The formation of nanostructures during two-step quench in binary polymer systems having various types of liquid miscibility gaps are investigated systematically via computer simulations using the phase field method. Coupled liquid spinodal decomposition and fluid flow processes are considered by solving simultaneously the Cahn-Hilliard and Navier-Stokes equations. Various interesting phenomena and morphological patterns are predicted. It is found that the primary microstructures developed at the first quench and isothermal holding temperature greatly affect the secondary microstructures developed during the second quench and isothermal holding. Depending on the morphology and scale of the primary microstructure, either multicore and multishell or unicore and unishell structures are predicted. The breakup of annuluses in a core-shell structure in two dimensions is analyzed. The effects of viscosity on the formation of core-shell structure and on the growth and coarsening behaviors of bimodal droplets produced by the two-step quench in systems are also investigated.

The equilibrium shapes of water droplets on shallow-grooved hydrophobic surfaces are studied experimentally. The dependence of the two final states, notably metastable Cassie-Baxter and Wenzel, on the underlying geometric pattern is analyzed and discussed. Surprisingly, in contrast to theoretical expectations, a significant portion of the droplets are in the Cassie-Baxter state. The anisotropy of the patterns, defined by the relative groove and ridge widths, allows studying the influence of different mechanisms of spreading in orthogonal directions on the final shape of the droplets. The validity of the Cassie-Baxter and Wenzel models in the case of anisotropic surfaces is investigated, comparing the experimental data with theoretical predictions in the two respective regimes. The influence of varying ridge widths for fixed groove widths on the final state adopted by the droplets, i.e., Cassie-Baxter or Wenzel, is discussed.

The postfragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. We use three-dimensional positional data of Klebsiella pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field to construct a probability density function of floc volumes after a fragmentation event. We provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. The postfragmentation probability density function has a strong dependence on the size of the original floc and indicates that most fragmentation events result in clumps of one to three bacteria eroding from the original floc. We also provide numerical evidence that exhaustive fragmentation yields a limiting density inconsistent with the log-normal density predicted in the literature, most likely due to the heterogeneous nature of K. pneumoniae flocs. To support our conclusions, artificial flocs were generated and display similar postfragmentation density and exhaustive fragmentation.

The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.

Plasma-wave behavior in multiple dimensions is studied using two- and three-dimensional particle-in-cell simulations. We find that large-amplitude waves with $k{\lambda }_D\gtrsim 0.2$, where $k$ is the wave number of the wave and ${\lambda }_D$ is the Debye length, localize in the transverse direction around their axis due to nonlinear, local damping caused by transiting particles. The center of the wave behaves like a plane wave in which trapped particles maintain a quasisteady state at approximately constant amplitude, while the transverse edges damp away.

We quantify the correlation between earthquakes and use the same to extract causally connected earthquake pairs. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski [M. Baiesi and M. Paczuski, Phys. Rev. E 69, 066106 (2004)]. A network of earthquakes is then constructed from the time-ordered catalog and with links between the more correlated ones. A list of recurrences to each of the earthquakes is identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. Data pertaining to three different seismic regions (viz., California, Japan, and the Himalayas) are comparatively analyzed using such a network model. The distribution of recurrence lengths and recurrence times are two of the key features analyzed to draw conclusions about the universal aspects of such a network model. We find that the unimodal feature of recurrence length distribution, which helps to associate typical rupture lengths with different magnitude earthquakes, is robust across the different seismic regions. The out-degree of the networks shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws, with two regimes having different exponents, are obtained with recurrence time distribution. The first regime confirms the Omori law for aftershocks while the second regime, with a faster falloff for the larger recurrence times, establishes that pure spatial recurrences also follow a power-law distribution. The crossover to the second power-law regime can be taken to be signaling the end of the aftershock regime in an objective fashion.

We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system’s behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.

We propose and study, by means of numerical simulations, the time evolution of interfaces in a generalized voter model in $d=2$ dimensions. In this model, a randomly selected voter can change his or her opinion (state) with a certain probability that is an algebraic function of the average opinion of his or her nearest neighbors. By starting with well-defined (sharp) interfaces between two different states of opinion, we measure the time dependence of the interface width $(w)$, which behaves as a power law, i.e., $w\propto t^{\delta }$. In this way we characterized three different types of interfaces: (i) between an ordered phase (consensus) and a disordered one ($\delta =1/2$); (ii) between ordered phases having different states of opinion ($\delta =1/2$), which corresponds to interface coarsening without surface tension; and (iii) as in (ii) but considering surface tension. Here, we observe a finite-size induced crossover with exponents $\delta =1/4$ and $\delta =1/2$ for early and longer times, respectively. So, our study allows for the characterization of interfaces of quite different nature in a unified fashion, providing insight into the understanding of interface coarsening with and without surface tension.

We apply a variant of the explosive percolation procedure to large real-world networks and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural properties of the network, as well as the number of unoccupied links considered for comparison in our procedure. We observe that in our social networks, the percolation clusters close to the critical point are related to the community structure. This relationship is further highlighted by applying the procedure to model networks with predefined communities.

We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.

