Finite Layer Research Articles

Напряжённое состояние композита в виде пакета из произвольного конечного числа конечных или полубесконечных упругих слоёв при антиплоской деформации.

Напряжённое состояние композита в виде пакета из произвольного конечного числа конечных или полубесконечных упругих слоёв при антиплоской деформации.

Fracture of a Circular Disk with Mixed Conditions on the Boundary

A model of a circular disk fracture based on consideration of the fracture process zone near the curvilinear crack tip is suggested. It is considered that mixed boundary conditions are given on the boundary of the disk. It is accepted that the fracture process zone is a finite length layer with a material with partially broken bonds between its separate structural elements (end zone). Analysis of equilibrium limit of the curvilinear crack is performed on the basis of ultimate extension of the material bonds.

Response analysis of structural building excited by seismic waves using finite difference method

The present article treats the finite difference modelling of multi-storey structures on flexible foundation due to seismic excitation. Previously, finite difference method has been used to analyse the wave propagation through medium comprising of layers of different physical properties. The same method is used for the problem considered here. The model here consists of a multilayer system comprising of structural building with a finite layer of sandy soil (as flexible foundation) and an inhomogeneous elastic half space embedded beneath the building structure. The displacement equations of inhomogeneous layer, flexible foundation and building are converted to finite difference algebraic equations. The phase and group velocities of the medium are being evaluated. Analysing these velocities it is observed that the wave energy do not make headway to the upper floors and even if it propagates, the shock imparted to the upper floors (beyond the flexible foundation) is very negligible.

Absorption and emission of finite layer of chiral photonic crystal

The peculiarities of absorption and emission of the finite layer of cholesteric liquid crystal are investigated. The influence of parameters characterizing the absorption and gain, as well as the layer thickness and the local dielectric anisotropy on the absorption and emission is studied. In particular, it is shown, that the increase of the parameter x′ characterizing the gain results in the increase of emission. However, there are the discrete points in the (λ, x′) plane, where the emission is maximal (λ is the wavelength of incident light). These points determine the critical values of gain at which the low-threshold laser generation takes place. The obtained results can be used to develop the strongly absorbing systems.

Cracking in a circular disk under mixed boundary conditions

A model of cracking in a circular disk with mixed boundary conditions on the boundary is suggested. It is assumed that the cracking process zone is a finite length layer containing a material with partially disturbed bonds between separate structural elements in the plastic flow state at constant stress. Limit equilibrium analysis of the zone of weakened interparticle bonds of the material (prefracture) is performed on the basis of the criterion of critical opening of prefracture zone faces.

Unconventional proximity-induced superconductivity in bilayer systems

We study the proximity-induced superconducting state in a general bilayer -- conventional $s$-wave superconductor hybrid structure. For the bilayer we include a general parabolic dispersion, Rashba spin-orbit coupling, and finite layer tunneling as well as the possibility to apply a bias potential and a magnetic Zeeman field, in order to address experimentally relevant bilayer systems, ranging from topological insulator thin films to generic double quantum well systems. By extracting the proximity-induced anomalous Green's function in the bilayer we show on a very rich structure for the superconducting pairing, including different spin states and odd-frequency pairing. Equal-spin spin-triplet $p_x\pm ip_y$-wave pairing is induced in both layers in the presence of a finite spin-orbit coupling and opposite-spin spin-triplet $s$-wave pairing with odd-frequency dependence appears for an applied magnetic Zeeman field. Finite interlayer pairing is also generally present in the bilayer. The interlayer pairing can be either even or odd in the layer index, with a complete reciprocity between parity in frequency and in layer index. We also find that a bilayer offers the possibility of sign reversal of the superconducting order parameters, both between the two layers and between multiple Fermi surfaces.

Bubble instability in overheated liquid Helium-3

The generation and the growth of vapor bubbles in metastable liquid Helium-3 are studied. The finite diffuse layer of vapor bubble, the temperature dependence of the surface tension and the relaxation processes are taken into consideration. We show that the growth of bubble in overheated liquid Helium-3 is significantly influenced by the memory effects caused by the dynamic Fermi-surface distortions. In particular, the increase of bubble is strongly hindered and accompanied by the characteristic oscillations of the bubble radius. The oscillations of the bubble radius disappear in a short relaxation-time limit where the memory effects are negligible.

Phosphorene nanoribbons

Edge-induced gap states in finite phosphorene layers are examined using analytical models and density functional theory. The nature of such gap states depends on the direction of the cut. Armchair nanoribbons are insulating, whereas nanoribbons cut in the perpendicular direction (with zigzag and cliff-type edges) are metallic, unless they undergo a reconstruction or distortion with cell doubling, which opens a gap. All stable nanoribbons with unsaturated edges have gap states that can be removed by hydrogen passivation. Armchair nanoribbon edge states decay exponentially with the distance to the edge and can be described by a nearly free electron model. This is used to prove the existence of the gap states in the limit of a semi-infinite plane.

