Simple and accurate analytical model of planar grids and high-impedance surfaces, comprising metal strips or patches

Simple analytical formulas are introduced for the grid impedance of electrically dense arrays of square patches and for the surface impedance of high-impedance surfaces based on the dense arrays of metal strips or square patches over ground planes. Emphasis is on the oblique-incidence excitation. The approach is based on the known analytical models for strip grids combined with the approximate Babinet principle for planar grids located at a dielectric interface. Analytical expressions for the surface impedance and reflection coefficient resulting from our analysis are thoroughly verified by full-wave simulations and compared with available data in open literature for particular cases. The results can be used in the design of various antennas and microwave or millimeter wave devices which use artificial impedance surfaces and artificial magnetic conductors (reflect-array antennas, tunable phase shifters, etc.), as well as for the derivation of accurate higher-order impedance boundary conditions for artificial (high-) impedance surfaces. As an example, the propagation properties of surface waves along the high-impedance surfaces are studied.

Analytical model of interwoven spiral arrays

Interweaving planar spiral conductors in doubly periodic arrays enable substantially sub-wavelength resonant response along with broadening fractional bandwidth. A self-contained analytical model is proposed to accurately predict the characteristics of the intertwined quadrifilar spiral array near the fundamental resonance. The model, based upon a multiconductor transmission line (MTL) approach, provides physical insight into the unique properties of the distributed interactions between the interleaved counter-wound spiral arms extended beyond a single unit cell and elucidates the mechanisms underlying the array performance at normal and oblique incidence of TE and TM polarised waves. The developed MTL model is instrumental in the design of the artificial surfaces with the specified response.

Analytical model for bar-end cover separation failure in RC beams strengthened with near-surface mounted FRP

The flexural performance of RC beams can be improved using the near-surface mounted (NSM) FRP strengthening technique. A likely failure mode of such FRP-strengthened RC beams is bar-end cover separation which involves the detachment of the NSM FRP reinforcement together with the concrete cover along the level of the steel tension reinforcement. This paper presents a new analytical strength model for this failure mode. The proposed strength model and two existing strength models for this failure mode are compared with test results to demonstrate the superior performance of the new analytical model.

An analytical model of mountain wave drag for wind profiles with shear and curvature

An analytical model is developed to predict the surface drag exerted by internal gravity waves on an isolated axisymmetric mountain over which there is a stratified flow with a velocity profile that varies relatively slowly with height. The model is linear with respect to the perturbations induced by the mountain, and solves the Taylor–Goldstein equation with variable coefficients using a Wentzel–Kramers–Brillouin (WKB) approximation, formally valid for high Richardson numbers, Ri. The WKB solution is extended to a higher order than in previous studies, enabling a rigorous treatment of the effects of shear and curvature of the wind profile on the surface drag. In the hydrostatic approximation, closed formulas for the drag are derived for generic wind profiles, where the relative magnitude of the corrections to the leading-order drag (valid for a constant wind profile) does not depend on the detailed shape of the orography. The drag is found to vary proportionally to Ri21, decreasing as Ri decreases for a wind that varies linearly with height, and increasing as Ri decreases for a wind that rotates with height maintaining its magnitude. In these two cases the surface drag is predicted to be aligned with the surface wind. When one of the wind components varies linearly with height and the other is constant, the surface drag is misaligned with the surface wind, especially for relatively small Ri. All these results are shown to be in fairly good agreement with numerical simulations of mesoscale nonhydrostatic models, for high and even moderate values of Ri.

