Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward-backward stochastic differential equations and introduce the new concept of ``auxiliary SDEs.''Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000014

Rough paths and 1d sde with a time dependent distributional drift. Application to polymers

Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the weak sense when the drift reads as the derivative of a H{\"o}lder continuous function. Regularity of the drift part is investigated carefully and a related stochastic calculus is also proposed, which makes the structure of the solutions more explicit than within the earlier framework of Dirichlet processes

A forward--backward stochastic algorithm for quasi-linear PDEs

We propose a time-space discretization scheme for quasi-linear parabolic PDEs. The algorithm relies on the theory of fully coupled forward--backward SDEs, which provides an efficient probabilistic representation of this type of equation. The derivated algorithm holds for strong solutions defined on any interval of arbitrary length. As a bypass product, we obtain a discretization procedure for the underlying FBSDE. In particular, our work provides an alternative to the method described in [Douglas, Ma and Protter (1996) Ann. Appl. Probab. 6 940--968] and weakens the regularity assumptions required in this reference.Comment: Published at http://dx.doi.org/10.1214/105051605000000674 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Eliminating social inequality by reinforcing standard language ideology? Language policy for Dutch in Flemish schools

Flanders, the northern, Dutch-speaking part of Belgium, is facing a growing intra- and interlingual diversity. On the intralingual level, Tussentaal ('in-between-language') emerged as a cluster of intermediate varieties between the Flemish dialects and Standard Dutch, gradually becoming the colloquial language. At the same time, Flanders counts a growing number of immigrants and languages. This paper analyses the way Flemish language-in-education policy deals with these (perceived) problems of substandardisation and multilingualism, in order to create equal opportunities for all pupils, regardless of their native language or social background. Both the policy and the measures it proposes are strongly influenced by different, yet intertwined ideologies of standardisation and monolingualism. By propagating Standard Dutch as the only acceptable language (variety) and denying all forms of language diversity, Flemish language-in-education policy not only fails to create equal opportunities, but reinforces ideologies that maintain inequality. Instead, language policy should be open towards language diversity, taking the role of teachers in forming and implementing policies into consideration

Mean field games with common noise

A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and it is used to prove existence and uniqueness of a strong solution under additional assumptions

Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations

We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, effectively rendering the theory completely local. A finite-volume implementation of the SPDE is described, and the approach is illustrated with preliminary results on the study of a system made of two like-charge ions immersed in a bath of counter-ions

Only standard Dutch at school? Perceptions of Flemish teachers

In the Flemish linguistic landscape, a remarkable shift has come about over the past few decades, from a typically diglossic to a diaglossic constellation. Diaglossia is characterized by intermediate forms between standard and dialect (Auer 2011), in Flanders typically lumped together under the generic term tussentaal ('intermediate language'). In spite of the increasing use of tussentaal in a wide range of situations and the assumed stabilization of this intermediate variety (De Caluwe 2009, Taeldeman 2008, Plevoets 2009), it is still subject to vigorous hostility, in the media as well as in the Flemish linguistic literature. As tussentaal is on the rise as Umgangssprache, the (spoken) standard variety is subject to growing pressure: it has always been considered as a largely virtual (and exoglossic) norm, reached only in artificial settings (e.g. news broadcasts) or highly formal situations. In a non-artificial setting, Belgian teachers are (perceived as) the speakers of "[t]he highest nonvirtual stratum of Belgian Dutch" (Grondelaers & Van Hout 2011:219). Indeed, teachers are often said to serve as an example, and students should emulate their language use. Most teachers also acknowledge that role: they proclaim themselves guardians of the standard language (Van de Velde & Houtermans 1999), and assert they always speak Standard Dutch when addressing students (Delarue 2011). To put that confidence of a lot of teachers in their standard language competence to the test, our research analyses the actual language use and perceptions of 80 teachers in elementary and secondary schools in Flanders (the Dutch-speaking northern part of Belgium), with data gathered from participant observation (audio recording of one class per teacher) as well as a qualitative sociolinguistic interview. In this paper, we focus on the latter, to shed some light on the perceptions of teachers towards Standard Dutch, dialect and tussentaal. How do teachers perceive the Flemish linguistic landscape? How important is standard language use, and how do they interpret their role as “last guardians of the standard”