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One of the main issues concerning the standard Vortex Lattice Method is its application to partially or fully detached flow conditions, where non-linear aerodynamic characteristics appear as the angle of attack increases and/or the aspect ratio decreases. In order to solve such limitations, a pure numerical approach based entirely on the Vortex Lattice Method concepts has been developed. The so-called steady "Full Multi-wake Vortex Lattice Method" comes from the main hypothesis that each discretized element on the body's surface detaches their own wakes downstream. The obtained results match for lift, drag and moment coefficients for the entire aspect ratio range configurations (under straight wakes and inviscid assumptions). Future unsteady versions of such a multi-wake approach could improve the current results obtained through Vortex Element Methods (as vortons or isolated vortex filaments). [ABSTRACT FROM AUTHOR]

Following some prehistory, we discuss the steps leading to the Abrikosov vortex lattice and type-II superconductivity. Dissipation due to flux flow and flux creep represented an important discovery and leads to the strong interest in magnetic flux pinning. High-temperature superconductors and pancake vortices started the new concepts of vortex matter. Nonlinear effects at high vortex velocities, flux-flow instabilities, and some resulting open questions are discussed. [ABSTRACT FROM AUTHOR]

The present hybrid vortex tube-vorton method is based entirely on the Full Multi-wake Vortex Lattice Method (FMVLM) concepts, which means detaching vorticity with precise vortex strength and orientation along all separation lines between each discretized element of a shell-body, including all external edges. Since the classic Vortex Particle Method (VPM) is unstable by itself because it does not conserve the total amount of circulation as time evolves (Kelvin's circulation theorem), an isolated Vortex (regularized) Filament Method (VFM) approach is implemented to obtain advection of vorticity, while the induced velocity field is obtained through its corresponding full vorton cloud. Further, a novel vortex squeezing/stretching scheme for such a vortex cylinder-sphere approach is proposed based on variation in time for vortex volumes in order to precisely (zero residual) conserve both circulation and vorticity at each time step (for each detached vortex element), while the viscous effect can be accounted for via the Core Spreading Method (CSM). [ABSTRACT FROM AUTHOR]

Time-dependent equations of the two-band Ginzburg-Landau model are simulated numerically. Calculations are performed for square thin films of the LiFeAs two-band superconductor in the vicinity of the superconducting transition temperature in the transverse magnetic field; the quasi-hexagonal nature of the vortex lattice in the intermediate state is demonstrated. [ABSTRACT FROM AUTHOR]

Many superconducting materials are composed of weakly coupled conducting layers. Such a layered structure has a very strong influence on the properties of vortex matter in a magnetic field. This review focuses on the properties of the Josephson vortex lattice generated by the magnetic field applied in the direction of the layers. The theoretical description is based on the Lawrence-Doniach model in the London limit, which takes only the phase degree of freedom of the superconducting order parameter into account. In spite of its simplicity, this model leads to an amazingly rich set of phenomena. We review in detail the structure of an isolated vortex line and various properties of the vortex lattice, in both dilute and dense limits. In particular, we extensively discuss the influence of the layered structure and thermal fluctuations on the selection of lattice configurations at different magnetic fields. [ABSTRACT FROM AUTHOR]

Evolution of the excess conductivity in optimally doped YBa 2 Cu 3 O 7 - δ single crystals is investigated after their irradiation with fast electrons at T ≲ 10 K at energies of 0.5–2.5 MeV and a dose of 3 × 10 18 cm - 2 . The measurements were performed in a magnetic field of 15 kOe applied at various angles with respect to the basal plane of the crystals. The temperature dependences of the paraconductivity were analyzed within the framework of the Aslamazov–Larkin theoretical model of fluctuation conductivity and revealed two major effects of the electron irradiation. Namely, (i) the vortex-lattice-melting kinks in the resistivity temperature dependences vanish after electron irradiation and (ii) the resistivity data in the irradiated state allow for a Kouvel-Fisher-type scaling pointing to the presence of a irradiation-induced vortex Bragg-glass phase. These effects are discussed in terms of a competition between intrinsic pinning due to point defects and volume pinning induced by electron irradiation. In all, our findings are relevant for YBCO-based circuitry which is exposed to fast electrons in moderately strong magnetic fields. [ABSTRACT FROM AUTHOR]

