Thermoelastic driving forces on singular surfaces

The paper deals with singular surfaces in thermoelastic materials. A new kinetic relation is obtained for surfaces with discontinuous temperature, which is generalizing the relation for the continuous case. It is shown that the deduced driving force naturally corresponds to the thermoelastic pseudomomentum balance previously proposed by Dascalu and Maugin [J. Elastic. 39 (1995) 201].     

Rotation of axisymmetric bodies in hydromagnetics

Summary This paper deals with the distrubance due to steady rotation of axisymmetric bodies in a viscous incompressible fluid of infinite conductivity in which the uniform ambient flow field is collinear with the uniform magnetic field. The known results of Sowerby¹) for the problem Couple on a rotating spheroid in a slow stream in an incompressible viscous fluid are generalized to apply to all ellipsoids of revolution and a special case of the circular disc has also been investigated in detail. The conditions of flow are assumed to be such as to permit the use of Oseen's approximation in the equations of motion. The coefficient of couple has been found to the first order approximation in terms ofR(1–S) orR(S–1) whereR is the Reynolds number andS=H ₀ ² /4W ² the pressure number which plays an important part. The couple exerted on the body is computed for various values ofS andR.     

Stability of a Maxwell fluid in hydromagnetics

The character of equilibrium of a Maxwell fluid in the presence of a magnetic field has been investigated. It is shown that the solution is characterized by a variational principle when the direction of magnetic field is either horizontal or vertical. For both directions, an approximate solution has been developed for a fluid layer of finite depth and exponentially varying density. It is found that the stability criterion remains unaffected by the viscosity parameters, although they influence the rate at which the unstable stratification departs from the equilibrium position. The question of excitation of waves has also been considered in detail.     

Rotation of axisymmetric bodies in hydromagnetics (finite conductivity)

Summary This paper deals with the disturbance due to the steady rotation of some axisymmetric bodies in a viscous incompressible fluid of finite conductivity in which the uniform ambient flow field is collinear with the uniform magnetic field. The known results of Sowerby [1] for the couple on a rotating spheroid in a slow stream in an incompressible viscous fluid are generalized. The special case of a disk is investigated in detail. The assumed conditions of flow permit the use of Oseen's approximation. The couple is found to first order approximation in terms of R and M, where R is the Reynolds number and M the Hartmann number.On leave from Meerut College, Meerut, INDIA.     

On singular perturbation method of perturbed bifurcation problems

In this paper, the general mathematical principle is over-all explained and a new general technique is presented in order to calculate uniformly asymptotic expansions of solutions of the perturbed bifurcation problem (1.6) in the vicinity of y=0, λ=0,δ=0, by means of singular perturbation method. Simultaneously, Newton’s polygon^[4] is generalized. Finally, the calculating results of two examples are given.     

On a singular integral equation in the theory of radiative transfer

Summary A singular integral equation arising in the theory of radiative transfer with polynomial scattering indicatrices is studied in this paper. In the case of a semi-infinite atmosphere, brightness coefficients and auxiliary functions satisfy this equation when the free term is suitably specified. The general solution of the singular equation is given a closed form in terms of its moments _n and of the fundamental solution of a homogeneous Hilbert problem. The _n's (n 1) are seen to satisfy a set of linear equations, and ₀ turns out to be simply related to the subsequent _n's.

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Sommario In questo articolo viene studiata un'equazione integrale singolare che si presenta nella teoria del trasporto radiativo con indicatrici di scattering polinomiali. I coefficienti di riflessione e trasmissione e le funzioni ausiliarie di un'atmosfera semiinfinita soddisfano questa equazione, con opportune determinazioni del termine noto. La soluzione generale dell'equazione viene espressa in forma chiusa mediante i suoi momenti _n e mediante la soluzione fondamentale di un problema omogeneo di Hilbert. Le _n (n 1) soddisfano a loro volta un sistema di equazioni lineari, e ₀ risulta legato alle successive _n da una semplice relazione.

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This work was done under the auspices of the CNR Research Groups.     

On fluid flow between rotating surfaces

Viscous fluid flow in the space between a spherical and an ellipsoidal surfaces rotating with different angular velocities was studied. The conditions of the occurrence and features of radial fluid flows are discussed. The results can be used to study a number of geophysical phenomena related to the dynamics of the flow of fluid.     

On the sliding instabilities at rough surfaces

In this paper, the onset of sliding between two elastic half-spaces in contact, subjected to a tangential force, is studied within the framework of critical phenomena. First, it is shown that the contact domain between two rough surfaces is a lacunar set and that the distribution of contact stresses is multifractal. By applying an increasing tangential force, under constant normal load, the so-called regime of partial-slip comes into play. However, the continuous and smooth transition to full sliding, predicted by the classical Cattaneo-Mindlin theory, is not confirmed by the experiments, which show marked frictional instabilities. A numerical multi-scale procedure is proposed, taking into account the redistribution of stress, consequent to partial-slip, among the contact areas at all scales. It is shown that the lacunarity of the contact domain delays the onset of instability, when compared to compact Euclidean domains. Independently of the assumptions made for the frictional behaviour at the scale of the asperities (Coulomb friction for meso-scale asperities, adhesion for micro-scales), renormalization permits the critical value of the tangential force which provides the instability to be found. Moreover, the multifractal analysis of the domains where the shear resistance is activated captures the size-scale effects on the friction coefficient, currently evidenced by the experiments.