Finite Layer Research Articles

Continuum theory of a nematic liquid crystal with a nonideal physical surface and the surfacelike elasticity

ABSTRACT The nematic surface violates the translational symmetry of unrestricted medium and induces novel elastic effects. An ideal surface, where the nematic order parameter and density vanish abruptly, induces the surface elastic term that cancels out the Nehring-Saupe divergence term. A more realistic, nonideal surface is represented by a thin layer where the order parameter and density smoothly vary from their bulk values to zero. This surface is shown to induce additional contributions to the effective surface elastic and terms. These terms are no longer total divergences which is employed to incorporate them in the elastic theory. It is shown how the higher order elasticity and the finite surface layer provide the lower free energy bound both for nonzero term and for term violating Ericksen’s stability condition for the uniform director ground state. The effective boundary condition and procedure of the free energy minimisation for arbitrary and are derived. It is shown how Ericksen’s condition is modified by the presence of the term, anchoring, and spatial boundedness. An example of the surfacelike-elasticity-induced spontaneous modulations of the uniform director ground state is presented.

Corrosion behavior of Ni62Nb33Zr5 bulk metallic glasses after annealing and cryogenic treatments

The microstructural evolution and corrosion behavior of Ni62Nb33Zr5 bulk metallic glasses (BMGs) after annealing treatment (AT) at different crystallization temperatures and cryogenic treatment (CT) at −100 ℃ are experimentally investigated. Appropriate AT and CT can both improve the thermal stability and comprehensive corrosion resistance of as-cast BMG in 3.5 wt.% NaCl solution. The annealed and cryo-treated BMGs exhibit one more finite diffusion layer loop in the electrical equivalent circuit than the as-cast BMG, indicating the complexity of the corrosion behavior. Superior corrosion resistance is obtained in the cryo-treated BMG because the high degree of amorphization caused by CT reduces the structural inhomogeneity. Lower Cd and higher Rd values are obtained for the cryo-treated BMG, revealing the formation of a more stable passive film. Among the annealed BMGs, the fully crystallized sample exhibits a higher anti-corrosion performance owing to the existence of Nb-rich oxides in the crystallization products. The passive film is found to be composed mainly of Nb2O5 and ZrO2, demonstrating that Nb and Zr are conducive to reacting with oxygen to form a passive film. Based on the goal of maintaining a fully amorphous phase, appropriate CT causing structural homogeneity of the BMG is a simple and effective means to improve the comprehensive corrosion resistance.

Debris flow seismo-acoustic wave in a finite layer waveguide

The seismo-acoustic wave detection is a popular method to detect debris flows. It has been successfully used in different early warning systems worldwide. However, more information is embedded in the signals related to flow conditions. This research uses theoretical derivation to connect signals with debris flow propagation speed. We assume debris flow generates seismo-acoustic stress acting on a river bed and the seismo-acoustic waves propagate in a finite layer waveguide below the channel. Then, the propagation of seismo-acoustic stress was solved with the elastic wave equations along the channel. For any fixed point in this waveguide, the frequency of the recording signal can be translated as a function of debris flow propagation speed and seismo-acoustic wave velocity. The result shows that there is a Doppler-like property for a recorded signal where debris flow propagation speed can cause a frequency shift. This result also indicates that different superior frequency bands would be recorded from different media.

MODES OF ADHESIVE BONDING LAYER FORMATION DURING ROLL MOTION IN THE PROCESS OF SHEET LAMINATION

Novel technologies for the synthesis and processing of materials and products based on these materials, such as additive manufacturing, require the use of mathematical modeling to study the accompanying physical and chemical phenomena. These technologies include sheet lamination, which today has a variety of applications and numerous modifications. This article presents a model of adhesion layer formation in the creation of multilayer composites, which is controlled by a hot roller moving along the surface of the top layer. The dynamics of reagent heating depends on the thermal properties and sizes of all layers, the temperature of the roller, and its pressure against the surface, with characteristic times and spatial scales for different processes. The transition to dimensionless variables allowed the identification of dimensionless complexes to determine different modes of development of the adhesion layer synthesis process. Based on the combustion theory and non-equilibrium thermodynamics, new criteria of the process initiation and transition to a quasi-stationary mode were elaborated. The behavior of various thermodynamic quantities was analyzed in detail, including heat storage in the heated layer, enthalpy excess, and entropy production. The reaction zone is wide in most cases. The dependences of the half-conversion time on the model parameters are plotted for a finite layer size. This is a new characteristic for sheet lamination technology. A controlled mode, a fast bulk synthesis mode, a slow transformation mode maintained by the heat stored in the inert materials, and a quasi-stationary mode are identified. Criteria were established for different modes of reactions under conjugate heat exchange conditions.

