Semi-analytical Scheme Research Articles

Muscle-ups: improved approximations of the matter field with the extended Press–Schechter formalism and Lagrangian perturbation theory

ABSTRACT Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to simulate the displacement of CDM is their inability to model the evolution of overdensities in the initial density field, a limit that can be circumvented by detecting halo particles in the initial conditions. We thus propose ‘MUltiscale Spherical Collapse Lagrangian Evolution Using Press–Schechter’ (muscle-ups), a new scheme that reproduces the results from Lagrangian perturbation theory on large scales, while improving the modelling of overdensities on small scales. In muscle-ups, we adapt the extended Press and Schechter formalism to Lagrangian algorithms of the displacement field. For regions exceeding a collapse threshold in the density smoothed at a radius R, we consider all particles within a radius R collapsed. Exploiting a multiscale smoothing of the initial density, we build a halo catalogue on the fly by optimizing the selection of halo candidates. This allows us to generate a density field with a halo mass function that matches one measured in N-body simulations. We further explicitly gather particles in each halo together in a profile, providing a numerical, Lagrangian-based implementation of the halo model. Compared to previous semi-analytical Lagrangian methods, we find that muscle-ups improves the recovery of the statistics of the density field at the level of the probability density function, the power spectrum, and the cross-correlation with the N-body result.

Beam-steering ultrasonic guided waves in a bone-mimicking plate by time-delaying the excitation of the elements in a multi-element array: a numerical study

We present a numerical simulation of the beam-steering of ultrasonic guided waves in an isotropic and viscoelastic solid plate, which mimics bovine cortex. The excitation was modeled by a group of five finite-size emitters, each exercised a normal force to the bone plate. Beam steering was achieved by delaying the emitters’ firing. The simulation technique was implemented by a semi-analytical finite element scheme to compute the wave fields. At small steering angles, the simulated time-offset signals show mainly two groups of arrivals. The first group is the fast-traveling and high-frequency bulk waves and the second one is slow-traveling and low-frequency guided waves. The fast-traveling waves gradually diminish with increasing steering angles, in agreement with the excitation function of the source influence theory. The frequency-phase velocity dispersion maps also illustrate the phenomenon. The study has demonstrated that the lowest order Lamb asymmetrical mode, A 0, which is useful for bone characterization, can best be excited when the cortical bone thickness is thin, the beam angle is large, and the excited frequency is low.

An innovative semi-analytical methodology for fracture mechanics assessment of complex geometrical singularities

This paper proposes a semi-analytical scheme for the determination of the J fracture mechanics parameter for defects located at geometrical singularities such as grooves or nozzle corners.The bases of this scheme remain the conventional influence function and reference stress formulations which rely here on an elastic-plastic Finite Modeling of the crack free structure for determining an effective elastic J (noted Jel˜ and representative of the effective primary stresses imposed to the structure) and the associated plastic correction.In a first part of the paper, influence function solutions are proposed for cracks in grooves. In second and third parts, a proposition for determining the reference stress is proposed then validated though comparison to direct calculations of J parameter and through comparison to a test result.

Analytical and semi-analytical solutions for Phi-four equation through three recent schemes

This manuscript investigates the analytical and semi-analytical solutions of nonlinear phi-four (PF) equation by applying the sech–tanh expansion method, modified Ψ′Ψ-expansion method and Adomian decomposition method. This equation is considered as a particular case of the well-known Klein–Fock–Gordon (KFG) equation. The KFG equation is derived by Oskar Klein and Walter Gordon and relates to Schrödinger equation. Many quantum effects can be studied based on the PF model’s solutions, such as wave-particle duality to describe reality in the form of waves is at the heart of quantum mechanics. The considered model is also used to explain de Broglie waves’ character, the spineless relativistic composite particles, relativistic electrons, etc., which are also the main icons for a good understanding of the phenomenon of quantum physics. Through two recent analytical schemes, handling this model gives many novel computational solutions that are tested through the semi-analytical scheme to investigate their accuracy. Demonstrating the obtained analytical and matching between analytical and semi-analytical through some distinct sketches shows the considered model’s novel physical properties.

