Surface Integral Method Research Articles

Integral and Surface Treatment Method of Waterproofing: A Review and Comparative Analysis

Water seepage into concrete can cause deterioration and other aesthetic issues that limit the life of concrete constructions. This paper examines and contrasts the various kinds of waterproofing techniques. There are essentially two types: surface treatment method and integral method. Water repellents, crystalline admixtures, and densifiers are examples of integral methods. Surface treatment methods encompass pore-blocking, hydrophobic impregnation, surface coating, and multifunctional surface treatment. The processes of various approaches are examined in this article, followed by a comparison of their durability and mechanical properties. We discuss several properties, such as sulfate attack, chloride penetration, carbonation, reinforcement corrosion, water absorption and permeability, compressive, flexural, and tensile strength. The findings indicate that each has merits and demerits of their own. The inclusion of an integral admixture to concrete offers a number of advantages over surface protection, including convenience of application, the removal of the need for ongoing maintenance, and minimal to no deterioration over time. While surface treatment methods significantly reduce water permeability and porosity. In conclusion, we give a succinct summary of certain issues regarding the present state of research and future directions for the hydrophobic modification of concrete.

A Curved Surface Integral Method for Reliability Analysis of Multiple Failure Modes System with Non-Overlapping Failure Domains

Abstract In the study of reliability of systems with multiple failure modes, approximations can be obtained by calculating the probability of failure for each state function. The first-order reliability method and the second-order reliability method are effective, but they may introduce significant errors when dealing with certain nonlinear situations. Simulation methods such as line sampling method and response surface method can solve implicit function problems, but the large amount of calculation results in low efficiency. The curved surface integral method (CSI) has good accuracy in dealing with nonlinear problems. Therefore, a system reliability analysis method (CSIMMS) is proposed on the basis of CSI for solving multiple failure modes system reliability problems with non-overlapping failure domains. The order of magnitude of the failure probability is evaluated based on the reliability index and the degree of nonlinearity, ignoring the influence of low order of magnitude failure modes, and reducing the calculation of the system failure probability. Finally, CSIMMS and other methods are compared by three numerical examples, and the results show the stability and accuracy of the proposed method.

Combined algorithms of high-frequency topographical effects for the boundary-value problems based on Helmert's second condensation method

The Helmert’s second condensation method is usually used to condense the topographical masses outside the boundary surface in the determination of the geoid and quasi-geoid based on the boundary-value theory. The condensation of topographical masses produces direct and indirect topographical effects. Nowadays, the Remove-Compute-Restore (RCR) technique has been widely utilized in the boundary-value problems. In view of spectral consistency, high-frequency direct and indirect topographical effects should be used in the Hotine-Helmert/Stokes–Helmert integral when the Earth gravitational model serves as the reference model in determining the (quasi-) geoid. Thus, the algorithms for high-frequency topographical effects are investigated in this manuscript. First, the prism methods for near-zone direct and indirect topographical effects are derived to improve the accuracies of near-zone effects compared with the traditional surface integral methods. Second, the Molodenskii spectral methods truncated to power H4 are put forward for far-zone topographical effects. Next, the "prism + Molodenskii spectral-spherical harmonic" combined algorithms for high-frequency topographical effects are further presented. At last, the effectiveness of the combined algorithms for the high-frequency topographical effects are verified in a mountainous test area.

Numerical study on the quadrupole sound source in aerodynamic noise of high-speed pantographs

ABSTRACT Insufficient consideration of aerodynamic noise source will affect the accurate evaluation of high-speed pantograph noise. In this study, we present an approach to separate and quantify the dipole and quadrupole noises of pantographs. The improved delayed detached eddy simulation (IDDES) was used for turbulence modelling and two acoustic surface integral methods were used to predict the noise. The results show that the pantograph noise is caused by the vortex shedding and interaction in the wake. The running speed does not change the distribution of the two aerodynamic noise sources, but the intensity increases significantly. Although the quadrupole noise increases with the speed level, the dipole noise still dominates. The sound pressure levels of the two noise sources increased by about 60 log10V and 70~80 log10V, respectively. The noise energy is concentrated in 160-2500 Hz, and the dominant frequency is proportional to the speed level.