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. [ABSTRACT FROM AUTHOR]

We introduce a 'Coulombian renormalized energy' W which is a logarithmic type of interaction between points in the plane, computed by a 'renormalization.' We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general remains open. Our motivation is the study of minimizers of the two-dimensional Ginzburg-Landau energy with applied magnetic field, between the first and second critical fields H and H. In that regime, minimizing configurations exhibit densely packed triangular vortex lattices, called Abrikosov lattices. We derive, in some asymptotic regime, W as a Γ-limit of the Ginzburg-Landau energy. More precisely we show that the vortices of minimizers of Ginzburg-Landau, blown-up at a suitable scale, converge to minimizers of W, thus providing a first rigorous hint at the Abrikosov lattice. This is a next order effect compared to the mean-field type results we previously established. The derivation of W uses energy methods: the framework of Γ-convergence, and an abstract scheme for obtaining lower bounds for '2-scale energies' via the ergodic theorem, that we introduce. [ABSTRACT FROM AUTHOR]

Ratchet devices allow turning an ac input signal into a dc output signal. A ratchet device is set by moving particles driven by zero averages forces on asymmetric potentials. Hybrid nanostructures combining artificially fabricated spin ice nanomagnet arrays with superconducting films have been identified as a good choice to develop ratchet nanodevices. In the current device, the asymmetric potentials are provided by charged Néel walls located in the vertices of spin ice magnetic honeycomb array, whereas the role of moving particles is played by superconducting vortices. We have experimentally obtained ratchet effect for different spin ice I configurations and for vortex lattice moving parallel or perpendicular to magnetic easy axes. Remarkably, the ratchet magnitudes are similar in all the experimental runs; i. e. different spin ice I configurations and in both relevant directions of the vortex lattice motion. We have simulated the interplay between vortex motion directions and a single asymmetric potential. It turns out vortices interact with uneven asymmetric potentials, since they move with trajectories crossing charged Néel walls with different orientations. Moreover, we have found out the asymmetric pair potentials which generate the local ratchet effect. In this rocking ratchet the particles (vortices) on the move are interacting each other (vortex lattice); therefore, the ratchet local effect turns into a global macroscopic effect. In summary, this ratchet device benefits from interacting particles moving in robust and topological protected type I spin ice landscapes. [ABSTRACT FROM AUTHOR]

Electric vertical take-off and landing (eVTOL) aircraft with multiple lifting rotors or prop-rotors have received significant attention in recent years due to their great potential for next-generation urban air mobility (UAM). Numerical models have been developed and validated as predictive tools to analyze rotor aerodynamics and wake dynamics. Among various numerical approaches, the vortex method is one of the most suitable because it can provide accurate solutions with an affordable computational cost and can represent vorticity fields downstream without numerical dissipation error. This paper presents a brief review of the progress of vortex methods, along with their principles, advantages, and shortcomings. Applications of the vortex methods for modeling the rotor aerodynamics and wake dynamics are also described. However, the vortex methods suffer from the problem that it cannot deal with the nonlinear aerodynamic characteristics associated with the viscous effects and the flow behaviors in the post-stall regime. To overcome the intrinsic drawbacks of the vortex methods, recent progress in a numerical method proposed by the authors is introduced, and model validation against experimental data is discussed in detail. The validation works show that nonlinear vortex lattice method (NVLM) coupled with vortex particle method (VPM) can predict the unsteady aerodynamic forces and complex evolution of the rotor wake. [ABSTRACT FROM AUTHOR]

