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Related Concept Videos

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...
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
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,...
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Static Equilibrium - II01:07

Static Equilibrium - II

Static equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the object within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...

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Related Experiment Video

Updated: Jun 12, 2026

Challenges in Rheological Characterization of Highly Concentrated Suspensions &#8212; A Case Study for Screen-printing Silver Pastes
08:42

Challenges in Rheological Characterization of Highly Concentrated Suspensions — A Case Study for Screen-printing Silver Pastes

Published on: April 10, 2017

Stability of active suspensions.

Christel Hohenegger1, Michael J Shelley

  • 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA. choheneg@cims.nyu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2010
PubMed
Summary
This summary is machine-generated.

Active suspensions of motile particles are theoretically analyzed. Pusher suspensions exhibit instability due to orientation oscillations, not concentration changes, suggesting the model is well-posed even without diffusion.

Related Experiment Videos

Last Updated: Jun 12, 2026

Challenges in Rheological Characterization of Highly Concentrated Suspensions &#8212; A Case Study for Screen-printing Silver Pastes
08:42

Challenges in Rheological Characterization of Highly Concentrated Suspensions — A Case Study for Screen-printing Silver Pastes

Published on: April 10, 2017

Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Biophysics

Background:

  • Active suspensions, fluids with motile particles, exhibit complex behaviors.
  • Previous models suggested potential ill-posedness in pusher-type active suspensions.
  • Understanding stability is crucial for predicting collective behaviors.

Purpose of the Study:

  • To theoretically investigate the stability of active suspensions.
  • To analyze the role of particle type (pusher vs. puller) on stability.
  • To determine the well-posedness of kinetic models for active suspensions.

Main Methods:

  • Linearized stability analysis of a kinetic model.
  • High wave-number asymptotic analysis.
  • Numerical simulations of rod-like swimmers.

Main Results:

  • Short-wave stability is independent of particle type; long-wave stability depends on swimming mechanism.
  • Pusher suspensions show instability driven by orientation oscillations, not concentration fluctuations.
  • Diffusion effects can lead to a critical concentration or size for instability onset.

Conclusions:

  • The kinetic model for active suspensions is well-posed, even without diffusion.
  • Oscillations in swimmer orientation are key to pusher instability.
  • Diffusion plays a critical role in long-wave instability at specific concentrations or system sizes.