Lifting the singular nature of a model for peeling of an adhesive tape

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. Due to the constraint between the pull force, peel angle and the peel force, the equations of motion derived earlier fall into the category of differential-algebraic equations (DAE) requiring an appropriate algorithm for its numerical solution. By including the kinetic energy arising from the stretched part of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics itself, thus circumventing the need to use any special algorithm. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier singular equations. We find that mass has a strong influence on the dynamics of the model rendering periodic solutions to chaotic and vice versa. Apart from the rich dynamics, the model reproduces several qualitative features of the different waveforms of the peel force function as also the decreasing nature of force drop magnitudes.

Disk-Outflow Coupling: Energetics Around Spinning BlacK Holes

The mechanism by which outflows and plausible jets are driven from black hole systems still remains observationally elusive. This notwithstanding, several observational evidences and deeper theoretical insights reveal that accretion and outflow/jet are strongly correlated. We model an advective disk-outflow coupled dynamics, incorporating explicitly the vertical flux. Inter-connecting dynamics of outflow andaccretion essentially upholds the conservation laws. We investigate the properties of the disk-outflow surface and its strong dependence on the rotation parameter of the black hole. The energetics of the disk outflow strongly depend on the mass, accretion rate, and spin of the black holes. The model clearly shows that the outflow power extracted from the disk increases strongly with the spin of the black hole, inferring that the power of the observed astrophysical jets has a proportional correspondence with the spin of the central object. In the case of blazars (BL Lacs and flat spectrum radio quasars, FSRQs), most of their emission are believed to be originated from their jets. It is observed that BL Lacs are relatively low luminous than FSRQs. The luminosity might be linked to the power of the jet, which in turn reflects that the nuclear regions of the BL Lac objects have a relatively low spinning black hole compared to that in the case of FSRQs. If extreme gravity is the source that powers strong outflows and jets, then the spin of the black hole, perhaps, might be the fundamental parameter to account for the observed astrophysical processes in an accretion powered system.

Dry sliding wear behavior of Al2O3 fiber reinforced aluminum composites

Dry sliding wear behavior of die-cast ADC12 aluminum alloy composites reinforced with short alumina fibers were investigated by using a pin-on-disk wear tester. The Al2O3 fibers were 4 mu m in diameter and were present in volume fractions (T-f)ranging from 0.03 to 0.26, The length of the fiber varied from 40 to 200 mu m. Disks of aluminum-alumina composites were rubbed against a pin of nitrided stainless steel SUS440B with a load of 10 N at a sliding velocity of 0.1 m/s. The unreinforced ADC 12 aluminum alloy and their composites containing low volume fractions of alumina (V-f approximate to 0.05) showed a sliding-distance-dependent transition from severe to mild wear. However, composites containing high volume fractions of alumina ( V-f > 0.05) exhibited only mild wear for all sliding distances. The duration of occurrence of the severe wear regime and the wear rate both decrease with increasing volume fraction. In MMCs the wear rate in the mild wear regime decreases with increase in volume fraction: reaching a minimum value at V-f = 0.09 Beyond V-f = 0.09 the wear rate increasesmarginally. On the other hand, the wear rate of the counterface (steel pin) was found to increase moderately with increase in V-f. From the analysis of wear data and detailed examination of (a) worn surfaces, (b) their cross-sections and (c) wear debris, two modes of wear mechanisms have been identified to be operative, in these materials and these are: (i) adhesive wear in the case of unreinforced matrix material and in MMCs with low Vf and (ii) abrasive wear in the case of MMCs with high V-f. (C) 2000 Elsevier Science Ltd. All rights reserved.

Behaviour of Bi-adhesive Joints

The use of relatively low modulus adhesive at the ends of overlap in a bi-adhesive bondline of a bonded joint can reduce the stress concentration significantly and, therefore, potentially lead to higher strength of the joint. This study presents the two-dimensional and three-dimensional nonlinear (geometric and material) finite element analyses of adhesively bonded single lap joints having modulus-graded bondline under monotonic loading conditions. The adhesives were modelled as an elasto-plastic multi-linear material, while the substrates were regarded as both linear elastic and bi-linear elasto-plastic material. The computational simulations have been performed to investigate the bondline behaviour by studying the stress and strain distributions both at the mid-plane as well as at the interface of the bondline. It has been observed that the static strength is higher for joints with bi-adhesive bondlines compared to those with single adhesives in bondline. Higher joint strength has also been observed for optimum bi-adhesive bondline ratio through parametric studies. Effects of load level, and bondline thickness on stress distribution in the bi-adhesive bondline have also been studied. 3D analysis results reveal the existence of complex multi-axial stress/strain state at the ends of the overlap in the bondline which cannot be observed in 2D plane strain analysis. About 1/3rd of the width of the joint from the free edge in the width direction has 3D stress state, especially in the compliant adhesive of the bondline. Magnitudes of longitudinal and lateral stress/strain components are comparable to peel stress/strain components. It has also been analytically shown that the in-plane global stiffness of the joint remains unaffected by modulus gradation of the bondline adhesive. (C) Koninklijke Brill NV, Leiden, 2010.

