Scattering Boundary Conditions Research Articles

A 3D frequency domain finite element formulation for solving the wave equation in the presence of rotating obstacles

A frequency domain numerical method aimed at solving the propagation of sound waves in a three-dimensional domain enclosing rotating obstacles is presented. It relies on a domain decomposition whereby rotating parts are all embedded in a cylindrically-shaped domain. Following the classical Arbitrary Lagrangian Eulerian formalism, the governing equation, which is written in the local rotating frame, takes the form of a convected wave equation. The transmission conditions at the interface between the fixed and rotating domains is accomplished via the Frequency Scattering Boundary Conditions which, after classical FEM discretization, give rise to a series of coupled problems associated with a discrete set of frequencies. The performances of the method are demonstrated through several test cases involving rotating sources and/or obstacles inserted in circular and rectangular ducts.

Lightning current analysis for tall tower strike using 3D FEM

In this study, the lightning current waveforms at the middle and bottom positions for 60 m tall tower strikes were observed using the three-dimensional finite element method (3D-FEM). When creating the model for lightning current waveform analysis at the middle and bottom positions of towers, base current speed and ground conductivity characteristics were taken into account. The model was developed using scattering boundary conditions to avoid wave reflections and limit computation time. We have considered ground conductivity of 5.98 e7 S/m, 0.1 S/m, and 0.01 S/m, respectively, in our model. Base current speeds were considered in our model to be equal to the velocity of light, half of the velocity of light, and one-third of the velocity of light, respectively. This investigation will aid in developing a lightning protection strategy and a better understanding of the properties of lightning.

Narrow-band notch filter and refractive index sensor based on rectangular-semi-annular cavity coupled with MIM waveguide structure

In this work, a symmetric structure based on a metal-insulator-metal (MIM) waveguide is proposed for narrow-band notch filters and refractive index sensors. The structure comprises a symmetrically intersecting rectangular-semi-annular cavity and a long straight waveguide. The transmission spectrum and magnetic field distribution of the notch filter are studied and analyzed by the finite element method (FEM) with scattering boundary conditions (SBC). Our analysis reveals that the band-stop filter exhibits a minimum transmittance of 0.35%, a bandwidth of 34 nm, and a quality factor (Q) of 35.16. These characteristics include low stop-band transmittance, a narrow bandwidth, and a high Q value. Furthermore, our structure allows for independent adjustment of the narrow band filtering range by varying geometric parameters such as H, d, R1, and d. Additionly, we conduct theoretical analysis to investigate the sensing properties of the structure. The refractive index sensitivity of the structure reaches a high value of 1222 nm RIU−1, accompanied by a figure of merit(FOM*) of up to 175.9. These results demonstrate the structure’s excellent filtering properties and high-sensitivity sensing characteristics.Consequently, it holds significant potential for application in high-density integrated circuits and nano-optics.

A 2D frequency domain finite element formulation for solving the wave equation in the presence of rotating obstacles

A numerical method is presented to solve the propagation of sound waves in a two-dimensional domain in the presence of rotating obstacles without flow. It relies on a domain decomposition whereby rotating components are all embedded in a circular domain and the Arbitrary Lagrangian Eulerian framework which consists in writing the wave equation in the rotating reference frame. The transmission conditions at the interface between both domains is accomplished via the Frequency Scattering Boundary Conditions which, after classical discretization with the Finite Element Method (FEM), give rise to a series of coupled problems associated with a discrete set of frequencies. The performances of the method are demonstrated through several test cases of increasing complexity.

NEUTRONIC CALCULATION FOR PWR MOX FUEL PIN CELLS WITH WIMSD-5B CODE

NEUTRONIC CALCULATION FOR PWR MOX FUEL PIN CELLS WITH WIMSD-5B CODE. The WIMSD-5B thermal reactor lattice cell code is used in many laboratories for research reactor calculations and power reactors. The program uses the Wigner-Seitz approximation for cell pin calculations. The approximation has been widely applied to the pin of UO2 cells and has shown good results in previous studies but can produce incorrect results when used for pin cells in MOX fuels. This paper investigates the use of the WIMS-5B code to calculate the neutron multiplication factor and depletion for MOX fuel pin cells. Calculations were performed using the WIMSD-5B code updated with the ENDF-BVIII.0 library. The outer scattering boundary condition was used to overcome the effect of the Wigner-Seitz approach on the lack of MOX fuel. Results of this study indicates that most of the results obtained using ENDF-BVIII.0 are better than ENDF-BVII.1, and this is in line with expectations. The difference in the maximum k-inf value obtained from this library occurs in the fuel that has the greatest enrichment. On the other hand, the addition of the outer scattering limit improves the results obtained using ENDF-BVIII.0, causing a slight improvement for other libraries. This shows that by using appropriate libraries and the addition of the scattering outer limit, the Wigner Seitz approximation for the MOX pin cell pins in WIMS-D5 can yield quite accurate results.Keywords: Wigner-Seitz approximation, WIMS-D5 code, MOX fuel, Doppler reactivity.

A Stable Node-Based Smoothed Finite Element Method with Transparent Boundary Conditions for the Elastic Wave Scattering by Obstacles

In this work, a stable node-based smoothed finite element method with TBC (SNS-FEM-TBC) is proposed to solve the scattering of elastic plane waves by a two-dimensional (2D) homogeneous isotropic elastic medium. First, using Helmholtz decomposition, two scalar potential functions are introduced to divide the Navier equation into Helmholtz equations with the coupled boundary conditions for the elastic scattering problem. Second, based on the analytical solutions of Helmholtz equations, TBC operators are deduced. Then, the gradient Taylor expansion is used to construct the stability term to deal with the instability of the original NS-FEM, the gradient of the solution is expressed into a linear formulation through approximating the node-based smoothing domain as a circle. Finally, based on smoothed Galerkin weak formula, the SNS-FEM-TBC formula of linear algebraic system with linear smoothing gradient is derived. Numerical examples show that SNS-FEM can obtain more stable and accurate solutions than standard FEM. Moreover, the convergence rates of [Formula: see text] and [Formula: see text] semi-norm errors of SNS-FEM are faster.

Non-negative Intensity for Target Strength Identification in Marine Ecosystem Research

In this paper, we propose non-negative intensity (NNI) as an alternative intensity-based technique for target strength identification in marine ecosystem research. NNI identifies local surface regions of a body with positive-only sound power contributions. NNI is employed for sound scattering by fluid-loaded, fluid-filled elastic structures with weak scattering boundary conditions. Three numerical case studies are presented for which fully coupled fluid-structure interaction models based on the finite element method (FEM) and the boundary element method (BEM) are developed. To validate the three-way coupling between the structural and fluid domains, an elastic shell submerged in water and filled with different internal fluids is initially considered. Results for the scattered acoustic intensity obtained numerically are compared with analytical results from the literature. Models representing Antarctic krill of simple and complex geometry are developed. A 3×3 cylinder array representing a simplified aggregation of krill is also presented. Target strength is calculated using both the scattered intensity and NNI for different incident excitation angles. Results for NNI identify the surface regions of an individual organism or group of organisms with the greatest contribution to the scattered sound at the target strength locations.

Calculation of electron transport in branched semiconductor nanostructures using quantum network model

Electron transport in branched semiconductor nanostructures provides many possibilities for creating fundamentally new devices. We solve the problem of its calculation using a quantum network model. The proposed scheme consists of three computational parts: S-matrix of the network junction, S-matrix of the network in terms of its junctions’ S-matrices, electric currents through the network based on its S-matrix. To calculate the S-matrix of the network junction, we propose scattering boundary conditions in a clear integro-differential form. As an alternative, we also consider the Dirichlet-to-Neumann and Neumann-to-Dirichlet map methods. To calculate the S-matrix of the network in terms of its junctions’ S-matrices, we obtain a network combining formula. We find electrical currents through the network in the framework of the Landauer–Büttiker formalism. Everywhere for calculations, we use extended scattering matrices, which allows taking into account correctly the contribution of tunnel effects between junctions. We demonstrate the proposed calculation scheme by modeling nanostructure based on two-dimensional electron gas. For this purpose we offer a model of a network formed by smooth junctions with one, two and three adjacent branches. We calculate the electrical properties of such a network (by the example of GaAs), formed by four junctions, depending on the temperature.

Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinate

Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a general theory for short-range potential scattering, but there is no general theory for long-range potential scattering. This is because the scattering boundary conditions for all short-range potentials are the same, but for different long-range potentials, they are different. In this paper, by introducing tortoise coordinates, we convert long-range potential scattering to short-range potential scattering. This allows us to deal with long-range potential scattering as short-range potential scattering. An explicit expression of the scattering wave function for long-range potential scattering is presented, in which the scattering wave function is represented by the tortoise coordinate and the scattering phase shift. We show that the long-range potential scattering wave function is just the short-range potential scattering wave function with a replacement of a common coordinate by a tortoise coordinate. The approach applies not only to scattering but also applies to bound states. Furthermore, in terms of tortoise coordinates, we suggest a classification scheme for potentials. We also discuss the duality between tortoise coordinates.

Highly Sensitive 1D Photonic Crystal Biosensor

Highly sensitive one-dimensional photonic crystal (1D PhC) sensor for hemoglobin (Hb) concentration monitoring is proposed and analyzed. The suggested design is based on Si/air periodic structure with a central defect filled by the blood sample. The transmission spectrum through the suggested design has a resonant peak which is sensitive to the hemoglobin concentration. High sensor sensitivity of 443 nm/RIU with high quality factor of 6630 is achieved for transverse electric (TE) polarized mode. Further, high sensitivity of 440 nm/RIU with quality factor of 5216 is obtained for the transverse magnetic (TM) polarized mode in the hemoglobin concentrations range of (0 – 300 g/L). The analysis is carried out using full-vectorial finite-element method with scattering boundary conditions.

High Order Local Farfield Expansions Absorbing Boundary Conditions for Multiple Scattering

High Order Local Farfield Expansions Absorbing Boundary Conditions for Multiple Scattering

Highly sensitive tetra-slotted gold-coated spiral plasmonic biosensor with a large detection range

An extremely highly sensitive photonic crystal fiber (PCF) based SPR or surface plasmon resonance biosensor is manifested in this article, in a cumulated form of circularly slotted spiral lattice structure (SLS). The numerical performance analysis of the sensor is critically interpreted using the finite element method (FEM), including a perfectly matched layer (PML) and scattering boundary conditions. Very well known chemically stable material gold is used as the plasmonic material and implanted inside the circular slots to lessen the fabrication challenge and oxidation problem. The prospective model shows the maximum value of sensitivity is 41,000 nm/RIU, employing the method of wavelength interrogation and a maximum value of sensitivity of 4242 RIU−1, using the method of amplitude interrogation. The proposed sensor has the capability of detecting analytes in a massive range of the refractive index 1.32 to 1.50 RIU (for wavelength 0.5 µm to 1.55 µm) with a highest sensor resolution of 2.44 × 10−6 RIU. It is highly capable of identifying biomolecules like benzene, carbon tetrachloride, ethyl alcohol, acetone, water, silicon oil, and glucose solution in water, fused silica, cornea, lens, liver cell, and intestinal mucosa of human, polylactic acid, vegetable oil, and glycerol, etc. The sensor exhibits high linearity by showing R2 value 0.97 with a maximum FOM of 683 RIU−1. For large detection range, immense sensitivity, high FOM, and low fabrication complexity, the illustrated sensor can be a supreme candidate in the realm of SPR biosensor.

Dual-core gold coated photonic crystal fiber plasmonic sensor: Design and analysis

A simple circular lattice dual-core photonic crystal fiber (PCF) based plasmonic sensor is numerically investigated in this paper within the visible to near-infrared (450 nm to 1150 nm) region. To examine the sensing performances and the guiding properties of the sensor, Finite Element Method (FEM) based mode solver software is applied in the presence of Perfectly Matched Layer (PML) and Scattering Boundary Conditions (SBC). Chemically inoperative plasmonic material gold is deposited at the outer surface of the raised sensor to create the Surface Plasmon Resonance (SPR) effect. This sensor proffers the maximum wavelength sensitivity of 11,200 nm/RIU and the amplitude sensitivity of 505.037RIU-1 according to the simulation results. It also allows the maximum Figure of Merit (FOM) of 275RIU-1 along with the sensor resolution of 8.92×10-6 RIU for wavelength sensing within the RI range of 1.33 to 1.44. Moreover, the impact of various structural parameters (e.g. air hole, pitch, plasmon layer thickness) on the sensing performance of the structure is also described in detail. All these results indicate that this fabrication friendly, highly sensitive sensor can be a promising applicant in the field of biosensing.

