On Rayleigh-Taylor and Richtmyer-Meshkov Dynamics With Inverse-Quadratic Power-Law Acceleration

Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities occur in many situations in Nature and technology from astrophysical to atomic scales, including stellar evolution, oceanic flows, plasma fusion, and scramjets. While RT and RM instabilities are sister phenomena, a link of RT-to-RM dynamics requires better understanding. This work focuses on the long-standing problem of RTI/RMI induced by accelerations, which vary as inverse-quadratic power-laws in time, and on RT/RM flows, which are three-dimensional, spatially extended and periodic in the plane normal to the acceleration direction. We apply group theory to obtain solutions for the early-time linear and late-time nonlinear dynamics of RT/RM coherent structure of bubbles and spikes, and investigate the dependence of the solutions on the acceleration’s parameters and initial conditions. We find that the dynamics is of RT type for strong accelerations and is of RM type for weak accelerations, and identify the effects of the acceleration’s strength and the fluid density ratio on RT-to-RM transition. While for given problem parameters the early-time dynamics is uniquely defined, the solutions for the late-time dynamics form a continuous family parameterised by the interfacial shear and include special solutions for RT/RM bubbles/spikes. Our theory achieves good agreement with available observations. We elaborate benchmarks that can be used in future research and in design of experiments and simulations, and that can serve for better understanding of RT/RM relevant processes in Nature and technology.

Hovering flight in hummingbird hawkmoths: kinematics, wake dynamics, and aerodynamic power

Hovering insects are divided into two categories: “normal” hoverers that moves the wing symmetrically in a horizontal stroke plane, and those with an inclined stroke plane. Normal hoverers have been suggested to support their weight during both down- and upstroke, shedding vortex rings each half stroke. Insects with an inclined stroke plane should, according to theory, produce flight forces only during downstroke, and only generate one set of vortices. The type of hovering is thus linked to the power required to hover. Previous efforts to characterize the wake of hovering insects have used low-resolution experimental techniques or simulated the flow using CFD, and so it remains to be determined if insect wakes can be represented by any of the suggested models. Here, we used tomographic PIV, with a horizontal measurement volume placed below the animals, to show that the wake shed by hovering hawkmoths are best be described as a series of bilateral, stacked vortex “rings”. While the upstroke is aerodynamically active, despite an inclined stroke plane, it produces weaker vortices than the downstroke. In addition, compared to the near wake, the far wake lacks structure and is less concentrated. Both near and far wakes are clearly affected by vortex interactions, suggesting caution is required when interpreting wake topologies. We also estimated induced power (Pind) from downwash velocities in the wake. Standard models predicted a Pind more than double that from our wake measurements. Our results thus question some model assumptions and we propose a reevaluation of the model parameters.

Quantitative Shape-Classification of Misfitting Precipitates during Cubic to Tetragonal Transformations: Phase-Field Simulations and Experiments

The effectiveness of the mechanism of precipitation strengthening in metallic alloys depends on the shapes of the precipitates. Two different material systems are considered: tetragonal γ′′ precipitates in Ni-based alloys and tetragonal θ′ precipitates in Al-Cu-alloys. The shape formation and evolution of the tetragonally misfitting precipitates was investigated by means of experiments and phase-field simulations. We employed the method of invariant moments for the consistent shape quantification of precipitates obtained from the simulation as well as those obtained from the experiment. Two well-defined shape-quantities are proposed: (i) a generalized measure for the particles aspect ratio and (ii) the normalized λ2, as a measure for shape deviations from an ideal ellipse of the given aspect ratio. Considering the size dependence of the aspect ratio of γ′′ precipitates, we find good agreement between the simulation results and the experiment. Further, the precipitates’ in-plane shape is defined as the central 2D cut through the 3D particle in a plane normal to the tetragonal c-axes of the precipitate. The experimentally observed in-plane shapes of γ′′-precipitates can be quantitatively reproduced by the phase-field model.

Generation of the current normal to the surface of antenna by electromagnetic waves and its application in the high responsive receiver

Generation of the initial current normal to the surface of antenna by electromagnetic waves has been considered. It has been shown that the angle of grazing (or sliding) for the wave with the electric vector in the plane normal to the surface varies the radiation resistance over a wide range. This property allows matching the radiation impedances and loads. Here, it has been proposed to use this property to create a highly- sensitive radiation detector. In relation with this task, a model of the radiation detection of the input radiation signal by a direct quadratic detector in the stationary mode with the diode included as the load has been considered. The obtained results prove that a diode with the high differential resistance can effectively operate with the antenna. The rise of the resistance increases the detector response voltage, its responsivity, and decreases the receiver noise equivalent power. Improvement of these characteristics by orders of magnitude is possible. The considered mechanism allows detectors to operate in the infrared spectral range, and the increase in the wavelength, in principle, does not limit its functioning.