Scattering by a uniaxially anisotropic chiral object under electromagnetic beam illumination

ABSTRACT We propose a semi-analytical scheme for investigating the electromagnetic beam scattering by a uniaxially anisotropic chiral object. The scattered and internal fields are expanded in terms of appropriate spherical vector wave functions, and the method of moments procedure is employed for determining the unknown expansion coefficients. Normalized differential scattering cross sections are evaluated for a uniaxially anisotropic chiral spheroid and circular cylinder of finite length, respectively illuminated by a Gaussian beam, Hermite-Gaussian beam and zero-order Bessel beam. The scattering properties are analyzed briefly.

Dual-Polarized All-Metallic Metagratings For Perfect Anomalous Reflection

We theoretically formulate and experimentally demonstrate the design of metagratings (MGs) composed of periodic rectangular grooves in a metallic medium, intended for perfect anomalous reflection. Using mode matching, a semianalytical scheme for analysis and synthesis of such MGs, containing multiple, arbitrarily arranged, grooves per period, is derived. Following the typical MG design approach, we use this formalism to identify the relevant Floquet-Bloch (FB) modes and conveniently formulate constraints for suppression of spurious scattering, directly tying the structure's geometrical degrees of freedom (DOFs) to the desired functionality. Solving this set of constraints, in turn, yields a detailed fabrication-ready MG design, without any full-wave optimization. Besides providing means to realize highly-efficient beam deflection with all-metallic formations, we show that the rectangular (two-dimensional) groove configuration enables \emph{simultaneous} manipulation of both transverse electric (TE) and transverse magnetic (TM) polarized fields, unavailable to date with common, printed-circuit-board-based, microwave MGs. In addition, we highlight a physical limitation on the TE-polarization performance, preventing the ability to achieve perfect anomalous reflection in any desired angle. These capabilities are verified using three MG prototypes, produced with standard computer numerical control (CNC) machines, demonstrating both single- and dual-polarized control of multiple diffraction modes. These results enable the use of MGs for a broader range of applications, where dual-polarized control is required, or all-metallic devices are preferable (e.g., spaceborne systems or at high operating frequencies).

A computational study of fractional model of atmospheric dynamics of carbon dioxide gas

In this paper, a fractional order nonlinear mathematical model describing the dynamics of atmospheric concentration of CO 2 is investigated and studied through the application of a semi-analytical homotopy scheme combined with Sumudu transform and homotopy polynomials. This study examines the consequences of the variations of forest biomass and human population on the dynamics of the concentration of CO 2 gas in the atmosphere. The Caputo fractional derivatives are engaged in this study. The computational work shows that the evaluated iterative terms are adequate for the refined approximations of the solutions for a fractional model of dynamics of atmospheric concentration of CO 2 , and thus authenticate the computational strength of the employed scheme. The variational behavior of concentration of CO 2 , forest biomass, and human population are demonstrated through the graphical presentation regarding the changing values of fractional order derivatives and time t . Moreover, this study also examines the analysis of obtained solutions for a fractional model in view of uniqueness and convergence.

Lightweight design of a bolt-flange sealing structure based on topology optimization

To date, sealing structures have been widely used in aerospace vehicles. This paper presents a normalized and systematic procedure realizing lightweight design for a square bolt-flange sealing structure of a rocket engine. To measure the sealing behavior, the contact force on the sealing interface is obtained by a nonlinear analysis of node-to-node contact. The topology optimization is established to achieve sufficient contact forces in the sealing area by acquiring the Kreisselmeier-Steinhauser (KS) function to condense multiple contact force constraints into a global sealing constraint. A three-field projection scheme is also adopted to obtain a clear result and a semi-analytical perturbation scheme is proposed to realize the sensitivity calculation. Then, the square flange cover is optimized by the proposed optimization framework and a lightweight design with a clear load-carrying path is obtained. The optimized design is reconstructed and further optimized in detail. Compared with several traditional designs, it shows better leakproofness under inner liquid pressure, which can be directly fabricated by additive manufacturing and used in the rocket engine. The optimization procedure is proved effective and practical in designing sealing structures for aerospace vehicles.

