$ and the hyperscaling violation exponent $\theta$. Our results also show that the larger $z$ or lower $\theta$ leads to more stable lattices thermodynamically., Comment: 23 pages, 5 figures

We analytically consider the spontaneous formation of a fermionic crystalline geometry in a gravity background with Lifshitz scaling and/or hyperscaling violation. Fermionic vortex lattice solution sourced by the lowest Laundau level has been obtained. Thermodynamic analysis shows that the fermionic vortex lattice favors a triangular configuration, regardless of the values of the Lifshitz scaling $z$ and the hyperscaling violation exponent $\theta$. Our results also show that the larger $z$ or lower $\theta$ leads to more stable lattices thermodynamically., Comment: 23 pages, 5 figures

We use small-angle neutron scattering to study the superconducting vortex lattice in La2-xSrxCuO4 as a function of doping and magnetic field. We show that near optimally doping the vortex lattice coordination and the superconducting coherence length. are controlled by a Van Hove singularity crossing the Fermi level near the Brillouin zone boundary. The vortex lattice properties change dramatically as a spin-density-wave instability is approached upon underdoping. The Bragg glass paradigm provides a good description of this regime and suggests that spin-density-wave order acts as a source of disorder on the vortex lattice.

We use small-angle neutron scattering to study the superconducting vortex lattice in La2-xSrxCuO4 as a function of doping and magnetic field. We show that near optimally doping the vortex lattice coordination and the superconducting coherence length. are controlled by a Van Hove singularity crossing the Fermi level near the Brillouin zone boundary. The vortex lattice properties change dramatically as a spin-density-wave instability is approached upon underdoping. The Bragg glass paradigm provides a good description of this regime and suggests that spin-density-wave order acts as a source of disorder on the vortex lattice.