Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice

Estrada, Ernesto; Hameed, Ehsan M.; Langer, Matthias; Puchalska, Aleksandra

doi:10.1016/j.laa.2018.06.026

Cited by 29 publications

(22 citation statements)

References 33 publications

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“…In order to account for a gradual influence of first, second, and thus nearest neighbors, we consider a transformation of the d-path Laplacian operators of the form [25,27,28] ∑ d=1 c d L d (11) with c d ∈ C and being the diameter of the graph. In particular, we will consider here the Mellin-transformed d-Laplacian…”

Section: Preliminariesmentioning

confidence: 99%

“…A year later, in November 2012, Riascos and Mateos proposed the use of fractional powers of the combinatorial Laplacian to capture nonlocalities in random walks on graphs [26]. Recently, Estrada et al [27,28] have proved analytically that the generalized diffusion equation with d-path Laplacians produces superdiffusive behavior in 1-and 2-dimensions, in agreement with recent experiments in physics, and have shown some other applications to real-world systems [29]. On the other hand, in 2015, Riascos and Mateos extended their fractional approach to quantum systems by studying quantum transport on simple graphs [30].…”

Section: Introductionmentioning

confidence: 99%

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d-Path Laplacians and Quantum Transport on Graphs

Estrada

2020

Mathematics

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We generalize the Schrödinger equation on graphs to include long-range interactions (LRI) by means of the Mellin-transformed d-path Laplacian operators. We find analytical expressions for the transition and return probabilities of a quantum particle at the nodes of a ring graph. We show that the average return probability in ring graphs decays as a power law with time when LRI is present. In contrast, we prove analytically that the transition and return probabilities on a complete and start graphs oscillate around a constant value. This allowed us to infer that in a barbell graph—a graph consisting of two cliques separated by a path—the quantum particle get trapped and oscillates across the nodes of the path without visiting the nodes of the cliques. We then compare the use of the Mellin-transformed d-path Laplacian operators versus the use of fractional powers of the combinatorial Laplacian to account for LRI. Apart from some important differences observed at the limit of the strongest LRI, the d-path Laplacian operators produces the emergence of new phenomena related to the location of the wave packet in graphs with barriers, which are not observed neither for the Schrödinger equation without LRI nor for the one using fractional powers of the Laplacian.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

d-Path Laplacians and Quantum Transport on Graphs

Estrada

2020

Mathematics

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“…These operators are the adjacency analogues of the d-path Laplacian operators of the graph [62,63,64]. The Mellin (power-law) transformed adjacency operator is then defined bỹ…”

Section: Supplementary Notementioning

confidence: 99%

“…Other transforms are also possible as the Laplace (exponential) one (see for instance [62,63,64] for the analogues in the path Laplacians), but we constraint ourselves here to the power-law one.…”

Section: Supplementary Notementioning

confidence: 99%

Mathematical modelling for sustainable aphid control in agriculture via intercropping

Allen‐Perkins

Estrada

2019

Proc. R. Soc. A.

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Agricultural losses to pest represent an important challenge in a global warming scenario. Intercropping is an alternative farming practice that promotes pest control without the use of chemical pesticides. Here we develop a mathematical model to study epidemic spreading and control in intercropped agricultural fields as a sustainable pest management tool for agriculture. The model combines the movement of aphids transmitting a virus in an agricultural field, the spatial distribution of plants in the intercropped field, and the presence of "trap crops" in an epidemiological Susceptible-Infected-Removed (SIR) model. Using this model we study several intercropping arrangements without and with trap crops and find a new intercropping arrangement that may improve significantly pest management in agricultural fields respect to the commonly used intercrop systems. arXiv:1903.05043v2 [q-bio.PE]

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“…For more definitions and terminologies, the readers are referred to [30][31][32][33][34][35][36][37][38][39][40][41]. …”

Section: Definition 1 ([228])mentioning

confidence: 99%

Energy of Pythagorean Fuzzy Graphs with Applications

Akram

Naz

2018

Mathematics

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Pythagorean fuzzy sets (PFSs), an extension of intuitionistic fuzzy sets (IFSs), inherit the duality property of IFSs and have a more powerful ability than IFSs to model the obscurity in practical decision-making problems. In this research study, we compute the energy and Laplacian energy of Pythagorean fuzzy graphs (PFGs) and Pythagorean fuzzy digraphs (PFDGs). Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of PFGs. Finally, we present numerical examples, including the design of a satellite communication system and the evaluation of the schemes of reservoir operation to illustrate the applications of our proposed concepts in decision making.

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Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice

Cited by 29 publications

References 33 publications

d-Path Laplacians and Quantum Transport on Graphs

d-Path Laplacians and Quantum Transport on Graphs

Mathematical modelling for sustainable aphid control in agriculture via intercropping

Energy of Pythagorean Fuzzy Graphs with Applications

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