Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel

The problem of interaction of a uniform current with a submerged horizontal circular cylinder in an ice-covered channel is considered. The fluid flow is described by linearized velocity potential theory and the ice sheet is treated as a thin elastic plate. The potential due to a source or the Green function satisfying all boundary conditions apart from that on the body surface is first derived. This can be used to derive the boundary integral equation for a body of arbitrary shape. It can also be used to obtain the solution due to multipoles by differentiating the Green function with its position directly. For a transverse circular cylinder, through distributing multipoles along its centre line, the velocity potential can be written in an infinite series with unknown coefficients, which can be determined from the impermeable condition on a body surface. A major feature here is that different from the free surface problem, or a channel without the ice sheet cover, this problem is fully three-dimensional because of the constraints along the intersection of the ice sheet with the channel wall. It has been also confirmed that there is an infinite number of critical speeds. Whenever the current speed passes a critical value, the force on the body and wave pattern change rapidly, and two more wave components are generated at the far-field. Extensive results are provided for hydroelastic waves and hydrodynamic forces when the ice sheet is under different edge conditions, and the insight of their physical features is discussed

Hydroelastic wave interaction with a circular crack of an ice-cover in a channel

Hydroelastic wave interaction with a circular crack of an ice-cover in a channel together with some related problems is considered, based on the linearized velocity potential theory and Kirchhoff plate theory. The domain decomposition method is adopted in the solution procedure. Two sub-domains are divided by the crack, one below the inner ice sheet and the other below the outer ice sheet. By using the Green function of an ice-covered channel, the velocity potential in the outer domain is established from the source distribution formula over an artificial vertical surface extended from the crack. The source distribution is expanded in both vertical and circumferential directions, which allows the velocity potential to be obtained in an explicit form with unknown coefficients. The velocity potential in the inner domain is expanded into a double series. An orthogonal inner product is used to impose continuity conditions on the artificial vertical surface and the edge conditions at the crack. The derived formulation is not just limited to the circular crack problem but can also be readily used in a variety of other problems, including wave diffraction by a surface-piercing vertical cylinder, polynya and circular disc floating on the free surface in a channel. Extensive results are provided for the forces on the inner ice sheet, the transmission and reflection coefficients. In particular, a detailed analysis is made on their behaviours near the natural frequencies of the channel, and the natural frequencies corresponding to the motion of the inner ice sheet

Surface wave interaction with floating elastic plates in channels

The interaction between surface waves and a finite rectangular floating plate in a channel is considered analytically, while the location of the plate is not restricted. The mathematical model is based on the linear velocity potential flow theory for the fluid and the Kirchhoff–Love plate theory for the plate. The problem is converted into an integral equation through using the Green function. The second-order singularity associated with a body with no thickness is treated with the Dirac delta function. The developed scheme is used for case studies of various edge constraints. Extensive results are provided for the hydrodynamic forces acting on the plate and the wave reflection and transmission coefficients. The effects of wave frequency, channel width, plate length, and edge conditions are analyzed, and their physical implications are highlighted. Significant findings comprise the highly oscillatory nature of force curves, influenced by the natural frequencies of the channels and the length of the plate, and substantial effects of edge conditions and the plate position on the results

Hydroelastic wave diffraction by a vertical circular cylinder standing in a channel with an ice cover

The problem of hydroelastic wave diffraction by a surface-piercing vertical circular cylinder mounted on the bottom of an ice-covered channel is considered. The ice sheet is modelled as an elastic thin plate with homogeneous properties, while the linearized velocity potential theory is adopted to describe the motion of the fluid. The solution starts from the Green function satisfying all other boundary conditions apart from that on the body surface. This is obtained through applying a Fourier transform in the longitudinal direction of the channel and adopting an eigenfunction expansion in the vertical direction. The boundary conditions on the side walls and ice edges are imposed through an orthogonal product. Through the Green function, the velocity potential due to a surface-piercing structure with arbitrary shape can be expressed through a source distribution formula derived in this work, in which only integrals over the body surface and its interaction line with the ice sheet need to be retained. For a vertical circular cylinder, the unknown source distribution can be expanded further into a Fourier series in the circumferential direction, and then the analytical solution of the velocity potential can be obtained further. Extensive results and discussions are provided for the hydrodynamic forces and vertical shear forces on the cylinder, as well as the deflection and strain of the ice sheet. In particular, the behaviour of the solution near one of the natural frequencies of the channel is investigated in detail

