Cubic Partial Cubes from Simplicial Arrangements

We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.Comment: 11 pages, 10 figure

On the variational interpretation of the discrete KP equation

We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice ${\mathbb Z}^{N}$ as well as on the root lattice $Q(A_{N})$. We prove that, on a lattice of dimension at least four, the corresponding Euler-Lagrange equations are equivalent to the dKP equation.Comment: 24 page

Making Nuclei Out Of The Skyrme Crystal

A new method for approximating Skyrme solutions is developed. It consists of cutting sections out of the Skyrme crystal and smoothly interpolating between the boundary and spatial infinity. Several field configurations are constructed, and their energies calculated. The surface energy (per unit area) of an infinite flat plane of the crystal is also calculated, and the result used to derive a formula analogous to the semi-empirical mass formula of nuclear physics. This formula can be used to give some idea of what the Skyrme model predicts about volume and surface energies of the nucleus over a broad range of baryon numbers.Comment: 20 pages, uuencoded ps file `crystal.uu'. The LaTeX version can be obtained by emailing [email protected] or [email protected]

Exploring spatiotemporal dynamics of urban fires: A case of Nanjing, China

Urban fire occurs within the built environment, usually involving casualties and economic losses, and affects individuals and socioeconomic activities in the surrounding neighborhoods. A good understanding of the spatiotemporal dynamics of fire incidents can offer insights into potential determinants of various fire events, therefore enabling better fire risk estimation which can assist with future allocation of prevention resources and strategic planning of mitigation programs. Using a twelve-year (2002–2013) dataset containing the urban fire events in Nanjing, China, this research explores the spatiotemporal dynamics of urban fires using a range of exploratory spatial data analysis (ESDA) approaches. Of particular interest here are the fire incidents involving residential properties and local facilities due to their relatively higher occurrence frequencies. The results indicate that the overall amount of urban fires has greatly increased in the last decade and the spatiotemporal distribution of fire events varies among different incident types. The identified spatiotemporal patterns of urban fires in Nanjing can be linked to the urban development strategies and how they have been reflected in reality in recent years

Configurations of lines and models of Lie algebras

The automorphism groups of the 27 lines on the smooth cubic surface or the 28 bitangents to the general quartic plane curve are well-known to be closely related to the Weyl groups of $E\_6$ and $E\_7$. We show how classical subconfigurations of lines, such as double-sixes, triple systems or Steiner sets, are easily constructed from certain models of the exceptional Lie algebras. For ${\mathfrak e}\_7$ and ${\mathfrak e}\_8$ we are lead to beautiful models graded over the octonions, which display these algebras as plane projective geometries of subalgebras. We also interpret the group of the bitangents as a group of transformations of the triangles in the Fano plane, and show how this allows to realize the isomorphism $PSL(3,F\_2)\simeq PSL(2,F\_7)$ in terms of harmonic cubes.Comment: 31 page

Glass foam granulate as growing medium for tomato and cucumber

Glass foam granulate was evaluated for use as a horticultural rooting medium with laboratory tests and cultivation experiments. The laboratory tests included moisture characteristics, rehydration rate and pH buffering analyses. Cucumbers and later on tomatoes were propagated in rockwool propagation cubes and planted on slabs of Growstones™ glass foam granulate. They were compared with cucumber respectively tomatoes grown on rockwool slabs. Lab results show that the coarse nature of the glass foam granulate (0.5-5 cm) limits the maximum moisture content to 50%. The rehydration rate is very high, reaching more than 80% of container capacity in 5 min. The tested material initially reacts with water, raising the pH to over 10 pH units. Based on lab results a recipe for rinsing the material prior to cultivation was calculated. Cucumber cultivation results show an equal production to plants grown on rockwool. The first yield on glass foam granulate is 1-2 days earlier. The susceptibility to Pythium is significantly lower than on rockwool. The wax layer on cucumbers grown on glass foam granulate is perceptibly thicker as consequence of an elevated silicon level of 0.25 to 1.6 mmol L-1 in the slab solution. Tomatoes on glass foam granulate show smaller stem diameters and recovered faster from blossom end rot. Yield levels on glass foam granulate and rockwool are equal. In conclusion growing on glass foam granulate is equally productive as rockwool growing. The material is drier and thus less susceptible to Pythium and more generative in nature. Glass foam granulate can be irrigated with small and frequent irrigation cycles and the material must be rinsed with an acid solution before planting. Small amounts of silicon are released into the nutrient solution

Synthetic Molecular Clouds from Supersonic MHD and Non-LTE Radiative Transfer Calculations

The dynamics of molecular clouds is characterized by supersonic random motions in the presence of a magnetic field. We study this situation using numerical solutions of the three-dimensional compressible magneto-hydrodynamic (MHD) equations in a regime of highly supersonic random motions. The non-LTE radiative transfer calculations are performed through the complex density and velocity fields obtained as solutions of the MHD equations, and more than 5x10^5 synthetic molecular spectra are obtained. We use a numerical flow without gravity or external forcing. The flow is super-Alfvenic and corresponds to model A of Padoan and Nordlund (1997). Synthetic data consist of sets of 90x90 synthetic spectra with 60 velocity channels, in five molecular transitions: J=1-0 and J=2-1 for 12CO and 13CO, and J=1-0 for CS. Though we do not consider the effects of stellar radiation, gravity, or mechanical energy input from discrete sources, our models do contain the basic physics of magneto-fluid dynamics and non-LTE radiation transfer and are therefore more realistic than previous calculations. As a result, these synthetic maps and spectra bear a remarkable resemblance to the corresponding observations of real clouds.Comment: 33 pages, 12 figures included, 5 jpeg figures not included (fig1a, fig1b, fig3, fig4 fig5), submitted to Ap