Full Boundary Research Articles

An in-flight investigation of a turbulent boundary layer at Reynolds numbers up to hbox {Re}_{theta }=49,400

The ongoing attempts to gain access to the realm of high Reynolds number turbulence have resulted in the dedicated development of major experimental facilities and novel diagnostic methodologies as well as in the probing of atmospheric surface flows. In contrast to this, the presented study discusses the feasibility of an in-flight laboratory for Reynolds number investigations up to rm {Re}_{theta },le ,49,400. The underpinning velocity data were obtained in flight tests by two moveable differential pressure probes and a stereo Particle Image Velocity (sPIV) system. The region of interest was located far downstream of the aircraft’s nose within the fuselage boundary layer. The pressure probes scanned the full boundary layer while the sPIV system remained fixed at certain wall-normal locations. The velocity data acquired exhibits distinct characteristics within the defect layer that deviate from Coles’ classical description of the wake. Furthermore, the streamwise turbulence intensities show a pronounced ‘outer peak’ further away from the wall at y^{+}=2000-5000 . The measurements were conducted under authentic flight conditions with an increased level of free-stream turbulence. These boundary conditions enabled an analysis of turbulent flows that are of relevance for various aeronautical applications. The manuscript elaborates on the main findings of this experimental study by presenting the velocity profiles captured by the moveable pressure probe system and samples of sPIV data. The capabilities and limitations of a flying laboratory for the investigation of high Reynolds number turbulence are discussed in detail.Graphic

Dirac equation perspective on higher-order topological insulators

In this Tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focusing on the low-energy description of higher-order topological insulators in terms of the Dirac equation. Our aim is to give a mostly self-contained treatment. After introducing the Dirac approximation of topological crystalline band structures, we use it to derive the anomalous end and corner states of first- and higher-order topological insulators in one and two spatial dimensions. In particular, we recast the classical derivation of domain wall bound states of the Su–Schrieffer–Heeger (SSH) chain in terms of crystalline symmetry. The edge of a two-dimensional higher-order topological insulator can then be viewed as a single crystalline symmetry-protected SSH chain, whose domain wall bound states become the corner states. We never explicitly solve for the full symmetric boundary of the two-dimensional system but instead argue by adiabatic continuity. Our approach captures all salient features of higher-order topology while remaining analytically tractable.

The ENUF method-Ewald summation based on nonuniform fast Fourier transform: Implementation, parallelization, and application.

Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between charged particles constitute a prominent factor in determining structures and states of model systems. How to efficiently calculate electrostatic interactions in simulation systems subjected to partial or full periodic boundary conditions has been a grand challenging task. In the past decades, a large variety of computational schemes has been proposed, among which the Ewald summation method is the most reliable route to accurately deal with electrostatic interactions between charged particles in simulation systems. In addition, extensive efforts have been done to improve computational efficiencies of the Ewald summation based methods. Representative examples are approaches based on cutoffs, reaction fields, multi-poles, multi-grids, and particle-mesh schemes. We sketched an ENUF method, an abbreviation for the Ewald summation method based on the nonuniform fast Fourier transform technique, and have implemented this method in particle-based simulation packages to calculate electrostatic energies and forces at micro- and mesoscopic levels. Extensive computational studies of conformational properties of polyelectrolytes, dendrimer-membrane complexes, and ionic fluids demonstrated that the ENUF method and its derivatives conserve both energy and momentum to floating point accuracy, and exhibit a computational complexity of with optimal physical parameters. These ENUF based methods are attractive alternatives in molecular simulations where high accuracy and efficiency of simulation methods are needed to accelerate calculations of electrostatic interactions at extended spatiotemporal scales.

Mean Conditions and Seasonality of the West Greenland Boundary Current System near Cape Farewell

