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In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
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If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not...
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Generalized energy equipartition in harmonic oscillators driven by active baths.

Claudio Maggi1, Matteo Paoluzzi2, Nicola Pellicciotta1

  • 1Dipartimento di Fisica, Università di Roma "Sapienza," I-00185 Roma, Italy.

Physical Review Letters
|December 20, 2014
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Summary

We investigated colloidal bead dynamics in E. coli bacteria, finding a generalized equipartition theorem. This reveals two distinct effective temperatures governing motion in different potential landscape directions.

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Area of Science:

  • Physics
  • Soft Matter Physics
  • Biophysics

Background:

  • Colloidal particles in bacterial baths exhibit complex dynamics due to active forces.
  • Understanding these active systems is crucial for fields ranging from materials science to microbiology.

Purpose of the Study:

  • To experimentally and numerically investigate the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria.
  • To develop a theoretical framework describing the observed active Brownian motion.

Main Methods:

  • Experimental realization of a colloidal bead system within an E. coli suspension.
  • Numerical simulations to model the particle dynamics.
  • Analysis using Langevin equations with active and thermal noise components.

Main Results:

  • The dynamics were accurately described by a Langevin equation for an overdamped oscillator.
  • The system exhibited a combination of white thermal noise and exponentially correlated active noise.
  • A generalized equipartition theorem was derived, showing two distinct effective temperatures.

Conclusions:

  • The coexistence of two effective temperatures arises from the interplay of confinement and active bacterial motion.
  • This generalized equipartition theorem provides a new perspective on energy distribution in active matter systems.
  • The findings offer insights into the behavior of active Brownian particles in confining potentials.