The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations

We consider the motion of a thin filament of viscous fluid in a Hele-Shaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts

Sequential inverse problems Bayesian principles and the\ud logistic map example

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection

Risk Mitigation through Diversified Farm Production Strategies: The Case in Northern Mozambique

Mozambique, like many other parts of the low-income world, faces perennial challenges with food security. With a rapidly growing population and arable land on the decline, sustainable agriculture is vital to managing the already depleted natural resources of Sub-Saharan Africa more effectively while increasing food security. Food security issues for subsistence farmers in most low-income countries are a product of endogenous (crop yields) and exogenous (currency fluctuations as many agricultural inputs are imported) factors. In Mozambique the value of the local currency, meticals, has decreased by approximately 50% since January 2015 compared to the U.S. dollar. While this makes exporting products out of Mozambique more attractive in a relative sense, it negatively effects those industries which rely on imported inputs such as animal feed and inorganic fertilizer. In response to this exogenous currency crisis, research was conducted in Nampula, Mozambique during the summer of 2016 on a method for implementing crop diversification to reduce the risk that accompanies the devaluation of the metical. This research was undertaken on a poultry operation which is heavily dependent on imported maize and soya. Similar to the market structure of the poultry industry in the United States, all birds are grown by individual out growers who typically also have small plots of land to farm. Objectives for the project included 1) perform on-site crop production evaluations, 2) determine profitability for various row crops, and 3) simulate alternative production practices to increase crop profitability. Of the crops grown (tomatoes, maize, and cabbage), maize required the least labor, lowest initial investment, and the highest probability of breaking even. This research concluded that if poultry producers in Mozambique who rely on imported feed grew maize simultaneously it would reduce the dependency on imported maize and reduce income variability associated with exogenous currency fluctuations. Implementing a program such as this could increase revenue streams as well as reduce variability, thereby enhancing regional food securit

Risk Mitigation through Diversified Farm Production Strategies: The Case in Northern Mozambique

Mozambique, like many other parts of the low-income world, faces perennial challenges with food security. With a rapidly growing population and arable land on the decline, sustainable agriculture is vital to managing the already depleted natural resources of Sub-Saharan Africa more effectively while increasing food security. Food security issues for subsistence farmers in most low-income countries are a product of endogenous (crop yields) and exogenous (currency fluctuations as many agricultural inputs are imported) factors. In Mozambique the value of the local currency, meticals, has decreased by approximately 50% since January 2015 compared to the U.S. dollar. While this makes exporting products out of Mozambique more attractive in a relative sense, it negatively effects those industries which rely on imported inputs such as animal feed and inorganic fertilizer. In response to this exogenous currency crisis, research was conducted in Nampula, Mozambique during the summer of 2016 on a method for implementing crop diversification to reduce the risk that accompanies the devaluation of the metical. This research was undertaken on a poultry operation which is heavily dependent on imported maize and soya. Similar to the market structure of the poultry industry in the United States, all birds are grown by individual out growers who typically also have small plots of land to farm. Objectives for the project included 1) perform on-site crop production evaluations, 2) determine profitability for various row crops, and 3) simulate alternative production practices to increase crop profitability. Of the crops grown (tomatoes, maize, and cabbage), maize required the least labor, lowest initial investment, and the highest probability of breaking even. This research concluded that if poultry producers in Mozambique who rely on imported feed grew maize simultaneously it would reduce the dependency on imported maize and reduce income variability associated with exogenous currency fluctuations. Implementing a program such as this could increase revenue streams as well as reduce variability, thereby enhancing regional food securit

Data assimilation using bayesian filters and B-spline geological models

This paper proposes a new approach to problems of data assimilation, also known as history matching, of oilfield production data by adjustment of the location and sharpness of patterns of geological facies. Traditionally, this problem has been addressed using gradient based approaches with a level set parameterization of the geology. Gradient-based methods are robust, but computationally demanding with real-world reservoir problems and insufficient for reservoir management uncertainty assessment. Recently, the ensemble filter approach has been used to tackle this problem because of its high efficiency from the standpoint of implementation, computational cost, and performance. Incorporation of level set parameterization in this approach could further deal with the lack of differentiability with respect to facies type, but its practical implementation is based on some assumptions that are not easily satisfied in real problems. In this work, we propose to describe the geometry of the permeability field using B-spline curves. This transforms history matching of the discrete facies type to the estimation of continuous B-spline control points. As filtering scheme, we use the ensemble square-root filter (EnSRF). The efficacy of the EnSRF with the B-spline parameterization is investigated through three numerical experiments, in which the reservoir contains a curved channel, a disconnected channel or a 2-dimensional closed feature. It is found that the application of the proposed method to the problem of adjusting facies edges to match production data is relatively straightforward and provides statistical estimates of the distribution of geological facies and of the state of the reservoir

Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis

Infrared aircraft measurements of stratospheric composition over Antarctica during September 1987

The JPL Mark IV interferometer recorded high resolution, infared solar spectra from the NASA DC-8 aircraft during flights over Antarctica in September 1987. The atmospheric absorption features in these spectra were analyzed to determine the overburdens of O3, NO, NO2, HNO3, ClONO2, HCl, HF, CH4, N2O, CO, H2O and CFC-12. The spectra were obtained at latitudes which ranged between 64 degrees S and 86 degrees S, allowing the composition in the interior of the polar vortex to be compared with that at the edge. The latitude dependence observed for NO, HO2, HNO3, ClONO2, HCl and HF are summerized. The values at 30 deg S were observed on the ferry flight from New Zealand to Hawaii. The dashed lines connecting the two were interpolated across the region for which there are no measurements. The chemically perturbed region is seen to consist of a collar of high HNO3 and ClONO2 surrounding a core in which the overburdens of these and of HCl and NO2 are very low. Clear increases in the overburdens of HF and HNO3 were observed during the course of September in the vortex core. HCl and NO2 exhibited smaller, less significant increases. The overburdens of the tropospheric source gases, N2O, CH4, CF2Cl2, and H2O were observed to much smaller over Antarctica than at mid-latitudes. This, together with the fact that HF over Antarctica was more that double its mid-latitude value, suggests that downwelling has occurred

Effects of Neutron Irradiation on Carbon Doped MgB2 Wire Segments

We have studied the evolution of superconducting and normal state properties of neutron irradiated Mg(B$_{.962}$C$_{.038}$)$_2$ wire segments as a function of post exposure annealing time and temperature. The initial fluence fully suppressed superconductivity and resulted in an anisotropic expansion of the unit cell. Superconductivity was restored by post-exposure annealing. The upper critical field, H$_{c2}$(T=0), approximately scales with T$_c$ starting with an undamaged T$_c$ near 37 K and H$_{c2}$(T=0) near 32 T. Up to an annealing temperature of 400 $^ o$C the recovery of T$_c$ tends to coincide with a decrease in the normal state resistivity and a systematic recovery of the lattice parameters. Above 400 $^ o$C a decrease in order along the c- direction coincides with an increase in resistivity, but no apparent change in the evolution of T$_c$ and H$_{c2}$. To first order, it appears that carbon doping and neutron damaging effect the superconducting properties of MgB$_2$ independently

Random polynomials, random matrices, and LL-functions

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit

Plasma density measurements using chirped pulse broad-band Raman amplification

Stimulated Raman backscattering is used as a non-destructive method to determine the density of plasma media at localized positions in space and time. By colliding two counter-propagating, ultra-short laser pulses with a spectral bandwidth larger than twice the plasma frequency, amplification occurs at the Stokes wavelengths, which results in regions of gain and loss separated by twice the plasma frequency, from which the plasma density can be deduced. By varying the relative delay between the laser pulses, and therefore the position and timing of the interaction, the spatio-temporal distribution of the plasma density can be mapped out