Modular Surface Research Articles

Layering and capillary waves in the structure factor of liquid surfaces.

Within the extended Capillary Wave Theory (ECWT), to extract the bending modulus of a liquid surface from the total structure factor of the interfacial region requires to separate the capillary waves (CW) signal from a non-CW background. Some years ago, Höfling and Dietrich (HD), working in the strict grazing incidence limit qz = 0, proposed a background that combines the liquid and vapor bulk structure factors in the amounts set by Gibbs's plane. We contrast that proposal with Molecular Dynamics (MD) simulations of the Lennard-Jones model analyzed with the Intrinsic Sampling Method (ISM). The study is extended to qz ≠ 0, to test the stronger consistency requirements of the ECWT and the experimental conditions; it shows a good MD-ECWT matching although we need some fine tuning over HD proposal. Then, the agreement with the ISM result for the surface bending modulus is good and that provides an interpretation, in terms of the molecular layering at the liquid edge, for the fluctuating surface represented by the CW signal in the surface structure factor, both for MD simulations and surface diffraction experiments.

Study on Early-Age Elastic Modulus of FRC Using Electrical Resistivity and Resonance Frequency

The correlation between surface electrical resistivity and modulus of elasticity of fiber-reinforced concrete (FRC) was studied within early ages in this study as a novel nondestructive method for predicting the modulus of elasticity of FRC. In addition to the relationship of the two quantities, the influence of various discrete fibers such as glass, nylon, polypropylene, and steel on the early age properties of FRC was investigated. Twenty-one FRC mixes were designed and tested; including four fiber types, three different fiber volume fractions for each fiber type, and three different water-to-cement ratios for all the different mixes. The surface electrical resistivity meter and resonance testing gauge were used to measure each specimen’s surface electrical resistivity and modulus of elasticity. Early-age dynamic modulus of FRC may be predicted using the mechanical properties and dimension of the fiber, according to proposed mathematical calculations. Statistical analysis was performed on the experimental results and the results acquired by the proposed equations, to examine and proof the accuracy of the proposed equations. The acceptable coefficient of variation of 5–9 percent confirmed the good agreement between the measured and predicted values.

Mechanical integrity of ceramic coatings on Kapton made by a dry aerosol deposition of lunar mare simulant

AbstractThe purpose of this paper is to demonstrate the use of lunar regolith and the dry aerosol deposition (DAD) method to produce ceramic coatings on polyimide polymer, and to test their mechanical integrity. Ceramic films were produced on Kapton substrates using a custom‐built DAD system and lunar mare simulant (LMS) feedstock. Ultrafine grains and impact densification were confirmed using atomic force and electron microscopy. Mechanical properties of the DAD–LMS Kapton samples were evaluated with indentation, tensile, and mandrel bend tests. DAD–LMS coatings tripled the hardness and doubled the indentation modulus of the Kapton surface. Coatings 3–16 µm thick did not have a predictable effect on the ultimate tensile strength or elongation to failure; however, the apparent modulus of elasticity did increase. The coatings were able to withstand significant bending before damage, with critical bend radii of 5 and 1.5 mm for 7.5 µm and 120 nm thicknesses, respectively. Modest heat treatment was shown to reduce the bending strain of coated substrates. Advanced ceramic coatings are of interest for the protection of space and satellite polymers from micrometeoroid impacts, radiation, and atomic oxygen. Lunar posts and habitats will require the development of space manufacturing techniques and in situ resource utilization.

Interfacial Dilational Rheology of Molecular Films in DC Electric Fields.

We present a novel technique to measure the interfacial dilational rheology of a molecular film adsorbed at a water-oil interface in a direct-current (dc) electric field. A film of a highly polar subfraction of asphaltenes was allowed to adsorb at a water drop interface, surrounded by an organic phase and subjected to a dc electric field. The measurements involved calculations of the dynamic interfacial tension (IFT), while the drop was sinusoidally oscillated, using our in-house axisymmetric drop shape analysis (ADSA) algorithm adapted for electric fields. The amplitude of the IFT waveform over equilibrium IFT and the phase difference from the applied area oscillations were used in the estimation of surface moduli. The asphaltene films were found to become more elastic on increasing bulk concentrations and electric field strengths. However, the effect was not monotonous and observed to be governed by combinations of these parameters. The Lucassen-van den Tempel (LVDT) model was used to further elucidate the experimentally obtained interfacial dilational moduli.

