An asymptotic model based on matching far and near field expansions for thin gratings problems

In this paper, we devise an asymptotic model for calculating electromagnetic diffraction and absorption in planar multilayered structures with a shallow surface-relief grating. Far from the grating, we assume that the solution can be written as a power series in terms of the grating thickness δ , the coefficients of this expansion being smooth up to the grating. However, the expansion approximates the solution only sufficiently far from the grating (far field approximation). Near the grating, we assume that there exists another expansion in powers of δ (near field approximation). Moreover, there is an overlapping zone where both expansion are valid. The proposed model is based on matching the two expansions on this overlapping domain. Then, by truncating terms of order δ 2 or higher, we obtain explicitly the equations satisfied by the lowest order terms in the power series. Under appropriate assumptions, we prove second order convergence of the error with respect to δ . Finally, an alternative form, more convenient for implementation, is derived and discretized with finite elements to perform some numerical tests.

Download Full-text

Analysis of the Effects of Multi-Clamps Fixture on Workpiece Location Errors

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.375-376.619 ◽

2008 ◽

Vol 375-376 ◽

pp. 619-625 ◽

Cited By ~ 1

Author(s):

Guo Hua Qin ◽

Shi Ping Sun ◽

Zhi Xiong Chen ◽

Tie Jun Wu ◽

Zhi Qiang Ao

Keyword(s):

Contact Forces ◽

Machining Accuracy ◽

Location Error ◽

Location Errors ◽

Numerical Tests ◽

Proposed Model ◽

One Step ◽

Fixture System ◽

The Impact ◽

Novel Design

Multiple clamps are frequently used to serve the purpose of workholding in a fixture. So multiple clamping forces including their magnitudes, placements and application sequences, greatly influence contact forces and workpiece machining accuracy. In this paper, the impact of multiple clamping forces on workpiece location error is formulated analytically for a workpiece-fixture system. The proposed model takes into account the varying contact forces and friction force during entire clamping operation. It reveals that the historical accumulation of clamping steps influences heavily the final distribution of contact forces in the workpiece-fixture system. In addition, based on effect of contact forces from one step to another on workpiece location, a novel design model is presented to optimize the multiple clamping forces in order to minimize the workpiece location errors. Some numerical tests are finally demonstrated to validate the proposed model and approach.

Download Full-text

Optical bistability in two-dimensional nonlinear composites of coated cylinders with nonlinear core and graded shell

EPJ Applied Metamaterials ◽

10.1051/epjam/2020006 ◽

2020 ◽

Vol 7 ◽

pp. 6

Author(s):

Ya M. Wu ◽

Guo Q. Chen ◽

Wen C. Wu ◽

Yi X. Wang ◽

Yang Huang

Keyword(s):

Optical Bistability ◽

Near Field ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

Geometrical Parameters ◽

Core Radius ◽

The Core ◽

Nonlinear Composite ◽

Incident Frequency

The intrinsic optical bistability of the nonlinear composite consisting of coated cylinders with nonlinear core and graded Drude shell is investigated with self-consistent mean-field approximation. We derive the nonlinear equation of near field for such graded composite in the quasistatic limit. We demonstrate that the bistability threshold and the bistable width are highly dependent on the core radius, the incident frequency, and the graded coefficient of the coated cylinder inclusion. It is found that the optical bistability appears only when the core radius and the incident frequency satisfy some specific conditions. Therefore, the optical bistability for nonlinear composite materials may be optimized by the suitable adjustment of the physical and geometrical parameters. Our results may be helpful for the design of the nonlinear device with appropriate bistability.

Download Full-text

Scattering-based focusing for imaging in highly complex media from band-limited, multi-component data

Geophysics ◽

10.1190/geo2020-0939.1 ◽

2021 ◽

pp. 1-64

Author(s):

David Vargas ◽

Ivan Vasconcelos ◽

Yanadet Sripanich ◽

Matteo Ravasi

Keyword(s):

A Priori ◽

Alternative Form ◽

Complex Media ◽

Subsurface Structures ◽

The Past ◽

Numerical Tests ◽

New Methods ◽

Band Limited ◽

Multicomponent Data ◽

Realistic Data

Reconstructing the details of subsurface structures deep beneath complex overburden structures, such as sub-salt, remains a challenge for seismic imaging. Over the past years, the Marchenko redatuming approach has proven to reliably retrieve full-wavefield information in the presence of complex overburden effects. When used for redatuming, current practical Marchenko schemes cannot make use of a priori subsurface models with sharp contrasts because of their requirements regarding initial focusing functions, which for sufficiently complex media can result in redatumed fields with significant waveform inaccuracies. Using a scattering framework, we present an alternative form of the Marchenko representation that aims at retrieving only the unknown perturbations to both focusing functions and redatumed fields. From this framework, we propose a two-step practical focusing-based redatuming scheme that first solves an inverse problem for the background focusing functions, which are then used to estimate the perturbations to focusing functions and redatumed fields. In our scheme, initial focusing functions are significantly different from previous approaches since they contain complex waveforms encoding the full transmission response of the a priori model. Our goal is the handling of not only highly complex media but also realistic data - band-limited, unevenly sampled, free-surface-multiple contaminated data. To that end, we combine the versatility of Rayleigh-Marchenko redatuming with the proposed scattering-based scheme allowing an extended version of the method able to handle single-sided band-limited multicomponent data. This Scattering-Rayleigh-Marchenko strategy accurately retrieves wavefields while requiring minimum pre-processing of the data. In support of the new methods, we present a comprehensive set of numerical tests using a complex 2D subsalt model. Our numerical results show that the scattering approaches retrieve accurate redatumed fields that appropriately account for the complexity of the a priori model. We show that the improvements in wavefield retrieval translate into measurable improvements in our subsalt images.

