Nonlinear magnetoacoustic waves in a cold plasma

The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field is not nearly perpendicular to the direction of wave propagation, this allows us to use a multiple-scale expansion to demonstrate the existence and nature of nonlinear wave solutions. Such solutions are found to have a rapid oscillation of constant amplitude superimposed on the underlying large-scale variation. The approximate equations for the large-scale variation are obtained by making an adiabatic approximation and in one limit, new explicit solitary pulse solutions are found. In the case of a perpendicular magnetic field, conditions for the existence of solitary pulses are derived. Our results are consistent with earlier studies which were restricted to waves having a velocity close to that of long-wavelength linear magnetoacoustic waves

Allan variance of frequency fluctuations due to momentum exchange and thermomechanical noises

We investigate the Allan variance of nanoresonators with random rough surfaces under the simultaneous influence of thermomechanical and momentum exchange noises. Random roughness is observed in various surface engineering processes, and it is characterized by the roughness amplitude w, the lateral correlation length ξ, and the roughness exponent 0<H<1. The roughness influence becomes significant for measurement time τA so that ωoτA~1, with ωo the fundamental resonance frequency. The Allan variance increases significantly with increasing roughness (decreasing H and/or increasing ratio w/ξ) if the quality factor due to gas collisions is smaller than the intrinsic quality factor associated with thermomechanical noise.

Role of the officer in Air Force Public Relations

Thesis (M.S.)--Boston Universit

A solitary-wave solution to a perturbed KdV equation

We derive the approximate form and speed of a solitary-wave solution to a perturbed KdV equation. Using a conventional perturbation expansion, one can derive a first-order correction to the solitary-wave speed, but at the next order, algebraically secular terms appear, which produce divergences that render the solution unphysical. These terms must be treated by a regrouping procedure developed by us previously. In this way, higher-order corrections to the speed are obtained, along with a form of solution that is bounded in space. For this particular perturbed KdV equation, it is found that there is only one possible solitary wave that has a form similar to the unperturbed soliton solution

A note on the switching adiabatic theorem

We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class $G^\alpha$ as a function of time, and we show that the error in adiabatic approximation remains small for running times of order $g^{-2}\,|\ln\,g\,|^{6\alpha}$. Here $g$ denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.Comment: 20 pages, no figures, to appear in JM

The Limiting Speed of the Bacterial Flagellar Motor

Recent experiments on the bacterial flagellar motor have shown that the structure of this nanomachine, which drives locomotion in a wide range of bacterial species, is more dynamic than previously believed. Specifically, the number of active torque-generating units (stators) was shown to vary across applied loads. This finding invalidates the experimental evidence reporting that limiting (zero-torque) speed is independent of the number of active stators. Here, we propose that, contrary to previous assumptions, the maximum speed of the motor is not universal, but rather increases as additional torque-generators are recruited. This result arises from our assumption that stators disengage from the motor for a significant portion of their mechanochemical cycles at low loads. We show that this assumption is consistent with current experimental evidence and consolidate our predictions with arguments that a processive motor must have a high duty ratio at high loads.Comment: 8 pages, 3 figures (main text); 7 pages, 3 figures (supplementary

Aromatic cyclotriphosphazenes

Four-Aminophenoxy cyclotriphosphazenes are reacted with maleic anhydride to produce maleamic acids which are converted to the maleimides. The maleimides are polymerized. By selection of starting materials (e.g., hexakis amino or trisaminophenoxy trisphenoxy cyclotrisphosphazenes), selection of molar porportions of reactants, use of mixtures of anhydrides and use of dianhydrides as bridging groups a variety of maleimides and polymers are produced. The polymers have high limiting oxygen indices, high char yields and other useful heat and fire resistant properties making them useful as, for example, impregnants of fabrics