Green's Functions with Applications

Monte Carlo study of radiation-induced demagnetization using the two-dimensional Ising model

“…We assume that the lattice is initially held at temperature (T 0 ). The solution to the above equation is determined by using the Fourier transform in space and Laplace transform in time [22]:…”

A semi-analytical approach to Green׳s functions for heat equation in regions of irregular shape

“…The comprehensive database of one-dimensional Green's functions for finite and semi-finite regions with different combinations of boundary conditions can be found, for example, in [24,25,27,40]. We will just provide several classical examples:…”

“…The elements of the matrix of Green's type to the problem setting in (39), which are presented in (40), have been used to from kernels of modified heat potentials resolving the problem. Omitting the algorithm's detail, we depict in Figs.…”

Analytical solutions for the coupled thermoelastic vibrations of Timoshenko beams by means of Green׳s functions

“…According to the Sturm-Liouville theory [24], the Dirac function δ(z-z 0 ) can be expanded by eigenfunctions [25], which satisfy the boundary conditions at x=±h/2 in (13).…”