Mellado, P., Concha, A., & Rica, S. (2020). Magnetoelectric Effect in Dipolar Clusters. Phys. Rev. Lett., 125(23), 237602.
Abstract: We combine the anisotropy of magnetic interactions and the point symmetry of finite solids in the study of dipolar clusters as new basic units for multiferroics metamaterials. The Hamiltonian of magnetic dipoles with an easy axis at the vertices of polygons and polyhedra, maps exactly into a Hamiltonian with symmetric and antisymmetric exchange couplings. The last one gives rise to a DzyaloshinskiiMoriya contribution responsible for the magnetic modes of the systems and their symmetry groups, which coincide with those of a particle in a crystal field with spinorbit interaction. We find that the clusters carry spin current and that they manifest the magnetoelectric effect. We expect our results to pave the way for the rational design of magnetoelectric devices at room temperature

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.

Mora, F., Coullet, P., Rica, S., & Tirapegui, E. (2018). Numerical path integral calculation of the probability function and exit time: an application to nongradient drift forces. Philos. Trans. R. Soc. AMath. Phys. Eng. Sci., 376(2135), 11 pp.
Abstract: We provide numerical solutions based on the path integral representation of stochastic processes for nongradient drift Langevin forces in the presence of noise, to follow the temporal evolution of the probability density function and to compute exit times even for arbitrary noise. We compare the results with theoretical calculations, obtaining excellent agreement in the weak noise limit. This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Picozzi, A., & Rica, S. (2012). Condensation of classical optical waves beyond the cubic nonlinear Schrodinger equation. Opt. Commun., 285(24), 5440–5448.
Abstract: A completely classical nonlinear wave is known to exhibit a process of condensation whose thermodynamic properties are analogous to those of the genuine BoseEinstein condensation. So far this phenomenon of wave condensation has been studied essentially in the framework of the nonlinear Schrodinger (NLS) equation with a pure cubic Kerr nonlinearity. We study wave condensation by considering two representative generalizations of the NLS equation that are relevant to the context of nonlinear optics, the nonlocal nonlinearity and the saturable nonlinearity. For both cases we derive analytical expressions of the condensate fraction in the weakly and the strongly nonlinear regime. The theory is found in quantitative agreement with the numerical simulations of the generalized NLS equations, without adjustable parameters. (C) 2012 Elsevier B.V. All rights reserved.

Reid, A., Lechenault, F., Rica, S., & AddaBedia, M. (2017). Geometry and design of origami bellows with tunable response. Phys. Rev. E, 95(1), 10 pp.
Abstract: Origami folded cylinders (origami bellows) have found increasingly sophisticated applications in space flight and medicine. In spite of this interest, a general understanding of the mechanics of an origami folded cylinder has been elusive. With a newly developed set of geometrical tools, we have found an analytic solution for all possible cylindrical rigidface states of both Miuraori and triangular tessellations. Although an idealized bellows in both of these families may have two allowed rigidface configurations over a welldefined region, the corresponding physical device, limited by nonzero material thickness and forced to balance hinge and platebending energy, often cannot stably maintain a stowed configuration. We have identified the parameters that control this emergent bistability, and we have demonstrated the ability to design and fabricate bellows with tunable deployability.

Rica, S. (2009). Analytical And Numerical Elements Of A Supersolid Model. Int. J. Bifurcation Chaos, 19(8), 2783–2800.
Abstract: In this article, the main properties of a model of supersolid in the frame of a GrossPitaevskii equation is reviewed. It was developed mainly by the author with Pomeau, Josserand and Sepulveda. Emphasis is placed on the numerical details and tools that are absent in our previous publications and maybe useful for authors who are eventually interested in the model. The model exhibits superfluid properties like nonclassical moment of inertia at T = 0K, quantized vortices and persistent currents without the presence of defects, moreover, only a transient flow is allowed by defects, akin to plastic flow in ordinary solids.

Rica, S. (2011). Phenomenological GinzburgLandau theory for supersolidity. Phys. Rev. B, 84(18), 8 pp.
Abstract: A GinzburgLandau theory is proposed in which the supersolid state is viewed as a system displaying features of an ordinary solid and of a superfluid. The theory shows that the superfluid part is responsible for a nonclassical rotational inertia (NCRI) behavior, but the ordinary part (the lattice) is responsible for elastic behaviors usually seen in solids. Moreover, the superfluid part contributes to an excess of heat capacity near the supersolidordinary solid transition. The theory provides a coherent picture, at least at the macroscopic scale, of supersolidity that reconciles (NCRI) and the heatcapacity measurements. The parameters of the GinzburgLandau free energy are estimated using experimental data, hence a healing length of the order of 100 nm and a critical speed of the order of 0.1 m/s are predicted, both results consistent with recent studies by Kubota and coworkers.

Rica, S., & Roberts, D. C. (2009). Induced interaction and crystallization of selflocalized impurity fields in a BoseEinstein condensate. Phys. Rev. A, 80(1), 13 pp.
Abstract: We model the behavior of N classical impurity fields immersed in a larger BoseEinstein condensate by N + 1 coupled nonlinear Schrodinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for selflocalization of the impurity fields. We derive analytically the attractive tail of the impurityimpurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which – combined with lattice orderis a characteristic of supersolidity.

