8,316 Results Found

Sustainable functionalization of renewable aromatics is a key step to supply our present needs for specialty chemicals and pursuing the transition to a circular, fossil-free economy. In the present work, three typically stable aromatic compounds, rep...

The ability of charcoal, a low-cost material derived from biomass pyrolysis, to be functionalized via cation exchange in an aqueous solution, providing new interesting fillers with possible antimicrobial and flame-retardant properties, is discussed h...

Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry deve...

Beam models are widely applied in civil engineering, transport, and industry because the beams are basic structural elements. When dealing with the high-order modes of beam in the context of applying the modal analysis method, the numerical instabili...

Green’s functions for Neumann boundary conditions have been considered in Math, Physics, and Electromagnetism textbooks, but often with mistakes of omission and commission. Special constraints and other properties required for Neumann boundary...

We look at estimates for the Green’s function of time-fractional evolution equations of the form $D_{0+\ast }^{\nu }u=Lu$ , where $D_{0+\ast }^{\nu }$ is a Caputo-type time-fractional derivative, depending on a Lév...

The present paper is dedicated to the examination of maximum and minimum results based on Green’s functions via delta fractional differences for a class of fractional boundary problems. For such a purpose, we built the corresponding Green&rsquo...

Green’s functions for linear two-point boundary-value problems subject to non-homogeneous Neumann’s boundary conditions are derived. It is shown that, for the differential operator $L\left(y\right)=y^{″}+ky$ with $k\ne n\pi /L$ where n is a natural n...

In marine hydrodynamics, the core of the boundary element method (BEM) lies in the numerical calculation of the free-surface Green’s function. With the rise of artificial intelligence, using neural networks to fit Green’s function has bec...

This work addresses the Cauchy problem for a linear equation with a first-order time derivative t and an arbitrary-order spatial derivative x. This equation is a generalization of the linear heat equation of the second order in the case of arbitrary...

In this paper, we introduce a mathematical framework for analyzing and optimizing district heating networks by leveraging the Green’s function method. Traditional numerical methods for simulating district heating networks often face computation...

In this paper, we were interested in obtaining the exact expression and studying the regions of constant sign of Green’s function related to a second-order perturbed periodic problem coupled with integral boundary conditions at the extremes of the in...

A generalization of the efficient interpolation of periodic Green’s functions is presented for a multilayer medium hosting transverse electric current densities and transverse equivalent magnetic current densities at different interfaces. The m...

In the first part of our review paper, we consider the problem of approximating the Green’s function of the Lagrange chain by continuous analogs. It is shown that the use of continuous equations based on the two-point Padé approximants g...

We construct a Green’s function for the three-term fractional differential equation $-D_{0+}^{\alpha }u+a{D}_{0^{+}}^{\mu }u+f\left(t\right)u=h\left(t\right)$, $0<t<b$, where $\alpha \in (2,3]$, $\mu \in (1,2]$, and f is continuous, satisfying the boundary conditions $u\left(0\right)=u^{\&}$...

Understanding the characteristics of underwater sound channels is essential for various remote sensing applications. Typically, the time-domain Green’s function or channel impulse response (CIR) is obtained using computationally intensive acous...

A novel time-domain Green’s function is developed for dealing with two-dimensional interaction between water waves and floating bodies with considering viscous dissipation effects based on the “fairly perfect fluid” model. In the Green’s function, th...

The paper gives an explicit representation of the Green’s function of the Dirichlet boundary value problem for the polyharmonic equation in the unit ball. The solution of the homogeneous Dirichlet problem is found. An example of solving the hom...

The frequency-domain free-surface Green’s function method is widely used in solving ship hydrodynamic problems, with its core challenge lying in the computation of the Green’s function and its partial derivatives. This study analyzes the...

Elliptic fuzzy PDEs bridge deterministic models and real-world uncertainty, enabling rigorous modelling of steady-state systems with imprecise parameters. The Green’s function method has been widely recognized as an effective technique for inve...

The Hermite-Hadamard inequalities for $\kappa$-Riemann-Liouville fractional integrals (R-LFI) are presented in this study using a relatively novel approach based on Abel-Gontscharoff Green’s function. In this new technique, we first established...

Dyadic Green’s function (DGF) is a powerful and elegant way of solving electromagnetic problems in the multilayered media. In this paper, we introduce the electric and magnetic DGFs in free space, respectively. Furthermore, the symmetry of diff...

The dyadic Helmholtz Green’s function for electromagnetic (EM) wave transmission/ diffraction through a subwavelength nano-hole in a two-dimensional (2D) plasmonic layer is discussed here analytically and numerically, employing “contact p...

Several iterative integro-differential formulations for two-point, second- and third-order, nonlinear, boundary-value problems of ordinary differential equations based on Green’s functions and the method of variation of parameters are presented...

