Non-conservatively loaded stochastic columns

A new finite element method is developed to analyse non-conservative structures with more than one parameter behaving in a stochastic manner. As a generalization, this paper treats the subsequent non-self-adjoint random eigenvalue problem that arises when the material property values of the non-conservative structural system have stochastic fluctuations resulting from manufacturing and measurement errors. The free vibration problems of stochastic Beck's column and stochastic Leipholz column whose Young's modulus and mass density are distributed stochastically are considered. The stochastic finite element method that is developed, is implemented to arrive at a random non-self-adjoint algebraic eigenvalue problem. The stochastic characteristics of eigensolutions are derived in terms of the stochastic material property variations. Numerical examples are given. It is demonstrated that, through this formulation, the finite element discretization need not be dependent on the characteristics of stochastic processes of the fluctuations in material property value.

A novel property of an Auto-Correlation Sequence and some Applications

In this article, we use some spectral properties of polynomials presented in 1] and map an auto-correlation sequence to a set of Line Spectral Frequencies(LSFs) and reflection coefficients. This novel characterization of an auto-correlation sequence is used to obtain a lattice structure of a Linear-Phase(LP) FIR filter.

FIR system identification based on subspaces of a higher order cumulant matrix

A new linear algebraic approach for identification of a nonminimum phase FIR system of known order using only higher order (>2) cumulants of the output process is proposed. It is first shown that a matrix formed from a set of cumulants of arbitrary order can be expressed as a product of structured matrices. The subspaces of this matrix are then used to obtain the parameters of the FIR system using a set of linear equations. Theoretical analysis and numerical simulation studies are presented to characterize the performance of the proposed methods.

Violin string shape functions for finite element analysis of rotating Timoshenko beams

Violin strings are relatively short and stiff and are well modeled by Timoshenko beam theory. We use the static part of the homogeneous differential equation of violin strings to obtain new shape functions for the finite element analysis of rotating Timoshenko beams. For deriving the shape functions, the rotating beam is considered as a sequence of violin strings. The violin string shape functions depend on rotation speed and element position along the beam length and account for centrifugal stiffening effects as well as rotary inertia and shear deformation on dynamic characteristics of rotating Timoshenko beams. Numerical results show that the violin string basis functions perform much better than the conventional polynomials at high rotation speeds and are thus useful for turbo machine applications. (C) 2011 Elsevier B.V. All rights reserved.

Proof of a conjecture of Frankl and Furedi

We give a simple linear algebraic proof of the following conjecture of Frankl and Furedi [7, 9, 13]. (Frankl-Furedi Conjecture) if F is a hypergraph on X = {1, 2, 3,..., n} such that 1 less than or equal to /E boolean AND F/ less than or equal to k For All E, F is an element of F, E not equal F, then /F/ less than or equal to (i=0)Sigma(k) ((i) (n-1)). We generalise a method of Palisse and our proof-technique can be viewed as a variant of the technique used by Tverberg to prove a result of Graham and Pollak [10, 11, 14]. Our proof-technique is easily described. First, we derive an identity satisfied by a hypergraph F using its intersection properties. From this identity, we obtain a set of homogeneous linear equations. We then show that this defines the zero subspace of R-/F/. Finally, the desired bound on /F/ is obtained from the bound on the number of linearly independent equations. This proof-technique can also be used to prove a more general theorem (Theorem 2). We conclude by indicating how this technique can be generalised to uniform hypergraphs by proving the uniform Ray-Chaudhuri-Wilson theorem. (C) 1997 Academic Press.

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.

Microwave heating in multiphase systems: evaluation of series solutions

The 1D electric field and heat-conduction equations are solved for a slab where the dielectric properties vary spatially in the sample. Series solutions to the electric field are obtained for systems where the spatial variation in the dielectric properties can be expressed as polynomials. The series solution is used to obtain electric-field distributions for a binary oil-water system where the dielectric properties are assumed to vary linearly within the sample. Using the finite-element method temperature distributions are computed in a three-phase oil, water and rock system where the dielectric properties vary due to the changing oil saturation in the rock. Temperature distributions predicted using a linear variation in the dielectric properties are compared with those obtained using the exact nonlinear variation.

Thermodynamic analysis of enzyme catalysed reactions: new insights into the Michaelis-Menten equation

A simple thermodynamic analysis of the well-known Michaelis-Menten equation (MME) of enzyme catalysis is proposed that employs the chemical potential mu to follow the Gibbs free energy changes attending the formation of the enzyme-substrate complex and its turnover to the product. The main conclusion from the above analysis is that low values of the Michaelis constant KM and high values of the turnover number k(cat) are advantageous: this supports a simple algebraic analysis of the MME, although at variance with current thinking. Available data apparently support the above findings. It is argued that transition state stabilisation - rather than substrate distortion or proximity - is the key to enzyme catalysis.

A new beam finite element for the analysis of functionally graded materials

A new beam element is developed to study the thermoelastic behavior of functionally graded beam structures. The element is based on the first-order shear deformation theory and it accounts for varying elastic and thermal properties along its thickness. The exact solution of static part of the governing differential equations is used to construct interpolating polynomials for the element formulation. Consequently, the stiffness matrix has super-convergent property and the element is free of shear locking. Both exponential and power-law variations of material property distribution are used to examine different stress variations. Static, free vibration and wave propagation problems are considered to highlight the behavioral difference of functionally graded material beam with pure metal or pure ceramic beams. (C) 2003 Elsevier Science Ltd. All rights reserved.

Magnetic properties and specific heat of LaMn1-xTixO3+delta (0 < x <= 0.2)

We present a magnetic study of the insulating perovskite LaMn1-xTixO3+delta (0algebraic functional form for times up to 2 h. The specific heat also displays characteristic features of a spin-glass system by a linear low-temperature dependence and a broadened peak near the temperature of the reentrant transition. (C) 2002 Elsevier Science B.V. All rights reserved.

Hardware implementation of 4x4 DCT/Quantization block using multiplication and error-free algorithm

The 4ÃÂ4 discrete cosine transform is one of the most important building blocks for the emerging video coding standard, viz. H.264. The conventional implementation does some approximation to the transform matrix elements to facilitate integer arithmetic, for which hardware is suitably prepared. Though the transform coding does not involve any multiplications, quantization process requires sixteen 16-bit multiplications. The algorithm used here eliminates the process of approximation in transform coding and multiplication in the quantization process, by usage of algebraic integer coding. We propose an area-efficient implementation of the transform and quantization blocks based on the algebraic integer coding. The designs were synthesized with 90 nm TSMC CMOS technology and were also implemented on a Xilinx FPGA. The gate counts and throughput achievable in this case are 7000 and 125 Msamples/sec.

Sliding mode control-based algorithms for consensus in connected swarms

In this article, finite-time consensus algorithms for a swarm of self-propelling agents based on sliding mode control and graph algebraic theories are presented. Algorithms are developed for swarms that can be described by balanced graphs and that are comprised of agents with dynamics of the same order. Agents with first and higher order dynamics are considered. For consensus, the agents' inputs are chosen to enforce sliding mode on surfaces dependent on the graph Laplacian matrix. The algorithms allow for the tuning of the time taken by the swarm to reach a consensus as well as the consensus value. As an example, the case when a swarm of first-order agents is in cyclic pursuit is considered.

Redundancy resolution using a tractrix and its application to real-time simulations of hyper-redundant manipulators, snakes and tying of knots

To realistically simulate the motion of flexible objects such as ropes, strings, snakes, or human hair,one strategy is to discretise the object into a large number of small rigid links connected by rotary or spherical joints. The discretised system is highly redundant and the rotations at the joints (or the motion of the other links) for a desired Cartesian motion of the end of a link cannot be solved uniquely. In this paper, we propose a novel strategy to resolve the redundancy in such hyper-redundant systems.We make use of the classical tractrix curve and its attractive features. For a desired Cartesian motion of the `head'of a link, the `tail' of the link is moved according to a tractrix,and recursively all links of the discretised objects are moved along different tractrix curves. We show that the use of a tractrix curve leads to a more `natural' motion of the entire object since the motion is distributed uniformly along the entire object with the displacements tending to diminish from the `head' to the `tail'. We also show that the computation of the motion of the links can be done in real time since it involves evaluation of simple algebraic, trigonometric and hyperbolic functions. The strategy is illustrated by simulations of a snake, tying of knots with a rope and a solution of the inverse kinematics of a planar hyper-redundant manipulator.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

A Kinematic Theory for Planar Hoberman and Other Novel Foldable Mechanisms

In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory.