Approximation of conformal mappings using conformally equivalent triangular lattices

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be approximated by such discrete conformal maps $f^\epsilon$. In particular, let $T$ be an infinite regular triangulation of the plane with congruent triangles and only acute angles (i.e.\ $<\pi/2$). We scale this tiling by $\epsilon>0$ and approximate a compact subset of the domain of $f$ with a portion of it. For $\epsilon$ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by $\log|f'|$ on the boundary. Furthermore we show that the corresponding discrete conformal maps $f^\epsilon$ converge to $f$ uniformly in $C^1$ with error of order $\epsilon$.Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some proofs extende

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

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

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

Depletion of angiotensin-converting enzyme 2 reduces brain serotonin and impairs the running-induced neurogenic response

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordPhysical exercise induces cell proliferation in the adult hippocampus in rodents. Serotonin (5-HT) and angiotensin (Ang) II are important mediators of the pro-mitotic effect of physical activity. Here, we examine precursor cells in the adult brain of mice lacking angiotensin-converting enzyme (ACE) 2, and explore the effect of an acute running stimulus on neurogenesis. ACE2 metabolizes Ang II to Ang-(1-7) and is essential for the intestinal uptake of tryptophan (Trp), the 5-HT precursor. In ACE2-deficient mice, we observed a decrease in brain 5-HT levels and no increase in the number of BrdU-positive cells following exercise. Targeting the Ang II/AT1 axis by blocking the receptor, or experimentally increasing Trp/5-HT levels in the brain of ACE2-deficient mice, did not rescue the running-induced effect. Furthermore, mice lacking the Ang-(1-7) receptor, Mas, presented a normal neurogenic response to exercise. Our results identify ACE2 as a novel factor required for exercise-dependent modulation of adult neurogenesis and essential for 5-HT metabolism

The E3-ubiquitin ligase MID1 catalyzes ubiquitination and cleavage of Fu

Sonic Hedgehog (SHH)-GLI signalling plays an important role during embryogenesis and in tumorigenesis. The survival and growth of several types of cancer depend on autonomously activated SHH-GLI signalling. A protein complex containing the ubiquitin-ligase MID1 and protein phosphatase 2A (PP2A) regulates the nuclear localization and transcriptional activity of GLI3, a transcriptional effector molecule of SHH, in cancer cell lines with autonomously activated SHH signalling. However, the exact molecular mechanisms that mediate the interaction between MID1 and GLI3 remained unknown. Here, we show that MID1 catalyses the ubiquitination and proteasomal cleavage of the GLI3-regulator Fu. Our data suggest that Fu ubiquitination and cleavage is one of the key elements connecting the MID1/PP2A protein complex with GLI3 activity control