162 research outputs found
Nonlinear Dynamics of Particles Excited by an Electric Curtain
The use of the electric curtain (EC) has been proposed for manipulation and
control of particles in various applications. The EC studied in this paper is
called the 2-phase EC, which consists of a series of long parallel electrodes
embedded in a thin dielectric surface. The EC is driven by an oscillating
electric potential of a sinusoidal form where the phase difference of the
electric potential between neighboring electrodes is 180 degrees. We
investigate the one- and two-dimensional nonlinear dynamics of a particle in an
EC field. The form of the dimensionless equations of motion is codimension two,
where the dimensionless control parameters are the interaction amplitude ()
and damping coefficient (). Our focus on the one-dimensional EC is
primarily on a case of fixed and relatively small , which is
characteristic of typical experimental conditions. We study the nonlinear
behaviors of the one-dimensional EC through the analysis of bifurcations of
fixed points. We analyze these bifurcations by using Floquet theory to
determine the stability of the limit cycles associated with the fixed points in
the Poincar\'e sections. Some of the bifurcations lead to chaotic trajectories
where we then determine the strength of chaos in phase space by calculating the
largest Lyapunov exponent. In the study of the two-dimensional EC we
independently look at bifurcation diagrams of variations in with fixed
and variations in with fixed . Under certain values of
and , we find that no stable trajectories above the surface exists;
such chaotic trajectories are described by a chaotic attractor, for which the
the largest Lyapunov exponent is found. We show the well-known stable
oscillations between two electrodes come into existence for variations in
and the transitions between several distinct regimes of stable motion for
variations in
Acoustic streaming, fluid mixing, and particle transport by a Gaussian ultrasound beam in a cylindrical container
A computational study is reported of the acoustic streaming flow field generated by a Gaussian ultrasound beam propagating normally toward the end wall of a cylindrical container. Particular focus is given to examining the effectiveness of the acoustic streaming flow for fluid mixing within the container, for deposition of particles in suspension onto the bottom surface, and for particle suspension from the bottom surface back into the flow field. The flow field is assumed to be axisymmetric with the ultrasound transducer oriented parallel to the cylinder axis and normal to the bottom surface of the container, which we refer to as the impingement surface. Reflection of the sound from the impingement surface and sound absorption within the material at the container bottom are both accounted for in the computation. The computation also accounts for thermal buoyancy force due to ultrasonic heating of the impingement surface, but over the time period considered in the current simulations, the flow is found to be dominated by the acoustic streaming force, with only moderate effect of buoyancy force
Principled Architecture-aware Scaling of Hyperparameters
Training a high-quality deep neural network requires choosing suitable
hyperparameters, which is a non-trivial and expensive process. Current works
try to automatically optimize or design principles of hyperparameters, such
that they can generalize to diverse unseen scenarios. However, most designs or
optimization methods are agnostic to the choice of network structures, and thus
largely ignore the impact of neural architectures on hyperparameters. In this
work, we precisely characterize the dependence of initializations and maximal
learning rates on the network architecture, which includes the network depth,
width, convolutional kernel size, and connectivity patterns. By pursuing every
parameter to be maximally updated with the same mean squared change in
pre-activations, we can generalize our initialization and learning rates across
MLPs (multi-layer perception) and CNNs (convolutional neural network) with
sophisticated graph topologies. We verify our principles with comprehensive
experiments. More importantly, our strategy further sheds light on advancing
current benchmarks for architecture design. A fair comparison of AutoML
algorithms requires accurate network rankings. However, we demonstrate that
network rankings can be easily changed by better training networks in
benchmarks with our architecture-aware learning rates and initialization
Prediction of User Temporal Interactions with Online Course Platforms Using Deep Learning Algorithms
The analysis of learning interactions during online studying is a necessary task for designing online courses and sequencing key interactions, which enables online learning platforms to provide users with more efficient and personalized service. However, the research on predicting the interaction itself is not sufficient and the temporal information of interaction sequences hasn’t been fully investigated. To fill in this gap, based on the interaction data collected from Massive Open Online Courses (MOOCs), this paper aims to simultaneously predict a user’s next interaction and the occurrence time to that interaction. Three different neural network models: the long short-term memory, the recurrent marked temporal point process, and the event recurrent point process, are applied on the MOOC interaction dataset. It concludes that taking the correlation between the user action and its occurrence time into consideration can greatly improve the model performance, and that the prediction results are conducive to exploring dropout rates or online learning habits and performances
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