Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotiv...

C = ladder network stage capacitance E = difference operator L = ladder network stage inductance ‘ = number of ladder network stages m = voltage measurement node n = ladder network node identifier, 0 n ‘ Rt = termination resistance s = Laplace variable V t = transmission line driving signal ~ Vn = Laplace transform of the voltage at any node n x = length of transmission line min = smallest wave...

Considering a grid cell with a single central point the solution of the discretized Laplace equation may be conceived as a weighted average of points on the cell boundary. Our grid control method is based on a local perturbation of the numerical solution to the Laplace equation by specifying line-wise central target points relative to the orientation of and the distance from the cell’s bounding...

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governi...

We introduce stochastic Discrete Laplacian Growth and consider its deterministic continuous version. These are reminiscent respectively to well-known Diffusion Limited Aggregation and Hele-Shaw free boundary problem for the interface propagation. We study correlation between stability of deterministic free-boundary problem and macroscopic fractal growth in the corresponding discrete problem. It...

We relate the fractional powers of the discrete Laplacian with a standard time-fractional derivative in the sense of Liouville by encoding the iterative nature of the discrete operator through a time-fractional memory term.

In this paper, we introduce two new flexible families of unimodal circular distributions obtained by wrapping onto the unit circle two recently explored heavytailed distributions defined on the real line. The first, the four-parameter wrapped normal–Laplace distribution, is nested within the second, the five-parameter wrapped generalized normal–Laplace distribution. Both families contain the wr...