Semi-infinite Substrate Research Articles

ANALYSIS OF SH-WAVES IN ANISOTROPIC FIBER-REINFORCED MEDIUM OVER LINEARLY VARYING INHOMOGENEOUS SUBSTRATE UNDER NON-LOCAL ELASTICITY

An analytical technique employing the variable separable method has been used in an attempt to precisely grasp and assess the impact of the property non-local elasticity upon the wave transmission response of an anisotropic fiber-reinforced material embedded over a semi-infinite, inhomogeneous medium that changes linearly. As depth increases, the stiffness and density of a semi-infinite substrate are believed to alter linearly. Availing the Whittaker function, a relation about dispersion has been acquired to analyze the response of SH waves. The visual representation depicts a significant influence of non-local elasticity on the propagation of SH-wave modes. Special cases have been found assessing the concurrency of the model with the original form equation of Love wave. The effects of non-locality, fiber-reinforcement parameters, and inhomogeneity parameters carry implications in designing and gradation of material characteristics some important parameters on the wave characteristics of the studied model.

Love waves propagation in layered viscoelastic waveguides characterized by a Zener model

This paper describes a theory of surface Love waves propagating in lossy waveguides consisting of a viscoelastic layer deposited on a semi-infinite elastic substrate. The Zener model to describe the viscoelastic behavior of a medium is used. This simple model captures both the relaxation and retardation. A new form of the unsteady momentum equation for viscoelastic waveguides has been established. By using appropriate boundary conditions, an analytical expression for the complex dispersion equation of Love waves has been deduced. The influence of the loss factor and the ratio of shear moduli of the surface layer on the dispersion curves of Love waves velocity and attenuation is analyzed numerically. The numerical solutions show the dependence of the velocity change and the wave attenuation in terms of the loss factor and the ratio of shear moduli. The obtained results show that the change in the ratio of shear moduli can represent a hardening or softening effect of the surface layer. These effects depend on the loss factor value of the surface layer. In addition, these results are novel, fundamental and can be applied in the characterization of the viscoelastic properties of soft biomaterials and tissues, in nondestructive testing of materials, in geophysics and seismology. Thus, the obtained complex dispersion equation can be very useful to interpret the experimental measurements of Love waves properties in viscoelastic waveguides.

Quantitative photothermal analysis and multispectral imaging of dental structures: insights into optical and thermal properties of carious and healthy teeth.

In the analysis of two-layered turbid dental tissues, the outer finite-thickness layer is modeled by an optical transport coefficient distinct from its underlying semi-infinite substrate layer. The optical and thermophysical parameters of healthy and carious teeth across the various wavelengths were measured leading to the determination of the degree of reliability of each of the fitted parameters, with most reliable being thermal diffusivity and conductivity, enamel thickness, and optical transport coefficient of the enamel layer. Quantitative pixel-by-pixel images of the key reliable optical and thermophysical parameters were constructed. We introduced a theoretical model of pulsed photothermal radiometry based on conduction-radiation theory and applied to quantitative photothermal detection and imaging of biomaterials. The theoretical model integrates a combination of inverse Fourier transformation techniques, avoiding the conventional cumbersome analytical Laplace transform method. Two dental samples were selected for analysis: the first sample featured controlled, artificially induced early caries on a healthy tooth surface, while the second sample exhibited natural defects along with an internal filling. Using an Nd:YAG laser and specific optical parametric oscillator (OPO) wavelengths (675, 700, 750, and 808nm), photothermal transient signals were captured from different points on these teeth and analyzed as a function of OPO wavelength. Measurements were also performed with an 808-nm laser diode for comparison with the same OPO wavelength excitation, particularly for the second sample with natural defects. The findings demonstrated that the photothermal transient signals exhibit a fast-decaying pattern at shorter wavelengths due to their higher scattering nature, while increased scattering and absorption in the carious regions masked conductive and radiative contributions from the underlayer. These observations were cross-validated using micro-computed tomography, which also enabled the examination of signal patterns at different tooth locations. The results of our study showed the impact of optical and thermal characteristics of two-layered turbid dental tissues via an inverse Fourier technique, as well as the interactions between these layers, on the patterns observed in depth profiles.

