Mechanistic Aspects of Nucleophilic Substitution at Half-Sandwich Metal Complexes

The hydrolysis reactions of organometallic ruthenium(II) piano-stool complexes of the type Ru-II(eta(6)-cymene)(L)Cl](0/+) (1-5, where L = kappa(1)- or kappa(2)-1,1-bis(diphenylphosphino)methane,1,1bis-(diphenylphosphino)methane oxide, kappa(1)-mercaptobenzothiazole) have been studied using density functional theory at the B3LYP level. In addition to considering a syn attack in an associative fashion, where the nucleophile approaches from the same side as the leaving group, we have explored alternative paths such as an anti attack in an associative manner, where the nucleophile attacks from the opposite side of the leaving group. During the anti attack, an intermediate is formed and there is a coordination mode change of the arene ring from eta(6) to eta(2) along with its rotation. When the intermediate goes to the product, the arene ring slips back from eta(2) to eta(6) coordination. This coordinated movement of the arene ring makes the associative anti attack an accessible pathway for the substitution process. Our calculations predict very similar activation barriers for both syn and anti attacks. In the dissociative path, the rate-determining step is the generation of a coordinatively unsaturated 16-electron ruthenium species. This turns out to be viable once solvent effects are included. The large size of the ancillary ligands on Ru makes the dissociative process as favorable as the associative process. Activation energy calculations reveal that although the dissociative path is favorable for kappa(1) complexes, both dissociative and associative processes can have significant contribution to the hydrolysis reaction in kappa(2) complexes. Once activated by hydrolysis, these complexes react with guanine and adenine bases of DNA. The thermodynamic stabilities of complexes formed with the nucleobases are also presented.

Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

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.

Binding of active site directed ligands to phospholipase A2: Implications on the molecular constraints and catalytic mechanism

Molecular constraints for the localization of active site directed ligands (competitive inhibitors and substrates) in the active site of phospholipase A2 (PLA2) are characterized. Structure activity relationships with known inhibitors suggest that the head : group interactions dominate the selectivity as well as a substantial part of the affinity. The ab initio fitting of the amide ligands in the active site was carried out to characterize the head group interactions. Based on a systematic coordinate space search, formamide is docked with known experimental constraints such as coordination of the carbonyl group to Ca2+ and hydrogen bond between amide nitrogen and ND1 of His48. An optimal position for a bound water molecule is identified and its significance for the catalytic mechanism is postulated. Unlike the traditional ''pseudo-triad'' mechanism, the ''Ca-coordinatedoxyanion'' mechanism proposed here invokes activation of the catalytic water to form the oxyanion in the coordination sphere of calcium. As it attacks the carbonyl carbon of the ester, a near-tetrahedral intermediate is formed. As the second proton of the catalytic water is abstracted by the ester oxygen, its reorientation and simultaneous cleavage form hydrogen bond with ND1 of His48. In this mechanism of esterolysis, a catalytic role for the water co-ordinated to Ca2+ is recognised.

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.

Al2O3---ZrO2 composite coatings for thermal-barrier applications

Graded alternate layers of Al2O3 and 8% Y2O3-ZrO2 and their admixtures were plasma sprayed onto bond-coated mild steel. They were evaluated for thermal-shock resistance, thermal-barrier characteristics, hot corrosion resistance (molten NaCl corrodant) and depth of attack, adhesion strength and the presence of phases. Although front-back temperature drops of 423-623 K were observed, some of the coatings showed good adherence even after 100 thermal shack cycles. In the sequence of the graded layers, the oxide which is directly in contact with the bond coat appears to influence the properties especially in coatings of 150 and 300 mu m thickness. Molten NaCl readily attacks the films at high hot-face temperatures (1273 K for 1 h) and the adhesive strength falls significantly by 50-60%. Diffusion of alkaline elements is also found to depend on the chemical composition of the outer coating directly facing the molten corrodant. (C) 1997 Elsevier Science Limited.

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.