Fusion of sessile droplets with body of different liquids is delayed when the approaching drops are sitting on a highly wettable solid substrate. Owing to the surface tension gradients between the mixing drops, a Marangoni driven flow through the connecting channel appears. Experiments of delayed coalescence were recently reported in [Langmuir 24, 6395 (2008)] for millimeters sized drops. For droplets of submillimeter dimensions, capillary forces dominate. The control of interfacial energies becomes an important strategy for manipulating tiny droplets along the solid surfaces. In this paper we present phase field simulations in two spatial dimensions for microdroplets of perfectly miscible liquids. For drops with a given geometry, systematic investigations were performed for different fluid viscosities. Different behaviors are observed from chasing droplets to droplets repelling.

This paper presents a study of transport parameters (diffusion, dynamic permeability, thermal permeability, trapping constant) of porous media by combining the homogenization of periodic media (HPM) and the self-consistent scheme (SCM) based on a bicomposite spherical pattern. The link between the HPM and SCM approaches is first established by using a systematic argument independent of the problem under consideration. It is shown that the periodicity condition can be replaced by zero flux and energy through the whole surface of the representative elementary volume. Consequently the SCM solution can be considered as a geometrical approximation of the local problem derived through HPM for materials such that the morphology of the period is “close” to the SCM pattern. These results are then applied to derive the estimates of the effective diffusion, the dynamic permeability, the thermal permeability and the trapping constant of porous media. These SCM estimates are compared with numerical HPM results obtained on periodic arrays of spheres and polyhedrons. It is shown that SCM estimates provide good analytical approximations of the effective parameters for periodic packings of spheres at porosities larger than 0.6, while the agreement is excellent for periodic packings of polyhedrons in the whole range of porosity.

We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of one-dimensional quantum systems, to simulate the time evolution of nonequilibrium stochastic systems. We describe this method in detail; a system’s probability distribution is represented by a matrix product state (MPS) of finite dimension and then its time evolution is efficiently simulated by repeatedly updating and approximately refactorizing this representation. We examine the use of MPS as an approximation method, looking at parallels between the interpretations of applying it to quantum state vectors and probability distributions. In the context of stochastic systems we consider two types of factorization for use in the TEBD algorithm: non-negative matrix factorization (NMF), which ensures that the approximate probability distribution is manifestly non-negative, and the singular value decomposition (SVD). Comparing these factorizations, we find the accuracy of the SVD to be substantially greater than current NMF algorithms. We then apply TEBD to simulate the totally asymmetric simple exclusion process (TASEP) for systems of up to hundreds of lattice sites in size. Using exact analytic results for the TASEP steady state, we find that TEBD reproduces this state such that the error in calculating expectation values can be made negligible even when severely compressing the description of the system by restricting the dimension of the MPS to be very small. Out of the steady state we show for specific observables that expectation values converge as the dimension of the MPS is increased to a moderate size.

A popular theory of self-organized criticality predicts that the stationary density of the Abelian sandpile model equals the threshold density of the corresponding fixed-energy sandpile. We recently announced that this “density conjecture” is false when the underlying graph is any of ${\mathbb{Z}}^2$, the complete graph $K_n$, the Cayley tree, the ladder graph, the bracelet graph, or the flower graph. In this paper, we substantiate this claim by rigorous proof and extensive simulations. We show that driven-dissipative sandpiles continue to evolve even after a constant fraction of the sand has been lost at the sink. Nevertheless, we do find (and prove) a relationship between the two models: the threshold density of the fixed-energy sandpile is the point at which the driven-dissipative sandpile begins to lose a macroscopic amount of sand to the sink.

Systems of self-propelled particles are known for their tendency to aggregate and to display swarm behavior. We investigate two model systems: self-propelled rods interacting via volume exclusion and sinusoidally beating flagella embedded in a fluid with hydrodynamic interactions. In the flagella system, beating frequencies are Gaussian distributed with a nonzero average. These systems are studied by Brownian-dynamics simulations and by mesoscale hydrodynamics simulations, respectively. The clustering behavior is analyzed as the particle density and the environmental or internal noise are varied. By distinguishing three types of cluster-size probability density functions, we obtain a phase diagram of different swarm behaviors. The properties of clusters such as their configuration, lifetime, and average size are analyzed. We find that the swarm behavior of the two systems, characterized by several effective power laws, is very similar. However, a more careful analysis reveals several differences. Clusters of self-propelled rods form due to partially blocked forward motion and are therefore typically wedge shaped. At higher rod density and low noise, a giant mobile cluster appears, in which most rods are mostly oriented toward the center. In contrast, flagella become hydrodynamically synchronized and attract each other; their clusters are therefore more elongated. Furthermore, the lifetime of flagella clusters decays more quickly with cluster size than of rod clusters.