The role of variable zeta potential on diffusiophoretic and diffusioosmotic transport

Diffusiophoresis is the spontaneous motion of colloidal particles induced by the presence of a local solute concentration gradient, and diffusioosmosis is the analogous motion of fluid near a surface. The zeta potential, a measure of the electrokinetic potential at the slipping plane in the Debye layer, plays an important role in these processes, as it is a measure of the strength of interactions between solute and surface molecules. Many previous studies on diffusiophoresis/diffusioosmosis have relied on the assumption of constant zeta potential, in part due to the significant theoretical simplification introduced by this assumption. However, in general the zeta potential varies as a function of solute concentration, which often varies by orders of magnitude in typical setups. We seek to characterize the role of variable zeta potential on diffusiophoresis/diffusioosmosis by revisiting recent studies that treated zeta potential as constant. For each case, we characterize and quantify the change in the particle/solute/fluid dynamics when a variable zeta potential model is considered. The four test problems that are considered are: (1) diffusiophoresis-induced particle banding in a stopped-flow diffusion cell, (2) one-dimensional particle injection in a dead-end pore, (3) arrested particle spreading in a solute/particle co-diffusion system, and (4) diffusioosmotic pumping in a micropore connecting solute streams. The results provide examples of the qualitative and quantitative differences that can result when using materials that satisfy constant potential, constant charge, or even charge-regulating surface properties, and stress the importance of selecting the appropriate surface model. This work provides guidance to experimentalists and modelers in selecting efficient and accurate models for their diffusiophoretic/diffusioosmotic systems, and these results indicate that finite Debye layer effects typically affect transport much more than variable zeta potential effects, but detailed problem-specific simulations are needed to quantify these effects.

Sound reflection by periodic acoustic metasurface in sheared grazing flows

The reflection performance of periodic acoustic metasurfaces (AMs) subjected to a grazing flow, consisting of a uniform region and a finite sheared layer, is studied. A convective generalized Snell’s law (CGSL) is derived to account for the effect of uniform mean flows on the reflection of AMs. Then, an AMs design method considering the mean flow profile is proposed based on the impedance transformation method. The strategy is to form a reflected phase gradient at the interface plane between the uniform and the sheared flow regions. The reflection characteristics of two acoustic porous metasurfaces (APMs), i.e., APM1 and APM2 designed for the uniform and the sheared flows, respectively, are numerically investigated. Results show that APM1 achieves efficient anomalous reflections in uniform flows, and the diffracted orders and directions of the reflected waves are well predicted by the proposed CGSL. However, the performance of APM1 deteriorates under oblique incidences if applied to a typical sheared flow. In contrast, APM2 realizes desired wavefront manipulations under the same conditions. Finally, the CGSL is extended into a three-dimensional (3D) space and is validated numerically. This study provides a means for AMs design in flow conditions, which holds good potential in aeroacoustic noise problems.

Time‐domain PML analysis of a fluid–solid interaction problem above a rough surface

This paper is concerned with the time‐dependent acoustic–elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well‐posedness and stability of the problem are first established by using the Laplace transform and the energy method. A perfectly matched layer (PML) is then introduced to truncate the interaction problem above a finite layer containing the elastic body, leading to a PML problem in a finite strip domain. We further establish the existence, uniqueness, and stability estimate of solutions to the PML problem. Finally, we prove the exponential convergence of the PML problem in terms of the thickness and parameter of the PML, based on establishing an error estimate between the DtN operators of the original problem and the PML problem.

Model for Quorum-Sensing Mediated Stochastic Biofilm Nucleation.

