Solitary waves and supersonic reaction front in metastable solids

Hendrik J Viljoen, Lee L. Lauderback, Didier Sornette

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Motivated by an increasing number of remarkable experimental observations on the role of pressure and shear stress in solid reactions, explosions, and detonations, we present a simple one-dimensional model that embodies nonlinear elasticity and dispersion as well as chemical or phase transformation. This generalization of the Toda lattice provides an effective model for the description of the organization during an abrupt transformation in a solid. One of the challenges is to capture both the equilibrium degrees of freedom as well as to quantify the possible role of out-of-equilibrium perturbations. In the Toda lattice, we verify that the particle velocities converge in distribution towards the Maxwell-Boltzmann distribution, thus allowing us to define a bonafide temperature. In addition, the balance between nonlinearity and wave dispersion may create solitary waves that act as energy traps. In the presence of reactive chemistry, we show that the trapping of the released chemical energy in solitary waves that are excited by an initial perturbation provides a positive feedback that enhances the reaction rate and leads to supersonic explosion front propagation. These modes of rupture observed in our model may provide a first-order description of ultrafast reactions of heterogeneous mixtures under mechanical loading.

Fingerprint

Toda Lattice
Solitary Waves
Explosion
solitary waves
Nonlinear Dispersion
Perturbation
Front Propagation
Nonlinear Elasticity
Detonation
Positive Feedback
explosions
Phase Transformation
Rupture
Reaction Rate
One-dimensional Model
Energy
Trapping
Shear Stress
Trap
Ludwig Boltzmann

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

Cite this

Solitary waves and supersonic reaction front in metastable solids. / Viljoen, Hendrik J; Lauderback, Lee L.; Sornette, Didier.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 65, No. 2, 01.01.2002.

Research output: Contribution to journalArticle

@article{45449a634fa2453baea802c495cf1fc7,
title = "Solitary waves and supersonic reaction front in metastable solids",
abstract = "Motivated by an increasing number of remarkable experimental observations on the role of pressure and shear stress in solid reactions, explosions, and detonations, we present a simple one-dimensional model that embodies nonlinear elasticity and dispersion as well as chemical or phase transformation. This generalization of the Toda lattice provides an effective model for the description of the organization during an abrupt transformation in a solid. One of the challenges is to capture both the equilibrium degrees of freedom as well as to quantify the possible role of out-of-equilibrium perturbations. In the Toda lattice, we verify that the particle velocities converge in distribution towards the Maxwell-Boltzmann distribution, thus allowing us to define a bonafide temperature. In addition, the balance between nonlinearity and wave dispersion may create solitary waves that act as energy traps. In the presence of reactive chemistry, we show that the trapping of the released chemical energy in solitary waves that are excited by an initial perturbation provides a positive feedback that enhances the reaction rate and leads to supersonic explosion front propagation. These modes of rupture observed in our model may provide a first-order description of ultrafast reactions of heterogeneous mixtures under mechanical loading.",
author = "Viljoen, {Hendrik J} and Lauderback, {Lee L.} and Didier Sornette",
year = "2002",
month = "1",
day = "1",
doi = "10.1103/PhysRevE.65.026609",
language = "English (US)",
volume = "65",
journal = "Physical review. E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "2",

}

TY - JOUR

T1 - Solitary waves and supersonic reaction front in metastable solids

AU - Viljoen, Hendrik J

AU - Lauderback, Lee L.

AU - Sornette, Didier

PY - 2002/1/1

Y1 - 2002/1/1

N2 - Motivated by an increasing number of remarkable experimental observations on the role of pressure and shear stress in solid reactions, explosions, and detonations, we present a simple one-dimensional model that embodies nonlinear elasticity and dispersion as well as chemical or phase transformation. This generalization of the Toda lattice provides an effective model for the description of the organization during an abrupt transformation in a solid. One of the challenges is to capture both the equilibrium degrees of freedom as well as to quantify the possible role of out-of-equilibrium perturbations. In the Toda lattice, we verify that the particle velocities converge in distribution towards the Maxwell-Boltzmann distribution, thus allowing us to define a bonafide temperature. In addition, the balance between nonlinearity and wave dispersion may create solitary waves that act as energy traps. In the presence of reactive chemistry, we show that the trapping of the released chemical energy in solitary waves that are excited by an initial perturbation provides a positive feedback that enhances the reaction rate and leads to supersonic explosion front propagation. These modes of rupture observed in our model may provide a first-order description of ultrafast reactions of heterogeneous mixtures under mechanical loading.

AB - Motivated by an increasing number of remarkable experimental observations on the role of pressure and shear stress in solid reactions, explosions, and detonations, we present a simple one-dimensional model that embodies nonlinear elasticity and dispersion as well as chemical or phase transformation. This generalization of the Toda lattice provides an effective model for the description of the organization during an abrupt transformation in a solid. One of the challenges is to capture both the equilibrium degrees of freedom as well as to quantify the possible role of out-of-equilibrium perturbations. In the Toda lattice, we verify that the particle velocities converge in distribution towards the Maxwell-Boltzmann distribution, thus allowing us to define a bonafide temperature. In addition, the balance between nonlinearity and wave dispersion may create solitary waves that act as energy traps. In the presence of reactive chemistry, we show that the trapping of the released chemical energy in solitary waves that are excited by an initial perturbation provides a positive feedback that enhances the reaction rate and leads to supersonic explosion front propagation. These modes of rupture observed in our model may provide a first-order description of ultrafast reactions of heterogeneous mixtures under mechanical loading.

UR - http://www.scopus.com/inward/record.url?scp=41349095612&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41349095612&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.65.026609

DO - 10.1103/PhysRevE.65.026609

M3 - Article

C2 - 11863680

AN - SCOPUS:41349095612

VL - 65

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 2

ER -