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We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, contain a cubic nonlinearity, and yet have a favorable $L^2$ energy structure. We consider the local and global in time well-posedness of these models and establish a difference between the behavior as $t\to \infty$ with respect to weak and strong norms., Comment: 24 pages

Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature $T_c$. Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin $S=0$, although they can also form parallel spin-triplet Cooper pairs with $S=1$ and an odd parity wavefunction. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation. Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations, uranium based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity. Indeed, UTe$_2$, which has a $T_c\approx 1.6$ K, has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability, although it also has antiferromagnetic (AF) spin fluctuations. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe$_2$ is coupled to a sharp magnetic excitation, termed resonance, at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability, its observation in UTe$_2$ suggests that AF spin fluctuations may also induce spin-triplet pairing or that electron pairing in UTe$_2$ has a spin-singlet component., 30 pages, 4 figures in main text and 7 figures in extended data

We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes., Comment: 16 pages, 9 figures, 2 tables

Controlling physical systems and their dynamics on the level of individual quanta propels both fundamental science and quantum technologies. Trapped atomic and molecular systems, neutral and charged, are at the forefront of quantum science. Their extraordinary level of control is evidenced by numerous applications in quantum information processing and quantum metrology. Studying the long-range interactions between these systems when combined in a hybrid atom-ion trap has lead to landmark results. Reaching the ultracold regime, however, where quantum mechanics dominates the interaction, e.g., giving access to controllable scattering resonances, has been elusive so far. Here we demonstrate Feshbach resonances between ions and atoms, using magnetically tunable interactions between $^{138}$Ba$^{+}$ ions and $^{6}$Li atoms. We tune the experimental parameters to probe different interaction processes - first, enhancing three-body reactions and the related losses to identify the resonances, then making two-body interactions dominant to investigate the ion's sympathetic cooling in the ultracold atomic bath. Our results provide deeper insights into atom-ion interactions, giving access to complex many-body systems and applications in experimental quantum simulation., 13 pages, 7 figures

Symmetry-broken electronic phases support neutral collective excitations. For example, monolayer graphene in the quantum Hall regime hosts a nearly ideal ferromagnetic phase at specific filling factors that spontaneously breaks the spin-rotation symmetry1–3. This ferromagnet has been shown to support spin-wave excitations known as magnons that can be electrically generated and detected4,5. Although long-distance magnon propagation has been demonstrated via transport measurements, important thermodynamic properties of such magnon populations—including the magnon chemical potential and density—have not been measured. Here we present local measurements of electron compressibility under the influence of magnons, which reveal a reduction in the gap associated with the ν = 1 quantum Hall state by up to 20%. Combining these measurements with the estimates of temperature, our analysis reveals that the injected magnons bind to electrons and holes to form skyrmions, and it enables the extraction of free magnon density, magnon chemical potential and average skyrmion spin. Our methods provide a means of probing the thermodynamic properties of charge-neutral excitations that are applicable to other symmetry-broken electronic phases.

openaire: EC/H2020/814753/EU//FLARE The structural damage of ships in navigational accidents is influenced by the hydrodynamic properties of surrounding water. Fluid structure interactions (FSI) in way of grounding contact can be idealized by combining commercial FEA tools and specialized hydrodynamic solvers. Despite the efficacy of these simulations, the source codes idealizing FSI are not openly available, computationally expensive and subject to limitations in terms of physical assumptions. This paper presents a unified FSI model for the assessment of ship crashworthiness following ship hard grounding. The method uses spring elements for the idealization of hydrostatic restoring forces in 3 DoF (heave, pitch, roll) and distributes the added masses in 6 DoF on the nodal points in way of contact. Comparison of results against the method of Kim et al. (2021) for the case of a barge and a Ro–Ro passenger ship demonstrate excellent idealization of ship dynamics. It is concluded that the method could be useful for rapid assessment of ship grounding scenarios and associated regulatory developments.

Understanding fluid flows in planetary cores and subsurface oceans, as well as their signatures in available observational data (gravity, magnetism, rotation, etc.), is a tremendous interdisciplinary challenge. In particular, it requires understanding the fundamental fluid dynamics involving turbulence and rotation at typical scales well beyond our day-to-day experience. To do so, laboratory experiments are fully complementary to numerical simulations, especially in systematically exploring extreme flow regimes for long duration. In this review article, we present some illustrative examples where experimental approaches, complemented by theoretical and numerical studies, have been key for a better understanding of planetary interior flows driven by some type of mechanical forcing. We successively address the dynamics of flows driven by precession, by libration, by differential rotation, and by boundary topography., Surveys in Geophysics, 43, ISSN:0169-3298, ISSN:1573-0956

A liquid marble is a liquid droplet coated usually with hydrophobic particles that can hold a very small liquid volume without wetting the adjacent surface. This combination gives rise to a set of unique properties such as resistance to contamination, low-friction mobility and flexible manipulation, making them appealing for a myriad of engineering applications including miniature reactors, gas sensing and drug delivery. Despite numerous experimental studies, numerical modelling investigations of liquid marbles are currently underrepresented in the literature, although such investigations can lead to a better understanding of their overall behaviour while overcoming the use of cost- and time-intensive experimental-only procedures. This paper therefore evaluates the capabilities of three well-established and widely-used particle-based numerical frameworks, namely Smoothed Particle Hydrodynamics (SPH)-based approaches, Coarse-Grained (CG)-based approaches and Lattice Boltzmann Method (LBM)-based approaches, to investigate liquid-marble properties and their key applications. Through a comprehensive review of recent advancements, it reveals that these numerical approaches demonstrate promising capabilities of simulating complex multiphysical phenomena involved with liquid-marble systems such as their floatation, coalescence and surface-tension-surface-area relationship. The paper further elaborates on the perspective that benefiting from particle-based numerical and computational techniques, liquid marbles can become an even more effective and exciting platform for many cutting-edge large-scale engineering applications.

