This paper discusses the effect of nonuniform varying communication delay on distributed consensus algorithms in discrete time. After introducing the delayed mathematical model, we first investigate the ergodicity of the delayed system using the properties of scrambling matrices. Subsequently, the effect of nonuniform varying delay on convergence is examined. It is shown theoretically that nonu...

This article is focused on a fractography study of cleavage cracking at triple grain boundary junctions in freestanding silicon thin films. At a triple junction, as the crystallographic orientations of the two grains ahead of the crack are different by only a few degrees, the cleavage front advance becomes quite jerky. The crack first enters the grain of smaller boundary toughness and then turn...

Self-organization of dislocation structures, slip line and band patterning, and macroscopic plastic instabilities are typical manifestations, at different scales of observation, of nonlinear cooperative phenomena. This general aspect is discussed with emphasis on the relations between the dynamic properties of dislocations, their collective behavior, the local plastic properties of a material a...

An efficient algorithm is presented for the computation of Fourier coefficients of piecewise-polynomial densities on flat geometric objects in arbitrary dimension and codimension. Applications range from standard nonuniform FFTs of scattered point data, through line and surface potentials in two and three dimensions, to volumetric transforms in three dimensions and higher. Input densities are s...

We give an exact solution of the 5D Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by th...

The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows on Banach spaces. The obtained results clarify differences between the uniform and nonuniform cases. Some examples are included to illustrate the results.

The aim of this paper is to present necessary and sufficient conditions for nonuniform power instability property of linear discrete-time systems in Banach spaces. A characterization of the nonuniform power instability in terms of Lyapunov sequences is also given.