Social media enhances languages differentiation: a mathematical description

Understanding and predicting the evolution of competing languages is a topic of high interest in a world with more than 6000 languages competing in a highly connected environment. We consider a reasonable mathematical model describing a situation of competition between two languages and analyse the effect of the speakers' connectivity (i.e. social networks). Surprisingly, instead of homogenizing the system, a high degree of connectivity helps to introduce differentiation for the appropriate parametersXunta de Galicia under Research grant no. GPC2015/014, the Spanish Ministerio de Economía y Competitividad and European Regional Development Fund under contract MAT2015-71119-R (MINECO/FEDER). The authors belong to the CRETUS Strategic Partnership (AGRUP2015/02). All these programmes are co-funded by FEDER (UE)S

Autoorganización de Estructuras de Turing en Presencia de Campos Externos

La autoorganización es uno de los mecanismos más importantes en la formación de patrones en los sistemas vivos. Normalmente, en la Naturaleza ello no ocurre de manera aislada sino en presencia de perturbaciones externas que modifican la dinámica difusiva de los procesos de orgranización. En este sentido se ha encontrado que uno de los sistemas más popularmente conocidos responsables de la formación de patrones, como la inestabilidad de Turing (compartimentada, Belousov-Zhabotinsky-aerosol-OT) responde muy sensiblemente a cambios en los procesos de difusión. Con el fin de modificar tales mecanismos difusivos, se aplica una perturbación con un carácter anisótropo. Las observaciónes experimentales y numéricas indican que la perturbación es capaz de modificar el patrón incluso forzar su aniquiliación. Se pueden ver cambios significantes tanto en la longitud de onda como en la morfología del patrón para diferentes valores la pertubación. Además, para forzamientos elevados la orientación de los patrones presenta un acoplamiento con la simetría de la perturbación

Externally controlled anisotropy in pattern-forming reaction-diffusion systems

The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.info:eu-repo/semantics/publishe

Harmonic vibration modifies the Turing pattern morphology from White-Spots to Black-Spots

info:eu-repo/semantics/nonPublishe

Harmonic vibration on a reactive fluid at boundary layer regime modifies the Turing instability

info:eu-repo/semantics/publishe

On the Morphology of Turing Instability under Microscopic Transport

info:eu-repo/semantics/nonPublishe

Mesoscopic perturbation on a reaction-diffusion system modifies the Turing instability

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Characterizing topological transitions in a Turing-pattern-forming reaction-diffusion system.

Turing structures appear naturally and they are demonstrated under different spatial configurations such as stripes and spots as well as mixed states. The traditional tool to characterize these patterns is the Fourier transformation, which accounts for the spatial wavelength, but it fails to discriminate among different spatial configurations or mixed states. In this paper, we propose a parameter that clearly differentiates the different spatial configurations. As an application, we considered the transitions induced by an external forcing in a reaction-diffusion system although the results are straightforwardly extended to different problems with similar topologies. The method was also successfully tested on a temporally evolving pattern.info:eu-repo/semantics/publishe

Data from: Social media enhances languages differentiation: a mathematical description

Understanding and predicting the evolution of competing languages is a topic of high interest in a world with more than 6000 languages competing in a highly connected environment. We consider a reasonable mathematical model describing a situation of competition between two languages and analyse the effect of the speakers' connectivity (i.e. social networks). Surprisingly, instead of homogenizing the system, a high degree of connectivity helps to introduce differentiation for the appropriate parameters

Manipulation of diffusion coefficients via periodic vertical forcing controls the mechanism of Turing pattern formation.

We study, theoretically and experimentally, the dynamical response of macroscopic Turing patterns to a mechanical periodic forcing which implies a sinusoidal modulation of gravity. Theoretical predictions indicate that the extra energy, due to the forcing, modifies the diffusion coefficient at a microscopic level, producing changes in the Turing domain and in the pattern characteristics, in particular its wavelength. To check the theoretical analysis, we perform numerical simulations with standard models. Experiments were also performed in the closed Belousov-Zhabotinsky reaction confined in AOT microemulsion (BZ-AOT system). Experiments as well as numerical and theoretical results show good agreement.info:eu-repo/semantics/publishe