Equivalent Surfaces Research Articles

Estimation of the Structure of Hydrophobic Surfaces Using the Cassie-Baxter Equation.

The effect of extreme water repellency, called the lotus effect, is caused by the formation of a Cassie-Baxter state in which only a small portion of the wetting liquid droplet is in contact with the surface. The rest of the bottom of the droplet is in contact with air pockets. Instrumental methods are often used to determine the textural features that cause this effect-scanning electron and atomic force microscopies, profilometry, etc. However, this result provides only an accurate texture model, not the actual information about the part of the surface that is wetted by the liquid. Here, we show a practical method for estimating the surface fraction of texture that has contact with liquid in a Cassie-Baxter wetting state. The method is performed using a set of ethanol-water mixtures to determine the contact angle of the textured and chemically equivalent flat surfaces of AlSI 304 steel, 7500 aluminum, and siloxane elastomer. We showed that the system of Cassie-Baxter equations can be solved graphically by the wetting diagrams introduced in this paper, returning a value for the texture surface fraction in contact with a liquid. We anticipate that the demonstrated method will be useful for a direct evaluation of the ability of textures to repel liquids, particularly superhydrophobic and superoleophobic materials, slippery liquid-infused porous surfaces, etc.

Anisotropic yielding model of lattice material and influencing factors

Experiments and numerical simulations were used to study and analyze the anisotropy of lattice materials, and the elastic-plastic properties of lattice materials were obtained. The equivalent continuum hypothesis was used to approximate the lattice material as a homogeneous continuous orthotropic material. The relevant equivalent yield parameters and plastic yield surfaces of the lattice materials were calculated using the Hill yield criterion. Comparisons of numerical simulations and experimental data show that they match very well. The effect of strut radius on anisotropic yield property and yield surface of lattice material was investigated.

Excitation of flatland surface-wave leakage on an equivalent reactance surface by a single-wire transmission line

Recently, researchers have demonstrated, both theoretically and experimentally, that low-dimensional version of conventional leaky waves, known as “flatland leaky waves” (FLWs). FLWs can be supported by planar junctions of metasurfaces and are completely confined to a plane. Here, we design a structure that places an equivalent reactance surface near the transmission line to excite the FLWs. By properly designing the geometry of the unit cell, conditions can be created for faster surface waves (SWs) to excite slower SWs on the surface, resulting in the desired form of two-dimensional (2D) leaky-wave radiation. A sample was fabricated and measured, and both the simulation results and the experimental results yielded the desired results. Finally, we design the equivalent impedance surface model on which we can also observe the 2D FLWs. Our research not only deepens the understanding of the phenomenon of FLWs but also brings the application of equivalent reactance surfaces in the field of electromagnetic phenomena research to a higher level.

Research on electromagnetic scattering and radio wave propagation algorithm based on machine learning in half-space

In this paper, to investigate the problem of radio wave propagation in complex environments, a new algorithm is proposed based on the equivalence principle algorithm and the domain decomposition method to rapidly and accurately predict electromagnetic scattering and radio wave propagation in half-space. First, equivalent surfaces are introduced to decompose the obstacle region and replace the scattering effect of obstacles within the equivalent surfaces with equivalent input and output electromagnetic currents. Then, the operator S, representing the relationship between the input and output equivalent electromagnetic currents on the equivalent surfaces, and the operator T, representing the interactions between the equivalent electromagnetic currents on each equivalent surface, are derived; this allows the calculation process of the overall spatial field in a complex environment to be simplified to the iterative calculation process of operators S and T. To reduce the complexity of calculating S, a neural network embedded with physical information is introduced to replace the calculation process. Finally, the training results are applied to an example and compared with the theoretical numerical results yielded by the method of moments in different cases with obstacles. The results reveal that the new method proposed in this paper is highly accurate and achieves a substantial improvement in calculation speed. Therefore, our proposed algorithm provides a new and reliable method for calculating the spatial field in complex environments.