Surface-attached bacterial biofilms cause disease and industrial biofouling, as well as being widespread in the natural environment. Density-dependent quorum sensing is one of the mechanisms implicated in biofilm initiation. Here we present and analyze a model for quorum-sensing triggered biofilm initiation. In our model, individual, planktonic bacteria adhere to a surface, proliferate, and undergo a collective transition to a biofilm phenotype. This model predicts a stochastic transition between a loosely attached, finite layer of bacteria near the surface and a growing biofilm. The transition is governed by two key parameters: the collective transition density relative to the carrying capacity and the immigration rate relative to the detachment rate. Biofilm initiation is complex, but our model suggests that stochastic nucleation phenomena may be relevant.

Theoretical analysis of relative diffusion impedance in finite layer: Spiral-shaped Nyquist plots in electrochemical impedance spectroscopy

The spiral shape is ubiquitous in everyday life, and the spiral is also present in electrochemical impedance spectroscopy. By analyzing the diffusion of two ions in the opposite direction in the finite layer, the relative diffusion impedance equation can be obtained and used to simulate a series of different shapes of the Nyquist plots, including spiral shapes. In this paper, the variation law of the spiral Nyquist plot under different conditions is analyzed, and the application of the relative diffusion impedance equation in the area of thin-film solar cells and hydrogen permeation is discussed.

Estimation of elastic settlement for skirted strip foundations subjected to vertical loading

Settlement calculations are an essential part of the design of offshore foundations, although most of the existing studies on skirted foundations focus on bearing capacity. In this study, finite element analysis is used to evaluate the elastic settlement (vertical displacement) of skirted strip foundations of arbitrary stiffness embedded in either a homogeneous or nonhomogeneous soil stratum with finite layer depth. Graphical solutions are presented, which enable the determination of the drained and undrained settlements at the center and edge of the skirted foundations. Closed-formed expressions that approximate the numerical solutions well are also proposed. Numerical examples are provided to illustrate how the solutions and expressions can be readily applied in hand calculation for preliminary design purpose.

Comparative Study on the Application of Different Slug Test Models for Determining the Permeability Coefficients of Rock Mass in Long-Distance Deep Buried Tunnel Projects

In large-scale water diversion projects, especially in the central and western regions of China, long-distance deep buried tunnels are generally involved. Therefore, it is essential to carry out field tests to obtain the permeability of the rock mass through which tunnels pass. However, the test holes of large-scale water diversion projects are basically located in mountain areas with complex hydrogeological conditions. Meanwhile, the test holes are far apart and large in depth. As a result, traditional pumping tests cannot meet the requirements. Therefore, the slug test was chosen as the main test method, and the calculation results of the water injection test, the water pressure test and the slug test are analyzed and compared. The calculation results of the three test methods are basically consistent. However, the water injection test and the water pressure test are difficult to implement at a large scale due to many environmental constraints, complex test equipment, long test periods and other factors. Furthermore, the Kipp model, the CBP model and the proposed HWS model, considering the effect of the finite thickness well-skin layer for the first time, were used to analyze and process the slug test data, respectively. The curve fitting effect of the Kipp model was the best, but the calculations were generally larger. The difference between the CBP model and the proposed HWS model is smaller in the calculation results; however, the curve fitting effect of the CBP model is the worst, and the CBP model needs to be further improved. The curve fitting effect of the proposed HWS model was between that of the Kipp model and the CBP model, and the proposed HWS model can be applied to the parameter calculations of the slug test with well-skin. In general, with reference to the criteria for the damping coefficient of the aquifer in the Kipp model, the Kipp model was applicable to the slug test for test holes without well-skin and an aquifer damping coefficient between 0.1 and 5.0. The CBP model was applicable to the slug test under the conditions of no well-skin and an aquifer damping coefficient greater than 2.0. The novel proposed HWS model was applicable to the slug test when the aquifer damping coefficient was greater than 1.0 under the conditions of no well-skin, positive well-skin and negative well-skin.

A Hermite-Family C1 Finite Layer Method for the Three-Dimensional Free Vibration Analysis of Exponentially Graded Piezoelectric Microplates Based on the Consistent Couple Stress Theory

