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

Direct visualization of a significant stenosis of the right coronary artery by transthoracic echocardiography. A case report

Non-invasive imaging of coronary arteries by transthoracic echocardiography is an emerging diagnostic tool to study the left main (LM), left descending artery (LAD), circumflex (Cx) and right coronary artery (RCA). Impaired coronary circulation can be assessed by measuring coronary velocity flow reserve (CVFR) by transthoracic Doppler echocardiography. Coronary artery stenoses can be identified as localized colour aliasing and accelerated flow velocities. We report a case with an acute coronary syndrome (ACS) of a 46-year-old man. With non-invasive imaging of coronary arteries by transthoracic echocardiography (TTE), we identified a segment of the mid right coronary artery (RCA) suggestive of stenosis with localized colour aliasing and accelerated flow velocity. We found a high ratio between the stenotic peak velocity and the prestenotic peak velocity, and a pathologic coronary flow velocity reserve (CFVR) distal to the stenosis in the posterior interventricular descending branch (RDP). Subsequent coronary angiography demonstrated one vessel disease with a stenosis in segment 3 of RCA, which was successfully treated with percutaneos coronary intervention PCI. Two weeks following the PCI procedure he was readmitted to hospital with chest pain. A subacute stent thrombosis was questioned, and repeated echocardiography was preformed. The mid portion of RCA showed normal and laminar flow. The CVFR of RCA measured in the RDP showed normal vasodilatory response, confirming an open RCA without any flow limitation. A repeated coronary angiogram demonstrated only a mild in stent intimal hyperplasia. This case illustrates the value of transthoracic echocardiography as a tool both in the diagnosis and the follow-up of chest pain disorders and coronary flow problems. Transthoracic echocardiography allows both direct visualization of the various coronary segments and assessment of the CVFR

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

On the equilibrium morphology of systems drawn from spherical collapse experiments

We present a purely theoretical study of the morphological evolution of self-gravitating systems formed through the dissipationless collapse of N-point sources. We explore the effects of resolution in mass and length on the growth of triaxial structures formed by an instability triggered by an excess of radial orbits. We point out that as resolution increases, the equilibria shift, from mildly prolate, to oblate. A number of particles N ~= 100000 or larger is required for convergence of axial aspect ratios. An upper bound for the softening, e ~ 1/256, is also identified. We then study the properties of a set of equilibria formed from scale-free cold initial mass distributions, ro ~ r^-g with 0 <= g <= 2. Oblateness is enhanced for initially more peaked structures (larger values of g). We map the run of density in space and find no evidence for a power-law inner structure when g <= 3/2 down to a mass fraction <~0.1 per cent of the total. However, when 3/2 < g <= 2, the mass profile in equilibrium is well matched by a power law of index ~g out to a mass fraction ~ 10 per cent. We interpret this in terms of less-effective violent relaxation for more peaked profiles when more phase mixing takes place at the centre. We map out the velocity field of the equilibria and note that at small radii the velocity coarse-grained distribution function (DF) is Maxwellian to a very good approximation.Comment: 16 page

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