Analyticity of Solutions to Nonlinear Parabolic Equations on Manifolds and an Application to Stokes Flow

We prove a general regularity result for fully nonlinear, possibly nonlocal parabolic Cauchy problems under the assumption of maximal regularity for the linearized problem. We apply this result to show joint spatial and temporal analyticity of the moving boundary in the problem of Stokes flow driven by surface tension.     

On the Asymptotic Properties of Solutions of Linear Functional Differential Equations with Constant Coefficients and Linearly Transformed Argument

We establish new properties of C ¹(0, +)-solutions of the linear functional differential equation in the neighborhood of the singular point t = +.     

Evolution Equations for the Surface Concentration of an Insoluble Surfactant; Applications to the Stability of an Elongating Thread and a Stretched Interface

The general form of the convection–diffusion equation governing the evolution of the surface concentration of an insoluble surfactant over an evolving interface is reviewed and discussed for three-dimensional, axisymmetric, and two-dimensional configurations. The linearized form of the evolution equation is then derived around cylindrical and planar shapes in a framework that is suitable for carrying out a linear stability analysis for axisymmetric or two-dimensional perturbations. Particular attention is paid to the cases of quiescent unperturbed fluids, unidirectional shear flow, and elongational flow. By way of application, the linearized transport equations are combined with Stokes-flow hydrodynamics to investigate the stability of an elongating cylindrical viscous thread suspended in an ambient viscous fluid or in a vacuum, and the stability of a two-dimensional interface separating two semi-infinite fluids and stretched under the action of an orthogonal stagnation-point flow. The results illustrate the possibly important role of the surfactant on the linear growth of periodic waves on the cylindrical interface, and reveal that the surfactant has no effect on the stability of the planar interface.     

Well-posedness and Ill-posedness for Linear Fifth-Order Dispersive Equations in the Presence of Backwards Diffusion

Journal of Dynamics and Differential Equations - Fifth-order dispersive equations arise in the context of higher-order models for phenomena such as water waves. For fifth-order variable-coefficient...     

An Application of the Kane and Mindlin Theory to Crack Problems in Plates of Arbitrary Thickness

Classical plane solutions of the theory of elasticity, which are sometimes more than 100 years old, are still used today and provide a framework for the analysis of many practical problems. But, strictly speaking, these analytical solutions are only applicable to plates with vanishing thickness or infinite thickness, where the stress state could be classified as plane stress or plane strain, respectively. However, the through-the-thickness stresses that exist in a plate of given thickness have a significant impact in a number of practical applications; and these stresses are often inevitably ignored due to the lack of analytical tools. This paper presents new analytical results for crack tip opening displacement (CTOD) for the through-the-thickness crack in infinite plates with various thicknesses. These results are based on the solution for an edge dislocation in infinite plate of arbitrary thickness and an application of the distributed dislocation technique. The analytical predictions of the CTOD and the constraint factor are compared with the three-dimensional elasto-plastic finite element (FE) results. It is shown that both analytical and numerical results are in good agreement when the numerical calculations are not affected by the size of the FE mesh and by the boundaries of the FE model.     

Estimate of the strength of a plate with an elliptic hole in tension and compression

The strength of a plate with an elliptic hole under uniaxial tension or compression is estimated for arbitrary angles between the ellipse axes and the direction of loading with the use of the gradient strength criterion. The calculated critical stress agrees with the existing experimental data. Institute of Physicotechnical Problems of the North, Siberian, Division, Russian Academy of Sciences, Yakutsk 677891. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 163–168, May–June, 2000.     

On the <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.     

Scheme of Investigation of the Spectrum of a Family of Perturbed Operators and Its Application to Spectral Problems in Thick Junctions

We develop a scheme for the investigation of the asymptotic behavior of eigenvalues and eigenvectors of a family of self-adjoint compact operators {A: > 0} that act in different spaces and lose their compactness in the limit case 0. We prove the Hausdorff convergence of the spectrum of the operator A to the spectrum of the limit operator A₀, obtain asymptotic estimates for this convergence both to points of the discrete spectrum and to points of the essential spectrum of the operator A₀, and prove asymptotic estimates for eigenvectors of A. This scheme is applied to the investigation of the asymptotic behavior of eigenvalues and eigenfunctions of the Neumann problem in a thick singularly degenerate junction that consists of two domains connected by an -periodic system of thin rods of fixed length.     

Application of an inverse mass transfer method to the measurement of turbulent fluctuations in the velocity gradient at the wall

The frequency response of the concentration boundarylayer is often a concern when flush mounted mass transfer probes are used to measure turbulent fluctuations in the velocity gradient at a wall. Present practice involves the use of a solution of the mass balance equation which is linear in the fluctuating quantities. An inverse mass transfer method is explored in this paper, which avoids the linearization assumption. Improved measurements of the amplitude probability distribution and of the frequency spectrum of the streamwise component of the fluctuating velocity gradient are presented. In particular, values of rms level, skewness and flatness of 0.37, 0.96, 4.2 are obtained, in good agreement with a recent study by Alfredson, Johansson, Haritonidis and Eckelmann.     

