Modular Surface Research Articles

Relative stability conditions on Fukaya categories of surfaces

It is shown that there is a useful notion of a relative Bridgeland stability condition on the partially wrapped Fukaya category of a marked surface, with respect to some part of the surface’s boundary. This construction has nice functorial properties, obeying cutting and gluing, and reducing the calculation of stability conditions on the Fukaya category of any fully stopped surface into three types of base cases. Calculations of these cases shows that every Bridgeland stability condition on such categories can be described by flat surfaces. In other words, when the surface is fully stopped, the map constructed by Haiden–Katzarkov–Kontsevich from the moduli of flat surfaces to the stability space of the Fukaya category is a global homeomorphism.

Tuning the rheology and microstructure of particle-laden fluid interfaces with Janus particles

HypothesisParticle-laden fluid interfaces are the central component of many natural and engineering systems. Understanding the mechanical properties and improving the stability of such interfaces are of great practical importance. Janus particles, a special class of heterogeneous colloids, might be used as an effective surface-active agent to control the assembly and interfacial rheology of particle-laden fluid interfaces. ExperimentsUsing a custom-built interfacial stress rheometer, we explore the effect of Janus particle additives on the interfacial rheology and microscopic structure of particle-laden fluid interfaces. FindingsWe find that the addition of a small amount of platinum-polystyrene (Pt-PS) Janus particles within a monolayer of PS colloids (1:40 number ratio) can lead to more than an order-of-magnitude increase in surface moduli with enhanced elasticity, which improves the stability of the interface. This drastic change in interfacial rheology is associated with the formation of local particle clusters surrounding each Janus particle. We further explain the origin of local particle clusters by considering the interparticle interactions at the interface. Our experiments reveal the effect of local particle structures on the macroscopic rheological behaviors of particle monolayers and demonstrate a new way to tune the microstructure and mechanical properties of particle-laden fluid interfaces.

Calabi–Yau 3-folds from projective joins of del Pezzo manifolds

In this paper, we will construct new examples of derived equivalent Calabi–Yau 3-folds with Picard number greater than one. We also study their mirror Calabi–Yau manifolds and find that they are given by Schoen's fiber products of suitable rational elliptic modular surfaces.

Effect of isothermal heat treatment on nanoindentation hardness and Young’s modulus of 4 mol% Y2O3-ZrO2 EB-PVD TBCs

4 mol% Y2O3–ZrO2 (4YSZ) is commonly used in thermal barrier coatings (TBCs) for high-temperature applications such as gas turbine engines. This study was investigated the effects of heat treatment at 1400 °C for 0, 2, 20, and 100 h on the hardness and Young’s modulus of 4YSZ coatings prepared by electron-beam physical vapor deposition. Nanoindentation measurements were performed on the top and side surfaces of the coating. The as-coated and the heat-treated coatings exhibited strong anisotropy in the mechanical properties; the hardness and Young’s modulus of the side surface of the coatings were lower than those of the top surface. Increasing the heat treatment time was found to increase the hardness and Young’s modulus in both the directions. This is correlated with the decrease in porosity with increase in the heat-treatment time and closure of gaps between the columns and arms of their (as-coated) featherlike microstructures, which are known to deleteriously affect both the toughness and thermal insulating properties of TBCs.

Surface structure and nanomechanical properties of Actinoplanes missouriensis sporangia analyzed via atomic force microscopy.

The surface structures of the sporangia produced by Actinoplanes missouriensis were analyzed at high resolution in air and liquid via atomic force microscopy. Results revealed a dynamic change in sporangium surface structure in response to the amount of moisture. Furthermore, the Young's modulus of the sporangium surface (1.95 ± 0.92 GPa) was calculated by analyzing the force-distance curves in air.

Strontium-Containing Barium Titanate-Modified Titanium for Enhancement of Osteointegration.

