195 research outputs found
Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme
A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model
Thin presentation of knots and lens spaces
This paper concerns thin presentations of knots K in closed 3-manifolds M^3
which produce S^3 by Dehn surgery, for some slope gamma. If M does not have a
lens space as a connected summand, we first prove that all such thin
presentations, with respect to any spine of M have only local maxima. If M is a
lens space and K has an essential thin presentation with respect to a given
standard spine (of lens space M) with only local maxima, then we show that K is
a 0-bridge or 1-bridge braid in M; furthermore, we prove the minimal
intersection between K and such spines to be at least three, and finally, if
the core of the surgery K_gamma yields S^3 by r-Dehn surgery, then we prove the
following inequality: |r| <= 2g, where g is the genus of K_gamma.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-23.abs.htm
Numerical bifurcation of predator-prey fractional differential equations with a constant rate harvesting
In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system
Universality in Systems with Power-Law Memory and Fractional Dynamics
There are a few different ways to extend regular nonlinear dynamical systems
by introducing power-law memory or considering fractional
differential/difference equations instead of integer ones. This extension
allows the introduction of families of nonlinear dynamical systems converging
to regular systems in the case of an integer power-law memory or an integer
order of derivatives/differences. The examples considered in this review
include the logistic family of maps (converging in the case of the first order
difference to the regular logistic map), the universal family of maps, and the
standard family of maps (the latter two converging, in the case of the second
difference, to the regular universal and standard maps). Correspondingly, the
phenomenon of transition to chaos through a period doubling cascade of
bifurcations in regular nonlinear systems, known as "universality", can be
extended to fractional maps, which are maps with power-/asymptotically
power-law memory. The new features of universality, including cascades of
bifurcations on single trajectories, which appear in fractional (with memory)
nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201
A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control
Many boundary controlled and observed Partial Differential Equations can be represented as port-Hamiltonian systems with dissipation, involving a Stokes-Dirac geometrical structure together with constitutive relations. The Partitioned Finite Element Method, introduced in Cardoso-Ribeiro et al. (2018), is a structure preserving numerical method which defines an underlying Dirac structure, and constitutive relations in weak form, leading to finite-dimensional port-Hamiltonian Differential Algebraic systems (pHDAE). Different types of dissipation are examined: internal damping, boundary damping and also diffusion models
Erratum to: Scaling up strategies of the chronic respiratory disease programme of the European Innovation Partnership on Active and Healthy Ageing (Action Plan B3: Area 5).
[This corrects the article DOI: 10.1186/s13601-016-0116-9.]
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