Radiation Problems Research Articles

Wave power extraction by an oscillating water column array embedded in comb-type breakwaters: Performance analysis and hydrodynamic mechanism

Cost-sharing, space-sharing, and multi-function can be achieved through integrating wave energy converters into coastal defense facilities. In this paper, we consider a periodical array of oscillating water columns (OWCs) embedded in the coast-based comb-type breakwater in the presence of the step bottom. Based on the linear potential flow theory and matched eigenfunction expansion method, a semi-analytical model for solving the diffraction and radiation problems of the periodic OWC array is developed. The mathematical model is verified using Haskind relations and energy conservation law. Parametrical studies are carried out to illustrate the hydrodynamic characteristics of the OWC array embedded in the comb-type breakwater. This study also reveals the constructive and destructive interference effects between the breakwater and OWCs. It is found that the wave amplification caused by the projecting caisson produces a constructive effect on the wave power extraction. However, the inherent strong wave reflection caused by the caisson array weakens the wave power extraction, particularly in the sensitive frequency range (i.e., 2 < kh1 < 5.5 in the present investigations).

Advanced integration of stereotaxis and real-time MRI for precise and safe medical navigation: a future paradigm for minimally invasive interventions

Minimally invasive techniques have transformed medicine by improving patient outcomes and reducing invasiveness. Existing navigation methods, which use fluoroscopy or pre-operative imaging, lack real-time visualization and precision during complex surgeries. Fluoroscopy may also expose patients and medical staff to ionizing radiation. We propose enhanced stereotaxis and real-time magnetic resonance imaging (MRI) integration to overcome these problems and improve minimally invasive intervention precision and safety. Stereotactic guiding and high-resolution real-time MRI imaging are combined in this research to improve medical navigation. The conceptual framework includes modeling the stereotactic system's magnetic field, real-time tracking of magnetic-sensored medical devices, and dynamic MRI imaging for continuous visibility throughout treatments. Stereotactic and MRI data can be fused for simultaneous vision and navigation, and adaptive path planning algorithms allow real-time targeting and avoidance of key structures. A simulated cardiac electrophysiology catheter ablation treatment shows the combined approach's potential benefits. Real-time adaptive navigation reduces radiation exposure and problems while targeting precisely. This research establishes a new medical navigation paradigm that improves precision, patient safety, and radiation exposure. This integrated method could revolutionize minimally invasive procedures across medical disciplines, despite limitations in patient-specific data integration and real-time algorithm development. This new navigation approach needs further research, validation, and clinical trials to confirm its feasibility and efficacy and improve medical patient care

Quale mechanics as a metaphysical weltanschauung of quantum mechanics

The term Quale Mechanics is proposed here as describing the qualitative aspects of Quantum Mechanics that are susceptible of metaphysical considerations. The aim of Quale Mechanics is to distill the quantum discourse to its pillars in order to construct its proper – philosophical in nature – quale discourse. The framework of the discussion is initiated by revisiting the platonic approach of the manner in which knowledge is perceived/processed, and then by discussing the four sapiential stages before arriving at concept of the eide. The sensible-suprasensible dichotomy is exposed by contrasting aistheta to the eide. A discussion on the historical development and the foundation of the pillars of Quantum Mechanics is followed. This includes Planck’s solution for the black-body radiation problem with the introduction of quanta – in conflict with Newtonian physics – followed by Einstein’s explanation of the photoelectric effect and the implications involving the dual nature of light (particle vs. wave) and two generalizations of the quantum character of matter: the planetary model of the atom by Bohr, and the dual particle-wave character of electron demonstrated by de Broglie. The subsequent distillation of these semi-classical concepts into more abstract mathematical concepts by Heisenberg, Born, Dirac and Pauli are then reviewed – with Heisenberg’s uncertainty principle and with the concept of wavefunction as landmarks that unmistakably departs from the classical deterministic view of matter. A representative illustration of these achievements is given by the Casimir effect – with implications for gravity and an illustration of how vacuum can in fact not be considered to be truly void. Quantum Mechanics, as the most accurate mathematical framework which can be employed in order to describe and predict the natural phenomena occurring at the atom-size dimensions of reality, may thus be considered as the root from which the concept of Quale Mechanics is emerged in order to construct the parallel between the metaphysical existence and the quantum physical wavefunction collapse. It is concluded that, within its underlying, Quantum Mechanics is a (hopefully fruitful) reiteration of the Ancient Greek Weltanschauung.

A body-of-revolution discontinuous Galerkin time domain method based on curved mesh for Maxwell equations

ABSTRACT Numerical simulation of body-of-revolution (BoR) or axisymmetric structures for scattering and radiation problems has a broad spectrum of technology applications in microwave and optical engineering. In this work, we propose a high-order BoR discontinuous Galerkin time-domain method (BoR-DGTD) for solving Maxwell equations in the cylindrical coordinate system. The presented approach is based on or (m is the mode number and φ is the azimuth) expansions for different field components and thus yields a real-valued final system of equations. It saves half of the unknowns as compared to the existing method in which all the field components are assumed to have the same φ variation, i.e. . In contrast to the common practice of deriving variational formulation for the BoR Maxwell equations on two-dimensional grids in the meridian plane, we build it on three-dimensional coaxial toroidal subdomains. As a result, the singularity difficulty induced by the cylindrical coordinates is eliminated naturally. In addition, for BoR with curved material interfaces in the angular cross-section, a solution using curved grids in conjunction with the low-storage weight-adjusted approximation scheme is provided, which significantly enhances the simulation quality. Particularly, to achieve a set of optimized interpolation shape functions for the isoparametric transformation, an essential assistant in calculating the coefficient matrices, a heuristic procedure is developed to properly position the geometric control points on the curved grids. Some numerical experiments are conducted to demonstrate the accuracy and performance of our proposed BoR-DGTD method.

Development and application of discontinuous Galerkin method for solidification problems in a semitransparent medium-filled cavity

Research on the phase change phenomenon has gained increasing attention due to its extensive engineering applications in the fields of energy storage and release. In the semitransparent medium, the phase change process is accompanied by the transfer of internal radiation energy, which can significantly affect the distributions of temperature and liquid fraction. Based on the enthalpy model, this work develops the discontinuous Galerkin method (DGM) to solve the enthalpy equation (EE) and radiative transfer equation (RTE) that govern the phase change process. By comparing with the analytic solution and other numerical results, the correctness of the proposed DGM framework for solving coupled radiation and phase change problems is validated. Results reveal that the DGM can accurately capture the heat and mass transfer process in solidification problems. The proposed DGM is further extended to analyze the solidification problem within a two-dimensional cavity considering the radiation effect. Effects of Planck number, medium scattering albedo, and refractive index on the temperature and liquid fraction distributions as well as the mushy zone location are investigated. It is found that these parameters have important impacts on the solidification rate. This work provides accurate numerical solutions on phase change problems in the presence of radiation.

Effect of a submerged or a surface piercing porous barrier on structure‐coupled gravity waves

Flexural or membrane‐coupled or capillary gravity wave scattering by a submerged or a piercing vertical porous barrier is analytically studied based on a connection that involves the solution potentials and few auxiliary potentials. The problems for the auxiliary potentials are relatively easy to handle for their solutions. The original problem is decomposed into two scattering or radiation problems of this type. The solution wave potential is determined in terms of those resolved wave potentials. Numerical results for the explicitly obtained scattering quantities are also presented.

Geometry and topological photonics

Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on the family of operators that describes the propagation of Bloch waves. Here, we highlight that there is a profound geometrical connection between topological physics and the topological theory of mathematical surfaces. We show that topological band theory can be understood as a generalization of the topological theory of surfaces and that the genus of a surface can be regarded as a Chern number of a suitable operator defined over the surface. We point out some nontrivial implications of topology in the context of radiation problems and discuss why for physical problems the topological index is often associated with a bulk-edge correspondence.

Numerical Solution of Nonlinear Problems with Multiple Roots Using Derivative-Free Algorithms

In the study of systems’ dynamics the presence of symmetry dramatically reduces the complexity, while in chemistry, symmetry plays a central role in the analysis of the structure, bonding, and spectroscopy of molecules. In a more general context, the principle of equivalence, a principle of local symmetry, dictated the dynamics of gravity, of space-time itself. In certain instances, especially in the presence of symmetry, we end up having to deal with an equation with multiple roots. A variety of optimal methods have been proposed in the literature for multiple roots with known multiplicity, all of which need derivative evaluations in the formulations. However, in the literature, optimal methods without derivatives are few. Motivated by this feature, here we present a novel optimal family of fourth-order methods for multiple roots with known multiplicity, which do not use any derivative. The scheme of the new iterative family consists of two steps, namely Traub-Steffensen and Traub-Steffensen-like iterations with weight factor. According to the Kung-Traub hypothesis, the new algorithms satisfy the optimality criterion. Taylor’s series expansion is used to examine order of convergence. We also demonstrate the application of new algorithms to real-life problems, i.e., Van der Waals problem, Manning problem, Planck law radiation problem, and Kepler’s problem. Furthermore, the performance comparisons have shown that the given derivative-free algorithms are competitive with existing optimal fourth-order algorithms that require derivative information.

