963 research outputs found
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 in , and two analytic non-vanishing orthogonal
vector fields and along , find an isothermic surface that is
tangent to and that has and 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 , 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 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
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