Finite-lattice expansion for Ising models on quasiperiodic tilings

Low-temperature series are calculated for the free energy, magnetisation, susceptibility and field-derivatives of the susceptibility in the Ising model on the quasiperiodic Penrose lattice. The series are computed to order 20 and estimates of the critical exponents alpha, beta and gamma are obtained from Pade approximants.Comment: 16 pages, REVTeX, 26 postscript figure

Influence of Crystal Structure on the Establishment of the Bone-Calcium Phosphate Interface In Vitro

An in vitro rat bone marrow cell system was used to examine the interfacial ultrastructure established between various calcium phosphates and mineralized tissue. The investigated calcium phosphates comprised hydroxyapatite (HA), fluorapatite (FA), tricalcium phosphate (TCP), tetracalcium phosphate (TECP) and magnesium whitlockite (MWL). Both scanning and transmission electron microscopy were used to examine the elaborated interface. The time in which a mineralized extracellular matrix was formed on the various materials differed from 2 weeks on HA, TCP and TECP, to 8 weeks on FA. It was only occasionally observed in some areas on MWL, which might have been due to aluminum impurities in the coating. With transmission electron microscopy, three distinct interfacial structures were observed. They differed in the presence or absence of a collagen free, 0. 7 to 0. 8 J.Lm wide, amorphous zone and a 20 to 60 nm thick electron dense layer , interposed between the material surface and the mineralized extracellular matrix. The electron dense layer was considered to be at least partially caused by protein adsorption , which would precede or concur with biological mineralization events , while the amorphous zone was regarded to represent partial degradation of the calcium phosphate surfaces. The results of this study show that plasma sprayed calcium phosphates will display different bone-bonding and biodegradation properties , depending on their chemical composition and crystal structures

Design, manufacturing and testing of a rotorcraft access panel door from recycled carbon fiber reinforced polyphenylenesulfide

An integrally-stiffened access panel for a rotorcraft is selected for detail design, testing and actual flight to demonstrate a novel recycling route for thermoplastic composites. The design, development and validation followed the ‘Building Block approach’. The used material is post-industrial carbon fiber reinforced polyphenylene sulfide waste. This material originates from thermoplastic components of the very same rotorcraft as the panel will be mounted on, improving traceability, logistics and fixing supply and demand. Material data have been gathered from mechanical tests and used to predict the panels strength and stiffness. A critical design detail was selected and tested for validation. This section was included in a manufacturing demo, along with other integrated design features, enabling testing the processability. The final panel design was successfully produced and tested on component level. The re-manufacturing process includes simultaneously applied heat and low-shear mixing, followed by compression molding in an isothermal mold. This offers the possibility to retain long fibers and therefore high mechanical properties at short cycle times. In comparison to the current carbon/epoxy solution, the resulting product is lighter, significantly more cost-effective and made of recycled material (fiber and matrix). The prototype panel is targeted for flight testing on the rotorcraft in 2019.Dutch Organization of Applied Research – SIA, projeto SIA-RAAK 2014-01-72PR

Evidence for local inflammation in complex regional pain syndrome type 1.

BACKGROUND: The pathophysiology of complex regional pain syndrome type 1 (CRPS 1) is still a matter of debate. Peripheral afferent, efferent and central mechanisms are supposed. Based on clinical signs and symptoms (e.g. oedema, local temperature changes and chronic pain) local inflammation is suspected. AIM: To determine the involvement of neuropetides, cytokines and eicosanoids as locally formed mediators of inflammation. METHODS: In this study, nine patients with proven CRPS 1 were included. Disease activity and impairment was determined by means of a Visual Analogue Scale, the McGill Pain Questionnaire, the difference in volume and temperature between involved and uninvolved extremities, and the reduction in active range of motion of the involved extremity. Venous blood was sampled from and suction blisters made on the involved and uninvolved extremities for measurement of cytokines interleukin (IL)-6, II-1beta and tumour necrosis factor-alpha (TNF-alpha), the neuropetides NPY and CRGP, and prostaglandin E2RESULTS: The patients included in this study did have a moderate to serious disease activity and impairment. In plasma, no changes of mediators of inflammation were observed. In blister fluid, however, significantly higher levels of IL-6 and TNF-alpha in the involved extremity were observed in comparison with the uninvolved extremity. CONCLUSIONS: This is the first time that involvement of mediators of inflammation in CRPS 1 has been so clearly and directly demonstrated. This observation opens new approaches for the succesful use and development of immunosuppressives in CRPS 1

On FPL configurations with four sets of nested arches

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde

A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials

We rigorously prove that a wide class of one-dimensional growth models with onsite periodic potential, such as the discrete sine-Gordon model, have no phase transition at any temperature $T>0$. The proof relies on the spectral analysis of the transfer operator associated to the models. We show that this operator is Hilbert-Schmidt and that its maximum eigenvalue is an analytic function of temperature.Comment: 6 pages, no figures, submitted to J Phys A: Math Ge

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Univalent Foundations and the UniMath Library

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander