Ith Layer Research Articles

Frank-van der Merwe growth in bilayer graphene

Frank-van der Merwe growth in bilayer graphene

On the uniform stress/uniform stretch states of prestressed arteries

This work examines the mechanics of the circumferentially prestressed N-layer artery, subject to axial tethering force and the internal pressure of blood, focusing on the uniform stretch state, the uniform circumferential stress states and the transitional states between them. Under increasing pressure the ith layer is shown to experience five distinct stages, two of which are the uniform stretch state and the uniform circumferential stress state. For arbitrary strain energy density, simple analytical expressions are presented for the stress distributions and the internal pressure at these specialized states. For the 1-layer, uniform tubular model of an artery without axial tethering force, the results coincide with those of Destrade et al. (2012). For the 2-layer composite tube, which models the mechanically significant medial and adventitial layers of large elastic arteries, numerical solutions are obtained employing two microstructurally based constitutive models for medial and adventitial arterial tissues, respectively. These results indicate that the uniform stretch state, the uniform circumferential stress state of the medial layer, and the uniform circumferential stress state of the adventitial layer occur at the diastolic blood pressure, the mean blood pressure, and the systolic blood pressure, respectively.

Synchronization of Chimera States in a Network of Many Unidirectionally Coupled Layers of Discrete Maps

We study numerically external synchronization of chimera states in a network of many unidirectionally coupled layers, each representing a ring of nonlocally coupled discretetime systems. The dynamics of each element in the network is described by either the logistic map or the bistable cubic map. We consider two cases: when all M unidirectionally coupled layers are identical and when (M − 1) identical layers differ from the first driving layer in their nonlocal coupling parameters. It is shown that the master chimera state in the first layer can be retranslating along the network with small distortions which are defined by a parameter mismatch. We also analyze the dependence of the mean-square deviation of the structure in the ith layer on the nonlocal coupling parameters.

Modifying the BET model for accurately determining specific surface area and surface energy components of aggregates

When adopting the vapor adsorption method to measure the surface energy components of aggregates, a critical step is to determine the specific surface area (SSA) using the traditionally-used BET (T-BET) model. However, this model is demonstrated to be valid only for a limited relative pressure range of 0.05–0.40. Furthermore, the determined total SSA from this model is arbitrarily utilized to calculate the spreading pressure of probe vapors on aggregates, which does not comply with the multilayer adsorption theory. All these would definitely lead to the erroneous values of SSA and surface energy components of aggregates.To overcome these deficiencies, this study develops a modified BET (M−BET) model in the light of the multilayer adsorption theory, based on which five steps are designed to determine the SSA and the surface energy components for aggregates. The vapor adsorption tests of three probe vapors are performed on four types of aggregates. The SSA, spreading pressure and surface energy components are then separately calculated using the two BET models. It is observed that the linear fit of M-BET model applies satisfactorily to the entire adsorption isotherm with the R2 value larger than 0.98. The adsorption heat of the probe vapor in the second to the ith layer is demonstrated to be less than the heat of liquefaction, which accounts for the derivations of the data points of the T-BET model from linearity over the limited pressure range. The accompanying calculation results of the M-BET model reveal significant differences from those of the T-BET model, while the separation of SSA of the non-zero adsorption site from the total SSA also produces a non-negligible effect on the calculated surface energy components, identifying the significance of accurate measuring the SSA. Thus, in the vapor adsorption method it is imperative to employ the M-BET model to determine the SSA of the non-zero adsorption site so as to obtain the accurate surface energy components for aggregates.

Adaptive convex skyline: a threshold-based project partitioned layer-based index for efficient-processing top-k queries in entrepreneurship applications

Many entrepreneurship applications use data as the core concept of their business to better understand the needs of their customers. However, as the size of databases used by these entrepreneurship applications grows and as more users access data through various interactive interfaces, obtaining the result for a top-k query may take long time if the query matches millions of the tuples in the database. Traditionally, layer-based indexing methods are representative for processing top-k queries efficiently. These methods form tuples into a list of layers where the ith layer holds the tuples that can be the top-i answer. Layer-based indexing methods enable us to obtain top-k answers by accessing at most k layers. Most of these methods achieve high accuracy of query answer at the expense of enlarged index construction time. However, we can adjust between accuracy and index construction time to achieve an optimal performance. Thus in this paper, we propose a method, called the adaptive convex skyline (AdaptCS) for efficient-processing top-k queries in entrepreneurship applications. AdaptCS first prunes the data with a virtual threshold point and finds skyline points over the pruned data. Here, by adjusting virtual threshold we are able to achieve optimal performance. Then, AdaptCS divides the skyline into m subregions with projection partitioning method and constructs the convex hull m times for each subregion with virtual objects. Lastly, AdaptCS combines the objects obtained by computing the convex hull. The experimental results show that the proposed method outperforms the existing methods.

Optimal Discrete Power Control in Poisson-Clustered Ad Hoc Networks

Power control in a digital handset is practically implemented in a discrete fashion, and usually, such a discrete power control (DPC) scheme is suboptimal. In this paper, we first show that in a Poison-distributed ad hoc network, if DPC is properly designed with a certain condition satisfied, it can strictly work better than no power control (i.e., users use the same constant power) in terms of average signal-to-interference ratio, outage probability, and spatial reuse. This motivates us to propose an N-layer DPC scheme in a wireless clustered ad hoc network, where transmitters and their intended receivers in circular clusters are characterized by a Poisson cluster process on the plane ℝ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The cluster of each transmitter is tessellated into N-layer annuli with transmit power P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> adopted if the intended receiver is located at the ith layer. Two performance metrics of transmission capacity (TC) and outage-free spatial reuse factor are redefined based on the N-layer DPC. The outage probability of each layer in a cluster is characterized and used to derive the optimal power scaling law P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ∈ Θ(η <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-(α/2)</sup> ), with η <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> as the probability of selecting power Pi and α as the path loss exponent. Moreover, the specific design approaches to optimize Pi and N based on η <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> are also discussed. Simulation results indicate that the proposed optimal N-layer DPC significantly outperforms other existing power control schemes in terms of TC and spatial reuse.

Approximate convex skyline: A partitioned layer-based index for efficient processing top-k queries

A top-k query returns k tuples with the highest (or the lowest) scores from a relation. Layer-based methods are the representative ones for processing top-k queries efficiently. These methods construct a list of layers, where the ith layer contains the tuples that can potentially be the top-i answer. Thus, the layer-based methods can answer top-k queries by reading at most k layers. To construct layers, the existing layer-based methods use convex skyline, convex hull or skyline methods. Among them, the convex skyline is constructed by computing the convex hull over the skyline. Accordingly, the layer size of the convex skyline is relatively smaller than those of the convex hull, and the index building time is relatively shorter than those of the skyline. However, for large and high-dimensional databases, the convex skyline suffers from long index building time and large memory usage, because most objects can become the skyline points. This paper focuses on how to build an index, which contains a smaller number of objects comparing to the skyline and uses less time to construct an index comparing to the convex skyline. Specifically, we propose a method, called the Approximate Convex Skyline Enhanced (simply, AppCSE), which reduces the index building time and memory usage of the convex skyline. In the proposed method, we first construct the skyline, and then, partition the region of the skyline into multiple subregions, and compute the convex hull in each subregion with virtual objects. After that, AppCSE combines the objects obtained by computing the convex hull. Through various experiments with synthetic and real datasets, we demonstrate that the proposed method significantly reduces the index building time and memory usage comparing to the existing methods. In addition, we show that the degradation of query performance is negligible when using AppCSE as the layering scheme.

Thermal Expansion Characteristic of Prestressed Single Helical Structure

In order to master the geometric and mechanical behavior of helical structure under complicated condition such as the hoisting rope in mine shaft and the transmitting cable in electric power, the thermal expansion characteristic of sin- gle helical structure is systematically investigated under temperature effect in dif- ferent layer. Linearly explicit expressions of axial strain and increment of helical angle for the helical unit of the ith layer are developed. Based on theory of curve by Love and theory of wire rope by Costello, the linearly explicit expressions of tension, torsion and bending moment of the helical unit are presented. After that, the linear expressions of deformation and thermal expansion coefficients for the single helical structure are proposed under two boundary conditions. For further evaluating the analytical expressions, the finite element model of the single helical structure is established by using the ABAQUS software package. The analytical method is accordant to the numerical method by comparison. Thus, the analytical method is applied to analysis multilayer structures. The results show that the ther- mal expansion coefficients are the nonlinear function for the parameters of helical angle, and these coefficients could be approximately considered as linear functions for the ratio of temperature increment under two boundary conditions; the geomet- ric and mechanical behaviors of helical unit in different layer have linear relation with temperature increment, and these characteristics are influenced obviously by boundary condition. The thermal expansion characteristic of helical twist structure is obtained, which is useful to investigate geometric and mechanical behavior of complicated helical structures.

One-Dimensional Rigid Pavement Temperature Prediction Using Laplace Transformation

AbstractThis paper presents an analytical solution for the prediction of the time-dependent one-dimensional temperature profile in an N-layered rigid pavement system using Laplace transformation. Temperature at any depth in a rigid pavement system can be estimated by using the proposed solution with input data such as pavement layer thicknesses, material thermal properties, and the measured air temperature and solar radiation intensities. The associated initial boundary value problem is governed by the classic heat conduction equation with the air temperature and solar radiation considered in the surface boundary condition. Interpolatory trigonometric polynomials, based on the method of discrete least-squares approximation, are used to fit the measured air temperature and solar radiation intensities during a user-defined time period. The relationship between the constants of integration for the ith layer and the first layer are deduced, which simplifies the solution process. Model validation with the meas...

The partitioned-layer index: Answering monotone top- k queries using the convex skyline and partitioning-merging technique

A top- k query returns k tuples with the highest (or the lowest) scores from a relation. The score is computed by combining the values of one or more attributes. We focus on top- k queries having monotone linear score functions. Layer-based methods are well-known techniques for top- k query processing. These methods construct a database as a single list of layers. Here, the ith layer has the tuples that can be the top- i tuple. Thus, these methods answer top- k queries by reading at most k layers. Query performance, however, is poor when the number of tuples in each layer (simply, the layer size) is large. In this paper, we propose a new layer-ordering method, called the Partitioned-Layer Index (simply, the PL Index), that significantly improves query performance by reducing the layer size. The PL Index uses the notion of partitioning, which constructs a database as multiple sublayer lists instead of a single layer list subsequently reducing the layer size. The PL Index also uses the convex skyline, which is a subset of the skyline, to construct a sublayer to further reduce the layer size. The PL Index has the following desired properties. The query performance of the PL Index is quite insensitive to the weights of attributes (called the preference vector) of the score function and is approximately linear in the value of k. The PL Index is capable of tuning query performance for the most frequently used value of k by controlling the number of sublayer lists. Experimental results using synthetic and real data sets show that the query performance of the PL Index significantly outperforms existing methods except for small values of k (say, k ⩽ 9 ).

A new fundamental equation for the band spectra of dielectric layer films

This paper derives and demonstrates a new fundamental equation for the frequency spectra of one-dimensional photonic crystals. Commonly, the frequency spectra ω(q) as a function of Brillouin wavevector q for waves propagating through a one-dimensional photonic crystal are calculated from the trace of the transfer matrix. This paper develops a novel factored expression for band spectra calculations, tan2qd/2 = tan(kNaN−αN) × tan(kNaN−βN), where N is the number of layers per period, d is the unit cell width and ki = niω/c is the local wavevector in the ith layer of width 2ai and refractive index ni. Angles (αN,βN) depend on the parameters of all N layers but are independent of aN; in particular, in the limit of two layers, (α2,β2) correspond to the even/odd parity solutions at the center and the edge of the Brillouin zone. The derived spectral expression for the first time provides separate eigenvalue conditions for consecutive band edges at the center and the edge of the Brillouin zone for any N, which is especially useful in separating nearly-degenerate band edges. Besides being applicable everywhere the transfer matrix formalism is used, such as in finding the Bloch phase that is necessary in finite crystal calculations, the formalism is especially convenient for tailoring bandgaps and for calculating impurity modes in dielectric stacks. Overall, the present results provide an alternate analytic structure for discussing and designing one-dimensional photonic crystals.

Evaluating the Irrigation Requirement at a Cornfield in the Yellow River Basin Based on the "Dynamic Field Capacity"

An irrigation experiment was conducted at an experimental cornfield established in the Yellow River basin, Inner Mongolia, China, in order to investigate the potential for a saving of irrigation water in this region. The root zone was divided into two layers; the first layer 40 cm thick and the second layer 60 cm thick, and the irrigation requirement, Wa (mm), was assumed to be expressed asWa=(max[W1FC - W1, 0]+ max[W2FC - W2, 0]) (1+ α)where Wi is the amount of water contained in the ith layer (mm)(i=1,2), WiFC is the field of the layer (mm), and α indicates a leaching part for salinity control and uniform distribution of water in the root zone. The dynamic field capacity WiFC is defined as the value of Wi when a balance of forces is made on an element of the water at the bottom surface of the ith layer, and is evaluated using the two-layer BBH model. This critical point is not static but dynamic in nature and depends on the depth of water table and the potential water extract by plant roots.The mean value of α for the experimental cornfield was evaluated to be 0.75 from the irrigation practiced as usual in 2004. It is apparent that this value was too large to be optimum and over-irrigation occurred, because the groundwater level rose up to within the root zone just after the irrigation and the lower part of the zone was almost saturated for a long time.

