Finite Surface Research Articles

Effect of Processing Parameters on the Strain Inhomogeneity and Processing Load in Vortex Extrusion of Al–Mg–Si Alloy

Vortex extrusion (VE), a single pass severe plastic deformation technique, can impose a high amount of effective strain obtained from simultaneously twisting and reduction in area on the processed material. In this study, a hybrid investigation based on finite element analysis (FEA) and response surface methodology (RSM) was carried out to investigate the effect of geometrical parameters involved in VE die design on the strain inhomogeneity and processing load in vortex extrusion of Al–Mg–Si alloy. The analysis of variance (ANOVA) was used for verifying the effect of input variables and the significance of mathematical modeling. Developed mathematical model from RSM was verified using results obtained from the experiment. Results showed that increasing the twist angle increases the effective strain inhomogeneity. Twist angle ( $$\varphi$$ ), reduction in area (RA), and interaction of twist angle and reduction in area ( $$\varphi \times RA$$ ) were determined as the most effective parameters affecting strain inhomogeneity, while the processing parameters of $$\varphi$$ , RA, and the interactions of $$\varphi \times RA$$ , $$\varphi \times \varphi$$ and $$RA\times RA$$ are the most effective parameters on the load of VE process.

Permittivity Determination Considering the Metal Surface Roughness Effect on the Microstrip Line Series Inductance and Shunt Capacitance

In this article, a method is presented to extract the frequency-dependent relative permittivity of printed circuit board dielectric laminates from S-parameter measurements of microstrip lines, which are typically used to implement test vehicles for material characterization. For this purpose, since the small thickness of advanced laminates makes the series inductance and shunt capacitance of the lines prone to variations from designed values due to the finite metal surface roughness, this effect is considered in the development of the proposed method. This is relevant due to the fact that the capacitance and inductance exhibit a direct relationship with the line phase constant, which is commonly used to determine the relative permittivity. Hence, in this article, a model and parameter extraction is proposed to consider the impact of the surface roughness on the determination of the effective permittivity. Then, by performing linear regression in experimental data, this parameter is obtained up to 40 GHz. The results are in agreement with data measured using a free-space technique and also allow to carry out a characterization in a quasi-continuous and wide frequency range.

Ensemble averaged Madelung energies of finite volumes and surfaces

Exact expressions for ensemble averaged Madelung energies of finite volumes are derived. The extrapolation to the thermodynamic limit converges unconditionally and can be used as a parameter-free real-space summation method of Madelung constants. In the large volume limit, the surface term of the ensemble averaged Madelung energy has a universal form, independent of the crystal structure. The scaling of the Madelung energy with system size provides a simple explanation for the structural phase transition observed in cesium halide clusters.

Unstructured PEEC method with the use of surface impedance boundary condition

PurposeThis paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation.Design/methodology/approachBecause of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed.FindingsThe new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh.Research limitations/implicationsThe propagation effects are not taken into account in the proposed formulation.Originality/valueThe formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.

Numerical and Optimal Study on Bending Moment Capacity and Stiffness of Mortise-and-Tenon Joint for Wood Products

Mortise-and-tenon (M–T) joint is a traditional joint type commonly used in wood constructions and wood products. Bending moment capacity (BMC) is a critical criterion to evaluate the strength of the M–T joint. In order to design the M–T joint structure more rationally, many researchers have been devoted to studying on this topic. However, the factors influencing the BMC are too many to conduct comprehensive studies using experimental tests, especially for tenon size. In this study, the BMC and bending stiffness of the M–T joint were studied using a combination of finite element method (FEM) and response surface method to optimize the tenon size of the M–T joint. The results showed that (1) the proposed finite element model was capable of predicting BMC of M–T joints with the ratios of FEM to observed, ranging from 0.852 to 1.072; (2) the BMC and stiffness were significantly affected by tenon size, and tenon length had a more significant effect on BMC than tenon width, while the tenon width affected the bending stiffness more significantly; (3) the response surface model proposed to predict and optimize the BMC of the M–T joint relating to tenon length and tenon width was capable of providing an optimal solution; (4) it was recommended to make the ratio of tenon length to tenon width higher than 1 to get higher BMC of M–T joints. In conclusion, this study will contribute to reducing the cost of a huge amount of experimental tests by applying FEM and the response surface method to design M–T joint wood products.

