Avoidance and Coalescence of Delamination Patterns

Delamination of coatings and thin films from substrates generates a fascinating variety of patterns, from circular blisters to wrinkles and labyrinth domains, in a way that is not completely understood. We report on large-scale numerical simulations of the universal problem of avoidance and coalescence of delamination wrinkles, focusing on a case study of graphene sheets on patterned substrates. By nucleating and growing wrinkles in a controlled way, we are able to characterize how their interactions, mediated by long-range stress fields, determine their formation and morphology. We also study how the interplay between geometry and stresses drives a universal transition from conformation to delamination when sheets are deposited on particle-decorated substrates. Our results are directly applicable to strain engineering of graphene and also uncover universal phenomena observed at all scales, as for example in geomembrane deposition

Universal Features in the Genome-level Evolution of Protein Domains

Protein domains are found on genomes with notable statistical distributions, which bear a high degree of similarity. Previous work has shown how these distributions can be accounted for by simple models, where the main ingredients are probabilities of duplication, innovation, and loss of domains. However, no one so far has addressed the issue that these distributions follow definite trends depending on protein-coding genome size only. We present a stochastic duplication/innovation model, falling in the class of so-called Chinese Restaurant Processes, able to explain this feature of the data. Using only two universal parameters, related to a minimal number of domains and to the relative weight of innovation to duplication, the model reproduces two important aspects: (a) the populations of domain classes (the sets, related to homology classes, containing realizations of the same domain in different proteins) follow common power-laws whose cutoff is dictated by genome size, and (b) the number of domain families is universal and markedly sublinear in genome size. An important ingredient of the model is that the innovation probability decreases with genome size. We propose the possibility to interpret this as a global constraint given by the cost of expanding an increasingly complex interactome. Finally, we introduce a variant of the model where the choice of a new domain relates to its occurrence in genomic data, and thus accounts for fold specificity. Both models have general quantitative agreement with data from hundreds of genomes, which indicates the coexistence of the well-known specificity of proteomes with robust self-organizing phenomena related to the basic evolutionary ``moves'' of duplication and innovation

Current quantization and fractal hierarchy in a driven repulsive lattice gas

Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the non-equilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density

Evolution of the Protein Universe. Time Scales and Selection

The availability of many genome sequences gives us abundant information, which is, however, very difficult to decode. As a consequence, in order to advance our understanding of biological processes at the whole-cell scale, it becomes very important to develop higher-level, synthetic descriptions of the contents of a genome. At the protein level, an effective scale of description is provided by protein domains. Domains are independent unit-shapes (or "folds") forming proteins. They are structurally stable and have thermodynamic origin. A domain determines a set of potential functions and interactions for the protein that carries it, for example DNA- or protein-binding capability or catalytic sites. Protein domains are found on genomes with notable statistical distributions, which bear a high degree of similarity. A stochastic growth model with two universal parameters, related to a minimal number of domains and to the relative time-scale of innovation to duplication reproduces two important features of these distributions: (i) the populations of domain classes (the sets, related to homology classes, containing realizations of the same domain in different proteins) follow common power-laws whose diversity is related to genome size measured by the total number of proteins or protein domains and (ii) the number of domain families is sublinear in genome size. In this evolutionary process, selective pressure can enter both as a global constraint on the innovation time-scale, and as a regulator of the population of specific domain classes, related to their modularity: some shapes are common to all genomes, some are contextual. These two features are sufficient to obtain general quantitative agreement with data from hundreds of genomes, and show that robust self-organizing phenomena encase specific selective pressures during evolution

