Nonlinear Sciences

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New submissions for Thu, 2 May 24

[1]  arXiv:2405.00370 [pdf, ps, other]

Title: Simple recursions displaying interesting evolutions

Authors: Francesco Calogero

Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

[2]  arXiv:2405.00388 [pdf, other]

Title: Delamination Detection in Layered Waveguides using Ostrovsky Wave Packets

Authors: J. S. Tamber, D. J. Chappell, M. R. Tranter

Comments: 9 pages, 7 figures

Subjects: Pattern Formation and Solitons (nlin.PS)

We examine the scattering of Ostrovsky wave packets, generated from an incident solitary wave, in a two layered waveguide with a delamination in the centre and soft (imperfect) bonding either side of the centre. The layers of the waveguide are assumed to consist of different materials, and the strains are described by a system of coupled Boussinesq equations. A semi-analytical approach consisting of matched asymptotic multiple-scale expansions is applied, leading to Ostrovsky equations in soft bonded regions and Korteweg-de Vries equations in the delaminated region. This semi-analytical method has good agreement with direct numerical simulations, validating the approach.
In the delaminated regions, Ostrovsky wave packets evolve into a train of solitary waves, which subsequently evolve into Ostrovsky wave packets in the second bonded region. Analysis of the phase shift in the wave packet, introduced from the delaminated region, allows us to predict both the position and the length of the delamination; the first time this has been achieved using nonlinear waves. These results motivate experiments to validate the theoretical results, with the aim of creating a tool to monitor the integrity of layered structures.

Cross-lists for Thu, 2 May 24

[3]  arXiv:2405.00271 (cross-list from math-ph) [pdf, ps, other]

Title: Exact solution of the propagation of ON-OFF signals by dispersive waves

Authors: Ken Yamamoto

Comments: 15 pages, 9 figures

Subjects: Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)

The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly calculated for two types of dispersion relations. Further, the analysis of these solutions shows that the ON-OFF signal propagates with the group velocity and that the boundary thickness of the signal increases with time, typically at a rate proportional to the square root of time, owing to dispersion. Additionally, an approximate solution for a general dispersion relation is derived, and a for a higher-complexity ON-OFF switching pattern is constructed.

[4]  arXiv:2405.00459 (cross-list from cs.SI) [pdf, other]

Title: U.S. Election Hardens Hate Universe

Authors: Akshay Verma, Richard Sear, Neil F. Johnson

Subjects: Social and Information Networks (cs.SI); Human-Computer Interaction (cs.HC); Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph)

Local or national politics can trigger potentially dangerous hate in someone. But with a third of the world's population eligible to vote in elections in 2024 alone, we lack understanding of how individual-level hate multiplies up to hate behavior at the collective global scale. Here we show, based on the most recent U.S. election, that offline events are associated with a rapid adaptation of the global online hate universe that hardens (strengthens) both its network-of-networks structure and the 'flavors' of hate content that it collectively produces. Approximately 50 million potential voters in hate communities are drawn closer to each other and to the broad mainstream of approximately 2 billion others. It triggers new hate content at scale around immigration, ethnicity, and antisemitism that aligns with conspiracy theories about Jewish-led replacement before blending in hate around gender identity/sexual orientation, and religion. Telegram acts as a key hardening agent - yet is overlooked by U.S. Congressional hearings and new E.U. legislation. Because the hate universe has remained robust since 2020, anti-hate messaging surrounding not only upcoming elections but also other events like the war in Gaza, should pivot to blending multiple hate 'flavors' while targeting previously untouched social media structures.

[5]  arXiv:2405.00518 (cross-list from math.CO) [pdf, ps, other]

Title: Graph-Based Multivariate Multiscale Dispersion Entropy: Efficient Implementation and Applications to Real-World Network Data

Authors: John Stewart Fabila-Carrasco, Chao Tan, Javier Escudero

Comments: 9 pages, 10 figures

Subjects: Combinatorics (math.CO); Computational Engineering, Finance, and Science (cs.CE); Chaotic Dynamics (nlin.CD)

We introduce Multivariate Multiscale Graph-based Dispersion Entropy (mvDEG), a novel, computationally efficient method for analyzing multivariate time series data in graph and complex network frameworks, and demonstrate its application in real-world data. mvDEG effectively combines temporal dynamics with topological relationships, offering enhanced analysis compared to traditional nonlinear entropy methods. Its efficacy is established through testing on synthetic signals, such as uncorrelated and correlated noise, showcasing its adeptness in discerning various levels of dependency and complexity.
The robustness of mvDEG is further validated with real-world datasets, effectively differentiating various two-phase flow regimes and capturing distinct dynamics in weather data analysis. An important advancement of mvDEG is its computational efficiency. Our optimized algorithm displays a computational time that grows linearly with the number of vertices or nodes, in contrast to the exponential growth observed in classical methods. This efficiency is achieved through refined matrix power calculations that exploit matrix and Kronecker product properties, making our method faster than the state of the art. The significant acceleration in computational time positions mvDEG as a transformative tool for extensive and real-time applications, setting a new benchmark in the analysis of time series recorded at distributed locations and opening avenues for innovative applications.

[6]  arXiv:2405.00541 (cross-list from q-bio.PE) [pdf, other]

Title: New Trends on the Systems Approach to Modeling SARS-CoV-2 Pandemics in a Globally Connected Planet

Authors: Giulia Bertaglia, Andrea Bondesan, Diletta Burini, Raluca Eftimie, Lorenzo Pareschi, Giuseppe Toscan

Subjects: Populations and Evolution (q-bio.PE); Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph)

This paper presents a critical analysis of the literature and perspective research ideas for modeling the epidemics caused by the SARS-CoV-2 virus. It goes beyond deterministic population dynamics to consider several key complexity features of the system under consideration. In particular, the multiscale features of the dynamics from contagion to the subsequent dynamics of competition between the immune system and the proliferating virus. Other topics addressed in this work include the propagation of epidemics in a territory, taking into account local transportation networks, the heterogeneity of the population, and the study of social and economic problems in populations involved in the spread of epidemics. The overall content aims to show how new mathematical tools can be developed to address the above topics and how mathematical models and simulations can contribute to the decision making of crisis managers.

Replacements for Thu, 2 May 24

[7]  arXiv:2403.00721 (replaced) [pdf, other]

Title: New cluster algebras from old: integrability beyond Zamolodchikov periodicity

Authors: Andrew N. W. Hone, Wookyung Kim, Takafumi Mase

Comments: Typos corrected, with new results and additional appendix added

Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Combinatorics (math.CO)

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