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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions.

Pierfrancesco Di Cintio1,2, Roberto Livi1,2, Hugo Bufferand3

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This study investigates anomalous dynamical scaling in one-dimensional systems, comparing two models. While verifying nonlinear fluctuating hydrodynamics for some correlations, it reveals violations in current correlations, hindering asymptotic scaling observations.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • One-dimensional systems exhibit unique dynamical scaling properties.
  • Nonlinear fluctuating hydrodynamics (NFH) predicts specific scaling behaviors for equilibrium correlations.
  • Understanding these dynamics is crucial for various physical phenomena.

Purpose of the Study:

  • To study the anomalous dynamical scaling of equilibrium correlations in 1D systems.
  • To compare the Fermi-Pasta-Ulam chain and a stochastic gas model.
  • To verify NFH predictions and identify deviations.

Main Methods:

  • Detailed numerical simulations were employed.
  • Two distinct models were analyzed: Fermi-Pasta-Ulam chain and a stochastic gas model.
  • Structure factors of density and energy fluctuations were computed.

Main Results:

  • NFH predictions for density and energy fluctuations were verified for both models.
  • Violations of expected scaling were observed in current correlations in certain regimes.
  • The gas model demonstrated a clear crossover in scaling behavior with changes in the coupling constant.

Conclusions:

  • The study confirms NFH predictions for some equilibrium correlations in 1D systems.
  • Deviations in current correlations indicate limitations or specific conditions for asymptotic scaling.
  • Further research is needed to understand the crossover phenomena and fully characterize scaling violations.