Implicit particle methods and their connection with variational data assimilation

The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothing as well as to data assimilation for perfect models. We show that the minimizations required by implicit particle methods are similar to the ones one encounters in variational data assimilation and explore the connection of implicit particle methods with variational data assimilation. In particular, we argue that existing variational codes can be converted into implicit particle methods at a low cost, often yielding better estimates, that are also equipped with quantitative measures of the uncertainty. A detailed example is presented

A random map implementation of implicit filters

Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined equation be solved for each particle and at each time an observation becomes available. We present a new implementation of implicit filters in which we find the solution of the equation via a random map. As examples, we assimilate data for a stochastically driven Lorenz system with sparse observations and for a stochastic Kuramoto-Sivashinski equation with observations that are sparse in both space and time

Topological character of hydrodynamic screening in suspensions of hard spheres: an example of universal phenomenon

Although in the case of polymer solutions the existence of hydrodynamic screening is considered as established, use of the same methods for suspensions of hard spheres so far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological, combinatorial and London-style qualitative arguments, we prove the existence of screening in suspensions. We show that the nature of hydrodynamic screening in suspensions is analogous to that known for the Meissner effect in superconductors. The extent of screening depends on volume fraction of hard spheres. The zero volume fraction limit corresponds to the normal state. The case of finite volume fractions-to the mixed state typical for superconductors of the second kind. Such a state is becoming fully "superconducting" at some critical volume fraction for which the (zero frequency) relative viscosity diverges. Our analytical results describing this divergence are in accord with known scaling results obtained by Brady and Bicerano et al which are well supported by experimental data. We provide theoretical explanation of the divergence of relative viscosity in terms of a topological-type transition which mathematically can be made isomorphic to the more familiar Bose-Einstein condensation transition. Because of this, the methods developed in this work are not limited to suspensions only. In concluding section we mention other applications of the developed formalism ranging from turbulence and magnetohydrodynamics to high temperature superconductors, QCD, string models, etc.Comment: 49 page

Contested Governance: Understanding Justice Interventions in Post-Qaddafi Libya

This contribution reflects upon the nexus between transitional justice and peacebuilding through a study of how transitional justice practices in post-Qadhafi Libya interacted with broader efforts to establish governance institutions in the aftermath of Libya’s 2011 armed conflict. It argues that dominant practices of transitional justice, promoted by external actors, prescribed narrow state-centric justice interventions that were ill-suited for a polity in which the state was highly contested. In fact, transitional justice proved divisive in Libya because attempts to project state-centric liberal justice practices were limited by their targeting of weak institutions that lacked local legitimacy and their inability to reconcile alternative normative frameworks that challenge the modern state. In addition, the weakness of Libya’s state institutions allowed thuwwar, or revolutionary armed groups, to dictate an exclusionary form of justice known as political isolation. Drawn from fieldwork conducted in Libya, this contribution provides lessons for both peacebuilding and transitional justice practice that call for a rethinking of teleological notions of transition and greater engagement with notions and concepts that fall outside dominant practices