Local thermal energy as a structural indicator in glasses.

Identifying heterogeneous structures in glasses-such as localized soft spots-and understanding structure-dynamics relations in these systems remain major scientific challenges. Here, we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change caused by thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses-an intrinsic signature of glassy frustration-anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal [Formula: see text] density of states of quasilocalized low-frequency vibrational modes. When the spatial thermal energy field-a "softness field"-is considered, this power law tail manifests itself by highly localized spots, which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal modes-based approach. These results offer a general, system/model-independent, physical/observable-based approach to identify structural properties of quiescent glasses and relate them to glassy dynamics.

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling.

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here, we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k†, where phonons are no longer quantized into bands. For k < k†, finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k†, we find that Γ(k) is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, Γ(k) follows a Rayleigh scattering scaling ∼k¯d+1 (¯d is the spatial dimension) and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form ∼k¯d+1 log(k0/k) emerges (k0 > k† is a characteristic wavenumber). Our results suggest that macroscopic glasses-and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations-exhibit Rayleigh scaling at the lowest wavenumbers k and a crossover to generalized-Rayleigh scaling at higher k. Some supporting experimental evidence from recent literature is presented.

The sandpile revisited: computer assisted determination of constitutive relations and the breaking of scaling.

We revisit the problem of the stress distribution in a frictional sandpile with both normal and tangential (frictional) inter-granular forces, under gravity, equipped with a new numerical method of generating such assemblies. Numerical simulations allow a determination of the spatial dependence of all the components of the stress field, principle stress axis, angle of repose, as a function of systems size, the coefficient of static friction and the frictional interaction with the bottom surface. We compare these results with the predictions of a theory based on continuum equilibrium mechanics. Basic to the theory of sandpiles are assumptions about the form of scaling solutions and constitutive relations for cohesive-less hard grains for which no typical scale is available. We find that these constitutive relations must be modified; moreover for smaller friction coefficients and smaller piles these scaling assumptions break down in the bulk of the sandpile due to the presence of length scales that must be carefully identified. Fortunately, for larger friction coefficient and for larger piles the breaking of scaling is weak in the bulk, allowing an approximate analytic theory which agrees well with the observations. After identifying the crucial scale, triggering the breaking of scaling, we provide a predictive theory to when scaling solutions are expected to break down. At the bottom of the pile the scaling assumption breaks always, due to the different interactions with the bottom surface. The consequences for measurable quantities like the pressure distribution and shear stress at the bottom of the pile are discussed. For example one can have a transition from no dip in the base-pressure to a dip at the center of the pile as friction increases.

What Determines the Static Force Chains in Stressed Granular Media?

The determination of the normal and transverse (frictional) interparticle forces within a granular medium is a long-standing, daunting, and yet unresolved problem. We present a new formalism that employs the knowledge of the external forces and the orientations of contacts between particles (of any given size), to compute all the interparticle forces. Having solved this problem, we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.

Effective forces in thermal amorphous solids with generic interactions.

In thermal glasses at temperatures sufficiently lower than the glass transition, the constituent particles are trapped in their cages for a sufficiently long time such that their time-averaged positions can be determined before diffusion and structural relaxation takes place. The effective forces are those that hold these average positions in place. In numerical simulations the effective forces F_{ij} between any pair of particles can be measured as a time average of the bare forces f_{ij}(r_{ij}(t)). In general, even if the bare forces come from two-body interactions, thermal dynamics dress the effective forces to contain many-body interactions. Here, we develop the effective theory for systems with generic interactions, where the effective forces are derivable from an effective potential and in turn they give rise to an effective Hessian whose eigenvalues are all positive when the system is stable. In this Rapid Communication, we offer analytic expressions for the effective theory, and demonstrate the usefulness and the predictive power of the approach.

Finite-time singularities in surface-diffusion instabilities are cured by plasticity.

A free material surface which supports surface diffusion becomes unstable when put under external nonhydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite-time cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.

Structure and ligand-binding site characteristics of the human P2Y11 nucleotide receptor deduced from computational modelling and mutational analysis.

The P2Y11-R (P2Y11 receptor) is a less explored drug target. We computed an hP2Y11-R (human P2Y11) homology model with two templates, bovine-rhodopsin (2.6 A resolution; 1 A=0.1 nm) and a hP2Y1-ATP complex model. The hP2Y11-R model was refined using molecular dynamics calculations and validated by virtual screening methods, with an enrichment factor of 5. Furthermore, mutational analyses of Arg106, Glu186, Arg268, Arg307 and Ala313 confirmed the adequacy of our hP2Y11-R model and the computed ligand recognition mode. The E186A and R268A mutants reduced the potency of ATP by one and three orders of magnitude respectively. The R106A and R307A mutants were functionally inactive. We propose that residues Arg106, Arg268, Arg307 and Glu186 are involved in ionic interactions with the phosphate moiety of ATP. Arg307 is possibly also H-bonded to N6 of ATP via the backbone carbonyl. Activity of ATP at the F109I mutant revealed that the proposed p-stacking of Phe109 with the adenine ring is a minor interaction. The mutation A313N, which is part of a hydrophobic pocket in the vicinity of the ATP C-2 position, partially explains the high activity of 2-MeS-ATP at P2Y1-R as compared with the negligible activity at the P2Y11-R. Inactivity of ATP at the Y261A mutant implies that Tyr261 acts as a molecular switch, as in other G-protein-coupled receptors. Moreover, analysis of cAMP responses seen with the mutants showed that the efficacy of coupling of the P2Y11-R with Gs is more variable than coupling with Gq. Our model also indicates that Ser206 forms an H-bond with Pgamma (the gamma-phosphate of the triphosphate chain of ATP) and Met310 interacts with the adenine moiety.

