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Patricia Goncalves

Publications and source records attributed to Patricia Goncalves.

14 recordsLinked to original sources
arXiv2025

Lessons Learned from the Use of Generative AI in Engineering and Quality Assurance of a WEB System for Healthcare

The advances and availability of technologies involving Generative Artificial Intelligence (AI) are evolving clearly and explicitly, driving immediate changes in various work activities. Software Engineering (SE) is no exception and stands to benefit from these new technologies, enhancing productivity and quality in its software development processes. However, although the use of Generative AI in SE practices is still in its early stages, considering the lack of conclusive results from ongoing research and the limited technological maturity, we have chosen to incorporate these technologies in the development of a web-based software system to be used in clinical trials by a thoracic diseases research group at our university. For this reason, we decided to share this experience report documenting our development team's learning journey in using Generative AI during the software development process. Project management, requirements specification, design, development, and quality assurance activities form the scope of observation. Although we do not yet have definitive technological evidence to evolve our development process significantly, the results obtained and the suggestions shared here represent valuable insights for software organizations seeking to innovate their development practices to achieve software quality with generative AI.

cs.SE↗
arXiv2021

Equilibrium fluctuations for diffusive symmetric exclusion with long jumps and infinitely extended reservoirs

We provide a complete description of the equilibrium fluctuations for diffusive symmetric exclusion processes with long jumps in contact with infinitely extended reservoirs and prove that they behave as generalized Ornstein-Uhlenbeck processes with various boundary conditions, depending mainly on the strength of the reservoirs. On the way, we also give a general statement about uniqueness of the Ornstein-Uhlenbeck process originated by the microscopic dynamics of the underlying interacting particle systems and adapt it to our study.

math-ph↗
arXiv2019

A Microscopic Derivation Of Coupled Spde's With A Kpz Flavor

We consider an interacting particles system composed of a Hamiltonian part and perturbed by a conservative stochastic noise so that the full system conserves two quantities: energy and volume. The Hamiltonian part is regulated by a scaling parameter vanishing in the limit. We study the form of the fluctuations of these quantities at equilibrium and derive coupled stochastic partial differential equations with a KPZ flavor.

math-ph↗
arXiv2017

Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps

We consider an exclusion process with long jumps in the box $Λ\_N=\{1, \ldots,N-1\}$, for $N \ge 2$, in contact with infinitely extended reservoirs on its left and on its right. The jump rate is described by a transition probability $p(\cdot)$ which is symmetric, with infinite support but with finite variance. The reservoirs add or remove particles with rate proportional to $κN^{-θ}$, where $κ>0$ and $θ\in\mathbb R$. If $θ>0$ (resp. $θ<0$) the reservoirs add and fastly remove (resp. slowly remove) particles in the bulk. According to the value of $θ$ we prove that the time evolution of the spatial density of particles is described by some reaction-diffusion equations with various boundary conditions.

math.PR↗
arXiv2016

Weakly harmonic oscillators perturbed by a conservative noise

We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable asymmetric L{é}vy process. For a critical value of the coupling, the energy diffusion is described by a family of L{é}vy processes which interpolates between these two processes.

math.PR↗
arXiv2014

Solar panels as cosmic-ray detectors

Due to fundamental limitations of accelerators, only cosmic rays can give access to centre-of- mass energies more than one order of magnitude above those reached at the LHC. In fact, extreme energy cosmic rays (1018 eV - 1020 eV) are the only possibility to explore the 100 TeV energy scale in the years to come. This leap by one order of magnitude gives a unique way to open new horizons: new families of particles, new physics scales, in-depth investigations of the Lorentz symmetries. However, the flux of cosmic rays decreases rapidly, being less than one particle per square kilometer per year above 1019 eV: one needs to sample large surfaces. A way to develop large-effective area, low cost, detectors, is to build a solar panel-based device which can be used in parallel for power generation and Cherenkov light detection. Using solar panels for Cherenkov light detection would combine power generation and a non-standard detection device.

astro-ph.IM↗
arXiv2012

Totally Asymmetric Zero-Range process in the Rarefaction Fan

We consider the one-dimensional totally asymmetric zero-range process starting from a step decreasing profile leading in the hydrodynamic limit to the rarefaction fan of the associate hydrodynamic equation. Under that initial condition, we show that the weighted sum of joint probabilities for second class particles sharing the same site, is convergent and we compute its limit. We derive the Law of Large Numbers for the position of a second class particle initially at the origin under the initial state in which all positive sites are empty and all negative sites are occupied and also for a slight perturbation of the invariant state.

math.PR↗
arXiv2010

Universality of KPZ equation

We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states are given by energy solutions of the KPZ equation. As a consequence, we prove that the Cole-Hofp solutions are also energy solutions of the KPZ equation.

math.PR↗
arXiv2009

Equilibrium Fluctuations for the Totally Asymmetric Zero Range process

We prove a Central Limit Theorem for the empirical measure in the one-dimensional Totally Asymmetric Zero-Range Process in the hyperbolic scaling $N$, starting from the equilibrium measure $ν_ρ$. We also show that when taking the direction of the characteristics, the limit density fluctuation field does not evolve in time until $N^{4/3}$, which implies the current across the characteristics to vanish in this longer time scale.

math.PR↗
arXiv2008

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate $p\in(1/2,1]$ and to the left at rate $1-p$, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and 1, and holes to the right of site 1. We show that the probability that the two second-class particles eventually collide is $(1+p)/3p$, where a_collision_ occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes, started from appropriate initial states and coupled using the so-called "basic coupling", eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case ($p=1$) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

math.PR↗
arXiv2008

Scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient

We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar result for the current through -1/2 for a zero-range process with bond disorder. For the CLT, we prove convergence to a fractional Brownian motion of Hurst exponent 1/4.

cond-mat.stat-mech↗
arXiv2007

Hydrodynamic Limit for a Particle System with degenerate rates

We study the hydrodynamic limit for some conservative particle systems with degenerate rates, namely with nearest neighbor exchange rates which vanish for certain configurations. These models belong to the class of {\sl kinetically constrained lattice gases} (KCLG) which have been introduced and intensively studied in physics literature as simple models for the liquid/glass transition. Due to the degeneracy of rates for KCLG there exists {\sl blocked configurations} which do not evolve under the dynamics and in general the hyperplanes of configurations with a fixed number of particles can be decomposed into different irreducible sets. As a consequence, both the Entropy and Relative Entropy method cannot be straightforwardly applied to prove the hydrodynamic limit. In particular, some care should be put when proving the One and Two block Lemmas which guarantee local convergence to equilibrium. We show that, for initial profiles smooth enough and bounded away from zero and one, the macroscopic density profile for our KCLG evolves under the diffusive time scaling according to the porous medium equation. Then we prove the same result for more general profiles for a slightly perturbed dynamics obtained by adding jumps of the Symmetric Simple Exclusion. The role of the latter is to remove the degeneracy of rates and at the same time they are properly slowed down in order not to change the macroscopic behavior. The equilibrium fluctuations and the magnitude of the spectral gap for this perturbed model are also obtained.

math.PR↗
arXiv2007

Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion

We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle at the origin. We also prove that the position of the Tagged Particle at time $t$ depends on the initial configuration, by the number of empty sites in the interval $[0,(p-q)αt]$ divided by $α$ in the hyperbolic and in a longer time scale, namely $N^{4/3}$.

math.PR↗