The Elementary Divisors of the Incidence Matrices of Skew Lines in PG(3,p)

The elementary divisors of the incidence matrices of lines in $PG(3,p)$ are computed, where two lines are incident if and only if they are skew.Comment: 9 page

Packing-limited growth of irregular objects

We study growth limited by packing for irregular objects in two dimensions. We generate packings by seeding objects randomly in time and space and allowing each object to grow until it collides with another object. The objects we consider allow us to investigate the separate effects of anisotropy and non-unit aspect ratio. By means of a connection to the decay of pore-space volume, we measure power law exponents for the object size distribution. We carry out a scaling analysis, showing that it provides an upper bound for the size distribution exponent. We find that while the details of the growth mechanism are irrelevant, the exponent is strongly shape dependent. Potential applications lie in ecological and biological environments where sessile organisms compete for limited space as they grow.Comment: 6 pages, 4 figures, 1 table, revtex

Externalities, Incentives, and Economic Reforms

The paper emphasizes the role of institutions and incentives in the presence of externalities. An economy with multiple public decision makers is likely to experience "overspending," "undertaxing," "overborrowing," and "overinflation" unless effective institutions exist for overcoming coordination failure. External financing may weaken incentives for adjustment over the longer run unless assistance is made conditional on fundamental institutional reforms. The paper also analyses reforms that strengthen incentives to provide effort. Uncertainty regarding future taxes reduces present effort and the responsiveness of output to market signals. In addition, the paper addresses the adverse effects of bank insurance and soft budget constraints.

Packing-Limited Growth

We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via simulation in d=2, 3, and 4. We show how a broad class of such models exhibit distributions of sphere radii with a universal exponent. We construct a scaling theory that relates the fractal structure of these models to the decay of their pore space, a theory that we confirm via numerical simulations. The scaling theory also predicts an upper bound for the universal exponent and is in exact agreement with numerical results for d=4.Comment: 6 pages, 5 figures, 4 tables, revtex4 to appear in Phys. Rev. E, May 200

Dielectric laser acceleration of electrons in the vicinity of single and double grating structures - theory and simulations

Dielectric laser acceleration of electrons close to a fused-silica grating has recently been observed (Peralta et al., Nature 503, 91 (2013); Breuer, Hommelhoff, PRL 111, 134803 (2013)). Here we present the theoretical description of the near-fields close to such a grating that can be utilized to accelerate non-relativistic electrons. We also show simulation results of electrons interacting with such fields in a single and double grating structure geometry and discuss dephasing effects that have to be taken into account when designing a photonic-structure-based accelerator for non-relativistic electrons. We further model the space charge effect using the paraxial ray equation and discuss the resulting expected peak currents for various parameter sets.Comment: 14 pages, 7 figure

The critical group of the Kneser graph on 22-subsets of an nn-element set

In this paper we compute the critical group of the Kneser graph $KG(n,2)$. This is equivalent to computing the Smith normal form of a Laplacian matrix of this graph.Comment: 16 pages, minor change

The Elementary Divisors of the Incidence Matrix of Skew Lines in PG(3,q)

The elementary divisors of the incidence matrix of lines in PG(3,q) are computed, where two lines are incident if and only if they are skew.Comment: 13 pages. The results of this paper supersede those in the paper arXiv:math/1001.2551 V2. Minor correction