Effective degrees of nonlinearity in a family of generalized models of two-dimensional turbulence

We study the small-scale behavior of generalized two-dimensional turbulence governed by a family of model equations, in which the active scalar $\theta=(-\Delta)^{\alpha/2}\psi$ is advected by the incompressible flow $\u=(-\psi_y,\psi_x)$. The dynamics of this family are characterized by the material conservation of $\theta$, whose variance is preferentially transferred to high wave numbers. As this transfer proceeds to ever-smaller scales, the gradient $\nabla\theta$ grows without bound. This growth is due to the stretching term $(\nabla\theta\cdot\nabla)\u$ whose ``effective degree of nonlinearity'' differs from one member of the family to another. This degree depends on the relation between the advecting flow $\u$ and the active scalar $\theta$ and is wide ranging, from approximately linear to highly superlinear. Linear dynamics are realized when $\nabla\u$ is a quantity of no smaller scales than $\theta$, so that it is insensitive to the direct transfer of the variance of $\theta$, which is nearly passively advected. This case corresponds to $\alpha\ge2$, for which the growth of $\nabla\theta$ is approximately exponential in time and non-accelerated. For $\alpha<2$, superlinear dynamics are realized as the direct transfer of entails a growth in \nabla\u, thereby enhancing the production of $\nabla\theta$. This superlinearity reaches the familiar quadratic nonlinearity of three-dimensional turbulence at $\alpha=1$ and surpasses that for $\alpha<1$. The usual vorticity equation ($\alpha=2$) is the border line, where \nabla\u and $\theta$ are of the same scale, separating the linear and nonlinear regimes of the small-scale dynamics. We discuss these regimes in detail, with an emphasis on the locality of the direct transfer.Comment: 6 journal pages, to appear in Physical Review

Ground state fluctuations in finite Fermi and Bose systems

We consider a small and fixed number of fermions (bosons) in a trap. The ground state of the system is defined at T=0. For a given excitation energy, there are several ways of exciting the particles from this ground state. We formulate a method for calculating the number fluctuation in the ground state using microcanonical counting, and implement it for small systems of noninteracting fermions as well as bosons in harmonic confinement. This exact calculation for fluctuation, when compared with canonical ensemble averaging, gives considerably different results, specially for fermions. This difference is expected to persist at low excitation even when the fermion number in the trap is large.Comment: 20 pages (including 1 appendix), 3 postscript figures. An error was found in one section of the paper. The corrected version is updated on Sep/05/200

Beware of simple methods for structure-based virtual screening: the critical importance of broader comparisons

We discuss how data unbiasing and simple methods such as protein-ligand Interaction FingerPrint (IFP) can overestimate virtual screening performance. We also show that IFP is strongly outperformed by target-specific machine-learning scoring functions, which were not considered in a recent report concluding that simple methods were better than machine-learning scoring functions at virtual screening

Euclidean-signature Supergravities, Dualities and Instantons

We study the Euclidean-signature supergravities that arise by compactifying D=11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D=8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multi-charge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D-3)-brane solutions.Comment: Latex, 50 pages, typos corrected and references adde

On the Microcanonical Entropy of a Black Hole

It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by considering three simple thermodynamic models whose energy spectrum may be defined in terms of one quantum number only, as in a non-rotating black hole. The first two pertain to collections of noninteracting bosons, with logarithmic and power-law spectra. The last is an area ensemble for a black hole with equi-spaced area spectrum. In this case, the many-body degeneracy factor can be obtained analytically in a closed form. We also show that in this model, the leading term in the entropy is proportional to the horizon area A, and the next term is ln A with a negative coefficient.Comment: 15 pages, 1 figur

The Angular Momentum of Brightest Cluster Galaxies

Massive Brightest Cluster Galaxies (BCGs) are observed to have a range of angular momenta, suggesting a variety of merging historie

Psr1p interacts with SUN/sad1p and EB1/mal3p to establish the bipolar spindle

Regular Abstracts - Sunday Poster Presentations: no. 382During mitosis, interpolar microtubules from two spindle pole bodies (SPBs) interdigitate to create an antiparallel microtubule array for accommodating numerous regulatory proteins. Among these proteins, the kinesin-5 cut7p/Eg5 is the key player responsible for sliding apart antiparallel microtubules and thus helps in establishing the bipolar spindle. At the onset of mitosis, two SPBs are adjacent to one another with most microtubules running nearly parallel toward the nuclear envelope, creating an unfavorable microtubule configuration for the kinesin-5 kinesins. Therefore, how the cell organizes the antiparallel microtubule array in the first place at mitotic onset remains enigmatic. Here, we show that a novel protein psrp1p localizes to the SPB and plays a key role in organizing the antiparallel microtubule array. The absence of psr1+ leads to a transient monopolar spindle and massive chromosome loss. Further functional characterization demonstrates that psr1p is recruited to the SPB through interaction with the conserved SUN protein sad1p and that psr1p physically interacts with the conserved microtubule plus tip protein mal3p/EB1. These results suggest a model that psr1p serves as a linking protein between sad1p/SUN and mal3p/EB1 to allow microtubule plus ends to be coupled to the SPBs for organization of an antiparallel microtubule array. Thus, we conclude that psr1p is involved in organizing the antiparallel microtubule array in the first place at mitosis onset by interaction with SUN/sad1p and EB1/mal3p, thereby establishing the bipolar spindle.postprin

BiTeCl and BiTeBr: a comparative high-pressure optical study

We here report a detailed high-pressure infrared transmission study of BiTeCl and BiTeBr. We follow the evolution of two band transitions: the optical excitation $\beta$ between two Rashba-split conduction bands, and the absorption $\gamma$ across the band gap. In the low pressure range, $p< 4$~GPa, for both compounds $\beta$ is approximately constant with pressure and $\gamma$ decreases, in agreement with band structure calculations. In BiTeCl, a clear pressure-induced phase transition at 6~GPa leads to a different ground state. For BiTeBr, the pressure evolution is more subtle, and we discuss the possibility of closing and reopening of the band gap. Our data is consistent with a Weyl phase in BiTeBr at 5$-$6~GPa, followed by the onset of a structural phase transition at 7~GPa.Comment: are welcom