Pi-pi Stacking

Pi-pi stacking is a noncovalent interaction between aromatic rings that influences molecular arrangement, stability, and recognition in chemistry. It arises from a combination of London dispersion forces, electrostatic interactions, and the distribution of pi electrons, with rings commonly adopting offset or slipped arrangements rather than perfectly face-to-face alignment. Pi-pi stacking helps organize molecules in crystal structures and supramolecular assemblies, and it contributes to interactions between aromatic ligands and biomolecular binding sites. Understanding this interaction supports the design of pharmaceuticals, catalysts, sensors, organic electronic materials, and other molecular systems whose properties depend on controlled structure and packing.

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Education

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...

Research

JoVE Journal - Bioengineering

Scaling of Engineered Vascular Grafts Using 3D Printed Guides and the Ring Stacking Method

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Cited by 6 •

2017

Scalable engineered blood vessels would improve clinical applicability. Using easily sizable 3D-printed guides, rings of vascular smooth muscle were created and stacked into a tubular form, forming a vascular graft. Grafts can be sized to meet the range of human coronary artery dimensions by simply changing the 3D-printed guide size.

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