Microwave Electronics

Contains reports on four research projects.Lincoln Laboratory (Purchase Order B-00306)United States Air Force (Contract AF19(604)-5200)United States NavyUnited States Arm

On the vanishing viscosity limit in a disk

We say that the solution u to the Navier-Stokes equations converges to a solution v to the Euler equations in the vanishing viscosity limit if u converges to v in the energy norm uniformly over a finite time interval. Working specifically in the unit disk, we show that a necessary and sufficient condition for the vanishing viscosity limit to hold is the vanishing with the viscosity of the time-space average of the energy of u in a boundary layer of width proportional to the viscosity due to modes (eigenfunctions of the Stokes operator) whose frequencies in the radial or the tangential direction lie between L and M. Here, L must be of order less than 1/(viscosity) and M must be of order greater than 1/(viscosity)

In vivo microCT-based time-lapse morphometry reveals anatomical site-specific differences in bone (re)modeling serving as baseline parameters to detect early pathological events

The bone structure is very dynamic and continuously adapts its geometry to external stimuli by modeling and remodeling the mineralized tissue. In vivo microCT-based time-lapse morphometry is a powerful tool to study the temporal and spatial dynamics of bone (re)modeling. Here an advancement in the methodology to detect and quantify site-specific differences in bone (re)modeling of 12-week-old BALB/c nude mice is presented. We describe our method of quantifying new bone surface interface readouts and how these are influenced by bone curvature. This method is then used to compare bone surface (re)modeling in mice across different anatomical regions to demonstrate variations in the rate of change and spatial gradients thereof. Significant differences in bone (re)modeling baseline parameters between the metaphyseal and epiphyseal are shown, as well as cortical and trabecular bone of the distal femur and proximal tibia. These results are validated using conventional static in vivo microCT analysis. Finally, the insights from these new baseline values of physiological bone (re)modeling were used to evaluate pathological bone (re)modeling in a pilot breast cancer bone metastasis model. The method shows the potential to be suitable to detect early pathological events and track their spatio-temporal development in both cortical and trabecular bone. This advancement in (re)modeling surface analysis and defined baseline parameters according to distinct anatomical regions will be valuable to others investigating various disease models with site-distinct local alterations in bone (re)modeling.ER

A Joint Soil-Vegetation-Atmospheric Modeling Procedure of Water Isotopologues: Implementation and Application to Different Climate Zones With WRF-Hydro-Iso

Water isotopologues, as natural tracers of the hydrological cycle on Earth, provide a unique way to assess the skill of climate models in representing realistic atmospheric-terrestrial water pathways. This study presents the newly developed WRF-Hydro-iso, which is a version of the coupled atmospheric-hydrological WRF-Hydro model enhanced with a joint soil-vegetation-atmospheric description of water isotopologue motions. It allows the consideration of isotopic fractionation processes during water phase changes in the atmosphere, the land surface, and the subsurface. For validation, WRF-Hydro-iso is applied to two different climate zones, namely Europe and Southern Africa under the present climate conditions. Each case is modeled with a domain employing a 5 km grid-spacing coupled with a terrestrial subgrid employing a 500 m grid-spacing in order to represent lateral terrestrial water flow. A 10-year slice is simulated for 2003–2012, using ERA5 reanalyses as driving data. The boundary condition of isotopic variables is prescribed with mean values from a 10-year simulation with the Community Earth System Model Version 1. WRF-Hydro-iso realistically reproduces the climatological variations of the isotopic concentrations σ$_{P}$$^{18}$O and σ$_{P}$$^{2}$H from the Global Network of Isotopes in Precipitation. In a sensitivity analysis, it is found that land surface evaporation fractionation increases the isotopic concentrations in the rootzone soil moisture and slightly decreases the isotopic concentrations in precipitation. Lateral terrestrial water flow minorly affects these isotopic concentrations through changes in evaporation-transpiration partitioning

Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold