Singular solution of a water wave problem

The Green's function for water wave problem in an unbounded region (half space) bounded internally by a circular cylinder has been obtained by the use of an appropriate fourier transform in the vertical direction. The technique used in this investigation is specially useful when the liquid is internally bounded by cylindrical regions of the form D × I where D is any two dimensional region in the undisturbed free surface and I is the interval [0, ∞).     

Green's function solution of a water wave problem in a stratified ocean of finite depth

A stratified ocean consisting of two layers of immissible fluids of finite thickness is considered. The waves are generated by a point source of oscillatory strength lying in the fluid. The Green's function solution is obtained by the use of an appropriately defined Fourier series. The same technique is used to study the waves, when the fluid is bounded internally by a cylinder.     

Analytical and numerical treatment of a dynamic crack model

We discuss the propagation of a running crack in a bounded linear elastic body under shear waves for a simplified 2D-model. This model is described by two coupled equations in the actual configuration: a two-dimensional scalar wave equation in a cracked, bounded domain and an ordinary differential equation derived from an energy balance law. The unknowns are the displacement fields u  =  u(y, t) and the one-dimensional crack tip trajectory h  =  h(t). We assume that the crack grows straight. Based on a paper of Nicaise-Sändig, we derive an improved formula for the ordinary differential equation of motion for the crack tip, where the dynamical stress intensity factor occurs. The numerical simulation is an iterative procedure starting from the wave field at time t  =  t _i . The dynamic stress intensity factor will be extracted at t  =  t _i . Its knowledge allows us to compute the crack-tip motion h(t _i+1) with corresponding nonuniform crack speed assuming (t _i+1 ? t _i ) is small. Now, we start from the cracked configuration at time t  =  t _i+1 and repeat the steps. The wave displacements are computed with the FEM-package PDE2D. Some numerical examples demonstrate the proposed method. The influence of finite length of the crack and finite size of the sample on the dynamic stress intensity factor will be discussed in detail.     

Stable identification of linear isotropic Cosserat parameters: bounded stiffness in bending and torsion implies conformal invariance of curvature

We describe a principle of bounded stiffness and show that bounded stiffness in torsion and bending implies a reduction of the curvature energy in linear isotropic Cosserat models leading to the so-called conformal curvature case ${\mu\,\frac{L_c^2}{2}\,\|\,{{\rm dev \, sym}\,\nabla{\rm axl}\,\overline{A}}^2\|}$ where ${\overline{A} \in \mathfrak{so}(3)}$ is the Cosserat microrotation. Imposing bounded stiffness greatly facilitates the Cosserat parameter identification and allows a well-posed, stable determination of the one remaining length scale parameter L _c and the Cosserat couple modulus μ _c .     

On Helmholtz and higher-order resonance of twin floating bodies

The Helmholtz mode and other symmetric modes of resonance of a moonpool between two heaving rectangular floating cylinders are investigated. The hydrodynamic behavior around these resonant modes is examined together with the associated mode shapes in the moonpool region. It is observed that near each of the resonance frequencies, the damping coefficient can vanish. The Helmholtz mode is characterized by a region of modest variation of added-mass value from negative to positive near the Helmholtz frequency. The peaks are, however, bounded with the cross-over point in sign corresponding to a bounded spike in damping. The higher-order resonant modes are characterized by the presence of standing waves in the moonpool, which leads to large spikes in the hydrodynamic behavior near the resonance frequencies. The Helmholtz frequency has a distinct value, while the higher-order resonances occur at fairly regular intervals of the frequency parameter, σ²(w ? b)/g, where w ? b is the moonpool gap. The parametric dependence of the hydrodynamic behavior on frequency and geometry is discussed. With best wishes to my colleague and good friend, Nick Newman, on the occasion of his 70th birthday. A leader and staunch supporter of marine hydrodynamics, Nick has expanded the reach and influence of this field through his insights and publications. His contributions have been wide-ranged and his graciousness to young researchers is exemplary. May he enjoy the best of health in the years to come. R.W. Yeung      

Apparent power-law distributions in animal movements can arise from intraspecific interactions

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight.     

