Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators

AbstractWe consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the strong law of large numbers for the number of solutions of the inequalities under consideration

Preliminary Investigation of the Frictional Response of Reptilian Shed Skin

Developing deterministic surfaces relies on controlling the structure of the rubbing interface so that not only the surface is of optimized topography, but also is able to self-adjust its tribological behaviour according to the evolution of sliding conditions. In seeking inspirations for such designs, many engineers are turning toward the biological world to correlate surface structure to functional behavior of bio-analogues. From a tribological point of view, squamate reptiles offer diverse examples where surface texturing, submicron and nano-scale features, achieve frictional regulation. In this paper, we study the frictional response of shed skin obtained from a snake (Python regius). The study employed a specially designed tribo-acoustic probe capable of measuring the coefficient of friction and detecting the acoustical behavior of the skin in vivo. The results confirm the anisotropy of the frictional response of snakes. The coefficient of friction depends on the direction of sliding: the value in forward motion is lower than that in the backward direction. In addition it is shown that the anisotropy of the frictional response may stem from profile asymmetry of the individual fibril structures present within the ventral scales of the reptil

Generic Continuous Spectrum for Ergodic Schr"odinger Operators

We consider discrete Schr"odinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition property. Assuming that the underlying dynamical system satisfies one of these repetition properties, we show using Gordon's Lemma that for a generic continuous sampling function, the associated Schr"odinger operators have no eigenvalues in a topological or metric sense, respectively. We present a number of applications, particularly to shifts and skew-shifts on the torus.Comment: 14 page

Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

Quantum Return Probability for Substitution Potentials

We propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete Schrodinger operators. We compute it for some non-periodic substitution potentials with different degrees of randomness, and do not find a complete qualitative agreement with the spectral type of the substitution sequences themselves, i.e., more random the sequence smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics

VIS: the visible imager for Euclid

Euclid-VIS is the large format visible imager for the ESA Euclid space mission in their Cosmic Vision program, scheduled for launch in 2020. Together with the near infrared imaging within the NISP instrument, it forms the basis of the weak lensing measurements of Euclid. VIS will image in a single r+i+z band from 550-900 nm over a field of view of ~0.5 deg2. By combining 4 exposures with a total of 2260 sec, VIS will reach to V=24.5 (10σ) for sources with extent ~0.3 arcsec. The image sampling is 0.1 arcsec. VIS will provide deep imaging with a tightly controlled and stable point spread function (PSF) over a wide survey area of 15000 deg2 to measure the cosmic shear from nearly 1.5 billion galaxies to high levels of accuracy, from which the cosmological parameters will be measured. In addition, VIS will also provide a legacy dataset with an unprecedented combination of spatial resolution, depth and area covering most of the extra-Galactic sky. Here we will present the results of the study carried out by the Euclid Consortium during the period up to the Preliminary Design Review. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

A chemical survey of exoplanets with ARIEL

Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number (~1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25–7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10–100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.Peer reviewedFinal Published versio

Surface structure and frictional properties of the skin of the Amazon tree boa Corallus hortulanus (Squamata, Boidae)

The legless locomotion of snakes requires specific adaptations of their ventral scales to maintain friction force in different directions. The skin microornamentation of the snake Corallus hortulanus was studied by means of scanning electron microscopy and the friction properties of the skin were tested on substrates of different roughness. Skin samples from various parts of the body (dorsal, lateral, ventral) were compared. Dorsal and lateral scales showed similar, net-like microornamentation and similar friction coefficients. Average friction coefficients for dorsal and lateral scales on the epoxy resin surfaces were 0.331 and 0.323, respectively. In contrast, ventral scales possess ridges running parallel to the longitudinal body axis. They demonstrated a significantly lower friction coefficient compared to both dorsal and lateral scales (0.191 on average). In addition, ventral scales showed frictional anisotropy comparing longitudinal and perpendicular direction of the ridges. This study clearly demonstrates that different skin microstructure is responsible for different frictional properties in different body regions

Kinematics of the Southern Rhodope Core Complex (North Greece)

The Southern Rhodope Core Complex is a wide metamorphic dome exhumed in the northern Aegean as a result of large-scale extension from mid-Eocene to mid-Miocene times. Its roughly triangular shape is bordered on the SW by the Jurassic and Cretaceous metamorphic units of the Serbo-Macedonian in the Chalkidiki peninsula and on the N by the eclogite bearing gneisses of the Sideroneron massif. The main foliation of metamorphic rocks is flat lying up to 100 km core complex width. Most rocks display a stretching lineation trending NEâ SW. The Kerdylion detachment zone located at the SW controlled the exhumation of the core complex from middle Eocene to mid-Oligocene. From late Oligocene to mid-Miocene exhumation is located inside the dome and is accompanied by the emplacement of the synkinematic plutons of Vrondou and Symvolon. Since late Miocene times, extensional basin sediments are deposited on top of the exhumed metamorphic and plutonic rocks and controlled by steep normal faults and flat-ramp-type structures. Evidence from Thassos Island is used to illustrate the sequence of deformation from stacking by thrusting of the metamorphic pile to ductile extension and finally to development of extensional Plio-Pleistocene sedimentary basin. Paleomagnetic data indicate that the core complex exhumation is controlled by a 30� dextral rotation of the Chalkidiki block. Extensional displacements are restored using a pole of rotation deduced from the curvature of stretching lineation trends at core complex scale. It is argued that the Rhodope Core Complex has recorded at least 120 km of extension in the North Aegean, since the last 40 My