A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Providing quality of service via opportunistic splitting using stochastic approximation

We consider the problem of wireless channel allocation to multiple users. A slot is given to a user with a highest metric (e.g., channel gain) in that slot. The scheduler may not know the channel states of all the users at the beginning of each slot. In this scenario opportunistic splitting is an attractive solution. However this algorithm requires that the metrics of different users form independent, identically distributed (iid) sequences with same distribution and that their distribution and number be known to the scheduler. This limits the usefulness of opportunistic splitting. In this paper we develop a parametric version of this algorithm. The optimal parameters of the algorithm are learnt online through a stochastic approximation scheme. Our algorithm does not require the metrics of different users to have the same distribution. The statistics of these metrics and the number of users can be unknown and also vary with time. Each metric sequence can be Markov. We prove the convergence of the algorithm and show its utility by scheduling the channel to maximize its throughput while satisfying some fairness and/or quality of service constraints.

On the Impact of MIMO Diversity on Higher Layer Performance

In this paper, we shed light on the cross-layer interactions between the PHY, link and routing layers in networks with MIMO links operating in the diversity mode. Many previous studies assume an overly simplistic PHY layer model that does not sufficiently capture these interactions. We show that the use of simplistic models can in fact lead to misleading conclusions with regards to the higher layer performance with MIMO diversity. Towards understanding the impact of various PHY layer features on MIMO diversity, we begin with a simple but widely-used model and progressively incorporate these features to create new models. We examine the goodness of these models by comparing the simulated performance results with each, with measurements on an indoor 802.11 n testbed. Our work reveals several interesting cross-layer dependencies that affect the gains due to MIMO diversity. In particular, we observe that relative to SISO links: (a) PHY layer gains due to MIMO diversity do not always carry over to the higher layers, (b) the use of other PHY layer features such as FEC codes significantly influence the gains due to MIMO diversity, and (c) the choice of the routing metric can impact the gains possible with MIMO.

A Complete Characterization of an Optimal Timer Based Selection Scheme

Timer-based mechanisms are often used in several wireless systems to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a function of its local suitability metric. In practice, the best node gets selected successfully only if no other node's timer expires within a `vulnerability' window after its timer expiry. In this paper, we provide a complete closed-form characterization of the optimal metric-to-timer mapping that maximizes the probability of success for any probability distribution function of the metric. The optimal scheme is scalable, distributed, and much better than the popular inverse metric timer mapping. We also develop an asymptotic characterization of the optimal scheme that is elegant and insightful, and accurate even for a small number of nodes.

Opportunistic splitting for scheduling via stochastic approximation

We consider the problem of scheduling a wireless channel among multiple users. A slot is given to a user with a highest metric (e.g., channel gain) in that slot. The scheduler may not know the channel states of all the users at the beginning of each slot. In this scenario opportunistic splitting is an attractive solution. However this algorithm requires that the metrics of different users form independent, identically distributed (iid) sequences with same distribution and that their distribution and number be known to the scheduler. This limits the usefulness of opportunistic splitting. In this paper we develop a parametric version of this algorithm. The optimal parameters of the algorithm are learnt online through a stochastic approximation scheme. Our algorithm does not require the metrics of different users to have the same distribution. The statistics of these metrics and the number of users can be unknown and also vary with time. We prove the convergence of the algorithm and show its utility by scheduling the channel to maximize its throughput while satisfying some fairness and/or quality of service constraints.

Multipath routing to provide quality of service in mobile ad hoc networks

Because of frequent topology changes and node failures, providing quality of service routing in mobile ad hoc networks becomes a very critical issue. The quality of service can be provided by routing the data along multiple paths. Such selection of multiple paths helps to improve reliability and load balancing, reduce delay introduced due to route rediscovery in presence of path failures. There are basically two issues in such a multipath routing Firstly, the sender node needs to obtain the exact topology information. Since the nodes are continuously roaming, obtaining the exact topology information is a tough task. Here, we propose an algorithm which constructs highly accurate network topology with minimum overhead. The second issue is that the paths in the path set should offer best reliability and network throughput. This is achieved in two ways 1) by choice of a proper metric which is a function of residual power, traffic load on the node and in the surrounding medium 2) by allowing the reliable links to be shared between different paths.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Shock tunnel study of spiked aerodynamic bodies flying at hypersonic Mach numbers

