We investigate the aggregation kinetics of a simulated telechelic polymer gel. In the hybrid molecular dynamics (MD)/Monte Carlo (MC) algorithm, aggregates of associating end groups form and break according to MC rules, while the position of the polymers in space is dictated by MD. As a result, the aggregate sizes change over time. In order to describe this aggregation process, we employ master equations. They define changes in the number of aggregates of a certain size in terms of reaction rates. These reaction rates indicate the likelihood that two aggregates combine to form a large one, or that a large aggregate splits into two smaller parts. The reaction rates are obtained from the simulations for a range of temperatures. Our results indicate that the rates are not only temperature dependent, but also a function of the sizes of the aggregates involved in the reaction. Using the measured rates, solutions to the master equations are shown to be stable and in agreement with the aggregate size distribution, as obtained directly from simulation data. Furthermore, we show how temperature-induced variations in these rates give rise to the observed changes in the aggregate distribution that characterizes the sol-gel transition.

Hydrodynamic interactions of swimming microorganisms can lead to coordinated behaviors of large groups. Using a mean-field theory and the Oldroyd-B constitutive equation, we show how linear viscoelasticity of the suspending fluid alters the hydrodynamic interactions and therefore the ability of the group to coordinate. We quantify the ability to coordinate by the initial growth rate of a small disturbance from the uniform isotropic state. For small wave numbers the response is qualitatively similar to a Newtonian fluid but the Deborah number affects an effective viscosity of the suspension. At higher wave number, the response of the fluid to small amplitude oscillatory shear flow, leads to a maximal growth rate at a particular wavelength unlike the Newtonian result.

We present high-accuracy quasistationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite-size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite-size scaling holds with exactly the same exponents of the annealed case, so we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.

Using computational modeling, we examine particle-laden flows along surfaces decorated with periodic arrays of tilted posts. We show that when high-aspect-ratio posts are tilted against the flow direction, cross-stream circulatory secondary flows emerge. These circulatory flows enhance the net lift force acting on finite-sized particles transported by fluid, thereby repelling the particles from the wall and preventing their deposition. This hydrodynamic effect can potentially be used for designing antifouling and self-cleaning surfaces.

Starting from Axelrod's model of cultural dissemination, we introduce a rewiring probability, enabling agents to cut the links with their unfriendly neighbors if their cultural similarity is below a tolerance parameter. For low values of tolerance, rewiring promotes the convergence to a frozen monocultural state. However, intermediate tolerance values prevent rewiring once the network is fragmented, resulting in a multicultural society even for values of initial cultural diversity in which the original Axelrod model reaches globalization.

Two research groups have measured turbulent velocity statistics in superfluid helium using different techniques. The results were in conflict: one experiment revealed Gaussian distributions (as observed in ordinary turbulence), the other experiment determined power laws. To solve the apparent puzzle, we numerically model quantum turbulence as a tangle of vortex filaments, and conclude that there is no contradiction between the two experiments. The transition from Gaussian to power law arises from the different length scales which are probed using the two techniques. We find that the average distance between the quantum vortices marks the separation between quantum and quasiclassical length scales.

We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory at a much lower density than the corresponding bulk system. We use fluctuating hydrodynamics, with confinement imposed through a periodic potential whose wavelength plays an important role in our treatment. To make the calculation tractable we implement a detailed calculation in one dimension. Although we do not expect simple $1d$ fluids to show a glass transition, our results are indicative of the behavior expected in higher dimensions. In a certain region of parameter space we observe a three-step relaxation reported recently in computer simulations [S. H. Krishnan, Ph.D. thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J. Special Topics 189, 135 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack [Phys. Rev. E 75, 031503 (2007)] and Lang et al. [Phys. Rev. Lett. 105, 125701 (2010)].

We study the behavior of the spectra corresponding to quantum systems subjected to a contractive noise, i.e., the environment reduces the accessible phase space of the system, but the total probability is conserved. We find that the number of long-lived resonances grows as a power law in $\hslash$, but surprisingly there is no relationship between the exponent of this power law and the fractal dimension of the corresponding classical attractor. This is in disagreement with the predictions of the fractal Weyl law which has been established for open systems, where the probability is lost under the effect of a projective opening.

We report the experimental study of the degassing dynamics through a thin layer of shear-thinning viscoelastic fluid when a constant air flow is imposed at its bottom. The fluid is an aqueous solution of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal). Over a large range of parameters, the air is periodically released through a series of successive bubbles, hereafter named cascades. Each cascade is followed by a continuous degassing, lasting for several seconds, corresponding to an open channel crossing the fluid layer. The periodicity between two cascades does not depend on the injected flow rate. Inside one cascade, the properties of the overpressure signal associated with the successive bubbles vary continuously. The pressure threshold above which the fluid starts flowing, fluid deformation and pressure drop due to degassing through the thin fluid layer can be simply described by a Maxwell model.

