For linear differential systems, the Sacker–Sell spectrum (dichotomy spectrum) and the contractible set are the same. However, we claim that this is not true for the linear difference equations. A counterexample is given. For the convenience of research, we study the relations between the dichotomy spectrum and the contractible set under the framework on time scales. In fact, by a counterexample, we show that the contractible set could be different from dichotomy spectrum on time scales established by Siegmund [J. Comput. Appl. Math., 2002]. Furthermore, we find that there is no bijection between them. In particular, for the linear difference equations, the contractible set is not equal to the dichotomy spectrum. To counter this mismatch, we propose a new notion called generalized contractible set and we prove that the generalized contractible set is exactly the dichotomy spectrum. Our approach is based on roughness theory and Perron's transformation. In this paper, a new method for roughness theory on time scales is provided. Moreover, we provide a time-scaled version of the Perron's transformation. However, the standard argument is invalid for Perron's transformation. Thus, some novel techniques should be employed to deal with this problem. Finally, an example is given to verify the theoretical results.

Metal additive manufacturing has enabled geometrically complex internal cooling channels for turbine and heat exchanger applications, but the process gives rise to large-scale roughness whose size is comparable to the channel height (which is 500 $\mathrm {\mu }$m). These super-rough channels pose previously unseen challenges for experimental measurements, data interpretation and roughness modelling. First, it is not clear if measurements at a particular streamwise and spanwise location still provide accurate representation of the mean (time- and plane-averaged) flow. Second, we do not know if the logarithmic layer survives. Third, it is unknown how well previously developed rough-wall models work for these large-scale roughnesses. To answer the above practical questions, we conduct direct numerical simulations of flow in additively manufactured super-rough channels. Three rough surfaces are considered, all of which are obtained from computed tomography scans of additively manufactured surfaces. The roughness’ trough to peak sizes are 0.1$h$, 0.3$h$ and 0.8$h$, respectively, where $h$ is the intended half-channel height. Each rough surface is placed opposite a smooth wall and the other two rough surfaces, leading to six rough-wall channel configurations. Two Reynolds numbers are considered, namely $Re_\tau =180$ and $Re_\tau =395$. We show first that measurements at one streamwise and spanwise location are insufficient due to strong mean flow inhomogeneity across the entire channel, second that the logarithmic law of the wall survives despite the mean flow inhomogeneity and third that the established roughness sheltering model remains accurate.

Here, we use a variety of microscopic imaging techniques, including scanning electron microscopy, 3D visible light microscopy, and portable microscopy to capture the topography of rough paper. Paper coated with a model soot was cleaned with either a firm vinyl eraser or softer, putty-like kneaded eraser and reimaged to characterize the disposition of remaining soot. Although both methods remove soot from the upper-most surface of the paper, only the kneaded eraser can conform to the complex topography to remove soot from the interstices between paper fibers.

We derive the surface and basal radar reflectance and backscatter coefficients of the southern McMurdo Ice Shelf (SMIS) and part of the nearby Ross Ice Shelf (RIS), Antarctica, from radar statistical reconnaissance using a 60-MHZ airborne survey. The surface coefficients are further inverted in terms of snow density and roughness, providing a spatial distribution of the processes contributing to the surface boundary conditions. We disentangle the basal coefficients from surface transmission losses, and we provide the basal coherent content, an indicator of the boundary geometric disorder that is also self-corrected from englacial attenuation. The basal radar properties exhibit sharp gradients along specific iso-depths, suggesting an abrupt modification of the ice composition and geometric structure. We interpret this behavior as locations where the pressure-melting point is reached, outlining fields of freezing and melting ice. Basal steps are observed at both SMIS and RIS, suggesting a common geometric expression of widespread basal processes. This technique offers a simultaneous view of both the surface and basal boundary conditions to help investigate the ice-shelf stability, while its application to airborne data significantly improves coverage of the difficult-to-observe ice–ocean boundary. It also provides constraints on thermohaline circulation in ice shelves cavities, which are analogs for ice-covered ocean worlds.