Towards the Glass Transition in Vibrated Granular Matter

Granular materials are large sets of macroscopic particles that interact solely via contact forces. The static behavior depends on the contact network and on the surface friction forces between grains; when they are set in motion (typically by vibrations) their dynamics is dominated by inelastic collisions. For these reasons granular media show an extremely rich phenomenology, ranging from fluid-like properties (if strongly vibrated), to "jamming", glassy, behavior (if weakly vibrated), to aging and hysteretical phenomena observed when they become trapped in frozen, amorphous states. The objective of this work is to study these states and transitions, and to characterize the analogies found between the dynamic behavior of vibrated granular media and the glass transition observed in thermal glass-formers. These analogies justify the interest in granular materials, because granular media can be seen as simplified model systems useful in the study of out of equilibrium thermodynamics, and, in general, to the larger framework known as "complexity". The granular materials considered here are composed of spheric, polished glass spheres. Since the surface state plays an important role in the grain-grain interaction, some measurements were also performed with acid etched beads, having different surface roughness. The samples are vertically vibrated to achieve vibrofluidization. Different kinds of vibration are used, to highlight different properties of the system. We first consider the transition between the fluid and the subcooled glassy phase, using different experimental techniques. The most important one is a torsion oscillator, that interacts with the granular media via immersed probes. The torsion oscillator can be used in forced mode. A torque is applied on the probe, and we measure the mechanical response function (complex susceptibility). In general, a relaxation is found and it is interpreted as the signature of the irreversible energy loss (damping) in granular collisions. This relaxation has an intrinsic time scale, and systematic analysis of it shows that a clear parallel can be traced to the behavior of "strong" glasses. In particular, it is found that (i) the relaxation time is a function of a unified control parameter, proportional to the square root of the average vibration, and phenomenologically equivalent to an effective temperature; (ii) the functional form with which the relaxation times approach the final "frozen" state has an Arrhenius, or Vögel-Fulcher-Tamman (VFT) behavior. The same torsion oscillator is employed in free mode. In this case, no external torque is applied, and the probe moves adapting its position under the effect of the continuous rearrangements in the sample. The system is studied by computing the power spectral density of the (angular position) time series. The resulting spectra represent a "configurational noise" as the system randomly hops from one configuration to the following. This allows to define, using a completely different approach, the same intrinsic time scale observed in forced mode measurements. The comparison of the two techniques allows to obtain a more complete and detailed picture of the dynamics in the jamming region. From this comparison, it was inferred that the system is also influenced by an effective vibration frequency, and that the relaxation time has indeed a non-Arrhenius behavior as a function of a control parameter defined as as = √ Γ/ωs. A model was developed combining rheological observations to a statistic approach describing extremal phenomena. This model justifies the appearance of both the control parameter and the VFT evolution of the relaxation. Furthermore, the model is predictive and exposes the effect of a few other rheologic properties of granular system. The effect of surface roughness are considered, showing that the static and dynamic surface friction coefficients are well described by the model. A second relevant part of this work is devoted to an explicit verification that macroscopic probes act as Brownian objects. This fact is often used to interpret experimental data (also in the present work) and to propose theoretical model. However, no explicit evidence has ever been discussed. This is hard to do, using a constrained system such as the torsion oscillator, because the restoring coefficient influences the dynamics of diffusion. To overcome the problem we built a different apparatus, called "Brownian motor", where the probes are mounted on ball bearings, so that they are free to turn without constraint. The properties of the time series of the position of the free turning probe and of the torsionally constrained oscillator can finally be analyzed and compared with simple simulations. The data show an overall diffusion-like behavior, that is influenced by the presence of constraints. Using fractal analysis we estimate the diffusion, or Hurst exponent. This allows to verify that a "macroscopic" object (the probe) immersed in the "microscopic" granular medium indeed behaves as a Brownian object, and that its dynamics can be studied in detail, showing that it undergoes anomalous diffusion. This work is concluded with a discussion on a few possible developments. The most promising idea is a novel approach to the study of the geometrical properties of the contact network of granular assemblies, that is responsible for many of the properties of the granular sample. By using Magnetic Resonance Imaging, the static 3-D structure of granular media can be reconstructed with unprecedented accuracy, resolution and ease of reproducibility. From the spatial information we can extract all the properties of static granular media: the compaction factor, the grain-grain correlation function, the free volume and other observables. Systematic studies could allow experimental confirmations of the many theoretical models that have been proposed in the last years and that still lack a thorough comparison with experiments. This idea does not conclude the perspectives of this work, that are vast and intriguing. A few promising subjects are reviewed more into detail in the corresponding Perspective section. To name a few we cite: measurements of induced aging in non-vibrated samples, the Brownian motor, stick and slip phenomena and their comparison with earthquakes

Deformation and failure of curved colloidal crystal shells

Designing and controlling particle self-assembly into robust and reliable high-performance smart materials often involves crystalline ordering in curved spaces. Examples include carbon allotropes like graphene, synthetic materials such as colloidosomes, or biological systems like lipid membranes, solid domains on vesicles, or viral capsids. Despite the relevance of these structures, the irreversible deformation and failure of curved crystals is still mostly unexplored. Here, we report simulation results of the mechanical deformation of colloidal crystalline shells that illustrate the subtle role played by geometrically necessary topological defects in controlling plastic yielding and failure. We observe plastic deformation attributable to the migration and reorientation of grain boundary scars, a collective process assisted by the intermittent proliferation of disclination pairs or abrupt structural failure induced by crack nucleating at defects. Our results provide general guiding principles to optimize the structural and mechanical stability of curved colloidal crystals

Deformation and failure of curved colloidal crystal shells

Designing and controlling particle self-assembly into robust and reliable high-performance smart materials often involves crystalline ordering in curved spaces. Examples include carbon allotropes like graphene, synthetic materials such as colloidosomes, or biological systems like lipid membranes, solid domains on vesicles, or viral capsids. Despite the relevance of these structures, the irreversible deformation and failure of curved crystals is still mostly unexplored. Here, we report simulation results of the mechanical deformation of colloidal crystalline shells that illustrate the subtle role played by geometrically necessary topological defects in controlling plastic yielding and failure. We observe plastic deformation attributable to the migration and reorientation of grain boundary scars, a collective process assisted by the intermittent proliferation of disclination pairs or abrupt structural failure induced by crack nucleating at defects. Our results provide general guiding principles to optimize the structural and mechanical stability of curved colloidal crystals

A link between short-range and long-range properties of random sphere packings

We present a high precision particle-by-particle 3D reconstruction of granular systems composed of monodispersed spheres (sphere packings); the experimental approach is based on magnetic resonance imaging techniques. Our measurements revealed a strong correlation between the volume defined by the distance to the first nearest neighbor and the long-range average density. The main contribution to the amplitude decay of the correlation function can be described as exponential rather than power law up to a range equal to 7 sphere diameters. No evidence of geometrical structural changes as a function of the density was observed and neither regular crystallites nor any other statistically significant structures could be ascribed to a specific local arrangement. We concluded that granular compaction is the result of a process through which the system changes the average size of local structures without changing their local geometrical characteristics. These conclusions are supported by two-body correlation functions and Voronoi polyhedra space decomposition. The results provide a different perspective on the mechanisms underlying compaction with respect to previous works, and allow to discriminate between the different existing theoretical approache