Broadband focusing of seismic Rayleigh waves by Luneburg lens in the semi-infinite soil

We propose a Luneburg lens for focusing the seismic Rayleigh waves composed of blind holes with varying radii in a semi-infinite soil substrate. Luneburg lenses have a broadband property of achieving a focusing effect from 6 Hz to 9 Hz. It can enhance the wave amplitude by almost 4 times at the focus, and concentrate about 71% of the incident seismic wave energy in the focal area. And its FWHM can reach a minimum of 0.7λ. The effect of wavefront conversion of the Luneburg lens from a cylindrical wave to a plane wave is effectively demonstrated.

Kinetic friction of structurally superlubric 2D material interfaces

The ultra-low kinetic friction Fk of 2D structurally superlubric interfaces, connected with the fast motion of the incommensurate moiré pattern, is often invoked for its linear increase with velocity v0 and area AS, but never seriously addressed and calculated so far. Here we do that, exemplifying with a twisted graphene layer sliding on top of bulk graphite – a demonstration case that could easily be generalized to other systems. Neglecting quantum effects and assuming a classical Langevin dynamics, we derive friction expressions valid in two temperature regimes. At low temperatures the nonzero sliding friction velocity derivative dFk/dv0 is shown by Adelman–Doll–Kantorovich type approximations to be equivalent to that of a bilayer whose substrate is affected by an analytically derived effective damping parameter, replacing the semi-infinite substrate. At high temperatures, friction grows proportional to temperature as analytically required by fluctuation–dissipation. The theory is validated by non-equilibrium molecular dynamics simulations with different contact areas, velocities, twist angles and temperatures. Using 6°-twisted graphene on Bernal graphite as a prototype we find a shear stress of measurable magnitude, from 25kPa at low temperature to 260kPa at room temperature, yet only at high sliding velocities such as 100m/s. However, it will linearly drop many orders of magnitude below measurable values at common experimental velocities such as 1μm/s, a factor 10−8 lower. The low but not ultra-low “engineering superlubric” friction measured in existing experiments should therefore be attributed to defects and/or edges, whose contribution surpasses by far the negligible moiré contribution.

Solute Profile during Diffusion Annealing of Thinly Coated Semi-Infinite Metallic Substrate

Solute Profile during Diffusion Annealing of Thinly Coated Semi-Infinite Metallic Substrate

Simulations of layer effects in confocal photothermal microscopy

This work presents a detailed study of how the thermal diffusivity measurement of a sample is affected by the deposition of an absorbent layer on its surface, when analyzed by confocal photothermal microscopy. First, the temperature distribution and surface curvature of a solid, which are related to the two basic mechanisms that modify the signal measured with that technique, are solved by means of the spatial Fourier transform, considering a semi-infinite substrate with a surface layer, which is heated by a modulated pump beam. Based on the calculated solutions, the typical signals of this technique are simulated, varying parameters such as the thickness of the layer, the material, and the pump beam radius. These signals are fitted by means of usual theoretical photothermal models that allow the retrieving of the substrate thermal diffusivity, but ignore the existence of the layer. In this way, the zones of validity of the same models are identified from the analysis of the fitting error, and the shift between the recovered and expected value.

Fourier spectral theory of pulsed photothermal radiometry, signal analysis, and parametric measurements in two-layered media

A theoretical model of pulsed photothermal radiometry based on conduction-radiation theory is introduced for a two-layered medium with a first layer having optical and thermal properties different from those of the semi-infinite substrate. This geometry closely represents the optical and thermal properties of biotissues, a major intended application. The theory derives the spatial distribution of the frequency spectrum of the pulsed photothermal signal from the composite two-layer boundary-value problem and matches the spectral frequency domain results to the measured photothermal transients through an efficient inverse Fourier transformation algorithm, which involves the optical, thermal, and geometric parameters of the experimental system. This approach avoids the complicated and computationally expensive analytical Laplace transform approach usually adopted in similar studies and yields a complete conduction–radiation description of photothermal signals without simplifying, yet restrictive, approximations encountered in the literature. Numerical and experimental tests of the model using intralipid solution as layer 1 and semi-infinite solid samples such black rubber and anodized aluminum as layer 2 of the medium are described. The radiation heat transfer coefficients from the air–intralipid and intralipid–solid interfaces were introduced to complement the conductive blackbody-radiated infrared signal component at the detecting camera. The best-fitted parameters and heat transfer coefficients are compared to theoretical and experimental data, and the results of these tests were found to be consistent with the theoretical model.

Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology

When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which further complexifies the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamental solution in order to address the specific poroelastic lubrication coupling associated with contactless colloidal-probe methods. In particular, we derive the conservative and dissipative components of the force associated with the oscillating vertical motion of a sphere close to the poroelastic substrate. Our results may be relevant for dynamic surface force apparatus and contactless colloidal-probe atomic force microscopy experiments on soft, living and/or fragile materials, such as swollen hydrogels and biological membranes.

Rate-dependent evolution of wrinkling films due to growth on semi-infinite planar viscoelastic substrates

A mechanistic understanding of morphogenesis in biology, the fabrication of advanced meta surfaces with specific functionalities and structures with enhanced energy dissipation often have in common that the combined effects of energy dissipation due to viscoelasticity and a loss of stability govern both their mechanical response and their final forms. In this paper we show that the interplay between viscoelasticity and multistability crucially influences the evolution of deformations in viscoelastic structures undergoing large deformations. The influence is studied on a prototypical system of a uniaxially growing film on a semi-infinite planar viscoelastic substrate, where it is shown that during the evolution of deformation the choice of multiple developing modes is greatly affected by this interplay. For the analysis of the underlying mechanics of the mode competition in the post-buckling regime, when the system undergoes large deformations, a 3D general finite-strain visco-hyperelastic theory is built. It includes kinematic and material nonlinearities in the film and in the substrate. For the case of ramp-loading time functions the phase space of the solutions is characterized and the evolution of a deformation pattern is analyzed. We find that the interaction between multistability and viscoelasticity greatly increases the evolution time of the system and that the growth rate and viscoelastic stress-relaxation rate influence the choice of the final equilibrium deformation state of the structure. This shows that viscoelastic structures can evolve into (meta)stable equilibrium states that are unattainable using purely elastic structures. The nonlinear problem is solved numerically with the use of the finite-element method. In parallel, we develop analytical solutions for a simplified problem that is based on Föppl–von Karman plate kinematics to describe the mechanics of the film and substrate that is modeled as a 2D linear-viscoelastic continuum. A remarkably good match between the analytical and the numerical results was obtained.

The Application of the Hybrid Projection Method for the Analysis

The problem of scattering of a plane electromagnetic wave by a 2D periodic structure formed by absorbing spherical radially inhomogeneous dielectric elements is considered. The elements have the type of electromagnetic black holes located on a semi-infinite substrate. The numerical algorithm of the solution is developed. The algorithm is based on the hybrid projection method and takes into account the peculiarities of the black hole construction. The algorithm is generalized to the case, when black holes are situated on aperfectly conducting screen. New expressions for calculating the power absorbed by the structure elements are derived. The numerical results characterizing the efficiency of the structure absorption are presented.

Finite element analysis on tunable solid/fluid phononic crystal for surface acoustic wave bandgaps with various fluid heights

In this study, the propagations of surface acoustic waves (SAWs) in two-dimensional solid/fluid phononic crystal (PC) structures were investigated. The PC structures are composed of a periodic sequence of hollow pillars deposited on a semi-infinite substrate, which can be filled with various kinds/heights of fluid. Finite element analysis was used to study the characteristics of SAW bandgaps for the unit cell of PCs. The results showed that the distribution of bandgaps varies with the fluid height. Additionally, the change of bandgaps is more sensitive to mercury than water. Furthermore, transmission properties of SAWs for the PCs filled with different mercury heights are analyzed. It can be found that the PCs can inhibit the propagation of SAWs with a frequency corresponding to the bandgaps validly. Meanwhile, comparing with the transmission spectra, it could be concluded that the transmission troughs shift to lower frequency overall as the mercury heights increase. The results obtained in this study are instructive and meaningful for the practical design of tunable SAW PCs.

Topological disclination states for surface acoustic waves

Surface acoustic waves (SAWs) are widely involved in today's communication and sensing networks. Recent exploration of topological SAWs has provided promising prospects for developing future hybrid SAW devices. In this paper, by designing tight-binding phononic crystals on a semi-infinite substrate, we revealed topological disclination states, i.e., a kind of bound state in topologically condensed matters, for the SAWs. Numerical simulations show that the bound states induced by disclination in the SAW system are more diverse than in previous electromagnetic and mechanical systems. SAW resonances in the disclinations can be efficiently excited by appropriate mechanical stimulation with decent qualities. These states are robust and flexible for design, providing options for future multifunctional and interdisciplinary SAW manipulators, processors, sensors, and other on-chip integrated components.

Dimensionless Analysis to Determine Elastoplastic Properties of Thin Films by Indentation

By assuming the elastoplastic properties of thin-film materials, a reverse analysis method is proposed by deriving a dimensionless function for the indentation process. The substrate effect is taken into account by assuming a perfect interface between thin-film and substrate materials. In order to obtain the applied load–penetration depth (P-h) curves, the indentation process is numerically modeled as an axisymmetric problem with a rigid-body Berkovich indenter on the semi-infinite substrate when performing finite element (FE) simulations. As a typical soft film/hard substrate problem, the elastic substrate is assumed and the power–law model is used to describe the constitutive properties of thin-film materials. Varying elastic modulus (10–50 GPa), yield strength (60–300 MPa), and hardening exponent (0.1–0.5) characterize different elastoplastic mechanical properties of thin-film materials with film thickness of 10–30 μm. Owing to the good trending P-h curves with the maximum indentation depth up to the 2/3 film thickness for different elastoplastic thin-film materials, a dimensionless function is derived and validated based on the predictions by reliable FE simulations. The proposed dimensionless function elegantly elucidates the essential relationship between the elastoplastic mechanical properties of the thin-film material and indentation responses (e.g., loading and unloading variables). The elastoplastic constitutive curves predicted by the proposed reverse method are confirmed to be in good agreement with the stress-strain curves of materials by FE simulations with the randomly selected elastoplastic mechanical properties and film thicknesses. This study provides a theoretical guidance to understand the explicit relationship between elastoplastic mechanical properties of the thin-film material and indentation responses.

Minkowski-like fractal seismic metamaterial with wide low-frequency band gaps on single and layered soil

In this paper, we propose a resource-efficient Minkowski-like fractal seismic metamaterial by hybridizing U-shaped and cross-shaped pillars, providing wide complete band gaps (BGs) due to its multi-scale self-similar property. Numerical modeling of seismic surface waves is used to study the band structure and transmission of our seismic metamaterial. A comparison of the band structures of the developed seismic metamaterial with various levels reveals that the iteration order itself is responsible for the increase in the number of frequency bands and the decrease in the center frequencies of the BGs. Furthermore, the vibrational modes are calculated and examined to understand the mechanism of BG generation. To demonstrate the efficiency of earthquake shielding in multiple complete BGs, investigations of seismic surface wave propagation on a 1D array of Minkowski-like fractal structure units on the surface of single and layered semi-infinite substrates are employed. The results show that the layered soil has the function of widening BGs by itself. Our proposed Minkowski-like fractal structure due to its multi-scale self-similarity mitigates the intrinsic drawback of the narrow BG of resonant metamaterial, providing a superior alternative in seismology and related areas of multi-frequency band vibration reduction. Moreover, its green design and manufacturing due to low filling rates, strong wear resistance, and ductility can realize the low-carbon and sustainable development of the construction industry.

Chiral Berry plasmon dispersion of the two-dimensional electron gas based on a quantum hydrodynamic model

We employ the quantum hydrodynamic model to investigate the properties of chiral Berry plasmons (CBPs) generated by a high-density two-dimensional electron gas (2DEG) film covering a semi-infinite dielectric substrate with a finite Berry flux. By coupling Maxwell's equations, Poisson's equation, and the boundary conditions, we derive the dispersion relations of plasmon with a nonzero Berry flux in detail. We present the difference in the dispersion of CBPs with quantum effects and the classical model. We show how the quantum effect, Berry curvature, the dielectric constant of the substrate, and electron density in 2DEG affect the behavior of the CBPs. Parameter dependence of the effects is calculated and discussed.