Possible multidrug-resistant (MDR) mechanisms of four resistant strains of Escherichia coli to a model β-lactam, ampicillin, were investigated using contact angle measurements of wettability, crystal violet assays of permeability, biofilm formation, fluorescence imaging, and nanoscale analyses of dimensions, adherence, and roughness. Upon exposure to ampicillin, one of the resistant strains, E. coli A5, changed its phenotype from elliptical to spherical, maintained its roughness and biofilm formation abilities, decreased its length and surface area, maintained its cell wall integrity, increased its hydrophobicity, and decreased its nanoscale adhesion to a model surface of silicon nitride. Such modifications are suggested to allow these cells to conserve energy during metabolic dormancy. In comparison, resistant strains E. coli D4, A9, and H5 elongated their cells, increased their roughness, increased their nanoscale adhesion forces, became more hydrophilic, and increased their biofilm formation upon exposure to ampicillin. These results suggest that these strains resisted ampicillin through biofilm formation that possibly introduces diffusion limitations to antibiotics. Investigations of how MDR bacterial cells modify their surfaces in response to antibiotics can guide research efforts aimed at designing more effective antibiotics and new treatment strategies for MDR bacterial infections.

A new type of polyelectrolyte–Al2O3/SiO2 composite nanoparticle with excellent dispersibility and superior polishing performance was successfully fabricated using a facile method. Silica acted as a bifunctional molecule by attaching to alumina via covalent bond and adsorbing polyelectrolytes by electrostatic interaction. The material removal rate of the polyelectrolyte–Al2O3/SiO2 abrasive was 30% higher than that of the pure Al2O3 abrasive. In addition, the sapphire surface was much smoother. The material removal mechanism was investigated during CMP using the microcontact and wear model. The enhanced removal rate was mainly attributed to the well-dispersed particles, which can accelerate mechanical removal process. The remarkably smooth surface was due to the decrease in penetration depth of the abrasive into the wafer. The results of this study provided a feasible strategy to satisfy the high efficiency and damage-free polishing requirements for sapphire planarization.

The aim of this study is to conduct an extended surface and cross-section characterization of a denture base acrylic resin subjected to 500, 650, and 750 W microwave irradiation for 2, 3, and 5 min to assess its morphological modifications. A commercial heat-cured powder was polymerized according to the manufacturer’s specifications and distributed into 20 circular samples. A stainless-steel wire was partially embedded in half of the discs, in order to investigate the metal–polymer interface. High-resolution scanning electron microscopy (SEM) imaging, white light interferometry, roughness measurements and Fourier transform infrared spectrometry were employed for morphological and structural evaluation of the irradiated polymer. Superficial adaptation was discovered after 5 min exposure at 500 W, 650 W, and 750 W, revealing significant roughness correction for 750 W. SEM characterization revealed the inner alteration of the resin for the 750 W protocol and a metal–polymer gap developed regardless of the irradiation conditions. The considerable temperature fluctuations that the samples were subject to during the experiments did not essentially change the poly(methyl-methacrylate) bond structure.

In instances where vegetation plays a dominant role in the riparian landscape, the type and characteristics of species, particularly a dominant invasive, can alter water velocity at high flows when vegetation is inundated. However, quantifying this resistance in terms of riparian vegetation has largely been ignored or listed as a secondary characteristic on roughness reference tables. We calculated vegetation roughness based on measurements of plant stem stiffness, plant frontal area, stem density, and stem area of three dominant herbaceous plants along the Sprague River, Oregon: the invasive reed canarygrass, native creeping spikerush, and native inflated sedge. Results show slightly lower roughness values than those predicted for vegetation using reference tables. In addition, native creeping spikerush and invasive reed canarygrass exhibit higher roughness values than native inflated sedge, which exhibits values lower than the other two species. These findings are of particular importance where the invasive reed canarygrass is outcompeting native inflated sedge, because with invasive colonization, roughness is increasing in channel zones and therefore is likely changing channel processes. Direct depositional measurements show similar results.

Hydraulic roughness exerts an important but poorly understood control on water pressure in subglacial conduits. Where relative roughness values are <5%, hydraulic roughness can be related to relative roughness using empirically-derived equations such as the Colebrook–White equation. General relationships between hydraulic roughness and relative roughness do not exist for relative roughness >5%. Here we report the first quantitative assessment of roughness heights and hydraulic diameters in a subglacial conduit. We measured roughness heights in a 125 m long section of a subglacial conduit using structure-from-motion to produce a digital surface model, and hand-measurements of the b-axis of rocks. We found roughness heights from 0.07 to 0.22 m and cross-sectional areas of 1–2 m2, resulting in relative roughness of 3–12% and >5% for most locations. A simple geometric model of varying conduit diameter shows that when the conduit is small relative roughness is >30% and has large variability. Our results suggest that parameterizations of conduit hydraulic roughness in subglacial hydrological models will remain challenging until hydraulic diameters exceed roughness heights by a factor of 20, or the conduit radius is >1 m for the roughness elements observed here.

