1,720,974 research outputs found
A hierarchical mean field model of interacting spins
No full textWe consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical diffusions of Ornstein-Uhlenbeck type. In particular, the diffusive variables enter in the spin-flip rates, effectively acting as dynamical magnetic fields. In absence of the diffusions, the spin-flip dynamics can be thought of as a modification of the Curie-Weiss model. We study the mean field and the two-level hierarchical model, in the latter case restricting to a subcritical regime, corresponding to high temperatures, obtaining macroscopic limits at different spatio-temporal scales and studying the phase transitions in the system. We also formulate a generalization of our results to the kth level hierarchical case, for any k finite, in the subcritical regime. We finally address the supercritical regime, in the zero-temperature limit, for the two-level hierarchical case, proceeding heuristically with the support of numerics. (C) 2021 Elsevier B.V. All rights reserved
Oscillatory Behavior in a Model of Non-Markovian Mean Field Interacting Spins
Full text linkWe analyze a non-Markovian mean field interacting spin system, related to the Curie–Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a distribution with memory. The resulting stochastic evolution for a single particle is a spin-valued renewal process, an example of a two-state semi-Markov process. We associate to the individual dynamics an equivalent Markovian description, which is the subject of our analysis. We study a corresponding interacting particle system, where a mean field interaction-depending on the magnetization of the system-is introduced as a time scaling on the waiting times between two successive particle’s jumps. Via linearization arguments on the Fokker–Planck mean field limit equation, we give evidence of emerging periodic behavior. Specifically, numerical analysis on the discrete spectrum of the linearized operator, characterized by the zeros of an explicit holomorphic function, suggests the presence of a Hopf bifurcation for a critical value of the temperature. The presence of a Hopf bifurcation in the limit equation matches the emergence of a periodic behavior obtained by simulating the N-particle system
A hierarchical mean field model of interacting spins
No full textWe consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical diffusions of Ornstein–Uhlenbeck type. In particular, the diffusive variables enter in the spin-flip rates, effectively acting as dynamical magnetic fields. In absence of the diffusions, the spin-flip dynamics can be thought of as a modification of the Curie–Weiss model. We study the mean field and the two-level hierarchical model, in the latter case restricting to a subcritical regime, corresponding to high temperatures, obtaining macroscopic limits at different spatio-temporal scales and studying the phase transitions in the system. We also formulate a generalization of our results to the kth level hierarchical case, for any k finite, in the subcritical regime. We finally address the supercritical regime, in the zero-temperature limit, for the two-level hierarchical case, proceeding heuristically with the support of numerics
Assessing the diversity pattern of cryophilous plant species in high elevation habitats
No full textThis study aimed to better document the diversity and distribution patterns of vascular cryophilous species across major habitat types in a high-elevation Mediterranean system in central Italy. The research addressed the following questions: (a) whether different habitats support similar levels of biodiversity in terms of total vascular plants richness and cryophilous species richness, and (b) how each habitat contributes to the total cryophilous species diversity. A random stratified sampling approach based on a habitat map was applied to construct rarefaction curves for overall cryophilous species richness and habitat type-specific cryophilous richness. Rarefaction curves were also constructed for all-species and exclusive species. To determine whether the targeted species represented a constant proportion of all species, the ratio between the rarefaction curves of the cryophilous species and all species was also calculated. The results highlight the importance of the different habitat types in overall and cryophilous species conservation because these different habitat types had progressively higher richness values. At the regional scale, steep slopes had the highest species diversity, the greatest exclusive species richness and a steep rarefaction curve. The diversity pattern of cryophilous taxa was not related to the general pattern of total species richness, with these species being more common in three habitat types with extreme environmental conditions: ridges, cliffs, and screes. For the establishment of successful biodiversity conservation programs, it is imperative to include species-poor habitats containing a high proportion of cryophilous species, which are considered to be threatened by climate warming
The role of the “Giardino della Flora Appenninica di Capracotta” (Molise-Italy) in the biodiversity conservation
No full text
- …
