The main objective of this paper is to answer the questions posed by Robinson and Sadowski [22, p. 505, Commun. Math. Phys., 2010] for the Navier–Stokes equations. Firstly, we prove that the upper box dimension of the potential singular points set $\mathcal {S}$ of suitable weak solution $u$ belonging to $L^{q}(0,T;L^{p}(\mathbb {R}^{3}))$ for $1\leq \frac {2}{q}+\frac {3}{p}\leq \frac 32$ with $2\leq q<\infty$ and $2< p<\infty$ is at most $\max \{p,q\}(\frac {2}{q}+\frac {3}{p}-1)$ in this system. Secondly, it is shown that $1-2s$ dimension Hausdorff measure of potential singular points set of suitable weak solutions satisfying $u\in L^{2}(0,T;\dot {H}^{s+1}(\mathbb {R}^{3}))$ for $0\leq s\leq \frac 12$ is zero, whose proof relies on Caffarelli–Silvestre's extension. Inspired by Barker–Wang's recent work [1], this further allows us to discuss the Hausdorff dimension of potential singular points set of suitable weak solutions if the gradient of the velocity is under some supercritical regularity.

TiAl alloys are potential structural high-temperature structural materials at a service temperature of ~900 °C, while poor ductility at room temperature and high creep rate at the elevated temperature limits the applications. To improve the room-temperature and high-temperature mechanical properties of Ti–44Al–5Nb–3Cr–1.5Zr, Mo and B were introduced into this system and Ti–44Al–5Nb–3Cr–1.5Zr–xMo–yB alloys were proposed. And then, we, respectively, studied the microstructures and mechanical properties of Ti–44Al–5Nb–3Cr–1.5Zr–xMo–0B and Ti–44Al–5Nb–3Cr–1.5Zr–1Mo–yB to elucidate the role for the addition of Mo and B. It is found that Mo can increase the fraction of B2 phase in the alloys and the microstructures of the alloys are greatly refined by the addition of B. The compression test results indicate that Mo has a positive influence on the high-temperature compressive properties of TiAl-based alloys, whereas B addition can improve their room-temperature compressive properties of Ti–44Al–5Nb–3Cr–1.5Zr–1Mo–yB alloys; the morphology of borides in each sample should be the structural origin for these phenomena.

The prefrontal cortex (PFC) is enormously important in suicide and major depressive disorder (MDD). However, little is known about the structural alterations in the brains of people with MDD and suicidal ideation. We examined the gray matter volume (GMV) of the PFC of individuals with MDD and suicidal ideation to determine if PFC volumetric differences contribute to suicidal ideation in patients with MDD. Thirty-five subjects with MDD and suicidal ideation, 38 subjects with MDD but without suicidal ideation, and 43 age- and gender-matched healthy control (HC) subjects underwent T1-weighted imaging. A voxel-based morphometric analysis was conducted to compare the PFC GMVs of the three groups. Further GMV reductions in the left and right dorsolateral PFC (DLPFC) and right ventrolateral PFC (VLPFC) were detected in the MDD with suicidal ideation group compared with those in the HC group and the MDD without suicidal ideation group, whereas the MDD without suicidal ideation group only exhibited significant differences in the left DLPFC relative to the HC group. Our findings demonstrated that left DLPFC reductions were associated with MDD and suicidal ideation, and diminished GMV reductions in the right DLPFC and right VLPFC were only associated with suicidal ideation. These results help us better understand the neuropathological changes in MDD with suicidal ideation.

Polylactic acid (PLA) filament 3D parts printed by fused deposition modeling (FDM) have poor mechanical properties because of weak fusion interfaces. This article shows that SiC-coated PLA filaments are effective means to increase mechanical performance of PLA composites that are microwave heated. Numerical calculations on temperature-rising characteristics and temperature distribution of the interface in the microwave field are shown. 3D-printed specimens of PLA/SiC composites were printed by FDM and heated in a microwave. The experiments show the SiC/PLA composite filaments have better temperature-rising characteristics and temperature distribution at 185 °C for 60 s in the microwave field, and this enabled the 3D-printed specimens to achieve in situ remelting on the interface and increased interface bonding between PLA filaments. The SiC/PLA composite specimens heated using microwave increased by 51% in tensile strength, 42% in tensile modulus, and 18.7% in interlayer breaking stress relative to PLA. These results provided a new approach for the improvement of FDM workpiece strength.

