Embedding formulae for wave diffraction by a circular arc

For certain wave diffraction problems, embedding formulae can be derived, which represent the solution (or far-field behaviour of the solution) for all plane wave incident angles in terms of solutions of a (typically small) set of other auxiliary problems. Thus a complete characterisation of the scattering properties of an obstacle can be determined by only determining the solutions of the auxiliary problems, and then implementing the embedding formula. The class of scatterers for which embedding formulae can be derived has previously been limited to obstacles with piecewise linear boundaries; here this class is extended to include a simple curved obstacle, consisting of a thin circular arc. Approximate numerical calculations demonstrate the accuracy of the new embedding formulae.     

Two contact problems for a wedge with a symmetric cut on the edge

In this paper, the solutions of two contact problems for a wedge with a symmetric cut on the edge are presented. First, special approximation methods and orthogonal polynomials are used to solve the auxiliary problem on the action of a lumped force on the cut edge. The obtained solutions are compared with known solutions in some special cases.     

Evaluation of hip fracture risk using a hyper-parametric model based on the Locally Linear Embedding technique

The hip fracture is one of the most common diseases for elder people and also, one of the most worrying one since it usually is the starting point of further complications for both, the health of the patient and their daily life. Additionally, reports shown that there exist differences between people living in different regions, thus limiting the use of global models. In this work we propose a hip fracture prediction tool for a local region, using clinical data of the population of that region. The data is processed with a dimensionality reduction tool in combination with and hyper-parametrization process and the corresponding hyper-parameter optimization process for obtaining good predictions in the diagnoses, as the results shown.     

Force and torque formulae for a sphere moving in an axisymmetric stokes flow with finite boundaries: asymmetric stokeslets near a hole in a plane wall

A sphere is allowed to move with three degrees of freedom in an axisymmetric flow field and general formulae, correct to the third power of the sphere's radius, are developed for the Stokes resistance experienced by the sphere. These are shown to depend on the behaviour within the sphere of the reflected velocity fields which arise from the presence of fixed boundaries at finite distances from stokeslets placed at the sphere's center. Application is made to the stagnation flow at a plane. Poiseuille flow and flow past a sphere and some comparisons made with exact formulae. Solutions are given for asymmetrically placed stokeslets near a hole in a plane wall or a disk.     

New numerical method for volterra integral equation of the second kind in piezoelastic dynamic problems

The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating.     

Excess pressure drop and drag calculations for strain-hardening fluids with mild shear-thinning: Contraction and falling sphere problems

This study extends our previous analysis on pressure-drops for strain-hardening Boger-type fluids in contraction flow settings, into those fluids that manifest mild shear-thinning properties. Numerical simulations are compared and contrasted for a variety of constitutive equations, categorised through their differences in viscometric functional response, considering application on 4:1:4 contraction-expansion flow and 2:1 flow past a sphere. Here, prior results on pressure-drop enhancement for constant shear-viscosity fluids have revealed the counter-influences of first normal stress differences and extensional viscosity. The present comparative work advances this study by selectively including the effects of shear-thinning. Suitable models to accomplish this are chosen from the class of Phan-Thien/Tanner (PTT) models, with cross-reference to FENE-models and Oldroyd-B. Furthermore, the work explores the falling sphere problem with comparison of the drag coefficient factor for various implementations. The numerical computations are performed by appealing to a well-founded hybrid finite element/finite volume algorithm, using structured triangular meshing, semi-implicit time-stepping and subcell technology. The cell-vertex finite volume scheme is particularly suited to the solution of the stress subsystem, and invokes fluctuation-distribution for upwinding and median-dual-cells for source-term representation.     

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.     

Numerical investigation of the flow of nitrogen past a sphere with allowance for rotational relaxation

The supersonic flow of nitrogen past a sphere is studied in the framework of the complete Navier-Stokes equations and the relaxation equation with allowance for rotational-translational relaxation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 170–174, March–April, 1980.I thank V. N. Gusev for interest in the work and valuable discussions and V. K. Molodtsov for assisting in the development of the numerical algorithm for solving the problem.     

Effect of yaw on the starting point of curvature for reflected diffracted shock wave (subsonic and sonic cases)

Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill (Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp. 225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves 13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and χ = 40° (χ is the angle of yaw).      

Time-dependent process of electric charge accumulation on a sphere in a viscous stream with the ion component

The problem of time-dependent charging of electrically insulated ideally-conducting bodies in a stream of an incompressible viscous medium with the ion component is considered. The following effects are included in the expression for the ion current: convective ion transfer with the velocity of the medium and the ion drift and diffusion in the electric field. In this formulation the problem of time-dependent charging of a sphere is formulated and solved. The role of the diffusion effects is clarified. The fields of hydrodynamic and electric parameters are found. The time dependences of the sphere charge and potential are obtained.     

