2,093 research outputs found
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
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