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Related Concept Videos

Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Diffusion01:12

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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Nodal Analysis01:10

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Nodal analysis is a fundamental method in electrical engineering used to simplify the process of circuit analysis. This method revolves around the concept of using node voltages as the primary variables for circuit analysis. The objective is to determine the voltage at each node in a circuit, which can then be used to find other quantities of interest, such as currents through specific components.
Consider, for instance, a simple circuit composed of three nodes and three resistors, as shown in...
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Nodal Analysis with Voltage Sources01:11

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Nodal analysis is a remarkably effective method used in electrical engineering to simplify the analysis of complex circuits, including those with dependent or independent voltage sources. Its strength lies in its systematic approach to breaking down circuits into manageable components, making it easier for engineers to understand and solve.
Consider a circuit that contains four resistors and two voltage sources, as shown in Figure 1. One of these voltage sources is connected between a...

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Related Experiment Video

Updated: May 23, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

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Published on: May 1, 2018

Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system.

Patrick Müller1, Katherine W Rogers, Ben M Jordan

  • 1Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, USA. pmueller@fas.harvard.edu

Science (New York, N.Y.)
|April 14, 2012
PubMed
Summary

Differential diffusivity, not clearance, explains signaling range differences in biological pattern formation. This study supports reaction-diffusion models for activator/inhibitor systems like Nodal/Lefty in zebrafish.

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Area of Science:

  • Developmental biology
  • Biophysics
  • Systems biology

Background:

  • Biological pattern formation often involves short-range activators and long-range inhibitors.
  • Reaction-diffusion models explain range differences via differential diffusivity or clearance.
  • The Nodal/Lefty system in zebrafish serves as a model for studying these mechanisms.

Purpose of the Study:

  • To experimentally test whether differential diffusivity or differential clearance determines the distinct signaling ranges of Nodal and Lefty.
  • To provide biophysical evidence supporting or refuting existing models of pattern formation.

Main Methods:

  • Analysis of Nodal and Lefty protein gradients in zebrafish embryos.
  • Pulse-labeling experiments to assess clearance kinetics.
  • Fluorescence recovery after photobleaching (FRAP) assays to measure effective diffusion coefficients.

Main Results:

  • Nodal proteins exhibited a shorter signaling range compared to Lefty proteins.
  • Nodal and Lefty proteins demonstrated similar clearance rates.
  • Lefty proteins displayed a higher effective diffusion coefficient than Nodal proteins.

Conclusions:

  • Differential diffusivity is the primary factor responsible for the differing signaling ranges of Nodal and Lefty.
  • These findings provide strong biophysical support for reaction-diffusion models in explaining activator-inhibitor mediated biological patterning.