This paper examines the effect of spatial roughness on the dynamical behaviour of electrostatic microactuators. We develop a comprehensive physical model that comprises a nonlinear electrostatic actuation force aswell as a squeeze-film damping term to accurately simulate the dynamical behavior of a cantilever beam actuator. Spatial roughness is modeled as a nonstationary stochastic process whose parameters can be estimated from profilometric measurements. We propagate the stochastic model through the physical system and examine the resulting uncertainty in the dynamical behavior that manifests as a variation in the quality factor of the device. We identify two distinct, yet coupled, modes of uncertainty propagation in the system, that result from the roughness causing variation in the electrostatic actuation force and the damping pressure, respectively. By artificially turning off each of these modes of propagation in sequence, we demonstrate that the variation in the damping pressure has a greater effect on the damping ratio than that arising from the electrostatic force. Comparison with similar simulations performed using a simplified mass-spring-damper model show that the coupling between these two mechanisms can be captured only when the physical model includes the primary nonlinear interactions along with a proper treatment of spatial variations. We also highlight the difference between nonstationary and stationary covariance formulations by showing that the stationary model is unable to properly capture the full range of variation as compared to its nonstationary counterpart.

A systematic analysis of effect of metallurgical defect and phase transition on geometric accuracy and wear resistance of iron-based parts fabricated by selective laser melting was conducted. By composition optimization of alloying elements, the desirable martensitic structure was directly obtained based on high-speed laser induction and the content of retained austenite was observed to be different under various laser parameters. Using an optimized scan speed of 1600 mm/s could lead to the highest densification level of 99.24% and the lowest content of retained austenite of 3.5%, hence acquiring a considerably high Rockwell hardness of 61.9 HRC, a reduced coefficient of friction of 0.40, and wear rate of 1.8 × 10−5 mm3/N m. A thorough investigation of dimension offset due to martensite transformation in conjunction with theoretical calculation was performed. Lower top surface roughness (5.25 μm) and reduced side roughness (13.84 μm) were achieved at the optimized scan speed of 1600 mm/s.

The surface roughness of the machined parts is one of the most important factors that have considerable influence on the quality and functional properties of products. The objective of this study is development of a surface roughness prediction model for machining Inconel 718 in high-pressure jet assisted turning using the fuzzy expert system, where the fuzzy system is optimized using two bioinspired algorithms: genetic algorithm and particle swarm optimization. The effect of various influential machining parameters, such as diameter of the nozzle, pressure of the jet, cutting speed, feed rate, and distance between the impact point of the jet and cutting edge were taken into consideration in this study. The predicted surface roughness values obtained from developed fuzzy expert systems were compared with the experimental data, and the results indicate that proposed systems can be effectively used to estimate the surface roughness in high-pressure jet assisted turning.

Today a wide range of instruments are available for the rapid roughness quantification ofoptical surfaces but especially for three dimensional measurement methods no standardizedprocess is established. This leads to different results, even if the same specimen istested with similar measurement devices. In order to solve this problem an exemplaryprocess development is described in this paper. To do this firstly the term of roughnessis defined as a surface deviation and then the functionality and importance of filters inroughness measurement as well as the used measurement devices are described. The followingchapter defines the used materials and methods which were used during the measurementprocess. In the last part of this paper the results are discussed and a process assignmentis suggested.

The response of titanium surface irradiated with high intensity (1013 – 1015 W/cm2) Ti:sapphire laser was studied in vacuum. Most of the reported investigations were conducted with nano- to femtosecond lasers in gas atmospheres while the studies of titanium surface interacting with femtosecond laser in vacuum are scarce. The laser employed in our experiment was operating at 800 nm wavelength and pulse duration of 60 fs in single pulse regime. The observed surface changes and phenomena are (1) creation of craters, (2) formation of periodic surface structures at the reduced intensity, and (3) occurrence of plasma in front the target. Since microstructuring of titanium is very interesting in many areas (industry, medicine), it can be concluded from this study that the reported laser intensities can effectively be applied for micromachining of the titanium surface (increasing the roughness, formation of parallel periodic surface structures etc.).