A 6M digital twin for modeling and simulation in subsurface reservoirs

A 6M digital twin for modeling and simulation in subsurface reservoirs

Retrieval of Secchi Disk Depth in Turbid Lakes from GOCI Based on a New Semi-Analytical Algorithm

The accurate remote estimation of the Secchi disk depth (ZSD) in turbid waters is essential in the monitoring the ecological environment of lakes. Using the field measured ZSD and the remote sensing reflectance (Rrs(λ)) data, a new semi-analytical algorithm (denoted as ZSDZ) for retrieving ZSD was developed from Rrs(λ), and it was applied to Geostationary Ocean Color Imager (GOCI) images in extremely turbid waters. Our results are as follows: (1) the ZSDZ performs well in estimating ZSD in turbid water bodies (0.15 m < ZSD < 2.5 m). By validating with the field measured data that were collected in four turbid inland lakes, the determination coefficient (R2) is determined to be 0.89, with a mean absolute square percentage error (MAPE) of 22.39%, and root mean square error (RMSE) of 0.24 m. (2) The ZSDZ improved the retrieval accuracy of ZSD in turbid waters and outperformed the existing semi-analytical schemes. (3) The developed algorithm and GOCI data are in order to map the hourly variation of ZSD in turbid inland waters, the GOCI-derived results reveal a significant spatiotemporal variation in our study region, which are significantly driven by wind forcing. This study can provide a new approach for estimating water transparency in turbid waters, offering important support for the management of inland waters.

The semianalytical analysis of nearly singular integrals in 2D potential problem by isogeometric boundary element method

AbstractBenefited from the accuracy improvement in modeling physical problem of complex geometry and integrating the discretization and simulation, the isogeometric analysis in boundary element method (IGABEM) has been drawn a great deal of attention. The nearly singular integrals of 2D potential problem in the IGABEM are addressed by a semianalytical scheme in the present work. We use the subtraction technique to separate the integrals to singular and nonsingular parts, where the singular parts can be calculated by the analytical formulae derived by utilizing a series of integration by parts, while the nonsingular parts are calculated numerically with fewer quadrature points. Comparing the present semianalytical results with the ones of exact solutions, we find that the present method can obtain precise potential and flux densities of inner points much closer to the boundary without refining the elements nearby. Sufficient comparisons with other regularization schemes, such as the exponential and sinh transformation methods, are also conducted. The results in the numerical examples show the competitiveness of the present method, especially when calculating the nearly strongly and highly singular integrals during the simulation of the flux density.

Hydrodynamic forces induced by a solitary wave interacting with a submerged square barrier: Physical tests and δ-LES-SPH simulations

A laboratory and numerical investigation on the features of the horizontal and vertical hydrodynamic loads given by a solitary wave on a submerged square barrier is presented. By the experimental viewpoint, the wave forces were deduced from the records of a discrete battery of pressure sensors located along the external surface of the barrier. As regards the numerical viewpoint, simulations were performed through the SPH model presented in Di Mascio et al. (2017), in which the governing equations are written considering a turbulence closure model. The numerical simulations allowed to extend the range of analyzed cases and highlighted the regions around the submerged barrier of higher dissipation occurring during the wave-structure interaction. A good agreement between the experimental and numerical peaks of the horizontal and vertical forces was found. Afterwards, a semi-analytical scheme able to determine the horizontal loads was adopted using the speed drop factor obtained by physical tests and simulations. For practical purposes, attention was finally paid to determine the critical conditions against the sliding of the barrier.

Observational signatures of wormholes with thin accretion disks

We numerically construct images of thin accretion disks in rotating wormhole backgrounds, for the Kerr-like and the Teo class of wormholes. Our construction is illustrated by two methods, a semi-analytic scheme where separated null geodesic equations obtained by analytically integrating the second order equations once are used, as well as by a numerical ray-tracing method utilizing a fourth order Runge-Kutta algorithm. Our result shows dramatic differences between accretion disk images in wormhole backgrounds, compared to black hole ones, specifically because a wormhole can in principle have accretion disks on both sides of its throat. We establish the nature of the images if the observer and the disk are on two opposite sides of the throat, and show that these can provide conclusive observational evidence of wormhole geometries.

