Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a lowcurvature universe can arise from tiny local contributions adding up coherently in large regions.
We present a new set of dissipationless N‐body simulations aiming to better understand the pure dynamical aspects of the ‘Fundamental Plane’ (FP) of elliptical galaxies. We have extended our previous hierarchical merger scheme by considering the Hernquist profile for the initial galaxy model. Two‐component Hernquist galaxy models were also used to study the effect of massive dark haloes on the end‐product characteristics. We have also performed new collapse simulations including initial spin. We found that the one‐component Hernquist mergers give results similar to those found for the one‐component King models, namely both were able to build up small scatter FP‐like correlations with slopes consistent with what is found for the near‐infrared FP of nearby galaxies. The two‐component models also reproduce a FP‐like correlation, but with a significantly steeper slope. This is in agreement with what has been found for elliptical galaxies at higher redshift (0.1 < z < 0.6). We discuss some structural properties of the simulated galaxies and their ability to build up FP‐like correlations. We confirm that collapses generally do not follow a FP‐like correlation regardless of the initial spin. We suggest that the evolution of gradients in the gravitational field of the merging galaxies may be the main ingredient dictating the final non‐homology property of the end products.
We report the analysis of measurements of the complex magnetic permeability (µ r ) and dielectric permittivity (ε r ) spectra of a rubber radar absorbing material (RAM) with various MnZn ferrite volume fractions. The transmission/reflection measurements were carried out in a vector network analyzer. Optimum conditions for the maximum microwave absorption were determined by substituting the complex permeability and permittivity in the impedance matching equation. Both the MnZn ferrite content and the RAM thickness effects on the microwave absorption properties, in the frequency range of 2 to 18 GHz, were evaluated. The results show that the complex permeability and permittivity spectra of the RAM increase directly with the ferrite volume fraction. Reflection loss calculations by the impedance matching degree (reflection coefficient) show the dependence of this parameter on both thickness and composition of RAM.
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