Sepulveda, N., Josserand, C., & Rica, S. (2010). Superfluid density in a twodimensional model of supersolid. Eur. Phys. J. B, 78(4), 439–447.
Abstract: We study in 2dimensions the superfluid density of periodically modulated states in the framework of the meanfield GrossPitaevskii model of a quantum solid. We obtain a full agreement for the superfluid fraction between a semitheoretical approach and direct numerical simulations. As in 1dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.

Slepneva, S., O'Shaughnessy, B., Vladimirov, A. G., Rica, S., Viktorov, E. A., & Huyet, G. (2019). Convective NozakiBekki holes in a long cavity OCT laser. Opt. Express, 27(11), 16395–16404.
Abstract: We show, both experimentally and theoretically, that the loss of coherence of a long cavity optical coherence tomography (OCT) laser can be described as a transition from laminar to turbulent flows. We demonstrate that in this strongly dissipative system, the transition happens either via an absolute or a convective instability depending on the laser parameters. In the latter case, the transition occurs via formation of localised structures in the laminar regime, which trigger the formation of growing and drifting puffs of turbulence. Experimentally, we demonstrate that these turbulent bursts arc seeded by appearance of NozakiBekki holes, characterised by the zero field amplitude and pi phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Soto, P. C., Cartes, C., Davies, T. P., Olivari, J., Rica, S., & VogtGeisse, K. (2020). The anatomy of the 2019 Chilean social unrest. Chaos, 30(7), 14 pp.
Abstract: We analyze the 2019 Chilean social unrest episode, consisting of a sequence of events, through the lens of an epidemiclike model that considers global contagious dynamics. We adjust the parameters to the Chilean social unrest aggregated public data available from the Undersecretary of Human Rights and observe that the number of violent events follows a welldefined pattern already observed in various public disorder episodes in other countries since the 1960s. Although the epidemiclike models display a single event that reaches a peak followed by an exponential decay, we add standard perturbation schemes that may produce a rich temporal behavior as observed in the 2019 Chilean social turmoil. Although we only have access to aggregated data, we are still able to fit it to our model quite well, providing interesting insights on social unrest dynamics.

Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., & Fleischer, J. W. (2012). Observation of the kinetic condensation of classical waves. Nat. Phys., 8(6), 469–473.
Abstract: The observation of BoseEinstein condensation, in which particle interactions lead to a thermodynamic transition into a single, macroscopically populated coherent state, is a triumph of modern physics(15). It is commonly assumed that this transition is a quantum process, relying on quantum statistics, but recent studies in wave turbulence theory have suggested that classical waves with random phases can condense in a formally identical manner(69). In complete analogy with gas kinetics, particle velocities map to wavepacket kvectors, collisions are mimicked by fourwave mixing, and entropy principles drive the system towards an equipartition of energy. Here, we use classical light in a selfdefocusing photorefractive crystal to give the first observation of classical wave condensation, including the growth of a coherent state, the spectral redistribution towards equilibrium, and the formal reversibility of the interactions. The results confirm fundamental predictions of kinetic wave theory and hold relevance for a variety of fields, ranging from BoseEinstein condensation to information transfer and imaging.

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.

Valle, M. A., Ruz, G. A., & Rica, S. (2018). Transactional Database Analysis by Discovering Pairwise Interactions Strengths. In 2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM) (Vol. 2018).

Valle, M. A., Ruz, G. A., & Rica, S. (2019). Market basket analysis by solving the inverse Ising problem: Discovering pairwise interaction strengths among products. Physica A, 524, 36–44.
Abstract: Large datasets containing the purchasing information of thousands of consumers are difficult to analyze because the possible number of different combinations of products is huge. Thus, market baskets analysis to obtain useful information and find interesting pattern of buying behavior could be a daunting task. Based on the maximum entropy principle, we build a probabilistic model that explains the probability of occurrence of market baskets which is equivalent to Ising models. This type of model allows us to understand and to explore the functional interactions among products that make up the market offer. Additionally, the parameters of the model inferred using Boltzmann learning, allow us to suggest that the buying behavior is very similar to the spinglass physical system. Moreover, we show that the resulting parameters of the model could be useful to describe the hierarchical structure of the system which leads to interesting information about the different market baskets. (C) 2019 Elsevier B.V. All rights reserved.

Vivanco, F., Rica, S., & Melo, F. (2012). Dynamical arching in a two dimensional granular flow. Granul. Matter, 14(5), 563–576.
Abstract: A study of grains flow in a two dimensional hopper using particle tracking and photoelastic methods is presented in this article. An intermittent network of contact forces consisting of force chains and arches is observed. This network is responsible for fluctuations in the average vertical velocity. The magnitude of these fluctuations depends on the hopper's geometry, and it quickly reduces for large aperture size and small inclination angles. The average velocity field is described using a combination of harmonic angular functions and a power law of radial position. The mass flow rate is determined through the average velocity field and a Beverloo type scaling is obtained. We found that the effect of the inclination angle on the mass flow rate is given by . It is also found that the critical aperture size, approaching jamming, depends linearly on . At small D/d, the time average of the network of contact forces shows a boundary with characteristics resembling the free fall arch. We show that an arch can be built following the principal compression orientation of the stress tensor which captures the characteristics of the arches observed experimentally.
