### Abstract

We numerically solve a discretized model of Levy random walks on a finite one-dimensional domain with a reflection coefficient r and in the presence of sources. At the domain boundaries, the steady-state density profile is nonanalytic. The meniscus exponent mu, introduced to characterize this singular behavior, uniquely identifies the whole profile. Numerical data suggest that mu = alpha/2 + r(alpha/2 - 1), where alpha is the Levy exponent of the step-length distribution. As an application, we show that this model reproduces the temperature profiles obtained for a chain of oscillators displaying anomalous heat conduction. Remarkably, the case of free-boundary conditions in the chain corresponds to a Levy walk with negative reflection coefficient.

Original language | English |
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Article number | 030107 |

Number of pages | 4 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 83 |

Issue number | 3 |

DOIs | |

Publication status | Published - 31 Mar 2011 |