One of the major challenges for Ti-based implants is insufficient osteointegration, which might result in the loosening of the implant. In this study, we fabricated strontium (Sr)-containing barium titanate (BST) on the surface of Ti to improve the bioactivity for osteointegration enhancement. The introduction of Sr significantly reduced the crystallization time and improved crystallinity, which was proved by X-ray diffraction, X-ray photoelectron spectroscopy, and transmission electron microscopy. Compared with Ti, the BST film showed greater wettability surface and lower elastic modulus and hardness. Furthermore, in synergy with the release of Sr ions, the BST film improved early adhesion and followed osteogenic differentiation of rat bone mesenchymal stem cells. Furthermore, the bone implantation experiment suggested that the BST film could significantly improve the in vivo osteogenesis and osteointegration capabilities of Ti implants. In summary, this study revealed that BST-modified Ti has potential application in bone repair.

The two-wheeled robotic swarm concept for Mars exploration

Recent Mars Exploration Rovers (MERs) launched in 2021 show the growing interest in the robot’s mobility improvement and application of cooperative robotics. Increased mobility has been addressed by launching the first flying robot to Mars, bringing new opportunities to explore previously inaccessible areas. Such collaborative solutions expand the possibilities for Mars exploration.This paper suggests a concept for using a modular robotic swarm consisting of several independent two-wheeled robots. To evaluate the proposed system, we introduce a development methodology for MERs along with metrics for assessing modular surface exploration systems. This article focuses on how cooperative modular robotic solutions for Mars exploration can improve such Figures of Merit (FOMs) as mission lifetime, exploration speed, and cost of the mission. To validate the FOMs for a proposed solution, we use Pareto Frontiers as a decision instrument for multi-objective optimization. Our results illustrate the engineering tradeoffs and potential advantages between two-wheeled rovers and existing Mars Exploration Rovers.

Squid inspired elastomer marine coating with efficient antifouling strategies: Hydrophilized defensive surface and lower modulus

In antifouling applications for the marine industry, low surface energy coatings entail turbulent water flow to release marine biofouling, which presents a substantial challenge for antifouling in the static situation. The traditional solution is to add environmentally friendly antifouling agents, but it has the problem of exhaustion. Therefore, the low surface energy elastic antifouling coating without antifoulants has high research value. Herein, inspired by soft body and epidermal mucus of squid, the stable polyvinylpyrrolidone (PVP) hydrophilic segments were introduced to modify the polydimethylsiloxane-based polyurethane (PDMS-PU), realizing low surface energy elastomer coatings with hydrophilized defensive surface and reduced elastic modulus (<1.1 MPa). In an aqueous environment, the tailored surface exposed sufficient stable hydrophilic segments, exerting excellent antifouling performance, which improved the anti-adsorption effect on biological proteins, bacteria (antibacterial rate 95.24%) and algae (cover rate <3%). The coating exhibited excellent marine antifouling performance within 150 days and also gave a new impetus to developing an eco-friendly and sustainable solution for no-antifoulant marine antifouling applications.

Single-Source SIE for 2-D Arbitrarily Connected Penetrable and PEC Objects With Nonconformal Meshes

We proposed a simple and efficient modular single-source surface integral equation (SS-SIE) formulation for electromagnetic analysis of arbitrarily connected penetrable and perfectly electrical conductor (PEC) objects in two-dimensional space. In this formulation, a modular equivalent model for each penetrable object consisting of the composite structure is first independently constructed through replacing it by the background medium, no matter whether it is surrounded by the background medium, other media, or partially connected objects, and enforcing an equivalent electric current density on the boundary to remain fields in the exterior region unchanged. Then, by combining all the modular models and any possible PEC objects together, an equivalent model for the composite structure can be derived. The troublesome junction handling techniques are not needed and non-conformal meshes are intrinsically supported. The proposed SS-SIE formulation is simple to implement, efficient, and flexible, which shows significant performance improvement in terms of CPU time compared with the original SS-SIE formulation and the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation. Several numerical examples including the coated dielectric cuboid, the large lossy objects, the planar layered dielectric structure, and the partially connected dielectric and PEC structure are carried out to validate its accuracy, efficiency and robustness.

Polylactic acid as a biocompatible polymer for three-dimensional printing of interim prosthesis: Mechanical characterization.