Orientation relationships between magnetite micro-inclusions and plagioclase host

<p>Magnetite micro-inclusions in silicate minerals are important carriers of the remanent magnetization of rocks. Their shape orientation relationships (SOR) and crystallographic orientation relationships (COR) to the host crystal are of interest in the context of the bulk magnetic properties of the inclusion-host assemblage. We investigated the SOR and COR of magnetite (MT) micro-inclusions in plagioclase (PL) from oceanic gabbro using correlated optical microscopy, scanning electron microscopy, Electron backscatter diffraction analysis and Transmission electron microscopy.</p><p>In the mm-sized PL crystals of the investigated gabbros MT is present as equant, needle- and lath-shaped (sub)micrometer sized inclusions. More than 95% of the needle-shaped inclusions show SOR and specific COR to the plagioclase host. Most of the needles are elongated perpendicular to one of the MT{111} planes, which is aligned parallel to one of the (112), (1-12), (-312), (-3-12), (150), (1-50) or (100) planes of plagioclase. These inclusions are classified as “plane-normal type”. The needle elongation parallel to MT<111>, which is the easy direction of magnetization, ensures high magnetic susceptibility of these inclusions. The underlying formation mechanism is related to the parallel alignment of oxygen layers with similar lattice spacing across the MT-PL interfaces that are parallel to the elongation direction [1].</p><p>Apart from the SOR and the alignment of a MT{111} with one of the PL low index planes, the MT crystals rotate about the needle elongation direction. The rotation angles are statistically distributed with several maxima representing specific orientation relationships. In some cases one of the MT<001> axes is aligned with PL[14 10 7] or PL[-14 10 -7], which ensures that FeO<sub>6 </sub>octahedra of MT well fit into channels // [001] of PL, which are formed by six membered rings of SiO<sub>4</sub> and AlO<sub>4</sub> tetrahedra [2]. This COR is referred to as the “nucleation orientation” of magnetite with respect to PL. There are several other possibilities to fit FeO<sub>6</sub> octahedra into the [001] channels of PL, but the alignment stated above allows for the additional parallel alignment of one of the MT{111} with one of the above mentioned low index lattice planes of PL. MT crystals with one of these nucleation orientations can undergo directional growth to develop laths and needles. MT crystals with other nucleation orientations that do not allow for the parallel alignment of MT{111} with the above mentioned PL lattice planes, do not significantly grow and form the equant inclusions.</p><p>For some needles one or more of the MT{011} planes that are parallel to the needle elongation direction, are aligned with low-index planes of plagioclase such as PL (112), PL(150), PL(1-50) etc., and form MT facets. This situation corresponds to achievement of the best possible match between the two crystal lattices. This can either be generated during primary growth or during re-equilibration of the micro-inclusions and the plagioclase host.</p><p>Funding by RFBR project 18-55-14003 and Austrian Science fund (FWF): I 3998-N29 is acknowledged.</p><p>Reference</p><p>[1] Ageeva et al (2020) Contrib. Mineral. Petrol. 175(10), 1-16.</p><p>[2] Wenk et al (2011) Am. Min. 96, 1316-1324</p>

Atomic scale structure of a plagioclase – magnetite interface

<p>Magnetite (Mt) is the foremost carrier of rock natural remanent magnetization (NRM). Needle- and lath shaped Mt micro-inclusions in plagioclase (Pl) from gabbro often have systematic crystallographic- and shape orientation relationships (CORs, SORs) with the Pl host. The SORs of Mt leads to magnetic anisotropy which may bias the NRM of the Mt-Pl inclusion-host assemblage. Thus, the origin of the CORs and SORs between Mt and Pl is important for paleomagnetic reconstructions. In this context, the atomic structures of Mt-Pl interfaces are of particular interest.</p><p>The CORs and SORs between Mt and Pl were reported earlier and the underlying systematics was revealed from correlated optical and scanning electron microscopy (SEM) including electron back scattered diffraction (EBSD) analyses [1] (and references therein). The so-called plane normal type Mt micro-inclusions extend parallel to the Mt<111> direction, which is perpendicular to the densely packed Mt{222} oxygen layers that are parallel to one of seven Pl lattice planes with nearly identical d-spacings, namely Pl(112), Pl(-312), Pl(1-50), Pl(150), Pl(100), Pl(31-2) and Pl(1-12). Direct imaging of Mt-Pl interfaces has rarely been reported due to the beam sensitivity of Pl. Here we present the microscopic structure of a Mt-Pl interface along the inclusion elongation direction using high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and integrated differential phase contrast STEM (iDPC-STEM) techniques.</p><p>The TEM foil was prepared using a focused Ga-ion beam (Ga-FIB) from a lath-shaped Mt micro-inclusion of 23 μm x 17 μm x 0.1 μm extending perpendicular to Mt{111}/Pl(-312). The foil is oriented so that the Mt<111>/Pl(-312)-pole are parallel and Mt{110}/Pl(150) planes are perpendicular to the foil.</p><p>The STEM images show that the Mt-Pl interface is perfectly straight and parallel to Mt{110}/Pl(150) and that it is devoid of steps. Electron diffraction patterns confirm that the elongation direction of the micro-inclusions is determined by the good fit of oxygen layers across the Pl-Mt interface. A 2.4% difference in the d-spacings between Pl(-312) and Mt{222} is likely accommodated by every about 42'nd Mt{222} plane forming an edge dislocation at the Mt-Pl interface. In addition, elastic strain is indicated by a deviation of d<sub>111</sub>/d<sub>110</sub> of Mt from the strain free reference lattice. Moreover, lattice fringes in iDPC-STEM images reveal coherence between Pl(22-1) and Mt{111} planes without misfit dislocations. This additional coherence may explain the particularly strong alignment of Mt{111} and Pl(-312) reflected by the EBSD data.</p><p>In summary, the elongation directions of the Mt inclusions are determined by the alignment of important oxygen layers of both phases across the Mt-Pl interface, which is parallel to oxygen-rich lattice planes in both phases. Misfit dislocations are presumably introduced to compensate the 2.4% lattice misfit along the elongation direction. The well-organized interface structure ensures a low interfacial energy and is a viable explanation for the observed Mt-Pl CORs and SORs.  </p><p>Acknowledgement</p><p>Funding by FWF project I 3998-N29 and RFBR project 18-55-14003 is acknowledged.</p><p>Reference</p><p>[1] Ageeva et al (2020) Contrib. Mineral. Petrol. 175(10), 1-16.</p>

A Lamination Model for Pressure-Assisted Sintering of Multilayered Porous Structures

This work describes a lamination model for pressure-assisted sintering of thin, multilayered, and porous structures based on the linear viscous constitutive theory of sintering and the classical laminated plate theory of continuum mechanics. A constant out-of-plane normal stress is assumed in the constitutive relation. The lamination relations between the force/moment resultants and the strain/curvature rates are presented. Numerical simulations were performed for a symmetric tri-layer laminate consisting of a 10% gadolinia doped ceria (Ce0.9Gd0.1O1.95-δ) composite structure, where porous layers were adhered to the top and bottom of a denser layer under uniaxially-applied pressures and the sinter forging conditions. The numerical results show that, compared with free sintering, the applied pressure can significantly reduce the sintering time required to achieve given layer thicknesses and porosities. Unlike free sintering, which results in a monotonic decrease of the laminate in-plane dimension, pressure-assisted sintering may produce an in-plane dimension increase or decrease, depending on the applied pressure and sintering time. Finally, the individual layers in the laminate exhibit different stress characteristics under pressure-assisted sintering.

Mathematical Model of Human Semicircular Canal Spatial Attitude

Located deep in the temporal bone, the semicircular canal is a subtle structure that requires a spatial coordinate system for measurement and observation. In this study,Fifty-five semicircular canal and eyeball models were obtained by segmentation of MRI data. The spatial coordinate system was established by taking the top of the common crus and the bottom of eyeball as the horizontal plane. Firstly, the plane equation is calculated according to the centerline of the semicircular canals. Then, according to the parameters of the plane equation, the plane normal vectors are obtained. Finally, the average unit normal vector of each semicircular canal plane can be obtained by calculating the average value of the vectors. It is more intuitive and accurate to calculate the average normal vector of semicircular canal plane with the vector average method, which is different from the angular average method in different degrees. The mathematical model of semicircular canal spatial attitude established in this study is more reliable, which can guide the vestibular function examination, and also help guide the diagnosis and treatment of BPPV.

Road Surface Reconstruction by Stereo Vision

This paper covers the problem of road surface reconstruction by stereo vision with cameras placed behind the windshield of a moving vehicle. An algorithm was developed that employs a plane-sweep approach and uses semi-global matching for optimization. Different similarity measures were evaluated for the task of matching pixels, namely mutual information, background subtraction by bilateral filtering, and Census. The chosen sweeping direction is the plane normal of the mean road surface. Since the cameras’ position in relation to the base plane is continuously changing due to the suspension of the vehicle, the search for the base plane was integrated into the stereo algorithm. Experiments were conducted for different types of pavement and different lighting conditions. Results are presented for the target application of road surface reconstruction, and they show high correspondence to laser scan reference measurements. The method handles motion blur well, and elevation maps are reconstructed on a millimeter-scale, while images are captured at driving speed.