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Related Concept Videos

Electric Flux01:15

Electric Flux

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The concept of flux describes how much of something goes through a given area. More formally, it is the dot product of a vector field within an area. For a better understanding, consider an open rectangular surface with a small area that is placed in a uniform electric field. The larger the area, the more field lines go through it and, hence, the greater the flux; similarly, the stronger the electric field (represented by a greater density of lines), the greater the flux. On the other hand, if...
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The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). Magnetic flux is a scalar quantity. It depends on three factors: the strength of the magnetic field B, the area through which the field lines pass, and the relative orientation of the field with the surface area.
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The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
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Consider the electric field of an oppositely charged, parallel-plate system and an imaginary box between those plates. Let the bottom face of the box be ABCD, and the top face be FGHK. The electric field between the plates is uniform and points from the positive plate toward the negative plate. The calculation of this field's flux through the box's various faces shows that the net flux through the box is zero. Why does the flux cancel out here?
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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How to quantify and avoid finite size effects in computational studies of crystal nucleation: The case of heterogeneous ice nucleation.

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Forward-flux sampling with jumpy order parameters.

Amir Haji-Akbari1

  • 1Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA.

The Journal of Chemical Physics
|August 24, 2018
PubMed
Summary

A new generalized forward-flux sampling (FFS) algorithm removes a key limitation for rare event simulations. This method accurately computes crystal nucleation rates, unlike conventional FFS which can underestimate results.

Area of Science:

  • Computational Chemistry and Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Forward-flux sampling (FFS) is a popular path sampling technique for rare event phenomena like crystallization and protein folding.
  • Conventional FFS requires a smooth order parameter to ensure sequential milestone crossing, a condition often unmet in aggregation processes.

Purpose of the Study:

  • To develop and present a generalized FFS algorithm that relaxes the stringent smoothness criterion for order parameters.
  • To apply the generalized FFS to accurately compute homogeneous crystal nucleation rates.

Main Methods:

  • Development of a generalized forward-flux sampling algorithm.
  • Application of the algorithm to simulate homogeneous crystal nucleation in multiple systems.

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  • Comparison of results with conventional FFS to identify discrepancies.

    • Main Results:

    • The generalized FFS algorithm successfully computes homogeneous crystal nucleation rates without requiring a smooth order parameter.
    • Numerical tests demonstrate that conventional FFS can significantly underestimate nucleation rates, by several orders of magnitude.
    • The new method overcomes limitations of traditional FFS for systems with complex order parameters, such as crystallization.

    Conclusions:

    • The generalized FFS algorithm provides a more robust and accurate approach for simulating rare event phenomena, particularly crystallization.
    • This advancement expands the applicability of FFS to a wider range of systems where order parameter smoothness is challenging.
    • The findings highlight the potential inaccuracies of conventional FFS and the necessity of the generalized approach for reliable rate calculations.