Rational points on nonlinear horocycles and pigeonhole statistics for the fractional parts of

AbstractIn this paper, we investigate pigeonhole statistics for the fractional parts of the sequence $\sqrt {n}$ . Namely, we partition the unit circle $ \mathbb {T} = \mathbb {R}/\mathbb {Z}$ into N intervals and show that the proportion of intervals containing exactly j points of the sequence $(\sqrt {n} + \mathbb {Z})_{n=1}^N$ converges in the limit as $N \to \infty $ . More generally, we investigate how the limiting distribution of the first $sN$ points of the sequence varies with the parameter $s \geq 0$ . A natural way to examine this is via point processes—random measures on $[0,\infty )$ which represent the arrival times of the points of our sequence to a random interval from our partition. We show that the sequence of point processes we obtain converges in distribution and give an explicit description of the limiting process in terms of random affine unimodular lattices. Our work uses ergodic theory in the space of affine unimodular lattices, building upon work of Elkies and McMullen [Gaps in $\sqrt {n}$ mod 1 and ergodic theory. Duke Math. J.123 (2004), 95–139]. We prove a generalisation of equidistribution of rational points on expanding horocycles in the modular surface, working instead on nonlinear horocycle sections.

Hip implant modular junction: The role of CoCrMo alloy microstructure on fretting-corrosion

Cobalt-chromium-molybdenum (CoCrMo) alloy is one of the most used metals in total hip replacement (THR) due to the alloy's superior corrosion qualities and biocompatibility. Over time these prostheses may undergo wear and corrosion processes in a synergistic process known as tribocorrosion. Implant retrieval studies have shown that damage patterns on THR modular junction surfaces indicating specifically in vivo fretting-corrosion to take place. To date, there have been no studies on the fretting-corrosion behaviors of CoCrMo alloy under the consideration of specific microstructural features. A custom-built flat-on-flat fretting-corrosion setup was utilized to test the synergistic tribocorrosion behavior of fretting-corrosion. The difference in microstructure was generated through the cutting orientations of the transverse and the longitudinal direction of the bar stock material, where the longitudinal cut exhibits a characteristic banded microstructure (banded group) and the transverse cut a homogenous microstructure (unbanded group). A three-electrode system was employed to monitor the induced currents. Two different types of electrolytes were used in the current study: 1. Bovine calf serum (BCS-30 g/L protein) (normal conditions) 2. BCS with Lipopolysaccharide (LPS, 0.15 μg/ml) (simulated infectious conditions). In the free potential mode, banded samples showed an increased potential compared to the unbanded samples. In potentiostatic conditions, the banded group also exhibited a higher induced current in both electrolyte environments, indicating more corrosion loss. Both Nyquist and Bode plots showed both orientations of metal becoming more corrosion resistant post-fretting when compared to pre-fretting data. The longitudinal group at OCP demonstrated a unique shape of the fretting-loop, which might be related to tribochemical reactions. Based on the mechanical, electrochemical, and surface characterization data, the transverse group (unbanded) microstructures demonstrates a higher resistance to fretting-corrosion damage.

The immediate and short-term degradation of the wood surface in a cement environment measured by AFM

This study aims to measure the pit torus and border to monitor the immediate and short-term degradation of wood surfaces after the concrete is cast and the cement hydration releases heat. The surface morphology and adhesion force curves were measured by atomic force microscopy during the treatments in saturated calcium hydroxide solutions ranging from 1 h to 27 days. The results showed that the pit torus and pit border showed different degradation processes. The adhesion force was sensitive to the type of the surface chemical components exposed during the degradation, while the surface modulus, deformation and jump-off force ratio were sensitive to the surface structural strength. The surface modulus of the pit torus degraded to 0.61–0.66 of the untreated original (95% CI) after 7-h treatments, and degraded almost completely after 48-h treatments. The surface modulus of the pit border degraded to 0.83–0.95 of the untreated original (CI) after 10 days and to 0.20–0.23 of the untreated original (95% CI) after 27 days of treatments. The treatment temperature 50 °C caused a 10-times faster degradation in the torus modulus compared to the temperature 20 °C.

