Green Potential Research Articles

Resonance frequencies of arbitrarily shaped dielectric cylinders

ABSTRACT We consider eigenvalue problems for dielectric cylindrical scatterers of arbitrary cross with generalized conditions at infinity that enable one to take into account complex eigenvalues. The existence of resonance (scattering) frequencies associated with these eigenvalues is proved. The technique involves the determination of characteristic numbers (CNs) of the Fredholm operator-valued functions of the problems constructed using Green's potentials. Separating principal parts in the form of meromorphic operator pencils, we apply the operator generalization of Rouché's theorem to verify the occurrence of CNs in close proximities of the pencil poles. The results are illustrated in detail using the case of a dielectric cylinder of circular cross section.

Assessing the green potential of existing buildings towards smart cities and districts

Buildings represent about 40% of the total primary energy consumption and contribute approximately to one-third of the total greenhouse gas emissions. Green building standards and certification systems include requirements for both new and existing buildings. However, a vast part of the existing building stock in cities was built with limited consideration for green design, energy efficiency and low carbon emissions, yet its refurbishment can help reach national energy reduction goals, decreasing environmental impact. Furthermore, retrofitting existing buildings can often be more cost-effective than building new facilities. The potential of an existing building to achieve certification under a certain Green Standard, defined in this work as its Green Potential (GP), depends heavily on factors that were determined during the original design and construction process. This paper will present the development of a method and tool for the analysis and determination of the GP of existing buildings, allowing quick evaluation of a single building or the comparison of different buildings in order to understand their potential and limitations, both by designers before their intervention or by planning authorities as ways of determining development plans and retrofitting potential in cities and districts.

Integral mean of Green’s potentials and their conjugate

The best possible estimates for Lebesgue integral means $m_q(r,F)\; (1\le q<+\infty)$ for the pair of functions $F= g+i\:\breve{g}$, here $g$ - Green's potential, $\breve{g}$ - function conjugate to $g$, was obtained. It generalizes well-known results of Ya.V. Vasyl'kiv and A.A. Kondratyuk for logarithms $\log\; B$ of Blaschke products $B$ in terms of counting function $n(r,0,B)\; (0<r<1)$ of their zeroes.

Heating of the Beurling operator: Sufficient conditions for the two-weight case

We establish sufficient conditions on the two weights $w$ and $v$ so that the Beurling–Ahlfors transform acts continuously from $L^2(w^{-1})$ to $L^2(v)$. Our conditions are simple estimates involving heat extensions and Green's potentials of the we

Analytical local electron-electron interaction model potentials for atoms

Analytical local potentials for modeling the electron-electron interaction in an atom reduce significantly the computational effort in electronic structure calculations. The development of such potentials has a long history, but some promising ideas have not yet been taken into account for further improvements. We determine a local electron-electron interaction potential akin to those suggested by Green et al. [Phys. Rev. 184, 1 (1969)], which are widely used in atom-ion scattering calculations, electron-capture processes, and electronic structure calculations. Generalized Yukawa-type model potentials are introduced. This leads, however, to shell-dependent local potentials, because the origin behavior of such potentials is different for different shells as has been explicated analytically [J. Neugebauer, M. Reiher, and J. Hinze, Phys. Rev. A 65, 032518 (2002)]. It is found that the parameters that characterize these local potentials can be interpolated and extrapolated reliably for different nuclear charges and different numbers of electrons. The analytical behavior of the corresponding localized Hartree-Fock potentials at the origin and at long distances is utilized in order to reduce the number of fit parameters. It turns out that the shell-dependent form of Green's potential, which we also derive, yields results of comparable accuracy using only one shell-dependent parameter.

METHOD OF SINGULAR INTEGRAL OPERATOR-VALUED FUNCTIONS FOR THE TRANSMISSION LINE PROBLEMS

ABSTRACT The transmission line problem for shielded fin-line structures is studied using integral representation of the field by means of Green's potentials. It is reduced to the eigenvalue problem for the singular integral operator-valued function. Galerkin method is applied for calculating frequency-dependent propagation constants of the normal waves and field components on the slots and strips. Numerical results for the dominant and higher-order modes in various structures are presented.

