3,753 research outputs found
Characterizing mixed mode oscillations shaped by noise and bifurcation structure
Many neuronal systems and models display a certain class of mixed mode
oscillations (MMOs) consisting of periods of small amplitude oscillations
interspersed with spikes. Various models with different underlying mechanisms
have been proposed to generate this type of behavior. Stochastic versions of
these models can produce similarly looking time series, often with noise-driven
mechanisms different from those of the deterministic models. We present a suite
of measures which, when applied to the time series, serves to distinguish
models and classify routes to producing MMOs, such as noise-induced
oscillations or delay bifurcation. By focusing on the subthreshold
oscillations, we analyze the interspike interval density, trends in the
amplitude and a coherence measure. We develop these measures on a biophysical
model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and
apply them on related models. The analysis highlights the influence of model
parameters and reset and return mechanisms in the context of a novel approach
using noise level to distinguish model types and MMO mechanisms. Ultimately, we
indicate how the suite of measures can be applied to experimental time series
to reveal the underlying dynamical structure, while exploiting either the
intrinsic noise of the system or tunable extrinsic noise.Comment: 22 page
Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogen-like ions
High precision multipole polarizabilities, for
of the ground state of the hydrogen isoelectronic series are obtained from
the Dirac equation using the B-spline method with Notre Dame boundary
conditions. Compact analytic expressions for the polarizabilities as a function
of with a relative accuracy of 10 up to are determined by
fitting to the calculated polarizabilities. The oscillator strengths satisfy
the sum rules for all multipoles from
to . The dispersion coefficients for the long-range H-H and H-He
interactions are given.Comment: 8 figures, 8 table
Hidden Tree Structure is a Key to the Emergence of Scaling in the World Wide Web
Preferential attachment is the most popular explanation for the emergence of
scaling behavior in the World Wide Web, but this explanation has been
challenged by the global information hypothesis, the existence of linear
preference and the emergence of new big internet companies in the real world.
We notice that most websites have an obvious feature that their pages are
organized as a tree (namely hidden tree) and hence propose a new model that
introduces a hidden tree structure into the Erd\H{o}s-R\'e}yi model by adding a
new rule: when one node connects to another, it should also connect to all
nodes in the path between these two nodes in the hidden tree. The experimental
results show that the degree distribution of the generated graphs would obey
power law distributions and have variable high clustering coefficients and
variable small average lengths of shortest paths. The proposed model provides
an alternative explanation to the emergence of scaling in the World Wide Web
without the above-mentioned difficulties, and also explains the "preferential
attachment" phenomenon.Comment: 4 Pages, 7 Figure
Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
Using the recently developed density matrix renormalization group approach,
we study the correlation function of the spin-1 chain with quadratic and
biquadratic interactions. This allows us to define and calculate the
periodicity of the ground state which differs markedly from that in the
classical analogue. Combining our results with other studies, we predict three
phases in the region where the quadratic and biquadratic terms are both
positive.Comment: 13 pages, Standard Latex File + 5 PostScript figures in separate (New
version with SUBSTANTIAL REVISIONS to appear in J Phys A
Mesoscopic Electron and Phonon Transport through a Curved Wire
There is great interest in the development of novel nanomachines that use
charge, spin, or energy transport, to enable new sensors with unprecedented
measurement capabilities. Electrical and thermal transport in these mesoscopic
systems typically involves wave propagation through a nanoscale geometry such
as a quantum wire. In this paper we present a general theoretical technique to
describe wave propagation through a curved wire of uniform cross-section and
lying in a plane, but of otherwise arbitrary shape. The method consists of (i)
introducing a local orthogonal coordinate system, the arclength and two locally
perpendicular coordinate axes, dictated by the shape of the wire; (ii)
rewriting the wave equation of interest in this system; (iii) identifying an
effective scattering potential caused by the local curvature; and (iv), solving
the associated Lippmann-Schwinger equation for the scattering matrix. We carry
out this procedure in detail for the scalar Helmholtz equation with both
hard-wall and stress-free boundary conditions, appropriate for the mesoscopic
transport of electrons and (scalar) phonons. A novel aspect of the phonon case
is that the reflection probability always vanishes in the long-wavelength
limit, allowing a simple perturbative (Born approximation) treatment at low
energies. Our results show that, in contrast to charge transport, curvature
only barely suppresses thermal transport, even for sharply bent wires, at least
within the two-dimensional scalar phonon model considered. Applications to
experiments are also discussed.Comment: 9 pages, 11 figures, RevTe
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