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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...
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
The Power Flow Problem and Solution01:26

The Power Flow Problem and Solution

Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the power flow program computes the...
Transmission Shafts: Problem Solving01:09

Transmission Shafts: Problem Solving

Designing a solid shaft that transmits power from a motor to a machine tool involves a series of calculations to ensure the shaft can withstand the stresses applied by bending moments and torques. First, calculate the torque exerted on the gear, considering the power transmitted by the shaft and its rotational speed. Following this, compute the tangential forces acting on the gears, which directly relate to the torque and the gear radius.
Next, use bending moment diagrams for the shaft to...
Bernoulli's Equation: Problem Solving01:16

Bernoulli's Equation: Problem Solving

A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity equation is...

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Related Experiment Video

Updated: Jun 3, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Calculation of transmission probability by solving an eigenvalue problem.

Sergiy Bubin1, Kálmán Varga

  • 1Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 16, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient eigenvalue method for calculating electron transmission probability in nanodevices. The approach determines quantum transmission eigenchannels, offering a faster alternative for quantum transport calculations.

Related Experiment Videos

Last Updated: Jun 3, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Quantum transport phenomena in nanoscale electronic devices.
  • Computational physics and condensed matter theory.

Background:

  • Electron transmission probability is crucial for understanding nanodevice functionality.
  • Current methods for calculating transmission can be computationally intensive.
  • Quantum transport relies on analyzing transmission eigenchannels.

Purpose of the Study:

  • To develop and present an efficient eigenvalue-based method for calculating electron transmission probability in nanodevices.
  • To demonstrate the method's effectiveness as an alternative to traditional quantum transport calculations.
  • To highlight the computational advantages of the proposed approach.

Main Methods:

  • Solving an eigenvalue problem to determine transmission probabilities.
  • Identifying the number of open quantum transmission eigenchannels from nonzero eigenvalues.
  • Implementing the method on a real space grid basis.
  • Utilizing calculations of outer eigenvalues for complex Hermitian matrices.

Main Results:

  • The number of open eigenchannels is typically limited (a few dozen).
  • The computational cost is reduced to calculating a few outer eigenvalues.
  • The real space grid basis offers an alternative to atomic orbital methods.
  • Numerical examples confirm the method's efficiency.

Conclusions:

  • The eigenvalue method provides an efficient way to calculate electron transmission probability.
  • This approach simplifies quantum transport calculations in nanodevices.
  • The real space grid implementation enhances computational feasibility.