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Thesis (Ed.M.)--Boston Universit

On the Meaning and Inapplicability of the Zeldovich Relations of Magnetohydrodynamics

Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two-dimensions, followed by others for three dimensions, and Zeldovich et al. (1983) have presented formulae of the form $=f(R_M){Bbar}^2$. Such ``Zeldovich relations'' have sometimes been interpreted to provide steady-state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function $f$ that depends on spatial dimension and a magnetic Reynolds number $R_M$. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2-D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. in relation to a seed value $Bbar$. In 3-D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of $R_M$ and the initially imposed $Bbar$, as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re-analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady-states of large $R_M$ MHD turbulence.Comment: 7 pages, accepted to Astronomische Nachrichte

Consequences of Propagating Torsion in Connection-Dynamic Theories of Gravity

We discuss the possibility of constraining theories of gravity in which the connection is a fundamental variable by searching for observational consequences of the torsion degrees of freedom. In a wide class of models, the only modes of the torsion tensor which interact with matter are either a massive scalar or a massive spin-1 boson. Focusing on the scalar version, we study constraints on the two-dimensional parameter space characterizing the theory. For reasonable choices of these parameters the torsion decays quickly into matter fields, and no long-range fields are generated which could be discovered by ground-based or astrophysical experiments.Comment: 16 pages plus one figure (plain TeX), MIT-CTP #2291. (Extraordinarily minor corrections.

Dynamical magnetic relaxation: A nonlinear magnetically driven dynamo

A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for large scale magnetic helicity, small scale magnetic helicity, velocity, and the electromotive force are solved. The magnetic helicity on small scales relaxes to drive significant large scale helical field growth on dynamical (Alfv\'en crossing) time scales, independent of the magnitude of finite microphysical transport coefficients, after which the growing kinetic helicity slows the growth to a viscously limited pace. This magnetically driven dynamo complements the nonlinear kinetic helicity driven dynamo; for the latter, the growing magnetic helicity fluctuations suppress, rather than drive, large scale magnetic helicity growth. A unified set of equations accommodates both types of dynamos.Comment: 13 pages, in press, Physics of Plasma

Resource music for teaching American history

Thesis (Ed.M.)--Boston Universit

Age Differences in Personal Risk Perceptions: A Note on an Exploratory Descriptive Study

The authors test for differences in risk perceptions among different age groups