711 research outputs found
The slow recirculating flow near the rear stagnation point of a wake
A model is suggested in which some of the important features of the circulating flow inside the two-dimensional near wake are derived by assuming a slow viscous flow. The theory considers the flow away from the body base. It is found that there is a region of constant speed merging, as we go downstream, into a region of stagnation-apex flow. The velocity returning from the rear stagnation point along the center streamline is shown to be a slowly varying function of the 'wedge-angle,' of the wake and to be roughly one half the velocity at the edge of the shear layers driving the wake-cavity flow. These results seem to be in agreement with experimental data
Spectral methods for discontinuous problems
Spectral methods yield high-order accuracy even when applied to problems with discontinuities, though not in the sense of pointwise accuracy. Two different procedures are presented which recover pointwise accurate approximations from the spectral calculations
Non-reflecting boundary conditions for the compressible Navier-Stokes equations
A small perturbation analysis, in the long wavelength regime, is used to obtain the downstream boundary condition for the pressure for the flow over a flat plate. The methodology is extendable to other geometries. Numerical results for high Reynolds number laminar flows show great improvement in convergence rate to steady state as well as the quality of the results
Multiple steady states for characteristic initial value problems
The time dependent, isentropic, quasi-one-dimensional equations of gas dynamics and other model equations are considered under the constraint of characteristic boundary conditions. Analysis of the time evolution shows how different initial data may lead to different steady states and how seemingly anamolous behavior of the solution may be resolved. Numerical experimentation using time consistent explicit algorithms verifies the conclusions of the analysis. The use of implicit schemes with very large time steps leads to erroneous results
Measuring spike train synchrony
Estimating the degree of synchrony or reliability between two or more spike
trains is a frequent task in both experimental and computational neuroscience.
In recent years, many different methods have been proposed that typically
compare the timing of spikes on a certain time scale to be fixed beforehand.
Here, we propose the ISI-distance, a simple complementary approach that
extracts information from the interspike intervals by evaluating the ratio of
the instantaneous frequencies. The method is parameter free, time scale
independent and easy to visualize as illustrated by an application to real
neuronal spike trains obtained in vitro from rat slices. In a comparison with
existing approaches on spike trains extracted from a simulated Hindemarsh-Rose
network, the ISI-distance performs as well as the best time-scale-optimized
measure based on spike timing.Comment: 11 pages, 13 figures; v2: minor modifications; v3: minor
modifications, added link to webpage that includes the Matlab Source Code for
the method (http://inls.ucsd.edu/~kreuz/Source-Code/Spike-Sync.html
Local dimension and finite time prediction in spatiotemporal chaotic systems
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett.
81 5878 (2001)] provides a direct relationship between dimension and
predictability in spatiotemporal chaotic systems. Regions of low dimension are
identified as having high predictability and vice-versa. This conclusion is
reached by using methods from dynamical systems theory and Bayesian modelling.
We emphasize in this work the consequences for short time forecasting and
examine the relevance for factor analysis. Although we concentrate on coupled
map lattices and coupled nonlinear oscillators for convenience, any other
spatially distributed system could be used instead, such as turbulent fluid
flows.Comment: 5 pagers, 7 EPS figure
Multivariate phase space reconstruction by nearest neighbor embedding with different time delays
A recently proposed nearest neighbor based selection of time delays for phase
space reconstruction is extended to multivariate time series, with an iterative
selection of variables and time delays. A case study of numerically generated
solutions of the x- and z coordinates of the Lorenz system, and an application
to heart rate and respiration data, are used for illustration.Comment: 4 pages, 3 figure
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization
We describe a simple experimental implementation of the Malkus-Lorenz water
wheel. We demonstrate that both chaotic and periodic behavior is found as wheel
parameters are changed in agreement with predictions from the Lorenz model. We
furthermore show that when the measured angular velocity of our water wheel is
used as an input signal to a computer model implementing the Lorenz equations,
high quality chaos synchronization of the model and the water wheel is
achieved. This indicates that the Lorenz equations provide a good description
of the water wheel dynamics.Comment: 12 pages, 7 figures. The following article has been accepted by the
American Journal of Physics. After it is published, it will be found at
http://scitation.aip.org/ajp
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