Oscillatory Systems
Oscillatory Systems - Related Videos
11:26
Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression
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Cited by 7 •
2014
Cerebral perfusion is maintained across a range of pressures via cerebral autoregulation. However, characterizing autoregulation requires prominent pressure fluctuations at regulated frequencies. The described protocol will show how oscillatory lower body negative pressure can generate pressure fluctuations to provide data for projection pursuit regression for quantification of the autoregulatory curve.
07:28
Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity
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Cited by 8 •
2017
Psychophysical methods such as the QUEST estimation procedure can efficiently yield robust estimates of the stimulation intensity at which nonpainful sensations transition into painful sensations. By stimulating repeatedly at the threshold intensity, the variability in rating responses can directly be attributed to perceptual classifications in subsequent analyses.
07:56
Preparation of Liquid Crystal Networks for Macroscopic Oscillatory Motion Induced by Light
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Cited by 11 •
2017
The goal of the protocol is to create liquid crystalline polymer films that can mechanically oscillate under continuous light irradiation. We describe in great detail the conception of free-standing films, from the liquid crystal alignment method to the photo-actuation. The experimental protocol applied to prepare this material is broadly applicable.
13:19
The Use of Chemostats in Microbial Systems Biology
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Cited by 67 •
2013
Cell growth rate is a regulated process and a primary determinant of cell physiology. Continuous culturing using chemostats enables extrinsic control of cell growth rate by nutrient limitation facilitating the study of molecular networks that control cell growth and how those networks evolve to optimize cell growth.
06:07
Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Cited by 14 •
2019
We present a detailed protocol outlining how to perform nonlinear oscillatory shear rheology on soft materials, and how to run the SPP-LAOS analysis to understand the responses as a sequence of physical processes.
FAQs
Restoring effects pull the modeled quantity toward equilibrium, while inertia sustains motion by resisting immediate changes. Damping reduces the motion over time, and external forcing supplies energy that can maintain or modify it. The balance among these influences determines whether oscillations decay, persist, grow in response to input, or settle into a different dynamic pattern.
Amplitude measures the size of variation, frequency describes how rapidly the pattern repeats, and phase specifies its position within that repetition. Together, these quantities distinguish solutions that may share a common period but differ in timing or magnitude. Tracking them helps mathematicians compare responses, identify changes caused by forcing, and characterize periodic behavior.
Resonance concerns a strong response associated with the relationship between a system’s oscillation and an external forcing pattern. Stability concerns whether behavior remains controlled near an equilibrium or reference state. A model may therefore require separate analysis of amplification and long-term behavior. These distinctions help predict when inputs produce pronounced oscillations and when disturbances decay.
Differential equations describe how a quantity changes continuously, whereas difference equations represent change across successive discrete steps. Both can model repeated variation, but they organize time and evolution differently. Choosing between them depends on whether the application treats motion as continuous or as a sequence of updates. The resulting analysis can reveal frequency, decay, stability, or other dynamic behavior.
Analysis begins by identifying the equilibrium or reference state and the equation governing change. The effects of restoring behavior, inertia, damping, and forcing are then examined to determine how they influence amplitude, frequency, phase, and stability. Mathematical predictions can subsequently be interpreted in terms of resonance, decay, synchronization, or bifurcation, depending on the behavior represented by the model.
These models support the study of mechanical vibrations, electrical circuits, biological rhythms, and control systems. In each setting, the equations provide a way to connect changing quantities with measurable or conceptually important behavior. Their analysis can predict decay, resonance, synchronization, and bifurcation, allowing researchers to compare dynamic responses across physical, biological, and engineered contexts.