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S M Mahajan

Publications and source records attributed to S M Mahajan.

15 recordsLinked to original sources

Topology of plasma equilibria and the current closure condition.

A virtually complete description of the topology of stationary incompressible Euler flows and the magnetic field satisfying the magnetostatic equation is given by a theorem due to Arnol'd. We apply this theorem to describe the topology of stationary states of plasmas with significant fluid flow, obeying the Hall magnetohydrodynamics model equations. In the context of the integrability (nonchaotic topology) of the magnetic and velocity fields, we discuss the validity of conditions analogous to that of Greene and Johnson, which, in the case of magnetostatic equations, states that the line integral dl/B is the same for each closed magnetic field line on a given magnetic surface. We also show how this property follows from the existence of a continuous volume-preserving symmetry of the magnetic field.

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Radiation reaction in fusion plasmas.

The effects of a radiation reaction on thermal electrons in a magnetically confined plasma, with parameters typical of planned burning plasma experiments, are studied. A fully relativistic kinetic equation that includes the radiation reaction is derived. The associated rate of phase-space contraction is computed and the relative importance of the radiation reaction in phase space is estimated. A consideration of the moments of the radiation reaction force show that its effects are typically small in reactor-grade confined plasmas, but not necessarily insignificant.

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Closed fluid description of relativistic, magnetized plasma interacting with radiation field.

A closed set of averaged fluid equations for a relativistic plasma immersed, simultaneously, in a slowly varying magnetizing field and a sharply varying electromagnetic field (radiation field, for example) of arbitrary intensity is derived. The modifications due to the radiation field on the plasma stress tensor and the Lorentz force are explicitly displayed. The resulting equations include the effects of radiation reaction as well as radiation pressure.

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Radiation reaction and relativistic hydrodynamics.

By invoking the radiation reaction force, first perturbatively derived by Landau and Lifschitz, and later shown by Rohrlich to be exact for a single particle, we construct a set of fluid equations obeyed by a relativistic plasma interacting with the radiation field. After showing that this approach reproduces the known results for a locally Maxwellian plasma, we derive and display the basic dynamical equations for a general magnetized plasma in which the radiation reaction force augments the direct Lorentz force.

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Angular momenta creation in relativistic electron-positron plasma.

Creation of angular momentum in a relativistic electron-positron plasma is explored. It is shown that a chain of angular momentum carrying vortices is a robust asymptotic state sustained by the generalized nonlinear Schrödinger equation characteristic to the system. The results may suggest a possible electromagnetic origin of angular momenta when it is applied to the MeV epoch of the early Universe.

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Temperature-transformed "minimal coupling": magnetofluid unification.

The dynamics of a relativistic, hot charged fluid is expressed in terms of a hybrid magnetofluid field which unifies the electromagnetic field with an appropriately defined but analogous flow field. The unification is affected by a well-defined prescription that allows the derivation of the equations of motion of a plasma embedded in an electromagnetic field from the field-free equations. The relationship of this prescription with the minimal coupling prescription of particle dynamics is discussed; the changes brought about by the plasma temperature are highlighted. A few consequences of the unification are worked out.

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Dynamics of self-trapped singular beams in an underdense plasma.

Dynamics of an intense short laser pulse with a phase singularity, propagating in an underdense cold plasma, is investigated. Such a pulse can propagate as a vortex soliton in a self-created channel. It is shown that vortices with the topological charge m=1,2 (and a corresponding angular momentum) are unstable against symmetry-breaking perturbations; the breakup of the original vortex leads to the formation of stable spatial solitons that steadily fly away tangentially from the initial ring of vortex distribution.

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Self-trapping of strong electromagnetic beams in relativistic plasmas.

Interaction of an intense electromagnetic (em) beam with a relativistic electron-positron (e-p) plasma is investigated. It is shown that the thermal pressure brings about a fundamental change in the dynamics-localized, high amplitude, em field structures, not accessible to a cold (but relativistic) plasma, can now be formed under well-defined conditions. The possibilities of trapping em beams in self-guiding regimes to form stable two-dimensional solitonic structures in a pure e-p plasma are worked out.

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Variational principles and self-organization in two-fluid plasmas.

Self-organization of an ordered structure occurs in a plasma under rather restrictive conditions. A new framework for a variational principle invokes a coercive form that results in a criterion for self-organizing relaxation of a two-fluid plasma. The constraints (constants of motion of the ideal model) are adjusted, through a weakly dissipative process, so that the relaxed state, under well-defined conditions, is a stable equilibrium independent of the direct effects of dissipation.

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Asymptotic analysis and renormalized perturbation theory of the non-Hermitian dynamics of an inviscid vortex.

An analysis of the non-Hermitian fluid systems described by the Rayleigh equation in an unbounded domain has been carried out in the regime of large wave numbers. The evolution of a special class of localized vorticities is also discussed. Asymptotic and perturbative approaches lead to the same final result. In the limit considered, the system is stable. The perturbation analysis reveals interesting pathologies of the non-Hermitian systems. Under specific conditions, the expansion is found to show secular growth. A discussion about the mechanism of insurgence of such singular behavior is presented. It is also shown that the divergent expansion is renormalizable by means of the renormalization group method-the renormalized results are in complete conformity with the asymptotic solutions.

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Vortex solitons: mass, energy, and angular momentum bunching in relativistic electron-positron plasmas.

It is shown that the interaction of large amplitude electromagnetic waves with a hot electron-positron (e-p) plasma (a principal constituent of the universe in the MeV epoch) leads to a bunching of mass, energy, and angular momentum in stable, long-lived structures. Electromagnetism in the MeV epoch, then, could provide a possible route for seeding the observed large-scale structure of the universe.

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Urinary screening tests for fetal Down syndrome: I. Fresh beta-core fragment.

