Persistence Problem in Two-Dimensional Fluid Turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Lambda to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent theta = 2.9 +/- 0.2.

Cracks emanating from pin-loaded lugs

Pin-loaded lugs were analysed in the presence of cracks emanating from circular holes. The analysis presents a unified treatment of interference, push or clearance fit pins. Both metallic (isotropic) and composite (orthotropic) plates were dealt with. The finite element model used special singular six-noded quadrilateral elements at the crack tip. The non-linear load contact behaviour at the pin-hole interface was dealt with by an inverse technique. A modified crack closure integral (MCCI) technique was used to evaluate the strain energy release rates (SERRs) and stress intensity factors (SIFs) at the crack tips. Numerical results are presented showing the non-linear variation of SIF with applied stress, and the influence of the amount of interference or clearance and the interfacial friction on SIF.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Ultrafast underdamped solvation: Agreement between computer simulation and various theories of solvation dynamics

A theoretical analysis of the three currently popular microscopic theories of solvation dynamics, namely, the dynamic mean spherical approximation (DMSA), the molecular hydrodynamic theory (MHT), and the memory function theory (MFT) is carried out. It is shown that in the underdamped limit of momentum relaxation, all three theories lead to nearly identical results when the translational motions of both the solute ion and the solvent molecules are neglected. In this limit, the theoretical prediction is in almost perfect agreement with the computer simulation results of solvation dynamics in the model Stockmayer liquid. However, the situation changes significantly in the presence of the translational motion of the solvent molecules. In this case, DMSA breaks down but the other two theories correctly predict the acceleration of solvation in agreement with the simulation results. We find that the translational motion of a light solute ion can play an important role in its own solvation. None of the existing theories describe this aspect. A generalization of the extended hydrodynamic theory is presented which, for the first time, includes the contribution of solute motion towards its own solvation dynamics. The extended theory gives excellent agreement with the simulations where solute motion is allowed. It is further shown that in the absence of translation, the memory function theory of Fried and Mukamel can be recovered from the hydrodynamic equations if the wave vector dependent dissipative kernel in the hydrodynamic description is replaced by its long wavelength value. We suggest a convenient memory kernel which is superior to the limiting forms used in earlier descriptions. We also present an alternate, quite general, statistical mechanical expression for the time dependent solvation energy of an ion. This expression has remarkable similarity with that for the translational dielectric friction on a moving ion.

Unsteady three-dimensional boundary layer flow due to a stretching surface

In this numerical study, the unsteady laminar incompressible boundary-layer flow over a continuously stretching surface has been investigated when the velocity of the stretching surface varies arbitrarily with time. Both the nodal and the saddle point regions of flow have been considered for the analysis. Also, constant wall temperature/concentration and constant heat/mass flux at the stretching surface have been taken into account. The quasilinearisation method with an implicit finite-difference scheme is used in the nodal point region (0 less-than-or-equal-to c less-than-or-equal-to 1) where c denotes the stretching ratio. This method fails in the saddle point region (-1 less-than-or-equal-to c less-than-or-equal-to 0) due to the occurrence of reverse flow in the y-component of velocity. In order to overcome this difficulty, the method of parametric differentiation with an implicit finite-difference scheme is used, where the values at c = 0 are taken as starting values. Results have been obtained for the stretching velocities which are accelerating and decelerating with time. Results show that the skin friction, the heat transfer and the mass transfer parameters respond significantly to the time dependent stretching velocities. Suction (A > 0) is found to be an important parameter in obtaining convergent solution in the case of the saddle point region of flow. The Prandtl number and the Schmidt number strongly affect the heat and mass transfer of the diffusing species, respectively.

Unsteady free convection flow under the influence of a magnetic field

The unsteady free convection boundary layer at the stagnation point of a two-dimensional body and an axisymmetric body with prescribed surface heat flux or temperature has been studied. The magnetic field is applied parallel to the surface and the effect of induced magnetic field has been considered. It is found that for certain powerlaw distribution of surface heat flux or temperature and magnetic field with time, the governing boundary layer equations admit a self-similar solution locally. The resulting nonlinear ordinary differential equations have been solved using a finite element method and a shooting method with Newton's corrections for missing initial conditions. The results show that the skin friction and heat transfer coefficients, and x-component of the induced magnetic field on the surface increase with the applied magnetic field. In general, the skin friction, heat transfer and x-component of the induced magnetic field for axisymmetric case are more than those of the two-dimensional case. Also they change more when the surface heat flux or temperature decreases with time than when it increases with time. The skin friction, heat transfer and x-component of the induced magnetic field are significantly affected by the magnetic Prandtl number and they increase as the magnetic Prandtl number decreases. The skin friction and x-component of the magnetic field increase with the dissipation parameter, but heat transfer decreases.

Glasslike elastic properties in the omega-beta alloys

We have measured the internal friction and speed of sound in several polycrystalline alloys, using compound torsional oscillators at frequencies between 60 kHz and 100 kHz and temperatures between 50 mK and 100 K. By combining these data with existing elastic and thermal data on similar alloys, we find that those alloys which can undergo diffusionsless phase transitions, such as Ti:Nb, Ti:V, or Zr:Nb in certain ranges of composition have glasslike excitations, since they have elastic properties which agree in magnitude and temperature dependence with those of amorphous solids. By contrast, crystalline continuous solution alloys, such as Nb:Ta, or alloys with diffusive phase transitions, such as high-pressure quenched Al94Si6, have the same elastic properties as are known for crystals.