We consider the effect of surface roughness on solid-solid contact in a Stokes flow.Various models for the roughness are considered, and a unified methodology is given toderive the corresponding asymptotics of the drag force in the close-contact limit. In thisway, we recover and clarify the various expressions that can be found in previousstudies.

Face au réchauffement climatique lié à l’effet de serre, les constructeurs automobilespoursuivent leurs efforts dans la réduction des émissions de CO2. Le ticketd’entrée pour répondre à ces contraintes, tout en réduisant les coûts d’investissement,est d’optimiser les technologies de finition des fûts de carter cylindres des moteurs.Toutefois, l’acceptation des surfaces issues de ces technologies de finition, notamment lerodage, est pilotée par un contrôle visuel associé à des critères empiriques d’état etaspect de surface. Le but du présent travail est de proposer une méthodologie objective decaractérisation de la qualité de surface, basée sur une analyse multi-échelle de latexture. Différents critères de topographie et d’aspect de surface ont été définis. Ilsont été appliqués pour l’étude de l’impact de la vitesse d’expansion des rodoirs sur lesvariations de la qualité de surface obtenue. Des essais instrumentés ont été menés, afinde suivre l’évolution des paramètres physiques relatifs au rodage, tels que les énergiesspécifiques requises à chacune des configurations. Cette étude démontre le potentiel de laméthode développée à définir des corrélations objectives entre les paramètres process etla qualité de surface après rodage.

Cet article propose d'analyser l'usinabilité en tournage d'un acier martensitique en fonction de la vitesse de coupe par observation topographique de la surface. Nous décrivons d'abord une méthodologie pour chercher le paramètre de rugosité le plus pertinent afin de caractériser l'influence de la vitesse de coupe sur la topographie de la surface obtenue. La moyenne des pentes du profil permet d'estimer une vitesse critique qui correspond à une transition de régime dans le mode d'usinage. Elle met également en évidence l'influence de la vitesse de coupe à l'intérieur de chacun de ces deux régimes, ce qu'un critère plus conventionnel tel que le Ra ne permet pas de différencier. Dans une deuxième partie de cette étude, l'usinabilité est analysée en utilisant la théorie du chaos. Partant de la topographie de la surface usinée, nous développons une méthode originale pour construire un attracteur qui s'avère être bidimensionnel. La construction de cet attracteur résulte de deux fonctions : la première caractérise l'effet de l'écrouissage dû à la coupe et la seconde l'effet de l'adoucissement thermique. À basse vitesse de coupe, ces deux mécanismes deviennent intimement liés et l'attracteur possède un point fixe : la coupe s'effectue par écrouissage généralisé. Au-delà d'une vitesse critique, l'attracteur présente deux états indiquant l'apparition d'une instabilité de coupe. Deux régimes  se succèdent : l'écrouissage par cisaillement localisé puis l'adoucissement causé par l'élévation de température. Cette instabilité est confirmée par une augmentation de la dimension fractale avec la vitesse de coupe du profil reconstruit d'après l'attracteur.

Les pièces travaillant en contact finissent par se dégrader par suite du phénomène d'usure. De ce fait, elles exigent un matériau à hautes caractéristiques des couches superficielles et une gamme de fabrication très poussée. Le galetage et le brunissage peuvent conférer au matériau un nouvel aspect de surface tant sur le plan micro-géométrique que physique. Ce travail a pour objectif de préciser par comparaison, les effets des deux procédés. Par ailleurs les influences des divers paramètres du régime de formage sur la rugosité et sur la dureté ont été étudiées. Les résultats obtenus montrent que le nouvel aspect de surface requis est d'un indice technico-économique appréciable. Les couches superficielles traitées se comportent à la fois comme des surfaces rectifiées (Ra = 0,22 à 0,9 $\mu $m) et écrouies (HRB = 87 à 90). Ces effets optimaux se déduisent d'un régime de travail spécifique à chaque caractéristique et à chaque procédé. Ceci permet une amélioration d'environ 98 % de la tenue à l'usure de ces couches et de les classer comme des surfaces rodées.