Counting statistics: a Feynman-Kac perspective

By building upon a Feynman-Kac formalism, we assess the distribution of the number of hits in a given region for a broad class of discrete-time random walks with scattering and absorption. We derive the evolution equation for the generating function of the number of hits, and complete our analysis by examining the moments of the distribution, and their relation to the walker equilibrium density. Some significant applications are discussed in detail: in particular, we revisit the gambler's ruin problem and generalize to random walks with absorption the arcsine law for the number of hits on the half-line.Comment: 10 pages, 6 figure

The critical catastrophe revisited

The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole neutron population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the neutrons may display a wild patchiness (clustering). On the contrary, imposing a population control on the total population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time.Comment: 16 pages, 6 figure

Properties of branching exponential flights in bounded domains

Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the properties of trajectories starting on the boundary and those starting inside the domain. Within this context, we show that the total length travelled by the walker and the number of performed collisions in bounded volumes can be assessed by resorting to the Feynman-Kac formalism. Other physical observables related to the branching trajectories, such as the survival and escape probability, are derived as well.Comment: 5 pages, 2 figure

Percolation properties of the neutron population in nuclear reactors

Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled stochastic systems however require to define intermediate quantities (e.g. the temperature field), which are bridging the gap between the stochastic neutron field and the deterministic feedback. By interpreting the branching random walk of neutrons in fissile media under the influence of a feedback mechanism as a directed percolation process and by leveraging on the statistical field theory of birth death processes, we will build a stochastic model of neutron transport theory and of reactor physics. The critical exponents of this model, combined to the analysis of the resulting field equation involving a fractional Laplacian will show that the critical diffusion equation cannot adequately describe the spatial distribution of the neutron population and shifts instead to a critical super-diffusion equation. The analysis of this equation will reveal that non-negligible departure from mean field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.Comment: 15 pages, 2 figures, 1 tabl

More than a Hundred Years in the Search for an Accurate Diagnosis for Chagas Disease: Current Panorama and Expectations

Chagas disease, or American trypanosomiasis, is a parasitic disease of the Americas. In nature, Trypanosoma cruzi is transmitted through various species of triatomine bugs. However, non-vectorial transmission can also occur, such as transmission through blood products or by transplanting infected organs, by vertical transmission, and lately by oral route. Currently, Chagas disease affects approximately 6–7 million people worldwide, and the process of urbanization in Latin America and migratory movements from endemic countries have led to Chagas disease being diagnosed in areas where the infection is not endemic. There are several methods for diagnosing Chagas disease. Some of these are mostly used for research purposes, while others are used in routine diagnostic laboratories. According to the World Health Organization (WHO), chronic Chagas disease diagnosis is based on two serological techniques. To establish a definitive diagnosis, the results must be concordant. In the case of discordances, the WHO proposes repeating serology in a new sample, and if results remain inconclusive, a confirmatory test should be performed. This chapter shows aspects of the diagnosis of Chagas disease, which varies in its sensitivity and specificity, and its use depends on the geographical location, the available resources, and the purpose of the diagnosis

Production optimisation of a DNA vaccine candidate against leishmaniasis in flask culture

Plasmid DNA (pDNA) vaccines are promising means to prevent and treat infectious diseases, such as leishmaniasis, but immunisation protocols require large amounts of supercoiled plasmid DNA (scpDNA). Although pDNA can be produced at a reasonable cost in bioreactors; this scale of production may not be the best method at the initial step of a vaccine development when many antigens need to be tested. Then, with the goal of improving the production of VR1012-NH36 and pVAX-NH36 pDNA vaccines against leishmaniasis, the effect of the culture medium and temperature on the pDNA yield was studied in flask cultures. The results indicate that the plasmid volumetric yield increased up to 65 mg/l in flask cultures by using a semi-defined medium, and shifting the culture temperature from 37 to 42°C at the late exponential growth phase. This pDNA production, with at least 80% of sc-pDNA at a laboratory scale seems sufficient to evaluate this and other pDNA vaccine candidates in the initial steps of vaccine development.Keywords: Plasmid DNA vaccine, plasmid DNA production, growth medium, flask culture, trace metal optimisation, leishmaniasisAfrican Journal of Biotechnology Vol. 12(31), pp. 4874-488

Development and experimental evaluation of a complete solar thermophotovoltaic system

We present a practical implementation of a solar thermophotovoltaic (TPV) system. The system presented in this paper comprises a sunlight concentrator system, a cylindrical cup-shaped absorber/emitter (made of tungsten coated with HfO2), and an hexagonal-shaped water-cooled TPV generator comprising 24 germanium TPV cells, which is surrounding the cylindrical absorber/emitter. This paper focuses on the development of shingled TPV cell arrays, the characterization of the sunlight concentrator system, the estimation of the temperature achieved by the cylindrical emitters operated under concentrated sunlight, and the evaluation of the full system performance under real outdoor irradiance conditions. From the system characterization, we have measured short-circuit current densities up to 0.95 A/cm2, electric power densities of 67 mW/cm2, and a global conversion efficiency of about 0.8%. To our knowledge, this is the first overall solar-to-electricity efficiency reported for a complete solar thermophotovoltaic system. The very low efficiency is mainly due to the overheating of the cells (up to 120 °C) and to the high optical concentrator losses, which prevent the achievement of the optimum emitter temperature. The loss analysis shows that by improving both aspects, efficiencies above 5% could be achievable in the very short term and efficiencies above 10% could be achieved with further improvements