A three-section pulse forming network (PFN) based on Guillemin type-C circuit was developed to meet the challenge of a compact design, high withstand voltage, and high-quality output waveform with fast rise time, flat-top duration, and 100-ns pulse width. A simplified pulse forming circuit was proposed and studied that includes only three LC-sections connected in parallel, with each section containing an inductor and a capacitor connected in series. The effect of the capacitance deviation on the output waveform was investigated. The simulation results show that when the capacitance deviation exceeds +3%, both the flat top and fall time of the output waveform of single PFN module deteriorate greatly. Fortunately, in a multi-stage PFN-Marx circuit, even if the capacitance deviation exceeds +10%, when the average capacitance of the same LC sections is close to the theoretical value, the output waveform maintains a good quality and is in good agreement with the theoretical prediction. The compact three-section PFN developed during this project has a size of only 360 mm × 342 mm × 65 mm, and a maximum withstand voltage of 120 kV. Sixteen PFN stages were assembled to form a Marx generator with design parameters to provide of an output peak power of 12 GW and a maximum peak current of 15 kA. The tested output waveform agrees well with the theoretical results, having a rise time of 31 ns, a flat-top of 104 ns, and a pulse with of 164 ns.

This paper introduces recent activities on Marx-based compact repetitive pulsed power generators at the Institute of Applied Electronics (IAE), China Academy of Engineering Physics (CAEP), over the period 2010–2018. A characteristic feature of the generators described is the use of a simplified bipolar charged Marx circuit, in which the normal isolation resistors or inductors to ground are removed to make the circuit simpler. Several pulse-forming modules developed to generate a 100 ns square wave output are introduced, including thin-film dielectric lines of different structures, a pulse-forming line based on a Printed Circuit Board, and non-uniform pulse-forming networks. A compact repetitive three-electrode spark gap switch with low-jitter, high-voltage, and high-current was developed and is used in the generators. A positive and negative series resonant constant current power supply with high precision and high power is introduced. As an important part of the repetitive pulse power generator, a lower jitter pulse trigger source is introduced. Several typical high-power repetitive pulsed power generators developed at IAE are introduced including a 30 GW low-impedance Marx generator, a compact square-wave pulse generator based on Kapton-film dielectric Blumlein line, a 20 GW high pulse-energy repetitive PFN-Marx generator, and a coaxial Marx generator based on ceramic capacitors. The research of key technologies and their development status are discussed, which can provide a reference for the future development and application of miniaturization of compact and repetitive Marx generators.

Laves phase plays a positive role in improving the strength of high-entropy alloys (HEAs); Nb and Ti elements have potential to promote Laves phase formation in some HEAs. For improving the strength of the face-centered cubic (FCC) CoCrFeMnNi HEA, a series of (CoCrFeMnNi)100−xNbx (atomic ratio: x = 0, 4, 8, 12, 16) and (CoCrFeMnNi)100−xTix (atomic ratio: x = 0, 2, 4, 6, 8, 12) HEAs were prepared by melting. The effects of Nb and Ti on the microstructure evolution and compressive properties of the CoCrFeMnNi HEAs were investigated. For (CoCrFeMnNi)100−xNbx HEAs, the second-phase (Laves and σ phase) volume fraction increased from 0 to 42%. The yield strength also increased gradually from 202 to 1010 MPa. However, the fracture strain decreased from 60% (no fracture) to 12% with increasing Nb content. For (CoCrFeMnNi)100−xTix HEAs, the yield strength increased from 202 to 1322 MPa. The Laves phase volume fraction also increased from 0 to 27%. However, the fracture strain decreased from 60% (no fracture) to 7.5% with increasing Ti content. Addition of Nb and Ti has a good effect on improving the strength of FCC CoCrFeMnNi HEA.

