arXiv subjects

Fernando Albuquerque Oliveira

Publications and source records attributed to Fernando Albuquerque Oliveira.

4 recordsLinked to original sources

arXiv2025

The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond

In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by the fluctuation-dissipation theorem (FDT). The conceptual foundation of FDT originates from the definition of the equilibrium state and Onsager's regression hypothesis. Over time, the fluctuation-dissipation relation has been vividly investigated also in systems far from equilibrium, which often exhibit wild fluctuations in measured parameters. In this review, we recall the major formulations of the FDT, including those proposed by Langevin, Onsager and Kubo. We discuss the role of fluctuations in a broad class of growth and diffusion phenomena and examine the violation of the FDT resulting from a transition from Euclidean to fractal geometry. Finally, we highlight possible generalizations of the FDT formalism and discuss situations where the relation breaks down and is no longer applicable.

cond-mat.stat-mech↗

arXiv2023

Modeling the diffusion-erosion crossover dynamics in drug release

A computational model is proposed to investigate drug delivery systems in which erosion and diffusion mechanisms are participating in the drug release process. Our approach allowed us to analytically estimate the crossover point between those mechanisms through the value of the parameter $b$ ($b_c = 1$) and the scaling behavior of parameter $τ$ on the Weibull function, $\exp[-(t/τ)^b]$, used to adjust drug release data in pharmaceutical literature. Numerical investigations on the size dependence of the characteristic release time $τ$ found it to satisfy either linear or quadratic scaling relations on either erosive or diffusive regimes. Along the crossover the characteristic time scales with the average coefficient observed on the extreme regimes ({\it i.e.}, $τ\sim L^{3/2}$), and we show that this result can be derived analytically by assuming an Arrhenius relation for the diffusion coefficient inside the capsule. Based on these relations a phenomenological expression for the characteristic release in terms of size $L$ and erosion rate $κ$ is proposed, which can be useful for predicting the crossover erosion rate $κ_c$. We applied this relation to the experimental literature data for the release of acetaminophen immersed in a wax matrix and found them to be consistent with our numerical results.

cond-mat.stat-mech↗

arXiv2019

A statistical mechanical model for drug release: relations between release parameters and porosity

A lattice gas model is proposed for investigating the release of drug molecules on devices with semi-permeable, porous membranes in two and three dimensions. The kinetic of this model was obtained through the analytical solution of the three-dimension diffusion equation for systems without membrane and with Monte Carlo simulations. Pharmaceutical data from drug release is usually adjusted to the Weibull function, $\exp [-(t/τ)^b ]$, also known as stretched exponential, and the dependence of adjusted parameters $b$ and $τ$ is usually associated, in the pharmaceutical literature, with physical mechanisms dominating the drug dynamics inside the capsule. The relation of parameters $τ$ and $b$ with porosity $λ$ are found to satisfy, a simple linear relation for between $τ$ and $λ^{-1}$, which can be explained through simple physically based arguments, and a scaling relation between $b$ and $λ$, with the scaling coefficient proportional to the system dimension.

cond-mat.soft↗

arXiv2015

Residual entropy and waterlike anomalies in the repulsive one dimensional lattice gas

The thermodynamic and kinetics of the one dimensional lattice gas with repulsive interaction is investigated using transfer matrix technique and Monte Carlo simulations. This simple model is shown to exhibit waterlike anomalies in density, thermal expansion coefficient and self diffusion. An unified description for the thermodynamic anomalies in this model is achieved based on the ground state residual entropy which appears in the model due to mixing entropy in a ground state phase transition.

cond-mat.soft↗