Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Intrinsic equations of steady rotating, incompressible viscous fluid flow

The equations governing the flow of a steady rotating incompressible viscous fluid are expressed in intrinsic form along the vortex lines and their normals. Using these equations the effects of rotation on the geometric properties of viscous fluid flows are studied. A particular flow in which the vortex lines are right circular helices is discussed.

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

An appendix to the paper "approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic"

The theory of Varley and Cumberbatch [l] giving the intensity of discontinuities in the normal derivatives of the dependent variables at a wave front can be deduced from the more general results of Prasad which give the complete history of a disturbance not only at the wave front but also within a short distance behind the wave front. In what follows we omit the index M in Eq. (2.25) of Prasad [2].

Benedict-Webb-Rubin equation of state constants for N2O4 ⇄ 2NO2,NO,and O2

Benedict-Webb-Rubin equation of state constants for NO, O2, and the equilibrium mixture N2O4 ⇄ 2NO2 are reported.

A Numerical-Simulation Of The Gneiss-Charnockite Transformations In Southern India

This paper presents a numerical simulation of the well-documented, fluid-controlled Kabbal and Ponmudi type gneiss-chamockite transformations in southern India using a free energy minimization method. The computations have considered all the major solid phases and important fluid species in the rock - C-O-H and rock - C-O-H-N systems. Appropriate activity-composition relations for the solid solutions and equations of state for the fluids have been included in order to evaluate the mineral-fluid equilibria attending the incipient chamockite development in the gneisses. The C-O-H fluid speciation pattern in both the Kabbal and Ponmudi type systems indicates that CO2 and H2O make up the bulk of the fluid phase with CO, CH4, H-2 and O2 as minor constituents. In the graphite-buffered Ponmudi-system, the abundance of CO, CH4 and H-2 is orders of magnitude higher than that in the graphite-free Kabbal system. Simulation with C-O-H-N fluids of varying composition demonstrates the complementary role of CO2 and N2 as rather inert dilutants of H2O in the fluid phase. The simulation, carried out on available whole-rock data, has demonstrated the dependence of the transformation X(H2O) on P,T, and phase and chemical composition of the precursor gneiss.

Influence of state of stress on the processing map for hot working of stainless steel type AISI 304L: compression vs. torsion

Processing maps for hot working of stainless steel of type AISI 304L have been developed on the basis of the flow stress data generated by compression and torsion in the temperature range 600–1200 °C and strain rate range 0.1–100 s−1. The efficiency of power dissipation given by 2m/(m+1) where m is the strain rate sensitivity is plotted as a function of temperature and strain rate to obtain a processing map, which is interpreted on the basis of the Dynamic Materials Model. The maps obtained by compression as well as torsion exhibited a domain of dynamic recrystallization with its peak efficiency occurring at 1200 °C and 0.1 s−1. These are the optimum hot-working parameters which may be obtained by either of the test techniques. The peak efficiency for the dynamic recrystallization is apparently higher (64%) than that obtained in constant-true-strain-rate compression (41%) and the difference in explained on the basis of strain rate variations occurring across the section of solid torsion bar. A region of flow instability has occurred at lower temperatures (below 1000 °C) and higher strain rates (above 1 s−1) and is wider in torsion than in compression. To achieve complete microstructure control in a component, the state of stress will have to be considered.

PVU and wave-particle splitting schemes for Euler equations of gas dynamics

A new way of flux-splitting, termed as the wave-particle splitting is presented for developing upwind methods for solving Euler equations of gas dynamics. Based on this splitting, two new upwind methods termed as Acoustic Flux Vector Splitting (AFVS) and Acoustic Flux Difference Splitting (AFDS) methods are developed. A new Boltzmann scheme, which closely resembles the wave-particle splitting, is developed using the kinetic theory of gases. This method, termed as Peculiar Velocity based Upwind (PVU) method, uses the concept of peculiar velocity for upwinding. A special feature of all these methods that the unidirectional and multidirectional parts of the flux vector are treated separately. Extensive computations done using these schemes demonstrate the soundness of the ideas.

Cyclization of enediyne radical cations through chemical, photochemical, and electrochemical oxidation: The role of state symmetry

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a �Full Text� option. The original article is trackable via the �References� option.

The Equations of Equilibrium in Orthogonal Curvilinear Reference Coordinates

Analytical solutions to problems in finite elasticity are most often derived using the semi-inverse approach along with the spatial form of the equations of motion involving the Cauchy stress tensor. This procedure is somewhat indirect since the spatial equations involve derivatives with respect to spatial coordinates while the unknown functions are in terms of material coordinates, thus necessitating the use of the chain rule. In this classroom note, we derive compact expressions for the components of the divergence, with respect to orthogonal material coordinates, of the first Piola-Kirchhoff stress tensor. The spatial coordinate system is also assumed to be an orthogonal curvilinear one, although, not necessarily of the same type as the material coordinate system. We show by means of some example applications how analytical solutions can be derived more directly using the derived results.

Exergetic analysis of carbon dioxide vapour compression refrigeration cycle using the new fundamental equation of state

The purpose of this paper is to present exergy charts for carbon dioxide (CO2) based on the new fundamental equation of state and the results of a thermodynamic analysis of conventional and trans-critical vapour compression refrigeration cycles using the data thereof. The calculation scheme is anchored on the Mathematica platform. There exist upper and lower bounds for the high cycle pressure for a given set of evaporating and pre-throttling temperatures. The maximum possible exergetic efficiency for each case was determined. Empirical correlations for exergetic efficiency and COP, valid in the range of temperatures studied here, are obtained. The exergy losses have been quantified. (C) 2003 Elsevier Ltd. All rights reserved.

Galois Theory and Solvable Equations of Prime Degree

In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.