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

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

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

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

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

Inhibition of the MID1 protein complex: a novel approach targeting APP protein synthesis

Alzheimer's disease (AD) is characterized by two neuropathological hallmarks: senile plaques, which are composed of amyloid-β (Aβ) peptides, and neurofibrillary tangles, which are composed of hyperphosphorylated tau protein. Aβ peptides are derived from sequential proteolytic cleavage of the amyloid precursor protein (APP). In this study, we identified a so far unknown mode of regulation of APP protein synthesis involving the MID1 protein complex: MID1 binds to and regulates the translation of APP mRNA. The underlying mode of action of MID1 involves the mTOR pathway. Thus, inhibition of the MID1 complex reduces the APP protein level in cultures of primary neurons. Based on this, we used one compound that we discovered previously to interfere with the MID1 complex, metformin, for in vivo experiments. Indeed, long-term treatment with metformin decreased APP protein expression levels and consequently Aβ in an AD mouse model. Importantly, we have initiated the metformin treatment late in life, at a time-point where mice were in an already progressed state of the disease, and could observe an improved behavioral phenotype. These findings together with our previous observation, showing that inhibition of the MID1 complex by metformin also decreases tau phosphorylation, make the MID1 complex a particularly interesting drug target for treating AD