The acoustical impulse response of a line source of finite length above an absorbing plane

It was shown in previous publications that the impulse response of an infinite line source, as well as a point source in the three-dimensional space above an absorbing plane, can be expressed in closed form. However, line sources of a finite length are much more practical. In this study, the impulse response of a finite line source above the absorbing ground is derived and presented in a closed form, which is the main result of the present work. The corresponding analytical solution is composed of three distinct signals. Those are the direct signal, the mirrored signal, and the "pressure tail." The direct signal is the line-of-sight signal. The mirrored signal is the signal emitted from the image source. It is weighted with the reflection coefficient of the infinite line source, which is a surprising mathematical result. The direct signal and the mirrored signal are both of finite duration. However, the third signal-the pressure tail-starts at the end of the mirrored signal and continues indefinitely for a finite surface impedance. In general, this last signal is relatively weak; it can be considered as the reverberation of the source caused by the infinite plane.

Propagation behaviour of a hemispherical blast wave on a dome roof

Dome structures are often employed for industrial buildings and may be potential targets of terrorist attacks or accidental explosion. Military design manuals that are commonly used for structural design practice are based on the assumption that the blast wave reflects on an infinite or finite flat surface. These semi-empirical formulae ignore the blast wave propagation behaviour on a finite and variable-curvature reflector. The purpose of this research work is to estimate the blast load on dome structures during an external explosion. To achieve this objective, two laboratory-scale spherical dome structures were tested experimentally with 11 different blast cases. Following the experimental analysis, numerical parametric analysis based on ANSYS/AUTODYN was carried out to study the propagation and reflection on dome roofs. In addition, the performance of the Mach effect, reflection effect, diffraction effect, clearing effect and decay coefficient of the blast wave on the dome roof were investigated for different structural and explosion parameters. Based on this, a series of empirical equations are proposed to describe the temporal and spatial blast load distribution on a dome roof mounted on a supporting structure. This new load model described in the paper has been validated as it is able to predict the results of the experimental measurement on dome structures within experimental error.

Uniform hyperbolicity of the graphs of nonseparating curves via bicorn curves

We show that the graphs of nonseparating curves for oriented finite type surfaces are uniformly hyperbolic. Our proof follows the proof of uniform hyperbolicity of the graphs of curves for closed surfaces due to Przytycki-Sisto, while introducing new arguments using homology to certify that certain curves are nonseparating. As demonstrated by Aramayona-Valdez, this proves also that the graph of nonseparating curves for any oriented infinite type surface with finite positive genus is hyperbolic.

Heat kernel asymptotics on sequences of elliptically degenerating Riemann surfaces

This is the first of two articles in which we define an elliptically degenerating family of hyperbolic Riemann surfaces and study the asymptotic behavior of the associated spectral theory. Our study is motivated by a result which Hejhal attributes to Selberg, proving spectral accumulation for the family of Hecke triangle groups. In this article, we prove various results regarding the asymptotic behavior of heat kernels and traces of heat kernels for both real and complex time. In Garbin et al. (2018) [8], we will use the results from this article and study the asymptotic behavior of numerous spectral functions through elliptic degeneration, including spectral counting functions, Selberg's zeta function, Hurwitz-type zeta functions, determinants of the Laplacian, wave kernels, spectral projections, small eigenfunctions, and small eigenvalues. The method of proof we employ follows the template set in previous articles which study spectral theory on degenerating families of finite volume Riemann surfaces (Huntley et al. (1995) [14] and (1997) [15], Jorgenson et al. (1997) [20] and (1997) [17]) and on degenerating families of finite volume hyperbolic three manifolds (Dodziuk et al. (1998) [4].) Although the types of results developed here and in Garbin et al. (2018) [8], are similar to those in existing articles, it is necessary to thoroughly present all details in the setting of elliptic degeneration in order to uncover all nuances in this setting.