Particle stabilized emulsions are ubiquitous in the food and cosmetics industry, but our understanding of the influence of microscopic fluid-particle and particle-particle interactions on the macroscopic rheology is still limited. In this paper we present a simulation algorithm based on a multicomponent lattice Boltzmann model to describe the solvents combined with a molecular dynamics solver for the description of the solved particles. It is shown that the model allows a wide variation of fluid properties and arbitrary contact angles on the particle surfaces. We demonstrate its applicability by studying the transition from a “bicontinuous interfacially jammed emulsion gel” (bijel) to a “Pickering emulsion” in dependence on the contact angle, the particle concentration, and the ratio of the solvents.

In this work we propose a statistical characterization of a linear stochastic volatility model featuring inverse-gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the inverse-gamma law in the emergence of fat tails and of the relevant correlation functions. We also propose a systematic methodology for estimating the parameters and we describe the empirical analysis of the Standard & Poor’s 500 index daily returns, confirming the ability of the model to capture many of the established stylized facts as well as the scaling properties of empirical distributions over different time horizons.

We introduce a two-dimensional walk model in which a random walker can only move on the first quarter of a two-dimensional plane. We calculate the partition function of this walk model using a transfer matrix method and show that the model undergoes a phase transition. Surprisingly the partition function of this two-dimensional walk model is exactly equal to that of a driven-diffusive system defined on a discrete lattice with periodic boundary conditions in which a phase transition occurs from a high-density to a low-density phase. The driven-diffusive system can be mapped to a zero-range process where the particles can accumulate in a single lattice site in the low-density phase. This is very reminiscent of real-space Bose-Einstein condensation.

It is shown that the inertia of a particle plays an important role in its motion in the direction normal to a fluid-liquid interface, and in determining its adsorption trajectory and orientation in the adsorbed state. Although the importance of inertia diminishes with decreasing particle size, on an air-water interface the inertia continues to be important even when the size is as small as a few nanometers. Furthermore, similar to an underdamped system, an adsorbed particle has characteristic linear and rotational frequencies that can be excited by an external forcing.

We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a depinning regime of high velocity clusters defined as avalanches and a pinning regime of very low-velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behavior.

The generation of higher harmonics of the magnetoplasmon frequency which has recently been reported in strongly coupled two-dimensional Yukawa systems is investigated in detail and, in addition, extended to two-dimensional Coulomb systems. We observe higher harmonics over a much larger frequency range than before and compare the theoretical prediction with the simulations. The influence of the coupling, structure, and thermal energy on the excitation of these modes is examined in detail. We also report on the effect of friction on the mode spectra to make predictions about the experimental observability of this new effect.

In the thermodynamic limit, the time evolution of isolated long-range interacting systems is properly described by the Vlasov equation. This equation admits nonequilibrium dynamically stable stationary solutions characterized by a zero order parameter. We show that the presence of external noise sources, such as a heat bath, can reduce their lifetime and induce at a specific time a dynamical phase transition marked by a nonzero order parameter. This transition may be used as a distinctive experimental signature of the temporary existence of nonequilibrium Vlasov-stable states. In particular, we present evidence of a regime characterized by an order parameter pulse. Our analytical results are corroborated by numerical simulations of a paradigmatic long-range model.

We consider magnetic friction between two systems of $q$-state Potts spins which are moving along their boundaries with a relative constant velocity $v$. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state, which is far from equilibrium. The problem is treated analytically in the limit $v=\infty$ (in one dimension, as well as in two dimensions for large-$q$ values) and for $v$ and $q$ finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and interparticle friction $\mu$ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Voronoï tessellation, we find the variance of the local volume fraction $\varphi$ monotonically decreases as the system becomes more dense, independent of boundary condition and $\mu$. We examine the universality and origins of this trend using experiments and the recent granocentric model [M. Clusel, E. I. Corwin, A. O. N. Siemens, and J. Brujić, Nature (London) 460, 611 (2009); E. I. Corwin, M. Clusel, A. O. N. Siemens, and J. Brujić, Soft Matter 6, 2949 (2010)], modified to draw particle locations from an arbitrary distribution $\mathcal{P}(s)$ of neighbor distances $s$. The mean and variance of the observed $\mathcal{P}(s)$ are described by a single length scale controlled by $\mathrm{\varphi ̄}$. Through the granocentric model, we observe that diverse functional forms of $\mathcal{P}(s)$ all produce the trend of decreasing fluctuations, but only the experimentally observed $\mathcal{P}(s)$ provides quantitative agreement with the measured $\varphi$ fluctuations. Thus, we find that both $\mathcal{P}(s)$ and $\mathcal{P}(\varphi )$ encode similar information about the ensemble of observed packings and are connected to each other by the local granocentric model.

The scalings in film growth by pulsed laser deposition (PLD) and modulated beam deposition (MBD) were investigated by Monte Carlo simulations. In PLD, an atomic pulse beam with a period $t_0$ were deposited instantaneously on a substrate, whereas in MBD, adatoms were deposited during a short time interval $t_1$ ($0⩽t_1⩽t_0$) within each period. If $t_1=0$, MBD will be identical to PLD and, if $t_1=t_0$, MBD will become usual molecular beam epitaxy (MBE). Specifically, logarithmic scaling was investigated for the nucleation density reported for PLD, and the scaling of island density was studied regarding the growth for $0<t_1<t_0$ in MBD. It was found that the logarithmic scaling held for the nucleation density when growing islands were fractal-like but the quality of data collapsing became worse when islands were compact by adatom diffusion along the edges of islands. A crossover behavior from PLD growth to MBE growth was observed as $t_1$ increased. The phase diagram was also presented.