Particle simulation of Coulomb collisions: Comparing the methods of Takizuka & Abe and Nanbu

The interactions of charged particles in a plasma are governed by long-range Coulomb collision. We compare two widely used Monte Carlo models for Coulomb collisions. One was developed by Takizuka and Abe in 1977, the other was developed by Nanbu in 1997. We perform deterministic and statistical error analysis with respect to particle number and time step. The two models produce similar stochastic errors, but Nanbu’s model gives smaller time step errors. Error comparisons between these two methods are presented.     

Airline network revenue management by multistage stochastic programming

A multistage stochastic programming approach to airline network revenue management is presented. The objective is to determine seat protection levels for all itineraries, fare classes, points of sale of the airline network and all dcps of the booking horizon such that the expected revenue is maximized. While the passenger demand and cancelation rate processes are the stochastic inputs of the model, the stochastic protection level process represents its output and allows to control the booking process. The stochastic passenger demand and cancelation rate processes are approximated by a finite number of tree structured scenarios. The scenario tree is generated from historical data using a stability-based recursive scenario reduction scheme. Numerical results for a small hub-and-spoke network are reported. This research is supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin.     

A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K ₁) and nuclei growth (described with K ₂). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.     

Quantum to classical transition for random walks

We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior and find analytical expressions for this in the long-time limit; we see that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth of the variance even for weak decoherence.     

Electron Kinetic Entropy across Quasi-Perpendicular Shocks

We use Magnetospheric Multiscale (MMS) data to study electron kinetic entropy per particle Se across Earth’s quasi-perpendicular bow shock. We have selected 22 shock crossings covering a wide range of shock conditions. Measured distribution functions are calibrated and corrected for spacecraft potential, secondary electron contamination, lack of measurements at the lowest energies and electron density measurements based on plasma frequency measurements. All crossings display an increase in electron kinetic entropy across the shock ΔSe being positive or zero within their error margin. There is a strong dependence of ΔSe on the change in electron temperature, ΔTe, and the upstream electron plasma beta, βe. Shocks with large ΔTe have large ΔSe. Shocks with smaller βe are associated with larger ΔSe. We use the values of ΔSe, ΔTe and density change Δne to determine the effective adiabatic index of electrons for each shock crossing. The average effective adiabatic index is 〈γe〉=1.64±0.07.     

Understanding the accuracy of Nanbu’s numerical Coulomb collision operator

We investigate the accuracy of and assumptions underlying the numerical binary Monte Carlo collision operator due to Nanbu [K. Nanbu, Phys. Rev. E 55 (1997) 4642]. The numerical experiments that resulted in the parameterization of the collision kernel used in Nanbu’s operator are argued to be an approximate realization of the Coulomb–Lorentz pitch-angle scattering process, for which an analytical solution for the collision kernel is available. It is demonstrated empirically that Nanbu’s collision operator quite accurately recovers the effects of Coulomb–Lorentz pitch-angle collisions, or processes that approximate these (such interspecies Coulomb collisions with very small mass ratio) even for very large values of the collisional time step. An investigation of the analytical solution shows that Nanbu’s parameterized kernel is highly accurate for small values of the normalized collision time step, but loses some of its accuracy for larger values of the time step. Careful numerical and analytical investigations are presented, which show that the time dependence of the relaxation of a temperature anisotropy by Coulomb–Lorentz collisions has a richer structure than previously thought, and is not accurately represented by an exponential decay with a single decay rate. Finally, a practical collision algorithm is proposed that for small-mass-ratio interspecies Coulomb collisions improves on the accuracy of Nanbu’s algorithm.     

Structural Changes in Lymphocytes Membrane of Chernobyl Clean-up Workers from Latvia

ABM (3-aminobenzanthrrone derivative) developed at the Riga Technical University, Riga, Latvia) has been previously shown as a potential probe for determination of the immune state of patients with different pathologies .The fist study (using probe ABM) of peripheral blood mononuclear cells (PBMC) membranes of 97 Chernobyl clean-up workers from Latvia was conducted in 1997. Now we repeatedly examine the same (n = 54) individuals in dynamics. ABM spectral parameters in PBMC suspension, fluorescence anisotropy and blood plasma albumin characteristics were recorded. In 1997 screening showed 5 different patterns of fluorescence spectra, from which in 2007 we obtained only two. These patterns of spectra had never been previously seen in healthy individuals or patients with tuberculosis, multiple sclerosis, rheumatoid arthritis, etc., examined by us. Patterns of ABM fluorescence spectra are associated with membrane anisotropy and conformational changes of blood plasma albumin. We observed that in dynamics 1997–2007 the lipid compartment of the membrane became more fluid while the lipid-protein interface became more rigid. The use of probe ANS and albumin auto-fluorescence allowed show conformational alterations in Chernobyl clean-up workers blood plasma. It is necessary to note that all investigated parameters significantly differ in observed groups of patients. These findings reinforce our understanding that that the cell membrane is a significant biological target of radiation. The role of the membrane in the expression and course of cell damage after radiation exposure must be considered. So ten years dynamic of PBMC membrane characteristics by ABM (spectral shift and anisotropy indexes) in Chernobyl clean-up workers reveal progressive trend toward certain resemblance with those of chronic B-cell lymphoid leukemia.     

NMR Spectroscopic Imaging Method for Static Magnetic Field Mapping

A previously published nuclear magnetic resonance (NMR) spectroscopic imaging method for mapping static magnetic fields has been modified, replacing the gradient echo sequence with an asymmetric spin echo sequence. The purpose of the modification is to reinforce the technique and make it useable even in conditions in which the gradient echo sequence cannot be operated. The modification performed was verified by an experiment performed on a low-field NMR scanner. The rough and fine errors due to the long time of measurement were corrected during the processing of the measured images. An optimization procedure was used to correct the fine errors. The map of the static magnetic field acquired using the new technique was compared to the map calculated from the phase images and both were compared to the result measured using a magnetometer. The verification confirmed the legitimacy of the modification and suitability of the novel technique. Some alternatives to the measured data processing have been suggested, shortening the global time of the measurement.