Nonlinear effects on rotating disk flow in a cylindrical casing

The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration, The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.

Non-uniform slot injection (suction) or wall enthalpy into a steady nonsimilar compressible laminar boundary layer

Steady two-dimensional and axisymmetric compressible nonsimilar laminar boundary-layer flows with non-uniform slot injection (or suction) and non-uniform wall enthalpy have been studied from the starting point of the streamwise co-ordinate to the exact point of separation. The effect of different free stream Mach number has also been considered. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) or wall enthalpy are removed by choosing appropriate non-uniform slot injection (suction) or wall enthalpy. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is observed that the non-uniform slot injection moves the point of separation downstream but the non-uniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) along the streamwise co-ordinate has very little effect on the skin friction and thus on the point of separation.

Rank dependence of orientational relaxation in dipolar systems

An important yet unsolved problem in the field of orientational relaxation in dipolar liquids is the dependence of the correlation functions C(l)(t), C(l)(t) = [4pi/(2l + 1)SIGMA(m = -l)l [Y(lm)(OMEGA(0)Y(lm)(OMEGA(t))] on the rank l (where Y(lm)(OMEGA) are the usual spherical harmonics). The existing theories on this effect differ in their predictions. To investigate this, we have carried out extensive computer simulations of a Brownian dipolar lattice. The dielectric friction was found to decrease rapidly with increasing l, in qualitative agreement with the predictions of Hubbard-Wolynes. However, the observed effect is much stronger than the predictions of the existing theories.

Effect of surfactant dispersed in oil on interaction force between an oil film and a steel substrate in water

The oil phase, in an oil-in-water emulsion on a steel substrate, is strongly repelled by the substrate. The oil in this situation does not wet the steel and steel/steel friction is high. In this work we disperse anionic surfactants in an oil film and study the effect of this dispersion on the force of interaction between a silica colloid probe (AFM) carrying the oil film and a steel substrate in water. It is observed that when the surfactant is oil insoluble and the interaction time is short the strong entropic repulsion (without the surfactant) is replaced by a strong attraction. The steel on steel sliding friction in this case is low compared to that what is achieved when the surfactant is soluble in oil. The rationale underlying these interactions is explored here. (C) 2011 Elsevier B.V. All rights reserved.

Effect of anchor width on pullout capacity of strip anchors in sand

By incorporating the variation of peak soil friction angle (phi) with mean principal stress (sigma(m)), the effect of anchor width (B) on vertical uplift resistance of a strip anchor plate has been examined. The anchor was embedded horizontally in a granular medium. The analysis was performed using lower bound finite element limit analysis and linear programming. An iterative procedure, proposed recently by the authors, was implemented to incorporate the variation of phi with sigma(m). It is noted that for a given embedment ratio, with a decrease in anchor width (B), (i) the uplift factor (F-gamma) increases continuously and (ii) the average ultimate uplift pressure (q(u)) decreases quite significantly. The scale effect becomes more pronounced at greater embedment ratios.

Seepage effects on sand-bed channels

ExperimentS were conducted to find the effects of seepage on flow over a sand bed in a straight rectangular flume under two conditions: (1) When the channel bed is plane, horizontal, and nontransporting; and (2) when the bed is transporting at a constant sediment concentration. Effects of both injection and suction, caused by seepage flow into and out of the channel bed, are studied for condition 1; and only suction effects are studied for condition 2, Three sands, sizes 0.34 mm, 0.53 mm, and 0.80 mm, are used in the study. It is found that seepage can cause an increase or decrease in the bed shear stress relative to no seepage for the two conditions. The change in bed shear stress depends on the relative magnitudes of the bed shear stress and the critical shear stress of particles under the no-seepage condition, sediment concentration, and the seepage rate. Quantitative relationships giving the ratio of bed shear stresses with and without seepage are presented for both conditions of the bed. A procedure to estimate the changes in bed shear stress, friction factor, Manning's n, and stream power due to seepage for known initial conditions of the channel and the amount of applied seepage is presented

Unsteady nonsimilar two-dimensional and axisymmetric water boundary layers with variable viscosity and prandtl number

The influence of temperature-dependent viscosity and Prandtl number on the unsteady laminar nonsimilar forced convection flow over two-dimensional and axisymmetric bodies has been examined where the unsteadiness and (or) nonsimilarity are (is) due to the free stream velocity, mass transfer, and transverse curvature. The partial differential equations governing the flow which involve three independent variables have been solved numerically using an implicit finite-difference scheme along with a quasilinearization technique. It is found that both the skin friction and heat transfer strongly respond to the unsteady free stream velocity distributions. The unsteadiness and injection cause the location of zero skin friction to move upstream. However, the effect of variable viscosity and Prandtl number is to move it downstream. The heat transfer is found to depend strongly on viscous dissipation, but the skin friction is little affected by it. In general, the results pertaining to variable fluid properties differ significantly, from those of constant fluid properties.

Vertical uplift capacity of horizontal anchors

The method of characteristics coupled with a log-spiral failure surface was used to develop a theory for vertical uplift capacity of shallow horizontal strip anchors in a general c-phi soil. Uplift-capacity factors F(c), F(q) and F(gamma), for the effects of cohesion, surcharge, and density, respectively, have been established as functions of embedment ratio lambda and angle of friction phi. The extent of the failure surface at the ground has also been determined. Comparisons made with existing test results support the predictive capability of the theory, and comparisons with the analysis proposed by Meyerhof and Adams show the proposed analysis provides slightly more conservative predictions of pullout capacity.