Gibbs Phenomenon
Gibbs Phenomenon - Related Videos
02:39
Gibbs Free Energy
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2020
One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
01:10
Tip-of-the-Tongue Phenomenon
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2025
The tip-of-the-tongue (TOT) phenomenon is a cognitive experience characterized by a temporary inability to retrieve specific information from memory despite having a strong feeling of knowing the information. Although individuals cannot access the target word or detail, they frequently recall related elements, such as its initial letter, syllable count, or context. This partial retrieval often causes frustration, as one might recognize a familiar face or know that a name starts with a specific...
01:29
The Reaction Gibbs Energy
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2026
The reaction Gibbs energy (ΔrG) is a crucial parameter that determines whether a reaction will occur spontaneously or not. It can be used to categorize reactions into two types: exergonic and endergonic.Exergonic reactions are those in which ΔrG is less than zero. This implies that these reactions can occur spontaneously without an external input of energy. In biological systems, a typical example of an exergonic reaction is the oxidation of carbohydrates. This reaction produces simple...
02:23
Gibbs Free Energy and Thermodynamic Favorability
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2023
The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered: The spontaneity of a process, as reflected in the...
12:55
Strategies for Tracking Anastasis, A Cell Survival Phenomenon that Reverses Apoptosis
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Cited by 32 •
2015
The term anastasis refers to the phenomenon in which dying cells reverse a cell suicide process at a late stage, repair themselves, and ultimately survive. Here we demonstrate protocols for detecting and tracking cells that undergo anastasis.
FAQs
Additional harmonics change where the oscillation appears more than how high its limiting peak becomes. As the truncated representation includes more terms, the overshoot and undershoot are compressed into a narrower region around the jump. The peak nevertheless approaches a fixed fraction of the jump, so increasing resolution alone cannot guarantee accurate boundary behavior.
Engineers can examine whether oscillations remain concentrated near an abrupt transition and how they change when more harmonics are included. Localization toward the jump, together with a persistent relative overshoot, indicates representation error associated with Gibbs Phenomenon. This assessment helps prevent ringing created by truncation from being interpreted as meaningful high-frequency information in spectral analysis or reconstruction.
The truncation level controls the number of harmonics retained in the representation and therefore affects the width of the oscillatory region. Increasing that level draws the ringing closer to the discontinuity, but it does not make the limiting peak disappear. Engineers should therefore evaluate both spatial or temporal localization and peak magnitude when judging approximation quality.
These strategies become relevant when an engineering result must represent an abrupt boundary accurately rather than merely capture its overall spectral behavior. Smoothing and windowing can be considered when ringing artifacts interfere with interpretation, while alternative approximations offer another way to represent the transition. The appropriate choice depends on whether boundary fidelity or preservation of sharp spectral features is the priority.
First locate abrupt transitions in the function, signal, image, or simulated result. Then compare reconstructions formed with different numbers of retained harmonics, watching whether oscillations become narrower while their peak remains a fixed fraction of the jump. If that pattern occurs, treat the feature as likely representation error and assess smoothing, windowing, or an alternative approximation.
In spectral analysis, ringing near abrupt signal changes can complicate the separation of genuine high-frequency content from truncation artifacts. During signal reconstruction, the same behavior can produce visible overshoot around transitions even as additional harmonics improve localization. Recognizing this pattern helps engineers interpret reconstructed signals cautiously and select processing methods when the transition region matters.
Image boundaries and simulated fields may contain abrupt transitions where truncated Fourier representations generate oscillatory artifacts. Those artifacts can appear close to edges or discontinuities and may be mistaken for physical or measured features. Awareness of Gibbs Phenomenon supports more reliable interpretation and encourages engineers to consider smoothing, windowing, or alternative approximations when accurate boundary behavior is required.