Based on the consistent couple stress theory (CCST), we develop a Hermite-family [Formula: see text] finite layer method (FLM) for the three-dimensional (3D) free vibration analysis of a simply-supported, exponentially graded (EG) piezoelectric microplate under open- and closed-circuit surface conditions. In the formulation of the FLM, the microplate is artificially divided into a number of finite microlayers, and Fourier functions and Hermite polynomials are used to interpolate the in-plane and out-of-plane variations of a number of primary variables, respectively, including elastic displacement components and the electric potential variable for each individual layer. The Hermite-family [Formula: see text] FLM for analyzing EG piezoelectric microplates is reduced to the Hermite-family [Formula: see text] FLM for analyzing EG piezoelectric macroscale plates and functionally graded (FG) elastic microplates by assigning a value of zero to the material length scale parameter and by ignoring the piezoelectric and flexoelectric effects in the formulation, respectively. The accuracy and convergence rate of the FLM are assessed by comparing their solutions with the benchmark solutions of both the EG piezoelectric macroplates and the power-law-type FG elastic microplates that are available in the relevant literature. We examine and discuss some key effects on the free vibration characteristics of an EG piezoelectric microplate, including the impact of the material length scale parameter, the material-property gradient index, the length-to-thickness ratio, the piezoelectric effect, and the flexoelectric effect.

Parallel PD-FEM simulation of dynamic fluid-driven fracture branching in saturated porous media

The dynamic hydraulic fracture in porous media is often characterized by crack diverting and/or branching that affects the connectivity of the fracture network. There is a need to understand the crack branching mechanism for enhancing the unconventional resource production. In the present manuscript, the dynamic fluid-driven fracture branching in saturated porous media is studied by a parallel PD-FEM coupling approach. Under the assumption of negligible relative acceleration of the fluid with respect to the mixture, the two-field u-p model is derived based on the Biot’s theory. The dynamic coupled system is discretized into two layers with the non-ordinary state-based peridynamics layer characterizing the deformation and fracture of the solid skeleton and finite element layer representing the fluid flow. A fully implicit scheme for the time integration of the dynamic coupled system within a nonlinear framework based on the Newmark method is employed and an alternate grid/particle updating OpenMP parallel programming scheme is proposed. The efficiency and accuracy of the coupled method is first verified by several benchmark examples with either experimental data or analytical solutions, followed by a study of crucial factors affecting dynamic hydraulic fracturing branching. The parametric study shows that in general the following factors favor the crack branching: lower critical energy release rate, higher injection rate, lower Young’s modulus, higher Poisson’s ratio, lower viscosity of the fluid and higher compressibility of the fluid.

Modulation effect of linear shear flow on interfacial waves in a two-layer fluid with finite layer depths

The modulation effect of linear shear flow (LSF) comprising uniform and shear flows with constant vorticity on interfacial waves in a two-layer fluid with finite layer depths is studied. Herein, lower-layer LSF is focused on. A nonlinear Schrödinger equation (NLSE) modified by lower-layer LSF is derived. By comparing and analyzing the dispersion relation of upper- and lower-layer LSFs, sufficient conditions of Kelvin–Helmholtz stability are afforded to ensure the applicability of NLSE. Based on the relationship between the modulational instability (MI) of NLSE and interfacial freak waves (IFWs) represented as Peregrine breather, existence conditions of IFWs affected by LSF are presented. The convergence effect of the flow field against the wave propagation direction, e.g., uniform up-flow and positive (negative) vorticity of the lower (upper) layer, increases the MI growth rate. This subsequently increases the wave height and promotes IFW generation. However, the divergent effect of the flow field along the wave propagation direction, including uniform down-flow and negative (positive) vorticity of lower (upper) layer, inhibits IFW generation. Moreover, eight kinds of LSFs are presented under uniform flow and vorticity, among which two promote generation, two inhibit generation, and the remaining four depend on the counteracting effect between uniform flow and vorticity.

Construction and optimization of numerically-statistical projection algorithms for solving integral equations

Abstract The problem of minimizing the root-mean-square error of the numerical-statistical projection estimation of the solution to an integral equation is solved. It is shown that the optimal estimator in this sense can be obtained by equalizing deterministic and stochastic components of the error in the case when the norm of the remainder of the utilized decomposition decreases inversely proportional to its length. As a test, the Milne problem of radiation transfer in a semi-infinite layer of matter is solved using Laguerre polynomials. To solve such a problem in the case of a finite layer, a special regularized projection algorithm is used.

