Related papers: Dynamic Green's functions in discrete flexural sys…
Elastic effects due to lattice strain modify the local equilibrium condition at the solid-solid interface compared to the classical dendritic growth. Both, the thermal and the elastic fields are eliminated by the Green's function techniques…
Scattering of waves due to a vertical array of equally-spaced cracks on a square lattice is studied. The convenience of Floquet periodicity reduces the study to that of scattering of specific wave-mode from single crack in a waveguide. The…
We study a discrete model of the Laplacian in $\mathbb{R}^2$ that preserves the geometric structure of the original continual object. This means that, speaking of a discrete model, we do not mean just the direct replacement of differential…
Two novel version of weak form quadrature elements are proposed based on Lagrange and Hermite interpolations, respectively, for a sec- ond strain gradient Euler-Bernoulli beam theory. The second strain gradient theory is governed by eighth…
The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems ranging from molecules to solids, and it gives rise to a plethora of physical phenomena experimentally accessible using…
We discuss the imaging properties of uniaxial epsilon-near-zero metamaterial slabs with possibly tilted optical axis, analyzing their sub-wavelength focusing properties as a function of the design parameters. We derive in closed analytical…
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and…
In this paper we shall propose a simple scheme for calculating Green's functions for photons propagating in complex structured dielectrics or other photonic systems. The method is based on an extension of the finite difference time domain…
This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an…
The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time…
Within the framework of time-dependent density functional theory combined with the Korringa-Kohn-Rostoker Green function formalism, we present a real space methodology to investigate dynamical magnetic excitations from first-principles. We…
In this technical report, we present estimations of the discrete Green's function of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes for singularly perturbed problems with characteristic layers.
We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
The equilibrium state of a system consisting of a large number of strongly interacting electrons can be characterized by its density operator. This gives a direct access to the ground-state energy or, at finite temperatures, to the free…
We investigate the geometrically nonlinear deformation and buckling of a slender elastic beam subject to time-dependent `fictitious' (non-inertial) forces arising from unsteady rotation. Using a rotary apparatus that accurately imposes an…
We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by…
This work focuses on the stability analysis of an Euler Bernoulli cantilever beam with a tip mass at the free end, subject to a follower force. This can serve as a viable model for analysis of elastic instability occurring due to…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence…