Ancient solutions for Andrews’ hypersurface flow

We construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. Andrews in 1994.As time {t\rightarrow 0^{-}} the solutions collapse to a round point where 0 is the singular time. But as {t\rightarrow-\infty} the solutions become more and more oval. Near the center the appropriately-rescaled pointed Cheeger–Gromov limits are round cylinder solutions {S^{J}\times\mathbb{R}^{n-J}}, {1\leq J\leq n-1}. These results are the analog of the corresponding results in Ricci flow ({J=n-1}) and mean curvature flow.

Takagi–Taupin dynamical X-ray diffraction simulations of asymmetric X-ray diffraction from crystals: the effects of surface undulations

Dynamical X-ray diffraction simulations from crystals with surface undulations are reported. The Takagi–Taupin equations are applied and used to derive results in good agreement with experimental data reported in a separate paper [Macrander, Pereira, Huang, Kasman, Qian, Wojcik & Assoufid (2020). J. Appl. Cryst. 53, 789–792]. The development of Uragami [J. Phys. Soc. Jpn, (1969), 27, 147–154] is followed. Although previous work by Olekhnovich & Olekhnovich [Acta. Cryst. (1980), A36, 22–27] treated a crystal in the shape of a round cylinder, there do not seem to be any reports of previous dynamical X-ray diffraction treatments specifically for surface undulations. The significance of the present work is that it bridges the diffraction treatment of more classical dynamical diffraction theory, which assumes a flat surface, and the simple kinematic diffraction theory. The kinematic theory has, to date, been the primary means of simulating X-ray diffraction from surfaces.

Effect of the internal pressure on oscillations of a cylindrical gas bubble

Natural and forced oscillations of a gas bubble are studied. The bubble has the shape of a round cylinder in the state of equilibrium. It is bounded in the axial direction by two parallel solid surfaces and is surrounded by an incompressible liquid of a finite volume with a free outer surface. The entire system is under an alternating pressure field. The velocity of the contact line of three media (gas-liquid-solid substrate) is proportional to the deviation of the contact angle from the equilibrium value. The frequency of eigenmodes of a gas bubble can increase with an increase in the Hocking parameter, in contrast to the frequencies of an incompressible liquid drop, which only decrease. It is shown that radial oscillations of a cylindrical bubble are possible only in a finite volume of liquid. The effect of crossing the modes of natural oscillations is considered for the dissipative case. The amplitude-frequency characteristics are constructed for different values of the internal gas pressure. Resonance phenomena are found. It is shown that the external influence excites, first of all, volumetric oscillations of the bubble. Variations in shape are caused by the movement of the contact line. Expressions are found for the vibration amplitude in the case of a fixed contact line and a fixed contact angle.

Investigation on stress distribution and pressure capacity of two-layer split high-pressure die based on finite element analysis

In order to obtain a higher pressure capacity for the high-pressure die with a larger sample cavity, two types of two-layer split dies with a round cylinder and a quadrate cylinder were designed based on the conventional belt-type die. Finite element analysis was performed to investigate the stress distributions and pressure capacities of the high-pressure dies using a derived Mohr–Coulomb criterion and the von Mises criterion for the cylinder and supporting rings, respectively. As predicted by the finite element analysis results, in the two-layer split dies with a round cylinder, the stress state of the cylinder can be only slightly improved; and the von Mises stress of the first layer supporting ring can be hardly decreased. However, in the two-layer split dies with a quadrate cylinder and sample cavity, the stress state of the cylinder can be remarkably improved. Simultaneously, the von Mises stress of the supporting rings, especially for the first-layer supporting ring, can be also effectively decreased. The pressure capacities of the two-layer split dies with a round cylinder and a quadrate cylinder are 16.5% and 63.9% higher with respect to the conventional belt-type die.

An Experimental Investigation of the Surface Pressure Fluctuations for Round Cylinders

An experimental study is carried out to investigate the unsteady pressure exerted on the surface of a round cylinder in the subcritical Reynolds number range. Results are presented for the surface pressure fluctuations, spanwise coherence, lateral correlation length, and peripheral coherence. Discussions are provided for the dominance of the first three vortex shedding tones at different regions of the cylinder and the size of the flow structures around the cylinder. The dataset provided have shed new light on the unsteady aerodynamic loading acting on cylinders and provides the impetus for further research on the aerodynamics and aeroacoustics of bluff bodies.

INFLUENCE MOISTURE FORMATION ON CYLINDER SURFACE ON THE DETERMINATION OF HEAT TRANSFER COEFFICIENT AIR DURING APPLICATION OF THE METHOD OF MELTING ICE

Circular cylinders with cross-flow are a component of many technical devices in power engineering, heat engineering and chemical technology. For the intensification of external heat exchange, various types of ribs are widely used, the use of which is associated with a large metal capacity of the equipment. Application of holes on the heat exchange surface can significantly improve the thermohydraulic and mass-grossing characteristics of heat and mass equipment. A simple and effective way of intensifying heat transfer is the spiral groove on the outer surface of the pipe. The purpose of this work is to develop a method for determining the average coefficient of heat transfer by the method of melting ice, taking into account the moisture that falls on the surface of the cylinder-calorimeter. The research was carried out in the range of the Reynolds number change, calculated from the outside diameter of the pipe, from 2000 to 17000. In this paper, the method of determining the average coefficient of heat transfer by the method of melting of ice at the cross-flow of a round cylinder is specified. It is shown that ignoring the air humidity flowing through the cylinder-calorimeter can lead to a large error in determining the average coefficient of heat transfer, especially when air humidity is more than 53%.

ON MATHEMATICAL MODELLING OF THE 2-D FILTRATION PROBLEM IN POROUS AXIAL SYMMETRICAL CYLINDER

In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs). One equation is expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetically equation for absorption. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM). This procedure allows reducing the 2-D axis-symmetrical mass transfer problem described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.