Potential of focusing retroreflectors as passive acoustic beacons for flash sonar

Human echolocation, in the form of flash sonar, can support spatial awareness and navigation for vision-impaired people. This paper examines the potential of acoustic focusing retroreflectors to support echolocation within an area. Parabolic dihedra and trihedra, along with other variants of focusing retroreflectors, return much stronger reflections to an arbitrarily located source than equivalent flat surfaces. A head-and-torso simulator was used to quantify the oral-binaural reflected energy for various surfaces, including physical focusing retroreflectors. The effect of focusing is most advantageous in relatively close-range scenarios (within a few metres). Suggested designs and application scenarios are presented.

Изучение термостойкости минеральных видов слюд

Mica are a group of minerals with a perfect cleavage. They can split into very thin leaves with equivalent surfaces. Among all known mineral mica species, muscovite and phlogopite are highly important industrially because can be easily split into thin leaves and simultaneously have very high electrical characteristics, incombustibility and a great chemical fastness. Additionally, they are thermally and chemically resistant, poorly hygroscopic, as well as flexible, resilient and transparent as thin leaves. Not only muscovite and phlogopite but also biotite and vermiculite are of practical importance. Biotite is sometimes used to replace muscovite or phlogopite. Vermiculite is a hydrated biotite; it can be hardly split into thin leaves, has low electrical properties and is poorly thermally-resistant. Affected by high temperatures, mica releases water and so gradually loses its brightness and transparency, strongly swells, splits and becomes fragile. Thus, the properties of mica affected by high temperatures largely reduce. Therefore, in order to apply the mineral in materials and devices operating at a very high temperature, we should decide for a relevant type of mica which thermal resistance meets the operating conditions. By the results of the differential-thermal analysis, the mica crystal structure increases in swelling. The authors have identified a temperature range in frames of which mica retains its working properties. Visual changes in swelling in the temperature range of 20–1200 °C have been identified and analyzed. The questions of mica thermal stability for its long-term use in the electric and radio industry have been solved. The technical use of mica in more critical cases has a temperature limit of 600–650 °C. The significant residual swelling allows for the practical use of mica as a heat insulating material.

A hybrid FDTD/MoM algorithm with a conformal Huygens' equivalent surface for MRI RF coil design and analysis

Accurate design and analysis of radiofrequency (RF) coils are crucial for ultra-high field (UHF) magnetic resonance imaging (MRI) applications. To improve the numerical accuracy of electromagnetic (EM) simulations, we propose a hybrid finite difference time domain (FDTD)/method of moments (MoM) method. Unlike conventional cuboid-like Huygens' equivalent surfaces (HES), we proposed to use a conformal HES to interface the EM data of the FDTD and MoM zone. The shape and size of the conformal surface can be adjusted to fit different RF coil models, thus broadening the application range of the hybrid FDTD/MoM method. Two numerical models: an 8-channel ellipse array, and an 8-channel bent dipole array, are simulated and compared with the conventional HES counterpart. Numerical results demonstrate the capability of the conformal HES method in the analysis of RF coils.

Gold nanohexagrams via active surface growth under sole CTAB control.

The synthesis of homochiral nanostructures involves not only the chiral ligand, but also CTAB. The latter is often treated as a weak ligand unable to compete with the thiol-based chiral ligand. Here, we show that CTAB alone is able to induce Active Surface Growth on Au nanoplates, giving curved tips and steep ridges in the resulting nano-hexagrams. The growth materials (Au0) are diverted to a few active sites, whereas the rest of the Au surfaces are inhibited. Modulation of the growth rate by the ratio of ascorbic acid to Au precursor gives a continuous change of the growth modes, explaining the main trends of shape evolution and the inequivalent growth of the equivalent surfaces. With only CTAB as the ligand, the fact that ridges and spikes could be formed in defiance of facet control suggests that the role of CTAB cannot be ignored in the chiral synthesis and that the precise modulation of the Active Surface Growth could be the key to rational synthetic controls.

