Model for Shock Wave Chaos

Handle URI:
http://hdl.handle.net/10754/552862
Title:
Model for Shock Wave Chaos
Authors:
Kasimov, Aslan R.; Faria, Luiz ( 0000-0001-8159-4442 ) ; Rosales, Rodolfo R.
Abstract:
We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Model for Shock Wave Chaos 2013, 110 (10) Physical Review Letters
Publisher:
American Physical Society (APS)
Journal:
Physical Review Letters
Issue Date:
8-Mar-2013
DOI:
10.1103/PhysRevLett.110.104104
Type:
Article
ISSN:
0031-9007; 1079-7114
Additional Links:
http://link.aps.org/doi/10.1103/PhysRevLett.110.104104
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKasimov, Aslan R.en
dc.contributor.authorFaria, Luizen
dc.contributor.authorRosales, Rodolfo R.en
dc.date.accessioned2015-05-14T12:16:20Zen
dc.date.available2015-05-14T12:16:20Zen
dc.date.issued2013-03-08en
dc.identifier.citationModel for Shock Wave Chaos 2013, 110 (10) Physical Review Lettersen
dc.identifier.issn0031-9007en
dc.identifier.issn1079-7114en
dc.identifier.doi10.1103/PhysRevLett.110.104104en
dc.identifier.urihttp://hdl.handle.net/10754/552862en
dc.description.abstractWe propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.en
dc.publisherAmerican Physical Society (APS)en
dc.relation.urlhttp://link.aps.org/doi/10.1103/PhysRevLett.110.104104en
dc.rightsArchived with thanks to Physical Review Lettersen
dc.titleModel for Shock Wave Chaosen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalPhysical Review Lettersen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USAen
kaust.authorKasimov, Aslan R.en
kaust.authorFaria, Luizen
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