Variational problem of the theory of Green's potential. II

Necessary and sufficient conditions for the solvability of the problem of the minimum of the Green's energy on condensers are found. A number of properties of extremals are found.

Boundary Behavior of Invariant Green's Potentials on the Unit Ball in C n

Boundary Behavior of Invariant Green's Potentials on the Unit Ball in C n

Boundary behavior of invariant Green’s potentials on the unit ball in 𝐶ⁿ

Let p ( z ) = ∫ B G ( z , w ) d μ ( w ) p(z) = \int _B {G(z,\,w)\,d\mu (w)} be an invariant Green’s potential on the unit ball B B in C n ( n ⩾ 1 ) {{\mathbf {C}}^n}\;(n \geqslant 1) , where G G is the invariant Green’s function and μ \mu is a positive measure with ∫ B ( 1 − | w | 2 ) n d μ ( w ) > ∞ \int _B {{{(1 - |w{|^2})}^n}\,d\mu (w) > \infty } . In this paper, a necessary and sufficient condition on a subset E E of B B such that for every invariant Green’s potential p p , \[ lim z → e inf ( 1 − | z | 2 ) n p ( z ) = 0 , e = ( 1 , 0 , … , 0 ) ∈ ∂ B , z ∈ E , \lim \limits _{z \to e} \,\inf {(1 - |z{|^2})^n}p(z) = 0,\qquad e = (1,\,0,\, \ldots ,\,0)\; \in \partial B,\;z \in E, \] is given. The condition is that the capacity of the sets E ∩ { z ∈ B | | z − e | > ε } E \cap \{ z \in B|\;|z - e| > \varepsilon \} , ε > 0 \varepsilon > 0 , is bounded away from 0 0 . The result obtained here generalizes Luecking’s result, see [L], on the unit disc in C {\mathbf {C}} .

Mechanical, Electrical, and Thermal Fields Produced by Moving Dislocations and Disclinations in Thermo‐Piezoelectric Continua

AbstractThe stress, electrical, and thermal fields produced by a continuous distribution of moving dislocations and disclinations (defects) are studied inanisotropic thermo‐piezoelectric continua. It is assumed that the plastic deformation caused by the movement of the defect does not affect the thermo‐piezoelectric effect of the materials. The electric field is assumed as quasistatic, and the electric charges associated with the defectand the production of heat caused by the movement of the defect are neglected. The expressions for the above‐mentioned fields are given in terms of the defect‐density and defect‐flux tensors by the aid of Green's functions and the dynamic Green's potentials.

Green's and Dirichlet spaces associated with fine Markov processes

This is the second paper in a series devoted to Green's and Dirichlet spaces. In the first paper, we have investigated Green's space K and the Dirichlet space H associated with a symmetric Markov transition function p t ( x, B). Now we assume that p is a transition function of a fine Markov process X and we prove that: (a) the space H can be built from functions which are right continuous along almost all paths; (b) the positive cone K + in K can be identified with a cone M of measures on the state space; (c) the positive cone H + in H can be interpreted as the cone of Green's potentials of measures μ ϵ M. To every measurable set B in the state space E there correspond a subspace K (B) of K and a subspace H (B) of H . The orthogonal projections of K onto K and of H onto H (B) can be expressed in terms of the hitting probabilities of B by the Markov process X. As the main tool, we use additive functionals of X corresponding to measures μ ϵ M.

Boundary limits of Green's potentials along curves II. Lipschitz domains

Boundary limits of Green's potentials along curves II. Lipschitz domains

Green's Potentials with Prescribed Boundary Values

Let U, C denote the open unit disk and unit circumference, respectively and G(z, w) be the Green's function on U. We say v is the Green's potential of a mass distribution v on U if

Boundary limits of Green's potentials along curves

Boundary limits of Green's potentials along curves