On accuracy of translations by kernel independent fast multipole methods

The paper concerns with accurate evaluation of local fields in problems, like those of fracture mechanics, for which extreme, rather than mean values, are of prime significance. We focus on large-scale problems, solved iteratively by a boundary element method (BEM) with employing the kernel independent fast multipole method (KI-FMM) for decreasing the complexity of matrix-to-vector multiplications. We aim to study the accuracy of individual translations far-fields for the major types of kernels (weakly singular, singular and hypersingular) entering the boundary integral equations (BIE) of harmonic and elasticity problems in 2D and 3D. It is revealed, analytically and numerically, that (i) the accuracy of individual translations of fields, generated by sources involving the normal at a source point, is notably less than that by sources independent on the normal; (ii) the accuracy is notably less for a hypersingular BIE, then for a singular BIE; and (iii) under the same complexity, the accuracy of translations, performed by using smooth (circular in 2D, spherical in 3D) equivalent surfaces (ES), is notably better than that when using non-smooth (square in 2D, cubic in 3D) ES. These conclusions yield recommendations for minimizing the complexity without loss of the accuracy of translated fields.

Synthesis of perovskite polyhedron nanocrystals with equivalent facets and the controlled growth of Pt nanoparticles with differing surface concentration of oxidized Pt4+/Pt2+ species

Co-existence of different surfaces in traditional polycrystalline heterogeneous catalysts imposes a challenge to induce different kinds of catalytic species and average reactivity. Supported metal/oxide model catalyst designed with equivalent well-defined surfaces and active species provides an opportunity to control the uniformity, maintain efficient activity, and understand catalytic mechanisms at the atomic and molecular levels. Herein, sub-20 nm perovskite-structure BaTiO3 polyhedron nanocuboids and Zr-substituted rhombic dodecahedron nanocrystals were synthesized and employed as the oxide support for the subsequent uniform growth of 1–2 nm Pt nanoparticles. These Pt nanoparticles were well dispersed on the 12 equivalent (110) facets of BaTi0.75Zr0.25O3 rhombic dodecahedra and on the 6 equivalent (100) facets of BaTiO3 nanocuboids. The main active centers on the Pt/BaTi0.75Zr0.25O3 catalysts in the oxidized surface layer of Pt (111) facets are Pt4+ versus Pt2+, which is in contrast to the oxidized surface layer of the Pt (100) facets on the Pt/BaTiO3 cuboids where there are a greater number of Pt2+ species. Compared with Pt/BaTiO3 nanocuboids, the Pt/BaTi0.75Zr0.25O3 catalysts demonstrated higher CO catalytic oxidation activity with a lower apparent Arrhenius activation energy. This work advances our ability to synthesize metal/oxide model catalyst that offer equivalent facets and highly uniform active centers with reasonable surface area in order to gain insight in reaction mechanisms.

CR-manifolds of infinite type in the sense of Bloom and Graham

An analogue of the Bloom–Graham theorem for germs of real analytic CR-manifolds of infinite type is devised, and a certain standard form to which they can be transformed (a reduced form) is described. The concept of Bloom–Graham type is refined (as a stratified type). The refined type is also holomorphically invariant. The concept of a quasimodel surface is introduced and it is shown that for biholomorphically equivalent manifolds such surfaces are quasilinearly equivalent. A criterion for the Lie algebra of infinitesimal holomorphic automorphisms to be finite-dimensional is obtained in the case when the type is uniformly infinite (that is, infinite at all points). In combination with the criterion of a finite-dimensional automorphism algebra for manifolds of finite type almost everywhere, this yields a complete criterion for this algebra to be finite-dimensional. The sets of fixed Blooom–Graham type are shown to be semi-analytic and the type of a generic point (lying outside a proper analytic subset) is minimal in a certain sense.

Antimicrobial Photodynamic Coatings Reduce the Microbial Burden on Environmental Surfaces in Public Transportation-A Field Study in Buses.