Download Full-text

A Model Based on Data Envelopment Analysis for the Measurement of Productivity in the Software Factory

International Journal of Information Technologies and Systems Approach ◽

10.4018/ijitsa.2020070101 ◽

2020 ◽

Vol 13 (2) ◽

pp. 1-26 ◽

Cited By ~ 1

Author(s):

Pedro Castañeda ◽

David Mauricio

Keyword(s):

Data Envelopment Analysis ◽

Data Envelopment ◽

Numerical Tests ◽

Model Based ◽

Software Production ◽

Software Factory ◽

Proposed Model ◽

Efficiency And Effectiveness ◽

Work Units ◽

Two Phases

Productivity in software factories is very important because it allows organizations to achieve greater efficiency and effectiveness in their activities. One of the pillars of competitiveness is productivity, and it is related to the effort required to accomplish the assigned tasks. However, there is no standard way to measure it, making it difficult to establish policies and strategies to improve the factory. In this work, a model based on data envelopment analysis is presented to evaluate the relative efficiency of the software factories and their projects, to measure the productivity in the software production component of the software factory through the activities that are carried out in their different work units. The proposed model consists of two phases in which the productivity of the software factory is evaluated and the productivity of the projects it conducts is assessed. Numerical tests on 6 software factories with 160 projects implemented show that the proposed model allows one to assess the software factories and the most efficient projects.

Download Full-text

Quasi-Stationary Turbulent Flow in Cylinder Channel with Irregular Walls

UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES ◽

10.18522/1026-2237-2020-1-4-10 ◽

2020 ◽

pp. 4-10

Author(s):

M.Yu. Zhukov ◽

N.M. Polyakova ◽

E.V. Shiryaeva

Keyword(s):

Kinematic Viscosity ◽

Stationary Flow ◽

Analytical Form ◽

Asymptotic Model ◽

Proposed Model ◽

Rotationally Symmetric ◽

Toroidal Vortices ◽

Flow Through ◽

Straight Segments ◽

Rotationally Symmetric Flow

A simple asymptotic model of a stationary rotationally symmetric flow in an infinite cylindrical channel with irregular walls is constructed and investigated. We assume that kinematic viscosity is depends on the radial and axial coordinates. The kinematic condition corresponding to the impermeability of the boundary for the liquid is chosen. It is assumed that the classical non-slip condition is completed only in straight segments of the boundary. For parts of the boundary that are not straight, any additional terms, in addition to the kinematic conditions, not required. It is shown that at any fluid flow rate in domains where the curvature of the cylinder boundary is negative, there are toroidal vortices in the stationary flow. The solution of the problem is constructed in analytical form. This solution is valid in any domain with sufficiently smooth cylinder boundaries. As an example, we consider the case of turbulent kinematic viscosity vanishing at the cylinder boundary. To prevent the velocity singularities the roughness of the wall is introduced. The proposed model can simulate the blood flow through the vessels and, in particular, be used to study the quasi-stationary motion of impurities, for example, erythrocytes, in the flow with the known structure.

Download Full-text

Far- and near-field approximation for diffraction radiation

Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms ◽

10.1016/j.nimb.2013.02.056 ◽

2013 ◽

Vol 309 ◽

pp. 194-197

Author(s):

V. Shpakov ◽

S.B. Dabagov ◽

M. Castellano ◽

A. Cianchi ◽

K. Honkavaara ◽

...

Keyword(s):

Near Field ◽

Field Approximation ◽

Diffraction Radiation

Download Full-text

Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed

Georgian Mathematical Journal ◽

10.1515/gmj.2007.109 ◽

2007 ◽

Vol 14 (1) ◽

pp. 109-123

Author(s):

Robert Gilbert ◽

Miao-Jung Ou

Keyword(s):

Green’S Function ◽

Green's Function ◽

Near Field ◽

Sound Field ◽

Hankel Transform ◽

Field Approximation ◽

Construction Scheme ◽

Stratified Ocean ◽

Asymptotic Representations ◽

Layer Waveguide

Abstract In this paper, the near-field approximation of the acoustic Green's function in a two-layer waveguide is constructed by using a variation of the method of Ahluwalia and Keller [Exact and asymptotic representations of the sound field in a stratified ocean, Springer, 1977]. The relation between the constructed multiple-scattering representation (suitable for near-field) and the Hankel transform representation (suitable for mid-range) is also discussed in this paper. The construction scheme presented in this paper can be generalized for an N-layer waveguide.

Download Full-text

Quasicontinuum Simulation of Nanotextile Based on the Microplane Model

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.714.143 ◽

2016 ◽

Vol 714 ◽

pp. 143-147 ◽

Cited By ~ 1

Author(s):

Karel Mikeš ◽

Milan Jirásek

Keyword(s):

Numerical Simulation ◽

Degrees Of Freedom ◽

Computational Cost ◽

Material Model ◽

Computational Technique ◽

Microplane Model ◽

Acceptable Error ◽

Numerical Tests ◽

Proposed Model ◽

Macroscopic Parameters

The quasicontinuum (QC) method is a relatively new computational technique, which combines fast continuum and exact atomistic approaches. The key idea of QC is to reduce the computational cost by reducing degrees of freedom of the fully atomistic approach. In this work, a material model based on the idea of microplanes is used to realize the QC simplification. A formulation convenient for numerical simulation of materials with the structure similar to nanotextile is proposed. The relations between microscopic and macroscopic parameters are derived. Numerical tests show that the proposed model can reach a significant reduction of computational cost for the price of an acceptable error.

Download Full-text