A discontinuous Galerkin method for the Vlasov-Poisson system

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86 figure

Competition between water and hydrogen peroxide at Ti center in Titanium zeolites. An ab initio study

A combined Car 12Parrinello molecular dynamics blue moon sampling approach has been adopted to study the competitive attack of H2O and H2O2 at a tetracoordinated Titanium site in a Ti 12zeolite. The results indicate that, although the attack of water to form a trigonal bipyramidal center is thermodynamically more stable, the attack of hydrogen peroxide to form a similar adduct is kinetically favored. In both cases, solvent cooperation is effective in the formation of the adducts. The relevance of such a result in relation to the catalytic properties of Ti 12zeolites is discussed

A new approach to the creation and propagation of exponential moments in the Boltzmann equation

We study the creation and propagation of exponential moments of solutions to the spatially homogeneous $d$-dimensional Boltzmann equation. In particular, when the collision kernel is of the form $|v-v_*|^\beta b(\cos(\theta))$ for $\beta \in (0,2]$ with $\cos(\theta)= |v-v_*|^{-1}(v-v_*)\cdot \sigma$ and $\sigma \in \mathbb{S}^{d-1}$, and assuming the classical cut-off condition $b(\cos(\theta))$ integrable in $\mathbb{S}^{d-1}$, we prove that there exists $a > 0$ such that moments with weight $\exp(a \min{t,1} |v|^\beta)$ are finite for $t>0$, where $a$ only depends on the collision kernel and the initial mass and energy. We propose a novel method of proof based on a single differential inequality for the exponential moment with time-dependent coefficients.Comment: 14 pages. Many typos corrected in this revised versio

TS-1 from First Principles

First principles Studies on periodic TS-1 models at Ti content corresponding to 1.35% and 2.7% in weight of TiO2 are presented. The problem of Ti preferential siting is addressed by using realistic models corresponding to the TS-1 unit cell [TiSi95O192] and adopting for the first time a periodic DFT approach, thus providing an energy scale for Ti in the different crystallographic sites in nondefective TS-1. The structure with Ti in site T3 is the most stable, followed by T4 (+0.3 kcal/mol); the less stable structure, corresponding to Ti in T1, is 5.6 kcal/mol higher in energy. The work has been extended to investigate models with two Ti's per unit cell [Ti2Si94O192] (2.7%). The possible existence of Ti-O-Ti bridges, formed by two corner-sharing TiO4 tetrahedra, is discussed. By using Cluster models cut from the optimized periodic DFT structures, both vibrational (DFT) and electronic excitation spectra (TDDFT) have been calculated and favorably compared with the experimental data available on TS-1. Interesting features emerged from excitation spectra: (i) Isolated tetrahedral Ti sites show a Beer-Lambert behavior, with absorption intensity proportional to concentration. Such a behavior is gradually lost when two Ti's occupy sites close to each other. (ii) The UV-vis absorption in the 200-250 nm region can be associated with transitions from Occupied states delocalized on the framework oxygens to empty d states localized on Ti. Such extended-states-to-local-states transitions may help the interpretation of the photovoltaic activity recently detected in Ti zeolites

Water in acid boralites: Hydration effects on framework B sites

Properties and behavior of protonated boron-containing zeolites at different hydration degree have been investigated by means of periodic DFT approaches. Geometry optimization and room-temperature Car-Parrinello molecular dynamics results, in line with experimental findings, indicate that the BO3-bound silanolic acid site typical of dry boralites should convert to a solvated H3O+ hydrogen bonded to tetrahedral BO4 at moderate water content. By increasing the water loading, the tetrahedral structure of the B site is stabilized and the physicochemical properties of the water molecules solvating the acid proton gradually approach the liquid-phase ones. A relevant role of structural and vibrational properties of the zeolite framework in the water-induced trigonal-to-tetrahedral transition at the B site is highlighted by simulation results

Sorting of multiple molecular species on cell membranes

Eukaryotic cells maintain their inner order by a hectic process of distillation of molecular factors taking place on the surface of their lipid membranes. To understand the properties of this molecular sorting process, a physical model of the process has been recently proposed [arXiv:1811.06760], based on (a) the phase separation of a single, initially dispersed molecular species into spatially localized sorting domains on the lipid membrane, and (b) domain-induced membrane bending leading to the nucleation of submicrometric lipid vesicles, naturally enriched in the molecules of the engulfed sorting domain. The analysis of the model has shown the existence of an optimal region of the parameter space where sorting is most efficient. Here, the model is extended to account for the simultaneous distillation of a pool of distinct molecular species. We find that the mean time spent by sorted molecules on the membrane increases with the heterogeneity of the pool (i.e., the number of distinct molecular species sorted) according to a simple scaling law, and that a large number of distinct molecular species can in principle be sorted in parallel on a typical cell membrane region without significantly interfering with each other. Moreover, sorting is found to be most efficient when the distinct molecular species have comparable homotypic affinities. We also consider how valence (i.e., the average number of interacting neighbors of a molecule in a sorting domain) affects the sorting process, finding that higher-valence molecules can be sorted with greater efficiency than lower-valence molecules