Asymptotic reflection of linear water waves by submerged horizontal porous plates

On the basis of linear water-wave theory, an explicit expression is presented for the reflection coefficient R ^?? when a plane wave is obliquely incident upon a semi-infinite porous plate in water of finite depth. The expression, which correctly models the singularity in velocity at the edge of the plate, does not rely on knowledge of any of the complex-valued eigenvalues or corresponding vertical eigenfunctions in the region occupied by the plate. The solution R ^?? is the asymptotic limit of the reflection coefficient R as a ?? ??, for a plate of finite length a bounded by a rigid vertical wall, and forms the basis of a rapidly convergent expansion for R over a wide range of values of a. The special case of normal incidence is relevant to the design of submerged wave absorbers in a narrow wave tank. Modifications necessary to account for a finite submerged porous plate in a fluid extending to infinity in both horizontal directions are discussed.     

Dielectric and microwave absorbing properties of low power plasma sprayed Al2O3/Nb composite coatings

Al₂O₃/Nb composite coatings were sprayed on graphite substrates by low power atmospheric plasma spraying (LPAPS) with an internally fed powder torch. The composite particles were agglomerated with different mass fractions by spray-drying technology. The microstructure and dielectric properties of coatings were investigated. The microstructure of composite coatings shows a uniform dispersion of metal particles in the composite coatings. Both the real (?′) and imaginary (?″) parts of the complex permittivity increase with increasing Nb content over the frequency range of 8.2-12.4 GHz, which is ascribed to space charge polarization and conductance loss, respectively. By calculating the microwave-absorption as a single-layer absorber, reflection loss values exceeding −10 dB can be obtained in the frequency range of 10.0-11.8 GHz with 10 wt% Nb content coating when the coating thickness is 1.5 mm.     

Padé extension of Bergman-series solutions to nonlinear boundary-value problems in heat conduction

Summary Bergman-type series solutions involving iterated complementary error integrals are constructed for nonlinear boundary-value problems associated with heat conduction in a region bounded internally by a cylindrical or spherical surface. In particular, a small-time solution is developed when the nonlinear boundary condition is of the Stefan-Boltzmann type. This solution is extended via Padé approximants.     

Homogenization of a heat transfer problem in a highly heterogeneous periodic medium

We consider the homogenization of a heat transfer problem in a periodic media made of two connected components having comparable conductivities separated by a third medium (insulating layer), the thickness of which is of the same order ? than the basic periodicity cell, and such that its conductance λ becomes infinitely small at the same time as ?, following a rate λ=λ(?). In the case where ?²/λ remains bounded, we identify the homogenized problem. Otherwise, we have to assume moreover that there are no sources in the third medium.     

Long-time behaviour of multi-component fluid mixtures in porous media

The long-time behaviour of a triply convective-diffusive fluid mixture saturating a porous horizontal layer in the Darcy-Oberbeck-Boussinesq scheme, is investigated. It is shown that the L²- solutions are bounded, uniquely determined (by the initial and boundary data) and asymptotically converging toward an absorbing set of the phase-space. The stability analysis of the conduction solution is performed. The linear stability is reduced to the stability of ternary systems of O.D.Es and hence to algebraic inequalities. The existence of an instability area between stability areas of the thermal Rayleigh number (“instability island”), is found analytically when the layer is heated and “salted” (at least by one “salt”) from below. The validity of the “linearization principle” and the global nonlinear asymptotic stability of the conduction solution when all three effects are either destabilizing or stabilizing, are obtained via a symmetrization.     

Determination of stresses from their stress trajectories in plane elastic systems: the five constant theorem

Let K be a cylindrical region of finite height, having a generator parallel to the z-axis and a bounded, simply connected cross section S whose boundary is a sufficiently smooth Jordan curve. Moreover, let the material in K be elastic and isotropic, and in a state of plane stress or plane strain of elastic equilibrium, under the action of a conservative, z-independent body-force field and appropriate boundary tractions. We prove that at each z the principal stress-trajectory net corresponding to the stresses τ _xx , τ _xy , τ _yy is a 2–5 real-parameter family, as conjectured by Neményi.     

