Theory and Simulations of Whistler Wave Propagation

A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic field topological structures consistent with the observations and our simulations in linear regime. In agreement with experiment, we find that the parallel group velocity of the wave is large compared to its perpendicular counterpart. Numerical simulations of collisional interactions demonstrate that the wave magnetic field either coalesces or repels depending upon the polarity of the associated current. In the nonlinear regime, our simulations demonstrate that the evolution of wave magnetic field is governed essentially by the nonlinear Hall force

Dynamics of Alfv\'en waves in partially ionized astrophysical plasmas

We develop a two dimensional, self-consistent, compressible fluid model to study evolution of Alfvenic modes in partially ionized astrophysical and space plasmas. The partially ionized plasma consists mainly of electrons, ions and significant neutral atoms. The nonlinear interactions amongst these species take place predominantly through direct collision or charge exchange processes. Our model uniquely describe the interaction processes between two distinctly evolving fluids. In our model, the electrons and ions are described by a single fluid compressible magnetohydrodynamic (MHD) model and are coupled self-consistently to the neutral fluid via compressible hydrodynamic equations. Both plasma and neutral fluids are treated with different energy equations that adequately enable us to monitor non adiabatic and thermal energy exchange processes between these two distinct fluids. Based on our self-consistent model, we find that the propagation speed of Alfvenic modes in space and astrophysical plasma is slowed down because these waves are damped predominantly due to direct collisions with the neutral atoms. Consequently, energy transfer takes place between plasma and neutral fluids. We describe the mode coupling processes that lead to the energy transfer between the plasma and neutral and corresponding spectral features.Comment: To appear in Journal of Plasma Physic

Spectral features of solar wind turbulent plasma

Spectral properties of a fully compressible solar wind Hall Magnetohydrodynamic plasma are investigated by means of time dependent three dimensional Hall MHD simulations. Our simulations, in agreement with spacecraft data, identify a spectral break in turbulence spectra at characteristic length-scales associated with electromagnetic fluctuations that are smaller than the ion gyroradius. In this regime, our 3D simulations show that turbulent spectral cascades in the presence of a mean magnetic field follow an omnidirectional anisotropic inertial range spectrum close to $k^{-7/3}$. The onset of the spectral break in our simulations can be ascribed to the presence of nonlinear Hall interactions that modify the spectral cascades. Our simulations further show that the underlying charachteristic turbulent fluctuations are spectrally anisotropic, the extent of which depends critically on the local wavenumber. The fluctuations associated with length scales smaller than the ion gyroradius are highly compressible and tend to exhibit a near equipartition in the velocity and magnetic fields. Finally, we find that the orientation of velocity and magnetic field fluctuations critically determine the character of nonlinear interactions that predominantly govern a Hall MHD plasma, like the solar wind.Comment: This paper is accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

"A Dynamic Approach to the Theory of Effective Demand"

This paper attempts to resituate the theory of effective demand within a dynamic nonequilibrium context. Existing theories of effective demand, which derive from the works of Keynes and Kalecki, are generally posed in static equilibrium terms. That is to say, they serve to define a given level of output which corresponds to the equilibrium point between aggregate demand and supply. We propose to generalize this analysis in three ways. First, we will extend the analysis to encompass a dynamic (i.e. moving) short run path of output, rather than a merely static level. Second, we will show that this dynamic short run path need not imply an equilibrium analysis, since it can arise from either stochastically sustained cycles or deterministic limit cycles. And third, we will prove that the preceding generalization of the theory of effective demand will allow us to solve a long standing problem in growth theory: namely, the puzzle surrounding the apparently intractable instability of warranted growth.

Microcredit using Equity Financing: an Alternate Approach to Equity Financing in an Interest Free Financing

Interest is prohibited in all monotheist religions; however, it features as an essential element in practiced capitalism. Interest based financial system has created two major havocs in last two decades i.e. in East Asia in 90s and in the Great Recession since 2007. This paper highlights the extent of development problems faced by the world. With interest at zero bound in U.S since 2008 and with unemployment at 11% level, scarcity of capital cannot solely explain this. However, interest based Microfinance has had mixed results. Interest based lending at Micro level is usually carried out at very high interest rates, more so when the lending takes place informally without institutional intermediation. Institutional intermediation serves a good purpose, but it can also be designed using equity modes of financing. This can relieve the financee and increase diversity of entrepreneurial activities as in debt based microfinance, not much diversity can happen with compulsory servicing of debt. The related questions as to how the institutional arrangement would work to carry out this system, how documentation problems be resolved, how trust level can be created, how effective monitoring can be undertaken and how the intermediaries generate finance themselves and mobilize funds are answered in this paper.nterest free economy, Public finance, Taxation, Inequality, Income redistribution, Islamic Economic System, fiscal policy, deficit financing.