On the electromagnetic force on a polarizable body

The force on a macroscopic polarizable body in an inhomogenous electromagnetic field is calculated for three simple exactly solvable situations. Comparing different approaches we pinpoint possible pitfalls and resolve recent confusion about the force density in ferrofluids.Comment: 8 pages, 3 figures, submitted to Am. J. Phy

Skill assessment of multiple hypoxia models in Chesapeake Bay and implications for management decisions

The Chesapeake Bay Program (CBP) has used their coupled watershed-water quality modeling system to develop a set of Total Maximum Daily Loads (TMDLs) for nutrients and sediment in an effort to reduce eutrophication impacts which include decreasing the seasonal occurrence of hypoxia within the Bay. The CBP is now considering the use of a multiple model approach to enhance the confidence in their model projections and to better define uncertainty. This study statistically compares the CBP regulatory model with multiple implementations of the Regional Ocean Modeling System (ROMS) in terms of skill in reproducing monthly profiles of hydrodynamics, nutrients, chlorophyll and dissolved oxygen at ~30 stations throughout the Bay. Preliminary results show that although all the models substantially underestimate stratification throughout the Bay, they all have significant skill in reproducing the mean and seasonal variability of bottom dissolved oxygen. This study demonstrates that multiple community models can be used together to provide independent confidence bounds for management decisions based on CBP model results

Symmetric hyperbolic systems for Bianchi equations

We obtain a family of first-order symmetric hyperbolic systems for the Bianchi equations. They have only physical characteristics: the light cone and timelike hypersurfaces. In the proof of the hyperbolicity, new positivity properties of the Bel tensor are used.Comment: latex, 7 pages, accepted for publication in Class. Quantum Gra

Machine Learning Enhanced Antenna Systems

Radio direction finding (DF) has long since been of interest to the antenna and greater RF community. DF helps address problems seen in both commercial and defense applications, and the needs are ever-growing. A substantial breadth of research addresses maximizing the performance of DF systems. High quality antenna design, high performance beamforming, and high resolution processing have been demonstrated with great success, though often sacrificing size, weight, power, or cost (SWAP-C). The widespread proliferation of the Internet of Things and generally increased connectivity opens up research areas that leverage unprecedented levels of networking and connectivity. These systems require low-cost, low-fidelity RF components to enable mass proliferation, which makes engineering well-performing solutions difficult by comparison to historically specialized sensors. This thesis seeks to provide low-cost sensing solutions, leveraging machine learning and modern processing techniques, that yield high performance and are compatible with modern day edge-computing requirements. An investigation into the feasibility of using machine learning for retrofitting --- the extraction of information for which a system is not conventionally designed for --- is explored in the context of polarimetry. Fundamental studies are used to demonstrate the practicality of machine learning to facilitate low-cost sensing capabilities. An ultra-wideband log periodic antenna is first designed for additive manufacturing to integrate the antenna and feeding structure (balun and impedance transformer) into the body of the sensor itself. The dual-polarized system enables wideband spectrum sensing at a relatively low cost. This system, in isolation, does not sense angle-of-arrival information, therefore antenna-induced distortions imparted on the signal cannot be corrected with DF-based calibration methods, making polarimetry difficult. A neural network solution is demonstrated which facilitates good accuracy in classifying the polarization of the incident signal, whereas polarimetry is otherwise unachievable. An extension of the retrofitting motif is further explored through the lens of DF. An ultrawideband circular antenna array is investigated for its ability to perform amplitude-only DF, despite its radiation patterns being suboptimal for the task. Machine learning is once again utilized, but with careful consideration to the practical deployment aspects of the algorithm. A novel, general, architecture is developed to leverage the rotational symmetry of the uniform circular array to perform single-snapshot azimuth angle-of-arrival estimation with as minimal a footprint as possible. The architecture scales favorably, and its relative performance only increases as a function of the number of elements, when compared to competing methods. An elevation sensing capability is also shown with the same sensor, which is unprecedented for other systems with similar field-of-view (FOV) and bandwidth. These concepts are then extended to the design of a structure. The design of as low-cost, low-complexity system is achieved, while maintaining azimuth and elevation DF capabilities with a single snapshot. Fundamental studies on the number of elements and element geometries are carried out, and a particular geometry is built and tested with a custom, four-channel receiver. A systematic neural network design methodology is introduced to facilitate the construction of neural networks for DF. Experimental validation is performed showing the efficacy of integrating machine learning for azimuth and elevation estimation, with a low-element count antenna array and receiver. Finally, the synthesis of all the prior investigations is achieved. Novel use of a four-arm spiral antenna sensor is proposed, using each arm of the spiral as its own amplitude-only channel. Traditionally, without mode-forming, DF is quite difficult. Frequency rotation modeling is deployed alongside a compact neural network architecture to facilitate ultrawideband amplitude-only DF in both azimuth and elevation with a cavity backed spiral in the absence of mode/beam-forming circuitry that is conventionally required. Integration with a four-channel receiver is demonstrated and performance over multiple octaves is obtained.</p

The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.Comment: 11 pages, 1 figur

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio