Gas gain on single wire chambers filled with pure isobutane at low pressure

The gas gain of single-wire chambers filled with isobutane, with cell cross-section 12x12 mm and wire diameters of 15, 25, 50 and 100 $\mu$m, has been measured at pressures ranging 12-92 Torr. Contrary to the experience at atmospheric pressure, at very low pressures the gas gain on thick wires is higher than that on thin wires at the same applied high voltage as was recently shown. Bigger wire diameters should be used in wire chambers operating at very low pressure if multiple scattering on wires is not an issue.Comment: 9 pages, 6 figure

Order statistics and heavy-tail distributions for planetary perturbations on Oort cloud comets

This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly computational. It is reasonable to wonder whenever statistical simulation of the perturbations can be much more easy to handle. The first step for answering such a question is to provide a statistical study of these perturbations in order to catch their main features. The statistical tools used are order statistics and heavy tail distributions. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the important planet. These characteristics were validated through statistical testing and a theoretical study based on Opik theory.Comment: 9 pages, 12 figures, submitted for publication in Astronomy and Astrophysic

Stable splitting of bivariate spline spaces by Bernstein-Bézier methods

We develop stable splitting of the minimal determining sets for the spaces of bivariate C1 splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer's method for solving fully nonlinear elliptic PDEs on polygonal domains

Optimization of the Spatial Distribution of Pollution Emission in Water Bodies

The environmental protection of water bodies in Europe is based on the Water Framework Directive, which combines the so called Emission Limits Value and the Water Quality Objective (QO) approaches. The first one sets limits to particular type of emissions, for example the Nitrate Directive, while the second establishes Quality Standards for Biological, Chemical and Hydromorphological Quality Elements, in order to ensure the functioning of freshwater and marine ecosystem and the sustainable use of water bodies. To this regard, mathematical models are valuable tools for reconciliating these approaches, since they allow one to establish a causal link between emission levels and the Quality Standards ("direct problem") and vice-versa ("inverse problem"). In general, Quality Elements are variables or proper combination of variables which define the "status" of a water body. For example, the "chemical status" can be defined by a set of concentrations of chemicals which are potentially harmful for the ecosystem and humans, or the biological status may be based on Quality Elements which include the density of phytoplankton, the presence/absence of Submerged Aquatic Vegetation, the presence/absence of sensitive species etc. In many instances, the Quality Standards can then be expressed as threshold values, below or above which the functioning of the ecosystem is compromised and/or the risk for human health is not acceptable. If this is the case, management policies should be aimed at improving the state of the system and meet those Standards in the near future. In order to be carried in a cost-effective manner, such interventions should be based on a quantitative understanding of the relationships between the Pressures on the system and its State. This task could be very complex in large water bodies, where transport processes play a major role in creating marked gradients and pollution sources may be spatially distributed and/or not well identified. From the scientific point of view, the problem can be stated as follows: a mathematical model should enable one to "map" the spatial distribution of inputs (emissions) into the spatial distribution of the requested output, namely the "indicator" or "metric", which is subjected to a given constraint, the Quality Standard (QS), within the computational dominion. Such analysis may reveal that the QS are not respected only in a given fraction of the water body and, in the most favorable circumstances, identify the pollution sources which cause the problem. In such a case, a selective intervention, aimed at lowering the emission levels of those sources, would probably be more cost effective than the general reduction of the emission levels in the whole area. The spatial distribution of emission sources may also affect the pollution level and, in some instances, a proper redistribution of those sources in a given area, which leaves unchanged the total load, could have positive effect on the pollution level. In this paper, we are going to investigate the above problems in the simplest possible setting, in order to provide a clear interpretation of the results in relation to the most relevant parameters. The paper is organized as follows: in the "methods" section, we present the basic equations and provide insights for solving the problem in the general case as well as in the specific one here presented. The analytical solutions are presented and discussed in the next two sessions and some concluding remarks are then summarized in the conclusive section

Local RBF approximation for scattered data fitting with bivariate splines

In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given

Benchmarking calculations of excitonic couplings between bacteriochlorophylls

Excitonic couplings between (bacterio)chlorophyll molecules are necessary for simulating energy transport in photosynthetic complexes. Many techniques for calculating the couplings are in use, from the simple (but inaccurate) point-dipole approximation to fully quantum-chemical methods. We compared several approximations to determine their range of applicability, noting that the propagation of experimental uncertainties poses a fundamental limit on the achievable accuracy. In particular, the uncertainty in crystallographic coordinates yields an uncertainty of about 20% in the calculated couplings. Because quantum-chemical corrections are smaller than 20% in most biologically relevant cases, their considerable computational cost is rarely justified. We therefore recommend the electrostatic TrEsp method across the entire range of molecular separations and orientations because its cost is minimal and it generally agrees with quantum-chemical calculations to better than the geometric uncertainty. We also caution against computationally optimizing a crystal structure before calculating couplings, as it can lead to large, uncontrollable errors. Understanding the unavoidable uncertainties can guard against striving for unrealistic precision; at the same time, detailed benchmarks can allow important qualitative questions--which do not depend on the precise values of the simulation parameters--to be addressed with greater confidence about the conclusions