A Level Set Approach to Eulerian-Lagrangian Coupling

We present a numerical method for coupling an Eulerian compressible flow solver with a Lagrangian solver for fast transient problems involving fluid-solid interactions. Such coupling needs arise when either specific solution methods or accuracy considerations necessitate that different and disjoint subdomains be treated with different (Eulerian or Lagrangian)schemes. The algorithm we propose employs standard integration of the Eulerian solution over a Cartesian mesh. To treat the irregular boundary cells that are generated by an arbitrary boundary on a structured grid, the Eulerian computational domain is augmented by a thin layer of Cartesian ghost cells. Boundary conditions at these cells are established by enforcing conservation of mass and continuity of the stress tensor in the direction normal to the boundary. The description and the kinematic constraints of the Eulerian boundary rely on the unstructured Lagrangian mesh. The Lagrangian mesh evolves concurrently, driven by the traction boundary conditions imposed by the Eulerian counterpart. Several numerical tests designed to measure the rate of convergence and accuracy of the coupling algorithm are presented as well. General problems in one and two dimensions are considered, including a test consisting of an isotropic elastic solid and a compressible fluid in a fully coupled setting where the exact solution is available

Predicting Stock Volatility Using After-Hours Information

We use realized volatilities based on after hours high frequency returns to predict next day volatility. We extend GARCH and long-memory forecasting models to include additional information: the whole night, the preopen, the postclose realized variance, and the overnight squared return. For four NASDAQ stocks (MSFT, AMGN, CSCO, and YHOO) we find that the inclusion of the preopen variance can improve the out-of-sample forecastability of the next day conditional day volatility. Additionally, we find that the postclose variance and the overnight squared return do not provide any predictive power for the next day conditional volatility. Our findings support the results of prior studies that traders trade for non-information reasons in the postclose period and trade for information reasons in the preopen period.

Rank-finiteness for modular categories

We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a generalization of the Cauchy theorem in group theory to the context of spherical fusion categories. For a modular category $\mathcal{C}$ with $N=ord(T)$, the order of the modular $T$-matrix, the Cauchy theorem says that the set of primes dividing the global quantum dimension $D^2$ in the Dedekind domain $\mathbb{Z}[e^{\frac{2\pi i}{N}}]$ is identical to that of $N$.Comment: 25 pages (last version). Version 2: removed weakly integral rank 6 and integral rank 7 section, improved rank 5 classification up to monoidal equivalence. Version 3: removed rank 5 classification (note title change)--this will be published separately. Significantly improved expositio

On classification of modular categories by rank

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an application, we determine all possible fusion rules for all rank=$5$ modular categories and describe the corresponding monoidal equivalence classes.Comment: arXiv admin note: substantial text overlap with arXiv:1310.705

Hearing Emerson, Lake, and Palmer Anew: Progressive Rock as "Music of Attractions"

Progressive rock is a loose label for music that combines some of the basic ingredients of early rock 'n' roll and elements of genres that are generally considered more prestigious, such as Western art music, jazz, and Indian classical music. After emerging in the late 1960s, progressive rock reached its peak in popularity in the early 1970s. Since the rise of punk in the mid 1970s, the genre has retreated to the college circuit, select clubs, and fringe festivals. Over the past quarter century, there have been two common stances on progressive rock. One builds upon rock critics' longstanding and overwhelmingly negative view of the genre. For most critics, such as Dave Marsh and Lester Bangs, the most important element of rock is the rather ambiguous concept of "authenticity." Theoretically, "authenticity" is connected with genuineness. A song is "authentic" when it is written (or at least arranged) by the performing musicians, and is about their lives and emotions. Although songwriting credits are easily conveyed, this notion of authenticity is not particularly useful in criticism. After all, how would a critic know whether or not the feelings expressed in a song are genuine? In practice, many critics track authenticity with more obvious qualities: a sense of rebelliousness, the inclusion of blues elements such as blues progressions and extended vocal melismas, and subtle inflections of the beat. Given these criteria, the negative critical reception of progressive rock-exemplified by the strongly worded Lester Bangs quote above-is hardly surprising. After all, progressive rock musicians diluted the influence of blues in rock music by incorporating elements of many other genres. They also took away the sexuality and rebelliousness often heard in rock's hard-driving beat, replacing it with complex meters that are not suited to dancing