Invariants and Labels in Lie-Poisson Systems

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system.Comment: 11 pages, RevTeX. To appear in Proceedings of the 13th Florida Workshop in Astronomy and Physic

Plasma fluctuations as Markovian noise

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.Physic

Mistaken Detonation: International and Domestic Legal Principles Applicable to Address the Accidental or Unintended Use of Nuclear Weapons

Accidental or unintended detonation of nuclear weapons is a virtually unregulated area of international law. Although the Treaty on the Prohibition of Nuclear Weapons and the Treaty on the Non- Proliferation of Nuclear Weapons seek to manage the risks of intentional nuclear use, these Treaties are silent on how the international community would assign legal liability for inadvertent detonations. This Note seeks to address this question by surveying and discussing how existing mechanisms of international and US domestic law could fill this legal void. Specifically, it analyzes the relevancy, benefits, and drawbacks of applying: international criminal law; international human rights law; the Rule of Precaution; the Treaty on the Prohibition of Nuclear Weapons; the American tort claims of civil negligence, res ipsa loquitur, the abnormally dangerous activities doctrine, and products liability; data security law; and criminal negligence. This Note ultimately proposes three practical recommendations as to how the international community can work together to determine which legal framework best addresses accidental or unintended use of nuclear weapons and implement the most worthwhile policies and procedures to address the risk

Multi-Faceted Risk: Exempting Trafficked Asylum Seekers from “Safe Third Country” Agreements in States Not in Compliance with TVPA Minimum Standards

The “Safe Third Country” principle in international refugee law refers to a State’s ability to reject a person’s asylum application if they have already been granted protection by another country in compliance with the 1951 Refugee Convention. However, asylum seekers face higher risks of human trafficking because of their transient and vulnerable circumstances, and some of the most frequently implicated Safe Third Countries are consistently ranked in Tier 2 or below in the US State Department’s annual Trafficking in Persons Report; this ranking indicates that they are not in full compliance with the minimum standards provided in the Trafficking Victims Protection Act. This Comment argues that asylum seekers who have experienced human trafficking throughout their migration journey should be exempted from Safe Third Country agreements with States that rank in Tier 2 or below. It will survey Greece, Turkey, and the Northern Triangle as examples of States often deemed to be Safe Third Countries, yet have recurring difficulties prosecuting human trafficking violations and protecting victims; this Comment will ultimately propose a solution as to how these exemptions can be implemented in practice

Two-fluid temperature-dependent relativistic waves in magnetized streaming pair plasmas

A relativistic two-fluid temperature-dependent approach for a streaming magnetized pair plasma is considered. Such a scenario corresponds to secondary plasmas created at the polar caps of pulsar magnetospheres. In the model the generalized vorticity rather than the magnetic field is frozen into the fluid. For parallel propagation four transverse modes are found. Two are electromagnetic plasma modes which at high temperature become light waves. The remaining two are Alfveacutenic modes split into a fast and slow mode. The slow mode is cyclotron two-stream unstable at large wavelengths and is always subluminous. We find that the instability cannot be suppressed by temperature effects in the limit of large (finite) magnetic field. The fast Alfveacuten mode can be superluminous only at large wavelengths, however it is always subluminous at high temperatures. In this incompressible approximation only the ordinary mode is present for perpendicular propagation. For oblique propagation the dispersion relation is studied for finite and large strong magnetic fields and the results are qualitatively described.Institute for Fusion Studie