Measurement bias and lack of terrain features often cause false peaks during underwater terrain matching positioning, that is, there is more than one peak near the real position. Previous methods to address this problem have increased the number of measurement beams, but this also increases the data processing time and energy consumption. At the same time, the ratio of measured information that is used does not increase. In other words, we should increase the ratio of measured information that is used, not simply increase the amount of information that is measured. Conventional matching algorithms only use the height of nodes without considering surface information, which is composed of height and the position of multiple nodes in three-dimensional space. Multi-beam sonar can obtain the three-dimensional distribution of terrain nodes. This node information is not just a height sequence, as it is used in previous methods. If we consider the nodes as a three-dimensional distribution of points with height and position information, this increases the matching position information and more of the terrain features can be extracted from the same measured data. Hence, in this paper, a terrain positioning method called the Node Multi-information Fusion (NMIF) is presented. This method focuses on improving the stability and accuracy degraded by bias in the Digital Elevation Map (DEM), terrain repeatability, and other factors. First, the concept of a Single Node Data Packet (SNDP) is introduced. The SNDP includes elevation and surface information surrounding the node, such as roughness, gradient, and slope. This additional topographic feature information improves the robustness and accuracy of the system. A computer simulation using actual ocean bottom topography verifies the advantages of the proposed NMIF algorithm.

Ti–47Al–1.0W–0.5Si (at.%) alloy was directionally solidified in the range of growth rate (V) (V = 3–100 μm/s) at a constant temperature gradient (G = 18 K/mm). It was found that α phase was the primary phase of the alloy. Both primary dendritic arm spacing (λ) and interlamellar spacing (λs) decreased with increase of the growth rate (V) according to the relationship of λ ∝ V −0.356 and λs ∝ V −0.49, respectively. The Solidification segregation occurred since the enrichment of the solute element W in primary α phase during solidification. The degree of the segregation increased with the increase of the growth rate (V). The results also revealed that the lamellar orientation was not always perpendicular to the growth direction (GD) because the GD of primary α dendritic deviated from the preferred $\left\langle {0001} \right\rangle$ direction. The microhardness increased with increasing growth rate (V) according to H V ∝ 289.5V 0.12 because of the microstructure refinement.

Three-dimensional (3D) morphological evolution and growth mechanisms of primary I-phase particles have been investigated in directionally solidified Al–6Mn–2.5Be (wt%) alloy at a wide range of growth rates (100–1500 μm/s). At relatively low growth rates (100–600 μm/s), the I-phase particles exhibit faceted growth with strong anisotropy, forming a hierarchical flower-like aggregate with icosahedral morphological symmetry composed of several attached irregular polyhedrons or pentagonal dodecahedrons. At higher growth rates (e.g., 1000 μm/s), the interface of the I-phases becomes unstable along the edges and corners of the pentagonal dodecahedron, thereby arousing growth perturbations. Correspondingly, a transition from faceted to nonfaceted growth occurs with increasing growth rate. Further increase of the growth rate leads to the formation of I-phase columnar dendrites' preferential growth along the 3-fold axis. The configurations of the flower-like aggregates can be adequately illustrated by a geometrical model in terms of the perfect and elongated pentagonal dodecahedrons. A growth mechanism for the flower-like aggregates has been proposed based on the clear understanding of the 3D morphological evolution of the I-phase particles.

A comprehensive understanding of the growth pattern of intermetallic compounds (IMCs) during solidification is critical to both the crystal-growth theory and its property optimization. In this article, growth pattern and three-dimensional (3D) morphology of primary Al6Mn IMC were investigated in directionally solidified Al–3 at.% Mn alloy at a wide range of growth rates. A transition from faceted (<60 μm/s) to nonfaceted growth (>100 μm/s) was observed with increasing growth rates. Correspondingly, 3D morphologies of primary Al6Mn change from a solid polyhedron to a hollow structure, and then to a dendrite. This kind of change is associated with the competitive growths of different crystal planes determined by the crystallographic anisotropy and growth kinetics of Al6Mn. A growth model based on atomic cluster attachment is proposed to reveal the growth transition, and a growth-rate ratio between different crystal planes is used to appropriately reveal the formation mechanism of different morphologies at low rates.

