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Related Concept Videos

Stability of structures01:14

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Introduction to Structures01:30

Introduction to Structures

A structure is defined as a system of interconnected members designed to support or transfer forces and successfully withstand the loads acting on them. The internal forces of a structure can be determined by decomposing the structure and analyzing the free-body diagrams of the individual members or of a combination of members. This helps in understanding the structural elements' behavior and ensuring that the structure is stable and can withstand the subjected loads.
There are three main...
Microtubule Instability02:17

Microtubule Instability

Microtubules are hollow cylindrical filaments having a diameter of approximately 25 nm and a length that varies from 200 nm to 25 μm. GTP-bound tubulin subunits form αβ-heterodimers for microtubule assembly. These core building blocks interact longitudinally, polymerizing into protofilaments. The protofilaments then interact with one another through lateral bonding forces to form stable cylindrical microtubules. These cylindrical filaments are dynamic as they undergo repeated assembly and...
Microtubule Instability02:17

Microtubule Instability

Microtubules are hollow cylindrical filaments having a diameter of approximately 25 nm and a length that varies from 200 nm to 25 μm. GTP-bound tubulin subunits form αβ-heterodimers for microtubule assembly. These core building blocks interact longitudinally, polymerizing into protofilaments. The protofilaments then interact with one another through lateral bonding forces to form stable cylindrical microtubules. These cylindrical filaments are dynamic as they undergo repeated assembly and...

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Related Experiment Video

Updated: Jul 13, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Analysis of structures causing instabilities.

Thomas Wilhelm1

  • 1Theoretical Systems Biology, Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7UA, United Kingdom. wilhelm@bbsrc.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 7, 2007
PubMed
Summary

We developed Instability Causing Structure Analysis (ICSA) to find network structures causing instability. This method helps predict system behaviors like oscillations and chaos in biological networks.

Area of Science:

  • Systems Biology
  • Network Theory
  • Biochemical Engineering

Background:

  • Understanding the dynamic behavior of complex biological networks is crucial.
  • Identifying network structures that lead to specific dynamic properties (e.g., instability) is a key challenge.

Purpose of the Study:

  • To present a novel method, Instability Causing Structure Analysis (ICSA), for systematically identifying topological structures that cause local instabilities.
  • To provide a necessary topological condition for the existence of unstable steady states in dynamical systems.

Main Methods:

  • The proposed method, ICSA, analyzes the network topology to identify specific structural motifs.
  • It establishes a necessary topological condition that must be met for a system to exhibit unstable steady states.

More Related Videos

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Related Experiment Videos

Last Updated: Jul 13, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Main Results:

  • Systems lacking an instability causing structure cannot possess unstable steady states.
  • The absence of such structures excludes common phenomena like bistability, multistability, and Hopf bifurcations.
  • Sustained oscillations and deterministic chaos are deemed highly unlikely in systems without these structures.

Conclusions:

  • ICSA offers new insights into the topological organization of chemical and biochemical systems.
  • The method is applicable to diverse networks, including metabolic, gene regulatory, and signal transduction networks.
  • ICSA provides a foundational tool for predicting and understanding complex system dynamics.