Temperature sensor based on modes coupling effect in a liquid crystal-filled microstructured optical fiber

A temperature sensor based on modes coupling effect in a liquid crystal-filled microstructured optical fiber was proposed and studied in this paper. The sensing characteristics were investigated by using a full-vectorial finite-element method (FEM) with perfectly matched layer and scattering boundary condition. For the purpose of temperature sensing, liquid crystal E7 was designed to be infiltrated into one cladding air hole in PCF to form a defect core. As the phase matching condition is satisfied, the core modes couple to several different ordered defect core modes, and finally experience a large increase in the confinement loss spectra. Furthermore, the loss spectra shift toward opposite directions in the two temperature segments (15–29 °C, 29–50 °C) for X-polarized (X-pol) direction, while it experiences a blue shift in the temperature range of 15–50 °C for Y-polarized (Y-pol) direction. Numerical simulation results show that the sensitivity reaches −5.26 nm/°C at 30 °C. The coupling effect between the core fundamental mode and high-order defect core modes utilized in this paper will be beneficial to the high-sensitivity detection.

Numerical Study of Circularly Slotted Highly Sensitive Plasmonic Biosensor: A Novel Approach

A highly sensitive Photonic Crystal Fiber (PCF) based Surface Plasmon Resonance (SPR) sensor is demonstrated in this paper in the optimized form of circular slotted lattice (CSL) structure. This proposed model performance is numerically scrutinized by using Finite Element Method (FEM) in presence of Perfectly Matched Layer (PML) and Scattering Boundary Condition. Plasmonic material ‘Gold’ which is chemically inert is used in this structure at the outer surface of the slotted area to mitigate fabrication challenge. This model indicates the highest wavelength sensitivity of 16000 nm/RIU using wavelength interrogation, the amplitude sensitivity of 780 RIU−1 by using amplitude interrogation method and the average spectral sensitivity of 6666 nm/RIU, respectively. Besides, this sensor has the potentiality of detecting analytes within Refractive Index (RI) range 1.4 to 1.46 with maximum wavelength resolution of 6.25 × 10−6 RIU and amplitude resolution of 1.28 × 10−6 RIU, respectively and the maximum figure of merits of 400 RIU−1. Moreover, the variation of structural parameters (such as pitch, plasmon layer thickness etc.) and the impact of these changes are also discussed in details. According to the high sensitivity performance, polynomial fit and high Figure of Merit (FOM), this amend structure can be a strong competitor in the field of biosensing.

Oligoporous-core Quasi cladding photonic crystal fiber based micro-sensor for alcohol detection

A novel quasi-fiber sensor is introduced for alcohol sensing applications with efficient optical guiding properties. The Finite Element Method (FEM) has been employed to explore the guiding properties over a wide range of 0.80 μm–2.8 μm wavelength. The integral purported sensor structure is implemented with scattering boundary condition (SBC) on its outer boundary. The numerical investigation of the optimum structure reveals its relative sensitivity as 60%~98% corresponding to the power fractional distribution of 75% and 72% respectively. Furthermore, a high Numerical Aperture (NA) of 0.68 is obtained from the introduced sensor at the operating wavelength of 2.6 μm. The overall results promise for better performances of proposing sensor, particularly in medical imaging applications.

Design, simulation and optimization of a nonreciprocal guided-wave optical isolator based on Mach-Zehnder interferometer

In this paper, an interferometric optical isolator which utilizes a nonreciprocal phase shift was designed, simulated and optimized. The purpose was to develop the waveguide optical isolator which is expected to be low loss, more compatible with integrated optics and also reduces the overall costs as it is integrable to the optical sources. The isolator consists of an asymmetric Mach–Zehnder interferometer with a transverse magnetized nonreciprocal phase shifter in one waveguide and a reciprocal phase shifter in the other waveguide. In the simulation process, the Boundary Mode Analysis was used to compute propagation constants. Furthermore, the Scattering Boundary Condition method was used to make boundaries transparent for dispersed waves. The design parameters, including phase shifter length, bend radius and directional coupler length, were optimized to cut down the insertion loss in the forward direction and increase the return loss in the reverse direction and achieve a 50 dB isolation ratio.

