Analysis of a Cavity Used for Medical Purposes with the Dyadic Green's Functions and the Moment method

The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.

Random Green's Function Method for Large-Scale Electronic Structure Calculation

We report a linear-scaling random Green's function(rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi–Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi–Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H_(2)O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H_(2)O clusters at T = 0 K can reach an error of~ 1 me V per H_(2)O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.

A New Speed Limit Recognition Methodology Based on Ensemble Learning:Hardware Validation

Advanced DriverAssistance Systems(ADAS)technologies can assist drivers or be part of automatic driving systems to support the driving process and improve the level of safety and comfort on the road.Traffic Sign Recognition System(TSRS)is one of themost important components ofADAS.Among the challengeswith TSRS is being able to recognize road signs with the highest accuracy and the shortest processing time.Accordingly,this paper introduces a new real time methodology recognizing Speed Limit Signs based on a trio of developed modules.Firstly,the Speed Limit Detection(SLD)module uses the Haar Cascade technique to generate a new SL detector in order to localize SL signs within captured frames.Secondly,the Speed Limit Classification(SLC)module,featuring machine learning classifiers alongside a newly developed model called DeepSL,harnesses the power of a CNN architecture to extract intricate features from speed limit sign images,ensuring efficient and precise recognition.In addition,a new Speed Limit Classifiers Fusion(SLCF)module has been developed by combining trained ML classifiers and the DeepSL model by using the Dempster-Shafer theory of belief functions and ensemble learning’s voting technique.Through rigorous software and hardware validation processes,the proposedmethodology has achieved highly significant F1 scores of 99.98%and 99.96%for DS theory and the votingmethod,respectively.Furthermore,a prototype encompassing all components demonstrates outstanding reliability and efficacy,with processing times of 150 ms for the Raspberry Pi board and 81.5 ms for the Nano Jetson board,marking a significant advancement in TSRS technology.

Study on Characteristics of 3-D Translating-Pulsating Source Green Function of Deep-Water Havelock Form and Its Fast Integration Method

The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green's functions

Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS

The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.

Source time functions of the Gonghe，China earthquake retrieved from long－period digital waveform data using empirical Green＇s function technique

An earthquake of Ms= 6, 9 occurred at the Gonghe, Qinghai Province, China on April 26, 1990. Three larger aftershocks took place at the same region, Ms= 5. 0 on May 7, 1990, Ms= 6. 0 on Jan. 3, 1994 and Ms= 5. 7on Feb. 16, 1994. The long-period recordings of the main shock from China Digital Seismograph Network (CDSN) are deconvolved for the source time functions by the correspondent0 recordings of the three aftershocks asempirical Green's functions (EGFs). No matter which aftershock is taken as EGF, the relative source time functions (RSTFs) Obtained are nearly identical. The RSTFs suggest the Ms= 6. 9 event consists of at least two subevents with approximately equal size whose occurrence times are about 30 s apart, the first one has a duration of 12 s and a rise time of about 5 s, and the second one has a duration of 17 s and a rise time of about & s. COmParing the RSTFs obtained from P- and SH-phases respectively, we notice that those from SH-phases are a slightly more complex than those from p-phases, implying other finer subevents exist during the process of the main shock. It is interesting that the results from the EGF deconvolution of long-Period way form data are in good agreement with the results from the moment tensor inversion and from the EGF deconvolution of broadband waveform data. Additionally, the two larger aftershocks are deconvolved for their RSTFs. The deconvolution results show that the processes of the Ms= 6. 0 event on Jan. 3, 1994 and the Ms= 5. 7 event on Feb. 16,1994 are quite simple, both RSTFs are single impulses.The RSTFs of the Ms= 6. 9 main shock obtained from different stations are noticed to be azimuthally dependent, whose shapes are a slightly different with different stations. However, the RSTFs of the two smaller aftershocks are not azimuthally dependent. The integrations of RSTFs over the processes are quite close to each other, i. e., the scalar seismic moments estimated from different stations are in good agreement. Finally the scalar seismic moments of the three aftershocks are compared. The relative scalar seismic moment Of the three aftershocks deduced from the relative scalar seismic moments of the Ms=6. 9 main shock are very close to those inverted directly from the EGF deconvolution. The relative scalar seismic moment of the Ms =6. 9 main shock calculated using the three aftershocks as EGF are 22 (the Ms= 6. 0 aftershock being EGF), 26 (the Ms= 5. 7 aftershock being EGF) and 66 (the Ms= 5. 5 aftershock being EGF), respectively. Deducingfrom those results, the relative scalar sesimic moments of the Ms= 6. 0 to the Ms= 5. 7 events, the Ms= 6. 0 tothe Ms= 5. 5 events and the Ms= 5. 7 to the Ms= 5. 5 events are 1. 18, 3. 00 and 2. 54, respectively. The correspondent relative scalar seismic moments calculated directly from the waveform recordings are 1. 15, 3. 43, and 3. 05.

Finite Volume Time Domain with the Green Function Method for Electromagnetic Scattering in Schwarzschild Spacetime

The finite volume time domain(FVTD) algorithm and Green function algorithm are extended to Schwarzschild spacetime for numerical simulation of electromagnetic scattering. The FVTD method in Schwarzschild spacetime is developed by filling the flat spacetime with an equivalent medium. The Green function in Schwarzschild spacetime is acquired by solving initial value problems. Both the FVTD code and the Green function code are validated by numerical results. Scattering in Schwarzschild spacetime is simulated with these methods.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.

Green Functions with Pulsating Sources in A Two-Layer Fluid of Finite Depth

The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.

Review of Collocation Methods and Applications in Solving Science and Engineering Problems

The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

Time Domain Rankine-Green Panel Method for Offshore Structures

To solve the numerical divergence problem of the direct time domain Green function method for the motion simulation of floating bodies with large flare, a time domain hybrid Rankine-Green boundary element method is proposed. In this numerical method, the fluid domain is decomposed by an imaginary control surface, at which the continuous condition should be satisfied. Then the Rankine Green function is adopted in the inner domain. The transient free surface Green function is applied in the outer domain, which is used to find the relationship between the velocity potential and its normal derivative for the inner domain. Besides, the velocity potential at the mean free surface between body surface and control surface is directly solved by the integration scheme. The wave exciting force is computed through the convolution integration with wave elevation, by introducing the impulse response function. Additionally, the nonlinear Froude-Krylov force and hydrostatic force, which is computed under the instantaneous incident wave free surface, are taken into account by the direct pressure integration scheme. The corresponding numerical computer code is developed and first used to compute the hydrodynamic coefficients of the hemisphere, as well as the time history of a ship with large flare; good agreement is obtained with the analytical solutions as well as the available numerical results. Then the hydrodynamic properties of a FPSO are studied. The hydrodynamic coefficients agree well with the results computed by the frequency method; the influence of the time interval and the truncated time is investigated in detail.

FROM WAVE FUNCTIONS TO TAU-FUNCTIONS FOR THE VOLTERRA LATTICE HIERARCHY

For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green’s function method for neutron-rich Ca,Ni,Zr,and Sn isotopes

The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Two-Stream Approximation to the Radiative Transfer Equation:A New Improvement and Comparative Accuracy with Existing Methods

Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.