A finite element-scaled boundary finite element coupled method for corner singularities in 2D second-order radiation problems

In potential flow analyses, singularities at the corners of bodies lead to erroneous pressure integrations and unsolved high-order velocity potentials. While much research has been devoted to addressing the former difficulty, fewer solutions have been proposed for the latter. In non-linear problems, higher derivatives are required on the boundaries, but usually, they are inaccurate and even singular at the corners. This paper introduces a coupling method that combines the scaled boundary finite element method (SBFEM) and the finite element method (FEM) to overcome this challenge. The SBFEM is semi-analytic and can accurately describe the singularities; the FEM is enhanced with Adini elements to achieve higher continuity. By integrating them, the proposed method allows for evaluating second derivatives on the body surface. The singular boundary conditions at the corners are automatically satisfied by the SBFEM, enabling the well-posed solution of boundary value problems (BVPs). The implementation of the proposed method is demonstrated through the solution of the second-order radiation problem of a rectangular box, with fine convergence observed for the first- and second-order velocity potentials and their gradients. The method also provides accurate and efficient direct pressure integrations for second-order wave forces, with results in good agreement with established indirect methods.

Benchmark Solutions for Radiative Transfer with a Moving Mesh and Exact Uncollided Source Treatments

The set of benchmark solutions used in the thermal radiative transfer community suffers some coverage gaps, in particular, nonlinear, nonequilibrium problems. Also, there are no nonequilibrium, optically thick benchmarks. These shortcomings motivated the development of a numerical method free from the requirement of linearity and easily able to converge on smooth optically thick problems, i.e., a moving mesh Discontinuous Galerkin framework that utilizes an uncollided source treatment. Having already proven this method on time-dependent scattering transport problems, we present here solutions to nonequilibrium thermal radiative transfer problems for familiar linearized systems together with more physical nonlinear systems in both optically thin and thick regimes, including both the full transport and the / solution. Geometric convergence is observed for smooth sources at all times and some nonsmooth sources at late times when there is local equilibrium. Also, accurate solutions are achieved for step sources when the solution is not smooth.

Space-angle discontinuous Galerkin method for 2D RTE with diffusively and specularly reflective boundary conditions

A space-angle discontinuous Galerkin (saDG) method for solving radiative transfer problems in arbitrary 2D domains is proposed. The space-angle domain is fully discretized by the DG formulation. The angular decomposition scheme is adopted to help accelerate the process by solving the radiative transfer equation iteratively. The performance of the method is analyzed in the square geometry with different types of boundary conditions. We found that the number of iteration or convergence rate of the iteration for the specular reflection problems is not only effected by the number of the reflective surfaces in the domain, but also by the scattering and extinction properties of the media. the uniformly and directionally diffuse reflective boundary conditions are compared in the same medium. In addition, the approach is applied to the simulation of radiative transfer in a parabolic reflector to obtain the localization at the focal point.

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

Axisymmetric geometries, such as cylindrical elements, are widely used in offshore structures. However, the presence of sharp edges in these geometries introduces challenges in numerical simulations due to singularities. To address this issue, one possible solution is to represent the singularities using analytic eigenfunctions. This approach can provide insights into the essence of the problem and has successfully applied to two-dimensional (2D) corner problems. However, finding appropriate eigenfunctions for the three-dimensional (3D) edges remains an open challenge. This paper proposes a semi-analytic scheme for 3D axisymmetric problems utilizing a scaled boundary finite element method (SBFEM). A dimensional reduction is introduced to the 3D Laplace equation, and a 3D edge is handled on the generatrix plane while governed by a complicated equation. The algorithm for resolving the SBFEM fundamental space is improved, and the singularities are approximated using a fractional-order basis. The effectiveness of the proposed method is demonstrated through its application to solve the radiation problem of a heaving cylinder. The method accurately captures the singular velocity field at the edge tip, ensuring that the boundary condition on the body surface is strictly satisfied in the neighborhood of the singularity. Accuracy of the mean drift force is ensured by performing direct pressure integrations over the body surface using a near-field formulation, which becomes as accurate as the middle-field formulation.

