Collective synchronization in the presence of reactive coupling and shear diversity

We analyze the synchronization dynamics of a model obtained from the phase reduction of the mean-field complex Ginzburg-Landau equation with heterogeneity. We present exact results that uncover the role of dissipative and reactive couplings on the synchronization transition when shears and natural frequencies are independently distributed. As it occurs in the purely dissipative case, an excess of shear diversity prevents the onset of synchronization, but this does not hold true if coupling is purely reactive. In this case the synchronization threshold turns out to depend on the mean of the shear distribution, but not on all the other distribution's moments.Comment: To appear in Phys. Rev.

Consensus and diversity in multi-state noisy voter models

We study a variant of the voter model with multiple opinions; individuals can imitate each other and also change their opinion randomly in mutation events. We focus on the case of a population with all-to-all interaction. A noise-driven transition between regimes with multi-modal and unimodal stationary distributions is observed. In the former, the population is mostly in consensus states; in the latter opinions are mixed. We derive an effective death-birth process, describing the dynamics from the perspective of one of the opinions, and use it to analytically compute marginals of the stationary distribution. These calculations are exact for models with homogeneous imitation and mutation rates, and an approximation if rates are heterogeneous. Our approach can be used to characterize the noise-driven transition and to obtain mean switching times between consensus states.Comment: 14 pages, 8 figure

Phase transitions induced by microscopic disorder: a study based on the order parameter expansion

Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two which describe the fluctuations around this mean value. With this tool we analyze phase-transitions induced by microscopic disorder in three prototypical models of phase-transitions which have been studied previously in the presence of thermal noise. We study how macroscopic order is induced or destroyed by time independent local disorder and analyze the limits of the approximation by comparing the results with the numerical solutions of the self-consistency equation which arises from the property of self-averaging. Finally, we carry on a finite-size analysis of the numerical results and calculate the corresponding critical exponents

Differential evolution to solve the lot size problem.

An Advanced Resource Planning model is presented to support optimal lot size decisions for performance improvement of a production system in terms of either delivery time or setup related costs. Based on a queueing network, a model is developed for a mix of multiple products following their own specific sequence of operations on one or more resources, while taking into account various sources of uncertainty, both in demand as well as in production characteristics. In addition, the model includes the impact of parallel servers and different time schedules in a multi-period planning setting. The corrupting influence of variabilities from rework and breakdown is explicitly modeled. As a major result, the differential evolution algorithm is able to find the optimal lead time as a function of the lot size. In this way, we add a conclusion on the debate on the convexity between lot size and lead time in a complex production environment. We show that differential evolution outperforms a steepest descent method in the search for the global optimal lot size. For problems of realistic size, we propose appropriate control parameters for the differential evolution in order to make its search process more efficient.Production planning; Lot sizing; Queueing networks; Differential evolution;

Weak Langmuir optical turbulence in a fiber cavity

We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied

Impact of quenched random fields on the ferroelectric-to-relaxor crossover in the solid solution (1−x)BaTiO3−xDyFeO3

Lead-based perovskite relaxor ferroelectrics are widely used as materials for numerous applications due to their extraordinary dielectric, piezoelectric, and electrostrictive properties. While the mechanisms of relaxor behavior are disputable, the importance of quenched (static) random electric fields created at nanoscale by the disordered heterovalent cations has been well recognized. Meanwhile, an increasing amount of scientific and technological efforts has been concentrated on lead-free perovskites, in particular, solid solutions of classical ferroelectric BaTiO 3 (BT), which better meet ecological requirements. Among BT-based solutions the homovalent systems are elaborately studied where strong random electric fields are absent, while the solubility limit of heterovalent solutions is typically too low to fully reveal the peculiarities of relaxor behavior. In this paper, we prepare a perovskite solid solution system (1 − x )Ba 2 + Ti 4 + O 3 − x Dy 3 + Fe 3 + O 3 (0 x 0 . 3) and study it as a model heterovalent lead-free system. We determine crystal structure, ferroelectric, and dielectric properties of ceramics in a wide range of temperatures and concentrations, construct a phase diagram, and find and analyze the concentration-induced crossover from normal ferroelectric to relaxor behavior. We demonstrate that quenched random electric fields of moderate strength promote the ferroelectric-to-relaxor crossover, but do not change qualitatively the peculiarities of relaxor behavior, while strong enough fields destroy the relaxor state, so that the material becomes an ordinary linear dielectric. The experimental results are compared with the predictions of known theories of relaxor ferroelectricity

Complex dynamics in coevolution models with ratio-dependent functional response

We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The underlying individual-based population dynamics are based on a ratio-dependent functional response [W.M. Getz, J. Theor. Biol. 108, 623 (1984)]. Analytical results for fixed-point population sizes in some simple communities are derived and discussed. In long kinetic Monte Carlo simulations we find quite robust, approximate 1/f noise in species diversity and population sizes, as well as power-law distributions for the lifetimes of individual species and the durations of periods of relative evolutionary stasis. Adaptive foraging enhances coexistence of species and produces a metastable low-diversity phase and a stable high-diversity phase.Comment: 19 page

Electron beam transfer line design for plasma driven Free Electron Lasers

Plasma driven particle accelerators represent the future of compact accelerating machines and Free Electron Lasers are going to benefit from these new technologies. One of the main issue of this new approach to FEL machines is the design of the transfer line needed to match of the electron-beam with the magnetic undulators. Despite the reduction of the chromaticity of plasma beams is one of the main goals, the target of this line is to be effective even in cases of beams with a considerable value of chromaticity. The method here explained is based on the code GIOTTO [1] that works using a homemade genetic algorithm and that is capable of finding optimal matching line layouts directly using a full 3D tracking code.Comment: 9 Pages, 4 Figures. A related poster was presented at EAAC 201

Secular dynamics of planetesimals in tight binary systems: Application to Gamma-Cephei

The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbital parameters of the secondary star. We construct a second-order theory (with respect to the masses) for the planar secular motion of small planetasimals and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for Gamma-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for Gamma-Cephei may affect the dynamics of small bodies in circunmstellar motion. For Gamma-Cephei, we find that the classical first-order expressions for the secular frequency and forced eccentricity lead to large inaccuracies around 50 % for semimajor axes larger than one tenth the orbital separation between the stellar components. Low eccentricities and/or masses reduce the importance of the second-order terms. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components, and the same result is found including the effects of a nonlinear gas drag. Thus, the possibility of planetary formation in this binary system largely appears insensitive to the orbital fits adopted for the stellar components, and any future alterations in the system parameters (due to new observations) should not change this picture. Finally, we show that planetesimals migrating because of gas drag may be trapped in mean-motion resonances with the binary, even though the migration is divergent.Comment: 11 pages, 9 figure