New Transforms for the Resolving Equations in Elastic Theory and New Integral Transforms, with Applications to Boundary-Value Problems of Mechanics

This paper reviews results from an analysis of exact boundary-value solutions of static and dynamic elasticity obtained by the method of integral transforms. Consideration is given to the solutions of problems for a half-space and a blunted hollow cone, the heat conduction problem for a cone, and the diffraction problem for a cone with a hole along the generatrix. Solutions of mechanics problems are analyzed and the method of integral transforms is generalized     

Estimate for the number of perturbed ultrasubharmonics of a system with one and a half degrees of freedom close to a Hamiltonian system

We consider a two-dimensional autonomous Hamiltonian system with heteroclinic contour under the action of a time-periodic perturbation. It is shown that the number of ultrasubharmonics in the perturbed system is estimated from below by a function proportional to the square of the logarithm of the perturbation parameter when this parameter tends to zero.     

Superposition principle for short-term solutions of Richards' equation: Application to the interaction of wetting fronts with an impervious surface

The interaction of a wetting front with an impervious layer is described by adding a reflected solution to the incoming solution for a semi-infinite medium. It is shown and checked by comparison with a numerical solution that the result is accurate during the early times of the interaction between the front and the impervious surface. This superposition principle is quite general and should prove especially useful to initiate numerical schemes by this analytical approximation as in the early times singularities are difficult to describe numerically.     

Plane Waves and Uniqueness Theorems in the Coupled Linear Theory of Elasticity for Solids with Double Porosity

This paper concerns with the coupled linear dynamical theory of elasticity for solids with double porosity. Basic properties of plane harmonic waves are established. Radiation conditions of regular vectors are given. Basic internal and external boundary value problems (BVPs) of steady vibrations are formulated, and finally, uniqueness theorems for regular (classical) solutions of these BVPs are proved.     

Correction to: Analysis of the Influence of the Thickness and the Hole Radius on the Calibration Coefficients in the Hole-Drilling Method for the Determination of Non-uniform Residual Stresses

Experimental Mechanics - Due to an error introduced during the production process, Fig.&nbsp;11 appeared incorrectly in the original publication of this article. It appears correctly here.     

Numerical study of mixed convection and conduction in a 2-D square ventilated cavity with an inlet at the vertical glazing wall and outlet at the top surface

A steady state numerical study of combined laminar mixed convection and conduction heat transfer in a ventilated square cavity is presented. The air inlet gap is located at the bottom of a vertical glazing wall and air exits the cavity via a gap located at the top surface. Three locations for the opening at the top surface: left (case a), center (case b) and right side (case c) are considered. All the remaining surfaces are considered adiabatic. The mass, momentum and energy conservation equations were solved using the finite volume method for different Rayleigh numbers in the interval of 10⁴ < Ra < 10⁶ and Reynolds number in the interval of 100 < Re < 700. Temperature, flow field, and heat transfer rates are analyzed. The effect of the interaction between ambient conditions outside the glazing and the air inlet gap at the bottom for different air outlet gap positions at the top surface modifies the flow structure and temperature distribution of the air inside the cavity. The Nusselt number as a function of the Reynolds number was determined for the three cases. It was found that configuration for case (a) removes a higher amount of heat entering the cavity compared to cases (b) and (c). This is due to the short distance between the main stream and the glass wall surface. Thus, the forced airflow entering the cavity is assisted by the buoyancy forces, and most of the cavity remains at the inlet flow temperature, which should be appropriate for warm climates. These results may provide useful information about the heat transfer and fluid flow for future studies.     

Application of the Spline-Collocation Method to Solve Problems of Statics and Dynamics for Multilayer Cylindrical Shells with Design and Manufacturing Features

International Applied Mechanics - We propose a spline-collocation technique for the analysis of the static stress–strain state and the free vibrations of ribbed multilayer orthotropic...     

Numerical and experimental investigation of the means for reducing the aeroacoustic loads in an extended rectangular cavity at subsonic and transonic freestream velocities

The results of a comprehensive investigation including numerical calculations and experiments with models in a wind tunnel and a vehicle under flight conditions aiming to find the ways of reducing the pressure fluctuation levels in an extended cavity at subsonic and transonic freestream velocities are presented. It is shown that the reduction of these loads can be achieved using the means which have demonstrated their effectiveness for cavities with the open-type flows, for example, a permeable deflector and the bevelling of the rear wall but only in the case of a given combination of their geometric parameters. The mechanisms of the action of these devices on the flow, thanks to which the intensity of the wave disturbances generated by the rear wall is reduced, the instability wave growth in the mixing layer behind the deflector is limited, and the fluctuation level in the cavity decreases, are investigated. The results of numerical investigations of the flow in a cavity with a permeable deflector are apparently among the first.     

Symmetrical Representation of Stresses in the Stroh Formalism and its Application to a Dislocation and a Dislocation Dipole in an Anissotropic Elastic Medium

Symmetrical stress representation in the Stroh formalism for anisotropic elastic bodies is introduced and the range of its applicability is analysed. By making use of this stress representation new formulae for influence functions giving stresses in an infinite anisotropic medium subjected to a straight dislocation and a straight dislocation dipole are derived. The advantage of the new formulae is that they explicitly show the symmetrical structure of these influence functions not referred to previously. Relations of these influence functions to influence functions giving stresses and Airy stress function due to a straight wedge disclination, whose explicit expressions are also introduced, are derived. Application of these results in computation of stresses by the hypersingular and regularized Somigliana stress identities is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.