Mechanical properties of polylactic acid (PLA), which is a biopolymer obtained via 3D-printing, were compared with conventional resins for the realization of interim prosthesis. A PLA built by fused deposition modeling and traditional interim resins (Unifast®, Integrity®, Temporary CB®) were divided into 4 groups (n=10). Each group was investigated for Young modulus, flexural strength, microhardness and analysis of the fractured surface. Data were analyzed by Kruskal-Wallis and ANOVA (α=0.05). The porosity of the PLA was calculated from the crystallinity degree and density. PLA-group showed an elastic modulus and flexural strength in the same range than Integrity®-group, better than Unifast®-group and inferior to Temporary CB®-group (p<0.05). PLA-group microhardness was equivalent to Unifast®-group and inferior to Integrity® and Temporary CB® groups (p<0.05). Due to mechanical properties similar to conventional resins and the low porosity rate, this biocompatible 3D-printed polymer may be an interesting alternative to conventional polymer to build temporary prosthesis.

Flexoelectricity and surface effects on coupled electromechanical responses of graphene reinforced functionally graded nanocomposites: A unified size-dependent semi-analytical framework

Owing to inhomogeneous strain and high surface-to-volume ratio in nanostructures, it is imperative to account for the flexoelectricity as well as surface effect while analyzing the size-dependent electromechanical responses of nano-scale piezoelectric materials. In this article, a semi-analytical ‘single-term extended Kantorovich method (EKM)’ and ‘Ritz method’ based powerful framework is developed for investigating the static and dynamic electromechanical responses of graphene reinforced piezoelectric functionally graded (FG) nanocomposite plates, respectively. The residual surface stresses, elastic and piezoelectric surface modulus, and direct flexoelectric effects are taken into account while developing the unified governing equations and boundary conditions. The modified Halpin Tsai model and rules of mixture are implemented to predict the effective bulk properties. Our results reveal that the static deflection and resonance frequency of the proposed FG nanoplates are significantly influenced due to the consideration of flexoelectricity and surface effects. While such outcomes emphasize the fact that such effects cannot be ignored, these also open up the notion of on-demand property modulation and active control. The effects are more apparent for nanoplates of lesser thickness, but they diminish as plate thickness increases, leading to the realization and quantification of a size-dependent behavior. Based on the developed unified formulation, a comprehensive numerical investigation is further carried out to characterize the electromechanical responses of nanoplates considering different critical parameters such as plate thicknesses, aspect ratios, flexoelectric coefficients, piezoelectric multiples, distribution, and weight fraction of graphene platelets along with different boundary conditions. With the recent advances in nano-scale manufacturing, the current work will provide the necessary physical insights in modeling size-dependent multifunctional systems for active control of mechanical properties and harvesting electromechanical energy.

Potential of Soft-Shell Rugby Headgear to Mitigate Linear and Rotational Peak Accelerations

Rugby union is a popular sport played across the world. The physical contact inherent in the game means that players are at increased risk of concussive injury. In 2019, World Rugby created a new category of permitted headgear under Law 4 as a medical device. This established a pathway for headgear designed to reduce peak accelerations to be worn in matches. Investigations of the potential of soft-shelled protective headgear to reduce head impact accelerations have been mostly limited to the analysis of linear kinematics. However rotational head impact accelerations have long been implicated as far more injurious. The aim of this study, therefore, was to assess the linear and rotational acceleration reduction brought about by soft-shelled rugby headgear. A Hybrid III headform and neck were dropped onto a modular elastomer programmer impact surface, impacting at four different velocities (1.7–3.4 m/s) in five different impact orientations. Impact surface angles were 0°, 30°, and 45°. Peak linear and rotational accelerations, PLA and PRA respectively, were recorded. All headgear significantly reduced PLAs and PRAs when compared to a no headgear scenario. The new generation, headgear reduced all measures significantly more than the older generation of headgear. Impact locations offset from the center of mass of the headform resulted in the highest PRAs measured. As the impact surface angle increased, both PLAs and PRAs decreased. The study demonstrated that headgear tested lowered PLAs by up to 50%, and PRAs by up to 60% compared to the bare headform. Our data suggest that new generation headgear could make a difference on the field in reducing injurious impact accelerations in a collision.

Geometric Interpretation of Hermitian Modular Forms via Burkhardt Invariants

We give an exact theta expression of a tuple of Hermitian modular forms as an inverse period mapping of lattice polarized K3 surfaces. Our result gives a non-trivial relation among moduli of K3 surfaces, theta functions and the finite complex reflection group of rank 5.