A three-component accelerometer balance system is used to study the drag reduction effect of an aerodisc on large angle blunt cones flying at hypersonic Mach numbers. Measurements in a hypersonic shock tunnel at a freestream Mach number of 5.75 indicate more than 50% reduction in the drag coefficient for a 120degrees apex angle blunt cone with a forward facing aerospike having a flat faced aerodisc at moderate angles of attack. Enhancement of drag has been observed for higher angles of attack due to the impingement of the flow separation shock on the windward side of the cone. The flowfields around the large angle blunt cone with aerospike assembly flying at hypersonic Mach numbers are also simulated numerically using a commercial CFD code. The pressure and density levels on the model surface, which is under the aerodynamic shadow of the flat disc tipped spike, are found very low and a drag reduction of 64.34% has been deduced numerically.

Studies on a new high-intensity low-emission burner

This paper presents computational and experimental results on a new burner configuration with a mild combustion concept with heat release rates up to 10 MW/m(3). The burner configuration is shown to achieve mild combustion by using air at ambient temperature at high recirculation rates (similar to250%-290%) both experimentally and computationally. The principal features of the configuration are: (1) a burner with forward exit for exhaust gases; (2) injection of gaseous fuel and air as multiple, alternate, peripheral highspeed jets at the bottom at ambient temperature, thus creating high enough recirculation rates of the hot combustion products into fresh incoming reactants; and (3) use of a suitable geometric artifice-a frustum of a cone to help recirculation. The computational studies have been used to reveal the details of the flow and to optimize the combustor geometry based on recirculation rates. Measures, involving root mean square temperature fluctuations, distribution of temperature and oxidizer concentration inside the proposed burner, and a classical turbulent diffusion jet flame, are used to distinguish between them quantitatively. The system, operated at heat release rates of 2 to 10 MW/m(3) (compared to 0.02 to 0.32 MW/m(3) in the earlier studies), shows a 10-15 dB reduction in noise in the mild combustion mode compared to a simple open-top burner and exhaust NOx emission below 10 ppm for a 3 kW burner with 10% excess air. The peak temperature is measured around 1750 K, approximately 300 K lower than the peak temperature in a conventional burner.

Surfaces of Bounded Mean Curvature In Riemannian Manifolds

Consider a sequence of closed, orientable surfaces of fixed genus g in a Riemannian manifold M with uniform upper bounds on the norm of mean curvature and area. We show that on passing to a subsequence, we can choose parametrisations of the surfaces by inclusion maps from a fixed surface of the same genus so that the distance functions corresponding to the pullback metrics converge to a pseudo-metric and the inclusion maps converge to a Lipschitz map. We show further that the limiting pseudo-metric has fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface F subset of M, together with bounds on the geometry of M, give an upper bound on the diameter of F. Our proof is modelled on Gromov's compactness theorem for J-holomorphic curves.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier-Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier-Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Trans -> Cis isomerization of trans-[(dPPM)(2)Ru(H)(L)][BF4] (L = P(OR)(3)) Complexes: Preparation of cis-[(dppm)(2)Ru(eta(2)-H-2)(L)][BF4](2)

A series of new dicationic dihydrogen complexes of ruthenium of the type cis-[(dppm)(2)Ru(eta(2)-H-2)(L)][BF4](2) (dppm = Ph2PCH2PPh2; L = P(OMe)(3), P(OEt)(3), PF((OPr)-Pr-i)(2)) have been prepared by protonating the precursor hydride complexes cis-[(dppm)(2)Ru(H)(L)][BF4] (L = P(OMe)(3), P(OEt)(3), P((OPr)-Pr-i)(3)) using HBF4.Et2O. The cis-[(dppm)(2)Ru(H)(L)][BF4] complexes were obtained from the trans hydrides via an isomerization reaction that is acid-accelerated. This isomerization reaction gives mixtures of cis and trans hydride complexes, the ratios of which depend on the cone angles of the phosphite ligands: the greater the cone angle, the greater is the amount of the cis isomer. The eta(2)-H-2 ligand in the dihydrogen complexes is labile, and the loss of H-2 was found to be reversible. The protonation reactions of the starting hydrides with trans PMe3 or PMe2Ph yield mixtures of the cis and the trans hydride complexes; further addition of the acid, however, give trans-[(dPPM)(2)Ru(BF4)Cl]. The roles of the bite angles of the dppm ligand as well as the steric and the electronic properties of the monodentate phosphorus ligands in this series of complexes are discussed. X-ray crystal structures of trans-[(dppm)(2)Ru(H)(P(OMe)(3))][BF4], cis-[(dppm)(2)Ru-(H)(P(OMe)(3))][BF4], and cis-[(dppm)(2)Ru(H)(P((OPr)-Pr-i)(3))][BF4] complexes have been determined.

