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Related Concept Videos

Types of Collisions - II01:19

Types of Collisions - II

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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 Collisions: Introduction01:00

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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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Elastic Collisions: Case Study01:15

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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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Collisions in Multiple Dimensions: Problem Solving01:06

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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.
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...
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Collisions in Multiple Dimensions: Introduction01:05

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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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Types Of Collisions - I01:04

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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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Evader Interdiction: Algorithms, Complexity and Collateral Damage.

Matthew P Johnson1, Alexander Gutfraind2, Kiyan Ahmadizadeh3

  • 1Pennsylvania State University.

Annals of Operations Research
|October 22, 2014
PubMed
Summary
This summary is machine-generated.

This study addresses network interdiction problems by developing algorithms for optimal sensor placement to intercept evaders. It balances interdiction gains with costs, considering various evader behaviors and network types.

Keywords:
Markov chainbridge policyfour color theoremminimal cutnetwork interdictionsubmodular set cover

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Area of Science:

  • Operations Research
  • Computer Science
  • Network Security

Background:

  • Network interdiction problems involve strategically placing sensors to intercept evaders moving through a network.
  • Evaders can exhibit diverse behaviors, including deterministic routes, Markov chains, or reactive strategies to avoid detection.
  • Balancing the cost of sensor deployment with the benefits of interdiction is a key challenge, considering impacts on legitimate network traffic.

Purpose of the Study:

  • To develop algorithms for optimal sensor placement in network interdiction problems.
  • To address two primary objectives: maximizing evader capture within a budget and minimizing cost for complete evader capture.
  • To analyze the problem for various evader types (deterministic, Markov chain, reactive) and network structures (special graphs, general graphs).

Main Methods:

  • Formulating network interdiction as an optimization problem.
  • Designing algorithms for optimal sensor placement in specific graph classes.
  • Establishing hardness and approximation results for general graphs.
  • Considering different evader models: deterministic, Markov chain-based, reactive, and unreactive.

Main Results:

  • Optimal sensor placement algorithms for special graph classes.
  • Hardness and approximation results for general graphs, applicable to diverse evader behaviors.
  • Analysis of a related problem with reactive evaders and innocent travelers, yielding similar algorithmic and complexity outcomes.

Conclusions:

  • The study provides effective strategies for sensor placement in network interdiction.
  • The findings offer insights into the computational complexity and potential solutions for intercepting various types of network evaders.
  • The research contributes to understanding and mitigating threats in network security and resource allocation problems.