An alternative BE–FE formulation for a raft resting on a finite soil layer

This work presents a numerical tool for simulating the interaction of a raft with the soil, which can be a half space or a finite layer supported by a rigid base. The soil is modelled using the boundary element method (BEM) with Kelvin fundamental solutions. Infinite boundary elements (IBEs) are employed for the far field simulation, allowing computational cost reduction without compromising the accuracy. The IBE formulation is based on a triangular boundary element with linear shape functions instead of the commonly used quadrilateral IBEs. Displacements are restrained at the rigid base, when it exists. The raft is modeled with the finite element method (FEM) using a triangular element, which is obtained by combining bending effects and membrane effects. For the FEM–BEM coupling, the BEM tractions are considered as nodal reactions in the FEM formulation. The coupling is established using equilibrium and compatibility conditions, obtaining a system of equations that represents the complete problem.

Propagation of surface SH waves on a half space covered by a nonlinear thin layer

The self modulation of surface shear horizontal (SH) waves (Love waves) propagating on a nonlinear half space covered by a nonlinear thin layer is examined. First a nonlinear thin layer approximation is derived by assuming that constituent materials are nonlinear,homogeneous, isotropic and compressible hyper-elastic. Then employing this approximation, a two medium problem is reduced to one for a nonlinear half space with a modified nonlinear boundary condition on the top surface. This new problem is analyzed by the method of multiple scales, and a nonlinear Schrödinger (NLS) equation is derived which describes the self modulation of the waves asymptotically. Then the results of the nonlinear thin layer approximation are compared with the results of the linear thin layer approximation and with the finite layer results obtained in a previous work. It has been observed that even in moderately low wave numbers, the propagation is affected considerably by the nonlinear material parameter of the layer.

Spin polarization of composite fermions and particle-hole symmetry breaking

We study the critical spin-polarization energy ($\alpha_{\rm C}$) above which fractional quantum Hall states in two-dimensional electron systems confined to symmetric GaAs quantum wells become fully spin-polarized. We find a significant decrease of $\alpha_{\rm C}$ as we increase the well-width. In systems with comparable electron layer thickness, $\alpha_{\rm C}$ for fractional states near Landau level filling $\nu=3/2$ is about twice larger than those near $\nu=1/2$, suggesting a broken particle-hole symmetry. Theoretical calculations, which incorporate Landau level mixing through an effective three-body interaction, and finite layer thickness, capture certain qualitative features of the experimental results.

Nonlinear Stability of Convection in a Porous Layer with Solid Partitions

We show that for many classes of convection problem involving a porous layer, or layers, interleaved with finite but non-deformable solid layers, the global nonlinear stability threshold is exactly the same as the linear instability one. The layer(s) of porous material may be of Darcy type, Brinkman type, possess an anisotropic permeability, or even be such that they are of local thermal non-equilibrium type where the fluid and solid matrix constituting the porous material may have different temperatures. The key to the global stability result lies in proving the linear operator attached to the convection problem is a symmetric operator while the nonlinear terms must satisfy appropriate conditions.

Time-harmonic response of transversely isotropic multilayered half-space in a cylindrical coordinate system

With the aid of the analytical layer-element method, a comprehensive analytical derivation of the response of transversely isotropic multilayered half-space subjected to time-harmonic excitations is presented in a cylindrical coordinate system. Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the Fourier expansion, Hankel and Laplace integral transform, analytical layer-elements for a finite layer and a half-space are derived. Considering the continuity conditions on adjacent layers׳ interfaces and the boundary conditions, the global stiffness matrix equations for multilayered half-space are assembled and solved. Finally, some numerical examples are given to make a comparison with the existing solution and to demonstrate the influence of parameters on the dynamic response of the medium.

Investigation of magnetic properties of Fe3O4 nanoparticles using temperature dependent magnetic hyperthermia in ferrofluids

Rate of heat generated by magnetic nanoparticles in a ferrofluid is affected by their magnetic properties, temperature, and viscosity of the carrier liquid. We have investigated temperature dependent magnetic hyperthermia in ferrofluids, consisting of dextran coated superparamagnetic Fe3O4 nanoparticles, subjected to external magnetic fields of various frequencies (188–375 kHz) and amplitudes (140–235 Oe). Transmission electron microscopy measurements show that the nanoparticles are polydispersed with a mean diameter of 13.8 ± 3.1 nm. The fitting of experimental dc magnetization data to a standard Langevin function incorporating particle size distribution yields a mean diameter of 10.6 ± 1.2 nm, and a reduced saturation magnetization (∼65 emu/g) compared to the bulk value of Fe3O4 (∼95 emu/g). This is due to the presence of a finite surface layer (∼1 nm thickness) of non-aligned spins surrounding the ferromagnetically aligned Fe3O4 core. We found the specific absorption rate, measured as power absorbed per gram of iron oxide nanoparticles, decreases monotonically with increasing temperature for all values of magnetic field and frequency. Using the size distribution of magnetic nanoparticles estimated from the magnetization measurements, we have fitted the specific absorption rate versus temperature data using a linear response theory and relaxation dissipation mechanisms to determine the value of magnetic anisotropy constant (28 ± 2 kJ/m3) of Fe3O4 nanoparticles.