55 - Dental Ceramic Surface Properties after Resin-Cement Removal by Burning Technique

There are situations in which resin-cement needs to be removed from the crown's intaglio surface before it can be recemented. Some authors have proposed to burn off this cement; however, questions remain related to the effect of this technique on the surface properties of the ceramics. The goal was to test the effect of burning cements off on the surface properties of zirconia and lithium disilicate dental ceramics. The mechanical properties (hardness and elastic modulus) and removal effectiveness were tested in this study. Two kinds of ceramics: zirconia (Cercon, Dentsply Sirona) and lithium disilicate glass-ceramics (Emax, Ivoclar Vivadent) and two universal resin-cements; Calibra Universal (Dentsply) and Multilink Automix (Ivoclar Vivadent), were used in this research. Samples (n=8) were 1.3 mm thick and were sintered according to manufacturer recommendations. Zirconia samples were sandblasted with 150 aluminum oxide, and lithium-disilicate were etched with 9.6% hydrofluoric acid and then thoroughly rinsed. The application of each resin-cement followed the manufacturer's recommendations, and the samples were light-cured for 20 s. After 15 days of storage (100% humidity and 36 C), the samples were placed into a furnace at a temperature of ~150 C then heated a rate of ~30 C/min until reaching a temperature of 400 C where the temperature was held for 1 minute. The samples were removed from the furnace and allowed to cool before the cement was removed. Fourier Transformed Infra-Red (FTIR) was used, before and after cementation, to check the surface chemical composition and the effectiveness of the resin-cement removal. A nanoindenter (Hysitron TI 750 Ubi Triboindenter) using a Berkovich tip (100 mN) was used to assess the surface properties. Statistical analyses of the results were performed using two-way ANOVA and a post hoc Tukey test (α = 0.05). FTIR showed that the burning technique was effective to remove the residual resin-cement from the ceramic samples. Also, there was no significant statistical difference between the hardness and the elastic modulus of the dental ceramic surfaces from before and after the burning technique. This study showed that the removal of the resin-cements from crowns intaglio by the burning technique could be a viable clinical solution before recementing dental ceramics.

Modular Multi-Domain Aware Autonomous Surface Vehicle for Inspection

A growing interest in ocean exploration for scientific and commercial research has been shown, mainly due to the technological developments for maritime and offshore industries. The use of Autonomous surface vehicles (ASV) have a promising role to revolutionize the transportation, monitorization, operation and maintenance areas, allowing to perform distinct task from offshore assets inspection to harbor patrolling. This work presents SENSE, an autonomouS vEssel for multi-domaiN inSpection and maintEnance. It provides an open-source hardware and software architecture that is easy to replicate for both research institutes and industry. This is a multi-purpose vehicle capable of acquiring multi-domain data for inspecting and reconstructing maritime infrastructures. SENSE provides a research platform which can increase the situational awareness capabilities for ASVs. SENSE full configuration provides multimodal sensory data acquired from both domains using a Light Detection And Ranging (LiDAR), a stereoscopic camera, and a multibeam echosounder. In addition, it supplies navigation information obtained from a real-time kinematic satellite navigation system and inertial measurement units. Moreover, the tests performed at the harbor of Marina de Leça, at Porto, Portugal, resulted in a dataset which captures a fully operational harbor. It illustrates several conditions on maritime scenarios, such as undocking and docking examples, crossings with other vehicles and distinct types of moored vessels. The data available represents both domains of the maritime scenario, being the first public dataset acquired for multi-domain observation using a single vehicle. This paper also provides examples of applications for navigation and inspection on multi-domain scenarios, such as odometry estimation, bathymetric surveying and multi-domain mapping.

On class number relations and intersections over function fields

The aim of this paper is to study class number relations over function fields and the intersections of Hirzebruch-Zagier type divisors on the Drinfeld-Stuhler modular surfaces. The main bridge is a particular "harmonic" theta series with nebentypus. Using the strong approximation theorem, the Fourier coefficients of this series are expressed in two ways; one comes from modified Hurwitz class numbers and another gives the intersection numbers in question.