Electromagnetic Radiation of Accelerated Charged Particle in the Framework of a Semiclassical Approach

AbstractThe problem of the electromagnetic radiation produced by charge distributions in the framework of a semiclassical approach proposed in the work by Bagrov, Gitman, Shishmarev, and Farias Jr. [J. Synchrotron Rad. 27, 902–911 (2020)] is addressed here. In this approach, currents, generating the radiation are considered classically, while the quantum nature of the radiation is kept exactly. Quantum states of the electromagnetic field are solutions of Schrödinger's equation, and relevant quantities to the problem are evaluated with the aid of transition probabilities. This construction allows us to introduce the quantum transition time in physical quantities and assess its role in radiation problems by classical currents. Radiated electromagnetic energies are studied in detail and a definition for the rate at which radiation is emitted from sources is presented. In calculating the total energy and rate radiated by a pointlike charged particle accelerated by a constant and uniform electric field, it is discovered that these results are compatible with results obtained by other authors in the framework of the classical radiation theory under an appropriate limit. Numerical and asymptotic analyses of the results are also performed.

Angular-spatial discontinuous Galerkin method for radiative heat transfer with a participating medium in complex three-dimensional geometries

The angular-spatial discontinuous Galerkin method (ASDGM) is a numerical technique developed to solve the radiative transfer equation (RTE) in complex three-dimensional geometries with absorbing, emitting, and scattering media. The ASDGM discretizes both the angular and spatial domains of the RTE using structured quadrilateral elements for the angular domain and unstructured tetrahedral elements for the spatial domain. In the solution process, the Riemann upwind solver separates the input and output information at the tetrahedral element boundary. Moreover, the discontinuous Galerkin (DG) sweep algorithm optimizes the order of the unstructured tetrahedral elements and reduces memory usage caused by the coupling of the discretization in the angular and spatial domains. The performance of the ASDGM has been evaluated using several radiative transfer cases in complex three-dimensional geometries, which demonstrate its good accuracy compared to available data from the literature. Additionally, the computational time in the angular domain for high-order DG is lower than that of the finite element method for the same discrete angles. Furthermore, the DG sweep algorithm provides a faster convergence rate in the spatial domain compared to the original sweep algorithm. Therefore, the ASDGM with the DG sweep algorithm is a preferable method for solving radiative transfer problems in complex three-dimensional geometries.

Discontinuous Galerkin Integral Equation Approach for Electromagnetic Modeling of Realistic and Complex Radiating Systems

An electric field integral equation (EFIE) discontinuous Galerkin (DG) formulation for the electromagnetic radiation analysis of realistic antennas is presented. Radiation problems are known to be computationally challenging, involving complex multiscale geometries often made up of a collection of closed and open surfaces. This complexity points to the convenience of separately building and meshing parts with different characteristics, either physical or geometric. This piecewise modelling approach is also desirable in the context of design optimization processes. The proposed formulation fits perfectly into this context by enabling the assembly of independently-meshed surfaces, yet without the need to enforce mesh conformity along the junction contours. The continuity of the normal components of the equivalent current at junctions is enforced using the interior penalty (IP) concept, which is extended to multiple conducting surfaces meeting at a junction.

An MLFMA-Based Eigenmode Theory for Electromagnetic Scattering Analysis From Electrically Large and Complex Conducting Objects

The eigenmode theory, which uses the modal currents solved from surface differential equations (SDEs) as the basis functions of the method of moment (MoM), has been applied to the analysis of electromagnetic scattering and radiation problems of electrically small and simple perfect electrically conducting (PEC) objects. In this article, a multilevel fast multipole algorithm (MLFMA)-based eigenmode theory is presented for analyzing electromagnetic scattering from electrically large and complex PEC objects. The method applies the MLFMA to accelerate the matrix-vector multiplications involved in filling the dense impedance matrix and therefore is much more efficient than the conventional eigenmode theory, especially for electrically large objects. Meanwhile, the way to determine a priori the number of the required modal currents for arbitrarily shaped objects is presented, which makes the MLFMA-based eigenmode theory applicable to the scattering analysis from complex objects. Numerical results verify the accuracy and efficiency of the proposed method.

