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Related Concept Videos

State Space to Transfer Function01:21

State Space to Transfer Function

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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:
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Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

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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...
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Transfer Function to State Space01:23

Transfer Function to State Space

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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...
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State Space Representation01:27

State Space Representation

782
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...
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Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

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Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....
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Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

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The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
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Updated: Apr 27, 2026

Dithranol as a Matrix for Matrix Assisted Laser Desorption/Ionization Imaging on a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer
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Dithranol as a Matrix for Matrix Assisted Laser Desorption/Ionization Imaging on a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

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S matrix from matrix product states.

Laurens Vanderstraeten1, Jutho Haegeman1, Tobias J Osborne2

  • 1Department of Physics and Astronomy, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium.

Physical Review Letters
|July 12, 2014
PubMed
Summary
This summary is machine-generated.

Researchers developed a new method using matrix product states to study quantum lattice systems. This approach accurately describes interactions between elementary excitations in one-dimensional spin chains.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Understanding elementary excitations in one-dimensional quantum systems is crucial for describing their low-energy dynamics.
  • Previous methods often struggle to accurately represent the interactions between these excitations in generic lattice systems.

Purpose of the Study:

  • To develop a novel theoretical framework for constructing stationary scattering states of elementary excitations.
  • To apply this formalism to a specific model, the spin-1 Heisenberg antiferromagnet, for detailed calculations.

Main Methods:

  • Utilized the matrix product state (MPS) formalism.
  • Constructed stationary scattering states for elementary excitations in one-dimensional quantum lattice systems.
  • Applied the method to calculate the S matrix, spectral function contributions, and magnetization corrections for the spin-1 Heisenberg antiferromagnet.

Main Results:

  • Successfully calculated the complete magnon-magnon S matrix for arbitrary momenta and spin in the spin-1 Heisenberg antiferromagnet.
  • Determined the two-particle contribution to the spectral function.
  • Computed higher-order corrections to the magnetization curve, validating the accuracy of the approach.

Conclusions:

  • The matrix product state formalism provides an accurate microscopic representation of interactions between elementary excitations.
  • This method enables the description of low-energy dynamics in one-dimensional spin chains using particlelike excitations.
  • The developed framework offers a powerful tool for future investigations into quantum magnetism and related phenomena.