Transmission spectra and valley processing of graphene and carbon nanotube superlattices with inter-valley coupling

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In vitro evaluation of modified surface microhardness measurement, focus variation 3D microscopy and contact stylus profilometry to assess enamel surface loss after erosive-abrasive challenges

The aim of the study was to compare surface loss values after erosion-abrasion cycles obtained with modified surface microhardness measurement (mSMH), focus variation 3D microscopy (FVM) and contact stylus profilometry (CSP). We cut human molars into buccal and lingual halves, embedded them in resin and ground 200 μm of enamel away. The resulting surfaces were polished. To maintain a reference area, we applied Block-Out resin to partly cover the enamel surface. The samples were incubated in artificial saliva (37°C; 1 h), then rinsed in deionized water (10 s) and dried with oil-free air (5 s). We immersed the specimens individually in 30 mL citric acid (1%, pH 3.6) for 2 min (25°C, 70 rpm dynamic conditions) before brushing them (50 strokes, 200 g) in an automatic brushing machine with toothpaste-slurry. We calculated the surface loss as per mSMH, by re-measuring the length of the same six indentations made before the abrasive challenge. The experiment consisted of five experimental groups that received between 2 and 10 erosion-abrasion cycles. Each group contained 15 specimens and samples in groups 1, 2, 3, 4 and 5 underwent a total of 2, 4, 6, 8 and 10 cycles, respectively. The resin was removed from the reference area in one piece under 10× magnification and the FVM and CSP were performed. Agreement between the methods was calculated with the intraclass correlation coefficient (ICC) and depicted in Bland-Altman plots. All methods presented a linear pattern of surface loss measurements throughout the experiment, leading overall to a strong, statistically significant correlation between the methods (ICC = 0.85; p<0.001). So, despite the different surface loss values, all methods presented consistent results for surface loss measurement

Steam reforming on transition-metal carbides from density-functional theory

A screening study of the steam reforming reaction (CH_4 + H_2O -> CO + 3H_2) on early transition-metal carbides (TMC's) is performed by means of density-functional theory calculations. The set of considered surfaces includes the alpha-Mo_2C(100) surfaces, the low-index (111) and (100) surfaces of TiC, VC, and delta-MoC, and the oxygenated alpha-Mo_2C(100) and TMC(111) surfaces. It is found that carbides provide a wide spectrum of reactivities towards the steam reforming reaction, from too reactive via suitable to too inert. The reactivity is discussed in terms of the electronic structure of the clean surfaces. Two surfaces, the delta-MoC(100) and the oxygen passivated alpha-Mo_2C(100) surfaces, are identified as promising steam reforming catalysts. These findings suggest that carbides provide a playground for reactivity tuning, comparable to the one for pure metals.Comment: 6 pages, 4 figure

Effect of bainite layer by LSMCIT on wear resistance of medium-carbon bainite steel at different temperatures

In this work, bainite layer was prepared by Laser surface melting combined with isothermal treatment (LSMCIT) at 250ºC. The microstructures of the samples were analyzed by scanning electron microscopy (SEM), X-ray Diffraction (XRD) and transmission electron microscopy (TEM). Their wear resistances at 20ºC, 100ºC and 200ºC were measured using reciprocating tribometer. After the wear test, the confocal laser scanning microscope and SEM were used to characterize the topography of all abrasion surfaces, and the phase transformations occurred on the contact surfaces were analyzed by XRD. The results show that the microstructure of the LSMCIT sample has been refined to nanoscale. The wear volume reduction ratio of LSMCIT sample is 40.9% at 20ºC. The wear resistances of the samples are decreased with increasing of the temperature, however, the decrease in amplitude of the bainite is relatively small. The harder surface of the LSMCIT sample can provides higher mechanical support, and the white-etching layer on surface are difficult to remove by the reciprocating friction. The wear resistances of the LSMCIT samples at 20ºC, 100ºC and 200ºC are excellent, which shows the wide temperature ranges in wear applications