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Related Concept Videos

Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Partial Differential Equations01:21

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
Free-falling Bodies: Example01:05

Free-falling Bodies: Example

An object falling without any air resistance under the influence of gravitational force is said to be in free-fall. For free-falling bodies, the acceleration due to gravity is constant, irrespective of their mass. Free-fall is experienced not only by objects falling downward, but also by all objects whose motion is influenced by gravitational force alone. The dynamics of free-fall motion can be calculated using kinematic equations of motion, since free-fall acceleration is constant.
The...
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
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 8, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Drops climbing uphill on a slowly oscillating substrate.

E S Benilov1

  • 1Department of Mathematics, University of Limerick, Limerick, Ireland. eugene.benilov@ul.ie

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary

Under specific vibration patterns, a drop can move uphill on an inclined surface. This phenomenon is enhanced by nonlinear effects in thicker drops, enabling uphill motion.

Area of Science:

  • Fluid dynamics
  • Non-Newtonian fluids
  • Surface physics

Background:

  • Understanding fluid behavior under external forces is crucial.
  • Contact line dynamics influence droplet motion.
  • Vibrational forces can alter fluid interfaces.

Purpose of the Study:

  • To investigate the uphill motion of a 2D drop on an inclined, vibrating substrate.
  • To determine the conditions under which a drop can overcome gravity and incline.
  • To analyze the role of vibration-induced inertial forces and nonlinear effects.

Main Methods:

  • Modeling the drop's shape using a quasistatic balance of forces (surface tension, gravity, inertial).
  • Analytical treatment for thin drops.
  • Numerical simulations for the general case.

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Evolution of Staircase Structures in Diffusive Convection
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Evolution of Staircase Structures in Diffusive Convection

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Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
08:49

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

Published on: February 17, 2019

Related Experiment Videos

Last Updated: Jun 8, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Evolution of Staircase Structures in Diffusive Convection
07:28

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
08:49

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

Published on: February 17, 2019

Main Results:

  • Uphill drop motion is possible when inertial forces exhibit specific temporal patterns (narrow/deep troughs and wide/low plateaus).
  • Analytical solutions confirm this for thin drops.
  • Numerical simulations show that nonlinear effects significantly enhance uphill motion for thicker drops.

Conclusions:

  • Specific vibrational conditions can induce uphill droplet locomotion.
  • Nonlinear effects play a critical role in amplifying this motion.
  • The findings have implications for microfluidics and material transport.