Influence of MgO overlayers on the electronic states of bct Co(001) thin film grown on bcc Fe(001)/GaAs(001

The spin polarization of the valence band electronic states of strained bcc Co(001) and MgO/Co(001) thin films grown onto a bcc Fe(001) seed layer on GaAs(001) are investigated by employing spin-resolved photoemission spectroscopy. The experimental results are compared with the calculated energy band structure of bcc and bct Co(001), and discussed in the framework of the interband transition model, which allows one to ascribe the observed spectral features to bands of given spin and spatial symmetry. In contrast to the positive spin polarization observed at the MgO/Fe(001) interface, a large negative spin polarization of the electronic states at the Fermi level is observed for the MgO/Co/Fe/GaAs(001) system. Such a large negative spin polarization is attributed to a change in the energy band structure at the bct Co/bcc Fe(001) interface

Kinetic models with randomly perturbed binary collisions

We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a background heat bath. Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. We show that the characterization of these stationary solutions is of independent interest, since the same profiles are shown to be solutions of different evolution problems, both in the econophysics context and in the kinetic theory of rarefied gases

ИССЛЕДОВАНИЕ ВОЗДЕЙСТВИЯ АПОЛЯРНЫХ РЕАГЕНТОВ НА ТЕКУЧЕСТЬ ВОДОУГОЛЬНЫХ СУСПЕНЗИЙ

В последнее время возник интерес к поведению водоугольных суспензий в связи с поиском альтернативных видов энергоресурсов [1-4]. Повышенный интерес к водо угольному топливу вызван ростом цен на нефть и нефтепродукты и ограниченностью запасов этого сырья. Водоугольные смеси широко изучаются в различных странах мира, так как они могут заменить и традиционное пылевидное топливо, перед которым имеют ряд существенных преимуществ. Особенности горения водоугольного топлива позволяют относить его к разряду экологически чистых видов топлива. При сжигании угля в виде водоугольной суспензии увеличивается скорость выгорания углерода, снижаются выбросы вредных веществ в атмосферу и образование оксидов азота

Formation of Structure in Snowfields: Penitentes, Suncups, and Dirt Cones

Penitentes and suncups are structures formed as snow melts, typically high in the mountains. When the snow is dirty, dirt cones and other structures can form instead. Building on previous field observations and experiments, this work presents a theory of ablation morphologies, and the role of surface dirt in determining the structures formed. The glaciological literature indicates that sunlight, heating from air, and dirt all play a role in the formation of structure on an ablating snow surface. The present work formulates a mathematical model for the formation of ablation morphologies as a function of measurable parameters. The dependence of ablation morphologies on weather conditions and initial dirt thickness are studied, focusing on the initial growth of perturbations away from a flat surface. We derive a single-parameter expression for the melting rate as a function of dirt thickness, which agrees well with a set of measurements by Driedger. An interesting result is the prediction of a dirt-induced travelling instability for a range of parameters.Comment: 28 pages, 13 figure

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the {\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference

Mesoscopic modelling of financial markets

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis

Conditional Intensity and Gibbsianness of Determinantal Point Processes

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition $(\Sigma_{\lambda})$ which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.Comment: revised and extende