It is well known that the interaction between defect-induced strain field and vortex lattice (VL) gives rise to vortex pinning behaviors. Likewise, magneto-elastic (ME) interaction is caused by the difference between specific volumes of normal phase and superconducting (SC) phase. Acting as inhomogeneous strain sources, the normal-state vortex cores produce local deformation in the surrounding SC matter and thus affect VL energy. ME interaction belongs to the fundamental physics of interdependences between vortex matter and crystal lattice. The review starts with the effects of ME interaction on magnetization, vortex morphology and intervortex interaction. In Sect. 2, theoretical descriptions of ME interaction are classified in terms of different simplifications. The core ideas and outstanding results of these theories are given. It is followed by Sect. 3, where the correlation and difference between ME and pinning interaction are outlined. Although pinning differs from ME interaction in their formation mechanisms, the pinning interaction is established upon the vortex-induced strain field from Ginzburg-Landau (GL) viewpoint. Section 4 goes further with the GL treatment for solving ME and pinning problem; the general thoughts and steps can be found in this section. The last section gives some outlooks which involve pressure dependence of Tc and anisotropy. [ABSTRACT FROM AUTHOR]

Recent experiments have shown that the complex spatio-temporal vortex structures emerging in active fluids are susceptible to weak geometrical constraints. This observation poses the fundamental question of how boundary effects stabilize a highly ordered pattern from seemingly turbulent motion. Here we show, by a combination of continuum theory and experiments on a bacterial suspension, how artificial obstacles guide the flow profile and reorganize topological defects, which enables the design of bacterial vortex lattices with tunable properties. To this end, the continuum model is extended by appropriate boundary conditions. Beyond the stabilization of square and hexagonal lattices, we also provide a striking example of a chiral, antiferromagnetic lattice exhibiting a net rotational flow, which is induced by arranging the obstacles in a Kagome-like array. Recent experiments showed that weak geometrical constraints can organize topological defects in turbulent bacterial suspensions. Here, the authors use a continuum model to study the connection between symmetry and stability of emergent vortex patterns and the geometry of constraining pillar arrays. [ABSTRACT FROM AUTHOR]

Aircraft design has become increasingly complex since it depends on technological advances and integration between modern engineering systems. These systems are multidisciplinary, i.e., any process or division of any aircraft design produces effects in all others, making the definition of each parameter a significant challenge. In this context, this work presents a general multidisciplinary design optimization method for the conceptual design of general aviation and hybrid-electric aircraft. The framework uses efficient computational methods comprising modules of engineering that include aerodynamics, flight mechanics, structures, and performance, and the integration of all of them. The aerodynamic package relies on a Nonlinear Vortex Lattice Method solver, while the flight mechanics package is based on an analytical procedure with minimal dependence on historical data. Moreover, the structural module adopts an analytical sizing approach using boom idealization, and the performance of the aircraft is computed based on energy and power required to accomplish a specific mission. The objective functions are to minimize the fuel consumption and to minimize the takeoff weight. The Pareto-optimal front encompasses aircraft with different propulsive architectures: turboelectric, hybrid electric, and fully electric. The degrees of hybridization defined by the optimization and the mission requirements chosen in this study directly affect the final weight breakdown of the aircraft, which is related to the sizing of the wings, propulsive system, and horizontal and vertical tails. [ABSTRACT FROM AUTHOR]

Experiments with the crossover superconductors between standard types I and II revealed exotic magnetic flux patterns where Meissner domains coexist with islands of the vortex lattice as well as with vortex clusters and chains. Until now a comprehensive theory for such configurations has not been presented. We solve this old-standing fundamental problem by developing an approach which combines the perturbation expansion of the microscopic theory with statistical simulations and which requires no prior assumption on the vortex distribution. Our study offers the most complete picture of the interchange of the superconductivity types available so far. The mixed state in this regime reveals a rich manifold of exotic configurations, which reproduce available experimental results. Our work introduces a pattern formation mechanism that originates from the self-duality of the theory that is universal and not sensitive to the microscopic details. Classification into type I and II reflects different responses of a superconductor to an applied magnetic field, however, there are intertype materials with unique properties and atypical vortex configurations. The authors study vortex patterns in this regime revealing that their properties are governed by a universal material independent mechanism, which amends the dual classification. [ABSTRACT FROM AUTHOR]

The vortex lattice in a Type II superconductor provides a versatile model system to investigate the order-disorder transition in a periodic medium in the presence of random pinning. Here, using scanning tunnelling spectroscopy in a weakly pinned Co0.0075NbSe2 single crystal, we show that the vortex lattice in a 3-dimensional superconductor disorders through successive destruction of positional and orientational order, as the magnetic field is increased across the peak effect. At the onset of the peak effect, the equilibrium quasi-long range ordered state transforms into an orientational glass through the proliferation of dislocations. At a higher field, the dislocations dissociate into isolated disclination giving rise to an amorphous vortex glass. We also show the existence of a variety of additional non-equilibrium metastable states, which can be accessed through different thermomagnetic cycling. [ABSTRACT FROM AUTHOR]

We study the dynamics of a rotating trapped Bose-Einstein condensate (BEC) at finite temperatures. Using the Zaremba-Nikuni-Griffin formalism, based on a generalized Gross-Pitaevskii equation for the condensate coupled to a semiclassical kinetic equation for a thermal cloud, we numerically simulate vortex lattice formation in the presence of a time-dependent rotating trap potential. At low rotation frequency, the thermal cloud undergoes rigid body rotation, while the condensate exhibits irrotational flow. Above a certain threshold rotation frequency, vortices penetrate into the condensate and form a vortex lattice. Our simulation result clearly indicates a crucial role for the thermal cloud, which triggers vortex lattice formation in the rotating BEC. [ABSTRACT FROM AUTHOR]

We study the spatial distribution of supercurrent circulated around an Abrikosov vortex in an SF bilayer in perpendicular magnetic field. Within the dirty limit regime and circular cell approximation for the vortex lattice, we derive the conditions when the Usadel equations the F-layer can be solved analytically. Using the obtained solutions, we demonstrate the possibility of reversal of direction of proximity induced supercurrents around the vortex in the F-layer compared to that in the S-layer. The direction of currents can be controlled either by varying transparency of the SF interface or by changing an exchange field in a ferromagnet. We argue that the origin of this effect is due the phase shift between singlet and triplet order parameter components induced in the F-layer. Possible ways of experimental detection of the predicted effect are discussed. [ABSTRACT FROM AUTHOR]

Order-disorder transitions of a vortex lattice transfer type-II superconductors from a low critical current state to a high one. The similar transition between different current states can be caused by electromagnetic granularity. A sigmoid curve is proposed to describe the corresponding peak in a field dependence of the macroscopic critical density. Using the extended critical state model, analytic expressions are obtained for the field dependencies of the local critical current density, the depth of equilibrium surface region, and the macroscopic critical current density. The expressions are well fit to published data. [ABSTRACT FROM AUTHOR]

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli-limit heavy-electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to the muon spin rotation (μSR) experiment. Based on the Ginzburg-Landau expansion for the superconductor free energy, we study the evolution with respect to the external field of the static linewidth both in the limit of independent vortices (low magnetic field) with a variational expression for the order parameter and in the near H( T) regime with an extension of the Abrikosov analysis to Pauli-limit superconductors. We conclude that in the Ginzburg-Landau regime in the Pauli-limit, anomalous variations of the static linewidth with the applied field are predicted as a result of the superconductor spin response around a vortex core that dominates the usual charge-response screening supercurrents. We propose the effect as a benchmark for studying new puzzling vortex lattice properties recently observed in CeCoIn. [ABSTRACT FROM AUTHOR]

