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Identifying the onset and decay of quasi-stationary families of almost-invariant sets with an application to atmospheric blocking events.
Chaos
December 2024
School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052, Australia.
Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organizes phase space. We introduce a method to identify time-parameterized families of almost-invariant sets in time-dependent dynamical systems, as well as the families' emergence and disappearance. In contrast to coherent sets, which may freely move about in phase space over time, our technique focuses on families of metastable sets that are quasi-stationary in space.
View Article and Find Full Text PDFEscape from a metastable state in non-Markovian population dynamics.
Phys Rev E
October 2024
Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Article Synopsis
- The study investigates long-term behavior in non-Markovian stochastic models, focusing on processes with heavy-tailed waiting time distributions to reflect long memory effects in populations.
- Three key cases are examined: genetic switching, population establishment, and extinction, using nonexponential rates of production.
- The research identifies two regimes based on the mean of waiting times, revealing how systems can stabilize or behave differently over time depending on the presence of memory and the initial conditions.
Increased projected changes in quasi-resonant amplification and persistent summer weather extremes in the latest multimodel climate projections.
Sci Rep
September 2024
Department of Earth & Environmental Science, University of Pennsylvania, Philadelphia, PA, USA.
High-amplitude quasi-stationary atmospheric Rossby waves with zonal wave numbers 6-8 associated with the phenomenon of quasi-resonant amplification (QRA) have been linked to persistent summer extreme weather events in the Northern Hemisphere. QRA is not well-resolved in current generation climate models, therefore, necessitating an alternative approach to assessing their behavior. Using a previously-developed fingerprint-based semi-empirical approach, we project future occurrence of QRA events based on a QRA index derived from the zonally averaged surface temperature field, comparing results from CMIP 5 and 6 (Coupled Model Intercomparison Project).
View Article and Find Full Text PDFInsights of infected Schwann cells extinction and inherited randomness in a stochastic model of leprosy.
Math Biosci
October 2024
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India. Electronic address:
Investigating disease progression, transmission of infection and impacts of Multidrug Therapy (MDT) to inhibit demyelination in leprosy involves a certain amount of difficulty in terms of the in-built uncertain complicated and complex intracellular cell dynamical interactions. To tackle this scenario and to elucidate a more realistic, rationalistic approach of examining the infection mechanism and associated drug therapeutic interventions, we propose a four-dimensional ordinary differential equation-based model. Stochastic processes has been employed on this deterministic system by formulating the Kolmogorov forward equation introducing a transition state and the quasi-stationary distribution, exact distribution analysis have been investigated which allow us to estimate an expected time to extinction of the infected Schwann cells into the human body more prominently.
View Article and Find Full Text PDFA Novel Methodology for Measuring Ambient Thermal Effects on Machine Tools.
Sensors (Basel)
April 2024
Department of Mechanical Engineering, Tekniker, Basque Research and Technology Alliance (BRTA), C/Iñaki Goenaga 5, 20600 Eibar, Spain.
Large machine tools are critically affected by ambient temperature fluctuations, impacting their performance and the quality of machined products. Addressing the challenge of accurately measuring thermal effects on machine structures, this study introduces the Machine Tool Integrated Inverse Multilateration method. This method offers a precise approach for assessing geometric error parameters throughout a machine's working volume, featuring a low level of uncertainty and high speed suitable for effective temperature change monitoring.
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