Comparison and Analysis of Two Different Calculation Schemes of SLEVE- Hybrid Coordinate in GRAPES_MESO Model

The calculation scheme of the smoothed-level and hybrid (SLEVE-hybrid for short) coordinates in numerical forecasting model is not limited in number. It is divided into the semi-analytical scheme and the finite differential scheme in terms of the various differential methods of the coordinate deformation variables. Having compared the dynamic equation and the long-time batch simulation results of the two schemes, the present study draws the following conclusions. The first-order finite difference accuracy of the coordinate deformation variables in the finite differential scheme is theoretically lower than that in the semi-analytical scheme. The larger the vertical gradient of the layer thickness is, the larger the relative errors of the finite differential scheme are. The long-time batch simulation test in the GRAPES model dynamic core demonstrates that the bias of the temperature and the geopotential height in the semi-analytical scheme is smaller under the default layering, while the simulation difference of the two schemes is greatly reduced when the layering is more uniform.

An iterative scheme for the generalized Peierls–Nabarro model based on the inverse Hilbert transform

A new and efficient semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls–Nabarro model. The numerical method developed here exploits certain basic properties of the Hilbert transform to achieve a reduction of the nonlocal and nonlinear equations characterizing the generalized Peierls–Nabarro model to a local model which is then solved using a fixed point iteration scheme. This is in sharp contrast to existing schemes for solving the generalized Peierls–Nabarro model like the semi-discrete variational Peierls–Nabarro model, or methods involving the fitting of the slip distribution to a linear combination of predefined elementary slip distributions, all of which involve the solution of nonlinear and nonlocal equations using gradient-based optimization tools. The key idea behind the proposed technique is to transform the nonlocal Peierls–Nabarro model into an equivalent local model, called the inverse Peierls–Nabarro model. From a computational viewpoint, the resulting local model is attractive since it can be solved without recourse to any gradient based algorithms; combined with appropriate acceleration schemes, the proposed algorithm provides a computationally expedient alternative to solving the generalized Peierls–Nabarro model. Further, the fixed point iterative scheme developed here easily lends itself to parallelization, unlike iterative methods for the fully nonlocal and nonlinear models currently in use. The proposed numerical scheme is validated both with simple examples involving the 1D Peierls–Nabarro model corresponding to a sinusoidal stacking fault energy, and with realistic examples involving calculations of the core structure of both edge and screw dislocations on the close-packed [Formula: see text] planes in Aluminum. An approximate technique to incorporate external stresses within the framework of the proposed iterative scheme is also discussed with applications to the equilibration of a dislocation dipole. Finally, the advantages, limitations and avenues for future extension of the proposed method are discussed.

A frequency-domain hybrid HOBEM for motion responses and added resistance of ships sailing in head and oblique waves

A hybrid higher-order boundary element method (HOBEM) within the framework of potential flow theory in frequency domain is developed for solving ship hydrodynamic problems with forward speed. The method introduces a wall-sided artificial control surface to decompose the fluid domain into two subdomains, one encompassing the ship and the other on the outside. To guarantee the radiation condition at infinite for any frequency, the translating-pulsating Green's function method with singularities distributed on the control surface is used in the outer domain. The panel integrals of the Green's function are evaluated by a robust and efficient semi-analytical scheme. In the inner domain, the Rankine panel method (RPM) is adopted, and the steady flow effects are considered in the free surface and body surface conditions. The integral equation imposed on the inner boundaries is discretized and solved by a numerical approach of HOBEM based on bi-quadratic isoparametric elements. By imposing the continuous conditions of velocity potential and its normal derivative on the control surface, the solutions in the two domains are matched and a coupled equation system is formulated for the velocity potential on boundaries. Through the calculations of radiation and diffraction forces on a mathematical ship model, the present method is proved to have good mesh convergence, and satisfactory results can be obtained in a relatively small computational domain.The present hybrid HOBEM is applied to evaluate the hydrodynamic responses of ships sailing in head and oblique waves. Numerical simulations are first conducted on the free motions of two slender ships (i.e., a modified Wigley hull and a non-wall-sided S175 containership) in head waves. By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating Green's function method and RPM, it is found that the present method is of better stability and accuracy, especially for the non-wall-sided ship. Then further investigations are conducted on the wave-induced motions and added resistance of S175, a newer container ship KCS and a full formed bulk carrier S-Cb84 with different forward speeds and heading angles. In all cases, the numerical results obtained by the present method are satisfactory in comparison with the experimental data.

