Fermi–Pasta–Ulam–Tsingou problem (original) (raw)
Das Fermi-Pasta-Ulam-Tsingou-Experiment (häufig auch Fermi-Pasta-Ulam-Experiment genannt) untersucht das Schwingungsverhalten komplexer Systeme. Das überraschende Ergebnis dieses Experiments zählt zu den wesentlichen Beiträgen der Chaosforschung. Außerdem beeinflusste es als eines der ersten Computerexperimente das Verfahren der Simulation als Experimentiertechnik wesentlich.
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| dbo:abstract | Das Fermi-Pasta-Ulam-Tsingou-Experiment (häufig auch Fermi-Pasta-Ulam-Experiment genannt) untersucht das Schwingungsverhalten komplexer Systeme. Das überraschende Ergebnis dieses Experiments zählt zu den wesentlichen Beiträgen der Chaosforschung. Außerdem beeinflusste es als eines der ersten Computerexperimente das Verfahren der Simulation als Experimentiertechnik wesentlich. (de) In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence (or Fermi–Pasta–Ulam recurrence) – instead of the expected ergodic behavior. This came as a surprise, as Fermi, certainly, expected the system to thermalize in a fairly short time. That is, it was expected for all vibrational modes to eventually appear with equal strength, as per the equipartition theorem, or, more generally, the ergodic hypothesis. Yet here was a system that appeared to evade the ergodic hypothesis. Although the recurrence is easily observed, it eventually became apparent that over much, much longer time periods, the system does eventually thermalize. Multiple competing theories have been proposed to explain the behavior of the system, and it remains a topic of active research. The original intent was to find a physics problem worthy of numerical simulation on the then-new MANIAC computer. Fermi felt that thermalization would pose such a challenge. As such, it represents one of the earliest uses of digital computers in mathematical research; simultaneously, the unexpected results launched the study of nonlinear systems. (en) L'expérience de Fermi-Pasta-Ulam-Tsingou (FPUT) fut la première simulation numérique. Elle étudiait la répartition à long terme de l'énergie d'un système dynamique unidimensionnel de 64 masses couplées entre elles par des ressorts harmoniques perturbés par une faible anharmonicité, sachant qu'un seul mode du système est initialement excité. (fr) In fisica, il problema di Fermi-Pasta-Ulam-Tsingou (noto in precedenza come problema di Fermi-Pasta-Ulam) è l'apparente paradosso in teoria del caos che molti sistemi fisici abbastanza complicati esibiscono un comportamento quasi esattamente periodico, chiamato ricorrenza di Fermi-Pasta-Ulam-Tsingou (o ricorrenza di Fermi-Pasta-Ulam), invece del comportamento ergodico atteso. Ciò fu una sorpresa, poiché Fermi, certamente, si aspettava che il sistema si termalizzasse in un tempo abbastanza breve. Questo vuol dire che ci si aspettava che tutti i modi vibrazionali del sistema alla fine apparissero con lo stesso peso, come previsto dal teorema di equipartizione dell'energia, o, più in generale, dall'ipotesi ergodica. Eppure questo era il caso di un sistema che sembrava ignorare l'ipotesi ergodica. Sebbene fenomeni di ricorrenza siano facilmente osservabili, alla fine diventò evidente che, andando su periodi di tempo molto, molto più lunghi, il sistema alla fine si termalizza. Sono state proposte molteplici teorie concorrenti per spiegare il comportamento del sistema, e rimane un argomento di ricerca attiva. L'intento originale era quello di trovare un problema di fisica che necessitasse di essere simulato numericamente sull'allora nuovo computer MANIAC. Fermi pensava che la termalizzazione costituisse un argomento valido. In quanto tale, rappresenta uno dei primi utilizzi dei computer digitali nella ricerca matematica e fisica; contemporaneamente, i risultati inattesi hanno stimolato lo studio dei sistemi non lineari. (it) フェルミ・パスタ・ウラムの問題（ふぇるみ・ぱすた・うらむのもんだい、英: Fermi–Pasta–Ulam problem）とは、物理学における非線形な相互作用を有するにおけるエネルギー分配の問題。