The original version of the article unfortunately contained an error. A new paragraph should be inserted as the last paragraph of Section 3 Flux Flow and Flux Creep. [ABSTRACT FROM AUTHOR]

The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-Tc superconductors, regardless of cuprate or pnictide family. The nematic state in high-Tc systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin films revealed the nematic superconducting state by Song et al. Here, motivated by the experiment, we construct the extended Ginzburg–Landau free energy to describe the elliptical vortex, where a mixed s-wave and d-wave superconducting order is coupled to the nematic order. The nematic order induces the mixture of two superconducting orders and enhances the anisotropic interaction between the two superconducting orders, resulting in a symmetry breaking from C4 to C2. Consequently, the vortex cores are stretched into an elliptical shape. In the equilibrium state, the elliptical vortices assemble a lozenge-like vortex lattice, being well consistent with experimental results. Superconductivity: multiple orders couple to produce elliptical vortex Theorists construct the extended Ginzburg-Landau free energy to explain the elliptical superconducting vortex, where multiple orders are coupled. A team led by Da-Chuan Lu and Jun Li from Nanjing University in China theoretically studied the nematic superconducting state, which is characterized by elliptical vortices, reported in a recent experiment. They construct the extended Ginzburg-Landau free energy by implementing finite element method to the time-dependent Ginzburg-Landau equations with open boundary conditions. The method describes the elliptical vortex, where a mixing of superconducting orders couple with a nematic order. The coupling further enhances the anisotropic interaction between superconducting orders and results in a four-fold to two-fold rotational symmetry breaking. The elliptical vortices assemble a lozenge-like vortex lattice, which is consistent with experimental results. [ABSTRACT FROM AUTHOR]

The dynamics of interacting quantized vortex filaments in a rotating Bose-Einstein condensate existing in the Thomas-Fermi regime at zero temperature and obeying the Gross-Pitaevskii equation has been considered in the hydrodynamic 'nonelastic' approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose-Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived. [ABSTRACT FROM AUTHOR]

It is shown that the thermodynamic instability at the half filling of L1 leads to the vortex lattice formation with the electronic spectrum analogous to that of graphene with two Dirac-Fermi points on Brillouin cell boundary. This result is used for the explanation of the observed current generated by a surface acoustic wave in the heterostructure on the surface of piezoelectric GaAs. Using the existence of two Fermi points instead of a Fermi surface suggested in the previous theoretical works, permit the explanation of the experimental results. [ABSTRACT FROM AUTHOR]

We theoretically show that a family of optical beams with vortex-lattice structures can be reliably generated by tilting the focal lens to introduce the relative phases between the interfering beams. We also experimentally generate the quasicrystal beams to confirm the theoretical analysis. With the analytical wave functions and experimental patterns, a variety of vortex-lattice structures are manifested. [ABSTRACT FROM AUTHOR]

Engineering optical lattices with laser-induced tunnelling amplitudes has enabled the realization of artificial magnetic fields with remarkable tunability. Here, we report on the observation of chiral Meissner currents in bosonic ladders exposed to a strong artificial magnetic field. By suddenly decoupling the individual ladders and projecting into isolated double wells, we are able to measure the currents on each side of the ladder. For large coupling strengths along the rungs of the ladder, we find a saturated maximum chiral current, which is analogous to the surface currents in the Meissner effect. Below a critical inter-leg coupling strength, the chiral current decreases in good agreement with our expectations for a vortex lattice phase. Our realization of a low-dimensional Meissner-like effect and spin-orbit coupling in one dimension opens the path to exploring interacting particles in low dimensions exposed to a uniform magnetic field. [ABSTRACT FROM AUTHOR]

