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Vieira, A. P., Goles, E., & Herrmann, H. J. (2021). Phase transitions in a conservative game of life. Phys. Rev. E, 103(1), 012132.
Abstract: We investigate the dynamics of a conservative version of Conway's Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway's rules but only by swapping their positions, irrespective of their mutual distance. Our study is based on squarelattice simulations as well as a meanfield calculation. As the density of dead cells is increased, we identify a discontinuous phase transition between an inactive phase, in which the dynamics freezes after a finite time, and an active phase, in which the dynamics persists indefinitely in the thermodynamic limit. Further increasing the density of dead cells leads the system back to an inactive phase via a second transition, which is continuous on the square lattice but discontinuous in the meanfield limit.
Keywords: SELFORGANIZED CRITICALITY; DYNAMICS

Domic, N. G., Goles, E., & Rica, S. (2011). Dynamics and complexity of the Schelling segregation model. Phys. Rev. E, 83(5), 13 pp.
Abstract: In this paper we consider the Schelling social segregation model for two different populations. In Schelling's model, segregation appears as a consequence of discrimination, measured by the local difference between two populations. For that, the model defines a tolerance criterion on the neighborhood of an individual, indicating wether the individual is able to move to a new place or not. Next, the model chooses which of the available unhappy individuals really moves. In our work, we study the patterns generated by the dynamical evolution of the Schelling model in terms of various parameters or the initial condition, such as the size of the neighborhood of an inhabitant, the tolerance, and the initial number of individuals. As a general rule we observe that segregation patterns minimize the interface of zones of different people. In this context we introduce an energy functional associated with the configuration which is a strictly decreasing function for the tolerant people case. Moreover, as far as we know, we are the first to notice that in the case of a nonstrictlydecreasing energy functional, the system may segregate very efficiently.

During, G., Josserand, C., & Rica, S. (2015). Selfsimilar formation of an inverse cascade in vibrating elastic plates. Phys. Rev. E, 91(5), 10 pp.
Abstract: The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a timedependent inverse cascade, opening up the possibility of selforganization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the shortwave fluctuations. This dynamics appears to be selfsimilar and possesses a powerlaw behavior in the shortwavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a longwave coherent structure in finite time.

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.

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.

Bottcher, L., WoolleyMeza, O., Goles, E., Helbing, D., & Herrmann, H. J. (2016). Connectivity disruption sparks explosive epidemic spreading. Phys. Rev. E, 93(4), 8 pp.
Abstract: We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptibleinfectedsusceptible model, typical of mathematical epidemiology, on a network. Infection spreads from infected to healthy nodes, with the addition that infected nodes can only recover when they remain connected to a predefined central node, through a path that contains only healthy nodes. In this system, clusters of infected nodes will absorb their noninfected interior because no path exists between the central node and encapsulated nodes. This gives rise to the simultaneous infection of multiple nodes. Interestingly, the system converges to only one of two stationary states: either the whole population is healthy or it becomes completely infected. This simultaneous cluster infection can give rise to discontinuous jumps of different sizes in the number of failed nodes. Larger jumps emerge at lower infection rates. The network topology has an important effect on the nature of the transition: we observed hysteresis for networks with dominating local interactions. Our model shows how local spread can abruptly turn uncontrollable when it disrupts connectivity at a larger spatial scale.

Ekman, R., Asenjo, F. A., & Zamanian, J. (2017). Relativistic kinetic equation for spin1/2 particles in the longscalelength approximation. Phys. Rev. E, 96(2), 8 pp.
Abstract: In this paper, we derive a fully relativistic kinetic theory for spin1/2 particles and its coupling to Maxwell's equations, valid in the longscalelength limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in (h) over bar. Our starting point is a FoldyWouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasidistribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is nontrivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as “hidden momentum” and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the AbrahamMinkowski dilemma.

Asenjo, F. A., & Mahajan, S. M. (2019). Diamagnetic field states in cosmological plasmas. Phys. Rev. E, 99(5), 7 pp.
Abstract: Using a generally covariant electrovortic (magnetofluid) formalism for relativistic plasmas, the dynamical evolution of a generalized vorticity (a combination of the magnetic and kinematic parts) is studied in a cosmological context. We derive macroscopic vorticity and magnetic field structures that can emerge in spatial equilibrium configurations of the relativistic plasma. These fields, however, evolve in time. These magnetic and velocity fields, selfconsistently sustained in a plasma with arbitrary thermodynamics, constitute a diamagnetic state in the expanding universe. In particular, we explore a special class of magnetic and velocity field structures supported by a plasma in which the generalized vorticity vanishes. We derive a highly interesting characteristic of such “superconductorlike” fields in a cosmological plasmas in the radiation era in the early universe. In that case, the fields grow proportional to the scale factor, establishing a deep connection between the expanding universe and the primordial magnetic fields.
