A Constrained Tectonics Model for Coronal Heating

An analytical and numerical treatment is given of a constrained version of the tectonics model developed by Priest, Heyvaerts, & Title [2002]. We begin with an initial uniform magnetic field ${\bf B} = B_0 \hat{\bf z}$ that is line-tied at the surfaces $z = 0$ and $z = L$. This initial configuration is twisted by photospheric footpoint motion that is assumed to depend on only one coordinate ($x$) transverse to the initial magnetic field. The geometric constraints imposed by our assumption precludes the occurrence of reconnection and secondary instabilities, but enables us to follow for long times the dissipation of energy due to the effects of resistivity and viscosity. In this limit, we demonstrate that when the coherence time of random photospheric footpoint motion is much smaller by several orders of magnitude compared with the resistive diffusion time, the heating due to Ohmic and viscous dissipation becomes independent of the resistivity of the plasma. Furthermore, we obtain scaling relations that suggest that even if reconnection and/or secondary instabilities were to limit the build-up of magnetic energy in such a model, the overall heating rate will still be independent of the resistivity

A study of energy concentration and drain in incompressible fluids

In this paper we examine two opposite scenarios of energy behavior for solutions of the Euler equation. We show that if $u$ is a regular solution on a time interval $[0,T)$ and if $u \in L^rL^\infty$ for some $r\geq \frac{2}{N}+1$, where $N$ is the dimension of the fluid, then the energy at the time $T$ cannot concentrate on a set of Hausdorff dimension samller than $N - \frac{2}{r-1}$. The same holds for solutions of the three-dimensional Navier-Stokes equation in the range $5/3<r<7/4$. Oppositely, if the energy vanishes on a subregion of a fluid domain, it must vanish faster than (T-t)^{1-\d}, for any \d>0. The results are applied to find new exclusions of locally self-similar blow-up in cases not covered previously in the literature.Comment: an update of the previous versio

Kinetic study of adsorption and photo-decolorization of Reactive Red 198 on TiO2 surface

Recycling and reuse of wastewater after purification will reduce the environmental pollution as well as fulfill the increasing demand of water. Adsorption-based water treatment process is very popular for dye-house wastewater treatment. The present study deals with treatment of wastewater contaminated by reactive dye. TiO2 is used as adsorbent and the spent adsorbent has been regenerated by Advanced Oxidation Process (AOP), without using any other chemicals. TiO2 adsorbs dye molecules and then those dye molecules have been oxidized via a photocatalytic reaction in presence of UV irradiation. Kinetics of dye adsorption and photocatalytic oxidation reaction has been developed in this study. Photocatalyst adsorbent (TiO2) has been reused several times after regeneration. The activity of catalyst decreases after each cycle; due to poisoning cause by intermediate by-products. Kinetic of this catalyst deactivation has been incorporated with L–H model to develop the photocatalytic reaction kinetic model