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Molecular dynamics simulations have been used in different scientific fields to investigate a broad range of physical systems. However, the accuracy of calculation is based on the model considered to describe the atomic interactions. In particular, ab initio molecular dynamics (AIMD) has the accuracy of density functional theory (DFT), and thus is limited to small systems and relatively short simulation time. In this scenario, Neural Network Force Fields (NNFF) have an important role, since it provides a way to circumvent these caveats. In this work we investigate NNFF designed at the level of DFT to describe liquid water, focusing on the size and quality of the training data-set considered. We show that structural properties are less dependent on the size of the training data-set compared to dynamical ones (such as the diffusion coefficient), and a good sampling (selecting data reference for training process) can lead to a small sample with good precision.

We propose a new method for constructing a polarizable classical force field using data obtained from QM and QM/MM calculations to account for the charge redistribution at the water/metal interface. The induced charge effects are described by adding dipoles to the system topology following the Rod Model (Iori, F, et al J. Comput. Chem.2009, 30, 1465). Furthermore, the force field uses the TIP3P water model, and its functional form is compatible with popular force fields such as AMBER, CHARMM, GROMOS, OPLS-AA, CVFF and IFF. The proposed model was evaluated and validated for water/Pd(111) systems. We tuned the model parameters to reproduce a few critical water/Pd(111) geometries and energies obtained from DFT calculations using both PBE and a non-local van der Waals xc-functional. Our model can reproduce the hexagonal ice layer for the Pd(111)/water systems typically present in low-temperature experiments, in agreement with information available from the literature. Additionally, the model can also reproduce the experimental metal-water interfacial tension at room temperature.

The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the search for ever more precise universal growth exponents. Notably, exact growth exponents are only known for 1 + 1 dimensions. In this work, we present physical and geometric analytical methods that directly associate these exponents to the fractal dimension of the rough interface. Based on this, we determine the growth exponents for the 2 + 1 dimensions, which are in agreement with the results of thin films experiments and precise simulations. We also make a first step towards a solution in d + 1 dimensions, where our results suggest the inexistence of an upper critical dimension.

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, $\exp [-(t/\tau)^b ]$, also known as stretched exponential, and the dependence of adjusted parameters $b$ and $\tau$ is usually associated, in the pharmaceutical literature, with physical mechanisms dominating the drug dynamics inside the capsule. The relation of parameters $\tau$ and $b$ with porosity $\lambda$ are found to satisfy, a simple linear relation for between $\tau$ and $\lambda^{-1}$, which can be explained through simple physically based arguments, and a scaling relation between $b$ and $\lambda$, with the scaling coefficient proportional to the system dimension., Comment: This paper has been accepted for publication in Physica A

In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a simple response to study certain processes in solids and fluids. However, in many situations we are not talking about a FDT, but about the noise intensity. For example, noise has enormous importance in diffusion and growth phenomena. Although we have an explicit FDT for diffusion phenomena, we do not have one for growth processes where we have a noise intensity. We show that there is a hidden FDT for the growth phenomenon, similar to the diffusive one. Moreover, we show that growth with correlated noise presents as well a similar form of FDT. We also call attention to the hierarchy within the theorems of statistical mechanics and how this explains the violation of the FDT in some phenomena.