56 research outputs found
Bifurcation analysis of rotating axially compressed imperfect nano-rod
Static stability problem for axially compressed rotating nano-rod clamped at
one and free at the other end is analyzed by the use of bifurcation theory. It
is obtained that the pitchfork bifurcation may be either super- or
sub-critical. Considering the imperfections in rod's shape and loading, it is
proved that they constitute the two-parameter universal unfolding of the
problem. Numerical analysis also revealed that for non-locality parameters
having higher value than the critical one interaction curves have two branches,
so that for a single critical value of angular velocity there exist two
critical values of horizontal force
Global Bifurcation of Rotating Vortex Patches
We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid velocity in the rotating frame becomes arbitrarily small. This is consistent with the conjectured existence [30, 38] of singular limiting patches with 90 corners at which the relative fluid velocity vanishes. For solutions close to the disk, we prove that there are “cat's-eyes”-type structures in the flow, and provide numerical evidence that these structures persist along the entire solution curves and are related to the formation of corners. We also show, for any rotating vortex patch, that the boundary is analytic as soon as it is sufficiently regular.</p
Hopf bifurcation in a gene regulatory network model:Molecular movement causes oscillations
Gene regulatory networks, i.e. DNA segments in a cell which interact with
each other indirectly through their RNA and protein products, lie at the heart
of many important intracellular signal transduction processes. In this paper we
analyse a mathematical model of a canonical gene regulatory network consisting
of a single negative feedback loop between a protein and its mRNA (e.g. the
Hes1 transcription factor system). The model consists of two partial
differential equations describing the spatio-temporal interactions between the
protein and its mRNA in a 1-dimensional domain. Such intracellular negative
feedback systems are known to exhibit oscillatory behaviour and this is the
case for our model, shown initially via computational simulations. In order to
investigate this behaviour more deeply, we next solve our system using Green's
functions and then undertake a linearized stability analysis of the steady
states of the model. Our results show that the diffusion coefficient of the
protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf
bifurcation. This shows that the spatial movement of the mRNA and protein
molecules alone is sufficient to cause the oscillations. This has implications
for transcription factors such as p53, NF-B and heat shock proteins
which are involved in regulating important cellular processes such as
inflammation, meiosis, apoptosis and the heat shock response, and are linked to
diseases such as arthritis and cancer
Smoothness of global positive branches of nonlinear elliptic problems over symmetric domains
On the gas-chromatographic determination of diethylcarbonate (DEC) in diethyldioarbonate (DEDC)
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