Fe3O4 and Ag micro/nano coating for high-efficiency flame retardancy and electromagnetic interference shielding

In order to solve the growing problem of electromagnetic radiation and accidental fires due to heat accumulation or electric heating smart clothing, electromagnetic shielding materials with fire resistance are urgently needed. Herein, a polydopamine-assisted polysulfonamide (PSA) nonwoven fabric was designed as a hydrophilic substrate and nano‑silver was employed as a conductive layer. A mixed solution of Fe3O4 with ammonium polyphosphate (APP) was further treated to obtain the surface of microspheres with incombustibility. Interestingly, the micro-nano electromagnetic wave loss gradient enabled the PSA/Ag/Fe3O4/APP-1(PSA/AFA-1) fabric to exhibit efficient absorption-dominant electromagnetic shielding performance, and the optimized fabric exhibited an EMI SE value of 45.5 dB at X-band (8.2–12.4 GHz) with a shielding efficiency of 99.99 %, which remained stable under multiple twisting and bending. This study opens up a new idea for the preparation of fireproof EMI shielding materials with broad application prospects as well as next-generation multi-purpose garments.

Analytical solutions for diffraction and radiation problems of an infinitely long floating compound breakwater with wide porous media

Presented herein is the analytical formulation for obtaining the hydrodynamic solutions of an infinitely long floating compound breakwater with wide porous media. Both the diffraction and radiation problems are tackled and the eigenfunction expansion method is used to obtain solutions based on the linear potential theory. The present formulation is versatile as floating box-type and compound-type breakwaters can be treated in the same formulation by changing porosity ε. The analytical solutions obtained by the present method are first verified for two limiting cases (ε=0or1) by using the authors’ numerical computer algorithm. Next, for the intermediate cases with porosity ranging between 0 and 1, the wave exciting forces are evaluated at the near-field and far-field. This implies that if the results obtained in two independent ways are agreeable, it can be said that both the diffraction and radiation problems are correctly solved. By using the verified formulation, parametric studies are conducted to investigate the wide porous media effects on major hydrodynamic quantities of a floating compound breakwater. The present formulation is useful as a benchmarking tool when developing a numerical algorithm or conducting an experiment for a floating breakwater with wide porous media.

Hydrodynamic coefficients in heave of a moonpool-type floater using theoretical, numerical and CFD methodologies

The present paper deals with the solution of the hydrodynamic radiation problem in the heave direction for a moonpool-type floater, which is exposed to the action of regular surface waves, in finite depth waters. For the solution of the problem three different computation methods were implemented and compared: a theoretical approach solving analytically the problem around the moonpool floater; a numerical panel methodology which uses pulsating singularities distributed over the floater's wetted surface to describe the fluid flow around it; and a computational fluid dynamics (CFD) solver considering the viscous effects near the body's sharp edges as non-negligible. Numerical results are given from the comparison of the three formulations, and some interesting phenomena created by the confined fluid resonance were discussed.

Semi-analytical method for solving the anti-plane seismic dynamic response of steep slope site in a layered half-space

In order to calculate the anti-plane seismic dynamic response of steep slope in a layered site, a semi-analytical method is proposed. The total wave fields are decomposed into known free-field waves with regular boundary conditions and scattered wave fields caused by the known wave fields acting at the irregular boundary of the steep slope. The problem of solving scattering fields is then transformed from the external input problem of the seismic waves to the internal radiation problem by applying the equivalent seismic loads on the irregular boundary of a steep slope site. Then, a modified scaled boundary finite element method (SBFEM) using splicing lines rather than a point as scaling center to computer the internal radiation problem of the steep slope site analytically along the radial direction and numerically along the curvilinear direction. Numerical examples are used to verify the accuracy, effectiveness, and convergence of this method. Finally, a parametric study of the seismic response of a steep slope in a layered half-space is performed in frequency domain. The results show that the amplification peak occurs at the incident wave angle is 30° for vertical slope. For non-vertical slope, the maximum displacement all occur at the position away from one times slope height form the crest of the slope. Moreover, compared with vertical slope, the topography effect of inclined steep slope is more obvious, and this effect tends to decrease with the increase of the slope angle. Therefore, it can be concluded that the angle of the incident wave and slope angle have a significant effect on the dynamic response of the steep slope.