Note on the stability of parallel magnetic fields

The stability characteristics of parallel magnetic fields when fluid motions are present along the lines of force is studied. The stability criterion for both symmetric (m=0) and asymmetric (m=1) modes are discussed and the results obtained by Trehan and Singh (1978) are amended in the present study. The results obtained for the cylindrical geometry are shown to play an important role forka<4, wherek is the wave number,a is the radius of the cylinder, compared to the results obtained by Geronicolas (1977) for the slab geometry.     

A numerical procedure for three-dimensional transient free surface seepage

A three-dimensional procedure based on the finite element method is proposed for transient free surface seepage. It involves solution of the governing equations by using a time integration scheme. The procedure is applied for solution of confined, and transient free surface flow; the latter includes verification with respect to test results from a laboratory model. It is also applied to free surface flow through a dam with a crack.     

A hierarchical approach for constitutive modelling of geologic materials

A hierarchical concept is proposed for the development of constitutive models to account for various factors that influence behaviour of (geologic) materials. It permits evolution of models of progressively higher grades from the basic model representing isotropic hardening with associative behaviour. Factors such as non-associativeness and induced anisotropy due to friction and cyclic loading, and softening are introduced as corrections or perturbations to the basic model. The influence of these factors is captured through non-associativeness manifested by deviation from normality of the plastic strain increments to the yield surface, F. Details of four models: isotropic hardening with associative behaviour, isotropic hardening with non-associative behavioural anisotropic hardening and strain-softening with a damage variable are presented. They are verified with respect to laboratory multiaxial test data under various paths of loading, unloading and reloading for typical soils, rock and concrete. The proposed concept is general, yet sufficiently simplified in terms of physical understanding, number of constants and their physical meanings, determination of the constants and implementation.     

Magnetoacoustic–Gravity Surface Waves with Evershed flow – A model for Running Penumbral Waves

The penumbral region of a sunspot is modelled as a two-layer plasma. The upper layer with magnetic field is taken with Evershed flow and the static lower layer is assumed to be field-free. The magnetoacoustic–gravity surface wave (MAGSW) propagation along this interface is studied. Our results show that the flow suppresses the fast MAGSW and allows only slow MAGSW. More importantly, we suggest that the running penumbral waves are more likely to be slow MAGSW.     

Compressibility effects on hydromagnetic surface waves

The dispersion equation for hydromagnetic surface waves along a plasma-plasma interface has been solved as a function of the compressibility factor c ₁/v _A1, where c ₁ and v _A1 are the acoustic and Alfvén wave speed in one of the medium, for general wave propagation direction. Both slow and fast magnetosonic surface waves can exist. The nature and existence of these waves depends on the values of c ₁/v _A1 and , the angle of wave propagation. For low- plasmas only fast mode exists. The slow mode does not propagate below a critical value of c ₁. When c ₁ the phase velocity of the slow wave tend to the Alfvén surface wave velocity in the incompressible media and for large the phase velocity of the fast wave approaches this value. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle .     

Bioreduction of Hexavalent Chromium by Live and Active Phanerochaete chrysosporium: Kinetics and Modeling

In this work the potential of live and active Phanerochaete chryosporium, a white rot fungi, to remove lower Cr(VI) concentration from aqueous solutions was reported for the first time. A medium pH had significant effect on the growth of the fungus and bioremoval of Cr(VI). Substrate inhibition on the growth of Phanerochaete chrysosporium was evident beyond 20 g L^?1 of dextrose concentration. A maximum biomass concentration of 15.64 g L^?1 was obtained for an initial dextrose concentration of 20 g L^?1 in metal free medium at pH 6.0. An increase in Cr(VI) concentration beyond 10 mg L^?1 inhibited the growth of the fungi, thereby, reducing the chromium bioremoval efficiency. A maximum reduction efficiency of 98.92% was reported for an initial metal concentration of 10 mg L^?1. A mathematical expression for the bioreduction of Cr(VI) considering the organic compounds in the cells was proposed.     

Assessment of the accuracy of the newmark method in transient analysis of wave propagation problems

The Newmark average acceleration method is non-dissipative and unconditionally stable, but its accuracy in transient analysis of wave propagation problems depends not only on the spatial discretization but also on the temporal discretization. It has been found that the effects of spatial and temporal discretization when considered separately as commonly done, are far from adequate for most transient analysis. A better criterion manipulating the interdependent relationship between mesh size and time-step magnitude is imperative to achieve sufficiently accurate results of analysis. In this paper, the accuracy of the Newmark method is investigated by considering the two basic sources of errors, namely, numerical amplitude dissipation and velocity dispersion. The effects of both spatial and temporal discretizations are considered. A new technique to describe the characteristics of various frequency spectra is established. A criterion for mesh design and the selection of time-step magnitude is also proposed based on the combined effects of the amplitude dissipation and velocity dispersion. The efficiency and effectiveness of the proposed criterion are demonstrated using two one-dimensional wave propagation problems. A two-dimensional application shows that this criterion is equally applicable to multidimensional problems.     

Long-term Variations in the Intensity of Plages and Networks as Observed in Kodaikanal Ca-K Digitized Data

In our previous article (Priyal et al. in Solar Phys. 289, 127, 2014) we have discussed the details of observations and methodology adopted to analyze the Ca-K spectroheliograms obtained at the Kodaikanal Observatory (KO) to study the variation of Ca-K plage areas, enhanced network (EN), and active network (AN) for Solar Cycles, namely 19, 20, and 21. Now, we have derived the areas of chromospheric features using KO Ca-K spectroheliograms to study the long-term variations of Solar Cycles 14 to 21. The comparison of the derived plage areas from the data obtained at the KO observatory for the period 1906?–?1985 with that of MWO, NSO for the period 1965?–?2002, earlier measurements made by Tlatov, Pevtsov, and Singh (Solar Phys. 255, 239, 2009) for KO data, and the SIDC sunspot numbers shows a good correlation. The uniformity of the data obtained with the same instrument remaining with the same specifications provided a unique opportunity to study long-term intensity variations in plages and network regions. Therefore, we have investigated the variation of the intensity contrast of these features with time at a temporal resolution of six months assuming that the quiet-background chromosphere remains unchanged during the period 1906?–?2005 and found that the average intensity of the AN, representing the changes in small-scale activity over solar surface, varies with solar cycle being less during the minimum phase. In addition, the average intensity of plages and EN varies with a very long period having a maximum value during Solar Cycle 19, which was the strongest solar cycle of twentieth century.     

A transient finite element analysis of linear viscoelastic material model

Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster¹¹ to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided.