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Related Concept Videos

State Space to Transfer Function01:21

State Space to Transfer Function

515
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
515
Transfer Function to State Space01:23

Transfer Function to State Space

710
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
710
State Space Representation01:27

State Space Representation

478
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
478
Multimachine Stability01:25

Multimachine Stability

506
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
506
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

344
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
344
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

292
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,...
292

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Scaling Hypothesis for Matrix Product States.

Bram Vanhecke1, Jutho Haegeman1, Karel Van Acoleyen1

  • 1Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium.

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Researchers use matrix product states to study critical spin systems and field theories. This method determines critical points and exponents by optimizing data for a collapse, crucial for lattice quantum field theories.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Statistical Mechanics

Background:

  • Critical phenomena in spin systems and field theories are challenging to study.
  • Matrix product states offer a powerful framework for analyzing quantum systems.

Purpose of the Study:

  • To develop and benchmark a method for studying critical phenomena using matrix product states.
  • To formulate a scaling hypothesis applicable to lattice field theories.

Main Methods:

  • Utilizing matrix product states to analyze critical spin systems and field theories.
  • Formulating a scaling hypothesis based on operators, transfer matrix eigenvalues, and lattice spacing.
  • Optimizing parameters to achieve data collapse for critical points and exponents.

Main Results:

  • Successfully benchmarked the method on critical Ising and Potts models.
  • Obtained scaling Ansatz for correlation length and entanglement entropy.
  • Demonstrated a double data collapse for the correlation length in λϕ⁴ theory.

Conclusions:

  • The proposed method is effective for determining critical points, exponents, and central charges.
  • Scaling functions are crucial for studying critical quantum field theories on the lattice.
  • The approach provides a robust framework for analyzing complex quantum systems.