We calculate fluctuation Hall conductivity of a strongly type-II superconductor in strong electric fields by using the time dependent Ginzburg-Landau approach. Thermal fluctuations, represented by the Langevin white noise, are assumed to be strong enough to melt the Abrikosov vortex lattice created by the magnetic field into a moving vortex liquid. The layered structure of the superconductor is accounted for by means of the Lawrence-Doniach model. The nonlinear interaction term in dynamics is treated within self-consistent Gaussian approximation and we go beyond the often used lowest Landau level approximation to treat arbitrary magnetic fields. The results are compared to experimental data on high- T superconductor YBaCuO. [ABSTRACT FROM AUTHOR]

We define a 'renormalized energy' as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of Sandier and Serfaty (From the Ginzburg-Landau model to vortex lattice problems, ; 1D log-gases and the renormalized energy, ). Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix β-sine processes on the real line ( β = 1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the β = 2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels. [ABSTRACT FROM AUTHOR]

We report on experimental measurements of the magnetically induced kinetic energy density ( E) in single-crystal samples of YBa Cu O (YBCO), with the oxygen contents x=6.72, 6.78, 6.85, and 6.90. Our study is restricted to the reversible region near the critical temperature ( T), where the pinning force acting on the vortices is negligible. We use the expression E=− M⋅ B ( M is the magnetization and B is the magnetic induction) to calculate the kinetic energy density from magnetization measurements carried out in magnetic fields up to 5 T. We analyze the behavior of E as a function of the temperature for several isofield curves and construct E versus B curves as well. We find that E rises with the increase of the charge carriers density. Granularity effects and dimensionality of the order parameter can also be important factors contributing to the kinetic energy density. [ABSTRACT FROM AUTHOR]

We have measured isofield curves for the kinetic energy density ( E) in the superconducting state of a BiSrCaCuO (Bi-2212) single crystal. These curves were determined from magnetization versus temperature experiments that were analyzed according to the prescription of the virial theorem of superconductivity. The magnetization measurements were carried out using the zero field cooling (ZFC) and field cooled cooling (FCC) protocols. This procedure allows the determination of the temperature interval where the magnetization behaves reversibly. This study is limited to the temperature region where the pinning effects are negligible. The field-induced kinetic energy is associated with the currents circulating around the vortices. The obtained results allow the estimation of the upper critical field and are in accordance to the expectations of the Abrikosov theory for type-II superconductors. [ABSTRACT FROM AUTHOR]

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space. [ABSTRACT FROM AUTHOR]

Recently, a dynamic vortex Mott transition has been observed in an array of superconducting nanodots. Here, we report the effect of the interaction of microwave radiation on this system and we show the occurrence of giant Shapiro steps. [ABSTRACT FROM AUTHOR]

An Unsteady Vortex Lattice Method is developed and validated. It is coupled with a decambering methodology to account for viscous effects on the aerodynamic coefficients. Two additional methodologies to select a unique solution when multiple solutions arise have been proposed. The transient nature of the aerodynamic loads of a suddenly moving wing at different angles of attack is examined. Sudden jumps are observed in the CL(t) at post-stall angles of attack. The jumps are followed by the presence of asymmetric solutions, which then decline with time and a change in the solution state. Higher angles of attack see an increasing number of jumps. [ABSTRACT FROM AUTHOR]

Matter under different equilibrium conditions of pressure and temperature exhibits different states such as solid, liquid, gas, and plasma. Exotic states of matter, such as Bose–Einstein condensates, superfluidity, chiral magnets, superconductivity, and liquid crystalline blue phases are observed in thermodynamic equilibrium. Rather than being a result of an aggregation of matter, their emergence is due to a change of a topological state of the system. These topological states can persist out of thermodynamics equilibrium. Here we investigate topological states of matter in a system with injection and dissipation of energy by means of oscillatory forcing. In an experiment involving a liquid crystal cell under the influence of a low-frequency oscillatory electric field, we observe a transition from a non-vortex state to a state in which vortices persist, topological transition. Depending on the period and the type of the forcing, the vortices self-organise, forming square lattices, glassy states, and disordered vortex structures. The bifurcation diagram is characterised experimentally. A continuous topological transition is observed for the sawtooth and square forcings. The scenario changes dramatically for sinusoidal forcing where the topological transition is discontinuous, which is accompanied by serial transitions between square and glassy vortex lattices. Based on a stochastic amplitude equation, we recognise the origin of the transition as the balance between stochastic creation and deterministic annihilation of vortices. Numerical simulations show topological transitions and the emergence of square vortex lattice. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states. [ABSTRACT FROM AUTHOR]

