8,685 research outputs found
A Kinetic Model for Cell Damage Caused by Oligomer Formation
It is well-known that the formation of amyloid fiber may cause invertible
damage to cells, while the underlying mechanism has not been fully uncovered.
In this paper, we construct a mathematical model, consisting of infinite ODEs
in the form of mass-action equations together with two reaction-convection
PDEs, and then simplify it to a system of 5 ODEs by using the maximum entropy
principle. This model is based on four simple assumptions, one of which is that
cell damage is raised by oligomers rather than mature fibrils. With the
simplified model, the effects of nucleation and elongation, fragmentation,
protein and seeds concentrations on amyloid formation and cell damage are
extensively explored and compared with experiments. We hope that our results
can provide a valuable insight into the processes of amyloid formation and cell
damage thus raised.Comment: 16 pages+ 5 figures for maintext; 8 pages+ 4 figures for Supporting
Material
On the connectedness of planar self-affine sets
In this paper, we consider the connectedness of planar self-affine set
arising from an integral expanding matrix with
characteristic polynomial and a digit set
. The necessary and sufficient conditions only
depending on are given for the to be connected.
Moreover, we also consider the case that is non-consecutively
collinear.Comment: 18 pages; 18 figure
Stationary states and quantum quench dynamics of Bose-Einstein condensates in a double-well potential
We consider the properties of stationary states and the dynamics of
Bose-Einstein condensates (BECs) in a double-well (DW) potential with pair
tunneling by using a full quantum-mechanical treatment. Furthermore, we study
the quantum quench dynamics of the DW system subjected to a sudden change of
the Peierls phase. It is shown that strong pair tunneling evidently influences
the energy spectrum structure of the stationary states. For relatively weak
repulsive interatomic interactions, the dynamics of the DW system with a
maximal initial population difference evolves from Josephson oscillations to
quantum self-trapping as one increases the pair tunneling strength, while for
large repulsion the strong pair tunneling inhibits the quantum self-trapping.
In the case of attractive interatomic interactions, strong pair tunneling tends
to destroy the Josephson oscillations and quantum self-trapping, and the system
eventually enters a symmetric regime of zero population difference. Finally,
the effect of the Peierls phase on the quantum quench dynamics of the system is
analyzed and discussed. These new features are remarkably different from the
usual dynamical behaviors of a BEC in a DW potential.Comment: 9 pages,7 figures,accepted for publication in Journal of Physics
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