Fermi-Pasta-Ulam<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>Model: Boundary Jumps, Fourier's Law, and Scaling

Aoki, Kenichiro; Kusnezov, Dimitri

doi:10.1103/physrevlett.86.4029

Cited by 129 publications

(132 citation statements)

References 24 publications

(33 reference statements)

Supporting

Mentioning

115

Contrasting

Order By: Relevance

“…It is now well established by computer simulations that the heat conductivity in FPU lattices diverges when the size of the lattice goes to infinity [8,9,10,11,12]. The simulations give a power law dependence of the heat conductivity on the number of particles N as approximately N 2/5 .…”

Section: Introductionmentioning

confidence: 94%

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

2003

View full text Add to dashboard Cite

The Peierls equation is considered for the Fermi-Pasta-Ulam β lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal mode energy as a function of wave vector k is estimated to be proportional to k 5/3 . This leads to the t −3/5 long time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained through the mode coupling theory our estimations give the same k dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam β lattice may lead to finite heat conductivity in this model.

show abstract

Section: Introductionmentioning

confidence: 94%

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

2003

View full text Add to dashboard Cite

show abstract

“…This was done largely to examine how small the higher order terms (e.g., cubic, quartic) must be in order to preserve the phenomenon. In addition, the many questions it spawned have been the subject of experts in non-linear dynamics for decades and tremendous progress has been made [15][16][17] . Excellent reviews of that progress are available elsewhere 14,[18][19][20] and one of the prevailing theories for understanding the origin of the phenomenon is that of mode-coupling theory, which was pioneered by Lepri, Livi, and Politi 19 , and the notion that the reduced dimensionality is the origin of the anomalous thermal transport 19 .…”

mentioning

confidence: 99%

Understanding Divergent Thermal Conductivity in Single Polythiophene Chains Using Green–Kubo Modal Analysis and Sonification

Winters

DeAngelis

et al. 2017

J. Phys. Chem. A

View full text Add to dashboard Cite

Abstract:We used molecular dynamics simulations, the Green-Kubo Modal Analysis (GKMA) method and sonification to study the modal contributions to thermal conductivity in individual polythiophene chains. The simulations suggest that it is possible to achieve divergent thermal conductivity and the GKMA method allowed for exact pinpointing of the modes responsible for the anomalous behavior. The analysis showed that transverse vibrations in the plane of the aromatic rings at low frequencies ~ 0.05 THz are primarily responsible. Further investigation showed that the divergence arises from persistent correlation between the three lowest frequency modes on chains. Sonification of the mode heat fluxes revealed regions where the heat flux amplitude yields a somewhat sinusoidal envelope with a long period similar to the relaxation time. This characteristic in the divergent mode heat fluxes gives rise to the overall thermal conductivity divergence, which strongly supports earlier hypotheses that attribute the divergence to correlated phonon-phonon scattering/interactions. Main text:In all substances, energy/heat is transferred through atomic motions. In electrically conductive materials, electrons can become the primary heat carriers, but in all phases of matter, atomic motions are always present and contribute to the thermal conductivity of every object. Here, we use the term "object" instead of "material" to emphasize that thermal conductivity is highly dependent on the actual structure of an object, that is, its internal atomic level structure and its larger nanoscale or microscale geometry [1][2][3][4][5][6] . In studying the physics of thermal conductivity, tremendous progress has been made over the last 20 years toward understanding various mechanisms that allow one to reduce thermal conductivity in solids 1,7 . This reduction is generally measured relative to a theoretical upper limiting maximum value that arises solely from the intrinsic anharmonicity within the interactions between atoms.In the limiting case, where the atomic interactions are perfectly harmonic, thermal conductivity tends to infinity because the normal modes of vibration do not interact, thus yielding effectively infinite phonon mean free paths and thermal conductivity. As a result, the notion of anharmonicity is critical, and perfectly harmonic interactions between atoms are physically unreasonable. This is because an asymmetry in the energetic well between atoms is an inherent consequence of finite bonding energy (e.g., at some point, the potential energy surface must become concave down). Although one can approach the harmonic limit at cryogenic temperatures, the notion that divergent thermal conductivity (e.g., anomalous thermal conductivity) might be realizable in a real material at room temperature seems theoretically impossible. However, in 1955 Fermi, Pasta, and Ulam (FPU) 8 made a "shocking little discovery" that even an anharmonic system can exhibit infinite thermal conductivity.FPU conducted a numerical experiment with a one-dimensio...

show abstract

“…Finally, we want to discuss the role of the boundary resistance in connection with the temperature dependence of conductivity. In fact, an interesting application of (2.128) has been proposed with reference to the FPU-β model [155]. There, it has been empirically found that the bulk conductivity scales with N and T as…”

Section: Numerical Studies Of the Divergence Of Heat Conductivitymentioning

confidence: 99%

Dynamics of Oscillator Chains

Lichtenberg

Livi

Pettini

et al.

The Fermi-Pasta-Ulam Problem

View full text Add to dashboard Cite

Abstract. The Fermi-Pasta-Ulam (FPU) nonlinear oscillator chain has proved to be a seminal system for investigating problems in nonlinear dynamics. First proposed as a nonlinear system to elucidate the foundations of statistical mechanics, the initial lack of confirmation of the researchers expectations eventually led to a number of profound insights into the behavior of high-dimensional nonlinear systems. The initial numerical studies, proposed to demonstrate that energy placed in a single mode of the linearized chain would approach equipartition through nonlinear interactions, surprisingly showed recurrences. Although subsequent work showed that the origin of the recurrences is nonlinear resonance, the question of lack of equipartition remained. The attempt to understand the regularity bore fruit in a profound development in nonlinear dynamics: the birth of soliton theory. A parallel development, related to numerical observations that, at higher energies, equipartition among modes could be approached, was the understanding that the transition with increasing energy is due to resonance overlap. Further numerical investigations showed that time-scales were also important, with a transition between faster and slower evolution. This was explained in terms of mode overlap at higher energy and resonance overlap at lower energy. Numerical limitations to observing a very slow approach to equipartition and the problem of connecting high-dimensional Hamiltonian systems to lower dimensional studies of Arnold diffusion, which indicate transitions from exponentially slow diffusion along resonances to power-law diffusion across resonances, have been considered. Most of the work, both numerical and theoretical, started from low frequency (long wavelength) initial conditions. Coincident with developments to understand equipartition was another program to connect a statistical phenomenon to nonlinear dynamics, that of understanding classical heat conduction. The numerical studies were quite different, involving the excitation of a boundary oscillator with chaotic motion, rather than the excitation of

show abstract

Fermi-Pasta-UlamβModel: Boundary Jumps, Fourier's Law, and Scaling

Cited by 129 publications

References 24 publications

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Understanding Divergent Thermal Conductivity in Single Polythiophene Chains Using Green–Kubo Modal Analysis and Sonification

Dynamics of Oscillator Chains

Contact Info

Product

Resources

About