The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

The origin of the E+ transition in GaAsN alloys

Optical properties of GaAsN system with nitrogen concentrations in the range of 0.9-3.7% are studied by full-potential LAPW method in a supercell approach. The E+ transition is identified by calculating the imaginary part of the dielectric function. The evolution of the energy of this transition with nitrogen concentration is studied and the origin of this transition is identified by analyzing the contributions to the dielectric function from different band combinations. The L_1c-derived states are shown to play an important role in the formation of the E+ transition, which was also suggested by recent experiments. At the same time the nitrogen-induced modification of the first conduction band of the host compound are also found to contribute significantly to the E+ transition. Further, the study of several model supercells demonstrated the significant influence of the nitrogen potential on the optical properties of the GaAsN system.Comment: 5 pages, 3 figure

Nonlinear magnetoinductive transmission lines

Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent capacitance. Extended numerical simulations reveal that power transmission along the array is also possible in other than the linear frequency bands, which are located close to the nonlinear resonances of a single nonlinear RLC circuit. Moreover, the effectiveness of power transmission for driving frequencies in the nonlinear bands is comparable to that in the linear band. Power transmission in the nonlinear bands occurs through the linear modes of the system, and it is closely related to the instability of a mode that is localized at the driven site.Comment: 11 pages, 11 figures, submitted to International Journal of Bifurcation and Chao

Active School Transport among Children from Canada, Colombia, Finland, South Africa, and the United States: A Tale of Two Journeys

Walking and biking to school represent a source of regular daily physical activity (PA). The objectives of this paper are to determine the associations of distance to school, crime safety, and socioeconomic variables with active school transport (AST) among children from five culturally and socioeconomically different country sites and to describe the main policies related to AST in those country sites. The analytical sample included 2845 children aged 9–11 years from the International Study of Childhood Obesity, Lifestyle and the Environment. Multilevel generalized linear mixed models were used to estimate the associations between distance, safety and socioeconomic variables, and the odds of engaging in AST. Greater distance to school and vehicle ownership were associated with a lower likelihood of engaging in AST in sites in upper-middle- and high-income countries. Crime perception was negatively associated to AST only in sites in high-income countries. Our results suggest that distance to school is a consistent correlate of AST in different contexts. Our findings regarding crime perception support a need vs. choice framework, indicating that AST may be the only commuting choice for many children from the study sites in upper-middle-income countries, despite the high perception of crime

Differential scanning calorimetry (DSC) and thermodynamic prediction of liquid fraction vs temperature for two high-performance alloys for semi-solid processing (Al-Si-Cu-Mg (319s) and Al-Cu-Ag (201))

There is a need to extend the application of semi-solid processing (SSP) to higher performance alloys such as 319s (Al-Si-Cu-Mg) and 201 (Al-Cu-Ag). The melting of these two alloys was investigated using differential scanning calorimetry (DSC) and thermodynamic prediction. The alloys had been processed by magneto-hydrodynamic (MHD) stirring before receipt to produce a microstructure suitable for SSP. The DSC results for the as-received MHD material were compared with those for material which has been taken through a complete DSC cycle and then reheated for a second DSC run. The effects of microsegregation were then analyzed. A higher liquid fraction for a particular temperature is found in the second DSC run than the first. Microstructural observations suggest this is because the intermetallics which form during the first cooling cycle tend to co-located. Quaternary and ternary reactions then occur during the second DSC heat and the co-location leads to enhanced peaks. The calculated liquid fraction is lower with 10 K/min DSC heating rate comparing with 3 K/min at a given temperature. The DSC scan rate must therefore be carefully considered if it is to be used to identify temperature parameters or the suitability of alloys for SSP. In addition, the starting material for DSC must represent the starting material for the SSP. With thermodynamic prediction, the equilibrium condition will provide better guidance for the thixoforming of MHD stirred starting material than the Scheil condition. The Scheil mode approximates more closely with a strongly microsegregated state

Three dimensional C-, S- and E-transforms

Three dimensional continuous and discrete Fourier-like transforms, based on the three simple and four semisimple compact Lie groups of rank 3, are presented. For each simple Lie group, there are three families of special functions ($C$-, $S$-, and $E$-functions) on which the transforms are built. Pertinent properties of the functions are described in detail, such as their orthogonality within each family, when integrated over a finite region $F$ of the 3-dimensional Euclidean space (continuous orthogonality), as well as when summed up over a lattice grid $F_M\subset F$ (discrete orthogonality). The positive integer $M$ sets up the density of the lattice containing $F_M$. The expansion of functions given either on $F$ or on $F_M$ is the paper's main focus.Comment: 24 pages, 13 figure

Human adipose stem cells cell sheet constructs impact epidermal morphogenesis in full-thickness excisional wounds

Among the wide range of strategies to target skin repair/regeneration, tissue engineering (TE) with stem cells at the forefront, remains as the most promising route. Cell sheet (CS) engineering is herein proposed, taking advantage of particular cell-cell and cell-extracellular matrix (ECM) interactions and subsequent cellular milieu, to create 3D TE constructs to promote full-thickness skin wound regeneration. Human adipose derived stem cells (hASCs) CS were obtained within five days using both thermoresponsive and standard cell culture surfaces. hASCs-based constructs were then built by superimposing three CS and transplanted into full-thickness excisional mice skin wounds with delayed healing. Constructs obtained using thermoresponsive surfaces were more stable than the ones from standard cell culture surfaces due to the natural adhesive character of the respective CS. Both CS-generating strategies lead to prolonged hASCs engraftment, although no transdifferentiation phenomena were observed. Moreover, our findings suggest that the transplanted hASCs might be promoting neotissue vascularization and extensively influencing epidermal morphogenesis, mainly through paracrine actions with the resident cells. The thicker epidermis, with a higher degree of maturation characterized by the presence of rete ridges-like structures, as well as a significant number of hair follicles observed after transplantation of the constructs combining the CS obtained from the thermoresponsive surfaces, reinforced the assumptions of the influence of the transplanted hASCs and the importance of the higher stability of these constructs promoted by cohesive cell-cell and cell-ECM interactions. Overall, this study confirmed the potential of hASCs CS-based constructs to treat full-thickness excisional skin wounds and that their fabrication conditions impact different aspects of skin regeneration, such as neovascularisation, but mainly epidermal morphogenesis.We would like to thank Hospital da Prelada (Porto), in particular, to Dr. Paulo Costa for the lipoaspirates collection and for financial support by Skingineering (PTDC/SAU-OSM/099422/2008), Portuguese Foundation for Science and Technology (FCT) funded project. The research leading to these results has also received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. REGPOT-CT2012-316331-POLARIS