Related Experiment Video
Updated: Apr 15, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Instabilities and relaxation to equilibrium in long-range oscillator chains
George Miloshevich1,2, Jean-Pierre Nguenang3,4, Thierry Dauxois4
1Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University, 0128 Tbilisi, Georgia.
Summary
We investigated instabilities in the Fermi-Pasta-Ulam-Tsingou (FPU) model. A long-range FPU model shows sporadic instabilities in narrow amplitude intervals, unlike the short-range model
Area of Science:
- Nonlinear dynamics
- Statistical mechanics
- Condensed matter physics
Background:
- The Fermi-Pasta-Ulam-Tsingou (FPU) problem investigates energy dynamics in nonlinear oscillator chains.
- Understanding energy equipartition and thermalization is crucial in statistical mechanics.
Purpose of the Study:
- To study instabilities and relaxation to equilibrium in a long-range FPU oscillator chain.
- To clarify the long-standing problem of relaxation to equilibrium in the short-range FPU model.
Main Methods:
- Numerical simulations of the FPU oscillator chain.
- Excitation of the lowest Fourier mode.
- Analysis of energy transfer and localization in mode space.
Main Results:
- Stronger localization in mode space for the long-range FPU model.
- Sporadic nature of instabilities, occurring in narrow amplitude intervals.
- Permanent instability regime for sufficiently large excitation amplitudes.
- Retarded energy transfer and longer relaxation timescales in the short-range FPU model due to weaker mode localization.
Conclusions:
- The long-range FPU model exhibits unique instability dynamics.
- Findings provide insight into the relaxation problem in the standard FPU model.
- Mode localization is a key factor governing energy transfer and system stability.
Related Concept Videos
01:04Oscillations about an Equilibrium Position
7.3K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
7.3K
01:28Atomic Nuclei: Types of Nuclear Relaxation
1.2K
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
1.2K
01:23Stability of Equilibrium Configuration
965
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
965
01:23Atomic Nuclei: Nuclear Relaxation Processes
1.4K
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.
1.4K
01:28Stability
486
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
486
01:07Damped Oscillations
7.7K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
7.7K