Lyapunov Instability of Fluids

Posch, Harald A.; Forster, Christina

doi:10.1007/3-540-26869-3_14

Cited by 2 publications

(4 citation statements)

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“…We also note that extrema are known in the long-time Lyapunov exponents of simple fluids near phase boundaries. For example, the sum of positive exponents exhibits a maximum near, but not at, the fluid-to-solid phase-transition density [31]. Other information theoretic quantities are also known to peak on the disorder side of an order-disorder transition, as was shown in a kinetic Ising model [41].…”

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confidence: 95%

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Critical fluctuations and slowing down of chaos

Das

Green

2019

Nat Commun

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Fluids cooled to the liquid–vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite a rich phenomenology, however, there is not currently an explanation of the mechanical instability in the molecular motion at this critical point. Here, we couple techniques from nonlinear dynamics and statistical physics to analyze the emergence of this singular state. Numerical simulations and analytical models show how the ordering mechanisms of critical dynamics are measurable through the hierarchy of spatiotemporal Lyapunov vectors. A subset of unstable vectors soften near the critical point, with a marked suppression in their characteristic exponents that reflects a weakened sensitivity to initial conditions. Finite-time fluctuations in these exponents exhibit sharply peaked dynamical timescales and power law signatures of the critical dynamics. Collectively, these results are symptomatic of a critical slowing down of chaos that sits at the root of our statistical understanding of the liquid–vapor critical point.

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confidence: 95%

“…1 [28,30]. For example, the magnitude of the largest Lyapunov exponent, λ 1 , is dominated by the fastest dynamical events in the system [31]. In simple fluids, the fastest events are pairwise interactions sampling the repulsive part of the potential [32].…”

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confidence: 99%

Critical fluctuations and slowing down of chaos

Das

Green

2019

Nat Commun

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“…Reprinted from Ref. [94] The sum of all Lyapunov exponents becomes negative for stationary non-equilibrium states. To demonstrate this effect, we show in Fig.…”

Section: Stationary Particle Systems Out Of Equilibriummentioning

confidence: 99%

“…Three Poincaré maps for the planes defining the first octant are shown. The system is in a stationary non-equilibrium state.Reprinted from Ref [94].…”

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confidence: 99%