The phenomenon of simplified scattering from rough surfaces to reflection in fractional space

Safdari, Hadiseh; Vahabi, M.; Jafari, G. R.

doi:10.1140/epjb/e2015-60286-y

Cited by 3 publications

(4 citation statements)

References 48 publications

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“…If K(τ ) ∝ δ(τ ) where δ(τ ) is Dirac delta function Eq. 1 will remain unchanged [18][19][20][21]. For a discrete dynamical procedure Eq.…”

Section: Non-markovian Boolean Dynamicsmentioning

confidence: 99%

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Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process

Ebadi¹,

Saeedian²,

Ausloos³

et al. 2016

EPL

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One successful model of interacting biological systems is the Boolean network. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function, -one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of a cell cycle network, we discover a power law memory with a more robust dynamics than the Markovian dynamics.

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“…If K(τ ) ∝ δ(τ ) where δ(τ ) is Dirac delta function Eq. 1 will remain unchanged [18][19][20][21]. For a discrete dynamical procedure Eq.…”

Section: Non-markovian Boolean Dynamicsmentioning

confidence: 99%

“…If K(τ ) = δ(τ ), where δ(τ ) is the Kronecker delta function, eq. ( 1) will remain unchanged [18][19][20][21]. Therefore eq.…”

mentioning

confidence: 99%

Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process

Ebadi¹,

Saeedian²,

Ausloos³

et al. 2016

EPL

View full text Add to dashboard Cite

show abstract

“…Since the publication of this seminal work by Berry, numerous studies have been published on related aspects of the problem, some of which can be found in Refs. [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78]. The overall majority of these studies are either purely numerical and/or the scattered intensity is not obtained in a closed form expression but rather more typically as an infinite series where the terms depend on the self-affine parameters.…”

Section: Introductionmentioning

confidence: 99%

Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces and its application to the retrieval of self-affine parameters

et al. 2018

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Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for the purpose of using the intensity scattered from them to obtain the Hurst exponent and topothesy that characterize the self-affine roughness. By the use of the Kirchhoff approximation a closed form mathematical expression for the angular dependence of the mean differential reflection coefficient is derived under the assumption that the surface is illuminated by a plane incident wave. It is shown that this quantity can be expressed in terms of the isotropic, bivariate (α-stable) Lévy distribution of a stability parameter that is two times the Hurst exponent of the underlying surface. Features of the expression for the mean differential reflection coefficient are discussed, and its predictions compare favorably over large regions of parameter space to results obtained from rigorous computer simulations based on equations of scattering theory. It is demonstrated how the Hurst exponent and the topothesy of the self-affine surface can be inferred from scattering data it produces. Finally several possible scattering configurations are discussed that allow for an efficient extraction of these self-affine parameters.

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“…An event in the far past is supposed to have less effect on the node's dynamics, when compared with the same event happening in a near past. As a result of this kernel, the governing equation for the node's dynamics is turned into a fractional [51][52][53][54][55][56] order BA-like equation.…”

Section: Introductionmentioning

confidence: 99%

Fractional Dynamics of Network Growth Constrained by Aging Node Interactions

et al. 2016

Self Cite

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In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of “commonly accepted beliefs” seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabási-Albert (BA) differential equation, generalizing the BA model. Our results show that, with passing time, an aging process is observed for the network dynamics. The aging process leads to a decay for the node degree values, thereby creating an opposing process to the preferential attachment mechanism. On one hand, based on the preferential attachment mechanism, nodes with a high degree are more likely to absorb links; but, on the other hand, a node’s age has a reduced chance for new connections. This competitive scenario allows an increased chance for younger members to become a hub. Simulations of such a network growth with aging constraint confirm the results found from solving the fractional BA equation. We also report, as an exemplary application, an investigation of the collaboration network between Hollywood movie actors. It is undubiously shown that a decay in the dynamics of their collaboration rate is found, even including a sex difference. Such findings suggest a widely universal application of the so generalized BA model.

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The phenomenon of simplified scattering from rough surfaces to reflection in fractional space

Cited by 3 publications

References 48 publications

Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process

Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process

Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces and its application to the retrieval of self-affine parameters

Fractional Dynamics of Network Growth Constrained by Aging Node Interactions

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