FPU の問題とも呼ばれる。1950年代に、ロスアラモス研究所で電子計算機を用いてこの問題に取り組んだ 3 人の数理物理学者エンリコ・フェルミ、、スタニスワフ・ウラムに名に因む。当初の予想では相互作用が非線形な系ではによって、長時間経過後に各モードにエネルギーが等分配された熱力学的平衡状態に達するはずであったが、計算機実験の結果はそれに反し、初期状態のモードに戻る再帰現象が観測された。後に、この再帰現象はKdV方程式の研究から可積分系におけるソリトンと関連した現象であることが明らかにされた。なお、電子計算機が物理学の研究に活用された初期の事例としても有名である。 (ja) |
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| rdfs:comment | Das Fermi-Pasta-Ulam-Tsingou-Experiment (häufig auch Fermi-Pasta-Ulam-Experiment genannt) untersucht das Schwingungsverhalten komplexer Systeme. Das überraschende Ergebnis dieses Experiments zählt zu den wesentlichen Beiträgen der Chaosforschung. Außerdem beeinflusste es als eines der ersten Computerexperimente das Verfahren der Simulation als Experimentiertechnik wesentlich. (de) L'expérience de Fermi-Pasta-Ulam-Tsingou (FPUT) fut la première simulation numérique. Elle étudiait la répartition à long terme de l'énergie d'un système dynamique unidimensionnel de 64 masses couplées entre elles par des ressorts harmoniques perturbés par une faible anharmonicité, sachant qu'un seul mode du système est initialement excité. (fr) フェルミ・パスタ・ウラムの問題（ふぇるみ・ぱすた・うらむのもんだい、英: Fermi–Pasta–Ulam problem）とは、物理学における非線形な相互作用を有するにおけるエネルギー分配の問題。FPU の問題とも呼ばれる。1950年代に、ロスアラモス研究所で電子計算機を用いてこの問題に取り組んだ 3 人の数理物理学者エンリコ・フェルミ、、スタニスワフ・ウラムに名に因む。当初の予想では相互作用が非線形な系ではによって、長時間経過後に各モードにエネルギーが等分配された熱力学的平衡状態に達するはずであったが、計算機実験の結果はそれに反し、初期状態のモードに戻る再帰現象が観測された。後に、この再帰現象はKdV方程式の研究から可積分系におけるソリトンと関連した現象であることが明らかにされた。なお、電子計算機が物理学の研究に活用された初期の事例としても有名である。 (ja) In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence (or Fermi–Pasta–Ulam recurrence) – instead of the expected ergodic behavior. This came as a surprise, as Fermi, certainly, expected the system to thermalize in a fairly short time. That is, it was expected for all vibrational modes to eventually appear with equal strength, as per the equipartition theorem, or, more generally, the ergodic hypothesis. Yet here was a system that appeared to evade the ergodic hypothesis. Although the recurrence is easily observed, it eventually became apparent that over much, much longer time periods (en) In fisica, il problema di Fermi-Pasta-Ulam-Tsingou (noto in precedenza come problema di Fermi-Pasta-Ulam) è l'apparente paradosso in teoria del caos che molti sistemi fisici abbastanza complicati esibiscono un comportamento quasi esattamente periodico, chiamato ricorrenza di Fermi-Pasta-Ulam-Tsingou (o ricorrenza di Fermi-Pasta-Ulam), invece del comportamento ergodico atteso. Ciò fu una sorpresa, poiché Fermi, certamente, si aspettava che il sistema si termalizzasse in un tempo abbastanza breve. Questo vuol dire che ci si aspettava che tutti i modi vibrazionali del sistema alla fine apparissero con lo stesso peso, come previsto dal teorema di equipartizione dell'energia, o, più in generale, dall'ipotesi ergodica. Eppure questo era il caso di un sistema che sembrava ignorare l'ipotesi ergod (it) |
| rdfs:label | Fermi-Pasta-Ulam-Tsingou-Experiment (de) Expérience de Fermi-Pasta-Ulam-Tsingou (fr) Fermi–Pasta–Ulam–Tsingou problem (en) Problema di Fermi-Pasta-Ulam-Tsingou (it) フェルミ・パスタ・ウラムの問題 (ja) |
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