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Fast and Accurate Exhaled Breath Ammonia Measurement
Published on: June 11, 2014
q-Breathers and the Fermi-Pasta-Ulam problem.
S Flach1, M V Ivanchenko, O I Kanakov
1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
Physical Review Letters
|August 11, 2005
Summary
The Fermi-Pasta-Ulam paradox is explained by discovering persistent periodic orbits called q-breathers. These q-breathers clarify energy non-equipartition in anharmonic atomic chains.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Statistical mechanics
Background:
- The Fermi-Pasta-Ulam (FPU) paradox describes energy's failure to equally distribute among normal modes in anharmonic systems.
- Normal modes in the harmonic limit are periodic orbits characterized by wave number q.
Purpose of the Study:
- To identify the underlying mechanism of the FPU paradox.
- To characterize the exact periodic orbits in the FPU parameter regime.
Main Methods:
- Continuing normal modes from the harmonic limit into the FPU regime.
- Analyzing the time periodicity, q-space localization, and stability of these orbits.
Main Results:
- Identified persistent periodic orbits, termed q-breathers (QB).
- QB exhibit time periodicity, exponential localization in q-space, and linear stability up to a threshold amplitude.
- FPU trajectories are perturbations around these exact QB solutions.
Conclusions:
- Q-breathers provide an explanation for the FPU paradox and energy non-equipartition.
- The q-breather concept is generalizable to other nonlinear lattices.
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