Construction of solid model from measured point data

This paper describes an algorithm for constructing the solid model (boundary representation) from pout data measured from the faces of the object. The poznt data is assumed to be clustered for each face. This algorithm does not require any compuiier model of the part to exist and does not require any topological infarmation about the part to be input by the user. The property that a convex solid can be constructed uniquely from geometric input alone is utilized in the current work. Any object can be represented a5 a combznatzon of convex solids. The proposed algorithm attempts to construct convex polyhedra from the given input. The polyhedra so obtained are then checked against the input data for containment and those polyhedra, that satisfy this check, are combined (using boolean union operation) to realise the solid model. Results of implementation are presented.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Experimental studies of a distorted turbulent spot in a three-dimensional flow

We report here on the results of a series of experiments carried out on a turbulent spot in a distorted duct to study the effects of a divergence with straight streamlines preceded by a short stretch of transverse streamline curvature, both in the absence of any pressure gradient. It is found that the distortion produces substantial asymmetry in the spot: the angles at which the spot cuts across the local streamlines are altered dramatically (in contradiction of a hypothesis commonly made in transition zone modelling), and the Tollmien-Schlichting waves that accompany the wing tips of the spot are much stronger on the outside of the bend than on the inside. However there is no strong effect on the internal structure of the spot and the eddies therein, or on such propagation characteristics as overall spread rate and the celerities of the leading and trailing edges. Both lateral streamline curvature and non-homogeneity of the laminar boundary layer into which the spot propagates are shown to be strong factors responsible for the observed asymmetry. It is concluded that these factors produce chiefly a geometric distortion of the coherent structure in the spot, but do not otherwise affect its dynamics in any significant way.

Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation

Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e(0)), (ii) e(0) is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e(0) is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e(0) in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit. (C) 2011 Elsevier Ltd. All rights reserved.

Effect of laser processing parameters on the structure of ductile iron

Laser processing of structure sensitive hypereutectic ductile iron, a cast alloy employed for dynamically loaded automative components, was experimentally investigated over a wide range of process parameters: from power (0.5-2.5 kW) and scan rate (7.5-25 mm s(-1)) leading to solid state transformation, all the way through to melting followed by rapid quenching. Superfine dendritic (at 10(5) degrees C s(-1)) or feathery (at 10(4) degrees C s(-1)) ledeburite of 0.2-0.25 mu m lamellar space, gamma-austenite and carbide in the laser melted and martensite in the transformed zone or heat-affected zone were observed, depending on the process parameters. Depth of geometric profiles of laser transformed or melt zone structures, parameters such as dendrile arm spacing, volume fraction of carbide and surface hardness bear a direct relationship with the energy intensity P/UDb2, (10-100 J mm(-3)). There is a minimum energy intensity threshold for solid state transformation hardening (0.2 J mm(-3)) and similarly for the initiation of superficial melting (9 J mm(-3)) and full melting (15 J mm(-3)) in the case of ductile iron. Simulation, modeling and thermal analysis of laser processing as a three-dimensional quasi-steady moving heat source problem by a finite difference method, considering temperature dependent energy absorptivity of the material to laser radiation, thermal and physical properties (kappa, rho, c(p)) and freezing under non-equilibrium conditions employing Scheil's equation to compute the proportion of the solid enabled determination of the thermal history of the laser treated zone. This includes assessment of the peak temperature attained at the surface, temperature gradients, the freezing time and rates as well as the geometric profile of the melted, transformed or heat-affected zone. Computed geometric profiles or depth are in close agreement with the experimental data, validating the numerical scheme.

Free convection in power-law fluids near a three-dimensional stagnation point

Numerical results are presented for the free-convection boundary-layer equations of the Ostwald de-Waele non-Newtonian power-law type fluids near a three-dimensional (3-D) stagnation point of attachment on an isothermal surface. The existence of dual solutions that are three-dimensional in nature have been verified by means of a numerical procedure. An asymptotic solution for very large Prandtl numbers has also been derived. Solutions are presented for a range of values of the geometric curvature parameter c, the power-law index n, and the Prandtl number Pr.

Surface-ray tracing solution of ellipsoid of revolution for UTD mutual coupling applications

An analytical surface-ray tracing has been carried out for the prolate ellipsoid of revolution using a novel geodesic constant method. This method yields closed form expressions for all the ray-geometric parameters required for the UTD mutual coupling calculations for the antennas located arbitrarily in three dimensions, on the ellipsoid of revolution.

Optimal control of arrivals to queues with delayed queue length information

We consider discrete-time versions of two classical problems in the optimal control of admission to a queueing system: i) optimal routing of arrivals to two parallel queues and ii) optimal acceptance/rejection of arrivals to a single queue. We extend the formulation of these problems to permit a k step delay in the observation of the queue lengths by the controller. For geometric inter-arrival times and geometric service times the problems are formulated as controlled Markov chains with expected total discounted cost as the minimization objective. For problem i) we show that when k = 1, the optimal policy is to allocate an arrival to the queue with the smaller expected queue length (JSEQ: Join the Shortest Expected Queue). We also show that for this problem, for k greater than or equal to 2, JSEQ is not optimal. For problem ii) we show that when k = 1, the optimal policy is a threshold policy. There are, however, two thresholds m(0) greater than or equal to m(1) > 0, such that mo is used when the previous action was to reject, and mi is used when the previous action was to accept.