Disturbances to a rotating fluid with a sphere moving along the axis of rotation

I.IntroductionWhenabodyprojectedinthewaterisintranslationalmotionthroughwateritwillcertainlycausesdisturbances.Howtodetectthedisturbancesf'arawayfromthebodyandhowtodetermillebytheintbrlnationobtainedthepositionandvelocityofthebodyandthesiteofprojectionareimportant.Astheprojectedbodyisrotating,thefluidaroundisinauniformlyrotationrelativetothereferenceframerotatinginsynchronismwiththebody,andthisisaquestionofthemotionofabodyinarotatingfluid.SuchproblemswerefirststudiedbyProudman(1916)l']andTay…     

Construction of fracture diagrams for plates with a crack-like cut with the use of necessary and sufficient criteria

The process of tension of a plate with a narrow crack-like cut whose vertices form finite-radius semi-circumferences is considered. The plate is made of a structured material whose mechanical characteristics are close to the characteristics of St.45 steel. Fracture diagrams are constructed by a numerical method, based on the necessary and sufficient criteria. A possibility of an analytical presentation of fracture diagrams is demonstrated.     

A general formula for the drag on a sphere placed in a creeping unsteady micropolar fluid flow

In the present work, we investigate the creeping unsteady motion of an infinite micropolar fluid flow past a fixed sphere. The technique of Laplace transform is used. The drag formula is obtained in the physical domain analytically by using the complex inversion formula of the Laplace transform. The well known formula of Basset for the drag on a sphere placed in an unsteady viscous fluid flow and that of Ramkissoon and Majumdar for steady motion in the case of micropolar fluids are recovered as special cases. The obtained formula is employed to calculate the drag force for some micropolar fluid flows. Numerical results are obtained and represented graphically.     

The inlet effect on the drag factor of a sphere in a tube

The creeping motion Ground a sphere situated axisymmetrically near the entrance of asemi-infinite circular cylindrical tube is analyzed using infinite series solutions for thevelocity components. pressure and the stream function. Truncating the infinite series. thecorresponding coefficients in the series are determined by a collocation technique. The dragfactor and the stress distribution on the surface of the sphere are calculated for the sphere inmotion in quiescent fluid and for the flow with uniform velocity at the entrance past a rigidlyheld sphere. The results indicate that a sphere near the entrance which has a uniformentrance velocity profile will suffer larger drag than that in infinite tube.Theconvergence of the collocation technique is tested by numerical calculation. It is shown thatthe technique has good convergence properties.     

Optimization of the damping decrement of free oscillations of a viscoelastic layered sphere with a limitation on weight

The problem of synthesis of a multilayer spherical shell with maximum damping of natural oscillations from a finite set of viscoelastic materials is considered with a limitation on weight. The necessary conditions of optimality are obtained, a computational algorithm is derived, and an example of calculation is presented. Institute of the Physiotechnical Problems of the North, Siberian Division, Russian Academy of Sciences, Yakutsk 677891. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 161–165, March–April, 2000.     

Analytic solution of the problem of rotation of a sphere in a rarefied molecular gas with allowance for the accommodation coefficients

In the case of the slip flow regime expressions both for the mass velocity of a rarefied molecular gas entrained by a rotating sphere and for the moment of the friction forces exerted on the sphere by the gas are obtained with allowance for the second-order correction with respect to the Knudsen number. It is demonstrated that these quantities depend on the Prandtl number and the accommodation coefficients of the tangential impulse of the gas molecules and its flux toward the sphere surface. The results are compared with analogous results obtained in the case of diffuse reflection of the gas molecules by the sphere surface.     

An analytic approximation of the drag coefficient for the viscous flow past a sphere

We give an analytic solution at the 10th order of approximation for the steady-state laminar viscous flows past a sphere in a uniform stream governed by the exact, fully non-linear Navier-Stokes equations. A new kind of analytic technique, namely the homotopy analysis method, is applied, by means of which Whitehead's paradox can be easily avoided and reasonably explained. Different from all previous perturbation approximations, our analytic approximations are valid in the whole field of flow, because we use the same approximations to express the flows near and far from the sphere. Our drag coefficient formula at the 10th order of approximation agrees better with experimental data in a region of Reynolds number R_d<30, which is considerably larger than that (R_d<5) of all previous theoretical ones.