A quasi-3D layer-wise finite element model for vibroacoustic analysis of finite sandwich plates with frequency-dependent viscoelastic core

This article presents a quasi-3D layer-wise finite element approach to investigate the vibroacoustic characteristics of finite constrained layer damping (CLD) plates with a viscoelastic material (VEM) core. The frequency-dependent properties of the VEM core are integrated into the kinematic governing equation. The sound transmission loss (STL) behavior under oblique plane sound wave excitation is studied in narrow frequency bands, thus the variation caused by resonance modes can be captured clearly. Results show that the STL values of the two CLD plates configurations are significantly increased in resonance frequency regions. The symmetric configuration is found to have better sound insulation performance.

On the interplay between interchange turbulence and sheared flows

The presence and the position of an X-point, namely, if the ion diamagnetic drift points toward it or not, strongly impact the edge plasma rotation in tokamaks. In the absence of kinetic effects such as magnetic ripple or ion orbit loss, the shape of the velocity profile results from the balance between neoclassical predictions and turbulent flow generation. In this contribution, we derive a reduced model of turbulence plunged in a shear flow. This model is based on (1) a description of the impact of a sheared flow on the interchange turbulence and (2) a prediction of the poloidal momentum generated by the turbulence. It includes the effects of both the magnetic topology and the finite shear layer width. The model is verified against 2D non-linear flux-driven simulations. Finally, the model predictions of the edge rotation resulting from the equilibrium between the neoclassical prediction and the poloidal momentum generation by the turbulence are invoked to describe the observations from experiment managed in the WEST tokamak. It points out the important role of the magnetic shear in the turbulence tilting and in the flow generation.

On analogues of Mazur-Tate type conjectures in the Rankin-Selberg setting

We study the Fitting ideals over the finite layers of the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ of Selmer groups attached to the Rankin--Selberg convolution of two modular forms $f$ and $g$. Inspired by the Theta elements for modular forms defined by Mazur and Tate in ``Refined conjectures of the Birch and Swinnerton-Dyer type'', we define new Theta elements for Rankin--Selberg convolutions of $f$ and $g$ using Loeffler--Zerbes' geometric $p$-adic $L$-functions attached to $f$ and $g$. Under certain technical hypotheses, we generalize a recent work of Kim--Kurihara on elliptic curves to prove a result very close to the \emph{weak main conjecture} of Mazur and Tate for Rankin--Selberg convolutions. Special emphasis is given to the case where $f$ corresponds to an elliptic curve $E$ and $g$ to a two dimensional odd irreducible Artin representation $\rho$ with splitting field $F$. As an application, we give an upper bound of the dimension of the $\rho$-isotypic component of the Mordell-Weil group of $E$ over the finite layers of the cyclotomic $\mathbb{Z}_p$-extension of $F$ in terms of the order of vanishing of our Theta elements.

Theoretical proposal for geometrical prevalences on a magnetic nanobulk

In this work, we study a magnetic nanowire system composed of finite layers, forming a nanobulk. The interaction between the layers (inter-layers) is given by an exchange term [Formula: see text] and the interactions within each layer (intra-layer) are given by a magneto-static interaction energy between the nanowires. We propose to create a geometrical pattern inside of each nanobulk in order to decrease the magneto-static energy through three geometrical configurations of the nanobulk: (i) rectangular–rectangular, (ii) rectangular-cylindrical and (iii) cylindrical–cylindrical. In addition, we incorporate surface/interface effects (another material) to study energy variations inside the nanobulk. As a result, we show that there are certain geometries that minimize drastically the magneto-static energy, also that when the intensity of the [Formula: see text] coupling between the layers is too intense it implies that the energy tends to dissipate inside the nanobulk. In addition, a drop in the magneto-static energy is observed when the interfaces/surfaces of the finite-layer nanobulk are modified.

Prediction of ground-borne vibrations induced by impact pile driving: experimental validation of an equivalent linear approach

Impact pile driving is one interesting possibility to install deep foundations from the economic and technical point of view. However, it is necessary to ensure that the ambiental drawbacks, namely ground-borne vibrations, are adequately met. In that way, the authors propose an axisymmetric finite element method-perfectly matched layer approach, where the nonlinear behavior of the soil is attended by an equivalent linear methodology. Given the complexity of the problem, an experimental test site was developed and fully characterized. The experimental work comprises in situ and laboratorial soil characterization as well as the measurement of vibrations induced during pile driving. The comparison between experimental and numerical results achieved a very good agreement, making the proposed numerical approach suitable for the prediction of vibrations induced by impact pile driving.