With increasing demand for rotor blades in engineering applications, improving the performance of such structures using morphing blades has received considerable attention. Resonant passive energy balancing (RPEB) is a relatively new concept introduced to minimize the required actuation energy. This study investigates RPEB in morphing helicopter blades with lag–twist coupling. The structure of a rotating blade with a moving mass at the tip is considered under aerodynamic loading. To this end, a three-degree-of-freedom (3DOF) reduced-order model is used to analyse and understand the complicated nonlinear aeroelastic behaviour of the structure. This model includes the pitch angle and lagging of the blade, along with the motion of the moving mass. First, the 3DOF model is simplified to a single-degree-of-freedom model for the pitch angle dynamics of the blade to examine the effect of important parameters on the pitch response. The results demonstrate that the coefficient of lag–twist coupling and the direction of aerodynamic moment on the blade are two parameters that play important roles in controlling the pitch angle, particularly the phase. Then, neglecting the aerodynamic forces, the 3DOF system is studied to investigate the sensitivity of its dynamics to changes in the parameters of the system. The results of the structural analysis can be used to tune the parameters of the blade in order to use the resonant energy of the structure and to reduce the required actuation force. A sensitivity analysis is then performed on the dynamics of the 3DOF model in the presence of aerodynamic forces to investigate the controllability of the amplitude and phase of the pitch angle. The results show that the bend–twist coupling and the distance between the aerodynamic centre and the rotation centre (representing the direction and magnitude of aerodynamic moments) play significant roles in determining the pitch dynamics.

In quantum fluids, the quantisation of circulation forbids the diffusion of a vortex swirling flow seen in classical viscous fluids. Yet, a quantum vortex accelerating in a superfluid may lose its energy into acoustic radiation, in a similar way an electric charge decelerates upon emitting photons. The dissipation of vortex energy underlies central problems in quantum hydrodynamics, such as the decay of quantum turbulence, highly relevant to systems as varied as neutron stars, superfluid helium and atomic condensates. A deep understanding of the elementary mechanisms behind irreversible vortex dynamics has been a goal for decades, but it is complicated by the shortage of conclusive experimental signatures. Here, we address this challenge by realising a programmable quantum vortex collider in a planar, homogeneous atomic Fermi superfluid with tunable inter-particle interactions. We create on-demand vortex configurations and monitor their evolution, taking advantage of the accessible time and length scales of our ultracold Fermi gas. Engineering collisions within and between vortex-antivortex pairs allows us to decouple relaxation of the vortex energy due to sound emission and interactions with normal fluid, i.e. mutual friction. We directly visualise how the annihilation of vortex dipoles radiates a sound pulse in the superfluid. Further, our few-vortex experiments extending across different superfluid regimes suggest that fermionic quasiparticles localised inside the vortex core contribute significantly to dissipation, opening the route to exploring new pathways for quantum turbulence decay, vortex by vortex., Comment: 7+9 pages, 4+7 figures

PURPOSE Identification of coherent structures in cardiovascular flows is crucial to describe the transport and mixing of blood. Coherent structures can highlight locations where minimal blood mixing takes place, thus, potential thrombus formation can be expected thither. Graph-based approaches have recently been introduced in order to describe fluid transport and mixing between multiple Lagrangian trajectories, where each trajectory serves as a node that can be connected to another trajectory based on their relative distance during the course of time. METHODS In this study, we compute the Lagrangian trajectories from in vitro planar instantaneous velocity fields in two models of abdominal aortic aneurysms, (AAA) namely single bulge and bi-lobed. Then, we construct unweighted and undirected graphs based on the pairwise distance of Lagrangian trajectories. We report local measures of the graph namely the degree and the clustering coefficient. We also perform spectral clustering of the graph Laplacian to extract the flow coherent sets. RESULTS Local graph measures reveal fluid regions of high mixing such as vortex boundaries. Through spectral clustering, the fluid is partitioned into a reduced number of coherent sets where within each set, inner mixing of fluid is maximized while the fluid mixing between different coherent sets is minimized. The approach reveals multiple coherent sets adjacent to the AAA bulge that have sustained this adjacency to the wall through their coherent motion during one cardiac cycle. CONCLUSION Identifying coherent sets enables tracking their transport during the cardiac cycle and identify their role in the flow dynamics. Moreover, the size and the transport of the long residing coherent sets inside the AAA bulges can be deduced which may aid in predicting thrombus formation at such location.

Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena and a deeper understanding of them. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice1,2. However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to two-dimensional (2D) systems. Here we introduce an imaging approach where matter wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in three-dimensional (3D) systems. By combining the site-resolved imaging with magnetic resonance techniques for local addressing of individual lattice sites, we demonstrate full accessibility to 2D local information and manipulation in 3D systems. We employ the high-resolution images for precision thermodynamics of Bose–Einstein condensates in optical lattices as well as studies of thermalization dynamics driven by thermal hopping. The sub-lattice resolution is demonstrated via quench dynamics within the lattice sites. The method opens the path for spatially resolved studies of new quantum many-body regimes, including exotic lattice geometries or sub-wavelength lattices3–6, and paves the way for single-atom-resolved imaging of atomic species, where efficient laser cooling or deep optical traps are not available, but which substantially enrich the toolbox of quantum simulation of many-body systems., Existing techniques for high-resolution imaging of trapped quantum gases are limited to two-dimensional systems, but the approach described here works in three dimensions by magnifying the quantum gas with matter wave optics.

