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

An analytic model of plasma-neutral coupling in the heliosphere plasma

We have developed an analytic model to describe coupling of plasma and neutral fluids in the partially ionized heliosphere plasma medium. The sources employed in our analytic model are based on a $\kappa$-distribution as opposed to the Maxwellian distribution function. Our model uses the $\kappa$-distribution to analytically model the energetic neutral atoms that result in the heliosphere partially ionized plasma from charge exchange with the protons and subsequently produce a long tail which is otherwise not describable by the Maxwellian distribution. We present our analytic formulation and describe major differences in the sources emerging from these two distinct distributions.Comment: This paper has been accepted in Journal of Plasma Physics. It is in pres

Statistics of magnetic field fluctuations in a partially ionized space plasma

{\em Voyager 1} and {\em 2} data reveals that magnetic field fluctuations are compressive and exhibit a Gaussian distribution in the compressed heliosheath plasma, whereas they follow a lognormal distribution in a nearly incompressible supersonic solar wind plasma. To describe the evolution of magnetic field, we develop a nonlinear simulation model of a partially ionized plasma based on two dimensional time-dependent multifluid model. Our model self-consistently describes solar wind plasma ions, electrons, neutrals and pickup ions. It is found from our simulations that the magnetic field evolution is governed by mode conversion process that leads to the suppression of vortical modes, whereas the compressive modes are amplified. An implication of the mode conversion process is to quench the Alfv\'enic interactions associated with the vortical motions. Consequently anisotropic cascades are reduced. This is accompanied by the amplification of compressional modes that tend to isotropize the plasma fluctuations and lead to a Gaussian distribution of the magnetic field.Comment: This paper is to appear in Physics Letters

Selecting the best locations for data centers in resilient optical grid/cloud dimensioning

For optical grid/cloud scenarios, the dimensioning problem comprises not only deciding on the network dimensions (i.e., link bandwidths), but also choosing appropriate locations to install server infrastructure (i.e., data centers), as well as determining the amount of required server resources (for storage and/or processing). Given that users of such grid/cloud systems in general do not care about the exact physical locations of the server resources, a degree of freedom arises in choosing for each of their requests the most appropriate server location. We will exploit this anycast routing principle (i.e., source of traffic is given, but destination can be chosen rather freely) also to provide resilience: traffic may be relocated to alternate destinations in case of network/server failures. In this study, we propose to jointly optimize the link dimensioning and the location of the servers in an optical grid/cloud, where the anycast principle is applied for resiliency against either link or server node failures. While the data center location problem has some resemblance with either the classical p-center or k-means location problems, the anycast principle makes it much more difficult due to the requirement of link disjoint paths for ensuring grid resiliency

Whistler Wave Cascade in Solar Wind Plasma

Nonlinear three dimensional, time dependent, fluid simulations of whistler wave turbulence are performed to investigate role of whistler waves in solar wind plasma turbulence in which characteristic turbulent fluctuations are characterized typically by the frequency and length scales that are respectively bigger than ion gyro frequency and smaller than ion gyro radius. The electron inertial length is an intrinsic length scale in whistler wave turbulence that distinguishably divides the high frequency solar wind turbulent spectra into scales smaller and bigger than the electron inertial length. Our simulations find that the dispersive whistler modes evolve entirely differently in the two regimes. While the dispersive whistler wave effects are stronger in the large scale regime, they do not influence the spectral cascades which are describable by a Kolmogorov-like $k^{-7/3}$ spectrum. By contrast, the small scale turbulent fluctuations exhibit a Navier-Stokes like evolution where characteristic turbulent eddies exhibit a typical $k^{-5/3}$ hydrodynamic turbulent spectrum. By virtue of equipartition between the wave velocity and magnetic fields, we quantify the role of whistler waves in the solar wind plasma fluctuations.Comment: Paper contains 3 figures. The paper is accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

May the Best Canon Win: Lockhart v. United States and the Battle of Statutory Interpretation

In Lockhart v. United States, the Supreme Court resolved a long-standing circuit split regarding 18 U.S.C. § 2252(b)(2), which triggered a mandatory minimum sentence for recidivists who had previously been convicted under federal or state crimes relating to “aggravated sexual abuse, sexual abuse, or abusive sexual conduct involving a minor or ward.” In expected fashion, the Court relied on the statute’s plain meaning to decide whether Lockhart’s previous crime had triggered the mandatory minimum. However, even with identical approaches to the text, the majority and dissent reached contrary conclusions. This commentary explores how a single approach could result in dueling interpretations, and whether judicial activism hides behind both opinions