Analytical and simulation studies of a multiprocessor system for high-speed numerical computations

This paper describes the architecture of a multiprocessor system which we call the Broadcast Cube System (BCS) for solving important computation intensive problems such as systems of linear algebraic equations and Partial Differential Equations (PDEs), and highlights its features. Further, this paper presents an analytical performance study of the BCS, and it describes the main details of the design and implementation of the simulator for the BCS.

A study of symbolic processing and computational aspects in helicopter dynamics

Even research models of helicopter dynamics often lead to a large number of equations of motion with periodic coefficients; and Floquet theory is a widely used mathematical tool for dynamic analysis. Presently, three approaches are used in generating the equations of motion. These are (1) general-purpose symbolic processors such as REDUCE and MACSYMA, (2) a special-purpose symbolic processor, DEHIM (Dynamic Equations for Helicopter Interpretive Models), and (3) completely numerical approaches. In this paper, comparative aspects of the first two purely algebraic approaches are studied by applying REDUCE and DEHIM to the same set of problems. These problems range from a linear model with one degree of freedom to a mildly non-linear multi-bladed rotor model with several degrees of freedom. Further, computational issues in applying Floquet theory are also studied, which refer to (1) the equilibrium solution for periodic forced response together with the transition matrix for perturbations about that response and (2) a small number of eigenvalues and eigenvectors of the unsymmetric transition matrix. The study showed the following: (1) compared to REDUCE, DEHIM is far more portable and economical, but it is also less user-friendly, particularly during learning phases; (2) the problems of finding the periodic response and eigenvalues are well conditioned.

On numerical implementation of an isotropic elastic-viscoplastic constitutive model for bulk metallic glasses

An efficient algorithm within the finite deformation framework is developed for finite element implementation of a recently proposed isotropic, Mohr-Coulomb type material model, which captures the elastic-viscoplastic, pressure sensitive and plastically dilatant response of bulk metallic glasses. The constitutive equations are first reformulated and implemented using an implicit numerical integration procedure based on the backward Euler method. The resulting system of nonlinear algebraic equations is solved by the Newton-Raphson procedure. This is achieved by developing the principal space return mapping technique for the present model which involves simultaneous shearing and dilatation on multiple potential slip systems. The complete stress update algorithm is presented and the expressions for viscoplastic consistent tangent moduli are derived. The stress update scheme and the viscoplastic consistent tangent are implemented in the commercial finite element code ABAQUS/Standard. The accuracy and performance of the numerical implementation are verified by considering several benchmark examples, which includes a simulation of multiple shear bands in a 3D prismatic bar under uniaxial compression.

Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Dynamic Structure Factor of Sponge Phases

We predict the dynamic light scattering intensity S(q,t) for the L3 phase (anomalous isotropic phase) of dilute surfactant solutions. Our results are based on a Landau-Ginzburg approach, which was previously used to explain the observed static structure factor S(q, 0). In the extreme limit of small q, we find a monoexponential decay with marginal or irrelevant hydrodynamic interactions. In most other regimes the decay of S(q,t) is strongly nonexponential; in one case, it is purely algebraic at long times.

Integrability and singularity structure of predator‐prey system

The ‘‘extended’’ ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevé or otherwise; to that end, it is required that the formal series—the Laurent series, logarithmic, algebraic psi series about a movable singularity—are shown to converge in the deleted neighborhood of the singularity. The determinations thus obtained are compared with those following from the α method of Painlevé. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist). All these ideas are illustrated by a comprehensive analysis of the general two‐dimensional predator‐prey system.

Minimal sets of generators for the relation ideals of certain monomial curves

Let O be a monomial curve in the affine algebraic e-space over a field K and P be the relation ideal of O. If O is defined by a sequence of e positive integers some e - 1 of which form an arithmetic sequence then we construct a minimal set of generators for P and write an explicit formula for mu(P).

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.

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.

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.

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.

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.