The connection between Ekman and Stewartson layers for a rotating disk

When a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, a so-called Stewartson layer exists at the edge of the disk. The properties of this layer outside the boundary layer of the disk have been given in a previous publication. In the present paper it is shown how the radial flow of the Ekman boundary layer turns into the axial flow of the Stewartson layer. This happens in a region of which both the radial and axial dimensions are O(E^1/2), where E is the Ekman number.     

The Stewartson layer of a rotating disk of finite radius

It is shown that if a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, an axial layer in the form of a cylindrical shell exists at the edge of the disk. This shell of thickness O(E ^1/3) has length O(E ^–1) in axial direction, where E is the Ekman number. Its most characteristic element is the axial velocity of O(E ^1/6) which is larger than everywhere else in the field. We calculate the velocity components and the pressure in this layer.     

On light attenuation in inhomogeneous colour centre layers

A procedure is presented how to estimate light attenuation in an inhomogeneous photosensitive layer. As an example the behaviour of radiation coloured NaCl crystals under light exposure is described.     

On the fracture of constrained layers

The problem of a crack embedded in a layer sandwiched between two elastic adherends is analysed accounting for the influence material property mismatch on the crack tip plastic deformation, which is contained in the layer. The cohesive crack model developed by Dugdale and Barrenblatt is adopted to model the strip yielding behaviour in a constrained layer. It is found that, due to the constraint imparted by elastic adherends with higher moduli, the near tip plastic deformation exhibits a sharp transition (plastic zone grows faster than the square of stress intensity factor) from small scale to large scale yielding. Because the region of singularity dominance for a crack embedded in a layer is generally much smaller than the layer thickness when the layer has a modulus much lower than the adherends, the prevailing failure mode of most bonded joints should be under large scale yielding conditions. A model based on energy balance is proposed to determine the fracture energy of bonded joints under such condition, taking into account of the plastic dissipation in the constrained layer. Comparison with experimental results demonstrates that the theory correctly predicts the dependence of fracture toughness on layer thickness as observed in experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

On partially absorbing layers and interference

The complex reflection and transmission coefficients of partially absorbing layers cannot be manipulated independently. The restrictions are evaluated by considering the layer as a beam splitter in an interferometric configuration and requiring the conservation of energy. It is also shown that interference effects can reduce the absorption in an absorbing beam splitter and, under certain conditions, absorption can be eliminated completely.     

On phase transition layers in certain micro-damaged two-phase solids

A continuum model of a moving transition layer separating two different solid phases of a certain micro-damaged material is proposed. An application of this model to the analysis of the propagation of this layer in a micro-cracked solid is shown. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the linear stability of Stokes layers

Oscillatory flows occur naturally, with applications ranging across many disciplines from engineering to physiology. Transition to turbulence in such flows is a topic of practical interest and this article discusses some recent work that has furthered our understanding of the stability of a class of time-periodic fluid motions. Our study starts with an examination of the linear stability of a classical flat Stokes layer. Although experiments conducted over many years have demonstrated conclusively that this layer is unstable at a sufficiently large Reynolds number, it has only been relatively recently that rigorous theoretical confirmation of this behaviour has been obtained. The analysis and numerical calculations for the planar Stokes layer were subsequently extended to flows in channels and pipes and for the flow within a torsionally oscillating circular cylinder. We discuss why our predictions for the onset of instability in these geometries are in disappointingly poor agreement with experimental results. Finally, some suggestions for future experimental work are given and some areas for future theoretical analysis outlined.     

On singular perturbations and parabolic boundary layers

Summary A singular perturbation problem involving parabolic boundary layers is investigated. The second approximation for the boundary layer is constructed and it is shown that this approximation cannot be obtained by the usual perturbation method.     

On the asymmetry of flow through a bifurcated channel

Summary Results are presented of detailed numerical simulation of spatially developed, three-dimensional laminar flow through a bifurcated channel for different inlet flow conditions. The flow development near the bifurcated part of the channel is observed to be very sensitive to the inlet velocity distribution. For an uniform axial inlet velocity, the flow visualization results indicate the formation of two counter rotating symmetric vortical structures, parallel to the port axis, in the bifurcated part of the channel. When a cross-flow (v-component of velocity) is introduced at the inlet, the flow behaviour near the bifurcated part of the channel changes drastically. For such an inlet flow condition one vortical structure becomes larger at the expense of the other, and the asymmetry prevails in the flow field. The phenomena get intensified with the increase of the Reynolds number. The present numerical prediction of the flow phenomena provides some explanation of the interesting observations reported in the previous experimental investigations.     

