Difference between heartwood and sapwood
Forest Products Laboratory (U.S.)
1919
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A modelacão estocástica nas ciências atuariais permite criar modelos para os Ramos
Vida e Não-Vida da atividade de uma seguradora, através dos quais se podem analisar
diversos parâmetros, e desta forma auxiliar na tomada de decisões e evitar desvios financeiros.
Neste trabalho pretende-se analisar o ramo não-vida das ciências atuariais, mais concretamente
a área designada por teoria da ruína, que consiste no estudo não só dos prémios,
como também das indemnizações de seguradoras, de forma a controlar desvios financeiros
e evitar a ruína. Assim, recorreu-se ao modelo clássico, conhecido por modelo de
Crámer-Lundberg, e efetuaram-se duas abordagens distintas considerando o tempo discreto
e o tempo contínuo. Além da obtenção de alguns resultados úteis nesta análise,
realizaram-se simulações teóricas e também a análise de uma base de dados...
Asymmetric exclusion Equilibrium fluctuations Boltzmann-Gibbs principle Tagged particle
Comment: 10 pages, no figures
Comment: 15 pages 3 figures. This paper has been improved and the title has
also changed to On the asymmetric zero-range in the rarefaction fan
Comment: 18 pages, 3 figures. arXiv admin note: substantial text overlap with
arXiv:0912.0640
Comment: 28 pages, no figures
In this work, I present an interacting particle system whose dynamics conserves the total number of particles but with gradient
transition rates that vanish for some configurations. As a consequence, the invariant pieces of the system, namely, the hyperplanes with a fixed
number of particles can be decomposed into an irreducible set of configurations plus isolated configurations that do not evolve under the
dynamics. By taking initial profiles smooth enough and bounded away from zero and one and for parabolic time scales, the macroscopic density
profile evolves according to the porous medium equation. Perturbing slightly the microscopic dynamics in order to remove the degeneracy of the
rates the same result can be obtained for more general initial profiles.
In this work I introduce a classical example of an Interacting Particle System: the Simple Exclusion Process. I present the notion of
hydrodynamic limit, which is a Law of Large Numbers for the empirical measure and an heuristic argument to derive from the microscopic dynamics
between particles a partial differential equation describing the evolution of the density profile. For the Simple Exclusion Process, in the
Symmetric case ($p=1/2$) we will get to the heat equation while in the Asymmetric case ($p\neq{1/2}$) to the inviscid Burgers equation. Finally,
I introduce the Central Limit Theorem for the empirical measure and the limiting process turns out to be a solution of a stochastic partial
differential equation.
In these notes we consider two particle systems: the totally asymmetric simple exclusion process and the totally asymmetric zero-range process.
We introduce the notion of hydrodynamic limit and describe the partial differential equation that governs the evolution of the conserved
quantity - the density of particles $\rho(t,\cdot)$. This equation is a hyperbolic conservation law of type $\partial_{t}\rho(t,u)+\nabla
F(\rho(t,u))=0$, where the flux $F$ is a concave function. Taking these systems evolving on the Euler time scale $tN$, a Central Limit Theorem
for the empirical measure holds and the temporal evolution of the limit density field is deterministic. By taking the system on a reference
frame with constant velocity, the limit density field does not evolve in time. In order to have a non-trivial limit, time needs to be speeded up ...
We consider the one-dimensional Totally Asymmetric Zero-Range process evolving
on $\mathbb{Z}$ and starting from the Geometric product measure $\mu_\rho$. On the hyperbolic time scale the
temporal evolution of the density fluctuation field is deterministic, in the sense that the limit
field at time $t$ is a translation of the initial one. We consider the system in a reference frame
moving at this velocity and we show that the limit density fluctuation field does not evolve in
time until $N^{4/3}$, which implies the current across a characteristic to vanish on this longer time
scale.
