Browsing by Author "Cisternas, Jaime"

Now showing 1 - 11 of 11
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    (33, 33) Cisternas, Jaime; Rohe, Kevin; Wehner, Stefan; 33
    A single-species reaction-diffusion model is used for studying the coexistence of multiple stable steady states. In these systems, one can define a potential-like functional that contains the stability properties of the states, and the essentials of the motion of wave fronts in one-and two-dimensional space. Using a quintic polynomial for the reaction term and taking advantage of the well-known butterfly bifurcation, we analyze the different scenarios involving the competition of two and three stable steady states, based on equipotential curves and points in parameter space. The predicted behaviors, including a front splitting instability, are contrasted to numerical integrations of reaction fronts in two dimensions.
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    (33, 33) Rosas, Alexandre; Cisternas, Jaime; Escaff, Daniel; Pinto, Italo'Ivo Lima Dias; Lindenberg, Katja; 33
    It is well established that ensembles of globally coupled stochastic oscillators may exhibit a nonequilibrium phase transition to synchronization in the thermodynamic limit (infinite number of elements). In fact, since the early work of Kuramoto, mean-field theory has been used to analyze this transition. In contrast, work that directly deals with finite arrays is relatively scarce in the context of synchronization. And yet it is worth noting that finite-number effects should be seriously taken into account since, in general, the limits N?? (where N is the number of units) and t?? (where t is time) do not commute. Mean-field theory implements the particular choice first N?? and then t??. Here we analyze an ensemble of three-state coupled stochastic units, which has been widely studied in the thermodynamic limit. We formally address the finite-N problem by deducing a Fokker-Planck equation that describes the system. We compute the steady-state solution of this Fokker-Planck equation (that is, finite N but t??). We use this steady state to analyze the synchronic properties of the system in the framework of the different order parameters that have been proposed in the literature to study nonequilibrium transitions.
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    (33, 33) Cisternas, Jaime; Cartes, Carlos; Descalzi, Orazio; Albers, Tony; Radons, Günter; 33
    The propagation of light pulses in dual-core nonlinear optical fibers is studied using a model proposed by Sakaguchi and Malomed. The system consists of a supercritical complex Ginzburg-Landau equation coupled to a linear equation. Our analysis includes single standing and walking solitons as well as walking trains of 3, 5, 6, and 12 solitons. For the characterization of the different scenarios, we used ensemble-averaged square displacement of the soliton trajectories and time-averaged power spectrum of the background waves. Power law spectra, indicative of turbulence, were found to be associated with random walks. The number of solitons (or their separations) can trigger anomalous random walks or totally suppress the background waves.
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    (33, 33) Cisternas, Jaime; Escaff, Daniel; Clerc, Marcel G.; Lefever, René; Tlidi, Mustapha; 33
    Nonuniform spatial distributions of vegetation in scarce environments consist of either gaps, bands often called tiger bush or patches that can be either self-organized or spatially localized in space. When the level of aridity is increased, the uniform vegetation cover develops localized regions of lower biomass. These spatial structures are generically called vegetation gaps. They are embedded in a uniform vegetation cover. The spatial distribution of vegetation gaps can be either periodic or randomly distributed. We investigate the combined influence of the facilitative and the competitive nonlocal interactions between plants, and the role of crow/root allometry, on the formation of gapped vegetation patterns. We characterize first the formation of the periodic distribution of gaps by drawing their bifurcation diagram. We then characterize localized and aperiodic distributions of vegetation gaps in terms of their snaking bifurcation diagram.
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    (33, 33) Cisternas, Jaime; Mellado, Paula; Urbina, Felipe; Portilla, Cristóbal; Carrasco, Miguel; Concha, Andrés; 33
    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.
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    (33, 33) Villegas, Nicolas; Carvajal, Joaquin; Alam, Shumiya; Pantha, Tanvir; Maggi, Cristobal; Cisternas, Jaime; Ni, Kai; Dutta, Sourav; Gomez, Jorge; 33
    In this work, we present and make openly available an optimized SPICE-compatible Landau-Khalatnikov (L-K) equivalent ferroelectric model. The proposed model maps L-K equations to a positive feedback (PF) loop, providing an intuitive and efficient pathway for direct implementation in SPICE, enabling direct integration with other circuital components within circuit simulations. Furthermore, the model parameters are directly mapped to experimentally accessible values, enabling a straightforward calibration of the static and dynamic behavior. Using the model on SPICE simulations, we can accurately replicate and provide insights of complex system interaction phenomena such as the dynamics of ferroelectric oscillators.
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    (33, 33) Anguita, Jaime; Cisternas, Jaime; 33
    We propose a method for identifying orbital angular momentum (OAM) states within a vortex superposition using a Shack-Hartmann (SH) sensor as a spatial-diversity detector. We define a local OAM at every pixel of the SH image, from which we construct an OAM spectrum. The topological charges are determined fromtheOAMspectrum using a low-complexity algorithm, resulting in estimates that are robust to beam wandering. Data from a 200 m experimental transmission are successfully tested using the proposed technique.
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    Competing ternary surface reaction CO + O2 +H2 on Ir(111)
    Rohe, Kevin; Cisternas, Jaime; Wehner, Stefan
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    Variational principles in image processing and the regularization of orientation fields
    Cisternas, Jaime; GÁlvez, Marcelo; Stieltjes, Bram; Laun, Frederik B.