Conductivity model and photoacoustic FT-IR surface depth profiling of heterogeneous polymers

A novel thermal model is developed for surface depth profiling of heterogeneous polymeric surfaces using step-scan photoacoustic Fourier transform (SS PA FT-IR) spectroscopy. This approach is based on the propagation of thermal waves generated during the photoacoustic effect which travel to the film–air (F–A) interface, thus generating acoustic signals above the surface, which upon Fourier transform, result in infrared spectra. The developed model volumetrically slices the surface into finite homogeneous layers parallel to the film–air (F–A) interface and a composition of each ith layer is assumed to be the same, but the layers among themselves ( ith+1 and ith−1) may or may not exhibit compositional changes. Overall thermal properties of the multi-layered surface consist of the sum of in-series connected thermal conductor layers. The proposed model can be utilized to polymeric films containing the following parametrically analyzed inclusions: (1) inclusions with no interphase between the matrix polymeric and (2) inclusions with a finite interphase. This model is flexible, allowing variations of the particle size, shape, and surface/interfacial microstructural changes. It was tested for depths of penetrations in the range of 5–50 μm for carbon black inclusions imbedded into a two-component (2K) polyurethane (PUR) film deposited on acrylonitrile–butadiene–styrene (ABS) substrate. These studies show that the experimental results are consistent with the proposed model, allowing predictions of interphase layers on particles; for example, a 10 nm water layer adsorbed on carbon black particle surfaces can be detected.

I th layer electrodynamics: A canonical approach

Exact analytic expressions for the fields and the power dissipated in the ith layer of an n-layered structure are derived under steady-state and normal incidence via continuum electrodynamics. Via a transmission-line analog, we recursively propagate the surface wave impedance backward. We incorporate a canonical approach via three transfer functions that recursively propagates the field forward. The results apply exactly for an arbitrary number of layers, composed of arbitrary uniaxial materials, and having layers of arbitrary thicknesses. We consider examples of the electrodynamics of a superconducting thin film atop a dielectric and backed by a normal metal as a function of the thickness of the dielectric.

On the inner structure of multidimensional simply generated trees

AbstractThe well‐known concept of a “simply generated family of trees” is generalized to the multidimensional case. Such trees represent a symbiosis of trees and tries and they essentially arise in the construction of search trees for multidimensional keys. The set of nodes in a d‐dimensional simply generated tree can be partitioned into layers according to the nodes appearing in the ith dimension. We shall present a detailed average‐case analysis of these trees including the number of such trees of given size, the size of the ith layer, and the number of special nodes. The main result is that a multidimensional simply generated tree tends to a structure consisting of a collection of linear chains, on the average; in other words, for large;i ∈ [1: d], the ith layer consists only of one‐node trees.

Deviation theorems for solutions of differential equations and applications to lower bounds on parallel complexity of sigmoids

Under a sigmoid with a depth d we understand a circuit with d layers where each real function computed at ( i+1)th layer is obtained as G( q) where q is a rational expression in the functions computed at ith layer and G is a gate operator from some admitted family. Two types of the families of gate operators are considered: first, we admit to substitute g( q) where g is a solution of a linear ordinary differential equation with the polynomial coefficients and second, as G( q) we take a solution of nonlinear first-order differential equation. The sigmoids of the first type compute any composition of the functions like exp, log, sin (thus, it includes, in particular, standard sigmoids corresponding to the gate g=(1+exp(− x)) −1), the sigmoids of the second type compute Pfaffian functions. The main result states that if two different functions f 1, f 2 are computed by means of the sigmoids with the parallel complexity d, then the difference | f 1− f 2| grows not slower than (exp (d)( p)) −1 (and not faster than exp (d)( p)) where exp ( d) is d times iteration of the exponential function and p is a certain polynomial, thus one cannot rather good approximate f 1 with a precise parallel complexity d by means of a function f 2 with a less parallel complexity. Also we estimate the number of zeroes in the intervals of a function computed by a sigmoid of the first type. All the obtained bounds are sharp.