Analytical model of pass-by-pass strain in rod (or bar) rolling and its applications to prediction of austenite grain size

Rod rolling is a process where the deformation state of the workpiece between the work rolls is quite different from the strip rolling process. However, in most microstructure evolution models, the simple area strains (natural logarithm of the area reduction ratio) multiplied by a constant have been used to compute pass-by-pass evolution of austenite grain size (AGS) in rod (or bar) rolling, without any verification. The strains at a given pass play a crucial role in determining the recrystallization behavior (static or dynamic). In this study, an analytical model that calculates the pass-by-pass strain and strain rate in rod rolling has been developed and verified by conducting four-pass (oval–round) bar and plate rolling experiments. Numerical simulations have then been carried out for the four-pass rolling sequence using the area strain model and the new analytical model, focusing on the effect of the method for calculating the strain on the recrystallization behavior and evolution of AGS. The AGS predicted was compared with those obtained from hot torsion tests. It is shown that the analytical model developed in this study is more appropriate in the analysis of bar (or rod) rolling. It was found that the recrystallization behavior and evolution of AGS during this process were influenced significantly by the calculation method for the deformation parameters (strain and strain rate). The pass-by-pass strain obtained from the simple area strain model is inadequate to be used as an input to the equations for recrystallization and AGS evolution under these rolling conditions.

An analytical model on the propagation of modern email worms

Email worms propagate across networks by taking advantage of email relationships. Modeling the propagation of email worms can help predict their potential damages and develop countermeasures. We propose a novel analytical model on the propagation process of modern reinfection email worms. It relies on probabilistic analysis, and thus can provide a steady and reliable assessment on the propagation dynamics. Additionally, by introducing virtual users to represent the repetitious spreading process, the proposed model overcomes the computational challenge caused by reinfection processes. To demonstrate the benefits of our model, we conduct a series of experimental evaluation. The results show that our novel approach achieves a greater accuracy and is more suitable for modeling modern email worms than previous models.

Analytical model to locate the fluidisation interface in a solid-gas vacuum fluidised bed

Vacuum fluidised beds have a distinct advantage of being operated with reduced mass consumption of the fluidising media. However, a low quality of fluidisation reduces the opportunity to utilise the bubbling regime in vacuum fluidised beds. Fluidisation maps are often used to depict the interface between the quiescent, bubbling and slugging regimes inside a fluidised bed. Such maps have been obtained by visual observations of the fluidisation interface in transparent fluidised beds. For beds which are visually inaccessible fluidisation maps are difficult to obtain. The present work therefore attempts to model the interface travel in a vacuum fluidised bed. The pressure gradient due to the bed weight has been determined to be a main contributor for fluidisation/defluidisation under vacuum. A simple analytical model based on the pressure gradient (PG model) is developed to predict the interface location in a vacuum fluidised bed. For a segregated bed, the Gibilaro-Rowe (GR) model is modified and used to predict the jetsam layer growth along with the fluidisation interface. The predictions are compared with the experimental data for minimally and highly segregated particles and it is seen that for non-segregated powders the predictions are quite accurate. Lack of sufficient knowledge of bubble characteristics, however, impeded accurate prediction of the jetsam growth especially at high flow rates. However, an approximate complete fluidisation interface is successfully predicted using the GR-PG model. © 2014 Elsevier B.V.

An analytical model for optimal spectrum leasing under constraints of quality of service in CRNs

Cognitive radio improves spectrum efficiency and mitigates spectrum scarcity by allowing cognitive users to opportunistically access idle chunks of the spectrum owned by licensed users. In long-term spectrum leasing markets, secondary network operators make a decision about how much spectrum is optimal to fulfill their users' data transmission requirements. We study this optimization problem in multiple channel scenarios. Under the constrains of expected user admission rate and quality of service, we model the secondary network into a dynamic data transportation system. In this system, the spectrum accesses of both primary users and secondary users are in accordance with stochastic processes, respectively. The main metrics of quality of service we are concerned with include user admission rate, average transmission delay and stability of the delay. To quantify the relationship between spectrum provisioning and quality of service, we propose an approximate analytical model. We use the model to estimate the lower and upper bounds of the optimal amount of the spectrum. The distance between the bounds is relatively narrow. In addition, we design a simple algorithm to compute the optimum by using the bounds. We conduct numerical simulations on a slotted multiple channel dynamic spectrum access network model. Simulation results demonstrate the preciseness of the proposed model. Our work sheds light on the design of game and auction based dynamic spectrum sharing mechanisms in cognitive radio networks.