Influence of viscoelastic nature on the intermittent peel-front dynamics of adhesive tape

We investigate the influence of viscoelastic nature of the adhesive on the intermittent peel front dynamics by extending a recently introduced model for peeling of an adhesive tape. As time and rate-dependent deformation of the adhesives are measured in stationary conditions, a crucial step in incorporating the viscoelastic effects applicable to unstable intermittent peel dynamics is the introduction of a dynamization scheme that eliminates the explicit time dependence in terms of dynamical variables. We find contrasting influences of viscoelastic contribution in different regions of tape mass, roller inertia, and pull velocity. As the model acoustic energy dissipated depends on the nature of the peel front and its dynamical evolution, the combined effect of the roller inertia and pull velocity makes the acoustic energy noisier for small tape mass and low-pull velocity while it is burstlike for low-tape mass, intermediate values of the roller inertia and high-pull velocity. The changes are quantified by calculating the largest Lyapunov exponent and analyzing the statistical distributions of the amplitudes and durations of the model acoustic energy signals. Both single and two stage power-law distributions are observed. Scaling relations between the exponents are derived which show that the exponents corresponding to large values of event sizes and durations are completely determined by those for small values. Th scaling relations are found to be satisfied in all cases studied. Interestingly, we find only five types of model acoustic emission signals among multitude of possibilities of the peel front configurations.

An unsteady flow due to eccentrically rotating porous disk and a fluid at infinity

An exact solution of the unsteady Navier-Stokes equations is obtained for the flow due to non-coaxial rotations of a porous disk, executing non-torsional oscillations in its own plane, and a fluid at infinity. It is shown that the infinite number of solutions existing for a flow confined between two disks reduce to a single unique solution in the case of a single disk. The adjustment of the unsteady flow near the rotating disk to the flow at infinity rotating about a different axis is explained.

Analysing local algorithms in location-aware quasi-unit-disk graphs

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.

Compressive tidal heating of a disk galaxy in a rich cluster

The restricted three-body method is used to model the effect of the mean tidal field of a cluster of galaxies on the internal dynamics of a disk galaxy falling into the cluster for the first time. In the model adopted the galaxy experiences a tidal field that is compressive within the core of the cluster. The planar random velocities of all components in the disk increase after the galaxy passes through the core of the cluster. The low-velocity dispersion gas clouds experience a relatively larger increase in random velocity than the hotter stellar components. The increase in planar velocities results in a strong anisotropy between the planar and vertical velocity dispersions. It is argued that this will make the disk unstable to the 'fire-hose instability' which leads to bending modes in the disk and which will thicken the disk slightly. The mean tidal fields in rich clusters were probably stronger during the epoch of cluster formation and relaxation than they are in present-day relaxed clusters.

Nonaxisymmetric unsteady motion over a rotating disk in the presence of free convection and magnetic field

The nonaxisymmetric unsteady motion produced by a buoyancy-induced cross-flow of an electrically conducting fluid over an infinite rotating disk in a vertical plane and in the presence of an applied magnetic field normal to the disk has been studied. Both constant wall and constant heat flux conditions have been considered. It has been found that if the angular velocity of the disk and the applied magnetic field squared vary inversely as a linear function of time (i.e. as (1??t*)?1, the governing Navier-Stokes equation and the energy equation admit a locally self-similar solution. The resulting set of ordinary differential equations has been solved using a shooting method with a generalized Newton's correction procedure for guessed boundary conditions. It is observed that in a certain region near the disk the buoyancy induced cross-flow dominates the primary von Karman flow. The shear stresses induced by the cross-flow are found to be more than these of the primary flow and they increase with magnetic parameter or the parameter ? characterizing the unsteadiness. The velocity profiles in the x- and y-directions for the primary flow at any two values of the unsteady parameter ? cross each other towards the edge of the boundary layer. The heat transfer increases with the Prandtl number but reduces with the magnetic parameter.

Transient Flow of a Compressible Viscous Fluid Near an Infinite Disk

We have consider ed the transient motion of art electrically conducting viscous compressible fluid which is in contact with an insulated infinite disk. The initial motion is considered to be due to the uniform rotation of the disk in an otherwise stationary fluid or due to the uniform rigid rotation of the fluid over a stationary disk. Different cases of transient motion due to finite impulse imparted either to the disk or to the distant fluid have been investigated. Effects of the imposed axial magnetic field and the disk temperature on the transient flow are included. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite-difference scheme along with the Newton's linearisation technique.

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.

Unsteady compressible flow due to relative rotation and translation of a viscous fluid on a disk

The modification of the axisymmetric viscous flow due to relative rotation of the disk or fluid by a translation of the boundary is studied. The fluid is taken to be compressible, and the relative rotation and translation velocity of the disk or fluid are time-dependent. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite difference scheme and Newton's linearisation technique. Numerical solutions are obtained at various non-dimensional times and disk temperatures. The non-symmetric part of the flow (secondary flow) describing the translation effect generates a velocity field at each plane parallel to the disk. The cartesian components of velocity due to secondary flow exhibit oscillations when the motion is due to rotation of the fluid on a translating disk. Increase in translation velocity produces an increment in the radial skin friction but reduces the tangential skin friction.

Flow induced by an asymmetrically placed disk rotating coaxially inside a cylindrical casing

In this paper, the flow due to a rotating disk non-symmetrically placed with respect to the height of the enclosing stationary cylinder is analyzed numerically. The full Navier-Stokes equations expressed in terms of stream function and vorticity are solved by successive over-relaxation for different disk radii, its distance from the bottom casing and rotational Reynolds numbers. It is observed that the flow pattern is strongly influenced by the size and the position of the disk. When the disk is very close to the top casing and small in radius, there are two regions of different scales and the vortices in the region of small scale are trapped between the disk and the top casing. Further, the variation of the moment coefficient is determined for different positions and sizes of the rotating disk. The calculations shows that the frictional torque increases rapidly, when the disk approaches the top casing. This finding is of importance for the design of vertical rotating disk reactors applied in chemical vapor deposition.