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Transfer Function to State Space01:23

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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.
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Related Experiment Video

Updated: Feb 3, 2026

Micro-Mechanical Characterization of Lung Tissue Using Atomic Force Microscopy
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Tissue Mechanical Forces and Evolutionary Developmental Changes Act Through Space and Time to Shape Tooth Morphology

Zachary T Calamari1,2, Jimmy Kuang-Hsien Hu2, Ophir D Klein2,3

  • 1Department of Natural Sciences, Baruch College, City University of New York, New York City, NY 10010, USA.

Bioessays : News and Reviews in Molecular, Cellular and Developmental Biology
|November 3, 2018
PubMed
Summary

Evolutionary and biomechanical studies reveal common genes control tooth formation. Signaling and tissue forces shape specialized dentitions and maintain dental stem cells.

Keywords:
evolutionmechanical forcesmorphogenesisnon-model organismsprogenitor cellsstem cellsteeth

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Area of Science:

  • Evolutionary Biology
  • Biomechanics
  • Developmental Biology

Background:

  • Tooth formation involves complex genetic, signaling, and mechanical processes.
  • Fossil and non-model organism studies highlight conserved genes in epithelial tooth development.
  • Phenotypic adaptations in dentitions are driven by changes in signaling environments.

Purpose of the Study:

  • To review recent advances in understanding dental development.
  • To discuss the roles of evolutionary and biomechanical approaches.
  • To identify gaps in current knowledge for future research.

Main Methods:

  • Integration of evolutionary studies and biomechanical experiments.
  • Analysis of genetic and signaling pathways in tooth development.
  • Examination of tissue forces and skeletal constraints during development.

Main Results:

  • A common genetic toolkit underlies tooth-forming potential across species.
  • Signaling environments and tissue forces act in parallel to shape teeth.
  • Specialized dentitions and stem cell maintenance are influenced by these factors.

Conclusions:

  • Evolutionary and biomechanical approaches provide crucial insights into dental development.
  • Continued research is needed to fill knowledge gaps in tooth formation and function.
  • Understanding these processes is key to addressing dental adaptations and diseases.