On the conductivity of polycrystals and a phase-interchange inequality

Marco Avellaneda, A. V. Cherkaev, K. A. Lurie, Graeme Milton

Research output: Contribution to journalArticle

Abstract

We establish new optimal bounds on the Ohmic conductivity tensor of a single-phase polycrystal through a comparison principle which uses a null-Lagrangian. A similar technique is used to obtain a sharp inequality correlating the conductivities of a two-phase composite material and the material which is obtained from it by interchanging the two phases.

Original languageEnglish (US)
Pages (from-to)148-153
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Volume157
Issue number1
DOIs
StatePublished - May 1 1989

Fingerprint

Polycrystal
polycrystals
Conductivity
conductivity
Optimal Bound
Sharp Inequality
Comparison Principle
Composite Materials
Null
Tensor
tensors
composite materials

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

On the conductivity of polycrystals and a phase-interchange inequality. / Avellaneda, Marco; Cherkaev, A. V.; Lurie, K. A.; Milton, Graeme.

In: Physica A: Statistical Mechanics and its Applications, Vol. 157, No. 1, 01.05.1989, p. 148-153.

Research output: Contribution to journalArticle

Avellaneda, Marco ; Cherkaev, A. V. ; Lurie, K. A. ; Milton, Graeme. / On the conductivity of polycrystals and a phase-interchange inequality. In: Physica A: Statistical Mechanics and its Applications. 1989 ; Vol. 157, No. 1. pp. 148-153.
@article{49a63e8b4dac45498a5b1ad20d577f13,
title = "On the conductivity of polycrystals and a phase-interchange inequality",
abstract = "We establish new optimal bounds on the Ohmic conductivity tensor of a single-phase polycrystal through a comparison principle which uses a null-Lagrangian. A similar technique is used to obtain a sharp inequality correlating the conductivities of a two-phase composite material and the material which is obtained from it by interchanging the two phases.",
author = "Marco Avellaneda and Cherkaev, {A. V.} and Lurie, {K. A.} and Graeme Milton",
year = "1989",
month = "5",
day = "1",
doi = "10.1016/0378-4371(89)90291-4",
language = "English (US)",
volume = "157",
pages = "148--153",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - On the conductivity of polycrystals and a phase-interchange inequality

AU - Avellaneda, Marco

AU - Cherkaev, A. V.

AU - Lurie, K. A.

AU - Milton, Graeme

PY - 1989/5/1

Y1 - 1989/5/1

N2 - We establish new optimal bounds on the Ohmic conductivity tensor of a single-phase polycrystal through a comparison principle which uses a null-Lagrangian. A similar technique is used to obtain a sharp inequality correlating the conductivities of a two-phase composite material and the material which is obtained from it by interchanging the two phases.

AB - We establish new optimal bounds on the Ohmic conductivity tensor of a single-phase polycrystal through a comparison principle which uses a null-Lagrangian. A similar technique is used to obtain a sharp inequality correlating the conductivities of a two-phase composite material and the material which is obtained from it by interchanging the two phases.

UR - http://www.scopus.com/inward/record.url?scp=45149142606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45149142606&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(89)90291-4

DO - 10.1016/0378-4371(89)90291-4

M3 - Article

VL - 157

SP - 148

EP - 153

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1

ER -