Crystal habit and crystal structure of fine chromium particles: An electron microscope and electron diffraction study of fine metallic particles prepared by evaporation in argon at low pressures (III)

Fine Cr particles formed by evaporation in argon at low pressures were found to have well-defined crystal habits corresponding to the following solids: (i) the icositetrahedron bounded by 24 {211} planes; (ii) the rhombic dodecahedron bounded by 12 {110} planes; and (iii) the cube or the rectangular parallelepiped bounded by six {100} planes. The first two particle shapes were consistent with δ-Cr and the third with ordinary b.c.c. Cr. Re-examination of the crystal structure of δ-Cr by means of fine single crystals suggested that it was consistent with the A-15 type structure proposed by Forssell and Persson (J. Phys. Soc. Japan, 29 (1970) 1532). A disordered structure derivable from the A-15 type, reported previously by the present authors, is therefore withdrawn.     

On the spatial behaviour of the transient and steady-state solutions in thin plates with transverse shear deformation

This paper studies the spatial behaviour of the transient and steady-state solutions in the problem of bending of a plane elastic plate. When the transient solutions are discussed a bounded or unbounded plane plate of an arbitrary regular form is considered. Then an appropriate time-weighted line-integral measure is introduced and, for each fixed t∈[0,T], it is shown that it vanishes at distances from the support of the given data on the time interval [0,T] greater than ct, where c is a characteristic material constant. Moreover, for distances to the support lower than ct, it is established a spatial decay estimate of Saint-Venant-type. For the harmonic vibrations the case of an elastic plate whose middle surface is like a (semi-infinite) strip is considered for which the lateral sides are clamped. Then a cross-sectional line-integral measure is associated with the amplitude of the vibration and the spatial estimate is established for describing the spatial behaviour of the amplitude, provided that the frequency of the harmonic vibration is lower than a critical frequency.     

Unsteady free convective flow through a porous medium

Unsteady 2-dimensional free-convective flow through a porous medium bounded by an infinite vertical plate is considered, when the temperature of the plate is oscillating with the time about a constant non-zero mean value. An analytical solution for the velocity field is derived and the effects of K (permeability parameter) and ω (parameter of frequency) on the velocity field are discussed.     

Asymptotic analysis of extinction behaviour in fast nonlinear diffusion

A number of initial-boundary-value problems for the equation of fast diffusion are analysed (at varying levels of detail and completeness), i.e., $$\frac{\partial u}{\partial t} = \nabla \cdot (u^{-n} \nabla u)$$ with n > 0, in dimension N > 2 and with zero-Dirichlet boundary data, namely (i) the Cauchy problem (no boundary), mainly summarising existing results, (ii) the interior problem for a simply connected bounded domain (in large part revisiting earlier results), (iii) the problem exterior to a simply connected bounded domain and (iv) the half-space problem (for which we include N =2). The critical (borderline) case ${n = n_{s} \equiv 4/(N+2)}$ , which arises in Yamabe flow, is the subject of particular focus, in part because it provides considerable insight into both the subcritical case, 0 < n < n _s , and the supercritical one, n _s < n < 1. The results are based on formal-asymptotic analysis and suggest a range of conjectures that could be the subject of rigorous studies. The role of distinct types of similarity solutions is highlighted.     

A mathematical analysis of unsteady flow and heat transfer in a porous medium

The unsteady two-dimensional free convective flow through a porous medium bounded by an infinite vertical plate is considered when the temperature of the plate is oscillating with time about a constant nonzero mean. The problem is solved by developing two asymptotic expansions in powers of the frequency parameter ω. For small values of ω, a regular expansion is obtained, and for a large frequency parameter the method of matched asymptotic expansion is used. The effects of the frequency parameter ω, the permeability parameter K and the amplitude parameter ϵ on the velocity and the temperature fields are discussed.     