Generation of synthetic seismograms with layer reduction

SUMMARY The surface motion in a plane multilayered half-space has been considered. Layer matrices of SH and P-SV motions are written as sums of matrices. Using these it is seen that when shear wave velocity of a layer, say the lth, is greater than the phase velocity, and layer thickness is large compared to wavelength, the surface motion can be written with the lth layer as the terminating half-space. Thus in computation of surface motion, the depth of the terminating half-space in a given structure depends on phase velocity and frequency. Further, if the source is below the terminating half-space, it has no contribution to surface motion at that phase velocity and frequency for which the terminating half-space has been obtained. This layer reduction formulation is applied in the generation of synthetic seismograms. As this generation requires computation over large ranges of phase velocity and frequency, the present method is important in avoiding excess computation time for unnecessary layers and in avoiding overflow due to the above mentioned Ith layer. The method is most useful in low phase velocity and high frequency ranges.

Derivation of analytic generalised inverses for transmission+reflection tomography

A methodology is presented for deriving analytic generalised inverses for arbitrary combinations of transmission and reflection traveltime data. These inverses are valid for negligible ray bending and one-dimensional velocity structure. The following conclusions are drawn from this analysis. (1) The slowness variance of a layer decreases with an increase in the number and length of rays which terminate in it. (2) The slowness variance associated with offset transmission VSP data will always be less than that associated with VSP reflection data. (3) The slowness covariance matrix for VSP transmission data is tridiagonal, i.e. the slowness errors in the ith layer only couple to those from the (i+1)th and (i-1)th layers. On the other hand, reflection VSP data will introduce a mutual coupling term between the slowness errors in the reflecting layer and the surface layer. (4) The slowness variance associated with transmission+reflection VSP data will generally be less than that from reflection or transmission VSP data. Moreover, the slowness covariance matrix for transmission+reflection data will be fully populated, meaning that there will be global coupling of slowness errors. However, if the segment lengths of reflecting rays are somewhat similar then the covariance matrix will be essentially tridiagonal. It is concluded from this analysis that the combination of reflection data with transmission data should most often improve the accuracy of slowness reconstruction. This assumes that the reflection traveltime errors are no more than twice that of the transmission traveltime errors.

An algorithm for computation of resistivity soundings over inhomogeneous layers

Calculation of dc resistivity sounding curves for a multilayer earth with transition layers has been treated by several authors since Mallick and Roy (1968). However, derivation of the kernel function for such problems has remained difficult for more than three‐layer models for want of a proper algorithm. The problem was first solved by Pekeris (1942) in the case of uniformly resistive layers. Other forms of recurrence relations for the kernel function of a half‐space containing such homogeneous layers were forwarded by Flathe (1955), Kunetz (1966), and Koefoed (1968). Patella (1977) considered the kernel function for a half‐space which contained a series of alternate layers, one having a linearly varying conductivity with depth while the other was homogeneously conductive. Koefoed (1979a) considered the case of a half‐space containing a transition layer situated anywhere among a series of homogeneous layers and possessing a resistivity that changed linearly with depth. In this article a very general form of algorithm is developed for generating the kernel function for a layered half‐space containing any number of transition layers having an arbitrary resistivity distribution [Formula: see text] in such ith layer. This new general form is very similar to the homogeneous form derived by Pekeris (1942).

The singularities of a Fourier-type integral in a multicylindrical layer problem

The singularities of the integrand of a Fourier-type integral obtained in solving the multicylindrical layer boundary value problem are discussed. The integrand is a function of the radial wavenumber k_{ip} of all the cylindrical layers, and the radial wavenumber in the ith layer is related to the axial wavenumber by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_{ip} = \sqrt{k_{i}^{2} - k^{2}}</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_{i}</tex> is the wavenumber of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> th layer, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_{z}</tex> is the axial wavenumber of all the layers which have to be the same by phase matching. On the complex <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_{z}</tex> -plane, there seemingly are branch points of logarithmic type and algebraic type for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_{z} = k_{i}</tex> for all the layers. However, by invoking uniqueness principle in the solution of this boundary value problem, one can show that the only singularities on the complex <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_{z}</tex> - plane are the branch-point singularity associated with the outermost medium which extends radially to infinity, and pole singularities which correspond to discrete guided modes in the multicylindrical medium.