On the asymmetry of elastic-plastic moduli for a class of pressure-dependent models in strain space

Summary For a general class of constitutive equations of plastic strain rates, which are normal to the loading surface in strain space, it is shown that for associated pressure-dependent plasticity the elastic-plastic moduli are nonsymmetric. The asymmetry is shown to be incompatible with the consequences of a work assumption due to Naghdi and Trapp.     

On the refractive index dispersions of ion-beam-synthesized β-FeSi2 layers

Continuous layers and precipitates of the β-FeSi₂ phase were formed by ion-beam synthesis followed by rapid thermal annealing. Two steps of Fe⁺ ion implantation in Si, at energies of 20 and 60 keV, were performed, using three different doses – 5×10¹⁵, 5×10¹⁶, and 10¹⁷ cm^?2. The infrared spectra were used as a criterion for the formation of the β-FeSi₂ phase. The refractive-index-energy dependences were calculated from the transmittance and reflectance spectra, using the general matrix method. From these dependences, the energy band gap and the energies of the higher-energy transitions in the vicinity of the gap were determined.     

On the nonlinear distortion of waves generated by interacting supersonic boundary layers

Summary In order to obtain uniformly valid solutions which describe the interaction between laminar boundary layers and supersonic flows it is necessary, in general, to account for the nonlinear distortion of the associated wave fields. Results obtained by means of the analytical method of characteristics are applied to typical examples such as the flow over compression ramps, the flow near the trailing edge of a flat plate and shock boundary layer interactions.With 6 FiguresDedicated to Prof. Dr. K. Oswatitsch on the occasion of his 75th birthday.     

Error asymmetry in causal and anticausal regression

Behaviormetrika - It is generally difficult to make any statements about the expected prediction error in an univariate setting without further knowledge about how the data were generated. Recent...     

Shock-spall asymmetry in high-velocity impact of solids

A new, previously unreported physical phenomenon has been observed in experiments with high-velocity impact of various strikers on metal targets of finite thickness. According to this, sufficiently strong and tough structural materials (armor steel, titanium alloys, etc.) exhibit fractionation of the spall plate formed upon dynamic contact with the striker or its deformed part. This always results in an odd number of fragments (three, five, seven, etc.) of similar configuration. Systematic experiments on retained samples revealed progressive fractionation of the spall plates, with the number of fragments increasing up to eleven. Further evolution was difficult to follow because trapping of the fragments was hindered by their high velocities, which led to unavoidable additional fragmentation of the spall plates in the course of their interaction with a gradient package of trapping material (ranging from felting to sand).     

Dielectric breakdown in monomolecular layers

This paper describes the different phenomena encountered in the breakdown of very thin insulating films made of 1 to 9 Langmuir monomolecular layers. Three steps are observed in the breakdown process: bubble formation, a sharp current increase and the breakdown proper; a mechanism is proposed for each of these phenomena. Values of breakdown voltages and fields are given for monomolecular layers of various molecules between aluminium electrodes. The respective roles of the oxide and of the organic layers are discussed.     

Boundary layers in engineering problems

In this paper it is shown that boundary layer type solutions, well known from the Navier-Stokes equations, are not restricted to the fluid-mechanics area but are present in a variety of engineering problems. The above fact is of considerable importance for the behavior of the solution of a large class of engineering problems and for the achievement of computational effective approximations using finite difference rsp. finite element techniques.     

Aging properties of gold layers with different adhesion layers

Adhesion layers of nickel-chromium, titanium and molybdenum were sputtered and evaporated onto thermally oxidized silicon wafers. On these adhesion layers pure gold layers were sputtered, evaporated or electroless-deposited. The layer composited were patterned by a photoresist process and were taken through isochronal and isothermal heat treatments at temperatures up to 350°C in vacuo and in corrosive atmospheres. Measurements of d.c. resistivity changes gave thermal activation energies between 0.8 and 2.4 eV. For the systems AuMo, AuTi and AuNiCr three aging mechanisms were identified: recrystallization; volume diffusion; volume diffusion with surface corrosion. A three-step aging model for metallic sandwich layer composites was established: (1) atomistic defect recovery; (2) structure transformation and adhesion losses; (3) layer degradation. The steady state creep stability of bonds on the films can be correlated to the aging process.