S. Teitel

Melting of icosahedral gold nanoclusters from molecular dynamics simulations

Molecular dynamics simulations show that gold clusters with about 600-3000 atoms crystallize into a Mackay icosahedron upon cooling from the liquid. A detailed surface analysis shows that the facets on the surface of the Mackay icosahedral gold clusters soften but do not premelt below the bulk melting temperature. This softening is found to be due to the increasing mobility of vertex and edge atoms with temperature, which leads to inter-layer and intra-layer diffusion, and a shrinkage of the average facet size, so that the average shape of the cluster is nearly spherical at melting.

Vortex-line fluctuations in model high-temperature superconductors

We carry out Monte Carlo simulations of the uniformly frustrated three-dimensional [ital XY] model, as a model for vortex-line fluctuations in a high-[ital T][sub [ital c]] superconductor in an external magnetic field. A density of vortex lines of [ital f]=1/25 is considered. We find two sharp phase transitions. The low-[ital T] superconducting phase is an ordered vortex-line lattice. The high-[ital T] normal phase is a vortex-line liquid, with much entangling, cutting, and loop excitations. An intermediate phase is found, which is characterized as a vortex-line liquid of disentangled, approximately straight, lines. In this phase, the system displays superconducting properties in the direction parallel to the magnetic field, but normal behavior in planes perpendicular to the field. A detailed analysis of the vortex structure function is carried out.

Yielding dynamics of a Herschel–Bulkley fluid: a critical-like fluidization behaviour

The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration tau_f decreases as a power law of the applied shear rate gp. We complete our previous findings by an investigation of the influence of the shearing geometry through the gap width e and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time tau_f, different fluidization processes are observed depending on gp and e: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow whereas at larger values of gp or e, the transient shear band is seen to invade the whole gap in a much smoother way. Finally, by comparing local and global rheological measurements, we emphasize that the steady state reached by our samples is fully compatible with that expected for a simple yield stress fluid described by a Herschel-Bulkley behaviour.The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration τf decreases as a power law of the applied shear rate . Here we go one step further by an exhaustive investigation of the influence of the shearing geometry through the gap width e and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time τf, different fluidization processes are observed depending on and e: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow, whereas at larger values of or e, the transient shear band is seen to invade the whole gap in a much smoother way. Still, the power-law behaviour appears to be very robust and hints to critical-like dynamics. To further discuss these results, we propose (i) a qualitative scenario to explain the induction-like period that precedes full fluidization and (ii) an analogy with critical phenomena that naturally leads to the observed power laws if one assumes that the yield point is the critical point of an underlying out-of-equilibrium phase transition.

Disorder Driven Melting of the Vortex Line Lattice

The 3D XY model with random in-plane couplings is simulated to model the phase diagram of a disordered type II superconductor as a function of temperature T and randomness strength p for fixed applied magnetic field. As p increases to a critical p(c), the first order vortex lattice melting line turns parallel to the T axis, continuing down to low temperatures, rather than ending at a critical point. Above p(c) preliminary results suggest the absence of a phase coherent vortex glass.

Glassiness, Rigidity and Jamming of Frictionless Soft Core Disks

The jamming of bidisperse soft core disks is considered, using a variety of different protocols to produce the jammed state. In agreement with other works, we find that cooling and compression can lead to a broad range of jamming packing fractions ϕ{J}, depending on cooling rate and initial configuration; the larger the degree of big particle clustering in the initial configuration, the larger will be the value of ϕ{J}. In contrast, we find that shearing disrupts particle clustering, leading to a much narrower range of ϕ{J} as the shear strain rate varies. In the limit of vanishingly small shear strain rate, we find a unique nontrivial value for the jamming density that is independent of the initial system configuration. We conclude that shear driven jamming is a unique and well-defined critical point in the space of shear driven steady states. We clarify the relation between glassy behavior, rigidity, and jamming in such systems and relate our results to recent experiments.

Finite-size scaling at the jamming transition: Corrections to scaling and the correlation-length critical exponent

We carry out a finite-size scaling analysis of the jamming transition in frictionless bidisperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent ν ≈ 1 and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding ν < 1 are due to the improper neglect of these corrections.

Quasistatic approximation to the scattering of elastic waves by a circular crack

The elastic‐wave scattering by a flat crack can be represented by an integral expression involving displacement and strain on the surface of the crack. We have explored the use of a modified static solution as an approximation to the displacement field of a penny‐shape crack in the long‐wavelength regime and then studied numerically how well it connects with the low‐freqency limit of the diffraction regime. Comparisons between this and several other existing approximations are made. We conclude that this quasistatic approximation is useful practically in both the long‐wavelength and beginning diffraction regime.

Critical scaling of shearing rheology at the jamming transition of soft-core frictionless disks

We perform numerical simulations to determine the shear stress and pressure of steady-state shear flow in a soft-disk model in two dimensions at zero temperature in the vicinity of the jamming transition ϕ{J}. We use critical point scaling analyses to determine the critical behavior at jamming, and we find that it is crucial to include corrections to scaling for a reliable analysis. We find that the relative size of these corrections are much smaller for pressure than for shear stress. We furthermore find a superlinear behavior for pressure and shear stress above ϕ{J}, both from the scaling analysis and from a direct analysis of pressure data extrapolated to the limit of vanishing shear rate.

Herschel-Bulkley Shearing Rheology Near the Athermal Jamming Transition

We consider the rheology of soft-core frictionless disks in two dimensions in the neighborhood of the athermal jamming transition. From numerical simulations of bidisperse, overdamped particles, we argue that the divergence of the viscosity below jamming is characteristic of the hard-core limit, independent of the particular soft-core interaction. We develop a mapping from soft-core to hard-core particles that recovers all the critical behavior found in earlier scaling analyses. Using this mapping we derive a relation that gives the exponent of the nonlinear Herschel-Bulkley rheology above jamming in terms of the exponent of the diverging viscosity below jamming.

Monte Carlo simulation of Fickian diffusion in the critical region

In this article we describe a novel, phenomenologically based computer simulation approach for studying relaxation dynamics in fluid systems. The method utilizes an ensemble consisting of two isothermal chambers initially separated by an impermeable partition. The fluid configurations in each chamber are initially pre-equilibrated at densities ρ+e and ρ−e respectively, where ρ reflects an average density of interest and e a small perturbation about this value. After the pre-equilibration step the partition is removed and the entire ensemble allowed to relax towards an equilibrium state guided by a kinetic Monte Carlo computer simulation algorithm. Fickian transport coefficients are found from quantities calculated during this relaxation process. We present an analysis of the approach and illustrate its application to transport property calculations in purely diffusive lattice-gas systems. Our results focus upon the critical region for which there are few published results and where simulation results f...