Millions of people use public transportation daily worldwide and frequently touch surfaces, thereby producing a reservoir of microorganisms on surfaces increasing the risk of transmission. Constant occupation makes sufficient cleaning difficult to achieve. Thus, an autonomous, permanent, antimicrobial coating (AMC) could keep down the microbial burden on such surfaces. A photodynamic AMC was applied to frequently touched surfaces in buses. The microbial burden (colony forming units, cfu) was determined weekly and compared to equivalent surfaces in buses without AMC (references). The microbial burden ranged from 0–209 cfu/cm2 on references and from 0–54 cfu/cm2 on AMC. The means were 13.4 ± 29.6 cfu/cm2 on references and 4.5 ± 8.4 cfu/cm2 on AMC (p < 0.001). The difference in microbial burden on AMC and references was almost constant throughout the study. Considering a hygiene benchmark of 5 cfu/cm2, the data yield an absolute risk reduction of 22.6% and a relative risk reduction of 50.7%. In conclusion, photodynamic AMC kept down the microbial burden, reducing the risk of transmission of microorganisms. AMC permanently and autonomously contributes to hygienic conditions on surfaces in public transportation. Photodynamic AMC therefore are suitable for reducing the microbial load and closing hygiene gaps in public transportation.

Assessment of nanoparticle immersion depth at liquid interfaces from chemically equivalent macroscopic surfaces

HypothesisWe test whether the wettability of nanoparticles (NPs) straddling at an air/water surface or oil/water interface can be extrapolated from sessile drop-derived macroscopic contact angles (mCAs) on planar substrates, assuming that both the nanoparticles and the macroscopic substrates are chemically equivalent and feature the same electrokinetic potential. ExperimentsPure silica (SiO2) and amino-terminated silica (APTES-SiO2) NPs are compared to macroscopic surfaces with extremely low roughness (root mean square [RMS] roughness ≤ 2 nm) or a roughness determined by a close-packed layer of NPs (RMS roughness ∼ 35 nm). Equivalence of the surface chemistry is assessed by comparing the electrokinetic potentials of the NPs via electrophoretic light scattering and of the macroscopic substrates via streaming current analysis. The wettability of the macroscopic substrates is obtained from advancing (ACAs) and receding contact angles (RCAs) and in situ synchrotron X-ray reflectivity (XRR) provided by the NP wettability at the liquid interfaces. FindingsGenerally, the RCA on smooth surfaces provides a good estimate of NP wetting properties. However, mCAs alone cannot predict adsorption barriers that prevent NP segregation to the interface, as is the case with the pure SiO2 nanoparticles. This strategy greatly facilitates assessing the wetting properties of NPs for applications such as emulsion formulation, flotation, or water remediation.

Laboratory for Validation of Rolling-Resistance Models

In this paper, a versatile drum setup for measuring rolling resistance of small wheels is presented. The purpose is to provide a flexible setup for testing of models for rolling resistance under controlled circumstances. To demonstrate this, measurements of rolling resistance with a series of sandpapers of different grit sizes representing surface textures were carried out. The measurements show a clear increase in the rolling-resistance coefficient with increasing surface roughness, rolling speed and load. Numerical calculations in the time domain for a visco-elastic contact model run on equivalent surfaces agree with the trends found experimentally. We conclude that this approach to simplifying the experiment in order to obtain a high degree of control, accuracy and repeatability is useful for validating and testing models for calculating the rolling resistance for a given surface texture.

On evaluation of local fields by fast multipole method employing smooth equivalent/check surfaces

The work aims to increase the efficiency of finding local fields in problems, like those of fracture mechanics, for which extreme, rather than average, values of fields are of prime significance. We focus on using kernel independent fast multipole methods (KI-FMM) when a problem is solved by a boundary element method. To accurately calculate local fields, we employ smooth equivalent surfaces (SES), used in translations of a KI-FMM, instead of non-smooth surfaces having singular lines (12 edges of a cube) and/or points (8 vertices of a cube in 3D; 4 vertices of a square in 2D). We develop and employ exact representations of circular (in 2D) and spherical (in 3D) equivalent surfaces and higher-order approximations of equivalent densities on them. It is established that the accuracy and stability of a KI-FMM with the SES suggested are notably higher than those of a similar KI-FMM employing non-smooth (square in 2D, cubic in 3D) equivalent surfaces. Theoretical considerations presented and numerical tests performed show that, when using the SES, the complexity of a KI-FMM does not exceed that of an analytical FMM of the same accuracy. Numerical examples illustrate the exposition. The subroutines developed are of immediate use in any code of the KI-FMM to increase the accuracy of translations without increasing their time expense.

