Derivation of an integral of Boros and Moll via convolution of Student t-densities

We show that the evaluation of an integral considered by Boros and Moll is a special case of a convolution result about Student t-densities obtained by the authors in 2008

On the scaling behavior of the abelian sandpile model

The abelian sandpile model in two dimensions does not show the type of critical behavior familar from equilibrium systems. Rather, the properties of the stationary state follow from the condition that an avalanche started at a distance r from the system boundary has a probability proportional to 1/sqrt(r) to reach the boundary. As a consequence, the scaling behavior of the model can be obtained from evaluating dissipative avalanches alone, allowing not only to determine the values of all exponents, but showing also the breakdown of finite-size scaling.Comment: 4 pages, 5 figures; the new version takes into account that the radius distribution of avalanches cannot become steeper than a certain power la

Renormalization group approach to an Abelian sandpile model on planar lattices

One important step in the renormalization group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. {\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690 (1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG transformations more quickly with large cell size, e.g. $3 \times 3$ cell for the square (sq) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51}, 1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent $\tau$ and the dynamical exponent $z$. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.Comment: 29 pages, 6 figure

The Role of Intrinsic and Surface States on the Emission Properties of Colloidal CdSe and CdSe/ZnS Quantum Dots

Time Resolved Photoluminescence (TRPL) measurements on the picosecond time scale (temporal resolution of 17 ps) on colloidal CdSe and CdSe/ZnS Quantum Dots (QDs) were performed. Transient PL spectra reveal three emission peaks with different lifetimes (60 ps, 460 ps and 9–10 ns, from the bluest to the reddest peak). By considering the characteristic decay times and by comparing the energetic separations among the states with those theoretically expected, we attribute the two higher energy peaks to ± 1Uand ± 1L bright states of the fine structure picture of spherical CdSe QDs, and the third one to surface states emission. We show that the contribution of surface emission to the PL results to be different for the two samples studied (67% in the CdSe QDs and 32% in CdSe/ZnS QDs), confirming the decisive role of the ZnS shell in the improvement of the surface passivation

Fine Structure of Avalanches in the Abelian Sandpile Model

We study the two-dimensional Abelian Sandpile Model on a square lattice of linear size L. We introduce the notion of avalanche's fine structure and compare the behavior of avalanches and waves of toppling. We show that according to the degree of complexity in the fine structure of avalanches, which is a direct consequence of the intricate superposition of the boundaries of successive waves, avalanches fall into two different categories. We propose scaling ans\"{a}tz for these avalanche types and verify them numerically. We find that while the first type of avalanches has a simple scaling behavior, the second (complex) type is characterized by an avalanche-size dependent scaling exponent. This provides a framework within which one can understand the failure of a consistent scaling behavior in this model.Comment: 10 page

Absorbing-state phase transitions in fixed-energy sandpiles

We study sandpile models as closed systems, with conserved energy density $\zeta$ playing the role of an external parameter. The critical energy density, $\zeta_c$, marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics in random media. Our results strongly suggest that there are at least three distinct universality classes for sandpiles.Comment: 41 pages, 23 figure

Prospects of nanoscience with nanocrystals

Colloidal nanocrystals (NCs, i.e., crystalline nanoparticles) have become an important class of materials with great potential for applications ranging from medicine to electronic and optoelectronic devices. Today's strong research focus on NCs has been prompted by the tremendous progress in their synthesis. Impressively narrow size distributions of just a few percent, rational shape-engineering, compositional modulation, electronic doping, and tailored surface chemistries are now feasible for a broad range of inorganic compounds. The performance of inorganic NC-based photovoltaic and light-emitting devices has become competitive to other state-of-the-art materials. Semiconductor NCs hold unique promise for near- and mid-infrared technologies, where very few semiconductor materials are available. On a purely fundamental side, new insights into NC growth, chemical transformations, and self-organization can be gained from rapidly progressing in situ characterization and direct imaging techniques. New phenomena are constantly being discovered in the photophysics of NCs and in the electronic properties of NC solids. In this Nano Focus, we review the state of the art in research on colloidal NCs focusing on the most recent works published in the last 2 years13923931sciescopu