Estimation of microscopic averages from metadynamics

With the help of metadynamics it is possible to calculate efficiently the free energy of systems displaying high energy barriers as a function of few selected "collective variables". In doing this, the contribution of all the other degrees of freedom ("microscopic" variables) is averaged out and, thus, lost. In the following, it is shown that it is possible to calculate the thermal average of these microscopic degrees of freedom during the metadynamics, not loosing this piece of information

Verification tools for probabilistic forecasts of continuous hydrological variables

In the present paper we describe some methods for verifying and evaluating probabilistic forecasts of hydrological variables. We propose an extension to continuous-valued variables of a verification method originated in the meteorological literature for the analysis of binary variables, and based on the use of a suitable cost-loss function to evaluate the quality of the forecasts. We find that this procedure is useful and reliable when it is complemented with other verification tools, borrowed from the economic literature, which are addressed to verify the statistical correctness of the probabilistic forecast. We illustrate our findings with a detailed application to the evaluation of probabilistic and deterministic forecasts of hourly discharge value

Interacting hard-core bosons and surface preroughening

The theory of the preroughening transition of an unreconstructed surface, and the ensuing disordered flat (DOF) phase, is formulated in terms of interacting steps. Finite terraces play a crucial role in the formulation. We start by mapping the statistical mechanics of interacting (up and down) steps onto the quantum mechanics of two species of one-dimensional hard-core bosons. The effect of finite terraces translates into a number-non-conserving term in the boson Hamiltonian, which does not allow a description in terms of fermions, but leads to a two-chain spin problem. The Heisenberg spin-1 chain is recovered as a special limiting case. The global phase diagram is rich. We find the DOF phase is stabilized by short-range repulsions of like steps. On-site repulsion of up-down steps is essential in producing a DOF phase, whereas an off-site attraction between them is favorable but not required. Step-step correlation functions and terrace width distributions can be directly calculated with this method.Comment: 15 pages, 13 figures, to appear on Phys. Rev.

Escaping free-energy minima

We introduce a novel and powerful method for exploring the properties of the multidimensional free energy surfaces of complex many-body systems by means of a coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates.A characteristic feature of this dynamics is the presence of a history-dependent potential term that, in time, fills the minima in the free energy surface, allowing the efficient exploration and accurate determination of the free energy surface as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissociation of a NaCl molecule in water and in the study of the conformational changes of a dialanine in solution.Comment: 3 figure

Spatial pattern formation induced by Gaussian white noise

The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable environmental disturbances, and (iii) a linear spatial coupling component, which provides spatial coherence and takes into account diffusion mechanisms. We investigate these dynamics using analytical tools, such as mean-field theory, linear stability analysis and structure function analysis, and use numerical simulations to confirm these analytical results.Comment: 11 pages, 8 figure

Finite temperature properties of clusters by replica exchange metadynamics: the water nonamer

We introduce an approach for the accurate calculation of thermal properties of classical nanoclusters. Based on a recently developed enhanced sampling technique, replica exchange metadynamics, the method yields the true free energy of each relevant cluster structure, directly sampling its basin and measuring its occupancy in full equilibrium. All entropy sources, whether vibrational, rotational anharmonic and especially configurational -- the latter often forgotten in many cluster studies -- are automatically included. For the present demonstration we choose the water nonamer (H2O)9, an extremely simple cluster which nonetheless displays a sufficient complexity and interesting physics in its relevant structure spectrum. Within a standard TIP4P potential description of water, we find that the nonamer second relevant structure possesses a higher configurational entropy than the first, so that the two free energies surprisingly cross for increasing temperature.Comment: J. Am. Chem. Soc. 133, 2535-2540 (2011