Understanding stakeholder participation in post-disaster recovery (case study: Nagapattinam, India)

Stakeholder participation is widely acknowledged as a critical component of post-disaster recovery because it helps create a shared understanding of local hazard risk and vulnerability, improves recovery and mitigation decision efficacy, and builds social capital and local resilience to future disasters. But approaches commonly used to facilitate participation and empower local communities depend on lengthy consensus-building processes which is not conducive to time-constrained post-disaster recovery. Moreover, these approaches are often criticized for being overly technocratic and ignoring existing community power and trust structures. Therefore, there is a need for more nuanced, analytical and applied research on stakeholder participation in planning for post-disaster recovery. This research examines participatory behavior of three stakeholder groups (government agencies, non-local non-government organizations, local community-based organizations) in three coastal village communities of Nagapattinam (India) that were recovering from the 2004 Indian Ocean tsunami. The study found eight different forms of participation and non-participation in the case study communities, ranging from 'transformative' participation to 'marginalized' non-participation. These forms of participation and non-participatory behavior emanated from the negotiation of four factors, namely stakeholder power, legitimacy, trust, and urgency for action. The study also found that the time constraints and changing conditions of recovery pose particular challenges for how these factors operated on the ground and over the course of recovery. Finally, the study uses these insights to suggest four strategies for recovery managers to use in the short- and long-term to facilitate more effective stakeholder participation in post-disaster recovery.

Dispersive estimates for the Schrödinger equation

In this document we explore the issue of $L^1\to L^\infty$ estimates for the solution operator of the linear Schr\"{o}dinger equation, \begin{align*} iu_t-\Delta u+Vu&=0 &u(x,0)=f(x)\in \mathcal S(\R^n). \end{align*} We focus particularly on the five and seven dimensional cases. We prove that the solution operator precomposed with projection onto the absolutely continuous spectrum of $H=-\Delta+V$ satisfies the following estimate $\|e^{itH} P_{ac}(H)\|_{L^1\to L^\infty} \lesssim |t|^{-\frac{n}{2}}$ under certain conditions on the potential $V$. Specifically, we prove the dispersive estimate is satisfied with optimal assumptions on smoothness, that is $V\in C^{\frac{n-3}{2}}(\R^n)$ for $n=5,7$ assuming that zero is regular, $|V(x)|\lesssim \langle x\rangle^{-\beta}$ and $|\nabla^j V(x)|\lesssim \langle x\rangle^{-\alpha}$, $1\leq j\leq \frac{n-3}{2}$ for some $\beta>\frac{3n+5}{2}$ and $\alpha>3,8$ in dimensions five and seven respectively. We also show that for the five dimensional result one only needs that $|V(x)|\lesssim \langle x\rangle^{-4-}$ in addition to the assumptions on the derivative and regularity of the potential. This more than cuts in half the required decay rate in the first chapter. Finally we consider a problem involving the non-linear Schr\"{o}dinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, \begin{align*} iu_t+d(t) u_{xx}+|u|^2 u=0. \end{align*} We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in $x$ and in the Fourier transform of $x$.