Equivalence of K3 surfaces from Verra threefolds

We study (2,2) divisors in $P^2 \times P^2$ giving rise to pairs of non-isomorphic, derived equivalent and L-equivalent K3 surfaces of degree 2. In particular, we confirm the existence of such fourfolds as predicted by Kuznetsov and Shinder in \cite{KS}.

Error-bounded compatible remeshing

We present a novel method to construct compatible surface meshes with bounded approximation errors. Given two oriented and topologically equivalent surfaces and a sparse set of corresponding landmarks, our method contains two steps: (1) generate compatible meshes with bounded approximation errors and (2) reduce mesh complexity while ensuring that approximation errors are always bounded. Central to the first step is a parameterization-based remeshing technique, which is capable of isotropically remeshing the input surfaces to be compatible and error-bounded. By iteratively performing a novel edge-based compatible remeshing and increasing the compatible target edge lengths, the second step effectively reduces mesh complexity while explicitly maintaining compatibility, regularity, and bounding approximation errors. Tests on various pairs of complex models demonstrate the efficacy and practicability of our method for constructing high-quality compatible meshes with bounded approximation errors.

Electro-osmotic flow enhancement over superhydrophobic surfaces

We demonstrate that electro-osmotic flow can be actuated over superhydrophobic surfaces on which charge is capacitively induced. Our experiments, supported by theoretical analysis, show that electro-osmotic flow over slipping surfaces based on microstructures is enhanced by at least one order of magnitude relative to equivalent flat surfaces and is entirely pH independent. This work opens the possibility that flow control by gate electrodes may be leveraged to create configurable high throughput fluidic devices.

A new method based on equivalent surfaces for simulation of the post-cooling in concrete arch dams during construction

In arch dams the thermal field has a crucial role on the structural behaviour. Throughout construction, the internal rise of temperature due to the heat released by cement hydration often results in significant volumetric deformations. When restrained either internally or externally, these deformations may lead to the development of considerable tensile stresses and, consequently, to the cracking of concrete. For this reason, establishment of temperature control measures is frequently deemed as necessary. One of the most relevant procedures is the circulation of water in embedded coils, which is also used to complete the cooling of concrete to the desired temperature for grouting the contraction joints.Despite its importance, detailed thermal analyses of arch dams during the construction phase are relatively scarce in literature, eventually because the existing methodologies based on the Finite Element Method (FEM), which represent the coils in a discrete way, require a huge computational effort. To overcome this drawback, the present paper proposes a new methodology to simulate the post-cooling effect, where the heat removal by the cooling coils is reproduced using fictitious convective boundaries. The framework to quantify the boundary coefficients is laid out, and comparisons are made in regard to analyses where explicit modelling of the cooling coils are performed. The proposed approach is also used to predict the thermal behaviour of a real arch dam monolith during construction, for which in-situ monitoring is available.

Cenomanian–Turonian drowning of the Arabian Carbonate Platform, the İnişdere section, Adıyaman, SE Turkey

Abstract The Cenomanian–Turonian carbonate ramp in the Adıyaman Region of SE Turkey (Northern Arabian Platform) records an abrupt shift from benthic carbonate deposits to pelagic deposits near the Cenomanian–Turonian boundary event (CTBE) in the İnişdere stratigraphic section and surrounding borehole sections. A positive δ 13 C excursion of up to 2.15% is recorded in carbonate and organic carbon deposited around the CTBE and provides evidence of a direct link between the CTBE and oceanic anoxic events and the demise of the shallow carbonate production in the Derdere Formation. The microfacies analyses, biostratigraphic dating and palaeoenvironmental interpretations suggest that the platform was drowned near the CTBE as a result of changing environmental conditions. The microfacies indicating significant deepening show a contemporaneity to equivalent surfaces globally and thus strongly support an isochronous formation of Cenomanian–Turonian facies by eustatic sea-level changes. Anoxia spreading over the platform drastically reduced the carbonate production as observed in the studied sections and, therefore, resulted in a reduction in carbonate accumulation rates. Regional/local subsidence and a coeval sea-level rise during the late Cenomanian to early Turonian interval were the cause of the drowning of the platform, including regional anoxia at the northern Arabian platform linked to the Cenomanian–Turonian oceanic anoxic event (OAE2).