Pi Electrons

Pi electrons are electrons occupying pi molecular orbitals formed when parallel p orbitals overlap sideways, a fundamental feature of multiple bonds and conjugated systems in chemistry. In a double bond, one electron pair occupies a pi orbital positioned above and below the plane of the bonded atoms; in aromatic and conjugated molecules, these electrons can delocalize across several atoms, lowering or redistributing molecular energy. Pi-electron behavior helps explain molecular shape, bond strength, absorption of ultraviolet and visible light, and patterns of chemical reactivity. Understanding pi electrons is essential for interpreting organic reactions, aromaticity, spectroscopy, and the design of functional molecular materials.

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JoVE Core - Civil Engineering

The Buckingham Pi Theorem

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2025

The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms. In analyzing flow through a pipe, variables that define the system include the pipe's diameter, the fluid's velocity, its density, and viscosity. These can be combined into a single dimensionless term, the Reynolds number (Re), which captures their essential relationship. The first step in applying the Buckingham Pi theorem is identifying...

Determination of Pi Terms

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2025

The Buckingham Pi theorem is a valuable method in dimensional analysis, reducing complex relationships between variables into dimensionless terms. Relevant variables in analyzing the lift force on an airplane wing include lift force, air density, wing area, aircraft velocity, and air viscosity. Expressing each variable in terms of fundamental dimensions — mass, length, and time — provides a consistent foundation for constructing these dimensionless terms. The theorem indicates that the number...

PI Controller: Design

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2024

Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...

Time and frequency -Domain Interpretation of PI Control

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2024

Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy. Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...

Electron Carriers

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2019

Electron carriers can be thought of as electron shuttles. These compounds can easily accept electrons (i.e., be reduced) or lose them (i.e., be oxidized). They play an essential role in energy production because cellular respiration is contingent on the flow of electrons. Over the many stages of cellular respiration, glucose breaks down into carbon dioxide and water. Electron carriers pick up electrons lost by glucose in these reactions, temporarily storing and releasing them into the electron...

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