A microstructure based analytical model for tensile twinning in a rod textured Mg alloy

Abstract A model for tensile twinning during the compression of rod textured magnesium is developed based on the idea that these twins nucleate at grain boundaries and that when the twin number density per grain is low these twins readily give rise to the formation of other 'interaction' twins in adjacent grains. Experimental observations of twin aspect ratios measured at a single grain size and twin number densities measured over four grain sizes were used to determine model material parameters. Using these, the model provides reasonable predictions for the observed magnitudes and trends for the following observations:Effect of grain size and stress on twin volume fraction, fractional twin length and the fraction of twin contact.Effect of grain size on the yield stress.Effect of grain size on the general shape of the stress-strain curve at low strains. A parametric study shows the model to be quite robust but that it is particularly sensitive to the value of the exponent assumed for the twin nucleation rate law. It is seen that preventing the formation of interaction twins provides an important avenue for hardening and that the flow stress is also particularly sensitive to the relaxation of the twin back stresses. The model shows the importance of taking microstructure into account when modelling twinning.

One-dimensional analytical model for oxide thin film growth on Ti metal layers during laser heating in air

This paper presents the theoretical and experimental results for oxide thin film growth on titanium films previously deposited over glass substrate. Ti films of thickness 0.1 μm were heated by Nd:YAG laser pulses in air. The oxide tracks were created by moving the samples with a constant speed of 2 mm/s, under the laser action. The micro-topographic analysis of the tracks was performed by a microprofiler. The results taken along a straight line perpendicular to the track axis revealed a Gaussian profile that closely matches the laser's spatial mode profile, indicating the effectiveness of the surface temperature gradient on the film's growth process. The sample's micro-Raman spectra showed two strong bands at 447 and 612 cm -1 associated with the TiO 2 structure. This is a strong indication that thermo-oxidation reactions took place at the Ti film surface that reached an estimated temperature of 1160 K just due to the action of the first pulse. The results obtained from the numerical integration of the analytical equation which describes the oxidation rate (Wagner equation) are in agreement with the experimental data for film thickness in the high laser intensity region. This shows the partial accuracy of the one-dimensional model adopted for describing the film growth rate. © 2001 Elsevier Science B.V.

Analytical model for heterogeneous crystallization kinetics of spherical glass particles

An analytical model developed to describe the crystallization kinetics of spherical glass particles has been derived in this work. A continuous phase transition from three-dimensional (3D)-like to 1D-like crystal growth has been considered and a procedure for the quantitative evaluation of the critical time for this 3D-1D transition is proposed. This model also allows straightforward determination of the density of surface nucleation sites on glass powders using differential scanning calorimetry data obtained under different thermal conditions. © 2009 The American Ceramic Society.

An Analytical Model for Virtual Topology Reconfiguration in Optical Networks and A Case Study

An analytical model for Virtual Topology Reconfiguration (VTR) in optical networks is developed. It aims at the optical networks with a circuit-based data plane and an IPlike control plane. By identifying and analyzing the important factors impacting the network performance due to VTR operations on both planes, we can compare the benefits and penalties of different VTR algorithms and policies. The best VTR scenario can be adaptively chosen from a set of such algorithms and policies according to the real-time network situations. For this purpose, a cost model integrating all these factors is created to provide a comparison criterion independent of any specific VTR algorithm and policy. A case study based on simulation experiments is conducted to illustrate the application of our models.

Surface-Potential-Based Drain Current Analytical Model for Triple-Gate Junctionless Nanowire Transistors

This paper proposes a drain current model for triple-gate n-type junctionless nanowire transistors. The model is based on the solution of the Poisson equation. First, the 2-D Poisson equation is used to obtain the effective surface potential for long-channel devices, which is used to calculate the charge density along the channel and the drain current. The solution of the 3-D Laplace equation is added to the 2-D model in order to account for the short-channel effects. The proposed model is validated using 3-D TCAD simulations where the drain current and its derivatives, the potential, and the charge density have been compared, showing a good agreement for all parameters. Experimental data of short- channel devices down to 30 nm at different temperatures have been also used to validate the model.