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Experimental Studies of Transitions in the Circular Hydraulic Jump
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The circular hydraulic jump occurs when a vertical jet hits a horisontal surface. It is a very rich system, which can be used to study separation, onset of turbulence and very non-linear hydrodynamical pattern formation.

In the experiment we control the height of the fluid layer outside the jump. The fluid (ethylenglycol (anti-freeze) seeded with aluminum powder) is directed vertically down on a flat plate of variable height inside a dish of fluid. When the plate is high, the "normal" jump occurs in which the fluid just outside the jump rotates forward on the surface and backwards at the bottom. When the plate is lowered into the fluid this flow-pattern is reversed. Here the fluid just outside the jump rotates slowly backwards on the top and forwards near the bottom. Between these two states is a strongly unstable regime, where the jump looses its symmetry and intermittent jets shoot out.

We want to find the criterion for the first transition and a good
characterization of the height of the fluid layer and the velocity
profile. We have made simplified numerical simulations of the
Navier-Stokes equations where the surface is fixed and find results in
rough agreement with the experiments.
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C. Ellegaard, T. Bohr, A. Espe Hansen and A. Haaning
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A Two-dimensional Granular Flow Experiment
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We have investigated a granular flow consisting of a single layer of
uniform balls passing through a two-dimensional funnel.
By changing the opening angle of the funnel, we can control the behavior of
the flow from a steady flow to an intermittent flow resulting from
quasi-periodic shock waves propagating against the flow.
The average flow rate for the steady flow is well described by a continuum
total energy argument. This argument fails for the intermittent flow.
We also measure local density fluctuations of the flow and their power spectra.
For both steady and intermittent flow, the power spectra are white at
low frequencies with peaks at higher frequencies due to local correlations.
We have also measured the flow in an hourglass in order to compare with
older experiments. We propose a simple stochastic process which can explain
the observed decade of 1/f noise.
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C. Veje and P. Dimon
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Excited Granular Flows
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The dynamics of granular flows are studied in the presence of excitations.
It has already been found in previous work that a gravity-driven
two-dimensional granular flow has both a steady flow regime and an
intermittent regime resulting from quasi-periodic shock waves.
What will now happen if these flows are excited either harmonically or
with noise? It has already been discovered that a harmonic excitation can
significantly affect the flow dynamics in an hourglass.
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K. Lindemann, C. Veje, and P. Dimon
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Shock Waves in a Two-dimensional Granular Flow
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Shock waves occur in a two-dimensional granular flow under some conditions.
They are responsible for intermittent flows previously observed.
Their behavior as a function of the various control parameters will
be determined by visualization techniques. It has already been observed
that although they are mostly produced at the outlet of the flow, they
can also be created in the middle of the system, affecting the shock
waves around them.
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S. Hørlück, C. Veje and P. Dimon
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Quantum Chaology in Quartz Resonators
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Out of the books in Landau and Lifshitz's *Course of Theoretical
Physics*, Vol. 7, the *Theory of Elasticity*, is the thinnest. One can
but wonder whether this is because there simply isn't much to say about the
deformation and motion of elastic bodies, or whether it is because the
authors were simply unable to say very much, within the confines of
standard analytical methods.

Few problems in elastodynamics are analytically solvable. The existence of approximate/numerical methods whereby accurate solutions to them can be obtained has, nevertheless, some bearing on mankind's wellbeing; engineers can use them to design both skyscrapers that will not collapse, hard disks that do not crash, and --in particular-- quartz resonators whose activities do not dip.

In recent years, physicists have gained a much better understanding of quantum systems whose dynamics are chaotic. Finite elastic bodies are analogous to closed quantum systems, in the sense that the trajectory of an acoustic wave bouncing between the bounding surfaces of an elastic body is similar to the trajectory of a quantum particle/wave bouncing inside the walls of a confining potential. Through this analogy, it is conjectured that the ``universal laws'', which govern the behaviour of closed quantum systems (both chaotic and regular), should also hold for finite elastic bodies, e.g. bulk-wave quartz resonators.

I have spent the last 12 months designing and building a system for
detecting the natural frequencies of vibration of quartz resonators at
elevated temperatures. The hideous details are best kept to myself.
The data obtained from this system will be used to verify/disprove the
abovementioned conjecture. The system is not yet operational.
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C. Ellegaard and M. Oxborrow
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Experimental Project in Acoustic Emission from Fracture and Failure Processes
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The purpose of the project is to test experimentally a new working hypothesis
for failure and fracturing in heterogenous systems. Our approach consists of
viewing the final stage of rupture as a kind of critical point, which can be
formalized within a renormalization group scheme. Recent findings suggest that
quenched disorder in fracturing will under certain conditions initiate a
dynamical process leading to the formation of an approximately hierarchical
system of stress-interactions and *discrete scale invariance.
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Clive Ellegaard, Anders Johansen and (Didier Sornette)
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The Circular Hydraulic Jump, Surface Waves and Geometric Orbits
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A circular hydraulic jump is produced when a vertical jet of water
strikes a horizontal surface. The flow spreads out in a thin layer,
and then at a certain radius, the height of the flow increases abruptly.
At low flow rates, the flow is stationary. At some critical flow
rate, the flow becomes unstable, the circular symmetry is broken,
and surface waves are generated. If a reflector is placed in the flow,
then the power spectrum of the surface fluctuations shows an oscillatory
behavior which can be interpreted as the interference of geometric orbits.
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S. Hansen, S. Hørlück, D. Zauner, P. Dimon, C. Ellegaard and (S.C. Creagh)
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Collective Phenomena in Pools of Coupled Oscillators
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An interesting feature is the possibility of spontaneous
synchronization, which has been observed in a wide range of
systems. Examples are charge density waves, oscillating chemical reactions,
fireflies flashing in unison. We are investigating a pool of 60 electronic
relaxation oscillators with an all to all coupling. The aim is to see how
robust theoretical results are under reallife conditions. For infinitely many i
oscillators with linear coupling no synchronization is expected. However, in
real systems this does happen. The
basic state is in theory incoherent and marginally stable in an extended
region of parameter space. Traces of this state is looked for in the
experiment.
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(B. Christiansen), and M.T. Levinsen
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Fri Mar 29 00:13:44 MET 1996