AbstractThe structure, transport, and seasonal variability of the West Greenland boundary current system near Cape Farewell are investigated using a high-resolution mooring array deployed from 2014 to 2018. The boundary current system is comprised of three components: the West Greenland Coastal Current, which advects cold and fresh Upper Polar Water (UPW); the West Greenland Current, which transports warm and salty Irminger Water (IW) along the upper slope and UPW at the surface; and the Deep Western Boundary Current, which advects dense overflow waters. Labrador Sea Water (LSW) is prevalent at the seaward side of the array within an offshore recirculation gyre and at the base of the West Greenland Current. The 4-yr mean transport of the full boundary current system is 31.1 ± 7.4 Sv (1 Sv ≡ 106m3s−1), with no clear seasonal signal. However, the individual water mass components exhibit seasonal cycles in hydrographic properties and transport. LSW penetrates the boundary current locally, through entrainment/mixing from the adjacent recirculation gyre, and also enters the current upstream in the Irminger Sea. IW is modified through air–sea interaction during winter along the length of its trajectory around the Irminger Sea, which converts some of the water to LSW. This, together with the seasonal increase in LSW entering the current, results in an anticorrelation in transport between these two water masses. The seasonality in UPW transport can be explained by remote wind forcing and subsequent adjustment via coastal trapped waves. Our results provide the first quantitatively robust observational description of the boundary current in the eastern Labrador Sea.

Logarithmic compactification of the Abel–Jacobi section

Given a smooth curve with weighted marked points, the Abel-Jacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using logarithmic and tropical geometry, we describe a modular modification of the moduli space of curves over which the Abel-Jacobi map extends. We also describe the attendant deformation theory and virtual fundamental class of this moduli space. This recovers the double ramification cycle, as well as variants associated to differentials.

Evaluation of scale-resolving simulations for a turbulent channel flow

Different variable resolution turbulence modelling approaches (Hybrid, Bridging models and LES) are evaluated for turbulent channel flow at Reτ=395, for cases using either streamwise periodic boundary conditions or a synthetic turbulence generator. The effect of iterative, statistical and discretisation errors is investigated. For LES, little difference between the different sub-filter modelling approaches is found on the finer grids, while on coarser grids ILES deviates from explicit LES approaches. The results for Hybrid models are strongly dependent on their formulation, and the corresponding blending between the RANS and LES regions. The application of PANS with different ratios of modelled-to-total kinetic energy, fk, shows that there is no smooth transition in the results between RANS and DNS. Instead a case-dependent threshold which separates two solution regimes is observed: fk values below 0.2 yield a proper turbulent solution, similar to LES results; higher fk values lead to a laminar flow due to filtering of the smallest scales in the inverse energy cascade. The application of a synthetic turbulence generator is observed to yield similar performance for all models. The reduced computational cost and increased flexibility makes it a suitable approach to enable the usage of SRS for industrial flow cases which depend on the development of a turbulent boundary layer. It ensures that sufficient large-scale structures develop over the full boundary layer height, thereby negating the problem of relying on the inverse energy cascade for the development of turbulence. Both LES and PANS with turbulence generator yield a better match with the reference data than Hybrid models; of these methods PANS is preferable due to the separation of modelling and discretisation errors.

Blow-up analysis and boundary regularity for variationally biharmonic maps

We consider critical points u:Ω→N of the bi-energy ∫Ω|Δu|2dx,where Ω⊂Rm is a bounded smooth domain of dimension m≥5 and N⊂RL a compact submanifold without boundary. More precisely, we consider variationally biharmonic maps u∈W2,2(Ω,N), which are defined as critical points of the bi-energy that satisfy a certain stationarity condition up to the boundary. For weakly convergent sequences of variationally biharmonic maps, we demonstrate that the only obstruction that can prevent the strong compactness up to the boundary is the presence of certain non-constant biharmonic 4-spheres or 4-halfspheres in the target manifold. As an application, we deduce full boundary regularity of variationally biharmonic maps provided such spheres do not exist.

A lattice Boltzmann study on Brownian diffusion and friction of a particle in a confined multicomponent fluid

We study the diffusivity of a small particle immersed in a square box filled with a non-ideal multicomponent fluid in the presence of thermal fluctuations. Our approach is based on the numerical integration of fluctuating lattice Boltzmann models (LBM) for multicomponent mixtures. At changing the wettability on the particle's surface, we measure the mean square displacement (MSD) and compare with the prediction of the Stokes-Einstein theory. Two main set-ups are tested, involving periodic boundary conditions and wall boundary conditions realized on the computational box. We find that full periodic boundary conditions give rise to random advection after millions of lattice Boltzmann time steps, while this effect is mitigated in the presence of wall boundary conditions. The matching with the Stokes-Einstein relation is therefore guaranteed when we use the appropriate frictional properties measured in the presence of confinement. Our results will help the exploration of nanoscale applications with multicomponent fluids using LBM in the presence of thermal fluctuations.