Influence of finite size and surface effects on the structural, electrical and magnetic properties of nanostructured nickel oxide

A detailed study on the influence of crystallite size variation on the structural, electrical and magnetic properties of nickel oxide nanoparticles is reported here. The characterization techniques reveal the structural modification of the samples which resulted from the variation in crystallite size. The grain boundaries and triple junctions in the interfacial regions play a pivotal role in deciding the transport properties of nanocrystalline NiO. The dielectric measurements confirm high value of dielectric constant for NiO nanoparticles at low frequency, which can be used for the fabrication of gate dielectric in metal oxide semiconductor field effect transistors. The superparamagnetic behaviour of samples with a size ~ 8 nm points out the significance of surface atoms and uncompensated surface spins. The results highlight the role of finite size and surface effects in determining the properties of nanostructured nickel oxide.

Graphene on an optical waveguide: comparison of simulation approaches

Recently, unusual properties of novel two-dimensional materials like graphene have revolutionized many branches of science and technology. Adequate numerical simulations of photonic devices comprising graphene layers require new approaches or modified methods. In this paper we present comparison of results obtained with three representations of a graphene monolayer: (1) an infinitely thin sheet with a finite surface complex conductivity, (2) a thin layer of a finite thickness exhibiting uniaxially anisotropic complex permittivity, and (3) anisotropic permittivity perturbation in an infinitely small volume. Numerical solutions of rigorous dispersion equations were compared to each other and also with the results obtained with several commercial as well as proprietary software packets. Under proper conditions, all approaches provide comparable results.

Effect of thermal radiation on conjugate natural convection flow of a micropolar fluid along a vertical surface

This article investigates the behavior of conjugate natural convection over a finite vertical surface immersed in a micropolar fluid in the presence of intense thermal radiation. The governing boundary layer equations are made dimensionless and then transformed into suitable form by introducing the non-similarity transformations. The reduced system of parabolic partial differential equations is integrated numerically along the vertical plate by using an implicit finite difference Keller-box method. The features of fluid flow and heat transfer characteristics for various values of micropolar or material parameter, K, conjugate parameter, B, and thermal radiation parameter, Rd, are analyzed and presented graphically. Results are presented for the local skin friction coefficient, heat transfer rate and couple stress coefficient for high Prandtl number. It is found that skin friction coefficient and couple stress coefficient reduces whereas heat transfer rate enhances when the micro-inertia parameter increases. All the physical quantities get augmented with thermal radiation.

Evaluation of Multicomponent Adsorption Kinetics for Carbon Dioxide Enhanced Gas Recovery from Tight Shales

