52,164 research outputs found
Dissertation question time: supporting the dissertation project through peer advice
Dissertation question time is a model for a workshop provided by the central academic skills department at Brunel and used to support dissertation writing. The analysis of the use of the model with students and their feedback raises interesting questions about peer learning and advice giving as a pedagogical method, especially when supporting researchers. The research focuses on the delivery of the dissertation question time workshop and the analysis of student feedback and follow up interviews. The positive impact of the workshop upon studentsâ understanding of the research processes led to in becoming an important aspect of central support provision for dissertation writing and research
Determination of Bootstrap confidence intervals on sensitivity indices obtained by polynomial chaos expansion
Lâanalyse de sensibilitĂ© a pour but dâĂ©valuer lâinfluence de la variabilitĂ© dâun ou plusieurs paramĂštres dâentrĂ©e dâun modĂšle sur la variabilitĂ© dâune ou plusieurs rĂ©ponses. Parmi toutes les mĂ©thodes dâapproximations, le dĂ©veloppement sur une base de chaos polynĂŽmial est une des plus efficace pour le calcul des indices de sensibilitĂ©, car ils sont obtenus analytiquement grĂące aux coefficients de la dĂ©composition (Sudret (2008)). Les indices sont donc approximĂ©s et il est difficile dâĂ©valuer lâerreur due Ă cette approximation. Afin dâĂ©valuer la confiance que lâon peut leur accorder nous proposons de construire des intervalles de confiance par rĂ©-Ă©chantillonnage Bootstrap (Efron, Tibshirani (1993)) sur le plan dâexpĂ©rience utilisĂ© pour construire lâapproximation par chaos polynĂŽmial. Lâutilisation de ces intervalles de confiance permet de trouver un plan dâexpĂ©rience optimal garantissant le calcul des indices de sensibilitĂ© avec une prĂ©cision donnĂ©e
The dynamics of laser droplet generation
We propose an experimental setup allowing for the characterization of laser
droplet generation in terms of the underlying dynamics, primarily showing that
the latter is deterministically chaotic by means of nonlinear time series
analysis methods. In particular, we use a laser pulse to melt the end of a
properly fed vertically placed metal wire. Due to the interplay of surface
tension, gravity force and light-metal interaction, undulating pendant droplets
are formed at the molten end, which eventually completely detach from the wire
as a consequence of their increasing mass. We capture the dynamics of this
process by employing a high-speed infrared camera, thereby indirectly measuring
the temperature of the wire end and the pendant droplets. The time series is
subsequently generated as the mean value over the pixel intensity of every
infrared snapshot. Finally, we employ methods of nonlinear time series analysis
to reconstruct the phase space from the observed variable and test it against
determinism and stationarity. After establishing that the observed laser
droplet generation is a deterministic and dynamically stationary process, we
calculate the spectra of Lyapunov exponents. We obtain a positive largest
Lyapunov exponent and a negative divergence, i.e., sum of all the exponents,
thus indicating that the observed dynamics is deterministically chaotic with an
attractor as solution in the phase space. In addition to characterizing the
dynamics of laser droplet generation, we outline industrial applications of the
process and point out the significance of our findings for future attempts at
mathematical modeling.Comment: 7 two-column pages, 8 figures; accepted for publication in Chaos
[supplementary material available at
http://www.matjazperc.com/chaos/laser.html
Using Resonances to Control Chaotic Mixing within a Translating and Rotating Droplet
Enhancing and controlling chaotic advection or chaotic mixing within liquid
droplets is crucial for a variety of applications including digital
microfluidic devices which use microscopic ``discrete'' fluid volumes
(droplets) as microreactors. In this work, we consider the Stokes flow of a
translating spherical liquid droplet which we perturb by imposing a
time-periodic rigid-body rotation. Using the tools of dynamical systems, we
have shown in previous work that the rotation not only leads to one or more
three-dimensional chaotic mixing regions, in which mixing occurs through the
stretching and folding of material lines, but also offers the possibility of
controlling both the size and the location of chaotic mixing within the drop.
Such a control was achieved through appropriate tuning of the amplitude and
frequency of the rotation in order to use resonances between the natural
frequencies of the system and those of the external forcing. In this paper, we
study the influence of the orientation of the rotation axis on the chaotic
mixing zones as a third parameter, as well as propose an experimental set up to
implement the techniques discussed.Comment: 15 pages, 6 figure
Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles
We study chaotic behavior of order parameters in two coupled ensembles of
self-sustained oscillators. Coupling within each of these ensembles is switched
on and off alternately, while the mutual interaction between these two
subsystems is arranged through quadratic nonlinear coupling. We show
numerically that in the course of alternating Kuramoto transitions to synchrony
and back to asynchrony, the exchange of excitations between two subpopulations
proceeds in such a way that their collective phases are governed by an
expanding circle map similar to the Bernoulli map. We perform the Lyapunov
analysis of the dynamics and discuss finite-size effects.Comment: 19 page
Controlling Mixing Inside a Droplet by Time Dependent Rigid-body Rotation
The use of microscopic discrete fluid volumes (i.e., droplets) as
microreactors for digital microfluidic applications often requires mixing
enhancement and control within droplets. In this work, we consider a
translating spherical liquid droplet to which we impose a time periodic
rigid-body rotation which we model using the superposition of a Hill vortex and
an unsteady rigid body rotation. This perturbation in the form of a rotation
not only creates a three-dimensional chaotic mixing region, which operates
through the stretching and folding of material lines, but also offers the
possibility of controlling both the size and the location of the mixing. Such a
control is achieved by judiciously adjusting the three parameters that
characterize the rotation, i.e., the rotation amplitude, frequency and
orientation of the rotation. As the size of the mixing region is increased,
complete mixing within the drop is obtained.Comment: 6 pages, 6 figure
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