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Related Concept Videos

Range00:59

Range

14.1K
The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
Measurements of the amount of soda in a 16-ounce can vary since different subjects record these measurements or since the exact amount - 16 ounces of liquid, was not...
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¹H NMR: Long-Range Coupling01:27

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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Variation: Normal Distribution, Range, and Standard Deviation02:32

Variation: Normal Distribution, Range, and Standard Deviation

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In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
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Angle of Twist - Elastic Range01:13

Angle of Twist - Elastic Range

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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Range Rule of Thumb to Interpret Standard Deviation01:13

Range Rule of Thumb to Interpret Standard Deviation

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The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height...
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Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

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Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
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Range effect on percolation threshold and structural properties for short-range attractive spheres.

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Percolation in colloidal systems is sensitive to interaction range, especially away from critical points. However, cluster structures and coordination numbers remain universal along percolation boundaries.

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Area of Science:

  • Physical Chemistry
  • Soft Matter Physics
  • Computational Science

Background:

  • Percolation and aggregation phenomena are crucial in colloidal systems across diverse scientific and technological fields.
  • Understanding these processes is key to controlling material properties and predicting system behavior.

Purpose of the Study:

  • To investigate the impact of interaction range on percolation thresholds in colloidal systems using molecular dynamics simulations.
  • To analyze how varying interaction parameters influences structural properties along percolation boundaries in the supercritical region.

Main Methods:

  • Employed molecular dynamics (MD) simulations to model colloidal systems composed of spheres with short-range square-well (SRSW) interactions.
  • Systematically varied the interaction range of SRSW potential to observe its effect on percolation behavior.

Main Results:

  • Percolation thresholds exhibit strong dependence on SRSW interaction ranges, particularly away from the liquid-liquid critical point.
  • Structural properties, such as coordination number distributions and cluster size distributions, show convergence and universality along percolation boundaries, especially at low packing fractions.
  • Bond percolation boundaries and average bond coordination number isolines align with the Baxter sticky model, supporting the extended law of corresponding states.

Conclusions:

  • The interaction range of SRSW potentials significantly dictates percolation thresholds in colloidal systems.
  • Despite variations in interaction range, the fundamental structure along percolation boundaries, particularly at low densities, remains remarkably consistent.
  • The findings validate the extended law of corresponding states for these systems, linking SRSW behavior to established models like the Baxter sticky model.