Numerical study of jet-plate interaction and its effects on aeroacoustics

In modern under-wing-mounted high-bypass engines, the exhausted jet from the engine will interact strongly with the wing and high-lift devices. In this paper, simulations of an isothermal jet flow at Mach number Ma = 0.5 and close to a flat plate are carried out using large-eddy simulation. Far-field acoustic results are obtained via the surface integral method of Ffowcs Williams and Hawkings (FW-H). The studied cases include an isolated jet and other three configurations with the jet and a plate spaced at the distance H/D j = 1.0, 1.5, and 2.0, respectively, from the jet axis. Validation against experimental data is carried out. Far-field acoustic results show that the overall noise levels are significantly increased for the installed cases, particularly for polar angles in upstream of the nozzle. The noise levels are increased more as the plate approaches the jet axis, indicating the installation effect is related to the H/D and the polar angle. The pressure fluctuations are shown to decay along the radial direction. The mean flow and power spectral density of the axial velocity show the characteristics of the jet flow is not significantly changed by the presence of the plate.

Analyzing electromagnetic scattering from complex multi-layer patch objects using a multi-trace domain decomposition method

The local-coupling multi-trace and domain decomposition method originally developed to analyze electromagnetic scattering from closed composite objects is extended to solve the scattering from complex multilayer patch objects. Different from the traditional global radiation coupling surface integral equation domain decomposition method and contact-region modeling method (CRM), the local-coupling property yields many excellent properties, highly sparse matrix, better computational performance, etc. In this novel proposed method, the multilayer patch objects are decomposed into many independent sub-domains, and each sub-domain is assumed as a homogeneous dielectric subdomain to formulate the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) for dielectrics as the governing equations. The corresponding boundary condition of the perfect electric conducting (PEC) surface sheet is then achieved by adopting Robin transmission conditions (RTCs) to PEC surfaces, termed PEC-RTCs. The final resulting equation yield a better performance than the traditional method. Numerical examples validate the advantages of the proposed method.

Numerical investigation of the cavitating flow and the cavitation-induced noise around one and two circular cylinders

In this work, we simulated a two-phase cavitating flow around one and two circular cylinders with the density based homogeneous mixture model. We discretized the governing equations with employing a high-order compact finite-difference scheme incorporating filtering scheme to account for the numerical instabilities and physical discontinuities. We applied a shock capturing sensor for discontinuities detection and switching between the second-order and high-order filtering and computed the far-field acoustic by the Ffowcs Williams-Hawkings surface integral method. We studied the flow features in the wake of a circular cylinder and two cylinders for noncavitating regime and cavitating conditions. In addition, we analyzed the cavitating flow for various gaps of two side-by-side cylinders. Results revealed that the shock waves due to the collapse of the cavity moving downstream of the cylinders is the main mechanism for the generation of the acoustic impulses. The results also showed that the noise peak can occur at lower frequencies for the smaller gap between the two cylinders. Furthermore, the wakes behind the side-by-side cylinders were merged together and a single vortex street was generated by the reduction of the gap between two cylinders.

The accuracy of mutual potential approximations in simulations of binary asteroids

Context. Simulations of asteroid binaries commonly use mutual gravitational potentials approximated by series expansions, leading to truncation errors, and also preventing correct computations of force and torque for certain configurations where the bodies have overlapping bounding spheres, such as in the rotational fission model for creating asteroid binaries and pairs. Aims. We address errors encountered when potentials truncated at order two and four are used in simulations of binaries, as well as other errors related to configurations with overlapping bounding spheres where the series diverge. Methods. For this we utilized a recently developed method where the gravitational interaction between two triaxial ellipsoids can be calculated without approximations for any configuration. The method utilizes surface integration for both force and torque calculations, and it is exact for ellipsoidal shapes. We also computed approximate solutions using potentials truncated at second and fourth order, and we compare these with the solutions obtained with the surface integral method. The approximate solutions were generated with the “General Use Binary Asteroid Simulator” (GUBAS). Results. If the secondary is located with its centroid in the equatorial plane of the primary, the error in the force increases as the secondary is moved closer to the primary, but is still relatively small for both second and fourth order potentials. For torque calculations, the errors become more significant, especially if the other body is located close to one of the extended principal axes. On the axes themselves, the second order series approximation fails by 100%. For dynamical simulations of components separated a few primary radii apart, the fourth order approximation is significantly more accurate than the second order. Furthermore, because of larger errors in the torque calculations, the rotational motion is subject to greater inaccuracies than the translational motion. For configurations resembling contact binaries where the bounding spheres overlap, the errors in both force and torque in the initial stages of the simulation are considerable, regardless of the approximation order, because the series diverge. A comparison of the computational efficiency of the force and torque calculations shows that the surface integration method is approximately 82 times and four times slower than the second and fourth order potentials, respectively, but approximately 16 times faster than the order eight potential. Comparing the computation efficiency of full simulations, including the calculations of the equations of motion, shows that the surface integration scheme is comparable with GUBAS when an order four potential is used. Conclusions. The errors generated when mutual gravitational potentials are truncated at second or fourth order lead to larger errors in the rotational than in the translational motion. Using a mathematically exact method for computing forces and torques becomes important when the bodies are initially close and the bounding spheres overlap, in which case both the translational and rotational motion of the bodies have large errors associated with them. For simulations with two triaxial ellipsoids, the computational efficiency of the surface integral method is comparable to fourth order approximations with GUBAS, and superior to eight order or higher.