A Novel Full Boundary Element Formulation for Transient Analysis of Elastic Membranes Coupled to Acoustics Fluids

A full time-direct Boundary Element Formulation for the dynamic analysis of elastic membranes coupled to acoustics fluid is presented. The elastic membranes is modeled using the classical linear elastic pre-stretched membrane theory. The acoustic fluid is modeled using the acoustic-wave equation for homogeneous, isotropic, inviscid and irrotational fluids. Elastostatic fundamental solution is used in the boundary element formulation for the elastic membrane. The boundary element formulation for the acoustic fluid is based on the fundamental solution of three dimensional Poisson equation. Domain integrals related to inertial terms and those related with distributed pressure on membrane, were treated using the Dual Reciprocity Boundary Element Method. Fluid-structure coupling equations were established considering the continuity of the normal acceleration of the particles and dynamic pressure at fluid-structure interfaces. The time integration is carried out using the Newmark method. Results obtained shows the accuracy and efficiency of the proposed boundary element formulation.

A Novel Full Boundary Element Formulation for Harmonic Analysis of Elastic Membranes Coupled to Acoustics Fluids

A novel full Boundary Element Formulation for the harmonic analysis of elastic membranes coupled to acoustics fluid is presented. The elastic membranes is modeled using the classical linear elastic pre-stretched membrane theory. The acoustic fluid is modeled using the acoustic-wave equation for homogeneous, isotropic, inviscid and irrotational fluids. Elastostatic fundamental solution is used in the boundary element formulation for the elastic membrane. The boundary element formulation for the acoustic fluid is based on the fundamental solution of three dimensional Poisson equation. Domain integrals related to inertial terms and those related with distributed pressure on membrane, were treated using the Dual Reciprocity Boundary Element Method. Fluid-structure coupling equations were established considering the continuity of the normal acceleration of the particles and dynamic pressure at fluid-structure interfaces. Results obtained shows the accuracy and efficiency of the proposed boundary element formulation.

Event-triggered Varying Speed Limit Control of Stop-and-go Traffic

This paper develops event-triggered boundary control strategies for varying speed limit (VSL) located at a freeway segment. The stop-and-go traffic oscillations are suppressed by regulating the velocity of vehicles that leave the segment. The controlled velocity signal is only updated when a event triggering condition is satisfied. Compared with the continuous input signal, the event-based controller presents as a more realistic setting to implement by VSL on a digital platform which allows the adaptation time for drivers to follow the advisory speed. The traffic dynamics of density and velocity are described with linearized Aw-Rascle-Zhang (ARZ) macroscopic traffic partial differential equation (PDE) model which results in a 2 × 2 coupled hyperbolic system. The event-triggered boundary controllers rely on the emulation of the full state backstepping boundary feedback and two different Lyapunov-based event-triggered strategies to determine the time instants at which the control value must be sampled/updated. One of the event-triggered strategies makes use of a dynamic triggering condition under which it is possible to state the existence of a uniform minimal dwell-time (independent of initial conditions). The exponential stability under event-triggered control is achieved and validated with numerical simulations.

A New Method to Assess Fiber Laser Welding Quality of Stainless Steel 304 Based on Machine Vision and Hidden Markov Models

High-power fiber laser welding has a broad range of applications in industrial processing and modern intelligent manufacturing, but how to assess the quality of laser welding has always been a concern. In the welding process, the geometric feature of the keyhole generated by the high temperature of laser can directly reflect quality of the laser welding. By using machine vision to acquire images in real time and analyze related features, the quality of laser welding can be evaluated, which reduce the cost and time in later inspection. Nevertheless, due to the dynamic complexity of the keyhole as well as the blurring of the keyhole and full penetration hole boundary caused by metal vapor and spatter, identification of multiple type defects through machine vision is still a problem that requires a solution. This paper presents a novel laser welding defect classification method using keyhole boundary-based feature based on machine vision and Hidden Markov process. After effective segmenting the collected welding image, the shapes of the keyhole as well as the full penetration hole were automatically extracted using the characteristics of gray projection distribution and the Poisson extinction method. Subsequently, a pre-trained Hidden Markov Model was employed to establish the connection between the keyhole's geometry and the welding quality defects. Experiments indicate that our theory can efficiently and accurately extract the key geometric shapes. Welding experimental data involving stainless steel 304 verifies the feasibility of the classification theory, which can monitor welding quality and reveal potential porosity and penetration defects.

Lattice Boltzmann Simulation of Micro-scale Couette Flow of Two-component Gas Mixtures in the Slip Regime

Lattice Boltzmann method (LBM) is considered as a promising numerical method for simulating the micro-scale flows. In this work, the LBM is employed to simulate the micro-scale Couette flow of two-component gas mixtures in the slip regime. The bounce-back and full diffusive boundary condition is proposed to deal with the gas-wall interaction. Based on the simulations, linear velocity profiles and obvious slip at the wall are observed, which are affected by the molar fraction, gas components, and Knudsen number. In comparison with the molar fraction and gas components, the Knudsen number has a more significant effect on the velocity profiles. The LBM provides an efficient way to capture the flow behavior of the micro-scale Couette flow of two-component gas mixtures. Furthermore, the proposed LBM can also be used to simulate other complex micro-scale flows of two-component gas mixtures.

Improved mixed elastohydrodynamic lubrication of hypoid gears by the optimization of manufacture parameters

Extensive wear appears in the case of dry contacts, or when the lubrication of the contacting surfaces is not appropriate. The aim of this research is to improve the mixed elastohydrodynamic lubrication in hypoid gears by the optimization of manufacture parameters for tooth surface processing.A full numerical analysis of the thermal mixed EHL in hypoid gears is applied. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions including the full film, mixed, and boundary lubrication. In the hydrodynamically lubricated areas the calculation method employed is based on the simultaneous solution of the Reynolds, elasticity, energy, and Laplace's equations. In the asperity contact areas the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. The real geometry and kinematics of the gear pair based on the manufacturing procedure is applied, thus the exact geometrical separation of the mating tooth surfaces is included in the oil film shape, and the real velocities of these surfaces are used in the Reynolds and energy equations. The transient nature of gear tooth mesh is included. The oil viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included. The non-Newtonian behaviour of the lubricant is considered. Using this model, the pressures, film thickness, temperatures, and power losses in the mixed lubrication regime are predicted. By using the developed method, the influence of the manufacturing parameters on the conditions of mixed elastohydrodynamic lubrication is investigated. On the basis of the obtained results recommendations are formulated to improve the mixed EHL and the efficiency of face-milled hypoid gears.

Improvements in the mixed elastohydrodynamic lubrication and in the efficiency of hypoid gears

In this paper, the influence of the manufacturing parameters on the conditions of mixed elastohydrodynamic lubrication is investigated. On the basis of the obtained results, recommendations are formulated to improve the mixed EHL and the efficiency of face-milled hypoid gears. A full numerical analysis of the mixed EHL in hypoid gears is applied. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions, including the full film, mixed, and boundary lubrication. In the hydrodynamically lubricated areas, the calculation method employed is based on the simultaneous solution of the Reynolds, elasticity, energy, and Laplace's equations. In the asperity contact areas, the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. The real geometry and kinematics of the gear pair based on the manufacturing procedure are applied; thus, the exact geometrical separation of the mating tooth surfaces is included in the oil film shape, and the real velocities of these surfaces are used in the Reynolds and energy equations. The transient nature of gear tooth mesh is included. The oil viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included. The non-Newtonian behaviour of the lubricant is considered. Using this model, the pressures, film thickness, temperatures, and power losses in the mixed lubrication regime are predicted. The effectiveness of the presented method is demonstrated by using hypoid gear examples.

On Exact Controllability of Infinite-Dimensional Linear Port-Hamiltonian Systems

Infinite-dimensional linear port-Hamiltonian systems on a 1-D spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission lines. The main result shows that well-posed port-Hamiltonian systems, with state space L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ((0,1); C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ) and input space C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , are exactly controllable.

Partial and full boundary regularity for non-autonomous functionals with Φ-growth conditions

Abstract We prove partial and full boundary Hölder continuity, under a suitable regularity on the boundary datum, of the minimizers of non-autonomous integral functionals of the type ∫ Ω Φ ⁢ ( ( A i ⁢ j α ⁢ β ⁢ ( x , u ) ⁢ D i ⁢ u α ⁢ D j ⁢ u β ) 1 2 ) ⁢ d ⁢ x , \int_{\Omega}\Phi\bigl{(}(A^{\alpha\beta}_{ij}(x,u)D_{i}u^{\alpha}D_{j}u^{% \beta})^{\frac{1}{2}}\bigr{)}\mathop{}\!dx, where Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} is a bounded domain, Φ ⁢ ( t ) = t p ⁢ log α ⁡ ( e + t ) {\Phi(t)=t^{p}\log^{\alpha}(e+t)} with 1 &lt; p ≤ n {1&lt;p\leq n} and α &gt; 0 {\alpha&gt;0} , and A ⁢ ( x , s ) = ( A i ⁢ j α ⁢ β ⁢ ( x , s ) ) {A(x,s)=(A^{\alpha\beta}_{ij}(x,s))} is a uniformly elliptic, bounded and continuous function.

