Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Variability of sif and cod of stochastic structural systems

Stochastic structural systems having a stochastic distribution of material properties and stochastic external loadings in space are analysed when a crack of deterministic size is present. The material properties and external loadings are considered to constitute independent, two-dimensional, univariate, real, homogeneous stochastic fields. The stochastic fields are characterized by their means, variances, autocorrelation functions or the equivalent power spectral density functions, and scale fluctuations. The Young's modulus and Poisson's ratio are treated to be stochastic quantities. The external loading is treated to be a stochastic field in space. The energy release rate is derived using the method of virtual crack extension. The deterministic relationship is derived to represent the sensitivities of energy release rate with respect to both virtual crack extension and real system parameter fluctuations. Taylor series expansion is used and truncation is made to the first order. This leads to the determination of second-order properties of the output quantities to the first order. Using the linear perturbations about the mean values of the output quantities, the statistical information about the energy release rates, SIF and crack opening displacements are obtained. Both plane stress and plane strain cases are considered. The general expressions for the SIF in all the three fracture modes are derived and a more detailed analysis is conducted for a mode I situation. A numerical example is given.

Vortex sheet simulation of a plane �canonical� mixing layer

Discrete vortex simulations of the mixing layer carried out in the past have usually involved large induced velocity fluctuations, and thus demanded rather long time-averaging to obtain satisfactory values of Reynolds stresses and third-order moments. This difficulty has been traced here, in part, to the use of discrete vortices to model what in actuality are continuous vortex sheets. We propose here a novel two-dimensional vortex sheet technique for computing mixing layer flow in the limit of infinite Reynolds number. The method divides the vortex sheet into constant-strength linear elements, whose motions are computed using the Biot-Savart law. The downstream far-field is modelled by a steady vorticity distribution derived by application of conical similarity from the solution obtained in a finite computational domain. The boundary condition on the splitter plate is satisfied rigorously using a doublet sheet. The computed large-scale roll-up of the vortex sheet is qualitatively similar to experimentally obtained shadow-graphs of the plane turbulent mixing layer. The mean streamwise velocity profile and the growth rate agree well with experimental data. The presently computed Reynolds stresses and third-order moments are comparable with experimental and previous vortex-dynamical results, without using any external parameter (such as the vortex core-size) of the kind often used in the latter. The computed autocorrelations are qualitatively similar to experimental results along the top and bottom edges of the mixing layer, and show a well-defined periodicity along the centreline. The accuracy of the present computation is independently established by demonstrating negligibly small changes in the five invariants (including the Hamiltonian) in vortex dynamics.

Graphical method to determine the parameters of the two-parameter fracture model for concrete

To evaluate the parameters in the two-parameter fracture model, i.e. the critical stress intensity factor and critical crack tip opening displacement for the fracture of plain concrete in Mode 1 for the given test configuration and geometry, considerable computational effort is necessary. A simple graphical method has been proposed using normalized fracture parameters for the three-point bend (3PB) notched specimen and the double-edged notched (DEN) specimen. A similar graphical method is proposed to compute the maximum load carrying capacity of a specimen, using the critical fracture parameters both for 3PB and DEN configurations.

Highly Efficient and Thermally Stable Second-Order Nonlinear Optical Chromophores and Electrooptic Polymers

Organic polymeric electro-optic (E-O) materials have attracted significant attention because of their potential use as fast and efficient components of integrated photonic devices (1,2). However, the practical application of these materials in optical devices is somewhat limited by the stringent material requirements imposed by the device design, fabrication processes and operating environments. Among the various material requirements, the most notable ones are large electro-optic coefficients (r(33)) and high thermal stability (3). The design of poled polymeric materials with high electro-optic activity (r(33)) involves the optimization of the percent incorporation of efficient (large beta mu) second order nonlinear optical (NLO) chromophores into the polymer matrices and the effective creation of poling-induced non-centrosymmetric structures. The factors that affect the material stability are a) the inherent thermal stability of the NLO chromophores, b) the chemical stability of the NLO chromophores during the polymer processing conditions, and c) the long-term dipolar alignment stability at high temperatures. Although considerable progress has been made in achieving these properties (4), organic polymeric materials suitable for practical E-O device applications are yet to be developed. This chapter highlights some of our approaches in the optimization of molecular and material nonlinear optical and thermal properties.

Nonequilibrium phase transitions in a driven sandpile model

We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope sigma(c), a parameter alpha, governing the local current-slope relation (beyond threshold), and j(in), the mean input current of sand. A non-equilibrium phase diagram is obtained in the alpha-j(in) plane. We find an infinity of phases, characterized by different mean slopes and separated by continuous or first-order boundaries, some of which we obtain analytically. Extensions to two dimensions are discussed.z

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.

Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics

In this paper, the critical budding temperature of single-walled carbon nanotubes (SWCNTs), which are embedded in one-parameter elastic medium (Winkler foundation) is estimated under the umbrella of continuum mechanics theory. Nonlocal continuum theory is incorporated into Timoshenko beam model and the governing differential equations of motion are derived. An explicit expression for the non-dimensional critical buckling temperature is also derived in this work. The effect of the nonlocal small scale coefficient, the Winkler foundation parameter and the ratio of the length to the diameter on the critical buckling temperature is investigated in detail. It can be observed that the effects of nonlocal small scale parameter and the Winkler foundation parameter are significant and should be considered for thermal analysis of SWCNTs. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the thermal buckling properties of embedded single-walled carbon nanotubes. (C) 2011 Elsevier B.V. All rights reserved.

Metamorphic-metasomatic fluids and Al, Si order/disorder of K-rich alkali feldspars from southern Indian high grade terrain

The structural state of K-feldspars in the quartzofeldspathic gneisses, charnockites, metapelites and pegmatites from the southern Kamataka, northern Tamil Nadu and southern Kerala high-grade regions of southern India has been characterized using petrographic and powder X-ray diffraction methods. The observed distribution pattern of structural state with a preponderance of disordered K-feldspar polymorphs in granulites compared to the ordered microclines in the amphibolite facies rocks is interpreted to reflect principally the varying H2O contents in the metamorphic-metasomatic fluids across metamorphic grade. The K-feldspars in the pegmatites of granitic derivation and in a pegmatite of inferred metamorphic origin also point to the important role of aqueous fluids in their structural state.

Velocity distribution function for a dilute granular material in shear flow

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle-wall collisions is large compared to particle-particle collisions. An asymptotic analysis is used in the small parameter epsilon, which is naL in two dimensions and na(2)L in three dimensions, where; n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle-wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution e(t) and e(n) in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (u(x), u(y)) = (+/-V, O) after repeated collisions with the wall, where u(x) and u(y) are the velocities tangential and normal to the wall, V = (1 - e(t))V-w/(1 + e(t)), and V-w and -V-w, are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions :in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to epsilon(1/2) in the limit epsilon --> 0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to epsilon(1/2) in the limit epsilon --> 0. The moments of the velocity distribution function are evaluated, and it is found that [u(x)(2)] --> V-2, [u(y)(2)] similar to V-2 epsilon and -[u(x)u(y)] similar to V-2 epsilon log(epsilon(-1)) in the limit epsilon --> 0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Hidden order in serrated flow of metallic glasses

We report results of statistical and dynamic analysis of the serrated stress-time curves obtained from compressive constant strain-rate tests on two metallic glass samples with different ductility levels in an effort to extract hidden information in the seemingly irregular serrations. Two distinct types of dynamics are detected in these two alloy samples. The stress-strain curve corresponding to the less ductile Zr65Cu15Ni10Al10 alloy is shown to exhibit a finite correlation dimension and a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. In contrast, for the more ductile Cu47.5Zr47.5Al5 alloy, the distributions of stress drop magnitudes and their time durations obey a power-law scaling reminiscent of a self-organized critical state. The exponents also satisfy the scaling relation compatible with self-organized criticality. Possible physical mechanisms contributing to the two distinct dynamic regimes are discussed by drawing on the analogy with the serrated yielding of crystalline samples. The analysis, together with some physical reasoning, suggests that plasticity in the less ductile sample can be attributed to stick-slip of a single shear band, while that of the more ductile sample could be attributed to the simultaneous nucleation of a large number of shear bands and their mutual interactions. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Physical interpretation of the Poynting-Robertson effect

Although the prevalent mathematical description of the Poynting-Robertson effect is correct, its physical interpretation is sometimes problematic. By means of a two-parameter model, we revisit the effect in order to get a better physical understanding of it. The principal conclusion is that the motion of a dust in circumsolar orbit is governed only by solar radiation absorption and not by the asymmetry of reemission, even when viewed in the rest-frame of the Sun. (C) 1999 Academic Press.

Resent radar observations of asteroid 1566 Icarus

We report Doppler-only radar observations of Icarus at Goldstone at a transmitter frequency of 8510 MHz (3.5 cm wavelength) during 8-10 June 1996, the first radar detection of the object since 1968. Optimally filtered and folded spectra achieve a maximum opposite-circular (OC) polarization signal-to-noise ratio of about 10 and help to constrain Icarus' physical properties. We obtain an OC radar cross section of 0.05 km(2) (with a 35% uncertainty), which is less than values estimated by Goldstein (1969) and by Pettengill et al. (1969), and a circular polarization (SC/OC) ratio of 0.5+/-0.2. We analyze the echo power spectrum with a model incorporating the echo bandwidth B and a spectral shape parameter it, yielding a coupled constraint between B and n. We adopt 25 Hz as the lower bound on B, which gives a lower bound on the maximum pole-on breadth of about 0.6 km and upper bounds on the radar and optical albedos that are consistent with Icarus' tentative QS classification. The observed circular polarization ratio indicates a very rough near-surface at spatial scales of the order of the radar wavelength. (C) 1999 Elsevier Science Ltd. All rights reserved.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.