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Related Concept Videos

Nodal Analysis01:10

Nodal Analysis

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...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Mesh Analysis01:20

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Nodal Analysis with Voltage Sources01:11

Nodal Analysis with Voltage Sources

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...
Mesh Analysis with Current Sources01:10

Mesh Analysis with Current Sources

Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:
Current Source in One Mesh: The analysis process is straightforward when a current source is found in only one mesh within the circuit. Mesh currents are assigned as usual, with the mesh containing the current source excluded from the analysis. Kirchhoff's voltage law (KVL)...

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A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
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Computation of nodal surfaces in fixed-node diffusion Monte Carlo calculations using a genetic algorithm.

Jordan A Ramilowski1, David Farrelly

  • 1Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300, USA. jordan.ramilowski@aggiemail.usu.edu

Physical Chemistry Chemical Physics : PCCP
|August 19, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a genetic algorithm to automatically find excited state nodal surfaces for quantum chemistry calculations. This method enhances the fixed-node diffusion Monte Carlo (DMC) algorithm, improving accuracy for complex molecular systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Molecular Modeling

Background:

  • The fixed-node diffusion Monte Carlo (DMC) algorithm is crucial for calculating excited state energies.
  • A key challenge in DMC is accurately determining the nodal surface of excited states.
  • Current methods for finding nodal surfaces are often approximations or ad hoc.

Purpose of the Study:

  • To develop a systematic and automated method for computing nodal surfaces.
  • To integrate a genetic algorithm into the DMC procedure for nodal surface optimization.
  • To apply this enhanced DMC approach to challenging quantum systems.

Main Methods:

  • Formulating nodal surface search as an optimization problem within DMC.
  • Employing a genetic algorithm to systematically determine nodal surfaces.
  • Applying the method to calculate excited states of HCN-(4)He and tunneling splittings in HCl-HCl.

Main Results:

  • Demonstrated the effectiveness of a genetic algorithm in automatically computing nodal surfaces.
  • Successfully applied the enhanced DMC method to complex molecular systems.
  • Obtained accurate excited state energies and tunneling splittings.

Conclusions:

  • Genetic algorithms offer a robust solution for the nodal surface determination problem in DMC.
  • This automated approach improves the reliability and applicability of DMC for excited state calculations.
  • The method shows promise for diverse applications in quantum chemistry and physics.