18,618 research outputs found
Datseris/FrameworkGlobalStability: v0.1.1
No full textFull Changelog: https://github.com/Datseris/FrameworkGlobalStability/compare/v0.1...v0.1.
Datseris/Zero2Hero-JuliaWorkshop: v2 - updated to Julia 1.9, to be presented in Exeter
No full text<h2>What's Changed</h2>
<ul>
<li>Fix typos by @pitmonticone in https://github.com/Datseris/Zero2Hero-JuliaWorkshop/pull/2</li>
<li>Update notebooks 1, 2 by @Datseris in https://github.com/Datseris/Zero2Hero-JuliaWorkshop/pull/3</li>
<li>Update notebook3 by @Datseris in https://github.com/Datseris/Zero2Hero-JuliaWorkshop/pull/4</li>
<li>Simplify exercises, compile everything by @Datseris in https://github.com/Datseris/Zero2Hero-JuliaWorkshop/pull/5</li>
</ul>
<h2>New Contributors</h2>
<ul>
<li>@pitmonticone made their first contribution in https://github.com/Datseris/Zero2Hero-JuliaWorkshop/pull/2</li>
<li>@Datseris made their first contribution in https://github.com/Datseris/Zero2Hero-JuliaWorkshop/pull/3</li>
</ul>
<p><strong>Full Changelog</strong>: https://github.com/Datseris/Zero2Hero-JuliaWorkshop/compare/v1...v2</p>
Datseris/Zero2Hero-JuliaWorkshop: Original release
No full textOriginally performed in Goettingen in February 2020
Datseris/ComplexityMeasuresPaper: Initial release (paper submitted)
No full textCode accompanying our paper for ComplexityMeasures.j
Phase space analysis of quantum transport in electronic nanodevices
No full textAbstract Electronic transport in nanodevices is commonly studied theoretically and numerically within the Landauer-Büttiker formalism: a device is characterized by its scattering properties to and from reservoirs connected by perfect semi-infinite leads, and transport quantities are derived from the scattering matrix. In some respects, however, the device becomes a ‘black box’ as one only analyses what goes in and out. Here we use the Husimi function as a complementary tool for quantitatively understanding transport in graphene nanodevices. It is a phase space representation of the scattering wavefunctions that allows to link the scattering matrix to a more semiclassical and intuitive description and gain additional insight in to the transport process. In this article we use the Husimi function to analyze some of the fascinating electronic transport properties of graphene, Klein tunneling and intervalley scattering, in two exemplary graphene nanodevices. By this we demonstrate the usefulness of the Husimi function in electronic nanodevices and present novel results e.g. on Klein tunneling outside the Dirac regime and intervalley scattering at a pn-junction and a tilted graphene edge
Estimating Lyapunov exponents in billiards
Full text linkDynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here, the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software on its implementation
Predicting spatio-temporal time series using dimension reduced local states
No full textWe present a method for both cross-estimation and iterated time series prediction of spatio-temporal dynamics based on local modelling and dimension reduction techniques. Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model
JuliaDynamics/Attractors.jl: v1.2.7
No full textAttractors v1.2.7
Diff since v1.2.6
Merged pull requests:
Successful step and plotting qol improvements (#57) (@Datseris
Estimating fractal dimensions: a comparative review and open source implementations
Full text linkThe fractal dimension is a central quantity in nonlinear dynamics and can be
estimated via several different numerical techniques. In this review paper we
present a self-contained and comprehensive introduction to the fractal
dimension. We collect and present various numerical estimators and focus on the
three most promising ones: generalized entropy, correlation sum, and extreme
value theory. We then perform an extensive quantitative evaluation of these
estimators, comparing their performance and precision using different datasets
and comparing the impact of features like length, noise, embedding dimension,
falsify-ability, among many others. Our analysis shows that for synthetic
noiseless data the correlation sum is the best estimator with extreme value
theory following closely. For real experimental data we found the correlation
sum to be more strongly affected by noise versus the entropy and extreme value
theory. The recent extreme value theory estimator seems powerful as it has some
of the advantages of both alternative methods. However, using four different
ways for checking for significance, we found that the method yielded
``significant' low-dimensional results for inappropriate data like stock market
timeseries. This fact, combined with some ambiguities we found in the
literature of the method applications, have implications for both previous and
future real world applications using the extreme value theory approach, as, for
example, the argument for small effective dimensionality in the data cannot
come from the method itself. All algorithms discussed are implemented as
performant and easy to use open source code via the DynamicalSystems.jl
library
- …
