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Related Concept Videos

Gravity between Spherical Bodies01:27

Gravity between Spherical Bodies

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...
Angular Momentum: Rigid Body01:11

Angular Momentum: Rigid Body

The total angular momentum of a rigid body can be calculated using the summation of the angular momentum of all the tiny particles rotating in the same plane. Considering all the tiny particles rotating in the x-y plane, the direction of angular momentum of all such particles and that of the rigid body would be perpendicular to the plane of the rotation along the z-axis.
This calculation can get complicated when tiny particles within the rigid body are not rotating in the same plane but have...
Angular Momentum: Single Particle01:10

Angular Momentum: Single Particle

Angular momentum is directed perpendicular to the plane of the rotation, and its magnitude depends on the choice of the origin. The perpendicular vector joining the linear momentum vector of an object to the origin is called the “lever arm.” If the lever arm and linear momentum are collinear, then the magnitude of the angular momentum is zero. Therefore, in this case, the object rotates about the origin such that it lies on the rim of the circumference defined by the lever arm magnitude.
The...
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

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...
Van der Waals Interactions01:24

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

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 we...

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Realistic Membrane Modeling Using Complex Lipid Mixtures in Simulation Studies
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Brownian dynamics simulations with hard-body interactions: spherical particles.

Hans Behringer1, Ralf Eichhorn

  • 1Johannes Gutenberg-Universität Mainz, Institut für Physik, Staudinger Weg 7, D-55128 Mainz, Germany. behringh@uni-mainz.de

The Journal of Chemical Physics
|November 7, 2012
PubMed
Summary

This study introduces a new Brownian dynamics simulation method to handle hard-body interactions in systems with force fields. The approach uses a half-line transition probability to accurately model particle motion and interactions.

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Area of Science:

  • Computational physics
  • Soft matter physics
  • Brownian dynamics simulations

Background:

  • Simulating systems with hard-body interactions and force fields is computationally challenging.
  • Existing methods may not accurately capture complex particle behaviors.

Purpose of the Study:

  • To develop a novel, efficient algorithm for Brownian dynamics simulations that accounts for hard-body interactions.
  • To provide a robust method for systems with non-vanishing force fields.

Main Methods:

  • Decomposition of Brownian particle motion into affected and unaffected components.
  • Incorporation of hard-body interactions using analytically known transition probabilities on a half-line.
  • Numerical validation using soft matter models like colloids and proteins.

Main Results:

  • The proposed scheme effectively models hard-body interactions in Brownian dynamics.
  • The algorithm is justified for systems with space-fixed obstacles and spherical particles.
  • Numerical simulations confirm the validity for colloids in flow and protein interactions.

Conclusions:

  • The novel approach offers a reliable method for simulating complex systems with hard-body interactions.
  • This technique enhances the accuracy and applicability of Brownian dynamics simulations in soft matter research.