The Stochastic Piston Problem

Abstract

We obtain analytical solutions for the perturbed shock paths induced by time-varying random motions of a piston moving inside an adiabatic tube of constant area. The variance of the shock location grows quadratically with time for early times and switches to linear growth for longer times. The analytical results are confirmed by stochastic numerical simulations, and deviations for large random piston motions are established.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 09, 2004
Accession Number
ADA461810

Entities

People

  • C. -h. Su
  • G. E. Karniadakis
  • G. Lin

Organizations

  • Brown University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Amplitude
  • Applied Mathematics
  • Equations
  • Euler Equations
  • High Resolution
  • Mach Number
  • Markov Chains
  • Mathematics
  • Monte Carlo Method
  • Numbers
  • Perturbations
  • Polynomials
  • Random Variables
  • Shock
  • Shock Tubes
  • Shock Waves
  • Simulations

Fields of Study

  • Mathematics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Fluid Dynamics.
  • Mathematical Modeling and Probability Theory.