Analytical and Approximate Solutions for Complex Nonlinear Schrödinger Equation via Generalized Auxiliary Equation and Numerical Schemes

This article studies the performance of analytical, semi-analytical and numerical scheme on the complex nonlinear Schrödinger (NLS) equation. The generalized auxiliary equation method is surveyed to get the explicit wave solutions that are used to examine the semi-analytical and numerical solutions that are obtained by the Adomian decomposition method, and B-spline schemes (cubic, quantic, and septic). The complex NLS equation relates to many physical phenomena in different branches of science like a quantum state, fiber optics, and water waves. It describes the evolution of slowly varying packets of quasi-monochromatic waves, wave propagation, and the envelope of modulated wave groups, respectively. Moreover, it relates to Bose-Einstein condensates which is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero. Some of the obtained solutions are studied under specific conditions on the parameters to constitute and study the dynamical behavior of this model in two and three-dimensional.

An Iterative Approach for the Numerical Solution of Fractional BVPs

In this article, an efficient numerical scheme is presented for the numerical solution of nonlinear multi-point boundary value problems. This method is a combination of Laplace transform and a decomposition procedure, commonly known as the Laplace Decomposition Method. This semi-analytical iterative scheme is highly accurate locally as it produces series solutions, which converges over a relatively short interval. In order to demonstrate the efficiency and simplicity of the method, the proposed strategy is implemented for a number of boundary value problems of fractional order. Comparisons with other existing techniques are reported. Few iterates of this iterative scheme are needed to obtain highly accurate solution, which indicates that the rate of convergence of the scheme is relatively high.

Retrieval of Suspended Particulate Matter in Inland Waters with Widely Differing Optical Properties Using a Semi-Analytical Scheme

Suspended particulate matter (SPM) directly affects the underwater light field and, as a consequence, changes the water clarity and can reduce the primary production. Remote sensing-based bio-optical modeling can provide efficient monitoring of the spatiotemporal dynamics of SPM in inland waters. In this paper, we present a novel and robust bio-optical model to retrieve SPM concentrations for inland waters with widely differing optical properties (the Tietê River Cascade System (TRCS) in Brazil). In this system, high levels of Chl-a concentration of up to 700 mg/m3, turbidity up to 80 NTU and high CDOM absorption highly complicate the optical characteristics of the surface water, imposing an additional challenge in retrieving SPM concentration. Since Kd is not susceptible to the saturation issue encountered when using remote sensing reflectance (Rrs), we estimate SPM concentrations via Kd. Kd was derived analytically from inherent optical properties (IOPs) retrieved through a re-parameterized quasi-analytical algorithm (QAA) that yields relevant accuracy. Our model improved the estimates of the IOPs by up to 30% when compared to other existing QAAs. Our developed bio-optical model using Kd(655) was capable of describing 74% of SPM variations in the TRCS, with average error consistently lower than 30%.

Cluster functional renormalization group and absence of a bilinear spin liquid in the J1−J2 Heisenberg model

The pseudofermion functional renormalization group (pf-FRG) has been put forward as a semi-analytical scheme that, for a given microscopic spin model, allows to discriminate whether the low-temperature states exhibit magnetic ordering or a tendency towards the formation of quantum spin liquids. However, the precise nature of the putative spin liquid ground state has remained hard to infer from the original (single-site) pf-FRG scheme. Here we introduce a cluster pf-FRG approach, which allows for a more stringent connection between a microscopic spin model and its low-temperature spin liquid ground states. In particular, it allows to calculate spatially structured fermion bilinear expectation values on spatial clusters, which are formed by splitting the original lattice into several sublattices, thereby allowing for the positive identification of a family of bilinear spin liquid states. As an application of this cluster pf-FRG approach, we consider the $J_1$-$J_2$ SU($N$)-Heisenberg model on a square lattice, which is a paradigmatic example for a frustrated quantum magnet exhibiting quantum spin liquid behavior for intermediate coupling strengths. In the well-established large-$N$ limit of this model, we show that our approach correctly captures the emergence of the $\pi$-flux spin liquid state at low temperatures. For small $N$, where the precise nature of the ground state remains controversial, we focus on the widely studied case of $N=2$, for which we determine the low-temperature phase diagram near the strongly-frustrated regime after implementing the fermion number constraint by the flowing Popov-Fedotov method. Our results suggest that the $J_1$-$J_2$-Heisenberg model does not support the formation of a fermion bilinear spin liquid state.