20,805 research outputs found
From random Poincar\'e maps to stochastic mixed-mode-oscillation patterns
We quantify the effect of Gaussian white noise on fast--slow dynamical
systems with one fast and two slow variables, which display mixed-mode
oscillations owing to the presence of a folded-node singularity. The stochastic
system can be described by a continuous-space, discrete-time Markov chain,
recording the returns of sample paths to a Poincar\'e section. We provide
estimates on the kernel of this Markov chain, depending on the system
parameters and the noise intensity. These results yield predictions on the
observed random mixed-mode oscillation patterns. Our analysis shows that there
is an intricate interplay between the number of small-amplitude oscillations
and the global return mechanism. In combination with a local saturation
phenomenon near the folded node, this interplay can modify the number of
small-amplitude oscillations after a large-amplitude oscillation. Finally,
sufficient conditions are derived which determine when the noise increases the
number of small-amplitude oscillations and when it decreases this number.Comment: 56 pages, 14 figures; revised versio
Open Spinning Strings
We find classical open string solutions in the AdS_5\times S^5/\Zop_2
orientifold with angular momenta along the five-sphere. The energy of these
solutions has an expansion in integral powers of with sigma-model
corrections suppressed by inverse powers of - the total angular momentum.
This gives a prediction for the exact anomalous dimensions of operators in the
large limit of an Super-Yang-Mills theory with matter.
We also find a simple map between open and closed string solutions. This gives
a prediction for an all-loop planar relationship between the anomalous
dimensions of single-trace and two-quark operators in the dual gauge theory
Mechanisms underlying sequence-independent beta-sheet formation
We investigate the formation of beta-sheet structures in proteins without
taking into account specific sequence-dependent hydrophobic interactions. To
accomplish this, we introduce a model which explicitly incorporates both
solvation effects and the angular dependence (on the protein backbone) of
hydrogen bond formation. The thermodynamics of this model is studied by
comparing the restricted partition functions obtained by "unfreezing"
successively larger segments of the native beta-sheet structure. Our results
suggest that solvation dynamics together with the aforementioned angular
dependence gives rise to a generic cooperativity in this class of systems; this
result explains why pathological aggregates involving beta-sheet cores can form
from many different proteins. Our work provides the foundation for the
construction of phenomenological models to investigate the competition between
native folding and non-specific aggregation.Comment: 20 pages, 5 figures, Revtex4, simulation mpeg movie available at
http://www-physics.ucsd.edu/~guochin/Images/sheet1.mp
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