Distribution of the reduced quadratic irrationals arising from the odd continued fraction expansion

This paper investigates the quadratic irrationals that arise as periodic points of the Gauss type shift associated to the odd continued fraction expansion. It is shown that these numbers, which we call O-reduced, when ordered by the length of the associated closed primitive geodesic on some modular surface Γ∖H, are equidistributed with respect to the Lebesgue absolutely continuous invariant probability measure of the Odd Gauss shift.

Initial bacterial retention on polydimethylsiloxane of various stiffnesses: The relevance of modulus (mis)match

Initial retention of the bacterium Escherichia coli on model poly(dimethylsiloxane) (PDMS) surfaces was studied as a function of substrate bulk and surface mechanical stiffness values. Our reference PDMS system was designed such that out of the parameters that govern bacterial adhesion only the mechanical stiffness was systematically varied. This was achieved by varying the crosslinking density of PDMS. Following crosslinking, we performed Soxhlet extraction of non-crosslinked, free chains to rule out their effect on bacterial response. Bulk moduli were assessed by dynamic mechanical analysis at 1 rad sec−1 frequency and the values obtained ranged between 0.03 and 1.8 MPa. The increase in crosslink density resulted in increasing surface modulus, as measured by atomic force microscopy, with values ranging between 0.7 and 9 MPa. The number of bacteria retained was then assessed. We observed a decreasing trend with the increase of both bulk and surface mechanical stiffnesses down to a limit corresponding to the Young’s modulus of the bacterial cell surface. For higher values than this threshold, the number of retained bacteria remained constant. We tentatively explain this observation by considering conformal overlay of bacterial and material surfaces.

Lagrangian loci in moduli of abelian surfaces

Lagrangian loci in moduli of abelian surfaces

Picard modular forms and the cohomology of local systems on a Picard modular surface

We formulate a detailed conjectural Eichler–Shimura type formula for the cohomology of local systems on a Picard modular surface associated to the group of unitary similitudes \operatorname{GU}(2,1, \mathbb{Q}(\sqrt{-3})) . The formula is based on counting points over finite fields on curves of genus three which are cyclic triple covers of the projective line. Assuming the conjecture we are able to calculate traces of Hecke operators on spaces of Picard modular forms. We provide ample evidence for the conjectural formula. Along the way we prove new results on characteristic polynomials of Frobenius acting on the first cohomology group of cyclic triple covers of any genus, dimension formulas for spaces of Picard modular forms and formulas for the numerical Euler characteristics of the local systems.

Utilization of Whey Protein Isolate as CO2 Foam Stabilizer for Enhanced Oil Recovery

Understanding the fundamental aspects of foaming properties will influence its generation and stabilization at different concentrations of the critical aggregation concentration (CAC), foam volume stability, foam height, salinity influences, and crude oil CO2-foam stability. Carbon-Dioxide based enhanced oil recovery techniques are widely employed to extract additional oil from the reservoir. The adsorption of protein at the interfaces produces extremely viscoelastic layers with high viscosity. This research aims to investigate whether whey protein isolate (WPI) is a foaming agent that can be used to improve oil recovery. WPI lowers the interfaces’ surface tension, which also has a propensity to disclose and stabilize the interface by forming a viscoelastic network and directing to high surface moduli. Comparatively, the surface tension is lowered by sodium dodecyl sulfate (SDS) surfactants than the WPI, but they do not produce a high modulus interface. WPI is demonstrated to be a greater foam stabilizer in oil and various salt conditions than SDS foam. Adding sodium chloride (NaCl) increased the half-life and volume of foam more on WPI foam compared to SDS foam. SDS foamability and foam consistency decreased dramatically at 2 wt% of NaCl concentration and above while WPI foam increased. The crude oil affected both foams, but WPI foam has not been affected as much as the SDS foam due to its high strength compared to traditional foams. The study shows that WPI reduced interfacial tension from 38 to 11 mN/m and reduced surface tension (72.3 to 48 mN/m). It was low enough and can be used as a substitute for a foaming agent to enhance the recovery of oil.

Damage law and mechanism of coal-rock joint structure induced by liquid nitrogen at low temperature

The width and degree of connectivity of coal-rock joints directly affect the seepage capacity of flow energy such as gas. To study the damage law and mechanism of the coal-rock joint structure under the action of liquid nitrogen, two methods of liquid nitrogen unloaded and liquid nitrogen freeze–thaw were used to carry out damage modification experiments on coal-rock with different water saturation. Using OLS4000 laser confocal microscope and MH-25 universal testing machine to conduct electron microscope scanning and uniaxial compression test, measure the joint width expansions and Young's modulus of the coal-rock surface before and after the test, establish a physical and mechanical model of freeze–thaw damage to analyze the ice-wedge expansion stress influence on the damage of coal-rock joint structure and establish damage criterion. The research results show that the ice-wedge expansion stress, confining pressure, and temperature stress in the joint jointly affect the structural damage of coal-rock joints, and the ice-wedge expansion stress contributes the most. With the increase of water saturation, the damage to the coal-rock joint structure intensifies, and the ice-wedge expansion stress under the water saturation state has the most obvious influence on the damage to the coal-rock joint structure. The damage criterion constructed by the freeze–thaw damage physical–mechanical model can reveal the damage mechanism of the effect of ice-wedge expansion stress on the coal-rock joint structure. This paper has certain practical significance for the safety and stability evaluation of rock engineering in cold and arid regions and provides new ideas for effectively extracting clean energy such as coalbed methane and preventing rock bursts.

Unbalanced bidirectional radial stiffness gradients within the organ of Corti promoted by TRIOBP

Hearing depends on intricate morphologies and mechanical properties of diverse inner ear cell types. The individual contributions of various inner ear cell types into mechanical properties of the organ of Corti and the mechanisms of their integration are yet largely unknown. Using sub-100-nm spatial resolution atomic force microscopy (AFM), we mapped the Young's modulus (stiffness) of the apical surface of the different cells of the freshly dissected P5-P6 cochlear epithelium from wild-type and mice lacking either Trio and F-actin binding protein (TRIOBP) isoforms 4 and 5 or isoform 5 only. Variants of TRIOBP are associated with deafness in human and in Triobp mutant mouse models. Remarkably, nanoscale AFM mapping revealed unrecognized bidirectional radial stiffness gradients of different magnitudes and opposite orientations between rows of wild-type supporting cells and sensory hair cells. Moreover, the observed bidirectional radial stiffness gradients are unbalanced, with sensory cells being stiffer overall compared to neighboring supporting cells. Deafness-associated TRIOBP deficiencies significantly disrupted the magnitude and orientation of these bidirectional radial stiffness gradients. In addition, serial sectioning with focused ion beam and backscatter scanning electron microscopy shows that a TRIOBP deficiency results in ultrastructural changes of supporting cell apical phalangeal microfilaments and bundled cortical F-actin of hair cell cuticular plates, correlating with messenger RNA and protein expression levels and AFM stiffness measurements that exposed a softening of the apical surface of the sensory epithelium in mutant mice. Altogether, this additional complexity in the mechanical properties of the sensory epithelium is hypothesized to be an essential contributor to frequency selectivity and sensitivity of mammalian hearing.

Moduli of surfaces in

The main goal of this paper is to construct a compactification of the moduli space of degree $d \geqslant 5$ surfaces in $\mathbb {P}^{3}_{{{\mathbb {C}}}}$, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth surfaces in $\mathbb {P}^{3}$ and whose boundary points correspond to degenerations of such surfaces. We consider a divisor $D$ on a Fano variety $Z$ as a pair $(Z, D)$ satisfying certain properties. We find a modular compactification of such pairs and, in the case of $Z = {{\mathbb {P}}}^{3}$ and $D$ a surface, use their properties to classify the pairs on the boundary of the moduli space.

Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers

We study the Coulomb branches of four-dimensional supersymmetric quantum field theories with mathcal{N} = 2 supersymmetry, including the KK theories obtained from the circle compactification of the 5d mathcal{N} = 1 En Seiberg theories, with particular focus on the relation between their Seiberg-Witten geometries and rational elliptic surfaces. More attention is given to the modular surfaces, which we completely classify using the classification of subgroups of the modular group PSL(2, ℤ), deriving closed-form expressions for the modular functions for all congruence and some of the non-congruence subgroups. Moreover, in such cases, we give a prescription for determining the BPS quivers from the fundamental domains of the monodromy groups and study how changes of these domains can be interpreted as quiver mutations. This prescription can be also generalized to theories whose Coulomb branches contain ‘undeformable’ singularities, leading to known quivers of such theories.

