Variations on Noetherianness

In constructive mathematics, several nonequivalent notions of finiteness exist. In this paper, we continue the study of Noetherian sets in the dependently typed setting of the Agda programming language. We want to say that a set is Noetherian, if, when we are shown elements from it one after another, we will sooner or later have seen some element twice. This idea can be made precise in a number of ways. We explore the properties and connections of some of the possible encodings. In particular, we show that certain implementations imply decidable equality while others do not, and we construct counterexamples in the latter case. Additionally, we explore the relation between Noetherianness and other notions of finiteness.Comment: In Proceedings MSFP 2016, arXiv:1604.0038

Spreading of Latex Particles on a Substrate

We have investigated both experimentally and theoretically the spreading behavior of latex particles deposited on solid substrates. These particles, which are composed of cross-linked polymer chains, have an intrinsic elastic modulus. We show that the elasticity must be considered to account for the observed contact angle between the particle and the solid substrate, as measured through atomic force microscopy techniques. In particular, the work of adhesion computed within our model can be significantly larger than that from the classical Dupr\'{e} formula.Comment: 7 pages, 7 figures, to appear in Europhys. Let

Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle

The equation of motions and the conditions on surfaces and edges between fluids and solids in presence of non-constant surface energies, as in the case of surfactants attached to the fluid particles at the interfaces, are revisited under the principle of virtual work. We point out that adequate behaviors of surface concentrations may drastically modify the surface tension which naturally appears in the Laplace and the Young-Dupr\'e equations. Thus, the principle of virtual work points out a strong difference between the two revisited concepts of surface energy and surface tension.Comment: 20 page

Experimental simulation of satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds

Relativistic electron beams above thunderclouds emit 100 kHz radio waves which illuminate the Earth's atmosphere and near-Earth space. This contribution aims to clarify the physical processes which are relevant for the spatial spreading of the radio wave energy below and above the ionosphere and thereby enables an experimental simulation of satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds. The simulation uses the DEMETER satellite which observes 100 kHz radio waves from fifty terrestrial Long Range Aid to Navigation (LORAN) transmitters. Their mean luminosity patch in the plasmasphere is a circular area with a radius of 300 km and a power density of 22 μW/Hz as observed at 660 km height above the ground. The luminosity patches exhibit a southward displacement of 450 km with respect to the locations of the LORAN transmitters. The displacement is reduced to 150 km when an upward propagation of the radio waves along the geomagnetic field line is assumed. This residual displacement indicates that the radio waves undergo 150 km sub-ionospheric propagation prior to entering a magnetospheric duct and escaping into near-Earth space. The residual displacement at low (<i>L</i> < 2.14) and high (<i>L</i> > 2.14) geomagnetic latitudes ranges from 100 km to 200 km which suggests that the smaller inclination of the geomagnetic field lines at low latitudes helps to trap the radio waves and to keep them in the magnetospheric duct. Diffuse luminosity areas are observed northward of the magnetic conjugate locations of LORAN transmitters at extremely low geomagnetic latitudes (<i>L</i> < 1.36) in Southeast Asia. This result suggests that the propagation along the geomagnetic field lines results in a spatial spreading of the radio wave energy over distances of 1 Mm. The summative assessment of the electric field intensities measured in space show that nadir observations of terrestrial 100 kHz radio waves, e.g., from relativistic electron beams above thunderclouds, are attenuated by at least 50 dB when taking into account a transionospheric attenuation of 40 dB

Development of a method for calculating the degree of use of the plasticity resource (DUPR) when rolling on a new continuous mill

A new design of a continuous mill is proposed in the article. A method has been developed for calculating the degree of use of the plasticity resource when rolling thin slabs on a new continuous mill using the data obtained in the MSC Super Forge environment. To determine the stress-strain state, it used measurement data in 5 stands. When rolling in the proposed mill steel D16 there is no violation of the continuity of the strip material. This is proved by calculation in the MSC Super Forge environment using the distribution of DUPR over the cross section of strips when rolling in a mill of a new design

Development of a method for calculating the degree of use of the plasticity resource (DUPR) when rolling on a new continuous mill

A new design of a continuous mill is proposed in the article. A method has been developed for calculating the degree of use of the plasticity resource when rolling thin slabs on a new continuous mill using the data obtained in the MSC Super Forge environment. To determine the stress-strain state, it used measurement data in 5 stands. When rolling in the proposed mill steel D16 there is no violation of the continuity of the strip material. This is proved by calculation in the MSC Super Forge environment using the distribution of DUPR over the cross section of strips when rolling in a mill of a new design