On a modelled rough heat equation

We use the formalism of Hairer's regularity structures theory \cite{hai-14} to study a heat equation with non-linear perturbation driven by a space-time fractional noise. Different regimes are observed, depending on the global pathwise roughness of the noise. To this end, and following the procedure exhibited in \cite{hai-14}, the equation is first "lifted" into some abstract "regularity structure" and therein solved through a fixed-point argument. Then we construct a consistent "model" above the fractional noise, by relying on a smooth Fourier-type approximation of the process.Comment: Accepted versio

Rough Volterra equations 1: the algebraic integration setting

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with H\"older exponent greater than 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with H\"older exponent in (1/3,1/2], we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H>1/3.Comment: 31 page

Biosynthesized silver nanoparticles to control fungal infections in indoor environments

Fungi grow especially in dark and moist areas, deteriorating the indoor environment and causing infections that particularly affect immunosuppressed individuals. Antimicrobial coatings have as principal objective to prevent biofilm formation and infections by incorporation of bioactive additives. In this sense, metallic nanoparticles, such as silver, have proven to be active against different microorganisms specially bacteria. Biosynthesized method is a promising environmentally friendly option to obtain nanoparticles. The aim of this research was assess the employment of plants extracts of Aloysia triphylla (cedrón), Laurelia sempervirens (laurel) and Ruta chalepensis (ruda) to obtain silver nanoparticles to be used as an antimicrobial additive to a waterborne coating formulation. The products obtained were assessed against fungal isolates from biodeteriorated indoor coatings. The fungi were identified by conventional and molecular techniques as Chaetomium globosum and Alternaria alternate. The results revealed that the coating with silver nanoparticles obtained with L. sempervirens extract at 60°C with a size of 9.8 nm was the most efficient against fungal biofilm development.Fil: Deya, Marta Cecilia. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones en Tecnología de Pinturas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones en Tecnología de Pinturas; ArgentinaFil: Bellotti, Natalia. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones en Tecnología de Pinturas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones en Tecnología de Pinturas; Argentin

Non-linear Rough Heat Equations

This article is devoted to define and solve an evolution equation of the form $dy_t=\Delta y_t dt+ dX_t(y_t)$, where $\Delta$ stands for the Laplace operator on a space of the form $L^p(\mathbb{R}^n)$, and $X$ is a finite dimensional noisy nonlinearity whose typical form is given by $X_t(\varphi)=\sum_{i=1}^N x^{i}_t f_i(\varphi)$, where each $x=(x^{(1)},...,x^{(N)})$ is a $\gamma$-H\"older function generating a rough path and each $f_i$ is a smooth enough function defined on $L^p(\mathbb{R}^n)$. The generalization of the usual rough path theory allowing to cope with such kind of systems is carefully constructed.Comment: 36 page