scholarly journals Quantifying the driving factors for language shift in a bilingual region

2017 ◽  
Vol 114 (17) ◽  
pp. 4365-4369 ◽  
Author(s):  
Katharina Prochazka ◽  
Gero Vogl
Keyword(s):  
Cellular Automata ◽  
Differential Equations ◽  
Large Scale ◽  
Language Shift ◽  
Reaction Diffusion ◽  
Agent Based Modeling ◽  
Reaction Diffusion Equations ◽  
Agent Based ◽  
Using Data ◽  
A Minor

Many of the world’s around 6,000 languages are in danger of disappearing as people give up use of a minority language in favor of the majority language in a process called language shift. Language shift can be monitored on a large scale through the use of mathematical models by way of differential equations, for example, reaction–diffusion equations. Here, we use a different approach: we propose a model for language dynamics based on the principles of cellular automata/agent-based modeling and combine it with very detailed empirical data. Our model makes it possible to follow language dynamics over space and time, whereas existing models based on differential equations average over space and consequently provide no information on local changes in language use. Additionally, cellular automata models can be used even in cases where models based on differential equations are not applicable, for example, in situations where one language has become dispersed and retreated to language islands. Using data from a bilingual region in Austria, we show that the most important factor in determining the spread and retreat of a language is the interaction with speakers of the same language. External factors like bilingual schools or parish language have only a minor influence.

Testing Scenarios to Achieve Workplace Sustainability Goals Using Backcasting and Agent-Based Modeling

2016 ◽  
Vol 49 (9) ◽  
pp. 1007-1037 ◽  
Author(s):  
Ricardo García-Mira ◽  
Adina Dumitru ◽  
Amparo Alonso-Betanzos ◽  
Noelia Sánchez-Maroño ◽  
Óscar Fontenla-Romero ◽  
...  
Keyword(s):  
Large Scale ◽  
Agent Based Modeling ◽  
Scenario Development ◽  
Dynamic Simulations ◽  
Environmental Behaviors ◽  
Agent Based ◽  
Work Related ◽  
Development Methodology ◽  
Effective Policy ◽  
Using Data

Pro-environmental behaviors have been analyzed in the home, with little attention to other important contexts of everyday life, such as the workplace. The research reported here explored three categories of pro-environmental behavior (consumption of materials and energy, waste generation, and work-related commuting) in a public large-scale organization in Spain, with the aim of identifying the most effective policy options for a sustainable organization. Agent-based modeling was used to design a virtual simulation of the organization. Psychologically informed profiles of employees were defined using data gathered through a questionnaire, measuring knowledge, motivations, and ability. Future scenarios were developed using a participatory backcasting scenario development methodology, and policy tracks were derived. Dynamic simulations indicated that, to be effective, organizational policy should strengthen worker participation and autonomy, be sustained over time, and should combine different measures of medium intensity for behavior change, instead of isolated policies of high intensity.

A PARALLEL SOLVER FOR REACTION–DIFFUSION SYSTEMS IN COMPUTATIONAL ELECTROCARDIOLOGY

2004 ◽  
Vol 14 (06) ◽  
pp. 883-911 ◽  
Author(s):  
PIERO COLLI FRANZONE ◽  
LUCA F. PAVARINO
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Ionic Currents ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Fiber Direction ◽  
Axially Symmetric ◽  
Reaction Diffusion Systems ◽  
Cardiac Model

In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain cardiac model, consisting of a system of two degenerate parabolic reaction–diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction–diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh–Nagumo (FHN) model to the more complex phase-I Luo–Rudy model (LR1). The solver employs structured isoparametric Q1finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to O(107) unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains.

TRANSITION WAVES THAT LEAVE BEHIND REGULAR OR IRREGULAR SPATIOTEMPORAL OSCILLATIONS IN A SYSTEM OF THREE REACTION–DIFFUSION EQUATIONS

1993 ◽  
Vol 03 (05) ◽  
pp. 1269-1279 ◽  
Author(s):  
JONATHAN A. SHERRATT
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Wave Front ◽  
Plane Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Spatiotemporal Oscillations ◽  
Transition Wave ◽  
Periodic Plane

Transition waves are widespread in the biological and chemical sciences, and have often been successfully modelled using reaction–diffusion systems. I consider a particular system of three reaction–diffusion equations, and I show that transition waves can destabilise as the kinetic ordinary differential equations pass through a Hopf bifurcation, giving rise to either regular or irregular spatiotemporal oscillations behind the advancing transition wave front. In the case of regular oscillations, I show that these are periodic plane waves that are induced by the way in which the transition wave front approaches its terminal steady state. Further, I show that irregular oscillations arise when these periodic plane waves are unstable as reaction–diffusion solutions. The resulting behavior is not related to any chaos in the kinetic ordinary differential equations.

Computation of Asymptotic Stability for a Class of Partial Differential Equations with Delay

2010 ◽  
Vol 16 (7-8) ◽  
pp. 1005-1022 ◽  
Author(s):  
D. Breda ◽  
S. Maset ◽  
R. Vermiglio
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Type Equation ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Reaction Diffusion Equations ◽  
Equation Modeling ◽  
Delay Differential ◽  
Equations With Delay ◽  
Functional Reaction

In this paper the question of asymptotic stability for retarded functional reaction diffusion equations is faced. Due to the infinite dimension of the problem a numerical approach is necessary. Here we propose a technique based on a pseudospectral discretization in time and on a spectral discretization in space of the infinitesimal generator associated to the semigroup of solution operators. Some numerical experiments on a Hutchinson-type equation modeling heat conduction in a rod with spatially variable gain delayed feedback are performed to show the efficiency of the scheme. This work represents a nontrivial extension of previous work of the authors on the computation of asymptotic stability for delay differential equations.

scholarly journals On the solution of reaction-diffusion equations with double diffusivity

1987 ◽  
Vol 10 (1) ◽  
pp. 163-172
Author(s):  
B. D. Aggarwala ◽  
C. Nasim
Keyword(s):  
Heat Conduction ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Partial Differential ◽  
Coupled Partial Differential Equations ◽  
Special Cases ◽  
Two Temperatures

In this paper, solution of a pair of Coupled Partial Differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more direct, and some new results are derived. Also, discussion about the propagation of initial discontinuities is given and illustrated with graphs of some special cases.

scholarly journals Compartmental and spatial rule-based modeling with Virtual Cell (VCell)

2017 ◽  
Author(s):  
M. L. Blinov ◽  
J. C. Schaff ◽  
D. Vasilescu ◽  
I. I. Moraru ◽  
J. E. Bloom ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Molecular Complexes ◽  
Reaction Diffusion Equations ◽  
Reaction Networks ◽  
The Novel ◽  
Modeling Framework ◽  
Rule Based ◽  
Agent Based ◽  
Virtual Cell ◽  
Stochastic Simulator

AbstractIn rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation (ODE) and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the novel rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations (PDE) deterministic solvers or the Smoldyn stochastic simulator.

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