Cyclometalated complexes derived from calix[4] arene bisphosphites and their catalytic applications in cross-coupling reactions

Palladium and platinum dichloride complexes of a series of symmetrically and unsymmetrically substituted 25,26;27,28-dibridged p-tert-butyl-calix[4]arene bisphosphites in which two proximal phenolic oxygen atoms of p-tert-butyl-or p-H-calix[4]arene are connected to a P(OR) ( R = substituted phenyl) moiety have been synthesized. The palladium dichloride complexes of calix[4]arene bisphosphites bearing sterically bulky aryl substituents undergo cyclometalation by C-C or C-H bond scission. An example of cycloplatinated complex is also reported. The complexes have been characterized by NMR spectroscopic and single crystal X-ray diffraction studies. During crystallization of the palladium dichloride complex of a symmetrically substituted calix[4]arene bisphosphite in dichloromethane, insertion of oxygen occurs into the Pd-P bond to give a P,O-coordinated palladium dichloride complex. The calix[4]arene framework in these bisphosphites and their metal complexes adopt distorted cone conformation; the cone conformation is more flattened in the metal complexes than in the free calix[4]arene bisphosphites. Some of these cyclometalated complexes proved to be active catalysts for Heck and Suzuki C-C cross-coupling reactions but, on an average, the yields are only modest. (C) 2011 Elsevier B.V. All rights reserved.

End-bearing capacity of driven piles in sand using the stress characteristics method: analysis and implementation

The method of stress characteristics has been employed to compute the end-bearing capacity of driven piles. The dependency of the soil internal friction angle on the stress level has been incorporated to achieve more realistic predictions for the end-bearing capacity of piles. The validity of the assumption of the superposition principle while using the bearing capacity equation based on soil plasticity concepts, when applied to deep foundations, has been examined. Fourteen pile case histories were compiled with cone penetration tests (CPT) performed in the vicinity of different pile locations. The end-bearing capacity of the piles was computed using different methods, namely, static analysis, effective stress approach, direct CPT, and the proposed approach. The comparison between predictions made by different methods and measured records shows that the stress-level-based method of stress characteristics compares better with experimental data. Finally, the end-bearing capacity of driven piles in sand was expressed in terms of a general expression with the addition of a new factor that accounts for different factors contributing to the bearing capacity. The influence of the soil nonassociative flow rule has also been included to achieve more realistic results.

Robust MMSE Tomlinson-Harashima Precoder for Multiuser MISO Downlink with Imperfect CSI

Non-linear precoding for the downlink of a multiuser MISO (multiple-input single-output) communication system in the presence of imperfect channel state information (CSI) is considered.The base station is equipped with multiple transmit antennas and each user terminal is equipped with a single receive antenna. The CSI at the transmitter is assumed to be perturbed by an estimation error. We propose a robust minimum mean square error (MMSE) Tomlinson-Harashima precoder (THP)design, which can be formulated as an optimization problem that can be solved efficiently by the method of alternating optimization(AO). In this method of optimization, the entire set of optimization variables is partitioned into non-overlapping subsets,and an iterative sequence of optimizations on these subsets is carried out, which is often simpler compared to simultaneous optimization over all variables. In our problem, the application of the AO method results in a second-order cone program which can be numerically solved efficiently. The proposed precoder is shown to be less sensitive to imperfect channel knowledge. Simulation results illustrate the improvement in performance compared to other robust linear and non-linear precoders in the literature.