Related Experiment Video
Updated: Mar 12, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Pattern formation with repulsive soft-core interactions: Discrete particle dynamics and Dean-Kawasaki equation
Jean-Baptiste Delfau1, Hélène Ollivier1,2, Cristóbal López1
1IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain.
Physical Review. E
|November 15, 2016
Summary
Repelling Brownian particles unexpectedly form clusters and crystals in low dimensions. This study reveals diffusion and inter-particle forces drive this self-assembly, accurately modeled by the Dean-Kawasaki equation.
Area of Science:
- Soft matter physics
- Statistical mechanics
- Nonlinear dynamics
Background:
- Brownian particles with repulsive interactions typically avoid aggregation.
- Spontaneous pattern formation and clustering are observed in various physical systems.
- Understanding self-assembly mechanisms is crucial for materials science and nanotechnology.
Purpose of the Study:
- To investigate the spontaneous aggregation of repulsive Brownian particles in low dimensions.
- To analyze the underlying mechanisms driving cluster and crystal formation.
- To validate the Dean-Kawasaki equation as a descriptive model for this phenomenon.
Main Methods:
- Numerical simulations of discrete particle dynamics.
- Linear and nonlinear analysis of the Dean-Kawasaki equation.
- Weakly nonlinear techniques to study pattern-forming bifurcations.
Main Results:
- Repulsive Brownian particles spontaneously form periodic crystals of clusters in 1D and 2D.
- The Dean-Kawasaki equation accurately describes particle dynamics, cluster width, and shape.
- Clustering instability arises from the interplay of diffusion, intracluster, and intercluster forces.
- Pattern-forming bifurcations in 1D and 2D are analyzed.
Conclusions:
- The deterministic Dean-Kawasaki equation effectively models self-assembly in repulsive soft-core systems.
- Low-dimensional systems exhibit complex emergent behavior from simple repulsive interactions.
- Analytical insights into clustering mechanisms are gained by neglecting fluctuations.
Related Concept Videos
01:18First Law: Particles in Two-dimensional Equilibrium
16.9K
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...
16.9K
01:10First Law: Particles in One-dimensional Equilibrium
8.3K
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...
8.3K
01:23Equilibrium Conditions for a Particle
2.4K
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...
2.4K
01:16Precipitate Formation and Particle Size Control
7.0K
In precipitation gravimetry, the precipitating agent should react specifically or selectively with the analyte. While a specific reagent reacts with the analyte alone, a selective reagent can react with a limited number of chemical species.
The obtained precipitate should be either a pure substance of known composition or easily converted to one by a simple process, such as ignition or drying. In addition, the precipitate should be insoluble and easily filterable. In general, filterability...
The obtained precipitate should be either a pure substance of known composition or easily converted to one by a simple process, such as ignition or drying. In addition, the precipitate should be insoluble and easily filterable. In general, filterability...
7.0K
02:43Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision
38.7K
The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.
38.7K
01:23Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving
1.1K
Consider a wooden box and a cylinder of known masses m1 and m2, respectively, hanging from a ceiling with the help of a massless pulley system.
1.1K