### 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 |

### Cite this

**Density profiles in open superdiffusive systems.** / Lepri, Stefano; Politi, Antonio.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 83, no. 3, 030107. https://doi.org/10.1103/PhysRevE.83.030107

}

TY - JOUR

T1 - Density profiles in open superdiffusive systems

AU - Lepri, Stefano

AU - Politi, Antonio

PY - 2011/3/31

Y1 - 2011/3/31

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.83.030107

DO - 10.1103/PhysRevE.83.030107

M3 - Article

VL - 83

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 3

M1 - 030107

ER -