Laser cooling exploits the physics of light scattering to cool atomic and molecular gases to close to absolute zero. It is the crucial initial step for essentially all atomic gas experiments in which Bose-Einstein condensation and, more generally, quantum degeneracy is reached. The ongoing development of laser-cooling methods has allowed more elements to be brought to quantum degeneracy, with each additional atomic species offering its own experimental opportunities. Improved methods are opening new avenues, for example, reaching Bose-Einstein condensation purely through laser cooling as well as the realization of continuous Bose-Einstein condensation. Here we review these recent innovations in laser cooling and provide an outlook on methods that may enable new ways of creating quantum gases., 13 pages, 4 figures

We show the existence of nontrivial stationary weak solutions to the surface quasi-geostrophic equations on the two dimensional periodic torus., 8 pages, improved regularity and added references

Let $$X_1,\ldots ,X_n$$ be an i.i.d. sample from symmetric stable distribution with stability parameter $$\alpha$$ and scale parameter $$\gamma$$ . Let $$\varphi _n$$ be the empirical characteristic function. We prove a uniform large deviation inequality: given preciseness $$\epsilon >0$$ and probability $$p\in (0,1)$$ , there exists universal (depending on $$\epsilon$$ and p but not depending on $$\alpha$$ and $$\gamma$$ ) constant $$\bar{r}>0$$ so that $$P\big (\sup _{u>0:r(u)\le \bar{r}}|r(u)-\hat{r}(u)|\ge \epsilon \big )\le p,$$ where $$r(u)=(u\gamma )^{\alpha }$$ and $$\hat{r}(u)=-\ln |\varphi _n(u)|$$ . As an applications of the result, we show how it can be used in estimation the unknown stability parameter $$\alpha$$ .

Active materials are characterized by continuous injection of energy at the microscopic level and typically cannot be adequately described by equilibrium thermodynamics. Here we study a class of active fluids in which equilibrium-like properties emerge when fluctuating and activated degrees of freedom are statistically decoupled, such that their mutual information is negligible. We analyse three paradigmatic systems: chiral active fluids composed of spinning frictional particles that are free to translate, oscillating granular gases and active Brownian rollers. In all of these systems, a single effective temperature generated by activity parameterizes both the equation of state and the emergent Boltzmann statistics. The same effective temperature, renormalized by velocity correlations, relates viscosities to steady-state stress fluctuations via a Green–Kubo relation. To rationalize these observations, we develop a theory for the fluctuating hydrodynamics of these non-equilibrium fluids and validate it through large-scale molecular dynamics simulations. Our work sheds light on the microscopic origin of odd viscosities and stress fluctuations characteristic of parity-violating fluids, in which mirror symmetry and detailed balance are broken. Active fluids exhibit properties reminiscent of equilibrium systems when their degrees of freedom are statistically decoupled. A theory for the fluctuating hydrodynamics of these fluids offers a probe of their anomalous transport coefficients.

We study a fluid-structure interaction problem describing movement of a rigid body inside a bounded domain filled by a viscous fluid. The fluid is modelled by the generalized incompressible Naiver–Stokes equations which include cases of Newtonian and non-Newtonian fluids. The fluid and the rigid body are coupled via the Navier slip boundary conditions and balance of forces at the fluid-rigid body interface. Our analysis also includes the case of the nonlinear slip condition. The main results assert the existence of strong solutions, in an $$L^p-L^q$$ setting, globally in time, for small data in the Newtonian case, while existence of strong solutions in $$L^p$$ -spaces, locally in time, is obtained for non-Newtonian case. The proof for the Newtonian fluid essentially uses the maximal regularity property of the associated linear system which is obtained by proving the $${\mathcal {R}}$$ -sectoriality of the corresponding operator. The existence and regularity result for the general non-Newtonian fluid-solid system then relies upon the previous case. Moreover, we also prove the exponential stability of the system in the Newtonian case.

Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for ground-state solutions of a target Hamiltonian. Although powerful, simulated annealing is known to have prohibitively slow sampling dynamics when the optimization landscape is rough or glassy. Here we show that, by generalizing the target distribution with a parameterized model, an analogous annealing framework based on the variational principle can be used to search for ground-state solutions. Modern autoregressive models such as recurrent neural networks provide ideal parameterizations because they can be sampled exactly without slow dynamics, even when the model encodes a rough landscape. We implement this procedure in the classical and quantum settings on several prototypical spin glass Hamiltonians and find that, on average, it substantially outperforms traditional simulated annealing in the asymptotic limit, illustrating the potential power of this yet unexplored route to optimization. Optimization problems can be described in terms of a statistical physics framework. This offers the possibility to make use of ‘simulated annealing’, which is a procedure to search for a target solution similar to the gradual cooling of a condensed matter system to its ground state. The approach can now be sped up significantly by implementing a model of recurrent neural networks, in a new strategy called variational neural annealing.

The large zero-point motion and rapid atomic exchange in quantum solids like helium make defects extremely mobile. Previous shear modulus measurements have shown that mobile dislocations can soften the shear modulus of high purity hcp $$^4$$ He by as much as 90%, and that isotopic impurities ( $$^3$$ He atoms) pin dislocations and restore the intrinsic shear modulus at low temperatures. In this paper, we report shear modulus and dissipation measurements on solid $$^3$$ He in its body-centred cubic (bcc) phase. The lighter mass makes $$^3$$ He an even more quantum solid, with much higher exchange frequencies, but its spin and different crystal structure can change the nature of dislocations and their behavior. Our measurements show that the shear modulus of bcc $$^3$$ He had many similarities to that of hcp $$^4$$ He, including a thermally activated transition from a stiff state to a soft state as $$^4$$ He impurities unbind from dislocations when the temperature increases. The impurity binding energies are smaller than those in hcp $$^4$$ He and depend more strongly on pressure than a simple elastic binding model would suggest. In contrast to hcp $$^4$$ He, the shear modulus of bcc $$^3$$ He continues to decrease at temperatures up to 1 K, accompanied by a second dissipation peak with a larger activation energy. This behavior suggests that dislocation motion may be limited by intersections in tangled network in bcc $$^3$$ He but can overcome these barriers at high temperatures by thermal activation.

