On the Blaschke-Lebesgue theorem for the Cheeger constant via areas and perimeters of inner parallel sets

The first main result presented in the paper shows that the perimeters of inner parallel sets of planar shapes having a given constant width are minimal for the Reuleaux triangles. This implies that the areas of inner parallel sets and, consequently, the inverse of the Cheeger constant are also minimal for the Reuleaux triangles. Proofs use elementary geometry arguments and are based on direct comparisons between general constant width shapes and the Reuleaux triangle

The density of Meissner polyhedra

We consider Meissner polyhedra in $\mathbb{R}^3$. These are constant width bodies whose boundaries consist of pieces of spheres and spindle tori. We define these shapes by taking appropriate intersections of congruent balls and show that they are dense within the space of constant width bodies in the Hausdorff topology. This density assertion was essentially proved by Sallee. However, we offer a modern viewpoint taking into consideration the recent progress in understanding ball polyhedra and in constructing constant width bodies based on these shapes

Inclusive Nucleon Emission Induced by Quasi--Elastic Neutrino--Nucleus Interactions

We study the quasi--elastic contribution to the inclusive $(\nu_l,\nu_l N)$, $(\nu_l,l^- N)$, $({\bar \nu}_l,{\bar \nu}_l N)$ and $({\bar \nu}_l,l^+ N)$ reactions in nuclei using a Monte Carlo simulation method to account for the rescattering of the outgoing nucleon. As input, we take the reaction probability from the microscopical many body framework developed in Phys. Rev. {\bf C70} (2004) 055503 for charged-current induced reactions, while for neutral currents we use results from a natural extension of the model described in that reference. The nucleon emission process studied here is a clear signal for neutral--current neutrino driven reactions, that can be used in the analysis of future neutrino experiments.Comment: 23 pages, 17 figures; Version 2: few typos correcte

Fast bragg grating inscription in PMMA polymer optical fibres:impact of thermal pre-treatment of preforms

In this work, fibre Bragg gratings (FBGs) were inscribed in two different undoped poly- (methyl methacrylate) (PMMA) polymer optical fibres (POFs) using different types of UV lasers and their inscription times, temperature and strain sensitivities are investigated. The POF Bragg gratings (POFBGs) were inscribed using two UV lasers: a continuous UV HeCd @325 nm laser and a pulsed UV KrF @248 nm laser. Two PMMA POFs are used in which the primary and secondary preforms (during the two-step drawing process) have a different thermal treatment. The PMMA POFs drawn in which the primary or secondary preform is not specifically pre-treated need longer inscription time than the fibres drawn where both preforms have been pre-annealed at 80 °C for 2 weeks. Using both UV lasers, for the latter fibre much less inscription time is needed compared to another homemade POF. The properties of a POF fabricated with both preforms thermally well annealed are different from those in which just one preform step process is thermally treated, with the first POFs being much less sensitive to thermal treatment. The influence of annealing on the strain and temperature sensitivities of the fibres prior to FBG inscription is also discussed, where it is observed that the fibre produced from a two-step drawing process with well-defined pre-annealing of both preforms did not produce any significant difference in sensitivity. The results indicate the impact of preform thermal pre-treatment before the PMMA POFs drawing, which can be an essential characteristic in the view of developing POF sensors technology

Bragg gratings inscription using PMMA polymer optical fibers drawn from preforms with specific thermal pre-treatment

In this work, fiber Bragg gratings (FBGs) are inscribed in various undoped poly(methyl methacrylate) (PMMA) polymer optical fibres (POFs) using different types of UV lasers and inscription time and their temperature and strain sensitivities are investigated. The polymer optical fiber Bragg gratings (POFBGs) were inscribed using two UV lasers: a continuous UV HeCd @325 nm laser and a pulsed UV KrF @248 nm laser. The PMMA POFs drawn from a preform without specific thermal pre-treatment need more inscription time than the fibers drawn from a preform that has been pre-annealed at 80ºC for 2 weeks. Using both UV lasers, for the latter fiber less than half the inscription time is needed compared with a commercial undoped PMMA POF and other homemade POFs, where the preforms have not had a well-defined thermal pre-treatment. The effect on a POF from a preform that has been annealed prior to drawing is different as previously shown in the literature, where these POFs are much less sensitive to thermal treatment. Also, a proper polymerization process plays a key role as will be discussed. These results indicate the impact of preform thermal pre-treatment as well as polymerization process before the PMMA POFs drawing, which can be an essential characteristic in view of developing POF sensors technology

