Один подход к численному решению основного уравнения магнитостатики для конечного цилиндра в произвольном внешнем поле

The magnetostatics direct problem of calculating the resulting magnetic field strength from a homogeneous cylinder of finite dimensions placed in an external magnetic field of arbitrary configuration is considered. With the help of sufficiently voluminous analytical transformations using the basic properties of hypergeometric functions and Legendre functions, the solution of the basic three-dimensional magnetostatic equation for this configuration is reduced to solving of a certain number of systems of three one-dimensional linear integral equations. A simplified form of these systems for special cases of a constant external field and the resulting field on the cylinder axis is obtained.

Dynamical instability of anisotropic homogeneous cylinder

In this paper, we consider a non-static cylindrically symmetric self-gravitating system with anisotropic matter configuration and investigate its stability regions by using a homogenous model. We establish perturbed form of dynamical equations by using Eulerian and Lagrangian approaches. The conservation of baryon number is applied to obtain adiabatic index as well as perturbed pressure. A variational principle is used to find characteristic frequency which helps to compute the instability criteria. It is found that dynamical instability can be prevented till the radius of a cylinder exceeds the limit R[Formula: see text]18. We conclude that the system becomes unstable against radial oscillations as the radial pressure increases relative to tangential pressure.

Rotation of a superhydrophobic cylinder in a viscous liquid

The hydrodynamic quantification of superhydrophobic slipperiness has traditionally employed two canonical problems – namely, shear flow about a single surface and pressure-driven channel flow. We here advocate the use of a new class of canonical problems, defined by the motion of a superhydrophobic particle through an otherwise quiescent liquid. In these problems the superhydrophobic effect is naturally measured by the enhancement of the Stokes mobility relative to the corresponding mobility of a homogeneous particle. We focus upon what may be the simplest problem in that class – the rotation of an infinite circular cylinder whose boundary is periodically decorated by a finite number of infinite grooves – with the goal of calculating the rotational mobility (velocity-to-torque ratio). The associated two-dimensional flow problem is defined by two geometric parameters – namely, the number $N$ of grooves and the solid fraction $\unicode[STIX]{x1D719}$. Using matched asymptotic expansions we analyse the large-$N$ limit, seeking the mobility enhancement from the respective homogeneous-cylinder mobility value. We thus find the two-term approximation,$$\begin{eqnarray}\displaystyle 1+{\displaystyle \frac{2}{N}}\ln \csc {\displaystyle \frac{\unicode[STIX]{x03C0}\unicode[STIX]{x1D719}}{2}}, & & \displaystyle \nonumber\end{eqnarray}$$ for the ratio of the enhanced mobility to the homogeneous-cylinder mobility. Making use of conformal-mapping techniques and inductive arguments we prove that the preceding approximation is actually exact for $N=1,2,4,8,\ldots$. We conjecture that it is exact for all $N$.

The Effects of Carburisation on Creep Response of Stainless Steel Components

Stainless steel components in the UK’s Advanced Gas-cooled Reactors can undergo microstructural changes near the surface due to the reactor carbon dioxide environment. Carburisation tends to increase the material’s elastic modulus, yield strength and creep resistance. However, the ductility of the material tends to be reduced. This paper assesses the effect on the component response of the changes in local elastic, plastic and creep material properties resulting from carburisation. A pressurised carburised cylinder is modelled analytically as a set of concentric, creeping homogeneous cylinders. The results show a reduced overall deformation rate in the steady state as expected. For completeness, it is shown quite generally that steady-state deformation in a creeping component is reduced by locally increased creep resistance. The cylinder model, however, shows that the locally increased creep and plastic resistance leads to higher stresses in the carburised region than in a homogeneous cylinder, particularly during the transition before steady-state conditions are established. The transient period before steady state creep is then examined in more detail numerically by allowing the material properties to change due to carburisation during the transient phase. This leads to reduced stresses in the carburised region. The influence of the results on deformation, triaxial stress fields and associated creep damage distributions are examined and used to provide guidance on both component assessment and on evaluation of carburised material properties from deformation measurements on test specimens.

Contact Angle for Spherical Nanodroplet in Cylindrical Cavity with Quadratic Curve Generatrix

<p class="1Body">Wetting of a spherical nanodroplet in smooth and homogeneous cylinder surface rotated by quadratic curve was studied by methods of thermodynamics. The solid-liquid-vapor system was separated into six parts using Gibbs method of dividing surface. The system free energy was calculated. A generalized Young equation for the equilibrium contact angle is proposed taking the line tension effects into consideration. On the basis of some assumptions, this generalized Young equation is the same as the classical Young’s equation.</p>