SummaryOnly 3 to 10% of gas from tight shale is recovered economically through natural depletion, demonstrating a significant potential for enhanced shale-gas recovery (ESGR). Experimental studies have demonstrated that shale kerogen/organic matter has higher affinity for carbon dioxide (CO2) than methane (CH4), which opens possibilities for carbon storage and new production strategies.This paper presents a new multicomponent adsorption isotherm that is coupled with a flow model for the evaluation of injection/production scenarios. The isotherm is dependent on the assumption that different gas species compete to adsorb on a limited specific surface area. Rather than assuming a capacity of a fixed number of sites or moles, this finite surface area is filled with species taking different amounts of space per mole. The final form is a generalized multicomponent Langmuir isotherm. Experimental adsorption data for CO2 and CH4 on Marcellus Shale are matched with the proposed isotherm using relevant fitting parameters. The isotherm is first applied in static examples to calculate gas-in-place reserves, recovery factors (RFs), and enhanced gas-recovery (EGR) potential according to the contributions from free-gas and adsorbed-gas components. The isotherm is further coupled with a dynamic flow model with application to CO2/CH4 substitution for CO2-ESGR, assuming only a gas phase exists in the system. We study the feasibility and effectiveness of CO2 injection in tight shale formations in an injection/production setting representative of laboratory and field implementation and compare that with regular pressure depletion.The production scenario we consider is a 1D shale-core or matrix system first saturated with free and adsorbed CH4 gas with only the left-side (well) boundary open. During primary depletion, gas is produced from the shale to the well by advection and desorption. This process tends to give low recovery and is entirely dependent on the well pressure. Stopping production and then injecting CO2 into the shale leads to an increase in pressure, where CO2 is preferentially adsorbed over CH4. The injected CO2 displaces but also mixes with the in-situ CH4. Restarting production from the well then allows CH4 gas to be produced in the gas mixture. Diffusion allows the CO2 to travel farther into the matrix while keeping CH4 accessible to the well. Surface substitution further reduces the CO2 content and increases the CH4 content in the gas mixture that is produced to the well. A result of the isotherm and its application of Marcellus experimental data is that adsorption of CO2 with resulting desorption of CH4 will lead to a reduction in total pressure if the CO2 content in the gas composition is increased. That is in itself an important drive mechanism because the pressure gradient driving fluid flow is maintained (pressure buildup is avoided). This is because CO2 takes approximately 24 times less space per mole than CH4.

Modification of relativistic beam fields under the influence of external conducting and ferromagnetic flat boundaries

AbstractWe derive analytical expressions for external fields of a relativistic bunch of charged particles with a circular and an elliptical cross section under different boundary conditions and interaction of the fields with an accelerator structural elements. The particle density in the bunch is assumed to be uniform as well as non-uniform. At distances far apart from the bunch, in free space the field reduces to the relativistic modified Coulomb form for a pointlike charge and at small distances the expressions reproduce the external fields of a continuous beam. In an ultra-relativistic limit the longitudinal components of the internal and external electric fields of the bunch are strongly suppressed by the Lorentz factor. If the bunch is surrounded by conducting surfaces, the bunch self-fields are modified. Image fields generated by a bunch between two parallel conducting plates are studied in detail. Exact summation of the electric, $E_y$, and magnetic, $B_x$, image field components allows the infinite series to be represented in terms of elementary trigonometric functions. The new expressions for modified fields are applied to study image forces acting on the bunch constituents and the bunch as a whole. The coherent and incoherent tune shifts for an arbitrary bunch displacement from the midplane are calculated in the framework of an improved linear theory, for both infinite and finite parallel flat surfaces. Moreover, the developed method allows us to generalize the Laslett image coefficients $\epsilon_1$, $\epsilon_2$, $\xi_1$, $\xi_2$ to the case of an arbitrary bunch offset and reveal relationships between these coefficients. Appendix C provides a brief historical background of the development of the method of electrical images.

Morphology-Dependent Photoelectrochemical and Photocatalytic Performance of γ-Bi₂O₃ Nanostructures.

Simple one-step solvothermal route was used to synthesize γ-Bi₂O₃ nanostructures. Well-defined nanoflowers and finite nanorods surface morphology of the samples were revealed. The physical characterization and material confirmation was explored by employing X-ray diffraction (XRD), Raman, photoluminescence (PL), and Fourier transform infrared (FTIR) studies. The optical bandgap of about 2.71 and 2.72 eV was observed for nanoflower and nanorods, respectively. The highest specific surface area of 0.877 m²/g with mesoporous feature was reported for nanoflower sample. The improved photocurrent of 12.47 μA/cm² was observed for the nanoflower photoanode with lowest internal resistance and the highest stability over 3600 s, with 87% retention in photocurrent was estimated from chronoamperometry (CA) study. The effective methyl orange degradation of MO as 94% was investigated by nanoflower photocatalyst. The synthesis of metastable γ-Bi₂O₃ nanostructures with hierarchical morphology to adapt as an efficient photoanode for solar water splitting and pollutant degradation applications was reported.