Cornstarch suspensions exhibit remarkable behavior. Here, we present two unexpected observations for a sphere settling in such a suspension: In the bulk of the liquid the velocity of the sphere oscillates around a terminal value, without damping. Near the bottom the sphere comes to a full stop, but then accelerates again toward a second stop. This stop-go cycle is repeated several times before the object reaches the bottom. We show that common shear thickening or linear viscoelastic models cannot account for the observed phenomena, and propose a minimal jamming model to describe the behavior at the bottom.

Order statistics of periodic, Gaussian noise with $1/f^{\alpha }$ power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap $d_k=\langle x_k-x_{k+1}\rangle$ between the $k$th and ($k+1$)st largest values of the signal. The result $d_k\sim k^{-1}$, known for independent, identically distributed variables, remains valid for $0⩽\alpha <1$. Nontrivial, $\alpha$-dependent scaling exponents, $d_k\sim k^{(\alpha -3)/2}$, emerge for $1<\alpha <5$, and, finally, $\alpha$-independent scaling, $d_k\sim k$, is obtained for $\alpha >5$. The spectra of average ordered values ${\varepsilon }_k=\langle x_1-x_k\rangle \sim k^{\beta }$ is also examined. The exponent $\beta$ is derived from the gap scaling as well as by relating ${\varepsilon }_k$ to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that $\beta (\alpha =2)=1/2$, $\beta \left(4\right)=3/2$, and $\beta \left(\infty \right)=2$ are exact values. We also show that parallels can be drawn between ${\varepsilon }_k$ and the quantum mechanical spectra of a particle in power-law potentials.

We analyze the ground states at boundaries of four-dimensional (full-dimensional) ground-state regions of the lattice-gas model on the infinite plane triangular lattice with nearest- and next-nearest-neighbor pairwise interactions and with additional interaction between three particles at the vertices of a nearest-neighbor triangle. In such a way we determine the ground states at fixed density of particles (coverage) and make the comparison to experiments possible. A surprisingly rich variety of structures is found: ordered periodic, ordered-but-aperiodic, disordered with various degree of disorder, and multiple-twin structures. The first-order and continuous phase transitions are identified. The degree of disorder for disordered ground states is analyzed. One of the most interesting results is the discovery of an infinite sequence of ground states at a boundary between two phases.

We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven quenched Kardar-Parisi-Zhang (qKPZ) equation. We fully characterize the spatial structure of these avalanches—we report universal scaling functions for size, height, and width distributions, and also local front heights. Furthermore, we resolve a problem that arises in many imaging experiments of crackling noise and avalanche dynamics, where the observed distributions are strongly distorted by a limited field of view. Through artificially windowed data, we show these distributions and their multivariable scaling functions may be written in terms of two control parameters: the window size and the characteristic length scale of the dynamics. For the entire system and the windowed distributions we develop accurate parametrizations for the universal scaling functions, including corrections to scaling and systematic error bars, facilitated by a novel software environment SloppyScaling.

When a spherical conducting bead is placed in an electrode, it experiences an electric force. In a plane capacitor, it can undergo a periodic bouncing between the electrodes. Using a fast video camera, we measured the acceleration of the bead and the period of its motion as a function of the applied voltage. A mathematical model based on the hypothesis of electrostatic equilibrium is proposed to describe the dynamics of the system. We observe a stabilization of the trajectories: A bead bouncing between two electrodes tends to oscillate on a quasivertical trajectory, whatever its initial horizontal velocity. When two identical beads are placed together in a capacitor, they oscillate at the same frequency and an antiphase synchronization effect occurs. We propose a simple mechanism based on a Kuramoto-like model to explain it.

The elastocapillary instability of a flexible plate plunged in a liquid bath is analyzed theoretically. We show that the plate can bend due to two separate destabilizing mechanisms, when the liquid is partially wetting the solid. For contact angles ${\theta }_e>\pi /2$, the capillary forces acting tangential to the surface are compressing the plate and can induce a classical buckling instability. However, a second mechanism appears due to capillary forces normal to surface. These induce a destabilizing torque that tends to bend the plate for any value of the contact angle ${\theta }_e>0$. We denote these mechanisms as “buckling” and “bending,” respectively and identify the two corresponding dimensionless parameters that govern the elastocapillary stability. The onset of instability is determined analytically and the different bifurcation scenarios are worked out for experimentally relevant conditions.

