840 research outputs found
Patrimônio em Campinas: a criação do CONDEPACC e as primeiras Resoluções de Tombamento. Entrevista com o Prof. Dr. Antonio Augusto Arantes Neto
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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
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
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
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
Exploiting the flexibility of a family of models for taxation and redistribution
We discuss a family of models expressed by nonlinear differential equation
systems describing closed market societies in the presence of taxation and
redistribution. We focus in particular on three example models obtained in
correspondence to different parameter choices. We analyse the influence of the
various choices on the long time shape of the income distribution. Several
simulations suggest that behavioral heterogeneity among the individuals plays a
definite role in the formation of fat tails of the asymptotic stationary
distributions. This is in agreement with results found with different
approaches and techniques. We also show that an excellent fit for the
computational outputs of our models is provided by the k-generalized
distribution introduced by G. Kaniadakis (Physica A 296 (2001) 405-425).Comment: 17 pages, 5 figures. Accepted for publication in Eur. Phys. J. B.
arXiv admin note: text overlap with arXiv:1109.060
A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker{Planck equations in space dimensions d>2 is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies and given external potentials, e.g. the porous medium equation and the fast diffusion equation. The key ingredient in our approach is the gradient ow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretisation, the fully discrete solution inherits energy estimates from the original gradient ow, and these lead to weak compactness of the trajectories in the continuous limit. Consistency is analyzed in the planar situation, d = 2. A variety of numerical experiments for the porous medium equation indicates that the scheme is well-adapted to track the growth of the solution's support
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
Basic kinetic wealth-exchange models: common features and open problems
We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social
Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati,
Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735],
Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B
17 (2000) 167], and of Dragulescu and Yakovenko [A. Dragulescu, V. M.
Yakovenko, Eur. Phys. J. B 17 (2000) 723]. Analytical fitting forms for the
equilibrium wealth distributions are proposed. The influence of heterogeneity
is investigated, the appearance of the fat tail in the wealth distribution and
the relaxation to equilibrium are discussed. A unified reformulation of the
models considered is suggested.Comment: Updated version; 9 pages, 5 figures, 2 table
Holocene thermokarst and pingo development in the Kolyma Lowland (NE Siberia)
© 2018 John Wiley & Sons, Ltd. Ground ice and sedimentary records of a pingo exposure reveal insights into Holocene permafrost, landscape and climate dynamics. Early to mid-Holocene thermokarst lake deposits contain rich floral and faunal paleoassemblages, which indicate lake shrinkage and decreasing summer temperatures (chironomid-based TJuly) from 10.5 to 3.5 cal kyr BP with the warmest period between 10.5 and 8 cal kyr BP. Talik refreezing and pingo growth started about 3.5 cal kyr BP after disappearance of the lake. The isotopic composition of the pingo ice (δ18O − 17.1 ± 0.6‰, δD −144.5 ± 3.4‰, slope 5.85, deuterium excess −7.7± 1.5‰) point to the initial stage of closed-system freezing captured in the record. A differing isotopic composition within the massive ice body was found (δ18O − 21.3 ± 1.4‰, δD −165 ± 11.5‰, slope 8.13, deuterium excess 4.9± 3.2‰), probably related to the infill of dilation cracks by surface water with quasi-meteoric signature. Currently inactive syngenetic ice wedges formed in the thermokarst basin after lake drainage. The pingo preserves traces of permafrost response to climate variations in terms of ground-ice degradation (thermokarst) during the early and mid-Holocene, and aggradation (wedge-ice and pingo-ice growth) during the late Holocene
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