During peritectic solidification, besides the longitudinal remelting of the primary phase at the temperature of peritectic reaction $\left( {T_{\rm{p}}^K} \right)$, a lateral remelting phenomenon of the primary phase below $T_{\rm{p}}^K$ is observed under high velocity in directionally solidified Cu–Ge alloys. The lateral remelting occurs continuously along a liquid channel as temperature decreases, and the lateral remelting velocity is larger than that of peritectic transformation. The lateral remelting leads to the morphological change of the primary dendrites, even the fragmentation of dendrite arms. The phenomenon also means that the classical theory calculating the volume fraction of the primary phase during peritectic transformation can need to be modified under some conditions. However, under low velocity, the phenomenon is not so significant. The phenomenon is explained by means of solidification and remelting theory.

During directional solidification of Cu–Ge peritectic alloys, a two-phase separated structure has been observed. With proper growth conditions, the peritectic ζ-Cu5Ge and primary α-Cu phases completely separate and form cylindrical layered structures. It is found that the formation of the separated structure is closely related to double diffusive convection and growth conditions. In the two-phase separated structure, a large trijunction region of peritectic reaction forms around the cylindrical α-Cu phase. During peritectic reaction, the morphological instabilities of ζ-Cu5Ge occur under high pulling velocities and are explained by the constitutional undercooling criterion. A new coupling growth between the ζ-Cu5Ge-phase and the groove of α-Cu phase near the trijunction is observed. Different from peritectic coupling growth, the diffusion coupling is established below the peritectic temperature. This two-phase separated growth process creates new opportunities for the fabrication of functionally layered materials.

The effects of hydrogen on the structure of Zr-based bulk metallic glasses were investigated by positron annihilation lifetime spectroscopy. Three lifetime components are identified, indicating the presence of three distinct size ranges for open volume defects in the glass. The concentration of the smallest sites identified as tetrahedral interstitial holes in the densely packed and the intermediate sites identified as flow defects, changes with hydrogen addition. The concentration of tetrahedral interstitial holes in Zr55Cu30Ni5Al10 alloys initially increases with the increase of hydrogen content. When Zr55Cu30Ni5Al10 alloys were prepared in Ar + 10%H2 atmospheres, the concentration of tetrahedral interstitial holes reaches a maximum, which may provide a more dense random-packed structure. For Zr57Al10Cu15.4Ni12.6Nb5alloys, the increase of hydrogen content causes a decrease in the concentration of tetrahedral interstitial holes and an increase in the concentration of flow defects.

Methods for creating speckle patterns on mouse arteries for use in deformation and strain field measurements in a stereomicroscope digital image correlation (DIC) system are described. Both fluorescent microsphere binding and ethidium bromide (EB) nuclear staining were used to generate high contrast, random patterns on mouse carotid arteries. To quantify the quality of each pattern, several metrics are used including (a) histogram distribution for each intensity pattern and (b) pixel-level variance in intensity pattern noise. Results demonstrate that both approaches provide sufficient pattern contrast for use in image-based methods to measure deformations in soft tissue. While fluorescent nuclear staining generates higher pixel-level intensity noise, this method provides better overall pattern quality (greater spatial uniformity and broader histogram) for automated DIC analysis when used at the appropriate magnification. Using recently developed theoretical predictions, estimates for the standard deviation in image-correlation-based displacements due to the measured intensity pattern variance are presented for fluorescent microsphere binding and EB nuclear staining patterns. Results confirm that both patterning approaches provide relatively small standard deviation in displacement measurements and hence are appropriate for measurement of deformations in small artery specimens.