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Visibility to discern local from nonlocal dynamic processes

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Bru Espino, Antonio and Gómez-Castro, David (2017) Visibility to discern local from nonlocal dynamic processes. Physica A: Statistical Mechanics and its Applications, 471 (1). pp. 718-723. ISSN 0378-4371

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Official URL: http://www.sciencedirect.com/science/article/pii/S0378437116310585


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Abstract

We compare using visibility the usual Kardar–Parisi–Zhang (KPZ) universality class and a fractional Edward–Wilkinson (EWf) equation with correlated noise, which share the same kinetic roughening exponents. The KPZ universality class is described by an equation in terms of the usual derivatives, uncorrelated noise and therefore is intrinsically local. The second model includes fractional powers of the Laplace operator and correlated noise, both of which are nonlocal. From their scaling properties, one could be tempted to conclude that both dynamics belong to the same universality class, specifically, to the KPZ universality class. However, this is a wrong conclusion that calls the attention against the indiscriminate application of this approach in real systems without taking into consideration basic physical assumptions (e.g. locality). These examples reveal the necessity of finding new algorithms for detecting characteristics that remain unnoticed to classical scaling analysis, where only the two first moments of the interface distribution (mean and variance) are used to classify the dynamics. We show that visibility and, in particular, the kinetic roughening exponents of the visibility interface, are able to distinguish between these two dynamics which are confused by standard techniques.


Item Type:Article
Uncontrolled Keywords:Fractional PDEs; Rough interfases; Scaling analysis; Visibility
Subjects:Sciences > Mathematics > Combinatorial analysis
ID Code:41480
Deposited On:27 Feb 2017 11:52
Last Modified:12 Dec 2018 15:06

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