Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications

We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy, Marseilles, France, 31 August - 4 September 200

The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem

Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is established for this problem. In fact, the techniques presented here allow treating generalizations of the Carleman system where the collision frequency is proportional to some power of the macroscopic density, with exponent in [-1,1]

Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system

We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.Comment: AMS-LaTeX, 21 page

Kinetic hierarchy and propagation of chaos in biological swarm models

We consider two models of biological swarm behavior. In these models, pairs of particles interact to adjust their velocities one to each other. In the first process, called 'BDG', they join their average velocity up to some noise. In the second process, called 'CL', one of the two particles tries to join the other one's velocity. This paper establishes the master equations and BBGKY hierarchies of these two processes. It investigates the infinite particle limit of the hierarchies at large time-scale. It shows that the resulting kinetic hierarchy for the CL process does not satisfy propagation of chaos. Numerical simulations indicate that the BDG process has similar behavior to the CL process

An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator

Metabolic and hormonal studies of Type 1 (insulin-dependent) diabetic patients after successful pancreas and kidney transplantation

Long-term normalization of glucose metabolism is necessary to prevent or ameliorate diabetic complications. Although pancreatic grafting is able to restore normal blood glucose and glycated haemoglobin, the degree of normalization of the deranged diabetic metabolism after pancreas transplantation is still questionable. Consequently glucose, insulin, C-peptide, glucagon, and pancreatic polypeptide responses to oral glucose and i.v. arginine were measured in 36 Type 1 (insulin-dependent) diabetic recipients of pancreas and kidney allografts and compared to ten healthy control subjects. Despite normal HbA1 (7.2±0.2%; normal <8%) glucose disposal was normal only in 44% and impaired in 56% of the graft recipients. Normalization of glucose tolerance was achieved at the expense of hyperinsulinaemia in 52% of the subjects. C-peptide and glucagon were normal, while pancreatic polypeptide was significantly higher in the graft recipients. Intravenous glucose tolerance (n=21) was normal in 67% and borderline in 23%. Biphasic insulin release was seen in patients with normal glucose tolerance. Glucose tolerance did not deteriorate up to 7 years post-transplant. In addition, stress hormone release (cortisol, growth hormone, prolactin, glucagon, catecholamines) to insulin-induced hypoglycaemia was examined in 20 graft recipients and compared to eight healthy subjects. Reduced blood glucose decline indicates insulin resistance, but glucose recovery was normal, despite markedly reduced catecholamine and glucagon release. These data demonstrate the effectiveness of pancreatic grafting in normalizing glucose metabolism, although hyperinsulinaemia and deranged counterregulatory hormone response are observed frequently

Moon phases and moon signs do not influence morbidity, mortality and long-term survival, after living donor kidney transplantation

Background: Approximately 11% of the German population are convinced that certain moon phases and moon signs may impact their health and the onset and clinical course of diseases. Before elective surgery, a considerable number of patients look to optimize the timing of the procedure based on the lunar cycle. Especially patients awaiting living donor kidney transplantation (LDKT) commonly look for an adjustment of the date of transplantation according to the moon calendar. This study therefore investigated the perioperative and long-term outcome of LDKT dependent on moon phases and zodiac signs. Methods: Patient data were prospectively collected in a continuously updated kidney transplant database. Two hundred and seventy-eight consecutive patients who underwent LDKT between 1994 and December 2009 were selected for the study and retrospectively assigned to the four moon phases (new-moon, waxing-moon, full-moon, and waning-moon) and the corresponding zodiac sign (moon sign Libra), based on the date of transplantation. Preexisting comorbidities, perioperative mortality, surgical outcome, and long-term survival data were analyzed. Results: Of all LDKT procedures, 11.9, 39.9, 11.5, and 36.5% were performed during the new, waxing, full, and waning moon, respectively, and 6.2% during the moon sign Libra, which is believed to interfere with renal surgery. Survival rates at 1, 5, and 10 years after transplantation were 98.9, 92, and 88.7% (patient survival) and 97.4, 91.6, and 80.6% (graft survival) without any differences between all groups of lunar phases and moon signs. Overall perioperative complications and early graft loss occurred in 21.2 and 1.4%, without statistical difference (p > 0.05) between groups. Conclusion: Moon phases and the moon sign Libra had no impact on early and long-term outcome measures following LDKT in our study. Thus, concerns of patients awaiting LDKT regarding the ideal time of surgery can be allayed, and surgery may be scheduled independently of the lunar phases

Dichlorodioxomolybdenum(VI) complexes bearing oxygen-donor ligands as olefin epoxidation catalysts

Treatment of the solvent adduct [MoO2Cl2(THF)2] with either 2 equivalents of N,N-dimethylbenzamide (DMB) or 1 equivalent of N,N'-diethyloxamide (DEO) gave the dioxomolybdenum(vi) complexes [MoO2Cl2(DMB)2] () and [MoO2Cl2(DEO)] (). The molecular structures of and were determined by single-crystal X-ray diffraction. Both complexes present a distorted octahedral geometry and adopt the cis-oxo, trans-Cl, cis-L configuration typical of complexes of the type [MoO2X2(L)n], with either the monodentate DMB or bidentate DEO oxygen-donor ligands occupying the equatorial positions trans to the oxo groups. The complexes were applied as homogeneous catalysts for the epoxidation of olefins, namely cis-cyclooctene (Cy), 1-octene, trans-2-octene, α-pinene and (R)-(+)-limonene, using tert-butylhydroperoxide (TBHP) as oxidant. In the epoxidation of Cy at 55 °C, the desired epoxide was the only product and turnover frequencies in the range of ca. 3150-3200 mol molMo(-1) h(-1) could be reached. The catalytic production of cyclooctene oxide was investigated in detail, varying either the reaction temperature or the cosolvent. Complexes and were also applied in liquid-liquid biphasic catalytic epoxidation reactions by using an ionic liquid of the type [C4mim][X] (C4mim = 1-n-butyl-3-methylimidazolium; X = NTf2, BF4 or PF6] as a solvent to immobilise the metal catalysts. Recycling for multiple catalytic runs was achieved without loss of activity