Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
arXiv:1802.03143 · doi:10.1103/PhysRevE.97.012221
Abstract
Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam- lattices and the asymmetric Fermi-Pasta-Ulam- lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.
arXiv comment18 pages, 4 figures
References in corpus (52)
- Thermal conduction in classical low-dimensional lattices
- Phononics: Manipulating heat flow with electronic analogs and beyond
- Energy Dissipation and Transport in Nanoscale Devices
- Length-dependent thermal conductivity in suspended single-layer graphene
- Heat Transport in low-dimensional systems
- Lévy walks
- Anomalous heat conduction in one dimensional momentum-conserving systems
- Nonlinear fluctuating hydrodynamics for anharmonic chains
- Heat conduction in one dimensional chains
- Finite thermal conductivity in 1d lattices
- Exact results for anomalous transport in one dimensional Hamiltonian systems
- Heat conduction in one dimensional nonintegrable systems
- Momentum conservation implies anomalous energy transport in 1d classical lattices
- Anomalous Heat Diffusion
- Anomalous Heat Diffusion
- Local Temperature and Universal Heat Conduction in FPU chains
- From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
- Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
- Intriguing Heat Conduction of a Polymer Chain
- Soliton Turbulence in Shallow Water Ocean Surface Waves
- Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
- FPU model: Boundary Jumps, Fourier's Law and Scaling
- Relaxation of classical many-body hamiltonians in one dimension
- Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels
- Dynamical heat channels
- Self-Consistent Mode-Coupling Approach to 1D Heat Transport
- Normal heat conduction in one dimensional momentum conserving lattices with asymmetric interactions
- Heat conduction in the α-β-Fermi-Pasta-Ulam chain
- Energy carriers in the Fermi-Pasta-Ulam lattice: Solitons or Phonons?
- Negaton and Positon Solutions of the KDV Equation
- Anomalous kinetics and transport from 1D self--consistent mode--coupling theory
- Energy transport and correlation between two attractors connected by Fermi-Pasta-Ulam chain
- Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
- Mode-coupling theory and molecular dynamics simulation for heat conduction in a chain with transverse motions
- Exact solution of a Levy walk model for anomalous heat transport
- Perturbation spreading in many-particle systems: a random walk approach
- Equilibrium time-correlation functions for one-dimensional hard-point systems
- The effect of discrete breathers on heat conduction in nonlinear chains
- Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials
- Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices
- Universality of One-Dimensional Heat Conductivity
- Free-energy transition in a gas of non-interacting nonlinear wave-particles
- Density Profiles in Open Superdiffusive Systems
- Space-time velocity correlation function for random walks
- Solitary waves in nonequilibrium molecular dynamics simulations of heat flow in one-dimensional lattices
- Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains
- Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean free paths
- Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
- Thermal rectification and negative differential thermal conductance in harmonic chains with nonlinear system-bath coupling
- Renormalized phonons in nonlinear lattices: A variational approach
- Levy walks with velocity fluctuations
- Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes