Local trace formulae and scaling asymptotics in Toeplitz quantization, II

In the spectral theory of positive elliptic operators, an important role is played by certain smoothing kernels, related to the Fourier transform of the trace of a wave operator, which may be heuristically interpreted as smoothed spectral projectors asymptotically drifting to the right of the spectrum. In the setting of Toeplitz quantization, we consider analogues of these, where the wave operator is replaced by the Hardy space compression of a linearized Hamiltonian flow, possibly composed with a family of zeroth order Toeplitz operators. We study the local asymptotics of these smoothing kernels, and specifically how they concentrate on the fixed loci of the linearized dynamics.Comment: Typos corrected. Slight expository change

Scaling asymptotics for quantized Hamiltonian flows

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map

Reflection High-Energy Electron Diffraction oscillations during epitaxial growth of artificially layered films of (BaCuOx)m /(CaCuO2)n

Pulsed Laser Deposition in molecular-beam epitaxy environment (Laser-MBE) has been used to grow high quality BaCuOx/CaCuO2 superlattices. In situ Reflection High Energy Electron Diffraction (RHEED) shows that the growth mechanism is 2-dimensional. Furthermore, weak but reproducible RHEED intensity oscillations have been monitored during the growth. Ex-situ x-ray diffraction spectra confirmed the growth rate deduced from RHEED oscillations. Such results demonstrate that RHEED oscillations can be used, even for (BaCuOx)2/(CaCuO2)2 superlattices, for phase locking of the growth.Comment: 9 pages, 5 figures. Corresponding author: Dr. A. Tebano: [email protected]

Ground Beetles From a Remnant Oak-Maple-Beech Forest and Its Surroundings in Northeastern Ohio (Coleoptera: Carabidae)

We report 66 ground beetle species in 14 tribes from a natural preserve in northeastern Ohio (Stark County). Six species are new state records. Data from pitfall trap transects across adjoining habitats suggest narrow habitat preferences in some species and broad tolerances in others. Trends toward flightlessness in forest species and macroptery in the fauna of disturbed agricultural sites are apparent

No more time to stay ‘single’ in the detection of Anisakis pegreffii, A. simplex (s. s.) and hybridization events between them: a multi-marker nuclear genotyping approach

A multi-marker nuclear genotyping approach was performed on larval and adult specimens of Anisakis spp. (N = 689) collected from fish and cetaceans in allopatric and sympatric areas of the two species Anisakis pegreffii and Anisakis simplex (s. s.), in order to: (1) identify specimens belonging to the parental taxa by using nuclear markers (allozymes loci) and sequence analysis of a new diagnostic nuclear DNA locus (i.e. partial sequence of the EF1 α−1 nDNA region) and (2) recognize hybrid categories. According to the Bayesian clustering algorithms, based on those markers, most of the individuals (N = 678) were identified as the parental species [i.e. A. pegreffii or A. simplex (s. s.)], whereas a smaller portion (N = 11) were recognized as F1 hybrids. Discordant results were obtained when using the polymerase chain reaction–restriction fragment length polymorphisms (PCR–RFLPs) of the internal transcribed spacer (ITS) ribosomal DNA (rDNA) on the same specimens, which indicated the occurrence of a large number of ‘hybrids’ both in sympatry and allopatry. These findings raise the question of possible misidentification of specimens belonging to the two parental Anisakis and their hybrid categories derived from the application of that single marker (i.e. PCR–RFLPs analysis of the ITS of rDNA). Finally, Bayesian clustering, using allozymes and EF1 α−1 nDNA markers, has demonstrated that hybridization between A. pegreffii and A. simplex (s. s.) is a contemporary phenomenon in sympatric areas, while no introgressive hybridization takes place between the two species

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

Measurement of angular momentum transport in turbulent flow between independently rotating cylinders

We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the \(\Omega_1, \Omega_2\) parameter space at high Reynolds numbers, where $\Omega_1$ \(\Omega_2\) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro = \(\Omega_1 - \Omega_2\)/\Omega_2 fully determines the state and torque $G$ as compared to G(Ro = \infty) \equiv \Gi. The ratio G/\Gi is a linear function of $Ro^{-1}$ in four sections of the parameter space. For flows with radially-increasing angular momentum, our measured torques greatly exceed those of previous experiments [Ji \textit{et al.}, Nature, \textbf{444}, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys., \textbf{347}, 734 (1999)].Comment: 4 pages, 4 figures, to appear in Physical Review Letter