In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for mixed formulation fourth-order problems. The derivation follows de Rham paradigm, leading to arbitrary-order construction that applies meshes composed general polygonal elements. is then used derive numerical scheme Kirchhoff–Love plates, which full stability and convergence analy...

An important issue in the development of higher-order methods for incompressible and low Mach number flows is how they perform when the flow is turbulent. A useful diagnostic of a method for turbulent flow is the minimum resolution that is required to adequately resolve the turbulent energy cascade at a given Reynolds number. In this paper, we present careful numerical experiments to assess the...

The purpose of this work is the derivation of closed form expressions for the linear vibration modes of catenary-shaped slender structures. The dynamic behaviour of the structure is described using the Euler–Bernoulli beam formulation with variable tension and angle terms. The desired expressions are obtained by treating the governing fourth-order partial differential equation of dynamic equili...

We consider the stability of equilibrium positions in the planar circular restricted four-body problem formulated on the basis of Lagrange’s triangular solution of the three-body problem. The stability problem is solved in a strict nonlinear formulation on the basis of Arnold–Moser and Markeev theorems. Peculiar properties of the Hamiltonian normalization are discussed, and the influence of the...

This short article is a brief account of the usage of fourth-order curvature flow in surface modelling.

We study travelling wave solutions for a class of fourth order parabolic equations. Travelling wave fronts of the form u(x, t) = U(x + ct), connecting homogeneous states, are proven to exist in various cases: connections between two stable states, as well as connections between an unstable and a stable state, are considered.

Efficient direct solvers based on the Chebyshev-Galerkin methods for second and fourth order equations are presented. They are based on appropriate base functions for the Galerkin formulation which lead to discrete systems with special structured matrices which can be efficiently inverted. Numerical results indicate that the direct solvers presented in this paper are significantly more accurate...

The approach combines second and fourth order statistics to perform BSS of instantaneous mixtures. It applies for any number of receivers if they are as many as sources. It is a batch algorithm that uses non-Gaussianity and stationarity of source signals. It is linear algebra based direct method, reliable and robust, though large dimensions of sources may slow down the computation significantly...

The study of parameter estimation under additive and multiplicative noise terms constitutes an interesting signal processing research topic with important consequences in the development of high-performance digital communication receivers. In this sense, the paper addresses the analysis of non-assisted digital synchronizers based on up to fourthorder moments and it shows how this alternative ou...