Andrea Parisi

Defects and multistability in eutectic solidification patterns

We use three-dimensional phase-field simulations to investigate the dynamics of the two-phase composite patterns formed upon during solidification of eutectic alloys. Besides the spatially periodic lamellar and rod patterns that have been widely studied, we find that there is a large number of additional steady-state patterns which exhibit stable defects. The defect density can be so high that the pattern is completely disordered, and that the distinction between lamellar and rod patterns is blurred. As a consequence, the transition from lamellae to rods is not sharp, but extends over a finite range of compositions and exhibits strong hysteresis. Our findings are in good agreement with experiments.

Impact of human mobility on the periodicities and mechanisms underlying measles dynamics

Three main mechanisms determining the dynamics of measles have been described in the literature: invasion in disease-free lands leading to import-dependent outbreaks, switching between annual and biennial attractors driven by seasonality, and amplification of stochastic fluctuations close to the endemic equilibrium. Here, we study the importance of the three mechanisms using a detailed geographical description of human mobility. We perform individual-based simulations of an SIR model using a gridded description of human settlements on top of which we implement human mobility according to the radiation model. Parallel computation permits detailed simulations of large areas. Focusing our research on the British Isles, we show that human mobility has an impact on the periodicity of measles outbreaks. Depending on the level of mobility, we observe at the global level multi-annual, annual or biennial cycles. The periodicity observed globally, however, differs from the local epidemic cycles: different locations show different mechanisms at work depending on both population size and mobility. As a result, the periodicities observed locally depend on the interplay between the local population size and human mobility.

Why Do Protein Folding Rates Correlate with Metrics of Native Topology

For almost 15 years, the experimental correlation between protein folding rates and the contact order parameter has been under scrutiny. Here, we use a simple simulation model combined with a native-centric interaction potential to investigate the physical roots of this empirical observation. We simulate a large set of circular permutants, thus eliminating dependencies of the folding rate on other protein properties (e.g. stability). We show that the rate-contact order correlation is a consequence of the fact that, in high contact order structures, the contact order of the transition state ensemble closely mirrors the contact order of the native state. This happens because, in these structures, the native topology is represented in the transition state through the formation of a network of tertiary interactions that are distinctively long-ranged.

Self-affine properties of fractures in brittle materials

We present the result of numerical simulations for a fracturing process in a three-dimensional solid subjected to a mode-I load in a quasi-static regime. The solid is described using the Born model on an FCC lattice with a starting notch. We obtain a value of the roughness exponent ζ≃0.5 in agreement with the value measured in microfracturing experiments. Our result supports the idea that at small length scales the fracturing process can be considered as quasi-static, which is the basic of the possible application of the model of line depinning to the case of fractures.

Role of surface waves on the relation between crack speed and the work of fracture

We show that the delivery of fracture work to the tip of an advancing planar crack is strongly reduced by surface phonon emission, leading to forbidden ranges of crack speed. The emission can be interpreted through dispersion of the group velocity, and Rayleigh and Love branches contribute as well as other high frequency branches of the surface wave dispersion relations. We also show that the energy release rate which enters the Griffith criterion for the crack advance can be described as the product of the continuum solution with a function that only depends on the lattice geometry and describes the lattice influence on the phonon emission. Simulations are performed using a new finite element model for simulating elasticity and fractures. The model, built to allow fast and very large three-dimensional simulations, is applied to the simplified case of two-dimensional samples.

Detecting and describing dynamic equilibria in adaptive networks

We review modeling attempts for the paradigmatic contact process (or SIS model) on adaptive networks. Elaborating on one particular proposed mechanism of topology change (rewiring) and its mean field analysis, we obtain a coarse-grained view of coevolving network topology in the stationary active phase of the system. Introducing an alternative framework applicable to a wide class of adaptive networks, active stationary states are detected, and an extended description of the resulting steady-state statistics is given for three different rewiring schemes. We find that slight modifications of the standard rewiring rule can result in either minuscule or drastic change of steady-state network topologies.

Periodicity, synchronization and persistence in pre-vaccination measles

We investigate the relationship between periodicity, synchronization and persistence of measles through simulations of geographical spread on the British Isles. We show that the establishment of areas of biennial periodicity depends on the interplay between human mobility and local population size and that locations undergoing biennial cycles tend to be, on average, synchronized in phase. We show however that occurrences of opposition of phase are actually quite common and correspond to stable dynamics. We also show that persistence is strictly related to circulation of the disease in the highly populated area of London and that this ensures survival of the disease even when human mobility drops to extremely low levels.

Relation between driving energy, crack shape, and speed in brittle dynamic fracture

We report results on the interrelation between driving force, roughness exponent, branching, and crack speed in a finite element model. We show that for low applied loadings the crack speed reaches the values measured in the experiments, and the crack surface roughness is compatible with logarithmic scaling. At higher loadings, the crack speed increases, and the crack roughness exponent approaches the value measured at short length scales in experiments. In the case of high anisotropy, the crack speed is fully compatible with the values measured in experiments on anisotropic materials, and we are able to interpret explicitly the results in terms of the efficiency function introduced by us in our previous work [A. Parisi and R. C. Ball, Phys. Rev. B 66, 165432 (2002)]. The mechanism which leads to the decrease of crack speed and the appearence of the logarithmic scaling is attempted branching, while power law roughness develops when branches succeed in growing to macroscopic size.

Human Mobility and the Dynamics of Measles in Large Geographical Areas

In recent years the global nature of epidemic spread has become a well established fact, however there have been limited studies on the detailed propagation of infectious diseases on regional scales. We have recently introduced a simulation program that explores disease propagation on such scales: the model uses a gridded geographical description of human settlements on top of which mobility is implemented using the Radiation Model. Parallel computation permits unlimited complexity. Both individual and equation based simulations of epidemiological models can be performed, thus permitting the exploration of the effects of mobility locally and globally. Using a SIR model parametrized for measles, we perform simulations for the area of British Isles, which we assume isolated. Exploring how the dynamics is influenced by human mobility, we show that mobility influences the dynamics globally and locally. In particular, the interplay of mobility and city size, enhances or reduces the contribution of the different mechanisms involved.