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Electron delocalization refers to the distribution of electrons across multiple atoms within a molecule rather than being confined to a single atom or bond. This phenomenon is common in systems with conjugated bonds—structures where alternating single and double bonds allow π-electrons to move freely across the network. The movement of electrons stabilizes the molecule and can affect various chemical properties, including vibrational frequencies observed in IR spectroscopy.
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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Activity induced delocalization and freezing in self-propelled systems.

Lorenzo Caprini1, Umberto Marini Bettolo Marconi2, Andrea Puglisi3

  • 1Gran Sasso Science Institute (GSSI), Via. F. Crispi 7, 67100, L'Aquila, Italy. lorenzo.caprini@gssi.it.

Scientific Reports
|February 6, 2019
PubMed
Summary
This summary is machine-generated.

Increasing particle activity time (τ) in confined systems causes particles to delocalize. Interactions can induce liquid or solid structures, with a surprising reentrant freezing effect at high activity.

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Area of Science:

  • Physics
  • Soft Matter Physics
  • Statistical Mechanics

Background:

  • Active particles exhibit self-propulsion and interactions, crucial for understanding biological systems and synthetic materials.
  • Confined active matter systems display complex behaviors influenced by particle activity and inter-particle forces.
  • Previous studies explored dilute suspensions of Janus particles in acoustic traps.

Purpose of the Study:

  • To investigate the phase behavior and structural properties of interacting active particles in a confining potential.
  • To understand the role of activity time (τ) and inter-particle interactions on particle delocalization and organization.
  • To explore non-equilibrium phenomena, including heat fluxes and potential reentrant transitions.

Main Methods:

  • Simulation of interacting active particles with colored noise propulsion and steric repulsion.
  • Analysis of particle density profiles and phase diagrams as a function of activity time (τ) and interaction length.
  • Computation of non-equilibrium heat fluxes to assess system thermodynamics.

Main Results:

  • Increasing activity time (τ) leads to particle delocalization from the potential minimum, reaching a saturation distance.
  • Inter-particle interactions do not suppress delocalization but induce liquid- or solid-like structures in dense regions.
  • A reentrant behavior is observed: initial increases in τ favor fluidization, while higher τ values induce freezing in dense regions.

Conclusions:

  • Particle activity and interactions significantly influence the collective behavior and emergent structures in confined systems.
  • The observed reentrant transition highlights the complex interplay between activity, confinement, and inter-particle forces.
  • The system exhibits non-equilibrium characteristics, with evidence of restored equilibrium in highly concentrated areas.