Mathematical Analysis of a Generalized Chiral Quark Soliton Model

A generalized version of the so-called chiral quark soliton model (CQSM) in nuclear physics is introduced. The Hamiltonian of the generalized CQSM is given by a Dirac type operator with a mass term being an operator-valued function. Some mathematically rigorous results on the model are reported. The subjects included are: (i) supersymmetric structure; (ii) spectral properties; (iii) symmetry reduction; (iv) a unitarily equivalent model.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Afterword: Narratives that Determine Writers and Social Justice Writing Center Work

Recently, I took over as my campus’ writing center director. I’ll be honest. I haven’t worked in a writing center since I was a graduate student at Oregon State (that was in the early 90s). I have a lot to learn. While I’ve helped assess and review the writing center at Fresno State and the one I’m currently directing, I haven’t read carefully in the literature for two decades. This summer has been one of rereading the literature on writing centers, and reading newer scholarship (to me). When I left writing centers and its scholarship in the early 90s, the discussions were about encouraging writers to take control of the consultation, to find ways to have them read and write on their drafts. It was about collaboration, agency-building, and student control. I remember working hard to find ways to be collaborators, not teachers, to have the writer read and mark on her draft. But we never talked about race or racism in writing center practices, never discussed the ways whiteness and whiteliness saturated writing centers and their practices. While in 2007 Geller, Eodice, Condon, Carroll, and Boquet identify the limited ways that writing center training texts address race and racism, the discussions I find in the literature today are ones that at least approach such concerns. These more recent discussions are ones about multilingual writers, diversity in writing centers, and the complexities around working alongside the growing numbers of international writers in U.S. colleges and universities. Many of these questions were initiated by Nancy Grimm in 1999, with other voices contributing important ideas, such as Victor Villanueva’s on the new racism, Paul Kei Matsuda’s on “the myth of linguistic homogeneity,” Vershawn Ashanti Young’s on “codemeshing,” Ben Rafoth’s on engaging with multilingual writers in writing centers, and of course, Greenfield and Rowan’s important 2011 collection, Writing Centers and the New Racism. But as Geller et al. discuss, there still is much work to be done around identifying white privilege and, I’ll add, white language privilege, in writing center practices.University Writing Cente

Ultra-Weak Time Operators of Schroedinger Operators

In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schroedinger operators H with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions $f$ such that $f(H)$ has an ultra-weak time operator is found.Comment: We add Sections 1.1,1.2 and 1.

Dry minor mergers and size evolution of high-z compact massive early-type galaxies

Recent observations show evidence that high-z (z\sim 2 - 3) early-type galaxies (ETGs) are more compact than those with comparable mass at z\sim 0. Such a size evolution is most likely explained by the `Dry Merger Sceanario'. However, previous studies based on this scenario are not able to consistantly explain both the properties of the high-z compact massive ETGs and the local ETGs. We investigate the effect of multiple sequential dry minor mergers on the size evolution of the compact massive ETGs. From an analysis of the Millennium Simulation Database, we show that such minor (stellar mass ratio $M_{2}/M_{1} < 1/4$) mergers are extremely common during hierarchical structure formation. We perform N-body simulations of sequential minor mergers with parabolic and head-on orbits, including a dark matter component and a stellar component. Typical mass ratios of the minor mergers are $1/20 < M_{2}/M_{1} < 1/10$. We show that sequential minor mergers of compact satellite galaxies are the most efficient at promoting size growth and decreasing the velocity dispersion of the compact massive ETGs in our simulations. The change of stellar size and density of the merger remnants is consistent with recent observations. Furthermore, we construct the merger histories of candidates for the high-z compact massive ETGs using the Millennium Simulation Database, and estimate the size growth of the galaxies by the dry minor merger scenario. We can reproduce the mean size growth factor between $z=2$ and $z=0$, assuming the most efficient size growth obtained during sequential minor mergers in our simulations. However, we note that our numerical result is only valid for merger histories with typical mass ratios between 1/20 and 1/10 with parabolic and head-on orbits, and that our most efficient size growth efficiency is likely to an upper limit.Comment: 23 pages, 15 figures, accepted for MNRAS, Fig. 5 is fixe

Cosmic evolution of bars in simulations of galaxy formation

We investigate the evolution of two bars formed in fully self-consistent hydrodynamic simulations of the formation of Milky Way-mass galaxies. One galaxy shows higher central mass concentration and has a longer and stronger bar than the other at $z = 0$. The stronger bar evolves by transferring its angular momentum mainly to the dark halo. Consequently the rotation speed of the bar decreases with time, while the amplitude of the bar increases with time. These features qualitatively agree with the results obtained by idealized simulations. The pattern speed of the stronger bar largely goes up and down within a half revolution in its early evolutionary stage. These oscillations occur when the bar is misaligned with the $m = 4$ mode Fourier component. These oscillations correlate with the oscillations in the triaxilality of the dark matter halo, but differently from the way identified by idealized simulations. The amplitude of the weaker bar does not increase despite the fact that its rotation slows down with time.This result contradicts what is expected from idealized simulations and is caused by the decline of the central density associated with the mass loss and feedback from the stellar populations. The amplitude of the weaker bar is further weakens by the angular momentum injection by the interactions with stellar clumps in the disk. In the both galaxies, the bars are terminated around the 4:1 resonance.Comment: 17 pages, 18 figures, accepted for publication in PAS

The Effect of Self-gravity of Gas on Gas Fueling in Barred Galaxies with a Supermassive Black Hole

In our previous paper, we have shown that a gas disk in the nuclear region of a barred galaxy which contains a central supermassive black hole (SMBH) rapidly evolves into a nuclear gas ring by the effect of an additional inner Lindblad resonance caused by the SMBH. In this paper, we investigate the fate of the gas ring, involving self-gravity of gas, using two-dimensional hydrodynamical simulations. We find that the gas ring becomes gravitationally unstable for a gas surface density of gas above a critical value, and fragments into several gas clumps. Some denser clumps increase their mass via the accretion of the surrounding gas and collisions with other clumps, and finally a very massive gas clump (10^7 M_sun) is formed. Due to the torque from the most massive clump, a part of the gas in the ring loses its angular momentum and falls into the galactic center. As a result, a nuclear gas disk (50 pc) is formed around the SMBH. The accretion rate for $R<50$ pc attains about 1 M_sun/yr for 3.5*10^7 yr. At the final phase of the bar-driven fueling, self-gravity is crucial for the angular momentum transfer of the gas. This is a new mechanism for gas fueling to the vicinity of the SMBH.Comment: 14 pages, 7 figures, AASTeX, submitted to Ap