Variable results have been reported using urine beta-core fragment as a marker for fetal Down syndrome. Initial studies by Cuckle et al. (1994) and Canick et al. (1995) indicated that beta-core fragment was an outstanding marker, detecting >80 per cent of Down syndrome cases. Since these reports, widely varying results have been published, indicating between 20 per cent and 66 per cent detection of cases at 5 per cent false-positive rate. The wide variation in the reported data has led to a loss of enthusiasm for this marker as a useful test for Down syndrome screening. Here we report the results of a three-year prospective study in which urine samples were collected daily from women undergoing fetal karyotype analysis for advanced maternal age. Samples were tested within one week of collection and then frozen. We also investigated the likely causes of the variability observed in beta-core fragment data. We collected 1157 urine samples over 955 days. Beta-core fragment levels were measured. A regression line was calculated for the weekly medians of the 1134 control samples and multiples of the control median (MoM) were determined. The median MoM for the controls was 1.0 and the logarithmic standard deviation (log SD) was 0.41. The median MoM for the 23 Down syndrome cases was 5.44 and the log SD was 0.45. Over the study period, 65 per cent of Down syndrome cases exceeded the 95th centile of the control group. The median MoM of control samples and the proportion of Down syndrome cases detected by the test was relatively constant during the study period. The unaffected cases were divided into three equal divisions, corresponding to approximately the first, second and third year of sample collection. No trend was found in the median control MoM values in three sample collection periods (r2=0.04). A similar number of cases exceeded the 95th centile of control samples in the three sample collection periods, 63 per cent, 66 per cent and 66 per cent. Consistent results were indicated during the three years of sample testing. Levels of total oestriol were determined in urine samples and MoM statistics derived. The median oestriol level in Down syndrome cases was 0.59 MoM. Only 12 per cent of cases had MoM levels below the fifth centile. Gaussian models were prepared combining biochemical data and maternal age distribution. While beta-core fragment by itself detected 65 per cent of Down syndrome cases, beta-core fragment modelled with maternal age detected 66 per cent, and modelled with age and total oestriol levels detected 82 per cent of cases at 5 per cent false-positive rate. At the completion of the study, we thawed and reassayed 20 random urine samples (10 control and 10 Down syndrome) collected at different times during the study period. While the control samples (74-1700 ng/ml) had slightly increased values when reassayed (mean value 137 per cent of original prospective value), the Down syndrome samples (360-20,500 ng/ml) all had decreased values when reassayed (mean=53 per cent, t-test, controls versus cases, p = 0.0003). The Down syndrome samples were decreased to between 93 per cent and 12 per cent of the original value. A relationship was identified between the magnitude of the original beta-core fragment value and the change in immunoreactivity when reassayed (r2=0.998). The higher the initial beta-core fragment value the greater the loss of immunoreactivity. We considered the possibility that the beta-core fragment molecules aggregate upon storage in the freezer. We repeated the assay of the 20 samples after treatment with a high salt buffer. Down syndrome samples recovered half of the lost beta-core fragment immunoreactivity (mean increase in beta-core fragment levels 56 per cent, t-test, controls versus cases, p=0.004). We infer that aggregation of beta-core fragment upon storage interferes with beta-core fragment measurements. This may be the cause of the poor beta-core fragment screening performance reported using sto

Biomarkers↗

Theory of creeping gravity currents of a non-Newtonian liquid.

Recently several experiments on creeping gravity currents have been performed, using highly viscous silicone oils and putties. The interpretation of the experiments relies on the available theoretical results that were obtained by means of the lubrication approximation with the assumption of a Newtonian rheology. Since very viscous fluids are usually non-Newtonian, an extension of the theory to include non-Newtonian effects is needed. We derive the governing equations for unidirectional and axisymmetric creeping gravity currents of a non-Newtonian liquid with a power-law rheology, generalizing the usual lubrication approximation. The equations differ from those for Newtonian liquids, being nonlinear in the spatial derivative of the thickness of the current. Similarity solutions for currents whose volume varies as a power of time are obtained. For the spread of a constant volume of liquid, analytic solutions are found that are in good agreement with experiment. We also derive solutions of the waiting-time type, as well as those describing steady flows from a constant source to a sink. General traveling-wave solutions are given, and analytic formulas for a simple case are derived. A phase plane formalism that allows the systematic derivation of self-similar solutions is introduced. The application of the Boltzmann transform is briefly discussed. All the self-similar solutions obtained here have their counterparts in Newtonian flows, as should be expected because the power-law rheology involves a single-dimensional parameter as the Newtonian constitutive relation. Thus one finds similarity solutions whenever the analogous Newtonian problem is self-similar, but now the spreading relations are rheology-dependent. In most cases this dependence is weak but leads to significant differences easily detected in experiments. The present results may also be of interest for geophysics since the lithosphere deforms according to an average power-law rheology.

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Role of ultimobranchial body and corpuscle of Stannius in regulation of the plasma calcium and phosphorus levels in the teleost Heteropneustes fossilis.

Effects of NaF, CaCl2, NaCl and mammalian calcitonin on the histology of ultimo-branchial (UTB) and corpuscle of Stannius (CS) and plasma levels of calcium and phosphorus in the teleost Heteropneustes fossilis are recorded. Administration of NaF, NaCl, and mammalian calcitonin resulted in varying degree of hypolcalcaemia and hyperphosphataemia, whereas hypercalcaemia and hypophosphataemia developed during CaCl2 treatment. These treatments also produced various histological changes in UTB and CS. It is suggested that CS and UTB are involved in metabolisms of Ca and P, and in osmoregulation. Moreover, it is an important hypocalcaemic mechanism in this fish in combating hypercalcaemia.

Animals↗