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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...
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When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
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If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Mechanical Systems01:22

Mechanical Systems

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Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically...
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Oscillations about an Equilibrium Position01:04

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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...
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Related Experiment Video

Updated: Jun 4, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability
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Dynamical localization in nonideal kicked rotors driven by two competing pulsatile modulations.

F Revuelta1, R Chacón2,3, F Borondo4

  • 1Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, <a href="https://ror.org/03n6nwv02">Universidad Politécnica de Madrid</a>, Avenida Puerta de Hierro 2-4, 28040 Madrid, Spain.

Physical Review. E
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Summary

Dynamical localization in ultracold atoms can be enhanced by quasiperiodic modulations. A strong correlation between chaos and localization persists, guiding control in optical lattice systems.

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Area of Science:

  • Quantum physics
  • Atomic physics
  • Condensed matter physics

Background:

  • Dynamical localization is a quantum phenomenon observed in periodically driven systems.
  • Optical lattices and ultracold atoms provide a controllable platform for studying quantum dynamics.
  • Understanding the influence of complex driving protocols is crucial for controlling quantum states.

Purpose of the Study:

  • To investigate dynamical localization in ultracold atoms subjected to dual competing pulsatile modulations.
  • To explore the impact of finite pulse widths, modulation waveforms, and driving period commensurability.
  • To determine the relationship between chaos and dynamical localization under quasiperiodic driving.

Main Methods:

  • Analytical calculations.
  • Numerical simulations of ultracold atom dynamics in an optical lattice.
  • Investigation of parameter space including modulation amplitudes, periods, and waveforms.

Main Results:

  • Dynamical localization can survive or increase when periodic modulation is replaced by quasiperiodic modulation.
  • A strong correlation exists between chaos strength (stochastic layer width) and dynamical localization (momentum dispersion difference).
  • This correlation is maintained irrespective of whether the driving is periodic or quasiperiodic.

Conclusions:

  • Dynamical localization is robust and can be controlled by tuning modulation parameters.
  • The identified correlation between chaos and localization offers a practical approach for enhancing dynamical localization.
  • Findings are applicable to real-world systems with finite-width pulses in optical lattices.