Related Experiment Video
Updated: Dec 14, 2025
12:34
Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
Published on: June 24, 2016
10.4K
Run-and-tumble particles in two dimensions: Marginal position distributions
Ion Santra1, Urna Basu1, Sanjib Sabhapandit1
1Raman Research Institute, Bengaluru 560080, India.
Physical Review. E
|July 22, 2020
Summary
Run-and-tumble particles (RTP) in two dimensions transition from ballistic to diffusive motion. This study reveals unique position distributions and fluctuations characteristic of active systems.
Area of Science:
- Physics
- Statistical Mechanics
- Soft Matter
Background:
- Run-and-tumble particle (RTP) models are fundamental to describing active matter dynamics.
- Understanding the transition from directed to random motion is crucial for active systems.
Purpose of the Study:
- To analyze the position distributions and dynamics of RTPs in two dimensions.
- To investigate the crossover behavior from ballistic to diffusive regimes in discrete and continuous orientation models.
- To characterize the signatures of activity through position distributions and fluctuation analysis.
Main Methods:
- Exact calculation of marginal position distributions for discrete (n=3, 4) and continuous orientation cases.
- Analysis of crossover dynamics from ballistic to diffusive regimes.
- Computation of large deviation functions to characterize fluctuations.
Main Results:
- RTPs exhibit a crossover from ballistic to diffusive motion in all studied cases.
- Ballistic regime shows nontrivial position distributions, indicative of active particle behavior.
- Atypical fluctuations at long times serve as a signature of system activity.
Conclusions:
- The study provides exact analytical results for RTP dynamics in 2D.
- Confirms the ballistic-to-diffusive crossover as a hallmark of active particle systems.
- Highlights the importance of fluctuation analysis for detecting activity in complex systems.
Related Concept Videos
01:18First Law: Particles in Two-dimensional Equilibrium
13.8K
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...
13.8K
01:10First Law: Particles in One-dimensional Equilibrium
7.7K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
7.7K
01:23Equilibrium Conditions for a Particle
2.0K
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
2.0K
01:27Distribution of Molecular Speeds
5.1K
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...
5.1K
01:11Relative Velocity in Two Dimensions
8.7K
Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by utilizing...
8.7K
01:20Maxwell-Boltzmann Distribution: Problem Solving
2.7K
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
2.7K