Hardy spaces and divergence operators on strongly Lipschitz domains in RnR^n

Let $\Omega$ be a strongly Lipschitz domain of \reel^n. Consider an elliptic second order divergence operator $L$ (including a boundary condition on $\partial\Omega$) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function $f$ via the Poisson semigroup for $L$ to be in$L^1$. Under suitable assumptions on $L$, we identify this maximal Hardy space with atomic Hardy spaces, namely with H^1(\reel^n) if \Omega=\reel^n, $H^{1}_{r}(\Omega)$ under the Dirichlet boundary condition, and $H^{1}_{z}(\Omega)$ under the Neumann boundary condition. In particular, we obtain a new proof of the atomic decomposition for $H^{1}_{z}(\Omega)$. A version for local Hardy spaces is also given. We also present an overview of the theory of Hardy spaces and BMO spaces on Lipschitz domains with proofs.Comment: submitte

Cumulative Risk and a Call for Action in Environmental Justice Communities

Health disparities, social inequalities, and environmental injustice cumulatively affect individual and community vulnerability and overall health; yet health researchers, social scientists and environmental scientists generally study them separately. Cumulative risk assessment in poor, racially segregated, economically isolated and medically underserved communities needs to account for their multiple layers of vulnerability, including greater susceptibility, greater exposure, less preparedness to cope, and less ability to recover in the face of exposure. Recommendations for evidence-based action in environmental justice communities include: reducing pollution in communities of highest burden; building on community resources; redressing inequality when doing community-based research; and creating a screening framework to identify communities of greatest risk

Ising-like dynamics and frozen states in systems of ultrafine magnetic particles

We use Monte-Carlo simulations to study aging phenomena and the occurence of spinglass phases in systems of single-domain ferromagnetic nanoparticles under the combined influence of dipolar interaction and anisotropy energy, for different combinations of positional and orientational disorder. We find that the magnetic moments oriente themselves preferably parallel to their anisotropy axes and changes of the total magnetization are solely achieved by 180 degree flips of the magnetic moments, as in Ising systems. Since the dipolar interaction favorizes the formation of antiparallel chain-like structures, antiparallel chain-like patterns are frozen in at low temperatures, leading to aging phenomena characteristic for spin-glasses. Contrary to the intuition, these aging effects are more pronounced in ordered than in disordered structures.Comment: 5 pages, 6 figures. to appear in Phys. Rev.

Frozen metastable states in ordered systems of ultrafine magnetic particles

For studying the interplay of dipolar interaction and anisotropy energy in systems of ultrafine magnetic particles we consider simple cubic systems of magnetic dipoles with anisotropy axes pointing into the $z$-direction. Using Monte Carlo simulations we study the magnetic relaxation from several initial states. We show explicitely that, due to the combined influence of anisotropy energy and dipole interaction, magnetic chains are formed along the $z$-direction that organize themselves in frozen metastable domains of columnar antiferromagnetic order. We show that the domains depend explicitely on the history and relax only at extremely large time scales towards the ordered state. We consider this as an indication for the appearence of frozen metastable states also in real sytems, where the dipoles are located in a liquid-like fashion and the anisotropy axes point into random directions