The Behavior of the Renewal Sequence in Case the Tail of the Waiting-Time Distribution Is Regularly Varying with Index -1

A second-order asymptotic result for the probability of occurrence of a persistent and aperiodic recurrent event is given if the tail of the distribution of the waiting time for this event is regularly varying with index -1

Influence of oxygen ordering kinetics on Raman and optical response in YBa_2Cu_3O_{6.4}

Kinetics of the optical and Raman response in YBa_2Cu_3O_{6.4} were studied during room temperature annealing following heat treatment. The superconducting T_c, dc resistivity, and low-energy optical conductivity recover slowly, implying a long relaxation time for the carrier density. Short relaxation times are observed for the B_{1g} Raman scattering -- magnetic, continuum, and phonon -- and the charge transfer band. Monte Carlo simulations suggest that these two relaxation rates are related to two length scales corresponding to local oxygen ordering (fast) and long chain and twin formation (slow).Comment: REVTeX, 3 pages + 4 PostScript (compressed) figure

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page

The spectral action for Moyal planes

Extending a result of D.V. Vassilevich, we obtain the asymptotic expansion for the trace of a "spatially" regularized heat operator associated with a generalized Laplacian defined with integral Moyal products. The Moyal hyperplanes corresponding to any skewsymmetric matrix $\Theta$ being spectral triples, the spectral action introduced in noncommutative geometry by A. Chamseddine and A. Connes is computed. This result generalizes the Connes-Lott action previously computed by Gayral for symplectic $\Theta$.Comment: 20 pages, no figure, few improvment

Challenges in microbial ecology: building predictive understanding of community function and dynamics

he importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth’s soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited. Building predictive models that link MC composition to function is a key emerging challenge in microbial ecology. Here, we argue that addressing this challenge requires close coordination of experimental data collection and method development with mathematical model building. We discuss specific examples where model–experiment integration has already resulted in important insights into MC function and structure. We also highlight key research questions that still demand better integration of experiments and models. We argue that such integration is needed to achieve significant progress in our understanding of MC dynamics and function, and we make specific practical suggestions as to how this could be achieved

Anomalously large oxygen-ordering contribution to the thermal expansion of untwinned YBa2Cu3O6.95 single crystals: a glass-like transition near room temperature

We present high-resolution capacitance dilatometry studies from 5 - 500 K of untwinned YBa2Cu3Ox (Y123) single crystals for x ~ 6.95 and x = 7.0. Large contributions to the thermal expansivities due to O-ordering are found for x ~ 6.95, which disappear below a kinetic glass-like transition near room temperature. The kinetics at this glass transition is governed by an energy barrier of 0.98 +- 0.07 eV, in very good agreement with other O-ordering studies. Using thermodynamic arguments, we show that O-ordering in the Y123 system is particularly sensitive to uniaxial pressure (stress) along the chain axis and that the lack of well-ordered chains in Nd123 and La123 is most likely a consequence of a chemical-pressure effect.Comment: 4 pages, 3 figures, submitted to PR

Upper critical field pecularities of superconducting YNi2B2C and LuNi2B2C

We present new upper critical field Hc2(T) data in a broad temperature region from 0.3K to Tc for LuNi2B2C and YNi2B2C single crystals with well characterized low impurity scattering rates. The absolute values for all T, in particular Hc2(0), and the sizeable positive curvature (PC) of Hc2(T) at high and intermediate T are explained quantitatively within an effective two-band model. The failure of the isotropic single band approach is discussed in detail. Supported by de Haas van Alphen data, the superconductivity reveals direct insight into details of the electronic structure. The observed maximal PC near Tc gives strong evidence for clean limit type II superconductors.Comment: 4 pages, 2 figures, Phys. Rev. Lett. accepte

Heat kernel and number theory on NC-torus

The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit on a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC $\phi^4$ theory on \T^4, we show that this theory can be made renormalizable at least at one loop, and may be even beyond

Infrared and optical properties of pure and cobalt-doped LuNi_2B_2C

We present optical conductivity data for Lu(Ni$_{1-x}$Co$_x$)$_2$B$_2$C over a wide range of frequencies and temperatures for x=0 and x=0.09. Both materials show evidence of being good Drude metals with the infrared data in reasonable agreement with dc resistivity measurements at low frequencies. An absorption threshold is seen at approximately 700 cm-1. In the cobalt-doped material we see a superconducting gap in the conductivity spectrum with an absorption onset at 24 +/- 2 cm-1 = 3.9$ +/- 0.4 k_BT_c suggestive of weak to moderately strong coupling. The pure material is in the clean limit and no gap can be seen. We discuss the data in terms of the electron-phonon interaction and find that it can be fit below 600 cm-1 with a plasma frequency of 3.3 eV and an electron-phonon coupling constant lambda_{tr}=0.33 using an alpha^{2}F(omega) spectrum fit to the resistivity.Comment: 10 pages with 10 embedded figures, submitted to PR

Inter- and Intragranular Effects in Superconducting Compacted Platinum Powders

Compacted platinum powders exhibit a sharp onset of diamagnetic screening at $T \simeq 1.9$ mK in zero magnetic field in all samples investigated. This sharp onset is interpreted in terms of the intragranular transition into the superconducting state. At lower temperatures, the magnetic ac susceptibility strongly depends on the ac field amplitude and reflects the small intergranular critical current density $j_{c}$. This critical current density shows a strong dependence on the packing fraction f of the granular samples. Surprisingly, $j_{c}$ increases significantly with decreasing f ($j_{c}(B=0, T=0) \simeq 0.07$ A/cm$^{2}$ for f = 0.67 and $j_{c}(B=0, T=0) \simeq 0.8$ A/cm$^{2}$ for f = 0.50). The temperature dependence of $j_{c}$ shows strong positive curvature over a wide temperature range for both samples. The phase diagrams of inter- and intragranular superconductivity for different samples indicate that the granular structure might play the key role for an understanding of the origin of superconductivity in the platinum compacts.Comment: 11 pages including 9 figures. To appear in Phys. Rev. B in Nov. 0