Collisionless galaxy simulations

Three-dimensional fully self-consistent computer models were used to determine the evolution of galaxies consisting of 100 000 simulation stars. Comparison of two-dimensional simulations with three-dimensional simulations showed only a very slight stabilizing effect due to the additional degree of freedom. The addition of a fully self-consistent, nonrotating, exponential core/halo component resulted in considerable stabilization. A second series of computer experiments was performed to determine the collapse and relaxation of initially spherical, uniform density and uniform velocity dispersion stellar systems. The evolution of the system was followed for various amounts of angular momentum in solid body rotation. For initally low values of the angular momentum satisfying the Ostriker-Peebles stability criterion, the systems quickly relax to an axisymmetric shape and resemble elliptical galaxies in appearance. For larger values of the initial angular momentum bars develop and the systems undergo a much more drastic evolution

Coupling Matrix Representation of Nonreciprocal Filters Based on Time Modulated Resonators

This paper addresses the analysis and design of non-reciprocal filters based on time modulated resonators. We analytically show that time modulating a resonator leads to a set of harmonic resonators composed of the unmodulated lumped elements plus a frequency invariant element that accounts for differences in the resonant frequencies. We then demonstrate that harmonic resonators of different order are coupled through non-reciprocal admittance inverters whereas harmonic resonators of the same order couple with the admittance inverter coming from the unmodulated filter network. This coupling topology provides useful insights to understand and quickly design non-reciprocal filters and permits their characterization using an asynchronously tuned coupled resonators network together with the coupling matrix formalism. Two designed filters, of orders three and four, are experimentally demonstrated using quarter wavelength resonators implemented in microstrip technology and terminated by a varactor on one side. The varactors are biased using coplanar waveguides integrated in the ground plane of the device. Measured results are found to be in good agreement with numerical results, validating the proposed theory

Resolution requirements for numerical simulations of transition

The resolution requirements for direct numerical simulations of transition to turbulence are investigated. A reliable resolution criterion is determined from the results of several detailed simulations of channel and boundary-layer transition

Nearly Equal Distributions of the Rank and the Crank of Partitions

Let $N(\leq m,n)$ denote the number of partitions of $n$ with rank not greater than $m$, and let $M(\leq m,n)$ denote the number of partitions of $n$ with crank not greater than $m$. Bringmann and Mahlburg observed that $N(\leq m,n)\leq M(\leq m,n)\leq N(\leq m+1,n)$ for $m<0$ and $1\leq n\leq 100$. They also pointed out that these inequalities can be restated as the existence of a re-ordering $\tau_n$ on the set of partitions of $n$ such that $|\text{crank}(\lambda)|-|\text{rank}(\tau_n(\lambda))|=0$ or $1$ for all partitions $\lambda$ of $n$, that is, the rank and the crank are nearly equal distributions over partitions of $n$. In the study of the spt-function, Andrews, Dyson and Rhoades proposed a conjecture on the unimodality of the spt-crank, and they showed that this conjecture is equivalent to the inequality $N(\leq m,n)\leq M(\leq m,n)$ for $m<0$ and $n\geq 1$. We proved this conjecture by combiantorial arguments. In this paper, we prove the inequality $N(\leq m,n)\leq M(\leq m,n)$ for $m<0$ and $n\geq 1$. Furthermore, we define a re-ordering $\tau_n$ of the partitions $\lambda$ of $n$ and show that this re-ordering $\tau_n$ leads to the nearly equal distribution of the rank and the crank. Using the re-ordering $\tau_n$, we give a new combinatorial interpretation of the function ospt$(n)$ defined by Andrews, Chan and Kim, which immediately leads to an upper bound for $ospt(n)$ due to Chan and Mao.Comment: 19 pages, 1 figur

Low Temperature Magnetic Properties of the Double Exchange Model

We study the {\it ferromagnetic} (FM) Kondo lattice model in the strong coupling limit (double exchange (DE) model). The DE mechanism proposed by Zener to explain ferromagnetism has unexpected properties when there is more than one itinerant electron. We find that, in general, the many-body ground state of the DE model is {\it not} globally FM ordered (except for special filled-shell cases). Also, the low energy excitations of this model are distinct from spin wave excitations in usual Heisenberg ferromagnets, which will result in unusual dynamic magnetic properties.Comment: 5 pages, RevTeX, 5 Postscript figures include