Vibration Controllability of Sandwich Structures with Smart Materials of Electrorheological Fluids and Magnetorheological Materials: A Review

Vibration control is very significant issue in various engineering fields such as flexible structures, rotor systems, cable and bridge, and vehicle suspension. So far, three different recipes to suppress or control unwanted vibrations are used: passive, semi-active and active. As well known, the passive method has several limitations, such as the lack of real-time avoidance of the time-varying resonances. On the one hand, active vibration control method is very effective, but it is not attractive in terms of cost due to the use of several actuators and sensors. Therefore, recently semi-active vibration control method is popularly used in many practical environments. This article reviews vibration control of flexible structures using the semi-active method associated with smart materials of electrorheological fluids, magnetorheological fluids and magnetorheological elastomers. Modal characteristics of beam, shell and plate incorporating the core (or layer) of smart materials are deeply investigated and discussed in terms of field-dependent controllability. The field-dependent natural frequency and damping property of the sandwich beam type, plate type and shell type are experimentally identified. Subsequently, an appropriate control scheme based on the field-dependent modal properties is formulated to avoid the resonance behavior. In addition, several sandwich beams which are partially filled and fully filled with the magnetorheological fluid are investigated to understand the effectiveness of the modal property change. It has shown that both damping and stiffness properties of the sandwich structures can be effectively controlled by several ways: the change of the field intensity, the location of cores zones, the partial and full treatment and boundary conditions of the structures. In addition, it has identified that mode shapes of the sandwich plates featuring electrorheological core can be partially and fully controlled by applying the input field to an appropriate zone. Smart flexible structures associated with the field-responsive materials can be effectively used for vibration control due to its controllability of the stiffness and damping as well. However, to successfully implement in real environment, a more sophisticated analytical model considering the microscopic aspects of the particle motions needs to developed. Moreover, the field-dependent bucking problem and acoustic characteristics of smart structures subjected to external disturbances need to be explored.

Holographic complexity for defects distinguishes action from volume

We explore the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect. We focus on a Randall-Sundrum type model of a thin AdS2 brane embedded in AdS3. We find that, using the “complexity=volume” proposal, the presence of the defect generates a logarithmic divergence in the complexity of the full boundary state with a coefficient which is related to the central charge and to the boundary entropy. For the “complexity=action” proposal we find that the logarithmically divergent term in the complexity is not influenced by the presence of the defect. This is the first case in which the results of the two holographic proposals differ so dramatically. We consider also the complexity of the reduced density matrix for subregions enclosing the defect. We explore two bosonic field theory models which include two defects on opposite sides of a periodic domain. We point out that for a compact boson, current free field theory definitions of the complexity would have to be generalized to account for the effect of zero-modes.

Modeling of grain growth under fully anisotropic grain boundary energy

A level set formulation is proposed that can accurately trace the evolution of grain boundary networks in a polycrystalline aggregate while respecting grain boundary energy anisotropy. Commonly adopted simplifying assumptions related to the grain boundary energy variation with local microstructure conditions are avoided and the grain boundary energy dependence on both crystallographic misorientation and boundary plane inclination is respected. Key components in the formulation are discussed, such as an efficient and simple scheme for unequivocal identification of crystal neighbors at grain boundary junctions where an arbitrary number of crystals intersect. The method works without modifications in both two and three dimensions and is shown to provide grain boundary junction configurations that comply with classical equilibrium conditions as well as topological transforms of the grain boundary network that agree with theoretical predictions. Full grain boundary energy anisotropy is considered by adopting a parametrization of the five-parameter grain boundary energy space, as previously proposed by Bulatov et al 2014 Acta Mater. 65 161–75. Examples are provided to illustrate the relevance of the level set framework for simulations of microstructure evolution in polycrystalline solids. For example, it is clearly shown that the proposed modeling framework provides a grain boundary inclination dependence of the grain boundary energy that cannot be neglected in mesoscale simulations of grain growth.