This paper presents finite difference calculations of a dipole skyrmion vortex in multiferroic BiFeO and demonstrates a stabilizing role of electrostatic dipole-dipole interaction. We consider the main approaches to producing vortex lattices in BiFeO and their potential applications in spintronics and diptronics. [ABSTRACT FROM AUTHOR]

The first-approach techniques for analytical evaluation of the airfoil shape and calculation of the aerodynamic coefficients for a box-wing aircraft are suggested. The reliability of the calculation results was estimated using FLZ code (the vortex lattice method). The comparison showed satisfactory convergence of coefficients for the clean configuration and some discrepancy for the take-off and landing configuration. [ABSTRACT FROM AUTHOR]

A method for static aeroelastic trim analysis and flight loads computation of a flexible aircraft with large deformations has been presented in this paper, which considers the geometric nonlinearity of the structure and the nonplanar effects of aerodynamics. A nonplanar vortex lattice method is used to compute the nonplanar aerodynamics. The nonlinear finite element method is introduced to consider the structural geometric nonlinearity. Moreover, the surface spline method is used for structure/aerodynamics coupling. Finally, by combining the equilibrium equations of rigid motions of the deformed aircraft, the nonlinear trim problem of the flexible aircraft is solved by iterative method. For instance, the longitudinal trim analysis of a flexible aircraft with large-aspect-ratio wings is carried out by both the nonlinear method presented and the linear method of MSC Flightloads. Results obtained by these two methods are compared, and it is indicated that the results agree with each other when the deformation is small. However, because the linear method of static aeroelastic analysis does not consider the nonplanar aerodynamic effects or structural geometric nonlinearity, it is not applicable as the deformations increase. Whereas the nonlinear method presented could solve the trim problem accurately, even the deformations are large, which makes the nonlinear method suitable for rapid and efficient analysis in engineering practice. It could be used not only in the preliminary stage but also in the detail stage of aircraft design. [ABSTRACT FROM AUTHOR]

The aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures is investigated. The geometric nonlinearity is introduced into the dynamic equilibrium equations of structures. The disturbances on the structural surface caused by the air flow are simulated by a vortex layer with infinite thickness in the structures. The unsteady Bernoulli equation and the circulation theorem are applied in order to express the aerodynamic pressure as the function of the vortex density. The vortex density is then obtained with the vortex lattice method considering the coupling boundary condition. From the analytical expressions of the unstable critical wind velocities, numerical results and some useful conclusions are obtained. It is found that the initial curvature of open cable-membrane structures has clear influence on the critical wind velocities of the structures. [ABSTRACT FROM AUTHOR]

The blade-tower interaction of upwind horizontal axis wind turbines has become important to aerodynamic loading as the systems become larger. However, there are not enough studies describing these phenomena. To investigate this interaction, we performed numerical simulations for uniform, yawed, wind shear flow conditions, and various tower cases using the nonlinear vortex correction method with time-marching free wake. At 5 m/s, the change in the normal force coefficient is approximately 10% of the average. The blade root region has a larger azimuth range of the interaction and a bigger change in aerodynamic loading. The blade-tower interaction decreases as the yaw error and wind shear exponent increases. The interaction due to tower radius variations is higher than that due to tower clearance variations. With regard to stochastic load, the blade-tower interaction may affect the total fatigue load at low wind speed and in a more unstable atmospheric condition. [ABSTRACT FROM AUTHOR]