CEAS Aeronautical Journal 13, 97-112 (2022). doi:10.1007/s13272-021-00555-1, Published by Springer, Wien [u.a.]

Molecular diffusion in liquids is a key process in numerous systems: it is often the reaction rate limiting factor in biological or chemical reaction. Molecular diffusion has been recognized as the ultimate mechanism by which substances concentration get homogenized and, thus, their mixing and dilution occur. Here, we propose a novel method to directly measure the diffusion coefficient D of solutes or suspensions in liquids. Differently from current methods, as Dynamic Light Scattering or Fluorescent Correlation Spectroscopy, our method does not rely on previous knowledge on the fluid or tracer properties, but it is based on directly measuring the concentration spatial profile of a considered tracer with optical techniques within a diffusion chamber. We test this novel method on a sample of mono-dispersed suspension of spherical colloids for which an estimate for D can be made based on Einstein–Stokes relation. We, then, use this technique to measure the diffusion coefficient of a non-spherical tracer. We further quantify mixing of the considered tracers in the confined domain of the diffusion chamber: we show that, since diffusion-limited mixing (quantified in terms of the dilution index) in a confined space happens faster than un-confined domain, the finite size of the diffusion chamber must be taken into account to properly estimate D and the tracer mixing degree.

Discrete mechanics proposes an alternative formulation of the equations of mechanics where the Navier-Stokes and Navier-Lam\'e equations become approximations of the equation of discrete motion. It unifies the fields of fluid and solid mechanics by extending the fields of application of these equations to all space and time scales. This article presents the essential differences induced by the abandonment of the notion of continuous medium and global frame of reference. The results of the mechanics of continuous medium validated by fluid and solid observations are not questioned. The concept of continuous medium is not invalidated, the discrete formulation proposed simply widens the spectrum of the applications of the classical equations. The discrete equation of motion introduces several important modifications, in particular the fundamental law of the dynamics on an element of volume becomes a law of conservation of the accelerations on an edge. The acceleration considered as an absolute quantity is written as a sum of two components, one soledoidal the other irrotational according to a local orthogonal Helmholtz-Hodge decomposition. The mass is abandoned and replaced by the compression and rotation energies represented by the scalar and vectorial potentials of the acceleration. The equation of motion and all the physical parameters are expressed only with two fundamental units, those of length and time. The essential differences between the two approaches are listed and some of them are discussed in depth. This is particularly the case with the known paradoxes of the Navier-Stokes equation or the importance of inertia for the Navier-Lam\'e equation., Comment: 16 pages, 5 figures

We report on an electron-spin resonance study of nuclear-polarized phases of hydrogen atoms embedded in solid H $$_{2}$$ films at temperatures 0.1–1.5 K and a high magnetic field of 4.6 T. The H atoms in solid H $$_{2}$$ were generated by two different dissociation techniques: a cryogenic rf-discharge and bombardment by 5.7 keV electrons via tritium decay. In both studies, we observed a build-up of a spontaneous nuclear-polarized phase (SNPP, p=0.35) at temperatures below $$\sim $$ 0.8 K similar to that reported in our previous work. We were also able to create a highly nuclear-polarized phase (HNPP, $$p\simeq $$ 0.75) using Dynamic Nuclear Polarization for samples exposed to a cryogenic rf discharge, whereas we failed to obtain this phase for the samples bombarded by 5.7 keV electrons. We suggest that failing to achieve the HNPP in the samples exposed to high-energy electrons released during tritium decay may be explained by an effect of faster nuclear relaxation stimulated by electrons bombarding the H $$_{2}$$ matrix and rapidly relaxing centers in the film substrate created during accumulation of H atoms in solid H $$_{2}$$ .

Quantum teleportation, the faithful transfer of an unknown input state onto a remote quantum system1, is a key component in long-distance quantum communication protocols2 and distributed quantum computing3,4. At the same time, high-frequency nano-optomechanical systems5 hold great promise as nodes in a future quantum network6, operating on-chip at low-loss optical telecom wavelengths with long mechanical lifetimes. Recent demonstrations include entanglement between two resonators7, a quantum memory8 and microwave-to-optics transduction9–11. Despite these successes, quantum teleportation of an optical input state onto a long-lived optomechanical memory is an outstanding challenge. Here we demonstrate quantum teleportation of a polarization-encoded optical input state onto the joint state of a pair of nanomechanical resonators. Our protocol also allows to store and retrieve an arbitrary qubit state onto a dual-rail encoded optomechanical quantum memory. This work demonstrates the full functionality of a single quantum repeater node and presents a key milestone towards applications of optomechanical systems as quantum network nodes. Quantum teleportation of a photonic qubit into mechanical modes of two silicon photonic crystal nanobeams is demonstrated. It allows to store and retrieve an arbitrary qubit state onto a dual-rail encoded long-lived optomechanical quantum memory.

Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure quantum or classical bracket when acting on pure quantum or classical variables. Any hybrid bracket obeying these natural requirements will produce the same dynamics for pure classical or quantum variables, given a hybrid Hamiltonian. Backreaction is manifested in the evolution of a nonvanishing commutator between classical variables. The more massive the classical system is, the less it is affected by backreaction. Interestingly, we show that while pure variables evolve to violate the pure canonical relations, they always obey the hybrid canonical relations. The dynamics of hybrid variables, on the other hand, is shown to require a fully specified and consistent hybrid bracket, otherwise evolution cannot be defined.

For any $h\in(1,2]$, we give an explicit construction of a compactly supported, uniformly continuous, and (weakly) divergence-free velocity field in $\mathbb{R}^2$ that weakly advects a measure whose support is initially the origin but for positive times has Hausdorff dimension $h$. These velocities are uniformly continuous in space-time and compactly supported, locally Lipschitz except at one point and satisfy the conditions for the existence and uniqueness of a Regular Lagrangian Flow in the sense of Di Perna and Lions theory. We then construct active scalar systems in $\mathbb{R}^2$ and $\mathbb{R}^3$ with measure-valued solutions whose initial support has co-dimension 2 but such that at positive times it only has co-dimension 1. The associated velocities are divergence free, compactly supported, continuous, and sufficiently regular to admit unique Regular Lagrangian Flows. This is in part motivated by the investigation of dimension conservation for the support of measure-valued solutions to active scalar systems. This question occurs in the study of vortex filaments in the three-dimensional Euler equations., 32 pages, 3 figures. This preprint has not undergone peer review (when applicable) or any post-submission improvements or corrections. The Version of Record of this article is published in Arch Rational Mech Anal, and is available online at https://doi.org/10.1007/s00205-021-01708-6

The most essential characteristic of any fluid is the velocity field, and this is particularly true for macroscopic quantum fluids1. Although rapid advances2–7 have occurred in quantum fluid velocity field imaging8, the velocity field of a charged superfluid—a superconductor—has never been visualized. Here we use superconducting-tip scanning tunnelling microscopy9–11 to image the electron-pair density and velocity fields of the flowing electron-pair fluid in superconducting NbSe2. Imaging of the velocity fields surrounding a quantized vortex12,13 finds electronic fluid flow with speeds reaching 10,000 km h–1. Together with independent imaging of the electron-pair density via Josephson tunnelling, we visualize the supercurrent density, which peaks above 3 × 107 A cm–2. The spatial patterns in electronic fluid flow and magneto-hydrodynamics reveal hexagonal structures coaligned to the crystal lattice and quasiparticle bound states14, as long anticipated15–18. These techniques pave the way for electronic fluid flow visualization studies of other charged quantum fluids. Atomic-scale visualization of the superfluid velocity field, the electron-pair density and the superfluid current density in an electron-pair superfluid surrounding an Abrikosov vortex in a superconducting sample of NbSe2 is demonstrated, using superconducting-tip scanning tunnelling microscopy.

Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and x-ray diffraction measurements with in-situ tunable strain (elasto-XRD) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of $Ba(Fe_{0.96}Co_{0.04})_{2} As_{2}$. The ratio of transport to structural quantities is nearly temperature-independent over a 74 K range and agrees between the ordered and disordered phases. These results show that elasto-XRD is a powerful technique to probe the nemato-elastic and nemato-transport couplings, which have important implications to the nearby superconductivity. It also enables the measurement in the large strain limit, where the breakdown of mean field description reveals the intertwined nature of nematicity., Comment: Main text 10 pages, 4 figures

Cavity quantum electrodynamics (QED) manipulates the coupling of light with matter, and allows several emitters to couple coherently with one light mode1. However, even in a many-body system, the light–matter coupling mechanism has so far been restricted to one-body processes. Leveraging cavity QED for the quantum simulation of complex, many-body systems has thus far relied on multi-photon processes, scaling down the light–matter interaction to the low energy and slow time scales of the many-body problem2–5. Here we report cavity QED experiments using molecular transitions in a strongly interacting Fermi gas, directly coupling cavity photons to pairs of atoms. The interplay of strong light–matter and strong interparticle interactions leads to well-resolved pair polaritons—hybrid excitations coherently mixing photons, atom pairs and molecules. The dependence of the pair-polariton spectrum on interatomic interactions is universal, independent of the transition used, demonstrating a direct mapping between pair correlations in the ground state and the optical spectrum. This represents a magnification of many-body effects by two orders of magnitude in energy. In the dispersive regime, it enables fast, minimally destructive measurements of pair correlations, and opens the way to their measurement at the quantum limit and their coherent manipulation using dynamical, quantized optical fields. Directly coupling cavity photons to the photo-association resonances of pairs of atoms in a strongly interacting Fermi gas generates pair polaritons—hybrid excitaions coherently mixing photons, atom pairs and molecules.

We use a canopy-resolving regional atmospheric–forest large-eddy simulation to investigate the impact of fetch on flow separation and microclimates within a peatland surrounded by a forest (representing a forest gap). We initiate our simulation with observed vegetation characteristics and meteorological data within a peatland and a forest to accurately estimate the natural surface roughness and energy dynamics. The heterogeneous landscape of the Boreal Plains region results in peatlands often experiencing turbulent sheltering and turbulent effects from their surrounding ecosystems. This landscape configuration results in spatially dynamic surface–atmosphere exchanges of momentum, heat, and moisture, produced by flow-separation dynamics within the peatland that regulate the transport of such scalars in the sheltered region while promoting transport in the reattachment zone. Peatlands of the Boreal Plains are often small irregular shapes, which add further complexity when estimating the transport of scalars within these systems. As evapotranspiration is the dominant hydrologic flux in Boreal Plains, it is necessary to understand the dynamics and controls on evapotranspiration within these fetch-limited peatlands. Our simulations show that fetch limitations have no impact on the turbulent and evaporative dynamics of the peatland relative to the distance from the surface transition. However, we observe that a combination of peatland geometry (i.e., the ratio of peatland length to width) and/or the shape of the exit transition influences the flow region where greater funnelling of the flow of the peatland increases the regional wind speeds.

