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Types of Collisions - II01:19

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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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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...
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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...
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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...
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When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...
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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.
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Critical transition for colliding swarms.

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We developed a new model to predict when colliding swarms will mill. This analytical method accurately forecasts critical interaction parameters for swarm dynamics, validated by simulations.

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Area of Science:

  • Physics
  • Robotics
  • Biology
  • Complex Systems

Background:

  • Swarming behavior in mobile agents is crucial across disciplines.
  • Interactions between multiple swarms can generate complex spatiotemporal patterns.
  • Understanding swarm-on-swarm dynamics, especially collisions, is an emerging research area.

Purpose of the Study:

  • To develop an analytical model for predicting milling states in colliding swarms.
  • To identify the critical parameters governing swarm-on-swarm interaction dynamics.
  • To extend numerical insights into the scattering of nonlinear, colliding swarms.

Main Methods:

  • Developed a self-propelled, rigid-body approximation for colliding swarms.
  • Assumed swarms oscillate near a limit cycle post-collision, maintaining uniform density.
  • Analyzed the critical interaction coupling predicting scattering versus milling states.

Main Results:

  • Predicted the critical swarm-on-swarm interaction coupling for milling.
  • Demonstrated this critical coupling is a function of physical swarm parameters.
  • Showed the critical coupling provides a lower bound for all impact parameters, including head-on collisions.
  • Identified the critical coupling with a saddle-node bifurcation in the uniform density approximation.

Conclusions:

  • The developed analytical method accurately predicts critical parameters for colliding swarm behavior.
  • The rigid-body approximation provides a robust framework for understanding swarm-on-swarm interactions.
  • Results align with both small and large multiagent simulations, validating the model.