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Classification of Systems-I01:26

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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Second Order systems I01:20

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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
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Potential Due to a Magnetized Object01:24

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Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
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The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
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On-Site Potential Creates Complexity in Systems with Disordered Coupling.

I Gershenzon1, B Lacroix-A-Chez-Toine1,2, O Raz1

  • 1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel.

Physical Review Letters
|June 24, 2023
PubMed
Summary
This summary is machine-generated.

Adding a weak nonlinear on-site potential drastically increases the number of critical points in many-body systems. This finding offers a comprehensive view of critical point organization in complex systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Understanding the energy landscape of many-body systems is crucial for various fields.
  • Disordered two-body interactions are common in physical systems like spin glasses.
  • The role of on-site potentials in shaping these landscapes is not fully understood.

Purpose of the Study:

  • To calculate the average number of critical points (N[over ¯]) in disordered many-body systems.
  • To investigate the impact of a weak nonlinear on-site potential on N[over ¯].
  • To provide a detailed understanding of critical point organization.

Main Methods:

  • Analytical calculation of the average number of critical points.
  • Analysis of many-body systems with disordered two-body interactions.
  • Inclusion of a weak nonlinear on-site potential in the model.

Main Results:

  • A weak nonlinear on-site potential dramatically increases N[over ¯].
  • The increase in N[over ¯] scales exponentially with system size.
  • A complete picture of critical point organization was established.

Conclusions:

  • Nonlinear on-site potentials significantly alter the complexity of energy landscapes.
  • Results extend solvable spin-glass models to more realistic scenarios.
  • Findings are relevant for glassy systems, nonlinear oscillator networks, and interacting many-body systems.