Comparative study of surface integral methods in aeroacoustic prediction

Introduction: Surface integral methods based on the acoustic analogy and Kirchhoff formulation are widely employed in computational aeroacoustics. The computational accuracy is usually highly dependent on the selections of the acoustic prediction method and of the integral surfaces.Methods: This paper analyzes the pros and cons of each aeroacoustic prediction method and studies numerically sound generated from flow past a circular cylinder by employing different surface integral methods. The acoustic analogy based on the impermeable solid surfaces either ignores the quadrupole contribution or needs high computational cost to calculate the quadrupole contribution, and the acoustic analogy based on the permeable integral surfaces usually suffers from the spurious source issue.Results: Both the pressure-based or density-based Kirchhoff formulations can be used in aeroacoustic prediction, however, the numerical results indicate that the pressure-based Kirchhoff formulation also suffers from the issue of the spurious sound because the pressure fluctuations at the permeable integral surfaces are contaminated by hydrodynamic component.Discussion: It seems that only the density-based Kirchhoff formulation does not suffer from the issue of the spurious sound, but this formulation requires the acoustic sources should be extracted from compressible flow simulations.

Fe/Zr-MOFs constructed by a sunlight-responsive ligand for efficient photocatalytic nitrogen fixation under ambient condition

Photocatalytic nitrogen fixation opens new opportunities for sustainable and healthier futures, and developing effective and inexpensive photocatalysts is the key. We use the ligand 3,3′,5,5′-azomellitic acid (H4abtc) to connect with Fe clusters and Zr clusters to form stable metal-organic frameworks (MOFs) Fe-abtc and Zr-abtc, both of which are responsive to visible lights for nitrogen fixation. It is worth noting that the presence of NN in the ligand makes it respond to visible lights. The tetracarboxyl group is connected to the metal cluster to form a stable structure. The field-only surface integral method verified that the ligands were successfully applied into the synthesized MOF particles, which expanded the photoresponse range and enhanced the photonic interactions of the synthesized photocatalysts compared with pure MOF particles. The best photocatalytic nitrogen fixation performance of Fe-abtc and Zr-abtc is 49.8 μmol·g(cat.)−1·h−1 and 35.7 μmol·g(cat.)−1·h−1, respectively, the apparent quantum efficiency (AQY) of the sample Fe-abtc is 0.56 %, and the reliability of the source of N element is proved by the isotope 15N2. This work provides a new idea for the design of cheap and effective MOFs for photocatalytic nitrogen fixation.

Prediction of the Radiative Properties of Triangular-Grating Surfaces from Electromagnetic Theory

In this paper, we present a study of the influence of roughness on the bidirectional reflectivity and on the emissivity of surfaces using Maxwell’s electromagnetic theory. In this framework, we solve the Helmholtz equations by using the surface integral method. We first proceed to a general description of this method, allowing to solve the propagation equations of the electromagnetic field. We then express the diffused directional flux using the surface field and its normal derivative (source terms), in the case of an incident plane wave in “p” polarization or in “s” polarization. This finally allows us to arrive at the desired radiative properties. We have developed two numerical calculation codes whose use we limit to cases of surfaces presenting cavities in the shape of a symmetrical or asymmetrical “V”. Particular interest was given to the influence of the geometric parameters of these surfaces on the bidirectional reflection function and on the emissivity of these surfaces. Finally, we present some very conclusive results.

Efficient sunlight promoted nitrogen fixation from air under room temperature and ambient pressure via Ti/Mo composites

Photocatalytic nitrogen fixation is an important pathway for carbon neutralization and sustainable development. Inspired by nitrogenase, the participation of molybdenum can effectively activate nitrogen. A novel Ti/Mo composites photocatalyst is designed by sintering the molybdenum acetylacetonate precursor with TiO2. The special carbon-coated hexagonal photocatalyst is obtained which photocatalytic nitrogen fixation performance is enhanced 16 times compared to pure TiO2 at room temperature and ambient pressure. The abundant surface defects in this composite were confirmed to be the key factor for nitrogen fixation. The 15N2 isotope labeling experiment was used to demonstrate the feasibility of nitrogen to ammonia conversion. Also, modelling on the interactions between light and the synthesized photocatalyst particle was examined for the light absorption. The optimum nitrogen fixation conditions have been examined, and the nitrogen fixation performance can reach up to 432 μg·gcat-1·h−1. Numerical simulations via the field-only surface integral method were also carried out to study the interactions between light and the photocatalytic particles to further confirm that it can be a useful material for photocatalyst. This newly developed Ti/Mo composites provide a simple and effective strategy for photocatalytic nitrogen fixation from air directly under ambient conditions.