Laboratory evaluation of an indigenous developed light weight deflectometer as a quality control tool for pavement construction

The mechanistic empirical pavement design concepts are largely based on the theory of elastic layers, and the design is assessed with the characterization of materials used in pavement construction. The present density-based quality assurance (QA) apparatus and its procedures are not effective in measuring the resilient modulus of compacted pavement layers. However, the use of high-cost field apparatus such as nuclear density gauges (NDG) is also encouraging the search for an alternative procedure. This article aims at the measurement of pavement surface modulus directly in the field using a low-cost laboratory developed Indigenous Light Weight Deflectometer (ILWD). The developed ILWDs will be employed for pavement construction QA for interpreting the stiffness of compacted pavement layers. The study was performed on the National Highway-161 in Sivampet, Sangareddy district, Telangana state. The laboratory developed ILWD was validated using the available Light Weight Deflectometer (LWD), Dynatest make, and layer modulus was also computed using a Dynamic Cone Penetrometer (DCP). The DCP was also fabricated in the laboratory as per the Transportation Research Laboratory (TRL), UK. The ILWD and DCP were used to ensure the stiffness characteristics like elastic and dynamic modulus. The field and lab test results indicate that the calculated elastic modulus and stiffness characteristics are close to each other layer moduli for the different pavement layers considered in the study, like sub-grade and granular sub-base (GSB). It is also observed that the test results from the field and laboratory have a good measure of statical correlation among the different stiffness values, and hence the developed ILWD is suitable for pavement compacted layer investigation as quality control.

Special curves in modular surfaces

AbstractWe show that geodesics in $\mathbf {H}$ attached to a maximal split torus or a real quadratic torus in $GL_{2, \mathbf {Q}}$ are the only irreducible algebraic curves in $\mathbf {H}$ whose image in $\mathbf {R}^2$ via the j-invariant is contained in an algebraic curve.

Freezing of few nanometers water droplets

Water-ice transformation of few nm nanodroplets plays a critical role in nature including climate change, microphysics of clouds, survival mechanism of animals in cold environments, and a broad spectrum of technologies. In most of these scenarios, water-ice transformation occurs in a heterogenous mode where nanodroplets are in contact with another medium. Despite computational efforts, experimental probing of this transformation at few nm scales remains unresolved. Here, we report direct probing of water-ice transformation down to 2 nm scale and the length-scale dependence of transformation temperature through two independent metrologies. The transformation temperature shows a sharp length dependence in nanodroplets smaller than 10 nm and for 2 nm droplet, this temperature falls below the homogenous bulk nucleation limit. Contrary to nucleation on curved rigid solid surfaces, ice formation on soft interfaces (omnipresent in nature) can deform the interface leading to suppression of ice nucleation. For soft interfaces, ice nucleation temperature depends on surface modulus. Considering the interfacial deformation, the findings are in good agreement with predictions of classical nucleation theory. This understanding contributes to a greater knowledge of natural phenomena and rational design of anti-icing systems for aviation, wind energy and infrastructures and even cryopreservation systems.

Site-specific variations in surface structure and Young's modulus of human hair surfaces at the nanometer scale as induced through bleach treatment

The effect of bleach treatments on the morphology and mechanical properties of hair surfaces was measured at the nanometer scale using atomic force microscopy. We used an ultrahigh-precision relocation technique to observe the variations in these properties at precise locations on hair surfaces in their virgin state and then after each of the two bleach treatments, to rule out position-dependent fluctuations. We demonstrate that statistically significant variations in roughness and Young's modulus are observed as a result of exposure to bleach, which is known to disrupt the disulfide linkage network throughout the fiber. The rate at which surface roughness changes increased with the number of treatments, with very little effect seen after 10 min, and an increase of up to 65% was observed after a further 10 min. The Young's modulus decreased by up to 40% after each treatment. We also investigate micropores and show that they are subsurface, but revealed through bleaching, and oriented along the direction of the hair shaft with a characteristic aspect ratio. This work demonstrates the profound effect bleaching has on the molecular structure of hair, which manifests as changes in morphology and stiffness, and this should be taken into account in the formulation of future hair-care products.