Combustion theory and modeling

In honor of the fiftieth anniversary of the Combustion Institute, we are asked to assess accomplishments of theory in combustion over the past fifty years and prospects for the future. The title of our article is chosen to emphasize that development of theory necessarily goes hand-in-hand with specification of a model. Good conceptual models underlie successful mathematical theories. Models and theories are discussed here for deflagrations, detonations, diffusion flames, ignition, propellant combustion, and turbulent combustion. In many of these areas, the genesis of mathematical theories occurred during the past fifty years, and in all of them significant advances are anticipated in the future. Increasing interaction between theory and computation will aid this progress. We hope that, although certainly not complete in topical coverage or reference citation, the presentation may suggest useful directions for future research in combustion theory

A discrete geometric approach for simulating the dynamics of thin viscous threads

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations is established formally in the limit of a vanishing discretization length. The discrete models lends itself naturally to numerical implementation. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous jets in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension

Streamer Propagation as a Pattern Formation Problem: Planar Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations.Comment: 4 pages, revtex, 3 ps file

Propagation and Structure of Planar Streamer Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations. In the present long paper, you find the physics of the model and the interfacial approach further explained. As a first ingredient of this approach, we here analyze planar fronts, their profile and velocity. We encounter a selection problem, recall some knowledge about such problems and apply it to planar streamer fronts. We make analytical predictions on the selected front profile and velocity and confirm them numerically. (abbreviated abstract)Comment: 23 pages, revtex, 14 ps file

Aid, growth and peace: A comparative analysis.

yesThe paper examines patterns of post-conflict aid in a sample of 14 countries, with in-depth, qualitative analysis of seven cases (Bosnia, Cambodia, El Salvador, Nicaragua, Guatemala, Mozambique and Rwanda). The study takes previous work by Paul Collier and associates in this area as a starting point, but disaggregates the data by type of aid, time intervals, and historical period. The findings significantly qualify the Collier conclusion to the effect that donors respond to a CNN-effect in a dysfunctional manner by rushing in aid soon after a peace agreement is concluded and scaling back too soon. Rather, disaggregated analysis shows that post-war aid follows several patterns and can best be understood as strategic behavior designed to promote a range of economic and political objectives. This paper also questions the related policy recommendation of the Collier research on post-conflict aid, namely that post-conflict aid should be phased in so as to maximize economic growth on the grounds that this is important to sustain peace during the first post-conflict decade. Instead, this paper finds, aid strategies that demonstrate early and firm donor commitment to the new order are more likely to stabilize peace in the short run, and aid strategies that address the underlying sources of conflict are important to sustain peace in the longer run

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

International Veterinary Epilepsy Task Force recommendations for systematic sampling and processing of brains from epileptic dogs and cats

Traditionally, histological investigations of the epileptic brain are required to identify epileptogenic brain lesions, to evaluate the impact of seizure activity, to search for mechanisms of drug-resistance and to look for comorbidities. For many instances, however, neuropathological studies fail to add substantial data on patients with complete clinical work-up. This may be due to sparse training in epilepsy pathology and or due to lack of neuropathological guidelines for companion animals. The protocols introduced herein shall facilitate systematic sampling and processing of epileptic brains and therefore increase the efficacy, reliability and reproducibility of morphological studies in animals suffering from seizures. Brain dissection protocols of two neuropathological centres with research focus in epilepsy have been optimised with regards to their diagnostic yield and accuracy, their practicability and their feasibility concerning clinical research requirements. The recommended guidelines allow for easy, standardised and ubiquitous collection of brain regions, relevant for seizure generation. Tissues harvested the prescribed way will increase the diagnostic efficacy and provide reliable material for scientific investigations

Mapping the Spatio-Temporal Pattern of the Mammalian Target of Rapamycin (mTOR) Activation in Temporal Lobe Epilepsy

Growing evidence from rodent models of temporal lobe epilepsy (TLE) indicates that dysregulation of the mammalian target of rapamycin (mTOR) pathway is involved in seizures and epileptogenesis. However, the role of the mTOR pathway in the epileptogenic process remains poorly understood. Here, we used an animal model of TLE and sclerotic hippocampus from patients with refractory TLE to determine whether cell-type specific activation of mTOR signaling occurs during each stage of epileptogenesis. In the TLE mouse model, we found that hyperactivation of the mTOR pathway is present in distinct hippocampal subfields at three different stages after kainate-induced seizures, and occurs in neurons of the granular and pyramidal cell layers, in reactive astrocytes, and in dispersed granule cells, respectively. In agreement with the findings in TLE mice, upregulated mTOR was observed in the sclerotic hippocampus of TLE patients. All sclerotic hippocampus (n = 13) exhibited widespread reactive astrocytes with overactivated mTOR, some of which invaded the dispersed granular layer. Moreover, two sclerotic hippocampus exhibited mTOR activation in some of the granule cells, which was accompanied by cell body hypertrophy. Taken together, our results indicate that mTOR activation is most prominent in reactive astrocytes in both an animal model of TLE and the sclerotic hippocampus from patients with drug resistant TLE