Design Optimization of PCB-Based Rotary-Inductive Position Sensors.

This paper introduces a novel methodology to optimize the design of a ratiometric rotary inductive position sensor (IPS) fabricated in printed circuit board (PCB) technology. The optimization aims at reducing the linearity error of the sensor and amplitude mismatch between the voltages on the two receiving (RX) coils. Distinct from other optimization techniques proposed in the literature, the sensor footprint and the target geometry are considered as a non-modifiable input. This is motivated by the fact that, for sensor replacement purposes, the target has to fit a predefined space. For this reason, the original optimization technique proposed in this paper modifies the shape of the RX coils to reproduce theoretical coil voltages as much as possible. The optimized RX shape was obtained by means of a non-linear least-square solver, whereas the electromagnetic simulation of the sensor is performed with an original surface integral method, which are orders of magnitude faster than commercial software based on finite elements. Comparisons between simulations and measurements performed on different prototypes of an absolute rotary sensor show the effectiveness of the optimization tool. The optimized sensors exhibit a linearity error below 0.1% of the full scale (FS) without any signal calibration or post-processing manipulation.

Different approaches to numerical modeling of sea waves

The main approaches in direct modeling of surface waves based on complete equations of dynamics of the inviscid liquid with a free surface are briefly considered. Most of the models are intended for study of the applied and engineering problems. It is assumed that the main model is written in the curvilinear coordinate system where the height is counted off from wave surface. In the two-dimensional periodic formulation, when using a conformal system, the problem is reduced to the system of one-dimensional equations that can be easily solved using Fourier-transform method. For three-dimensional waves such simplifications do not exist, thus, the vertical velocity on the surface is calculated by solving a three-dimensional Poisson equation or using a surface integral method. An approximate scheme based on the two-dimensional equations is considered. The scheme allows reproducing the statistical mode of waves with high accuracy consistent with the similar results obtained from the accurate three-dimensional model.

Inverse Solution of Thermoacoustic Wave Equation for Cylindrical Layered Media

Thermoacoustic imaging is a crossbred approach taking advantages of electromagnetic and ultrasound disciplines, together. A significant number of current medical imaging strategies are based on reconstruction of source distribution from information collected by sensors over a surface covering the region to be imaged. Reconstruction in thermoacoustic imaging depends on the inverse solution of thermoacoustic wave equation. Homogeneous assumption of tissue to be imaged results in degradation of image quality. In our paper, inverse solution of the thermoacoustic wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section is investigated for cross-sectional thermoacustic imaging of breast and brain. By using Green’s functions and surface integral methods we derive an exact analytic inverse solution of thermoacoustic wave equation in frequency domain. Our inverse solution is an extension of conventional solution to layered cylindrical structures. By carrying out simulations, using numerical test phantoms consisting of thermoacoustic sources distributed in the layered model, our layered medium assumption solution was tested and benchmarked with conventional solutions based on homogeneous medium assumption in frequency domain. In thermoacoustic image reconstruction, where the medium is assumed as homogeneous medium, the solution of nonhomogeneous thermoacoustic wave equation results in geometrical distortions, artifacts and reduced image resolution due to inconvenient medium assumptions.

A Non‐Singular, Field‐Only Surface Integral Method for Interactions between Electric and Magnetic Dipoles and Nano‐Structures

AbstractWith the development of condensed‐matter physics and nanotechnology, attention has turned to the fields near and on surfaces that result from interactions between electric dipole radiation and mesoscale structures. It is hoped that studying these fields will further the understanding of optical phenomena in nano‐optics, quantum mechanics, electromagnetics, and sensing using solid‐state photon emitters. Here, a method for implementing dynamic electric and magnetic dipoles in the frequency domain into a non‐singular field‐only surface integral method is described. It is shown that the effect of dipoles can conveniently be described as a relatively simple term in the integral equations, which fully represents how they drive the fields and interactions. Also, due to the non‐singularity, this method can calculate the electric and magnetic fields on the surfaces of objects in both near and far fields with the same accuracy, which makes it an ideal tool to investigate nano‐optical phenomena. The derivation of the framework is given and tested against a Mie theory alike formula. Some interesting examples are shown involving the interaction of dipoles with different types of mesoscale structures including parabolic nano‐antennas and gold probes.

