Project/scholarship details


  • Funder

    FCT - Fundação para a Ciência e a Tecnologia, I.P.

  • Funder's country

    Portugal

  • Funding program

    5876-PPCDTI

  • Funding amount

    40,284.00 €

  • Start date

    2011-01-01

  • End date

    2014-06-30

Documents


Crossover to the KPZ equation

Gonçalves, Patrícia; Jara, Milton

We consider the weakly asymmetric simple exclusion process and we show that the density field is governed by an Ornstein-Uhlenbeck process for strength asymmetry n2-γ if γϵ (1=2; 1), while for γ= 1=2 it is an energy solution of the KPZ equation.; FCT


Scaling limits of additive functionals of interacting particle systems

Gonçalves, Patrícia; Jara, Milton

Em publicação; Using the renormalization method introduced in [arXiv:1003.4478v1], we prove what we call the local Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension d=1. As applications of this result, we obtain various scaling limits of additive functionals of particle systems, like the occupation time of a given site or extensive additive fields of the dynamics. ...


On the supercritical KDV equation with time-oscillating nonlinearity

Panthee, Mahendra; Scialom, Marcia

For the initial value problem (IVP) associated to the generalized Korteweg-de Vries (gKdV) equation with supercritical nonlinearity, \begin{equation*} u_{t}+\partial_x^3u+\partial_x(u^{k+1}) =0,\qquad k\geq 5, \end{equation*} numerical evidence [Bona J.L., Dougalis V.A., Karakashian O.A., McKinney W.R.: Conservative, high-order numerical schemes for the generalized Korteweg–de Vries equation. Philos. Trans. Roy...


Hydrodynamical behavior of symmetric exclusion with slow bonds

Franco, Tertuliano; Gonçalves, Patrícia; Neumann, Adriana

We consider the exclusion process in the one-dimensional discrete torus with $N$ points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance $N^{-\beta}$, with $\beta\in[0,\infty)$. We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter $\beta$. If $\beta\in [0,...


Phase transition in equilibrium fluctuations of symmetric slowed exclusion

Franco, Tertuliano; Gonçalves, Patrícia; Neumann, Adrian

We analyze the equilibrium fluctuations of density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow bond where it is $\alpha n^-\beta$, with $\alpha,\beta\geq{0}$ and $n$ is the scaling parameter. Depending on the regime of $\beta$, we find three different behaviors for the limi...


On the asymmetric zero-range in the rarefaction fan

Gonçalves, Patrícia

We consider one-dimensional asymmetric zero-range processes starting from a step decreasing profile leading, in the hydrodynamic limit, to the rarefaction fan of the associated hydrodynamic equation. Under that initial condition, and for {\em{ totally asymmetric jumps}}, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. ...


Nonlinear fluctuations of weakly asymmetric interacting particle systems

Gonçalves, Patrícia; Jara, Milton

We introduce what we call the second-order Boltzmann-Gibbs principle, which allows to replace local functionals of a conservative, one-dimensional stochastic process by a possibly nonlinear function of the conserved quantity. This replacement opens the way to obtain nonlinear stochastic evolutions as the limit of the fluctuations of the conserved quantity around stationary states. As an application of this seco...


Occupation time of exclusion processes with conductances

Franco, Tertuliano; Gonçalves, Patrícia; Neumann, Adriana

Em publicação em "Journal of statistical physics". ISSN 0022-4715.; We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates ({\em conductances}) are driven by a general function $W$. The approach does not require sharp bounds on the spectral gap of the system nor the jump rates to be bounded from above or below. We present...


Occupation times of exclusion processes

Gonçalves, Patrícia

In this paper we consider exclusion processes $\{\eta_t: t\geq{0}\}$ evolving on the one-dimensional lattice $\mathbb{Z}$, under the diffusive time scale $tn^2$ and starting from the invariant state $\nu_\rho$ - the Bernoulli product measure of parameter $\rho\in{[0,1]}$. Our goal consists in establishing the scaling limits of the additive functional $\Gamma_t:=\int_{0}^{tn^2} \eta_s(0)\, ds$ - {\em{ the occupa...


Slowed exclusion process : hydrodynamics, fluctuations and phase transitions

Franco, Tertuliano; Gonçalves, Patrícia; Neumann, Adriana

This is a short survey on recent results obtained by the authors on dynamical phase transitions of interacting particle systems. We consider particle systems with exclusion dynamics, but it is conjectured that our results should hold for a general class of particle systems. The parameter giving rise to the phase transition is the ``slowness" of a single bond in the discrete lattice. The phase transition is veri...

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