Related Experiment Video
Updated: Nov 14, 2025
08:39
Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
Published on: October 16, 2017
12.9K
Pair-distribution function of active Brownian spheres in two spatial dimensions: Simulation results and analytic
Julian Jeggle1, Joakim Stenhammar2, Raphael Wittkowski1
1Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany.
The Journal of Chemical Physics
|March 9, 2021
Summary
Researchers studied active Brownian particles, finding an analytic expression for their pair-distribution function that matches simulation data. This aids theoretical models for active matter and statistical physics.
Area of Science:
- Statistical Physics
- Soft Matter Physics
- Active Matter
Background:
- Active Brownian particles (ABPs) are fundamental models for self-propelled entities.
- Understanding their collective behavior requires detailed knowledge of particle interactions and distributions.
- The pair-distribution function is crucial for characterizing these systems.
Purpose of the Study:
- To compute and analyze the full pair-distribution function for a 2D suspension of active Brownian particles.
- To develop and validate an approximate analytic expression for the pair-distribution function and interparticle force product.
- To provide tools for theoretical modeling of active matter systems.
Main Methods:
- Brownian dynamics simulations were employed to generate the pair-distribution function.
- The simulations considered spherical active Brownian particles with Weeks-Chandler-Andersen potential.
- The five-dimensional pair-distribution function was analyzed across various parameters.
Main Results:
- The full pair-distribution function was successfully computed, revealing its complex dependence on particle positions, orientations, activity (Péclet number), and density.
- An approximate analytic expression for the product of the pair-distribution function and interparticle force was derived.
- The analytic expression demonstrated good agreement with simulation results.
Conclusions:
- The derived analytic expression is a valuable tool for theoretical investigations of active Brownian particles.
- This work contributes to a deeper understanding of nonequilibrium statistical physics.
- The findings facilitate the development of more accurate analytical models for active matter dynamics.
Related Concept Videos
01:20Maxwell-Boltzmann Distribution: Problem Solving
2.0K
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
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
2.0K
02:44Atomic Orbitals
40.8K
An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
40.8K
01:27Distribution of Molecular Speeds
4.4K
The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
4.4K
00:54Distribution and Dispersion
23.5K
To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
23.5K
01:18First Law: Particles in Two-dimensional Equilibrium
11.5K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
Newton's first law tells us about...
11.5K
03:06The Pauli Exclusion Principle
57.3K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
57.3K