Correspondence between the surface integral and linear combination of atomic orbitals methods for ionic-covalent interactions in mutual neutralization processes involving H−/D−

The surface integral method for estimating ionic-covalent interactions in diatomic systems been successful in producing cross sections for mutual neutralization (MN) in reasonable agreement with experimental results for branching fractions between final states in systems such as ${\mathrm{O}}^{+}\text{/}{\mathrm{O}}^{\ensuremath{-}}$ and ${\mathrm{N}}^{+}\text{/}{\mathrm{O}}^{\ensuremath{-}}$. However, for simpler cases of MN involving ${\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{D}}^{\ensuremath{-}}$, such as ${\mathrm{Li}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$ and ${\mathrm{Na}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$, it has not produced results that are in agreement with experiments and other theoretical calculations; in particular, for ${\mathrm{Li}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$ calculations predict the wrong ordering of importance of final channels, including the incorrect most populated channel. The reason for this anomaly is investigated, and a leading constant to the asymptotic ${\mathrm{H}}^{\ensuremath{-}}$ wave function is found that is different by roughly a factor of $1\text{/}\sqrt{2}$ from that which has been used in previous calculations with the surface integral method involving ${\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{D}}^{\ensuremath{-}}$. With this correction, far better agreement with both experimental results and calculations with full quantum and linear combination of atomic orbitals (LCAO) methods is obtained. Further, it is shown that the surface integral method and LCAO methods have the same asymptotic behavior, in contrast to previous claims. This result suggests the surface integral method, which is comparatively easy to calculate, has greater potential for estimating MN processes than earlier comparisons had suggested.

Carbene Ligand-Doped Fe2O3 Composite for Rapid Removal of Multiple Dyes under Sunlight

Contaminated water due to industrial organic dyes presents a significant challenge to sustainability. As a material of green energy, photocatalysts offer an effective and environmentally friendly way to deal with organic dyes for water treatment. A series of simple and highly efficient iron photocatalysts with carbene ligands were developed, which, under the illumination of sunlight, can rapidly degrade multiple organic dyes in water at room temperature, including rhodamine B (RhB), indigo carmine (IC), methyl blue (MB), and congo red (CR). The field-only surface integral method was carried out to determine the absorption spectrum of photocatalyst particles. Under the optimized experimental conditions which were selected by the orthogonal experiments for four dyes, 0.5a@Fe2O3 and 2c@Fe2O3 demonstrated good stability and photocatalytic activity. These two composite materials not only have the ability to remove 98.0% of the degradation in 10 s, but also maintain high reactivity after a few cycles of repeated use.

Energy Based Calculation of the Second-Order Levitation in Magnetic Fluid

A permanent magnet immersed in magnetic fluid experiences magnetic levitation force which is of the buoyant type. This phenomenon commonly refers to self-levitation or second-order buoyancy. The stable levitation height of the permanent magnet can be attained by numerical evaluation of the force. Various authors have proposed different computational methods, but all of them rely on force formulation. This paper presents an alternative energy approach in the equilibrium height calculation, which was settled on the minimum energy principle. The problem, involving a cylindrical magnet suspended in a closed cylindrical container full of magnetic fluid, was considered in the study. The results accomplished by the proposed method were compared with those of the well-established surface integral method already verified by experiments. The difference in the results gained by both methods appears to be under 2.5%.

Deterministic normal contact of rough surfaces with adhesion using a surface integral method.

The fundamental problem of adhesion in the presence of surface roughness and its effect on the prediction of friction has been a hot topic for decades in numerous areas of science and engineering, attracting even more attention in recent years in areas such as geotechnics and tectonics, nanotechnology, high-value manufacturing and biomechanics. In this paper a new model for deterministic calculation of the contact mechanics for rough surfaces in the presence of adhesion is presented. The contact solver is an in-house boundary element method that incorporates fast Fourier transform for numerical efficiency. The adhesive contact model considers full Lennard-Jones potentials and surface integration at the asperity level and is validated against models in the literature. Finally, the effect of surface roughness on the adhesion between surfaces was studied, and it was shown that the root mean square gradient of surface roughness can change the adhesive pressures irrespective of the root mean square surface roughness. We have tested two adhesion parameters based on Johnson's modified criteria and Ciavarella's model. We showed that Civarella's model introduces the most reasonable criteria suggesting that the RMS roughness and large wavelength of surfaces roughness are the important parameters of adhesion between rough surfaces.