Finite Time Adaptive Neural Dynamic Surface Control of Nonstrict Feedback Nonlinear Systems Including Dead-Zone and Full State Restrictions

In this paper, finite time adaptive neural network (NN) tracking control is investigated for a class of uncertain nonstrict feedback systems with unknown dead-zone and unmodeled dynamics as well as full state restrictions. Using the linearized representation of dead-zone, finite-time adaptive control is presented by the aid of dynamic surface control (DSC) technique and the property of Gaussian function. By introducing logarithmic function as invertible nonlinear mapping, the full state restriction problem is solved. The dynamic signal generated by the low-pass filter is used to handle unmodeled dynamics. Through finite-time stability theory and introducing the bounded closed set in the proof, all the signals in the closed-loop system are proved to be semi-globally practical finite time stable (SGPFS). The restriction conditions are not triggered for all the states. Finally, two numerical examples are used to illustrate the feasiability of the finite time adaptive control strategy.

SQUARE-INTEGRABILITY OF THE MIRZAKHANI FUNCTION AND STATISTICS OF SIMPLE CLOSED GEODESICS ON HYPERBOLIC SURFACES

Given integers$g,n\geqslant 0$satisfying$2-2g-n<0$, let${\mathcal{M}}_{g,n}$be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus$g$with$n$cusps. We study the global behavior of the Mirzakhani function$B:{\mathcal{M}}_{g,n}\rightarrow \mathbf{R}_{{\geqslant}0}$which assigns to$X\in {\mathcal{M}}_{g,n}$the Thurston measure of the set of measured geodesic laminations on$X$of hyperbolic length${\leqslant}1$. We improve bounds of Mirzakhani describing the behavior of this function near the cusp of${\mathcal{M}}_{g,n}$and deduce that$B$is square-integrable with respect to the Weil–Petersson volume form. We relate this knowledge of$B$to statistics of counting problems for simple closed hyperbolic geodesics.

Modelling of Terrain Effect from the Magnetotelluric (MT) Field Data

Magnetotelluric (MT) data were recorded over highly undulating terrain in Himalayan region from Roorkee to Gangotri section in period 0.001-1000 second. In the presence of topographic distortion the interpretation may become misleading. A simple scheme based on finite difference method for the simulation of the topographic distortion in magnetotelluric response is presented. The finite difference based, forward response computation algorithm, has been extended for undulating topography. The distortion coefficients, representing the topographic effect, are designed for correcting the observed distorted impedance tensor recorded in the vicinity of topographic features. The accuracy of the scheme is checked by comparing the computed responses with the finite element, Rayleigh scattering and transmission surface results for transverse electric (TE-mode) and transverse magnetic (TM-mode) responses. The modified algorithm is used to model the terrain effect on MT data recorded from Himalayan terrain.

Effective Equidistribution of the Horocycle Flow on Geometrically Finite Hyperbolic Surfaces

Abstract We prove effective equidistribution of the horocycle flow in the unit tangent bundle of infinite-volume geometrically finite hyperbolic surfaces.

The effect of resolution on the deterministic finite element elastic-plastic rough surface contact under combined normal and tangential loading

Three-dimensional deterministic models of rough surfaces can enrich the understanding of the influence of surface texture on contact and friction. However, most of the existing finite element contact models simply use the data measured from real rough surfaces directly and consider the shape between every two neighboring points to be a straight line. In this study, we proposed a possible harmonic description for the shape between the measured points. This is accomplished by using harmonic interpolation. The effect of resolution on the contact properties under normal loading and combined normal and tangential loading are investigated. This study provides a methodology to the finite element analysis of rough surface contact that may push the simulation results closer to reality.