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Related Concept Videos

Transfer Function to State Space01:23

Transfer Function to State Space

778
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...
778
State Space to Transfer Function01:21

State Space to Transfer Function

569
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:
569
Transfer function and Bode Plots-II01:23

Transfer function and Bode Plots-II

732
In the standard form, the transfer function is shown in constant gain, poles/zeros at origin, simple poles/zeros, and quadratic poles/zeros; each contributing uniquely to the system's overall response. The term represents the magnitude of the simple zero:
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Transfer Function in Control Systems01:21

Transfer Function in Control Systems

1.5K
The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
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Transfer function and Bode Plots-I01:19

Transfer function and Bode Plots-I

717
A transfer function presented in its standard form integrates elements' constant gain, the zeros, and poles at the origin, simple zeros and poles, and quadratic poles and zeros. The transfer function can be written as H(ω):
717
Protein-protein Interfaces02:04

Protein-protein Interfaces

14.6K
Many proteins form complexes to carry out their functions, making protein-protein interactions (PPIs) essential for an organism's survival. Most PPIs are stabilized by numerous weak noncovalent chemical forces. The physical shape of the interfaces determines the way two proteins interact. Many globular proteins have closely-matching shapes on their surfaces, which form a large number of weak bonds. Additionally, many PPIs occur between two helices or between a surface cleft and a...
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Updated: Jan 26, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
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Proton Transfers at a Dopamine-Functionalized TiO2 Interface.

Costanza Ronchi1, Daniele Selli1, Waranyu Pipornpong1,2

  • 1Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, via R. Cozzi 55, I-20125 Milano, Italy.

The Journal of Physical Chemistry. C, Nanomaterials and Interfaces
|April 13, 2019
PubMed
Summary
This summary is machine-generated.

This study reveals how dopamine molecules interact with titanium dioxide (TiO2) surfaces at an atomic level. Understanding these interactions is key for developing advanced TiO2 nanohybrids.

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Area of Science:

  • Materials Science
  • Surface Chemistry
  • Computational Chemistry

Background:

  • Dopamine-functionalized TiO2 nanohybrids have numerous applications.
  • An atomistic understanding of dopamine's interaction with TiO2 surfaces is lacking.

Purpose of the Study:

  • To elucidate the adsorption modes, growth patterns, and configurations of dopamine on the anatase (101) TiO2 surface.
  • To provide an atomistic perspective on dopamine-TiO2 interactions, using catechol as a reference.

Main Methods:

  • Dispersion-corrected hybrid density functional theory (DFT) calculations.
  • Density functional tight binding (DFTB) molecular dynamics simulations.

Main Results:

  • At low coverage, dopamine coordinates to Ti5c ions via its NH2 group.
  • At high coverage, proton transfer to the ethyl-amino group forms NH3+ species, stabilizing the monolayer through Coulombic interactions.
  • Monolayer configurations are stabilized by strong Coulombic interactions between protonated dopamine molecules.

Conclusions:

  • The study provides a detailed atomistic understanding of dopamine adsorption on TiO2.
  • Optimizing growth conditions can promote full protonation of dopamine, enhancing monolayer stability.
  • Findings pave the way for designing improved dopamine-functionalized TiO2 materials.