Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
The Small x Assumption02:20

The Small x Assumption

If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may occur if the initial concentrations of reactants are high and the Kc value is small. In such circumstances, the equilibrium concentration is approximately equal to its initial concentration. This estimation can be used to simplify the equilibrium calculations by assuming that some equilibrium concentrations are equal to the initial...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Production Efficiency01:01

Production Efficiency

Net production efficiency (NPE) is the efficiency at which organisms assimilate energy into biomass for the next trophic level. Due to low metabolic rates and less energy spent on thermoregulatory processes, the NPE of ectotherms (cold-blooded animals) is 10 times higher than endotherms (warm-blooded animals).
Improper Integrals: Infinite Intervals01:29

Improper Integrals: Infinite Intervals

An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The effect of direction of force to the craniofacial skeleton on the severity of brain injury in patients with a fronto-basal fracture.

International journal of oral and maxillofacial surgery·2016
Same author

Applied anatomy of the anterior cranial fossa: what can fracture patterns tell us?

International journal of oral and maxillofacial surgery·2015
Same author

Approximations of polydispersed extinction.

Applied optics·2010
Same author

Approximations to extinction from randomly oriented circular and elliptical cylinders.

Applied optics·2010
Same author

Analytic approximation to randomly oriented spheroid extinction.

Applied optics·2010
Same author

Bridging the gap between the Rayleigh and Thomson limits for spheres and spheroids.

Applied optics·2010
Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026
Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026
Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026
Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026
Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026
Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026
See all related articles

Related Experiment Video

Updated: Jun 12, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Simple approximation to extinction efficiency valid over all size parameters.

B T Evans, G R Fournier

    Applied Optics
    |June 26, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new approximation for extinction efficiency, improving upon the anomalous diffraction formula. The method accurately models aerosol behavior across various sizes and refractive indices, offering computational benefits.

    More Related Videos

    Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
    07:41

    Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

    Published on: July 30, 2019

    Automated Two-dimensional Spatiotemporal Analysis of Mobile Single-molecule FRET Probes
    08:26

    Automated Two-dimensional Spatiotemporal Analysis of Mobile Single-molecule FRET Probes

    Published on: November 23, 2021

    Related Experiment Videos

    Last Updated: Jun 12, 2026

    Setting Limits on Supersymmetry Using Simplified Models
    07:46

    Setting Limits on Supersymmetry Using Simplified Models

    Published on: November 15, 2013

    Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
    07:41

    Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

    Published on: July 30, 2019

    Automated Two-dimensional Spatiotemporal Analysis of Mobile Single-molecule FRET Probes
    08:26

    Automated Two-dimensional Spatiotemporal Analysis of Mobile Single-molecule FRET Probes

    Published on: November 23, 2021

    Area of Science:

    • Atmospheric Optics
    • Radiative Transfer
    • Aerosol Science

    Background:

    • Accurate calculation of extinction efficiency is crucial for understanding light interaction with atmospheric aerosols.
    • Existing methods like Mie computations can be computationally intensive, necessitating efficient approximations.
    • The anomalous diffraction formula provides a basis for approximations but requires refinement for broad applicability.

    Purpose of the Study:

    • To develop and validate a semiempirical approximation for extinction efficiency.
    • To compare the approximation's accuracy against exact Mie computations.
    • To assess the approximation's applicability to aerosol models like LOWTRAN.

    Main Methods:

    • Modification of the anomalous diffraction formula to create a semiempirical approximation.
    • Verification of the approximation using complex refractive indices (m = n-ikappa) within specified ranges (1.01 ≤ n ≤ 2.00, 0 ≤ κ ≤ 10).
    • Comparison with exact Mie scattering computations across all size parameters.

    Main Results:

    • The proposed approximation demonstrates uniform validity across all size parameters.
    • The approximation correctly reproduces Rayleigh and large particle asymptotic behaviors.
    • The method shows good accuracy and significant computational advantages over exact methods.

    Conclusions:

    • The modified anomalous diffraction formula offers an accurate and computationally efficient alternative for calculating extinction efficiency.
    • This approximation is suitable for use with various aerosol models, including LOWTRAN.
    • The validated approximation advances the study of radiative transfer in the atmosphere.