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Cisternas, J., Mellado, P., Urbina, F., Portilla, C., Carrasco, M., & Concha, A. (2021). Stable and unstable trajectories in a dipolar chain. Phys. Rev. B, 103(13), 134443.
Abstract: In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most of the times if the experimental realization is adiabatic, they are considered just a nuisance. Here we use a small number of XY magnetic dipoles subject to an external magnetic field for studying the origin of their collective magnetic response. Using bifurcation theory we have found all the possible solutions being stable or unstable, and explored how those solutions are naturally connected by points where the symmetries of the system are lost or restored. Unstable solutions that reveal the symmetries of the system are found to be the culprit that shape hysteresis loops in this system. The complexity of the solutions for the nonlinear dynamics is analyzed using the concept of boundary basin entropy, finding that the damping timescale is critical for the emergence of fractal structures in the basins of attraction. Furthermore, we numerically found domain wall solutions that are the smallest possible realizations of transverse walls and vortex walls in magnetism. We experimentally confirmed their existence and stability showing that our system is a suitable platform to study domain wall dynamics at the macroscale.
Keywords: MAGNETIC MONOPOLES; CRYSTAL STATISTICS; INTERFERENCE; HYSTERESIS; RELAXATION; ENTROPY

MontalvaMedel, M., Rica, S., & Urbina, F. (2020). Phase space classification of an Ising cellular automaton: The Q2R model. Chaos Solitons Fractals, 133, 14 pp.
Abstract: An exact classification of the different dynamical behaviors that exhibits the phase space of a reversible and conservative cellular automaton, the socalled Q2R model, is shown in this paper. Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of configurations grows exponentially with the system size. As a consequence of the intrinsic reversibility of the model, the phase space is composed only by configurations that belong to a fixed point or a cycle. In this work, we classify them in four types accordingly to well differentiated topological characteristics. Three of them which we call of type SI, SII, and SIII share a symmetry property, while the fourth, which we call of type AS does not. Specifically, we prove that any configuration of Q2R belongs to one of the four previous types of cycles. Moreover, at a combinatorial level, we can determine the number of cycles for some small periods which are almost always present in the Q2R. Finally, we provide a general overview of the resulting decomposition of the arbitrary size Q2R phase space and, in addition, we realize an exhaustive study of a small Ising system (4 x 4) which is thoroughly analyzed under this new framework, and where simple mathematical tools are introduced in order to have a more direct understanding of the Q2R dynamics and to rediscover known properties like the energy conservation. (C) 2020 Elsevier Ltd. All rights reserved.

RodriguezValdecantos, G., Manzano, M., Sanchez, R., Urbina, F., Hengst, M. B., Lardies, M. A., et al. (2017). Early successional patterns of bacterial communities in soil microcosms reveal changes in bacterial community composition and network architecture, depending on the successional condition. Appl. Soil Ecol., 120, 44–54.
Abstract: Soil ecosystem dynamics are influenced by the composition of bacterial communities and environmental conditions. A common approach to study bacterial successional dynamics is to survey the trajectories and patterns that follow bacterial community assemblages; however early successional stages have received little attention. To elucidate how soil type and chemical amendments influence both the trajectories that follow early compositional changes and the architecture of the community bacterial networks in soil bacterial succession, a time series experiment of soil microcosm experiments was performed. Soil bacterial communities were initially perturbed by dilution and subsequently subjected to three amendments: application of the pesticide 2,4dichlorophenoxyacetic acid, as a pesticideamended succession; application of cycloheximide, an inhibitor affecting primarily eukaryotic microorganisms, as a eukaryoticinhibition bacterial succession; or application of sterile water as a nonperturbed control. Terminal restriction fragment length polymorphism (TRFLP) analysis of the 16S rRNA gene isolated from soil microcosms was used to generate bacterial relative abundance datasets. BrayCurtis similarity and beta diversity partitionbased methods were applied to identify the trajectories that follow changes in bacterial community composition. Results demonstrated that bacterial communities exposed to these three conditions rapidly differentiated from the starting point (less than 12 h), followed different compositional change trajectories depending on the treatment, and quickly converged to a state similar to the initial community (4872 h). Network inference analysis was applied using a generalized LotkaVolterra model to provide an overview of bacterial OTU interactions and to follow the changes in bacterial community networks. This analysis revealed that antagonistic interactions increased when eukaryotes were inhibited, whereas cooperative interactions increased under pesticide influence. Moreover, central OTUs from soil bacterial community networks were also persistent OTUs, thus confirming the existence of a core bacterial community and that these same OTUs could plastically interact according to the perturbation type to quickly stabilize bacterial communities undergoing succession.

Urbina, F., Franco, A. F., & Concha, A. (2022). Frequency dynamics of a chain of magnetized rotors: dumbbell model vs LandauLifshitz equation. J. Phys. Condens. Matter, 34(48), 485801.
Abstract: During the past decades magnetic materials and structures that span several length scales have been of interest mainly due to their application in data storage and processing, flexible electronics, medicine, between others. From a microscopic point of view, these systems are typically studied using the LandauLifshitz equation (LLE), while approaches such as the dumbbell model are used to study macroscopic magnetic structures. In this work we use both the LLE and the dumbbell model to study spin chains of various lengths under the effect of a time dependentmagnetic field, allowing us to compare qualitatively the results obtained by both approaches. This has allowed us to identify and describe in detail several frequency modes that appear, with additional modes arising as the chain length increases. Moreover, we find that high frequency modes tend to be absorbed by lower frequency ones as the amplitude of the field increases. The results obtained in this work are of interest not only to better understand the behavior of the macroscopic spins chains, but also expands the available tools for qualitative studies of both macroscopic and microscopic versions of the studied system, or more complex structures such as junctions or lattices. This would allow to study the qualitative behavior of microscopic systems (e.g. nanoparticles) using macroscopic arrays of magnets, and vice versa.
Keywords: macroscopic system; magnetic rotors; frequency modes

Urbina, F., & Rica, S. (2016). Master equation approach to reversible and conservative discrete systems. Phys. Rev. E, 94(6), 9 pp.
Abstract: A master equation approach is applied to a reversible and conservative cellular automaton model (Q2R). The Q2R model is a dynamical variation of the Ising model for ferromagnetism that possesses quite a rich and complex dynamics. The configuration space is composed of a huge number of cycles with exponentially long periods. Following Nicolis and Nicolis [G. Nicolis and C. Nicolis, Phys. Rev. A 38, 427 (1988)], a coarsegraining approach is applied to the time series of the total magnetization, leading to a master equation that governs the macroscopic irreversible dynamics of the Q2R automata. The methodology is replicated for various lattice sizes. In the case of small systems, we show that the master equation leads to a tractable probability transfer matrix of moderate size, which provides a master equation for a coarsegrained probability distribution. The method is validated and some explicit examples are discussed.