In molecular dynamics (MD) simulations, interactions between water molecules and graphitic surfaces are often modeled as a simple Lennard-Jones potential between oxygen and carbon atoms. A possible method for tuning this parameter consists of simulating a water nanodroplet on a flat graphitic surface, measuring the equilibrium contact angle, extrapolating it to the limit of a macroscopic droplet, and finally matching this quantity to experimental results. Considering recent evidence demonstrating that the contact angle of water on a graphitic plane is much higher than what was previously reported, we estimate the oxygen-carbon interaction for the recent SPC/Fw water model. Results indicate a value of about $0.2$ kJ/mol, much lower than previous estimations. We then perform simulations of cylindrical water filaments on graphitic surfaces, in order to compare and correlate contact angles resulting from these two different systems. Results suggest that a modified Young's equation does not describe the relation between contact angle and drop size in the case of extremely small systems and that contributions different from the one deriving from contact line tension should be taken into account.

In the $B2$ phase formed by bent-shaped molecules a dense line texture is frequently observed. For the texture description a model is proposed consisting of a periodic system of anticlinic antiferroelectric bulk domains with opposite chiralities separated by $\pi$ walls in which polarization rotates. The bulk domains are situated between layers of synclinic ferroelectric phase near the upper and lower surfaces. In the surface layers induced by polar anchoring domains of opposite chirality are separated by defect lines. Under the electric field the ferroelectric layer near one sample surface is growing against the antiferroelectric structure in the sample bulk and the stripe texture is fading out, but still in the saturated field surface lines or walls persist separating ferroelectric domains of opposite chirality. The proposed model is adapted also for a case when the anticlinic antiferroelectric structure in the sample bulk is sandwiched between anticlinic ferroelectric layers near the surfaces. In that case the applied electric field eliminates all the lines because the resulting anticlinic ferroelectric structure is racemic, with no chiral domains.

We introduce an inflexible contrarian opinion (ICO) model in which a fraction $p$ of inflexible contrarians within a group holds a strong opinion opposite to the opinion held by the rest of the group. At the initial stage, stable clusters of two opinions, $A$ and $B$, exist. Then we introduce inflexible contrarians which hold a strong $B$ opinion into the opinion $A$ group. Through their interactions, the inflexible contrarians are able to decrease the size of the largest $A$ opinion cluster and even destroy it. We see this kind of method in operation, e.g., when companies send free new products to potential customers in order to convince them to adopt their products and influence others to buy them. We study the ICO model, using two different strategies, on both Erdös-Rényi and scale-free networks. In strategy I, the inflexible contrarians are positioned at random. In strategy II, the inflexible contrarians are chosen to be the highest-degree nodes. We find that for both strategies the size of the largest $A$ cluster decreases to 0 as $p$ increases as in a phase transition. At a critical threshold value, $p_c$, the system undergoes a second-order phase transition that belongs to the same universality class of mean-field percolation. We find that even for an Erdös-Rényi type model, where the degrees of the nodes are not so distinct, strategy II is significantly more effective in reducing the size of the largest $A$ opinion cluster and, at very small values of $p$, the largest $A$ opinion cluster is destroyed.

We examine the evolution of a liquid drop on an inclined substrate oscillating vertically. The drop is assumed thin, and the oscillations are assumed weak and slow (the latter makes the liquid’s inertia and viscosity negligible, so the drop’s shape is determined by a balance of surface tension, gravity, and vibration-induced inertial force). On the basis of these approximations, asymptotic expressions are derived for the mean velocities of two- (2D) and three-dimensional (3D) drops. It is shown that, if the amplitude of the substrate’s oscillations exceeds a certain threshold value, both 2D and 3D drops climb uphill. The two cases, however, exhibit different behaviors of the threshold amplitude of the oscillations on their frequency, in the low-frequency limit: to make 2D drops climb uphill, the oscillations must be much stronger than those in the 3D case. This difference is important, as the 2D behavior does not fit the existing experimental results.

We show that the presence of a localized drive in an otherwise diffusive system results in steady-state density and current profiles that decay algebraically to their global average value, away from the drive in two or higher dimensions. An analogy to an electrostatic problem is established, whereby the density profile induced by a driving bond maps onto the electrostatic potential due to an electric dipole located along the bond. The dipole strength is proportional to the drive, and is determined self-consistently by solving the electrostatic problem. The profile resulting from a localized configuration of more than one driving bond can be straightforwardly determined by the superposition principle of electrostatics. This picture is shown to hold even in the presence of exclusion interaction between particles.