In this paper we apply the method proposed in our previous paper [Int. J. Solids Struct. 40(13–14) (2003) 3293] to quantitatively estimate the violation of Saint-Venant s principle in the problem of flexural vibration of a two-dimensional strip. A probabilistic approach is used to determine the relative magnitude of the penetrating stress state and the results of computations are presented as a...

In dynamics, Saint-Venant s principle of exponential decay of stress resulting from a self-equilibrating load is not valid. For a beam type structure, a self-equilibrated load may penetrate well inside the beam. Although this effect has been known for a long time, at least since Lamb s paper [Proc. Roy. Soc. Lon. Ser. A 93 (1916) 114], it was not clear how to characterize it quantitatively. In ...

Most of arithmetically significant Dirichlet series such as the Riemann zeta-function ζ(s), Dirichlet L-functions, and Hecke L-functions associated with various cusp forms satisfy Riemannian functional equations connecting values at s = σ + it and 1 − s of respective functions. Essentially best possible estimates for these functions near the line σ = 1 and σ = 0 can usually be deduced from the ...

In this paper we study the spatial behavior of solutions to the equations obtained by taking formal Taylor approximations to the heat conduction dual-phase-lag and three-phaselag theories, reflecting Saint-Venant’s principle. Depending on the relative order of derivation with respect to the time we propose different arguments. One is inspired by the arguments for parabolic problems and the othe...

In EEG/MEG source analysis, a mathematical dipole is widely used as the “atomic” structure of the primary current distribution. When using realistic finite element models for the forward problem, the current dipole introduces a singularity on the right-hand side of the governing differential equation that has to be treated specifically. We evaluated and compared three different numerical approa...

The election methods introduced in 1894–1895 by Phragmén and Thiele, and their somewhat later versions for ordered (ranked) ballots , are discussed in detail. The paper includes definitions and examples and discussion of whether the methods satisfy some properties, including monotonicity, consistency and various proportionality criteria. The relation with STV is also discussed. The paper also c...

We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Sai...

We study the asymptotic behavior of solutions to variational inequalities with pointwise constraint on the value and gradient of the functions as the domain becomes unbounded. First, as a model problem, we consider the case when the constraint is only on the value of the functions. Then we consider the more general case of constraint also on the gradient. At the end we consider the case when th...

Within the framework of linear viscoelasticity this paper deals with the study of spatial behavior of solutions describing harmonic vibrations in a right cylinder of finite extent. Some exponential decay estimates of Saint–Venant type, in terms of the distance from the excited end of the cylinder are obtained from a first-order differential inequality concerning an appropriate measure associate...

A topological derivative is defined, which is caused by kinking of a crack, thus, representing the topological change. Using variational methods, the anti-plane model of a solid subject to a non-penetration condition imposed at the kinked crack is considered. The objective function of the potential energy is expanded with respect to the diminishing branch of the incipient crack. The respective ...