TY - JOUR

T1 - Renormalisation group theory for two problems in linear continuum mechanics

AU - Goldenfeld, Nigel

AU - Oono, Y.

N1 - Funding Information:
This work is partially supported by the National Science Foundation through grant no. NSF-DMR-90-15791. One of us (NDG) gratefully acknowledges the support of the Alfred P. Sloan Foundation.

PY - 1991/9/15

Y1 - 1991/9/15

N2 - We consider the problems of: (1) the stress field in an infinite wedge when a moment is applied at the tip, and (2) the flow of an inviscid incompressible fluid past an infinite wedge. Both problems are linear, but nevertheless exhibit anomalous dimensions for wedge angles, α, larger than a critical value αc. In (1) it is the stress field and in (2) it is the velocity potential which can have anomalous power law behaviour in distance from the tip. We use these problems as simple examples to illustrate how partial differential equations can be solved using the renormalisation group.

AB - We consider the problems of: (1) the stress field in an infinite wedge when a moment is applied at the tip, and (2) the flow of an inviscid incompressible fluid past an infinite wedge. Both problems are linear, but nevertheless exhibit anomalous dimensions for wedge angles, α, larger than a critical value αc. In (1) it is the stress field and in (2) it is the velocity potential which can have anomalous power law behaviour in distance from the tip. We use these problems as simple examples to illustrate how partial differential equations can be solved using the renormalisation group.

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U2 - 10.1016/0378-4371(91)90156-7

DO - 10.1016/0378-4371(91)90156-7

M3 - Article

AN - SCOPUS:0042288650

VL - 177

SP - 213

EP - 219

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-3

ER -