An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction

23 p. -- An extended abstract of this work appears in the proceedings of the 2012 ACM/IEEE Symposium on Logic in Computer Science

Stability analysis of RF amplifiers based on MIMO pole-zero identification

Spurious oscillations are one of the principal issues faced by microwave and RF circuit designers. The rigorous detection of instabilities or the characterization of measured spurious oscillations is still an ongoing challenge. This project aims to create a new stability analysis CAD program that tackles this chal- lenge. Multiple Input Multiple Output (MIMO) pole-zero identification analysis is introduced on the program as a way to create new methods to automate the stability analysis process and to help designers comprehend the obtained results and prevent incorrect interpretations. The MIMO nature of the analysis contributes to eliminate possible controllability and observability losses and helps differentiate mathematical and physical quasi-cancellations, products of overmodeling. The created program reads Single Input Single Output (SISO) or MIMO frequency response data, and determines the corresponding continuous transfer functions with Vector Fitting. Once the transfer function is calculated, the corresponding pole/zero diagram is mapped enabling the designers to analyze the stability of an amplifier. Three data processing methods are introduced, two of which consist of pole/zero elimina- tions and the latter one on determining the critical nodes of an amplifier. The first pole/zero elimination method is based on eliminating non resonant poles, whilst the second method eliminates the poles with small residue by assuming that their effect on the dynamics of a system is small or non-existent. The critical node detection is also based on the residues; the node at which the effect of a pole on the dynamics is highest is defined as the critical node. In order to evaluate and check the efficiency of the created program, it is compared via examples with another existing commercial stability analysis tool (STAN tool). In this report, the newly created tool is proved to be as rigorous as STAN for detecting instabilities. Additionally, it is determined that the MIMO analysis is a very profitable addition to stability analysis, since it helps to eliminate possible problems of loss of controllability, observability and overmodeling.

Microwave Resonant and Zero-Field Absorption Study of Doped Magnetite Prepared by a Co-Precipitation Method

Fe3O4 and ZnxFe3-xO4 pure and doped magnetite magnetic nanoparticles (NPs) were prepared in aqueous solution (Series A) or in a water-ethyl alcohol mixture (Series B) by the co-precipitation method. Only one ferromagnetic resonance line was observed in all cases under consideration indicating that the materials are magnetically uniform. The shortfall in the resonance fields from 3.27 kOe (for the frequency of 9.5 GHz) expected for spheres can be understood taking into account the dipolar forces, magnetoelasticity, or magnetocrystalline anisotropy. All samples show non-zero low field absorption. For Series A samples the grain size decreases with an increase of the Zn content. In this case zero field absorption does not correlate with the changes of the grain size. For Series B samples the grain size and zero field absorption behavior correlate with each other. The highest zero-field absorption corresponded to 0.2 zinc concentration in both A and B series. High zero-field absorption of Fe3O4 ferrite magnetic NPs can be interesting for biomedical applications.

Higher order vortex gyrotropic modes in circular ferromagnetic nanodots

Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50-100 nm) circular Ni80Fe20 dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators.

Surface plasmons and effects of losses in propagating modes in a chain of silver nanoparticles

In this work a chain of 4000 silver nanoparticles embedded in a glass medium is considered, and its leftmost particle is excited by an electric field pulse of Gaussian shape. Considering Drude’s model, losses of the system are taken into account by γ factor, which stands for the Ohmic losses, and different quantities, such as frequencies of excited modes and group velocities are calculated. Besides, these results are compared to those obtained from the dispersion relation of an infinite chain. The increase of losses affects the lifetime and propagation length of the plasmon; besides, although the response dispersion relation for an infinite chain seems to remain invariable, this is not the case for a finite chain. The mismatches are bigger for higher losses. Furthermore, plasmon propagation velocities are analysed, and an explanation for the mismatch of longitudinal modes close to the intersection point with the dispersion of light is suggested. Finally, some concepts to treat this problem from the energy transport point of view are introduced.