Behavior of Geosynthetic Clay Liners due to the Migration of Heavy Metal

To protect the underlying soil and groundwater from landfills, the landfills are commonly lined with layered liner systems. Geosynthetic clay liners (GCL) have been increasingly used in the landfill liner systems to substitude the traditional compacted clay liners (CCL) because of their low cost, easily construction behavior and low leakage rate. To study the behavior of the GM+GCL liner system used in China due to the migration of Pb2+, we introduce in detail GM+GCL liner systems proposed by the Chinese specification. Then one dimensional finite layer model is used to investigate the anti-pollution behavior of the CM+GCL composite liner systems, with the focuses on the heavy metal Pb2+. It could be concluded that the main migration way through the GM+GCL composite liner system is that the transport of Pb2+through a GM+GCL composite liner system of a landfill cover takes place primarily through the holes in the GM. The findings provide useful reference for preventing, controlling and treating groundwater pollution in the GM+GCL liner system technically and scientifically.

How does a shear boundary layer affect the stability of a capillary jet?

The stability of a capillary jet with a shear boundary layer growing over its free surface is studied theoretically. The effect of an infinitely thin boundary layer is first examined from the corresponding singularly perturbed eigenvalue problem. Then, a linear stability analysis of the Navier-Stokes equations for a finite boundary layer thickness verifies the consistency of the previous asymptotic study. We show that, for sufficiently long distances from the boundary layer origin, Rayleigh's dispersion relation is recovered, which means that the layer does not affect the jet's stability in that case. However, for distances on the order of the jet's radius, the perturbation growth factor, the most unstable wave number, and the range of unstable wave numbers increase, while the convective-to-absolute instability transition delays drastically. These results establish a general framework to explain a variety of capillary jet phenomena, from the extended jetting regime of capillary jets in gas co-flows to fundamental features of the dripping faucet.

Transfer matrix method for the solution of multiple elliptic layers with different elastic properties. Part II: exterior finite elliptic matrix case

This paper provides the transfer matrix method for the solution of multiple elliptic layers with different elastic properties. In the study, the medium is composed of an elliptic inclusion and many confocal elliptic layers. In the present study, the exterior layer is a finite confocal elliptic layer. Some derivations in the present study are similar to those in Chen (Acta Mech 2014). However, some derivations in the present study are quite different from those in Chen (Acta Mech 2014). Equations for evaluating the coefficients in the Laurent series for complex potentials are suggested, which are derived from the transfer matrix and the boundary condition. A numerical example for the case of an elliptic inclusion and two confocal elliptic layers is provided in this paper.

Triviality of the ℓ-class groups in -extensions of for split primes p ≡ 1 modulo 4

AbstractIn this paper we study the class numbers in the finite layers of certain non-cyclotomic $\mathbb{Z}$p-extensions of the imaginary quadratic field $\mathbb{Q}(\sqrt{-1})$, for all primes p ≡ 1 modulo 4. By studying the Mahler measure of elliptic units, we are able to show that there are only finitely many primes ℓ congruent to a primitive root modulo p2 that divide any of the class numbers in the $\mathbb{Z}$p-extension.

Fourier modal method formulation for fast analysis of two-dimensional periodic arrays of graphene

Recently, an approximate boundary condition [Opt. Lett.38, 3009 (2013)] was proposed for fast analysis of one-dimensional periodic arrays of graphene ribbons by using the Fourier modal method (FMM). Correct factorization rules are applicable to this approximate boundary condition where graphene is modeled as surface conductivity. We extend this approach to obtain the optical properties of two-dimensional periodic arrays of graphene. In this work, optical absorption of graphene squares in a checkerboard pattern and graphene nanodisks in a hexagonal lattice are calculated by the proposed formalism. The achieved results are compared with the conventional FMM, in which graphene is modeled as a finite thickness dielectric layer. We show that for the same truncation order, computation time can be reduced to one-ninth by the proposed formulation in comparison with the conventional FMM. Furthermore, the convergence rate is increased. Therefore, thanks to the improved convergence rate and reduced computational cost for a given truncation order, the computational time is saved more than 100 times for relative error of less than 1%. This is crucially important in analyzing two-dimensional periodic structures of graphene by the FMM.

Unsteady Seepage Applied to Lining Design in Stilling Basins

AbstractCases of damages experienced in stilling basins and on the toe of chute spillways are recognized to be due to global instantaneous uplift force resulting from imbalance between the instantaneous pressure distribution both above and below slabs. The latter is due to pressure fluctuation propagation forced though unsealed slab joints. In the past, several theoretical approaches were developed to estimate the uplift contribution due to pressure transmission underneath the slabs. In the paper, a model is presented, based on unsteady flow analysis of seepage through porous media, that shows that the propagation models proposed in literature are particular cases of this more comprehensive formulation. In addition, the use of the unsteady seepage model makes it possible to account for finite thickness foundation layers, typical in the cases of earth dams, rock-fill dams, and in other dam types, whenever the slabs are posed on alluvial substrates. Experimental results obtained in laboratory facilities, as...