Social media-based systems: an emerging area of information systems research and practice

This article presents a review of the social media-based systems; an emerging area of information system research, design, and practice shaped by social media phenomenon. Social media-based system (SMS) is the application of a wider range of social software and social media phenomenon in organizational and non-organization context to facilitate every day interactions. To characterize SMS, a total of 274 articles (published during 2003–2011) were analyzed that were classified as computer science information system related in the Web of Science data base and had at least one social media phenomenon related keyword—social media; social network analysis; social network; social network site; and social network system. As a result, we found four main research streams in SMS research dealing with: (1) organizational aspect of SMS, (2) non-organizational aspect of SMS, (3) technical aspect of SMS, and (4) social as a tool. The results indicates that SMS research is fragmented and has not yet found way into the core IS journals, however, it is diverse and interdisciplinary in nature. We also proposed that unlike the conventional and socio-technical IS where information is bureaucratic, formal, bounded within the intranet, and tightly controlled by organizations; in the SMS context, information is social, informal, boundary-less (i.e. boundary is within the internet), has less control, and more sharing of information may lead to higher value/impact.     

Generalised plane strain problem for a circular inclusion in anisotropic elasticity

This paper is concerned with a generalised plane deformation problem in the linear theory of anisotropic elasticity. As is well known, the generalised plane deformation is the deformation of a body of infinite length bounded by a cylindrical surface, when all the stress and strain components exist but they are functions of two co-ordinates x₁, and x₂ only. It may be shown that if u₃ = 0, it is impossible to satisfy all the three equations of equilibrium of anisotropic elastic body. One has to choose u₃ as a non-zero function of x₁, x₂ for satisfying equations of equilibrium. In isotropic elasticity, u₃ = 0, makes the third equation of equilibrium identically equal to zero.The problem in this paper concerns an elastic circular cylindrical inclusion embedded in a matrix of different anisotropic material. The matrix and the inclusion are perfectly bonded at the interface. Each of the two materials possesses anisotropy of a general form with all the 21 elastic constants. The matrix is subjected to a uniform stress at infinity. The equations of elasticity theory demand that the rotation component ω₃ must also be prescribed at infinity. The complex variable technique is used and exact analytical expressions are derived for the elastic field in both the regions.     

Acoustic waves in hydrogels: A bi-phasic model for ultrasound tissue-mimicking phantom

In the present paper a continuum poroelastic model for high frequency acoustic waves in hydrogels has been developed. The model has been used to obtain the acoustic longitudinal wave equation for ultrasound.In order to obtain a satisfactory model for hydrogels, a viscoelastic force describing the interaction between the polymer network of the matrix and the bounded water is introduced.The model is validated by means of ultrasound (US) wave speed and attenuation measurements in polyvinylalcohol (PVA) hydrogel samples as a function of their water volume fraction “β” and polymer matrix cross-linking.The model predicts that the law ∝ ν^(1 + δ) for ultrasound attenuation can be applied as a function of the frequency ν, where δ is the frequency exponent of the polymer-bounded water viscosity. This outcome can well explain the attenuation of the US frequency in natural gels where δ is typically about 0.25÷0.50 while the value for pure water is 1.The theory and experiments show that US attenuation in hydrogels decreases steadily with the increase of its water volume fraction β in a linear.The new proposed dissipative mechanism leads to a US wave speed c that follows the law: c = c_w(β ? ?)^? 3/2, where c_w is the US wave speed in water and ? is the volume fraction of the bounded water.Since 0 < β < 1 and ? > 0, the hydrogel US velocity is always higher than that of pure water.If β tends to 1 (100% water), then the US speed in hydrogels converges to a higher value than that of pure water.The US speed gap at β = 1, between hydrogels and water, is the direct consequence of the introduction of the polymer network-bounded water interaction. This is in line with the experimental results that show that the US speed gap at β = 1 decreases in the gel samples with a more cross-linked polymer matrix that has a lower bounded water volume fraction.On the contrary, if the water content is very low (i.e., β < 0.4), the measured US speed converges to that of the dry hydrogel matrix which increases in the samples with a higher degree of network cross-linking with greater elastic moduli.