Microstructure optical fiber based plasmonic refractive index sensor

This work proposes a highly sensitive plasmonic sensing scheme on a simple circular lattice microstructure optical fiber (MOF) structure. The proposed sensor performance is evaluated by using the finite element method (FEM) in the presence of perfectly matched layer (PML) and scattering boundary conditions. The highest amplitude sensitivity of 1582.95 RIU−1 and wavelength sensitivity of 11,000 nm/RIU is gained using amplitude interrogation and wavelength interrogation method, respectively, for the proposed device. In addition, the maximum sensor resolution of 9.09 × 10−6 RIU is obtained and the suggested sensor gives the same sensing performance for both x- and y-polarized modes due to its symmetrical structure, hence, capable to identify any analyte having refractive index (RI) from 1.34 to 1.40. Moreover, the value of the coefficient of determination (R2 = 0.9926) of the resonance wavelength is achieved close to unity using the quadratic curve fitting. Due to having these promising results, the proposed RI sensor can be useful in the area of bio-sensing.

Molscat: A program for non-reactive quantum scattering calculations on atomic and molecular collisions

molscat is a general-purpose program for quantum-mechanical calculations on nonreactive atom–atom, atom–molecule and molecule–molecule collisions. It constructs the coupled-channel equations of atomic and molecular scattering theory, and solves them by propagating the wavefunction or log-derivative matrix outwards from short range to the asymptotic region at long range. It then applies scattering boundary conditions to extract the scattering matrix (S matrix). Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, rigid diatom + asymmetric top, and diffractive scattering of an atom from a crystal surface. Interaction potentials may be specified either in program input (for simple cases) or with user-supplied routines. For the built-in coupling cases, molscat can loop over total angular momentum (partial wave) and total parity to calculate elastic and inelastic integral cross sections and spectroscopic line-shape cross sections. Post-processors are available to calculate differential cross sections, transport, relaxation and Senftleben–Beenakker cross sections, and to fit the parameters of scattering resonances. molscat also provides an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in; plug-in routines are supplied to handle collisions of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field. For low-energy scattering, molscat can calculate scattering lengths and effective ranges and can locate and characterise scattering resonances as a function of an external variable such as the magnetic field. Program summaryProgram Title:molscatProgram Files doi:http://dx.doi.org/10.17632/rtzgf5mwpn.1Licensing provisions: GPLv3Programming language: Fortran 90External routines/libraries: LAPACK, BLASNature of problem: Quantum-mechanical calculations of scattering properties for non-reactive collisions between atoms and molecules.Solution method: The Schrödinger equation is expressed in terms of coupled equations in the interparticle distance, R. Solutions of the coupled-channel equations are propagated outwards from the classically forbidden region at short range to the asymptotic region. The program calculates scattering S matrices and uses them to calculate scattering properties including elastic, inelastic and line-shape cross sections.Unusual features:1. molscat contains numerous features to handle quantities important in low-energy collisions. It can propagate very efficiently to very long range, and it can calculate low-energy properties such as the scattering length (complex and energy-dependent if required) and the effective range.2. molscat can construct and solve sets of coupled equations using basis sets that are not eigenfunctions of the Hamiltonians of the colliding particles at long range. The propagation is carried out in the primitive basis set, and the solutions are transformed to the asymptotic basis set before applying long-range boundary conditions to extract the S matrix.3. molscat provides an interface that allows users to specify the coupled equations that arise from additional Hamiltonians and basis sets.4. molscat provides an interface that allows users to include multiple external fields in the Hamiltonian. This same interface also allows users to include a factor which scales the interaction potential, and to investigate how properties vary with this factor.5. molscat can locate and characterise low-energy Feshbach resonances either as a function of collision energy or as a function of external fields or of the potential scaling factor.

Transient temperature calculation method for complex fluid-solid heat transfer problems with scattering boundary conditions

A calculation method for engine temperatures is presented. Special focus is placed on the transient and scattering boundary conditions within the combustion chamber, including fired and coasting conditions, as well as the dynamic heat transfer of the water jacket. Model reduction is achieved with dimensional analysis and the application of probability density functions, which allows for a timescale separation. Stationary in-cylinder pressure measurements are used as input values and, according to the transient behavior, modified with an own part-load model.A turbocharged spark ignition race engine is equipped with 70 thermocouples at various positions in proximity to the combustion chamber. Differentiating from already published works, the method deals with the transient engine behavior during a race lap, which undergoes a frequency range of 0.1–1 Hz. This includes engine speed build-ups under gear changes, torque variations, or the transition from fired to coasting conditions.Different thermal behaviors of various measuring positions can be simulated successfully. Additionally, cylinder individual temperature effects resulting from an unsymmetrical ignition sequence and different volumetric efficiencies with unequal residual gas can be predicted. Up to a few percent, the energy balance of the water jacket is fulfilled and variations of water inlet temperatures can be simulated accurately enough.