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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Second Order systems I01:20

Second Order systems I

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.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
Second-Order Circuits01:17

Second-Order Circuits

Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
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...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...

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Related Experiment Video

Updated: May 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

General second-order scalar-tensor theory and self-tuning.

Christos Charmousis1, Edmund J Copeland, Antonio Padilla

  • 1LPT, CNRS UMR 8627, Université Paris Sud-11, 91405 Orsay Cedex, France.

Physical Review Letters
|March 10, 2012
PubMed
Summary
This summary is machine-generated.

We identified a unique scalar-tensor theory action enabling consistent self-tuning of the cosmological constant on cosmological backgrounds. This approach evades the Weinberg no-go theorem by breaking Poincaré invariance, allowing for novel cosmological solutions.

Related Experiment Videos

Last Updated: May 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Theoretical physics
  • Cosmology
  • Gravitation

Background:

  • Scalar-tensor theories are extensions of Einstein's general relativity.
  • Cosmological constant problem and the Weinberg no-go theorem pose challenges.
  • Friedmann-Lemaître-Robertson-Walker (FLRW) backgrounds describe a homogeneous and isotropic universe.

Purpose of the Study:

  • To establish a unique action for a consistent self-tuning mechanism in scalar-tensor gravity.
  • To investigate the evasion of the Weinberg no-go theorem in cosmological settings.
  • To explore the potential for nontrivial cosmological solutions.

Main Methods:

  • Formulation of the most general scalar-tensor theory with second-order field equations.
  • Identification of a unique action composed of four base Lagrangians.
  • Analysis of scalar field's role in breaking Poincaré invariance on self-tuning vacua.

Main Results:

  • A unique action is established for self-tuning on FLRW backgrounds.
  • The action combines four Lagrangians with specific geometric dependencies.
  • Poincaré invariance breaking by the scalar field screens spacetime curvature from the cosmological constant.

Conclusions:

  • The developed theory provides a consistent self-tuning mechanism for the cosmological constant.
  • The framework evades the Weinberg no-go theorem, offering new avenues in cosmology.
  • The structure of the theory allows for the generation of nontrivial cosmological solutions.