Impact of thermal pre-treatment on preforms for fast Bragg gratings inscription using undoped PMMA POFs

In this work, improvements in the photosensitivity of undoped POFs, where there was a welldefined pre-annealing of both preforms in two-step process, were reported. We have noticed that when the primary and secondary preforms are annealed, the fiber photosensitivity is higher; otherwise, if any preform (primary or secondary) is not annealed, the fiber photosensitivity is lower. Two PMMA mPOFs are used where the primary and secondary preforms, during the two-step drawing process, have a different thermal treatment. The PMMA POFs drawn where the primary or secondary preform is not specifically pre-treat need longer inscription time than the fibres drawn where both preforms have been pre-annealed at 80°C for 2 weeks. Using two different UV lasers, for the latter fibre much less inscription time is needed compared to another homemade POF. The properties of a POF fabricated where there are both preform process with thermal treatment is different from those where just one preform step process is thermal treated, as previously shown in the literature, where these POFs are much less sensitive to thermal treatment. Some important parameters were considered such as drawing tension and water content, where using fibers drawn in different tensions give us a similar FBG inscription time

A Finite Element Study of Corrugated Steel Deck Subjected to Concentrated Loads

An extensive parametric study was initiated to get a better understanding of steel deck behavior under concentrated loads and to develop design recommendations for a wide range of deck profiles. This paper presents first results from the study related to 1.5-in. deep roof decks of types B and F. The study was performed on non-linear finite element models of deck validated against available test data. Deck gage, span length, span condition, concentrated load locations along and across the deck span were varied in the study. The observed deck behavior under concentrated loads, as well as the effects of the studied parameters on the effective distribution widths governed by the deck strength and stiffness, was presented and discussed. Design equations for predicting the effective distribution width for the studied deck profiles were presented

Coupling Nuclear Induced Phonon Propagation with Conversion Electron Mössbauer Spectroscopy

Mössbauer spectroscopy is a very sensitive measurement technique (10-8 eV) which prompted motivation for the experiment described in this thesis. Namely, can a sensitive detection system be developed to detect nuclear recoils on the order of 10 to 100 of eVs? The hypothesis that this thesis tests is: Nuclear induced phonon bursts caused by Rutherford scattered alphas, decayed from 241Am, in a type-310 stainless steel material can couple with 7.3 keV conversion electron Mössbauer events at the other end of the material which will have a statistically significant effect on a Mössbauer spectrum. The phonon bursts produced by the alpha collisions are expected to be very low energy at the other end of length of material. Since Mössbauer spectroscopy is sensitive and can detect the very low energy phonons, the spectrum is expected to change in at least one of the five areas after coupling occurs: broadening in the spectrum peaks, increased/decreased background counting rate, Mossbauer peak asymmetry, increased/decreased counting rate under the peak, and/or a peak centroid shift. This research aims to determine the significance of changes between spectra with phonon bursts and with no phonon bursts through hypothesis testing, where the null hypothesis is where phonons do not affect Mössbauer spectra in one of the five areas mentioned previously. After the spectra and results were analyze using an f-test and t-test comparisons, this experiment failed to reject the null result. Leading to the conclusion that additional research must be conducted

Pinnacle Syngenetic Karst in Nambung National Park, Western Australia

Simultaneous karstification and lithification of aeolian calcarenite in the southwest coastal part of Western Australia produced syngenetic karstic geomorphological features, such as solution pipes, maze caves, collapsed dolines and pinnacles. The formation of these geomorphological features was greatly influenced by the poor cementation and matrix porosity of the calcarenite. Pinnacles, calcarenite pillars up to 5 metres tall with one or more peaks and various types of sediment layers, are most numerous and densest in an area called the Pinnacles in Nambung National Park, Western Australia. $eir detailed characteristics and origin are still partially unknown and controversial. Theories suggest that the pinnacles are the final product of one or more of corrosive expansion and coalescence of solution pipes, cemented sediment surrounding the roots, cemented fill of solution pipes, products of focused cementation or remainders of tree-trunks. This article presents descriptions of pinnacles in Nambung National Park based on my fieldwork and suggests a polygenetic origin for the pinnacles, with roots playing a major role. The genesis of pinnacles is far more complex than the theories presented so far