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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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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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Related Experiment Videos

Defense of Cyber Infrastructures Against Cyber-Physical Attacks Using Game-Theoretic Models.

Nageswara S V Rao1, Stephen W Poole1, Chris Y T Ma2

  • 1Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA.

Risk Analysis : an Official Publication of the Society for Risk Analysis
|April 8, 2015
PubMed
Summary

Game theory models analyze cyber and physical infrastructure defense strategies. The study reveals computable Nash equilibria for infrastructure survival, with results favoring attackers when failures are considered.

Keywords:
Cyber infrastructurescyber-physical networksgame theory

Related Experiment Videos

Area of Science:

  • Cybersecurity
  • Game Theory
  • Infrastructure Resilience

Background:

  • Cyber infrastructures integrate cyber and physical components vulnerable to various degradations.
  • Understanding strategic interactions between attackers and defenders is crucial for infrastructure security.

Purpose of the Study:

  • To develop and analyze game-theoretic models for cyber and physical infrastructure attack-defense scenarios.
  • To determine conditions for infrastructure survival and analyze the impact of probabilistic failures.

Main Methods:

  • Utilized game-theoretic models to represent strategic interactions between attackers and defenders.
  • Developed Boolean and component-based attack-defense models for cyber-physical infrastructures.
  • Analyzed Nash equilibria under uniform costs and incorporated probabilities of attack, defense, and incidental failures.

Main Results:

  • Nash equilibria are computable in polynomial time for both Boolean and component models under uniform costs.
  • The models provide deterministic conditions for infrastructure survival.
  • Probabilistic failures shift the balance in favor of the attacker, though results remain qualitatively similar.

Conclusions:

  • The game-theoretic approach provides generalizable insights into cyber-physical infrastructure security.
  • The findings are applicable to various infrastructures, including cloud and high-performance computing systems.
  • Strategic analysis is essential for enhancing the resilience of critical cyber infrastructures.