Numerical and experimental methods in free and forced vibrations of the rotating structure consisting of the rigid hub and three flexible beams are considered. Firstly, the system of four mutually coupled dimensionless differential governing equations is presented and then forced response of the system as well as synchronization phenomenon are investigated. Next, the finite elements method is used to design the rotating structure and analyse complex dynamic response. During the numerical calculations symmetric, as well as de-tuned rotor are analyzed. Finally, results obtained from ordinary differential equations and numerical simulations are compared with experimental tests.

Existence of predator is routinely used to induce fear and anxiety in prey which is well known for shaping entire ecosystem. Fear of predation restricts the development of prey and promotes inducible defense in prey communities for the survival. Motivated by this fact, we investigate the dynamics of a Leslie–Gower predator prey model with group defense in a fearful prey. We obtain conditions under which system possess unique global-in-time solutions and determine all the biological feasible states of the system. Local stability is analyzed by linearization technique and Lyapunov direct method has been applied for global stability analysis of steady states. We show the occurrence of Hopf bifurcation and its direction at the vicinity of coexisting equilibrium point for temporal model. We consider random movement in species and establish conditions for the stability of the system in the presence of diffusion. We derive conditions for existence of non-constant steady states and Turing instability at coexisting population state of diffusive system. Incorporating indirect prey taxis with the assumption that the predator moves toward the smell of prey rather than random movement gives rise to taxis-driven inhomogeneous Hopf bifurcation in predator–prey model. Numerical simulations are intended to demonstrate the role of biological as well as physical drivers on pattern formation that go beyond analytical conclusions.

Dynamic stall, which has a significant effect on the aerodynamic performances of dynamic airfoils, is closely related to the physics of the dynamic stall vortex (DSV). The physics of the DSV on the NACA 0012 airfoil was experimentally studied using unsteady pressure measurements with high time accuracy. The experimental Reynolds number was Re = 1.5 × 106, and the reduced frequency was k = 0.069. The propagation of the unsteady pressure field during the dynamic stall process was analyzed in detail. The motion characteristics of the DSV were examined, including its near-wall development characteristics and near-wall evolution velocity. Moreover, the frequency characteristics of the near-wall DSV were studied using wavelet analysis combined with proper orthogonal decomposition (POD) technology. In addition, the effects of the mean angle of attack (AoA) and the amplitude on the DSV motion and frequency characteristics were examined in detail. The effects of the mean AoA on the near-wall DSV strength and the propagation velocity were linear, while the effects of amplitude were nonlinear. The mean AoA and amplitude had a significant influence on the frequency of the leading-edge vortex (LEV) at the initial stage of the DSV development (x/c = 0.10–0.20). This work allows the DSV physics to be understood more deeply. Graphic abstract

Abstract The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

This paper presents the numerical results for inclined dense effluent discharges into a shallow receiving water body. Two jet discharge angles relative to the horizontal (30° and 45°) were investigated based on the experimental results from Jiang et al. (J Hydraul Eng 140:241–253, 2014). Five Reynolds-averaged Navier–Stokes (RANS) turbulence models were examined in this study: realizable k-e and k-ω SST models (known as two-equation turbulence models), v2f (four equations to model anisotropic behavior) and LRR and SSG turbulence models (known as Reynolds stress models—six equations to model anisotropic behavior). Three mixing regimes introduced in Jiang et al. (J Hydraul Eng 140:241–253, 2014) were reproduced numerically for both discharge angles applying various turbulence models: full submergence, plume contact and centerline impingement regimes (i.e., FSR, PCR and CIR). Key geometrical and dilution properties of these jets at surface contact (Xs, Ss) and jet centerline return point (Xr, Sr) were compared to those available from experiments. Normalization parameter that was selected for jets in shallow waters is H/D (water depth above discharge point over nozzle diameter). It was found that surface attachment increases the return point length from the nozzle and that surface dilution decreases from FSR toward CIR. Among turbulence models tested herein, Reynolds stress models (LRR and SSG) predicted the effluent discharge kinematic and dilution properties better compared to two- and four-equations models. This is mainly attributed to the anisotropic nature of the effluent discharge problem studied herein and that these models are better capable to account for anisotropies.

In this paper, chaos-guided artificial neural learning-based session key coordination for industrial internet-of-things (IIoT) to enhance the security of critical energy infrastructures (CEI) is proposed. An intruder might pose several security problems since the data are transferred across a public network. Although there have been substantial efforts to solve security problems in the IIoT, the majority of them have relied on traditional methods. A wide range of privacy issues (secrecy, authenticity, and access control) must be addressed to protect IIoT systems against attack. Owing to the unique characteristics of IIoT nodes, existing solutions do not properly address the entire security range of IIoT networks. To deal with this, a chaos-based triple layer vector-valued neural network (TLVVNN) is proposed in this paper. A chaos-based exchange of common seed value for the generation of the identical input vector at both transmitter and receiver is also proposed. This technique has several advantages, including (1) it protects IIoT devices by utilizing TLVVNN synchronization to improve CEI security. (2) Here, artificial neural coordination is utilized for the exchange of neural keys between two IIoT nodes. (3) Using this suggested methodology, chaotic synchronization can be achieved, enabling the chaos-based PRNG seed exchange. (4) Vector-valued inputs and weights are taken into consideration for TLVVNN networks. (5) The deep internal architecture is made up of three hidden layers of the neural network and a vector value as input. As a result, the attacker would have great difficulty interpreting the internal structure. Experiments to verify the performance of the proposed technique are conducted, and the findings demonstrate that the proposed technique has greater performance benefits than the existing related techniques.

