Metastable energy strata in numerical discretizations of weakly nonlinear wave equations [PDF]
, 2016 The quadratic nonlinear wave equation on a one-dimensional torus with small initial values located in a single Fourier mode is considered. In this situation, the formation of metastable energy strata has recently been described and their long-time ...
Gauckler, Ludwig, Weiss, Daniel
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Numerical Methods That Preserve a Lyapunov Function for Ordinary Differential Equations [PDF]
, 2022 The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e., numerical approximations whose energy decreases, just like in the original differential equation.
Atencia-Ruiz, Miguel Alejandro +1 more
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A robust numerical method to study oscillatory instability of gap solitary waves [PDF]
, 2004 The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to ...
Alexander J. +3 more
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A universal constitutive model for the interfacial layer between a polymer melt and a solid wall [PDF]
, 2003 In a preceeding report we derived the evolution equation for the bond vector probability distribution function (BVPDF) of tethered molecules. It describes the behavior of polymer molecules attached to a solid wall interacting with an adjacent flowing ...
Molenaar, J. +2 more
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Modulated rotating waves in the magnetized spherical Couette system [PDF]
, 2019 We present a study devoted to a detailed description of modulated rotating waves (MRW) in the magnetized spherical Couette system. The set-up consists of a liquid metal confined between two differentially rotating spheres and subjected to an axially ...
Garcia, F. +3 more
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Numerical study of a thin liquid film flowing down an inclined wavy plane [PDF]
, 2011 International audienceWe investigate the stability of a thin liquid film flowing down an inclined wavy plane using a direct numerical solver based on a finite element/arbitrary Lagrangian Eulerian approximation of the free-surface Navier--Stokes ...
Ern, Alexandre +2 more
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Control of bifurcation structures using shape optimization [PDF]
, 2021 Many problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability or bring forward a bifurcation to enable rapid switching between states.
Boullé, Nicolas +2 more
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Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation [PDF]
, 2017 A contraction metric for an autonomous ordinary differential equation is a Riemannian metric such that the distance between adjacent solutions contracts over time.
A. Iske +23 more
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An invariance kernel representation of ISDS Lyapunov functions [PDF]
, 2005 We apply set valued analysis techniques in order to characterize the input-to-state dynamical stability (ISDS) property, a variant of the well known input-to-state stability (ISS) property. Using a suitable augmented differential inclusion we are able to
Grüne, Lars, Saint-Pierre, Patrick
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Dynamics of chains grafted on solid wall during polymer melt extrusion [PDF]
, 2003 The objective of the present work is the mathematical modeling of the dynamics of polymer molecules grafted on a solid boundary during polymer melt extrusion.
Molenaar, J. +2 more
core +1 more source