A Phase-Space Approach to Collisionless Stellar Systems Using a Particle Method

A particle method for reproducing the phase space of collisionless stellar systems is described. The key idea originates in Liouville's theorem which states that the distribution function (DF) at time t can be derived from tracing necessary orbits back to t=0. To make this procedure feasible, a self-consistent field (SCF) method for solving Poisson's equation is adopted to compute the orbits of arbitrary stars. As an example, for the violent relaxation of a uniform-density sphere, the phase-space evolution which the current method generates is compared to that obtained with a phase-space method for integrating the collisionless Boltzmann equation, on the assumption of spherical symmetry. Then, excellent agreement is found between the two methods if an optimal basis set for the SCF technique is chosen. Since this reproduction method requires only the functional form of initial DFs but needs no assumptions about symmetry of the system, the success in reproducing the phase-space evolution implies that there would be no need of directly solving the collisionless Boltzmann equation in order to access phase space even for systems without any special symmetries. The effects of basis sets used in SCF simulations on the reproduced phase space are also discussed.Comment: 16 pages w/4 embedded PS figures. Uses aaspp4.sty (AASLaTeX v4.0). To be published in ApJ, Oct. 1, 1997. This preprint is also available at http://www.sue.shiga-u.ac.jp/WWW/prof/hozumi/papers.htm

Maximum entropy models for antibody diversity

Recognition of pathogens relies on families of proteins showing great diversity. Here we construct maximum entropy models of the sequence repertoire, building on recent experiments that provide a nearly exhaustive sampling of the IgM sequences in zebrafish. These models are based solely on pairwise correlations between residue positions, but correctly capture the higher order statistical properties of the repertoire. Exploiting the interpretation of these models as statistical physics problems, we make several predictions for the collective properties of the sequence ensemble: the distribution of sequences obeys Zipf's law, the repertoire decomposes into several clusters, and there is a massive restriction of diversity due to the correlations. These predictions are completely inconsistent with models in which amino acid substitutions are made independently at each site, and are in good agreement with the data. Our results suggest that antibody diversity is not limited by the sequences encoded in the genome, and may reflect rapid adaptation to antigenic challenges. This approach should be applicable to the study of the global properties of other protein families

Evolution and instabilities of disks harboring super massive black holes

The bar formation is still an open problem in modern astrophysics. In this paper we present numerical simulation performed with the aim of analyzing the growth of the bar instability inside stellar-gaseous disks, where the star formation is triggered, and a central black hole is present. The aim of this paper is to point out the impact of such a central massive black hole on the growth of the bar. We use N-body-SPH simulations of the same isolated disk-to-halo mass systems harboring black holes with different initial masses and different energy feedback on the surrounding gas. We compare the results of these simulations with the one of the same disk without black hole in its center. We make the same comparison (disk with and without black hole) for a stellar disk in a fully cosmological scenario. A stellar bar, lasting 10 Gyrs, is present in all our simulations. The central black hole mass has in general a mild effect on the ellipticity of the bar but it is never able to destroy it. The black holes grow in different way according their initial mass and their feedback efficiency, the final values of the velocity dispersions and of the black hole masses are near to the phenomenological constraints.Comment: 10 pages, 8 figures, accepted for pubblication in "Astrophysics and Space Science

The Radial Orbit Instability in Collisionless N-Body Simulations

Using a suite of self-gravitating, collisionless N-body models, we systematically explore a parameter space relevant to the onset and behavior of the radial orbit instability (ROI), whose strength is measured by the systemic axis ratios of the models. We show that a combination of two initial conditions, namely the velocity anisotropy and the virial ratio, determines whether a system will undergo ROI and exactly how triaxial the system will become. A third initial condition, the radial shape of the density profile, plays a smaller, but noticeable role. Regarding the dynamical development of the ROI, the instability a) begins after systems collapse to their most compact configuration and b) evolves fastest when a majority of the particles have radially anisotropic orbits while there is a lack of centrally-concentrated isotropic orbits. We argue that this is further evidence that self-reinforcing torques are the key to the onset of the ROI. Our findings support the idea that a separate orbit instability plays a role in halting the ROI.Comment: accepted for publication in ApJ. 9 figures in emulateapj styl

The Self-Regulated Growth of Supermassive Black Holes

We present a series of simulations of the self--regulated growth of supermassive black holes (SMBHs) in galaxies via three different fueling mechanisms: major mergers, minor mergers, and disk instabilities. The SMBHs in all three scenarios follow the same black hole fundamental plane (BHFP) and correlation with bulge binding energy seen in simulations of major mergers, and observed locally. Furthermore, provided that the total gas supply is significantly larger than the mass of the SMBH, its limiting mass is not influenced by the amount of gas available or the efficiency of black hole growth. This supports the assertion that SMBHs accrete until they reach a critical mass at which feedback is sufficient to unbind the gas locally, terminating the inflow and stalling further growth. At the same time, while minor and major mergers follow the same projected correlations (e.g., the $M_{BH}-\sigma$ and Magorrian relations), SMBHs grown via disk instabilities do not, owing to structural differences between the host bulges. This finding is supported by recent observations of SMBHs in pseudobulges and bulges in barred systems, as compared to those hosted by classical bulges. Taken together, this provides support for the BHFP and binding energy correlations as being more "fundamental" than other proposed correlations in that they reflect the physical mechanism driving the co-evolution of SMBHs and spheroids.Comment: 15 pages, 16 figures, accepted for publication in Ap

A Protocol for Space Charge Measurements in Full-size HVDC Extruded Cables

This position paper, prepared by the IEEE DEIS HVDC Cable Systems Technical Committee, illustrates a protocol recommended for the measurement of space charges in full-size HVDC extruded cables during load cycle qualification tests (either prequalification load cycles or type test load cycles). The protocol accounts for the experimental practices of space charge measurements in the thick insulation of coaxial cables in terms of poling time, depolarization time, heating and cooling of specimens, as well as for the experience gained very recently from such kind of measurements performed in the framework of qualification tests relevant to ongoing HVDC cable system projects. The goal of the protocol is not checking the compliance with any maximum acceptable limit of either space charge or electric field. Rather, this protocol aims at assessing the variation of the electric field profile in the cable insulation wall during poling time at the beginning and at the end of load cycle qualification tests for full-size HVDC extruded cables. Indeed, in the design stage the electric field distributions are determined by the cable geometry and by temperature gradient in the insulation. Thus, the design is based on macroscopic parameters conductivity and permittivity and how they depend upon temperature. Any disturbance of the electric field due to space charge accumulation will only be revealed during space charge measurements either in as-manufactured state or in the aged state after load cycle qualification tests