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Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Elastic Collisions: Case Study01:15

Elastic Collisions: Case Study

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision02:43

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

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.
Elastic Collisions: Introduction01:00

Elastic Collisions: Introduction

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
Types of Collisions - II01:19

Types of Collisions - II

When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...

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Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System
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A hierarchic collision detection algorithm for simple Brownian dynamics.

Zoe Katsimitsoulia1, William R Taylor

  • 1Division of Mathematical Biology, MRC National Institute for Medical Research, The Ridgeway, Mill Hill, London NW7 1AA, UK.

Computational Biology and Chemistry
|March 9, 2010
PubMed
Summary

This study introduces an efficient algorithm to prevent collisions between hierarchical bodies. The non-graphical C implementation significantly outperformed graphical systems, enabling large-scale simulations.

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Area of Science:

  • Computational physics
  • Computer graphics
  • Algorithm development

Background:

  • Steric violations, or collisions, are a common challenge in simulations involving multiple interacting bodies.
  • Hierarchical arrangements of bodies require efficient methods for collision detection and resolution.

Purpose of the Study:

  • To develop and evaluate a novel algorithm for preventing steric violations in hierarchical body arrangements.
  • To compare the performance of a recursive, focus-directing collision detection algorithm in graphical and non-graphical environments.

Main Methods:

  • A recursive algorithm was designed to direct collision detection resources to areas of parent-child collision within a hierarchy.
  • The algorithm was implemented in both OpenGL/Java3D (graphical) and C (non-graphical) environments.
  • Performance was evaluated based on speed, accuracy in preventing steric violations, and resource utilization.

Main Results:

  • The non-graphical C implementation, using a simple collision algorithm, was 50 times faster than the graphical OpenGL/Java3D implementation.
  • The C implementation was also more effective at preventing steric violations.
  • A three-level hierarchy with 100 bodies per level allowed simulation of one million atomic bodies for 100,000 steps in 12 hours on a laptop.

Conclusions:

  • A recursive, focus-directing algorithm significantly improves the efficiency of collision detection in hierarchical systems.
  • Non-graphical implementations with optimized algorithms offer superior performance for large-scale body simulations compared to graphical systems.
  • The developed algorithm is highly scalable and suitable for simulating complex physical systems on standard hardware.