In the present work, a novel approach was proposed to optimize the teleportation cost in Distributed Quantum Circuits (DQCs) by applying a new approach. To overcome the difficulty with keeping a large number of qubits next to each other, DQCs, as a well-known solution, have always been employed. In a distributed quantum system, qubits are transferred from a subsystem to another subsystem by a quantum protocol such as teleportation. First, we proposed a heuristic approach through which we could replace the equivalent circuits in the initial quantum circuit. Then, we used a genetic algorithm to partition the placement of qubits so that the number of teleportations could be optimized for the communications of a DQC. Finally, results showed that the proposed approach could impressively work.

Data Management of Astronomy Data is often a laborious task and it is even more challenging for the extraordinary amounts of data expected from the world’s largest radio telescope, Square Kilometre Array. There are overt issues in transferring the voluminous data and the traditional data transfer methods are fragile especially for the data transfer between two continents. To address this, a new data transfer framework is proposed and the data transfer is achieved using two steps: international and local transfers. The efficiency of different end-to-end data transfer tools used in is evaluated on different dataset sizes. Further, a comparative study of two IRIS grid data transfer methods is made to understand each methods’ advantages and disadvantages. This study can be used as a reference for the development of future SKA’s data transfer operations.

The EMDrive is a proposed propellantless propulsion concept claiming to be many orders of magnitude more efficient than classical radiation pressure forces. It is based on microwaves, which are injected into a closed tapered cavity, producing a unidirectional thrust with values of at least 1 mN/kW. This was met with high scepticism going against basic conservation laws and classical mechanics. However, several tests and theories appeared in the literature supporting this concept. Measuring a thruster with a significant thermal and mechanical load as well as high electric currents, such as those required to operate a microwave amplifier, can create numerous artefacts that produce false-positive thrust values. After many iterations, we developed an inverted counterbalanced double pendulum thrust balance, where the thruster can be mounted on a bearing below its suspension point to eliminate most thermal drift effects. In addition, the EMDrive was self-powered by a battery-pack to remove undesired interactions due to feedthroughs. We found no thrust values within a wide frequency band including several resonance frequencies and different modes. Our data limit any anomalous thrust to below the force equivalent from classical radiation for a given amount of power. This provides strong limits to all proposed theories and rules out previous test results by at least two orders of magnitude.

In this work, a numerical scheme based on combined Lucas and Fibonacci polynomials is proposed for one- and two-dimensional nonlinear advection–diffusion–reaction equations. Initially, the given partial differential equation (PDE) reduces to discrete form using finite difference method and $$\theta -$$ θ - weighted scheme. Thereafter, the unknown functions have been approximated by Lucas polynomial while their derivatives by Fibonacci polynomials. With the help of these approximations, the nonlinear PDE transforms into a system of algebraic equations which can be solved easily. Convergence of the method has been investigated theoretically as well as numerically. Performance of the proposed method has been verified with the help of some test problems. Efficiency of the technique is examined in terms of root mean square (RMS), $$L_2$$ L 2 and $$L_\infty $$ L ∞ error norms. The obtained results are then compared with those available in the literature.

In this paper, we consider the nonlinear discrete-time dynamic model proposed by Bischi and Baiardi (Chaos Solitons Fractals 79:145-156, 2015a). The model considers players with adaptive adjustment mechanisms towards the best reply and a form of inertia in adopting such mechanism. Moreover, we formulate an extension of the original model, where endogenous market size is considered. Through numerical simulations, we show that multiple attractors may exist in the presence of homogeneous agents and the emergence of non-synchronized trajectories both in the short (on-off intermittency) and long (global riddling) run. Therefore, the article highlights that strategic contexts exist in which the players’ knowledge of the market and the adoption of the best reply do not always allow the use of the representative agent’s rhetoric to describe the dynamics of the model.

Eddy covariance is an established technique for registering sensible heat fluxes. However, this method is less adequate for smaller surfaces that cannot match the associated footprint. As an alternative technique, a recently constructed acoustic anemometer (Ly-ATOM) is tested, which operates horizontally at an extension of circa 1 m and a data-acquisition frequency of 1 Hz. The Ly-ATOM device reproduces both the acoustic virtual temperature and the horizontal wind components registered by a three-dimensional sonic anemometer. As this Ly-ATOM device can be applied much closer to the ground compared with a sonic anemometer, the size of the related source area is significantly reduced (by a factor of 25). Two methods are used to retrieve the sensible heat flux from variance characteristics of temperature and the horizontal wind components recorded by the Ly-ATOM device: combining the flux-variance-similarity and alternative-flux-variance methods for use in unstable and stable stratification, respectively, yields good results for the sonic measurements. Therefore, these methods can be applied to the Ly-ATOM device as well. In investigating the sensitivity to detect modified surface characteristics, specifically increased evapotranspiration and decreased surface albedo, the Ly-ATOM device proves to be superior to the sonic anemometer which is more vertically removed from the surface of interest.

