Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

A new type of high-order elements based on the mesh-free interpolations

We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].

Vanadate stimulates oxidation of NADH to generate hydrogen peroxide

Vanadate in the polymeric form of decavanadate, but not other forms, stimulated oxidation of NADH to NAD+ NADPH was also oxidized with comparable rates. This oxidation of NADH was accompanied by uptake of oxygen and generated hydrogen peroxide with the following stoichiometry: NADH + H+ + O2 → NAD+ + H2O2. The reaction followed second-order kinetics. The rate was dependent on the concentration of both NADH and vanadate and increased with decreasing pH. The reaction had an obligatory requirement for phosphate ions. Esr studies in the presence of the spin trap dimethyl pyrroline N oxide indicated the involvement of Superoxide anion as an intermediate. The reaction was sensitive to Superoxide dismutase and other scavengers of superoxide anions.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

f Gravity and gravitational singularities

TRAUTMAN has postulated1 that the usual space−time singularity occurring in classical cosmological models and in the gravitational collapse of massive objects could be averted if intrinsic spin effects are incorporated into general relativity by adding torsion terms to the usual Einstein field equations, that is through the Einstein−Cartan theory. Invoking a primordial magnetic field for aligning all the individual nuclear spins he shows that his universe consisting of 1080 aligned neutrons collapses to a minimum radius of the order of 1 cm with a corresponding matter density of 1055 g cm-3.

Nature of dependence of spin-orbit splittings on atomic number

It has been shown that Dirac equation employing a constant value of the screening constant Z0 does not explain the variation of spin-orbit splittings of 2p and 3p levels with atomic number Z. A model which takes into account the variation of Z0 withZ is shown to satisfactorily predict the dependence of spinorbit splittings onZ.

Order to pay Gershom Seixas for keeping school

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Order to pay Aaron Levy, regarding K. K. Mikve Israel

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Part of order of service and Hebrew prayer, recommended during the revolution

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Localised spin wave modes in a Heisenberg ferromagnet with biquadratic interaction

The presence of biquadratic exchange in a one-dimensional ferromagnetic Heisenberg chain with an impurity spin is shown to change the nature of the impurity modes and its eigenvalues considerably which can be observed experimentally.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.