In atomic and many-particle physics, Green functions often occur as propagators to formally represent the (integration over the) complete spectrum of the underlying Hamiltonian. However, while these functions are very crucial to describing many secon...

An exponentially graded magneto-electro-elastic (MEE) half-plane subjected to anti-plane mechanical and in-plane electric and magnetic time-harmonic external load is considered. Green’s function in the MEE half-plane is analytically derived usi...

In this paper, we examine a fourth-order equation that has parameter dependency and boundary conditions in three different places. We prove some of the features of the relevant asymmetric Green’s function and infer its exact form. The resulting...

The particular solutions of inhomogeneous differential equations with polynomial coefficients in terms of the Green’s function are obtained in the framework of distribution theory. In particular, discussions are given on Kummer’s and the hypergeometr...

According to the Riemann mapping theorem, for an arbitrary simply connected domain B ⊂ C and a point ...

We consider a Keller–Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity in the system is removed via the inverse Hopf–Cole transformation. We then linearize the system around a constant equilibri...

In this paper, we obtain the explicit expression of the Green’s function related to a general n-th order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, an n dimensional parameter dependence is also...

The meteorology data assimilation applications often encounter variational problems with unknown weights, where the corresponding Euler equation is an elliptic partial differential equation. This research focused on retrieving the weights in remote s...

Green’s function plays an important role in the relationship of a future strong earthquake epicenter to the average earthquake potential score. In the frame of the latter, the fractal dimension of the unified scaling law for earthquakes natural...

A novel time-domain body-nonlinear Green’s function method is developed for evaluating large-amplitude roll damping of two-dimensional floating bodies with consideration of viscous dissipation effects. In the method, the instantaneous wetted surface...

A method was proposed for solving the dyadic Green’s functions (DGF) and scalar Green’s functions (SGF) of multi-layered plane media in this paper. The DGF and SGF were expressed in matrix form, where the variables of the boundary conditions (BCs) ca...

The computation of Green’s function is a basic and time-consuming task in realizing seismic imaging using integral operators because the function is the kernel of the integral operators and because every image point functions as the source poin...

High-rise buildings are inherently vulnerable to substantial wind-induced forces. The increasing complexity of building designs has posed challenges in calculating wind loads, while traditional methods involving physical models have proven to be intr...

In this article, we study a fractional lower-order differential equation, $-D_{0+}^{\alpha }{\rm Y}\left(\xi \right)+\mathrm{a}\left(\xi \right){\rm Y}\left(\xi \right)=\mathrm{y}\left(\xi \right),\xi \in (0,1),\alpha \in (1,2),$ with a Dirichlet-type boundary condition, where $\mathrm{a}\left(\xi \right)\in L^1[0,1]$ permits...

The paper investigates the dynamics of the thermal field of the ACCC (aluminum conductor composite core) line. The system was heated by solar radiation and current flow. Conductor cooling was modeled using the total heat transfer coefficient as the s...

Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green’s function. In a paper, the problem is treated in dist...

By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has on...

This manuscript aims to assess some new refinements of right Hadamard’s and Simpson’s-like inequalities by bridging the concepts of Green function theory and convexity framework. It is a known fact that Green functions are convex and symm...

Terrestrial water storage (TWS) is an important indicator of the hydrological cycle. In this study, GNSS-derived TWS changes across the contiguous United States and southern Canada were estimated using Green’s function (GF) and Slepian basis fu...

Seismic oceanography can provide a two- or three-dimensional view of the water column thermocline structure at a vertical and horizontal resolution from the multi-channel seismic dataset. Several seismic imaging methods and techniques for seismic oce...

In this work we present a formalism based on scalar Green’s functions to deal with electromagnetic scattering problems. Although the formulations of the Mie theory and Born approximations in terms of electromagnetic scattering are well known an...

The stochastic Green’s function method has been widely used in the field of ground motion simulation in recent years. It is generally assumed that the rise time of each subfault is the same in this method. Since the rise time significantly infl...

In this paper, we consider a fourth-order three-point boundary value problem. Despite the fact that the corresponding Green’s function changes its sign on the square of its definition, we obtain the existence of at least one positive and decrea...

A compact high-selective band-pass frequency selective surface (FSS) with the unit cell less than λ/7 is presented. For the simulation of the structure, the multilevel Green’s function interpolation method (MLGFIM) using Floquet theory i...

The applicability ranges of macroscopic and microscopic electromagnetism are contrasting. While microscopic electromagnetism deals with point sources, singular fields, and discrete atomistic materials, macroscopic electromagnetism concerns smooth ave...

Green design pursues maximum economic efficiency and minimum environmental impact. Green design of mechanical equipment can ensure environmentally friendly design and manufacturing. A rust-off machine is a crucial piece of equipment in remanufacturin...