Bubble Behavior and Its Effect on Surface Integrity in Laser-Induced Plasma Micro-Machining Silicon Wafer

Abstract Laser-induced plasma micro-machining (LIPMM) process does well in fabricating high-quality surface microstructures of hard and brittle materials. However, the liquid medium is overheated to induce lots of bubbles to defocus the laser beam, reducing machining stability, and explosive behavior of bubbles destroys the surface quality. Thus, the static and dynamical behaviors of bubbles in LIPMM are comprehensively investigated in this article. First, a series of mechanisms including bubble generation and growth, bubble motion and explosion, and the effect of bubbles behavior on machining characteristics were explained. Second, a volume of fluid (VOF) model of bubble motions in laser-induced plasma micro-machining was established to simulate the dynamical behavior of bubbles under different depths of water layer, which reflect the growth of microbubbles, the aggregation of multiple bubbles, and the floating movement of bubbles. Then, a series of experiments were carried out to reveal bubble static behaviors, and further bubble explosion behaviors on surface integrity, surface defects, and hardness were analyzed. The increase of laser frequency leads to the increase of the maximum attached bubble size. Obstructed by bubble dynamical behaviors, a discontinuous section and the unablated area are observed in the microchannel. The elastic modulus and surface hardness of surface impacted by explosion bubbles are reduced. This research contributes to better understanding bubble behavior related to machining performances in LIPMM of single-crystal silicon.

The variance of closed geodesics in balls and annuli on the modular surface

We asymptotically estimate the variance for the distribution of closed geodesics in small random balls or annuli on the modular surface Γ﹨H. A probabilistic model in which closed geodesics are modeled using random geodesic segments is proposed, and we rigorously analyze this model using mixing of the geodesic flow in Γ﹨H. This leads to a conjecture for the asymptotic behavior of the variance, which unlike in previously explored cases is not equal to the expected value. We prove this conjecture for small balls and annuli, resolving a question left open by Humphries and Radziwiłł.

Bio-inspired liquid crystal gel with adjustable viscoelasticity to modulate cell behaviors and fate

Poly( D, l -lactide) (PDLLA) as a kind of bone repair material has been widely concerned, however, the development of PDLLA material with remarkable cell affinity and osteogenic activity is still a big challenge. Inspired by the unique liquid crystal property and viscoelasticity of bone extracellular matrix (ECM), here, a new kind of chitin whisker gel (nCG) with the bone ECM-like liquid crystal phase and viscoelasticity was developed, which was further stably adhered to PDLLA membrane to obtain the nCG-coated composite membrane (PP@nCG) taking advantage of polydopamine. The design of bone ECM-like liquid crystal gel surface on the PDLLA membrane could not only improve cell adhesion and proliferation, but also highly enhance calcium phosphate mineralization. Creatively, the modulus of surface coated nCG can be easily adjusted by changing the degree of deacetylation of chitin whiskers to simulate the viscoelasticity of bone ECM and regulate cell behaviors and fate. Interestingly, the PP@nCG membrane with high-modulus nCG coating shows a stronger effect on promoting cell affinity and osteogenic activity compared with that with low-modulus nCG coating. This study opens a new window to bionic designing novel composite materials with bone ECM-like liquid crystal characteristic and viscoelasticity for bone repair.

Thermal-shock-induced surface softening and conductivity evolution of hydraulic fracture in enhanced geothermal system

To reveal the thermal shock effect on micromechanical properties and conductivity evolution of hydraulic fracture in enhanced geothermal system, nanoindentation tests and fracture conductivity tests were performed on granite samples after different thermal treatments. Experimental results show that the hardness and the Young's modulus of fracture surface decreased with the increasing thermal treatment temperature. This degradation of micromechanical properties indicates the softening of fracture surface due to thermal shock effect which further influence the conductivity evolution. For propped fractures, the higher thermal treatment temperature, the lower fracture conductivity under the same closure stress. Particularly, at the thermal treatment temperature of 300°C, the dominant mechanism of quick fracture conductivity loss transformed from the proppant crushing under high closure stress (>50 MPa) to the enhancement of proppant embedment under low closure stress (<30 MPa). For self-propped fracture with small roughness, the thermal shock effect enhanced the conductivity under in-situ closure condition, while reduced that in case of shear slip. When the rough fracture was characterized by a local hump, it increased the flow resistance of in-situ closed fracture under high closure stress and reduced the fracture conductivity, but may form an effective flow channel with ultra-high conductivity once shear slip occurred.