Implementation of the Integrated Green’s Function Method for 3D Poisson’s Equation in a Large Aspect Ratio Computational Domain

The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

The Bivariate Normal Integral via Owen’s T Function as a Modified Euler’s Arctangent Series

The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10-16. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

Integral formulations are widely used for full-wave analysis of microstrip interconnects. A weak point of these formulations is the inclusion of the proper planar-layered Green’s Functions (GFs), because of their computational cost. To overcome this problem, usually the GFs are decomposed into a quasi-dynamic term and a dynamic one. Under suitable approximations, the ?rst may be given in closed form, whereas the second is approximated. Starting from a general criterion for this decomposition, in this paper we derive some simple criteria for using the closed-form quasi-dynamic GFs instead of the complete GFs, with reference to the problem of evaluating the full-wave current distribution along microstrips. These criteria are based on simple relations between frequency, line length, dielectric thickness and permittivity. The layered GFs have been embedded into a full-wave transmission line model and the results are ?rst benchmarked with respect to a full-wave numerical 3D tool, then used to assess the proposed criteria.

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.

Multisensory mechanisms of gait and balance in Parkinson’s disease:an integrative review

Understanding the neural underpinning of human gait and balance is one of the most pertinent challenges for 21st-century translational neuroscience due to the profound impact that falls and mobility disturbances have on our aging population.Posture and gait control does not happen automatically,as previously believed,but rather requires continuous involvement of central nervous mechanisms.To effectively exert control over the body,the brain must integrate multiple streams of sensory information,including visual,vestibular,and somatosensory signals.The mechanisms which underpin the integration of these multisensory signals are the principal topic of the present work.Existing multisensory integration theories focus on how failure of cognitive processes thought to be involved in multisensory integration leads to falls in older adults.Insufficient emphasis,however,has been placed on specific contributions of individual sensory modalities to multisensory integration processes and cross-modal interactions that occur between the sensory modalities in relation to gait and balance.In the present work,we review the contributions of somatosensory,visual,and vestibular modalities,along with their multisensory intersections to gait and balance in older adults and patients with Parkinson’s disease.We also review evidence of vestibular contributions to multisensory temporal binding windows,previously shown to be highly pertinent to fall risk in older adults.Lastly,we relate multisensory vestibular mechanisms to potential neural substrates,both at the level of neurobiology(concerning positron emission tomography imaging)and at the level of electrophysiology(concerning electroencephalography).We hope that this integrative review,drawing influence across multiple subdisciplines of neuroscience,paves the way for novel research directions and therapeutic neuromodulatory approaches,to improve the lives of older adults and patients with neurodegenerative diseases.

Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.

Fuzzy Henstock-Kurzweil Triple Integral

In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.

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.

Functional Integrals and Excitation Energy in Three-Band Hubbard Model

The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.

Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex

In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.

THE HADAMARD INEQUALITY FOR CONVEX FUNCTION VIA FRACTIONAL INTEGRALS

In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.

An integrated approach to evaluation on ecological service functions for urban green space and its application

This methodological investigation deals with measurement and valuation of ecological service functions for urban green space. Social, economic and ecological dimensions for such types of function were analyzed and a concept “integrated ecological service functions” (IESF) was put forward for evaluation. Based upon this conceptual approach, an index system for measuring IESF for urban green space was established. With a methodological integration of fuzzy mathematics, decision making analysis and Delphi method, an AHP fuzzy evaluation techniques for IESF for urban green space, called AFIFUG method, was developed. Such a method has been directly applied to the land use strategic planning of Tianjin out ring green belt(TOGB), and its analysis results have been successfully put into operation.

THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS

In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.

Singularity-free Green's function for EM sources embedded in a stratified medium

We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.

The Green's function of the harmonic horizontal force applied at the interior of the saturated half-space soil

By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.

Some Integral Inequalities of Simpson Type for Strongly Extended s-Convex Functions

The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.

The research on the highly efficient calculation method of 3-D frequency-domain Green function

The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the computing process is complex with many cycles, which has greatly affected the computing efficiency. To improve the computing efficiency, this paper introduces Gaussian integral to the numerical calculation of the frequency-domain Green function and its partial derivatives. It then compares the calculation result with that in existing references. The comparison results demonstrate that, on the basis of its sufficient accuracy, the method has greatly simplified the computing process, reduced the zoning and improved the computing efficiency.

纳米分子器件量子传导中的Green's Function模型

将纳米分子器件的电极和分子本体作为一个系统,考虑到入射电子在原子电极和分子本体中的传导,在电极与分子之间界面上的透射的量子状态,在满足Fisher-Lee关系式的基础上,一个新型的Green’sFunction被设计出来。这一理论模型把三个区域上的不同量子状态完整地表达在一个方程式里,符合物理学基本原理,可以系统地用来研究纳米分子器件的量子传导特性。