Amplitude Quantization as a Fundamental Property of Coupled Oscillator Systems

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Amplitude Quantization as a Fundamental Property
of Coupled Oscillator Systems

• W. J. WilsonDepartment of Engineering and
  Physics
• University of Central Oklahoma
• Edmond, OK 73034email wwilson_at_uco.edu

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Outline

• Introduction
• Argumental Oscillator (Doubochinski Pendulum)
• Theory of Amplitude Quantization
• Oscillator Trap
• Self-organization Behavior
• Implications and Conclusions

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ITS A TRAP!
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Argumentally Coupled Oscillators
Introduced by Russian physicists to describe
classical systems where the configuration of an
oscillating system, enters as a variable into the
functional expression for the external,
oscillating force acting upon it The possibility
of self-regulation of energy-exchange is a
general characteristic of argumental oscillations.
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Classical Problems

• Concept of force implies a rigid, slave-like
  obeisance of a system to an external applied
  force.
• A force can act, without itself being changed
  or being influenced by the system upon which it
  is acting. Newtons third law of action and
  reaction is not enough to remedy that flaw,
  because it assumes a simplistic form of
  point-to-point vector action.
• Attempt to break up the interactions of physical
  systems into a sum of supposedly elementary,
  point-to-point actions.

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Classical Coupled Oscillators

• The idea of an external force, while it may serve
  as a useful fiction for the treatment of
  certain problems in mechanics, should never be
  taken as more than that.
• An external force is a simplistic
  approximation, for an interaction of physical
  systems
• Interacting systems never exist as isolated
  entities in the first place, but only as
  subsystems of the Universe as a whole, as an
  organic totality.

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Doubochinski Pendulum
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Doubochinski Pendulum

• Doubochinski Pendulum
• Low Friction Pivot Pendulum with iron mass (f0
  1-2 Hz)
• Alternating Magnetic Fieldat base (f 20 3000
  Hz) driven by V V0 sin (2p f t)

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Small Amplitude Oscillations
Give familiar resonance physics for Zone 1
oscillations
More interesting to look at nonlinear effects and
f 10f0 -1000f0
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Yields Quantized Amplitudes

• f 50 Hz, f0 2 Hz
• Stable amplitudes are quantized
• System Choice of stable mode determined by
  i.c.s
• Remarkably stable, large disturbances can cause
  the pendulum to jump from one stable mode to
  another

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Period for all Oscillations, T0
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Energy Quantized Like Harmonic Oscillator
E E0 (n ½)
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Computational Analysis
Numerical integration is surprisingly ineffective.
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Perturbative Schemes More Effective
But require assuming oscillateswith T0

• In this case, since the total number of
  decelerating half-cycles will be one less than
  the number of accelerating half-cycles, after
  cancellation of pairs of oppositely acting
  half-cycles, the net effect will be equivalent to
  that of the first half cycle. In this case, the
  pendulum will gain energy.

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Phase Dependence

• Changes in the pendulums velocity, and also in
  the time during which the pendulum remains in the
  interaction zone, as a result of the interaction
  with the electromagnet.
• A surprising asymmetry arises in the process,
  leading to a situation, in which the pendulum can
  draw a net positive power from the magnet, even
  without a tight correlation of phase having been
  established.

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Ratio f/f0 101 103 105 107 109 111
Observed Amplitude 30º 43º 53º 60º 68º 74º
Calculated Amplitude 23º 39º 50º 59º 66º 72º
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• Multiple pendulums with
• different natural
• frequencies can be driven
• by a single
• high-frequency
• magnetic field

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Trap Oscillator

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Spatial Analogue
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Gravitational Segregation
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Possible Applications

• Electric motors having a discrete multiplicity of
  rotor speeds for one and the same frequency of
  the supplied current
• Vibrational Methods for Sorting
• Cooling Processes

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Conclusions

• Argumental oscillations can efficiently couple
  oscillation processes at frequencies differing by
  two or more orders of magnitude
• This coupling can be used to transfer energy into
  or out of trapped oscillators
• Fundamental physics can be investigated using
  particle traps and their interactions with
  oscillatory fields at much higher frequencies.
• Paradoxically one can energize to cool, transmit
  to receive, and add kinetic energy to reach lower
  energy state.

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References

• J. Tennebaum, Amplitude Quantization as an
  Elementary Property of Macroscopic Vibrating
  Systems, 21st Century Science Technology, Vol.
  18, No. 4, 50-63 (2006).http//www.21stcenturysc
  iencetech.com/2006_articles/Amplitude.W05.pdf
• D.B.Doubochinski, J. Tennenbaum, On the
  Fundamental Properties of Coupled Oscillating
  Systems (2007). arXiv0712.2575v1
  physics.gen-ph
• D.B. DoubochinskiI, J. Tennenbaum, The
  Macroscopic Quantum Effect in Nonlinear
  Oscillating Systems a Possible Bridge between
  Classical and Quantum Physics (2007).
  arXiv0711.4892v1 physics.gen-ph
• D.B. DoubochinskiI, J. Tennenbaum, On the
  General Nature of Physical Objects and their
  Interactions as Suggested by the Properties of
  Argumentally-Coupled Oscillating Systems (2008).
  arXiv0808.1205v1 physics.gen-ph

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