Navigator-3, a modulator of cell migration, may act as a suppressor of breast cancer progression.

Dissemination of primary tumor cells depends on migratory and invasive attributes. Here, we identify Navigator-3 (NAV3), a gene frequently mutated or deleted in human tumors, as a regulator of epithelial migration and invasion. Following induction by growth factors, NAV3 localizes to the plus ends of microtubules and enhances their polarized growth. Accordingly, NAV3 depletion trimmed microtubule growth, prolonged growth factor signaling, prevented apoptosis and enhanced random cell migration. Mathematical modeling suggested that NAV3-depleted cells acquire an advantage in terms of the way they explore their environment. In animal models, silencing NAV3 increased metastasis, whereas ectopic expression of the wild-type form, unlike expression of two, relatively unstable oncogenic mutants from human tumors, inhibited metastasis. Congruently, analyses of > 2,500 breast and lung cancer patients associated low NAV3 with shorter survival. We propose that NAV3 inhibits breast cancer progression by regulating microtubule dynamics, biasing directionally persistent rather than random migration, and inhibiting locomotion of initiated cells.

Elasticity and plasticity in stiff and flexible oligomeric glasses.

In this paper we focus on the mechanical properties of oligomeric glasses (waxes), employing a microscopic model that provides, via numerical simulations, information about the shear modulus of such materials, the failure mechanism via plastic instabilities, and the geometric responses of the oligomers themselves to a mechanical load. We present a microscopic theory that explains the numerically observed phenomena, including an exact theory of the shear modulus and of the plastic instabilities, both local and system spanning. In addition we present a model to explain the geometric changes in the oligomeric chains under increasing strains.

Propagation mechanism of brittle cracks.

We employ a recently developed model that allows the study of two-dimensional brittle crack propagation under fixed grip boundary conditions. The crack development highlights the importance of voids which appear ahead of the crack as observed in experiments on the nanoscale. The appearance of these voids is responsible for roughening the crack path on small scales, in agreement with theoretical expectations. With increasing speed of propagation one observes the branching instabilities that were reported in experiments. The simulations allow understanding the phenomena by analyzing the elastic stress field that accompanies the crack dynamics.

Relaxation mechanisms in glassy dynamics: the Arrhenius and fragile regimes.

Generic glass formers exhibit at least two characteristic changes in their relaxation behavior, first to an Arrhenius-type relaxation at some characteristic temperature and then at a lower characteristic temperature to a super-Arrhenius (fragile) behavior. We address these transitions by studying the statistics of free energy barriers for different systems at different temperatures and space dimensions. We present a clear evidence for changes in the dynamical behavior at the transition to Arrhenius and then to a super-Arrhenius behavior. A simple model is presented, based on the idea of competition between single-particle and cooperative dynamics. We argue that Arrhenius behavior can take place as long as there is enough free volume for the completion of a simple T1 relaxation process. Once free volume is absent one needs a cooperative mechanism to "collect" enough free volume. We show that this model captures all the qualitative behavior observed in simulations throughout the considered temperature range.

Effect of the interparticle potential on the yield stress of amorphous solids.

A crucially important material parameter for all amorphous solids is the yield stress, which is the value of the stress for which the material yields to plastic flow when it is strained quasistatically at zero temperature. It is difficult in laboratory experiments to determine what parameters of the interparticle potential affect the value of the yield stress. Here we use the versatility of numerical simulations to study the dependence of the yield stress on the parameters of the interparticle potential. We find a very simple dependence on the fundamental scales that characterize the repulsive and attractive parts of the potential, respectively, and offer a scaling theory that collapses the data for widely different potentials and in different space dimensions.

Athermal brittle-to-ductile transition in amorphous solids.

Brittle materials exhibit sharp dynamical fractures when meeting Griffith's criterion, whereas ductile materials blunt a sharp crack by plastic responses. Upon continuous pulling, ductile materials exhibit a necking instability that is dominated by a plastic flow. Usually one discusses the brittle to ductile transition as a function of increasing temperature. We introduce an athermal brittle to ductile transition as a function of the cutoff length of the interparticle potential. On the basis of extensive numerical simulations of the response to pulling the material boundaries at a constant speed we offer an explanation of the onset of ductility via the increase in the density of plastic modes as a function of the potential cutoff length. Finally we can resolve an old riddle: In experiments brittle materials can be strained under grip boundary conditions and exhibit a dynamic crack when cut with a sufficiently long initial slot. Mysteriously, in molecular dynamics simulations it appeared that cracks refused to propagate dynamically under grip boundary conditions, and continuous pulling was necessary to achieve fracture. We argue that this mystery is removed when one understands the distinction between brittle and ductile athermal amorphous materials.

Statistical physics of elastoplastic steady states in amorphous solids: finite temperatures and strain rates.

The effect of finite temperature T and finite strain rate γ on the statistical physics of plastic deformations in amorphous solids made of N particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, T

Statistical mechanics and dynamics of a three-dimensional glass-forming system.

In the context of a classical example of glass formation in three dimensions, we exemplify how to construct a statistical-mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of upscaled quasispecies that allow the construction of a theory with a finite number of "states." Once constructed, the theory identifies a typical scale xi that increases rapidly with lowering the temperature and which determines the alpha-relaxation time tau(alpha) as tau(alpha) approximately exp(muxi/T), with mu a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.