Fracture mechanics solutions and operative formulae for isotropic bi-material layers with large elastic mismatch

Following previous works in the literature on the fracture of layered composites, semi-analytical expressions for energy release rate and mode-mixity phase angle in isotropic bi-material layers subjected to arbitrary end loadings are extended to materials characterized by a large elastic mismatch described by Dundurs’ parameters |α| ≤ 0.99 and |β| ≤ 0.4. The solutions depend on elementary bending, axial and shear loads acting at the crack tip cross section, elastic constants and relative thickness of the layers, and dimensionless coefficients describing the fracture parameters of single elementary loads. The coefficients associated to the shear forces are presented in the literature only for combinations with β = 0; here they are determined numerically for different values β ≠ 0 to describe materials used in current applications. Simplified fitting formulae having general validity, as polynomials, which highlight the dependence on Dundurs’ parameters and are practical to support laboratory tests, are derived for layers with mid-thickness delaminations and thin layers on semi-infinite substrates. Applications to some mixed mode fracture specimens highlight the effects of β ≠ 0 on the fracture parameters and the limitations of estimates based on the commonly adopted assumption β = 0. As expected, the results for mid-thickness delaminations show that such effects are stronger on mode-mixity phase angle than on energy release rate.

Extended topological valley-locked surface acoustic waves

Stable and efficient guided waves are essential for information transmission and processing. Recently, topological valley-contrasting materials in condensed matter systems have been revealed as promising infrastructures for guiding classical waves, for they can provide broadband, non-dispersive and reflection-free electromagnetic/mechanical wave transport with a high degree of freedom. In this work, by designing and manufacturing miniaturized phononic crystals on a semi-infinite substrate, we experimentally realized a valley-locked edge transport for surface acoustic waves (SAWs). Critically, original one-dimensional edge transports could be extended to quasi-two-dimensional ones by doping SAW Dirac “semimetal” layers at the boundaries. We demonstrate that SAWs in the extended topological valley-locked edges are robust against bending and wavelength-scaled defects. Also, this mechanism is configurable and robust depending on the doping, offering various on-chip acoustic manipulation, e.g., SAW routing, focusing, splitting, and converging, all flexible and high-flow. This work may promote future hybrid phononic circuits for acoustic information processing, sensing, and manipulation.

Localised states in defective CdTe/CdZnTe multi-quantum wells

ABSTRACT The current paper presents a theoretical study of the transmission rate and band structure for a multi-quantum wells (MQWs) composed of periodic arrangement of barrier () and well () materials, containing a defect barrier layer. The theoretical calculations of this study are based on the transfer matrix method (TMM) formalism. First, we consider a barrier of thickness d 1 bounded by two semi-infinite substrates. This barrier has its Eigen states with both a high transmission rate and a low quality factor. Then, we take the perfect MQWs system (without defect), whose structure exhibits passbands separated by electronic band gaps (EBGs). These EBGs move towards high energies when the Zn concentration in the barrier increases. Hence the proposed system, behaves like an electronic mirror able to control and manipulate the transfer of electrons by modifying the concentration of the barrier. On the other hand, the insertion of barrier defect induces localised states located in the band gaps, which depends clearly on the concentration (x 0) and the thickness (d 0) of the barrier defect layer made of material. These induced localised states shift to lower energies when increasing the defect thickness. Due to the symmetry of our system, the transmission rates of these localised states reach maximum values and very high quality factors when the defect layer is placed in the middle of the structure. This finding is useful for applications such as light-emitting diodes, semiconductor micro-lasers or in infrared radiation detectors.

Thickness Analyses of 4-(Acetyl Amino)-2-Aminobenzoic Acid on ITO Thin Film Using Analytic Based of X-Ray Photoelectron Spectroscopy Method

In this study, the binding energies of 4-(acetyl amino)-2-aminobenzoic acid molecules that coated on the Indium Tin Oxide (ITO) surface with the self-assembled technique is measured by the XPS method. The thickness of the layer formed on the modified ITO surface is calculated by using XPS technique with an analytical approach. It is reported that the formation of commercially benzoic acid -based self-assembled monolayers (SAMs) is coated surely on ITO that is proved by this technique. According to this approach, the intensity of the substrate-originated photoemission peak from a semi-infinite substrate with a uniform over layer thickness, tXPS(SAM), is obtained from the SAM peak to In3d and Sn3d oxide (ITO) intensity peaks ratio (ISAM/IITO) that the Hill equation allows thin film thickness calculation from XPS data.