Structure–property relationship in superconducting cuprates

An examination of the structure and superconducting properties of the various families of cuprates suggests several interesting structural commonalities. Relations between some of the structural parameters of the cuprates and the superconducting transition temperature, T-c, provide useful insights. Variations of T-c on the hole concentration, the in-plane Cu-O and the apical Cu-O distances, as well as the Madelung potentials and bond valence sums are particularly noteworthy. The Cu-O charge-transfer energy appears to be fundamental in determining the properties of cuprates.

Large deformation finite element analysis of laminated circular composite plates

A 48 d.o.f., four-noded quadrilateral laminated composite shell finite element is particularised to a sector finite element and is used for the large deformation analysis of circular composite laminated plates. The strain-displacement relationships for the sector element are obtained by reducing those of the quadrilateral shell finite element by substituting proper values for the geometric parameters. Subsequently, the linear and tangent stiffness matrices are formulated using conventional methods. The Newton-Raphson method is employed as the nonlinear solution technique. The computer code developed is validated by solving an isotropic case for which results are available in the literature. The method is then applied to solve problems of cylindrically orthotropic circular plates. Some of the results of cylindrically orthotropic case are compared with those available in the literature. Subsequently, application is made to the case of laminated composite circular plates having different lay-up schemes. The computer code can handle symmetric/unsymmetric lay-up schemes. The large displacement analysis is useful in estimating the damage in composite plates caused by low-velocity impact.

Common underlying steering curves for motorcycles in steady turns

We study the steady turn behaviours of some light motorcycle models on circular paths, using the commercial software package ADAMS-Motorcycle. Steering torque and steering angle are obtained for several path radii and a range of steady forward speeds. For path radii much greater than motorcycle wheelbase, and for all motorcycle parameters including tyre parameters held fixed, dimensional analysis can predict the asymptotic behaviour of steering torque and angle. In particular, steering torque is a function purely of lateral acceleration plus another such function divided by path radius. Of these, the first function is numerically determined, while the second is approximated by an analytically determined constant. Similarly, the steering angle is a function purely of lateral acceleration, plus another such function divided by path radius. Of these, the first is determined numerically while the second is determined analytically. Both predictions are verified through ADAMS simulations for various tyre and geometric parameters. In summary, steady circular motions of a given motorcycle with given tyre parameters can be approximately characterised by just one curve for steering torque and one for steering angle.

Piezoelectrically stimulated dielectric dispersion in KAP single crystals

The frequency response of the dielectric constant (epsilon(r)), the loss tangent (tan delta) and impedance Z of potassium acid phthalate (KAP) single crystals, monitored along the polar axis, exhibit strong resonances in the frequency range 50-200 kHz, depending on the dimensions of the sample. The observed resonance effect, which is strongly dependent on the geometric shape and size of the sample, is attributed to its piezoelectric nature. The resonance peak positions have been monitored as a function of both temperature and uniaxial pressure. The stiffness coefficient (C), computed based on the resonance data, is found to decrease with increasing temperature and increase with increasing pressure. The electro-mechanical coupling coefficient (k), obtained by resonance-anti-resonance method, has also been found to increase with rise in temperature. The epsilon(r) behaviour along the polar axis, as a function of temperature is consistent with that of k. The preliminary results on the influence, of partial replacement of K+ ions in the KAP crystal by Cs+ and Li+ ions, on the observed piezoelectric resonance effects are also included.

Recommendations for driver licensing and traffic law enforcement in India aiming to improve road safety

During the last decade, developing countries such as India have been exhibiting rapid increase in human population and vehicles, and increase in road accidents. Inappropriate driving behaviour is considered one of the major causes of road accidents in India as compared to defective geometric design of pavement or mechanical defects in vehicles. It can result in conditions such as lack of lane discipline, disregard to traffic laws, frequent traffic violations, increase in crashes due to self-centred driving, etc. It also demotivates educated drivers from following good driving practices. Hence, improved driver behaviour can be an effective countermeasure to reduce the vulnerability of road users and inhibit crash risks. This article highlights improved driver behaviour through better driver education, driver training and licensing procedures along with good on-road enforcement; as an effective countermeasure to ensure road safety in India. Based on the review and analysis, the article also recommends certain measures pertaining to driver licensing and traffic law enforcement in India aimed at improving road safety.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Volume modelling for emerging manufacturing technologies

The next generation manufacturing technologies will draw on new developments in geometric modelling. Based on a comprehensive analysis of the desiderata of next generation geometric modellers, we present a critical review of the major modelling paradigms, namely, CSG, B-Rep, non-manifold, and voxel models. We present arguments to support the view that voxel-based modellers have attributes that make it the representation scheme of choice in meeting the emerging requirements of geometric modelling.