Motivated by a limited understanding of how valleys affect near-surface turbulence, characterizations of neutrally stable atmospheric-boundary-layer flows over isolated valleys are presented. In particular, the influence of the slopes of the three-dimensional ridges that form the idealized valleys are investigated. Flows over three distinct symmetric valley geometries were modelled in a large boundary-layer wind tunnel. For each valley geometry, the high-resolution measurements from the crests of each of the ridges and the midpoint between them are compared with an undisturbed moderately rough classed boundary-layer flow over flat terrain with homogeneous surface roughness. Flow separation originates above the crests of the first ridges of all geometries and generates recirculation zones. These are characterized by slope-dependent increases in three-dimensional near-surface turbulence when compared with the attached flows further upstream. The recirculation zones longitudinally extend to roughly half the valley width. Above the crests of the second ridges, the longitudinal velocity component decreases and turbulence intensity increases when compared with the flows above the crests of the first ridges. Results also exhibit significant increases of turbulence above the inner-valley regions of all geometries.

This study is to numerically test the interfacial instability of ferrofluid flow under the presence of a vacuum magnetic field. The ferrofluid parabolized stability equations (PSEs) are derived from the ferrofluid stability equations and the Rosensweig equations, and the characteristic values of the ferrofluid PSEs are given to describe the ellipticity of ferrofluid flow. Three numerical models representing specific cases considering with/without a vacuum magnetic field or viscosity are created to mathematically examine the interfacial instability by the computation of characteristic values. Numerical investigation shows strong dependence of the basic characteristic of ferrofluid Rayleigh-Taylor instability (RTI) on viscosity of ferrofluid and independence of the vacuum magnetic field. For the shock wave striking helium bubble, the magnetic field is not able to trigger the symmetry breaking of bubble but change the speed of the bubble movement. In the process of droplet formation from a submerged orifice, the collision between the droplet and the liquid surface causes symmetry breaking. Both the viscosity and the magnetic field exacerbate symmetry breaking. The computational results agree with the published experimental results.

A modified phase-field model is presented to numerically study the dynamics of flowing foam in an obstructed channel. The bubbles are described as smooth deformable fields interacting with one another through a repulsive potential. A strength of the model lies in its ability to simulate foams with wide range of gas fraction. The foam motion, composed of about hundred two-dimensional gas elements, was analyzed for gas fractions ranging from 0.4 to 0.99, that is below and beyond the jamming transition. Simulations are preformed near the quasi-static limit, indicating that the bubble rearrangement in the obstructed channel is primarily driven by the soft collisions and not by the hydrodynamics. Foam compression and relaxation upstream and downstream of the obstacle are reproduced and qualitatively match previous experimental and numerical observations. Striking dynamics, such as bubbles being squeezed by their neighbors in negative flow direction, are also revealed at intermediate gas fractions.

The horizontal convection in a square enclosure driven by a linear temperature profile along the bottom boundary is investigated numerically by using a finite difference method. The Prandtl number is fixed at 4.38, and the Rayleigh number Ra ranges from 107 to 1011. The convective flow is steady at a relatively low Rayleigh number, and no thermal plume is observed, whereas it transits to be unsteady when the Rayleigh number increases beyond the critical value. The scaling law for the Nusselt number Nu changes from Rossby’s scaling Nu ∼ Ra1/5 in a steady regime to Nu ∼ Ra1/4 in an unsteady regime, which agrees well with the theoretically predicted results. Accordingly, the Reynolds number Re scaling varies from Re ∼ Ra3/11 to Re ∼ Ra2/5. The investigation on the mean flows shows that the thermal and kinetic boundary layer thickness and the mean temperature in the bulk zone decrease with the increasing Ra. The intensity of fluctuating velocity increases with the increasing Ra.

The main aim of glaucoma treatment is to reduce the intraocular pressure (IOP). One of the most common surgical treatments of glaucoma is the implantation of a glaucoma drainage device to drain the aqueous humor from the anterior chamber to a filtration bleb, where the aqueous humor is absorbed. In some cases, the excess of drainage causes ocular hypotony, which constitutes a sight-threatening complication. To prevent hypotony after this intervention, surgeons frequently introduce a suture into the device tube, which increases the hydraulic resistance of the tube and, therefore, the IOP. This study aims to provide an analytical model to correct hypotony following implantation surgery of a glaucoma drainage device, which may help glaucoma surgeons decide on hypotony treatment. The results indicate that the IOP after implanting a cylindrical tube around 300 μm in diameter is essentially the same as that built up in the filtering bleb and can hardly be controlled by introducing a straight suture unless the suture diameter is slightly lower than that of the tube. On the contrary, when the tube diameter is smaller than, for example, 100 μm, significant reductions of the IOP can be obtained by introducing a thin suture into the tube.

This work aims at the characterization of a modern concrete material. For this purpose, we perform two experimental series of inverse planar plate impact (PPI) tests with the ultra-high performance concrete B4Q, using two different witness plate materials. Hugoniot data in the range of particle velocities from 180 to 840 m/s and stresses from 1.1 to 7.5 GPa is derived from both series. Within the experimental accuracy, they can be seen as one consistent data set. Moreover, we conduct corresponding numerical simulations and find a reasonably good agreement between simulated and experimentally obtained curves. From the simulated curves, we derive numerical Hugoniot results that serve as a homogenized, mean shock response of B4Q and add further consistency to the data set. Additionally, the comparison of simulated and experimentally determined results allows us to identify experimental outliers. Furthermore, we perform a parameter study which shows that a significant influence of the applied pressure dependent strength model on the derived equation of state (EOS) parameters is unlikely. In order to compare the current results to our own partially reevaluated previous work and selected recent results from literature, we use simulations to numerically extrapolate the Hugoniot results. Considering their inhomogeneous nature, a consistent picture emerges for the shock response of the discussed concrete and high-strength mortar materials. Hugoniot results from this and earlier work are presented for further comparisons. In addition, a full parameter set for B4Q, including validated EOS parameters, is provided for the application in simulations of impact and blast scenarios.