Stochastic Shell Models driven by a multiplicative fractional Brownian--motion

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in front of the noise which satisfies special regularity conditions. The appearing stochastic integrals are defined in a fractional sense. First, we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise, for which we are able to derive important uniform estimates in some functional spaces. Then, thanks to a compactness argument and these estimates, we prove that these variational solutions converge to a limit solution, which turns out to be the unique pathwise mild solution associated to the shell--model with fractional noise as driving process.Comment: 23 page

Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients

In this paper we study the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpose we have to show the existence and uniqueness of a cocycle solution of such an equation. We do not assume that the noise is given in additive form or that it is a very simple multiplicative noise. However, we need some smoothing property for the coefficient in front of the noise. The main idea of this paper consists of expressing the stochastic integral in terms of non-stochastic integrals and the noisy path by using an integration by parts. This latter term causes that in a first moment only a local mild solution can be obtained, since in order to apply the Banach fixed point theorem it is crucial to have the H\"older norm of the noisy path to be sufficiently small. Later, by using appropriate stopping times, we shall derive the existence and uniqueness of a global mild solution. Furthermore, the asymptotic behavior is investigated by using the {\it Random Dynamical Systems theory}. In particular, we shall show that the global mild solution generates a random dynamical system that, under an appropriate smallness condition for the time lag, have associated a random attractor

Stochastic lattice dynamical systems with fractional noise

This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such systems by the Young integration setting and prove that the solution generates a random dynamical system. Further, we analyze the exponential stability of the trivial solution

Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2,1)(1/2,1)

This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by H\"older continuous functions with H\"older index greater than $1/2$. The results can be applied to the case of equations whose noisy inputs are given by a fractional Brownian motion $B^H$ with covariance operator $Q$, provided that $H\in (1/2,1)$ and ${\rm tr}(Q)$ is sufficiently small.Comment: 19 page

Kinetics and compositional dependence on the microwave power and DiH4/N flow ratio of silicon nitride deposited by electron cyclotron resonance plasmas

The archival version of this work was published in Journal of The Electrochemical Society. Hernández, M. J., Garrido, J., Martínez, J. and J. Piqueras. Kinetics and compositional dependence on the microwave power and DiH4/N flow ratio of silicon nitride deposited by electron cyclotron resonance plasmas. Journal of The Electrochemical Society 141.11 (1994): 3234-3237Silicon nitride layers have been deposited at a low temperature, 150ºC in an electron cyclotron plasma from nitrogen and silane as gas precursors. Deposition conditions have been varied in a wide range. Nitrogen flows from 25 to 400 sccm and silane flows from 2.5 to 35 sccm have been used in our experiments. The microwave power was varied from 100 to 1500 W. The result of the nitride growth kinetics show strong dependence on the silane to nitrogen flow ratio and on the microwave power. For large flow ratios and small powers the kinetics exhibits a nearly linear behavior whereas for low flow ratios and high powers a saturated regime was observed. Ellipsometry, infrared spectroscopy, and etch rate studies showed that the best material quality, 95% Si3N4, is obtained in the saturated regime for the lowest flow ratios and the highest powers used

Construyendo el significado del cuidado ambiental: un estudio de caso en educación secundaria

Cada vez se hace más evidente que los mayores problemas de nuestro tiempo no pueden comprenderse aisladamente. Los crecientes cambios en el entorno, así como en la sociedad, están llevando a ver la necesidad de tener una transformación de valores, no solo por el bien ecológico, sino por el de la humanidad misma. En la presente investigación se identifican las concepciones que tienen los alumnos de secundaria acerca del medio ambiente y su deterioro, así como la percepción de los docentes en relación con su desempeño en la formación en valores y actitudes en la educación secundaria, con el fin de contribuir a un cambio de actitudes que fomenten el cuidado del entorno y, por ende, elevar los niveles de la calidad de vida. Para la recolección de datos se emplearon las redes semánticas naturales y la entrevista semiestructurada, el primer instrumento proporcionó la aproximación hacia la articulación del significado construido por los alumnos en relación con el deterioro ambiental, mientras que la entrevista permitió la evaluación de la perspectiva docente en el abordaje de esta dimensión cognitiva en el proceso educativo