Pattern orientation in finite domains without boundaries

We investigate the orientation of nonlinear stripe patterns in finite domains. Motivated by recent experiments, we introduce a control parameter drop from supercritical inside a domain to subcritical outside without boundary conditions at the domain border. As a result, stripes align perpendicular to shallow control parameter drops. For steeper drops, non-adiabatic effects lead to a surprising orientational transition to parallel stripes with respect to the borders. We demonstrate this effect in terms of the Brusselator model and generic amplitude equations

Systematic extension of the Cahn-Hilliard model for motility-induced phase separation

We consider a continuum model for motility-induced phase separation (MIPS) of active Brownian particles [J. Chem. Phys. 142, 224149 (2015)]. Using a recently introduced perturbative analysis [Phys. Rev. E 98, 020604(R) (2018)], we show that this continuum model reduces to the classic Cahn-Hilliard (CH) model near the onset of MIPS. This makes MIPS another example of the so-called active phase separation. We further introduce a generalization of the perturbative analysis to the next higher order. This results in a generic higher order extension of the CH model for active phase separation. Our analysis establishes the mathematical link between the basic mean-field MIPS model on the one hand, and the leading order and extended CH models on the other hand. Comparing numerical simulations of the three models, we find that the leading order CH model agrees nearly perfectly with the full continuum model near the onset of MIPS. We also give estimates of the control parameter beyond which the higher order corrections become relevant and compare the extended CH model to recent phenomenological models.Comment: 10 pages, 5 figure

Periodic patterns displace active phase separation

In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially periodic pattern or, in a complementary parameter region, by a novel hybrid state with spatially alternating homogeneous and periodic states. The transition from phase separation to extended spatially periodic patterns is hysteretic. We show that the resulting patterns are multistable, as they show stability beyond the bifurcation for different wavenumbers belonging to a wavenumber band. The transition from active phase separation to the hybrid states is continuous. Both transition scenarios are systems-spanning phenomena in particle conserving systems. They are predicted with a generic dissipative model introduced in this work. Candidates for specific systems, in which these generic secondary transitions are likely to occur, are, for example, generalized models for motility-induced phase separation in active Brownian particles, models for cell division or chemotactic systems with conserved particle dynamics.Comment: 17 pages, 7 figure

Can policies improve language vitality? The Sámi languages in Sweden and Norway

Introduction: Language policies are often aimed at changing language behaviours, yet it is notoriously difficult to assess their effects. This study investigates language use and competence in the Indigenous Sámi populations of Norway and Sweden in light of the national-level policies the two countries have adopted. Methods: We provide a cross-country comparison of relevant educational, linguistic and budgetary policies in Sweden and Norway. Next, we present novel data from a survey with 5,416 Sámi and non-Sámi participants in 20 northern municipalities, examining Sámi language use and proficiencies across generations and contexts. Lexical proficiency in North Sámi was tested in a small subset of participants. Results: Sámi language use has dropped considerably over the past three generations. Only a small proportion of Sámi are highly fluent and use a Sámi language with their children (around 4% in Sweden and 11% in Norway). One fifth of Sámi adults use a Sámi language at least ‘occasionally’, and use is most common in the home context. Sámi language knowledge remains negligible in the majority population. Discussion: The higher levels of language use and proficiency in Norway seem at least in part to reflect the more favourable policies adopted there. In both countries, more work is needed to increase speaker numbers, also in the majority population

Program for sound generation based on image color spectrum with using the recurrent neural network

This work is devoted to development and approbation of the program for sound generation based on image color spectrum with using the recurrent neural network. The work contains a description of the transition between color and music characteristics, the rationale for choosing and the description of a recurrent neural network. The choices of the neural network implementation technology as well as the results of the experiment are described

Long-Term Profile Variability in Active Galactic Nuclei with Double-Peaked Balmer Emission Lines

An increasing number of Active Galactic Nuclei (AGNs) exhibit broad, double-peaked Balmer emission lines,which represent some of the best evidence for the existence of relatively large-scale accretion disks in AGNs. A set of 20 double-peaked emitters have been monitored for nearly a decade in order to observe long-term variations in the profiles of the double-peaked Balmer lines. Variations generally occur on timescales of years, and are attributed to physical changes in the accretion disk. Here we characterize the variability of a subset of seven double-peaked emitters in a model independent way. We find that variability is caused primarily by the presence of one or more discrete "lumps" of excess emission; over a timescale of a year (and sometimes less) these lumps change in amplitude and shape, but the projected velocity of these lumps changes over much longer timescales (several years). We also find that all of the objects exhibit red peaks that are stronger than the blue peak at some epochs and/or blueshifts in the overall profile, contrary to the expectations for a simple, circular accretion disk model, thus emphasizing the need for asymmetries in the accretion disk. Comparisons with two simple models, an elliptical accretion disk and a circular disk with a spiral arm, are unable to reproduce all aspects of the observed variability, although both account for some of the observed behaviors. Three of the seven objects have robust estimates of the black hole masses. For these objects the observed variability timescale is consistent with the expected precession timescale for a spiral arm, but incompatible with that of an elliptical accretion disk. We suggest that with the simple modification of allowing the spiral arm to be fragmented, many of the observed variability patterns could be reproduced.Comment: 74 pages, 4 tables, 35 figure