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Related Concept Videos

Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
Second Order systems II01:18

Second Order systems II

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.
If  ζ...
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Properties of Fourier series II

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Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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BIBO stability of continuous and discrete -time systems01:24

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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First Order Systems01:21

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
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Measurement & Analysis of the Temporal Discrimination Threshold Applied to Cervical Dystonia
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Temporal disorder in up-down symmetric systems.

Ricardo Martínez-García1, Federico Vazquez, Cristóbal López

  • 1IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

Temporal disorder creates "temporal Griffiths phases" (TGPs) in systems with Z_{2} symmetry. These phases, analogous to spatial Griffiths phases, show unique scaling and diverging responses, confirming their robustness.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems Theory
  • Dynamical Systems

Background:

  • Systems with up-down Z_{2} symmetry are fundamental in statistical mechanics.
  • Temporal disorder, or fluctuating conditions, can significantly alter system behavior.
  • Griffiths phases are known phenomena in systems with quenched spatial disorder.

Purpose of the Study:

  • To investigate the impact of temporal disorder on systems exhibiting Z_{2} symmetry.
  • To analyze the emergence and characteristics of novel phases under fluctuating global conditions.
  • To explore the universality of these phenomena in the Ising and generalized voter models.

Main Methods:

  • Analysis of phase transitions in the Ising and generalized voter universality classes.
  • Introduction of temporal disorder by fluctuating the control parameter.
  • Characterization of emergent phases through scaling of mean first-passage times and system response.

Main Results:

  • Discovery of
  • temporal Griffiths phases
  • (TGPs) in systems with Z_{2} symmetry under temporal disorder.
  • TGPs exhibit algebraic scaling of mean first-passage times with system size.
  • System response, such as susceptibility, diverges within TGPs.
  • TGPs are robust and ubiquitous across the studied universality classes.

Conclusions:

  • Temporal disorder induces robust and ubiquitous TGPs in systems with Z_{2} symmetry.
  • TGPs represent a novel phase analogous to spatial Griffiths phases, with time and space roles exchanged.
  • The findings have potential implications for understanding complex systems, including ecological models.