A robust numerical method to study oscillatory instability of gap solitary waves

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 eigenvalues. These problems may exhibit oscillatory instabilities where eigenvalues detach from the edges of the continuous spectrum, so called edge bifurcations. A numerical framework, based on a fast robust shooting algorithm using exterior algebra is described. The complete algorithm is robust in the sense that it does not produce spurious unstable eigenvalues. The algorithm allows to locate exactly where the unstable discrete eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows for stable shooting along multi-dimensional stable and unstable manifolds. The method is illustrated by computing the stability and instability of gap solitary waves of a coupled mode model.Comment: key words: gap solitary wave, numerical Evans function, edge bifurcation, exterior algebra, oscillatory instability, massive Thirring model. accepted for publication in SIAD

Kinetic pathways of the Nematic-Isotropic phase transition as studied by confocal microscopy on rod-like viruses

We investigate the kinetics of phase separation for a mixture of rodlike viruses (fd) and polymer (dextran), which effectively constitutes a system of attractive rods. This dispersion is quenched from a flow-induced fully nematic state into the region where the nematic and the isotropic phase coexist. We show experimental evidence that the kinetic pathway depends on the overall concentration. When the quench is made at high concentrations, the system is meta-stable and we observe typical nucleation-and-growth. For quenches at low concentration the system is unstable and the system undergoes a spinodal decomposition. At intermediate concentrations we see the transition between both demixing processes, where we locate the spinodal point.Comment: 11 pages, 6 figures, accepted in J. Phys.: Condens. Matter as symposium paper for the 6th Liquid Matter Conference in Utrech

A stability criterion for the non-linear wave equation with spatial inhomogeneity

In this paper the non-linear wave equation with a spatial inhomogeneity is considered. The inhomogeneity splits the unbounded spatial domain into three or more intervals, on each of which the non-linear wave equation is homogeneous. In such setting, there often exist multiple stationary fronts. In this paper we present a necessary and sufficient stability criterion in terms of the length of the middle interval(s) and the energy associated with the front in these interval(s). To prove this criterion, it is shown that critical points of the length function and zeros of the linearisation have the same order. Furthermore, the Evans function is used to identify the stable branch. The criterion is illustrated with an example which shows the existence of bi-stability: two stable fronts, one of which is non-monotonic. The Evans function also give a sufficient instability criterion in terms of the derivative of the length function

Kinetics of absorption of carbon dioxide in aqueous ammonia solutions

AbstractIn the present work the absorption of carbon dioxide into aqueous ammonia solutions has been studied in a stirred cell reactor, at low temperatures and ammonia concentrations ranging from 0.1 to about 7 kmol m−3. The absorption experiments were carried out at conditions where the so-called pseudo first order mass transfer regime was obeyed–and hence the kinetics of the reaction between carbon dioxide and ammonia could be derived. The results were interpreted according to the well-established zwitterion mechanism

The Combinatorialization of Linear Recurrences

We provide two combinatorial proofs that linear recurrences with constant coefficients have a closed form based on the roots of its characteristic equation. The proofs employ sign-reversing involutions on weighted tilings

Existence of stationary fronts in a system of two coupled wave equations with spatial inhomogeneity

We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, "hat-like" spatial inhomogeneity. The spatial inhomogeneity corresponds to a spatially dependent scaling of the sine-Gordon potential term. The uncoupled inhomogeneous sine-Gordon equation has stable stationary front solutions that persist in the coupled system. Carrying out a numerical investigation it is found that these inhomogeneous sine-Gordon fronts loose stability, provided the coupling between the two inhomogeneous sine-Gordon equations is strong enough, with new stable fronts bifurcating. In order to analytically study the bifurcating fronts, we first approximate the smooth spatial inhomogeneity by a piecewise constant function. With this approximation, we prove analytically the existence of a pitchfork bifurcation. To complete the argument, we prove that transverse fronts for a piecewise constant inhomogeneity persist for the smooth "hat-like" spatial inhomogeneity by introducing a fast-slow structure and using geometric singular perturbation theory

The Effectiveness of Online Stress Management Training Interventions: A Systematic Literature review

The central aim of this systematic literature review study was to investigate the effectiveness of online stress management training interventions that aimed to improve employees’ well-being. The study focused both on the effectiveness of online stress management training interventions and the sustainability of the intervention effects over time. Within this literature review 18 intervention studies, conducted worldwide among 3085 participants between 2002 and 2017, were evaluated. Methodological quality was examined using the Mixed Methods Appraisal Tool (MATT). In general, the main outcomes showed that most of the interventions turned out to be effective in decreasing employees’ levels of stress. In addition, some of these studies also revealed sustainability of intervention effects over time. This suggests that online stress management interventions are a promising tool for organizations to foster employee well-being