We develop theory for the dynamics and fluctuations in some cyclic and linear biochemical reactions. We use the approach of maximum caliber, which computes the ensemble of paths taken by the system, given a few experimental observables. This approach may be useful for interpreting single-molecule or few-particle experiments on molecular motors, enzyme reactions, ion-channels, and phosphorylation-driven biological clocks. We consider cycles where all biochemical states are observable. Our method shows how: (1) the noise in cycles increases with cycle size and decreases with the driving force that spins the cycle and (2) provides a recipe for estimating small-number features, such as probability of backward spin in small cycles, from experimental data. The back-spin probability diminishes exponentially with the deviation from equilibrium. We believe this method may also be useful for other few-particle nonequilibrium biochemical reaction systems.

Nanoparticles with multiple ligands have been proposed for use in nanomedicine. The multiple targeting ligands on each nanoparticle can bind to several locations on a cell surface facilitating both drug targeting and uptake. Experiments show that the distribution of conjugated ligands is unexpectedly broad, and the desorption rate appears to depend exponentially upon the mean number of attached ligands. These two findings are explained with a model in which ligands conjugate to the nanoparticle with a positive cooperativity of $\approx 4\text{kT}$, and that nanoparticles bound to a surface by multiple bonds are permanently affixed. This drives new analysis of the data, which confirms that there is only one time constant for desorption, that of a nanoparticle bound to the surface by a single bond.

The fidelity decay in a microwave billiard is considered, where the coupling to an attached antenna is varied. The resulting quantity, coupling fidelity, is experimentally studied for three different terminators of the varied antenna: a hard-wall reflection, an open wall reflection, and a $50\Omega$ load, corresponding to a totally open channel. The model description in terms of an effective Hamiltonian with a complex coupling constant is given. Quantitative agreement is found with the theory obtained from a modified VWZ approach [J. J. M. Verbaarschot et al., Phys. Rep. 129, 367 (1985)].

Influence of the interaction time delay on the noise-induced system size resonance in a system of all-to-all electrically coupled FitzHugh-Nagumo excitable neurons is studied. It is observed that small time lags decrease and that large time lags increase the coherence of spiking. Bifurcations of the system’s stationary state are used to explain the observed nonmonotonic dependence of coherence on the time lag.

Motivated by studies on current magnification in quantum mesoscopic systems, we consider sound and heat transmission in classical models of oscillator chains. A loop of coupled oscillators is connected to two leads through which one can either transmit monochromatic waves or white-noise signal from heat baths. We look for the possibility of current magnification in this system due to some asymmetry introduced between the two arms in the loop. We find that current magnification is indeed obtained for particular frequency ranges. However, the integrated current shows the effect only in the presence of a pinning potential for the atoms in the leads. We also study the effect of anharmonicity on current magnification.

A new formulation of the stochastic potential switching algorithm is presented. This reformulation naturally leads us to a generalized Fourtuin-Kasteleyn representation of the partition function $Z$. A formula for internal energy $E$ and that of heat capacity $C$ are derived from derivatives of the partition function. We also derive a formula for the exchange probability in the replica exchange Monte Carlo method. By combining the formulas with the Stochastic cutoff method, we can greatly reduce the computational time to perform internal energy and heat capacity measurements and the replica exchange Monte Carlo method in long-range interacting systems. Numerical simulations in three-dimensional magnetic dipolar systems show the validity of the method.

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluidlike behavior up to a density ${\rho }_c\left(L\right)$, which is the finite-size counterpart of the critical density ${\rho }_c={\rho }_c\left(L\to \infty \right)$. We determine this density from the crossover behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation, the persistence properties of the largest cluster, and the correlations in its motion are studied.

In the past decade low-temperature Glauber dynamics for the one-dimensional Ising system has been several times observed experimentally and occurred to be one of the most important theoretical approaches in a field of molecular nanomagnets. On the other hand, it has been shown recently that Glauber dynamics with the Metropolis flipping probability for the zero-temperature Ising ferromagnet under synchronous updating can lead surprisingly to the antiferromagnetic steady state. In this paper the generalized class of Glauber dynamics at zero temperature will be considered and the relaxation into the ground state, after a quench from high temperature, will be investigated. Using Monte Carlo simulations and a mean field approach, discontinuous phase transition between ferromagnetic and antiferromagnetic phases for a one-dimensional ferromagnet will be shown.

In this work we study the presence of both a minimum and clear oscillations in the frequency dependence of the translocation time of a polymer described as a unidimensional Rouse chain driven by a spatially localized oscillating linear potential. The observed oscillations of the mean translocation time arise from the synchronization between the very mean translocation time and the period of the external force. We have checked the robustness of the frequency value for the minimum translocation time by changing the damping parameter, finding a very simple relationship between this frequency and the correspondent translocation time. The translocation time as a function of the polymer length has been also evaluated, finding a precise $L^2$ scaling. Furthermore, the role played by the thermal fluctuations described as a Gaussian uncorrelated noise has been also investigated, and the analogies with the resonant activation phenomenon are commented.

The growth of linear cell colony fronts is investigated from the morphology of cell monolayer colonies, the cell size and shape distribution, the front displacement velocity, and the dynamic scaling analysis of front roughness fluctuations. At the early growth stages, colony patterns consist of rather ordered compact domains of small cells, whereas at advanced stages, an uneven distribution of cells sets in, and some large cells and cells exhibiting large filopodia are produced. Colony front profiles exhibit overhangs and behave as fractals with the dimension $D_F=1.25\pm 0.05$. The colony fronts shift at $0.22\pm 0.02\mu \text{m}{\text{min}}^{-1}$ average constant linear velocity and their roughness $\left(w\right)$ increases with time $\left(t\right)$. Dynamic scaling analysis of experimental and overhang-corrected growth profile data shows that $w$ versus system width $l$ log-log plots collapse to a single curve when $l$ exceeds a certain threshold value $l_o$, a width corresponding to the average diameter of few cells. Then, the influence of overhangs on the roughness dynamics becomes negligible, and a growth exponent $\beta =0.33\pm 0.02$ is derived. From the structure factor analysis of overhang-corrected profiles, a global roughness exponent ${\alpha }_s=0.50\pm 0.05$ is obtained. For $l>200\mu \text{m}$, this set of exponents fulfills the Family-Vicsek relationship. It is consistent with the predictions of the continuous Kardar-Parisi-Zhang model.

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by the Poisson random impulses, but their difference has not been fully quantified. Here, we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between the regular periodic and the random Poisson impulses. Their dynamics are characterized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.

We study experimentally the slowing of viscous vortex rings. In particular we do so using the concept of drag coefficient, which is a bulk coefficient which aims to capture the various mechanisms of slowing that can occur. At early times of flight the ring slows at a certain rate. After some time, instabilities (which we refer to as Kelvin waves) begin to form on the ring and there is a transient increase in the measured drag coefficient. After this brief transient the rings enter another regime with constant drag coefficient, which is larger than the early time one. In particular, our data illustrate that there appears to be a direct link between the number of waves that form on the ring and the relative increase in drag coefficient.

We numerically find three types of steady solutions of viscoelastic flows and flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Weissenberg (Wi) and Reynolds (Re) numbers using a spectral element method. The solutions are called “convective,” “transition,” and “elastic” in ascending order of Wi. In the convective region in the Wi-Re parameter space, convective effect and pressure gradient balance on average. As Wi increases, elastic effect becomes comparable, and the first transition sets in. Through the transition, a separation vortex disappears, and a jet flow induced close to the wall by the viscoelasticity moves into the bulk; the viscous drag significantly drops, and the elastic wall friction rises sharply. This transition is caused by an elastic force in the streamwise direction due to the competition of the convective and elastic effects. In the transition region, the convective and elastic effects balance. When the elastic effect becomes greater than the convective effect, the second transition occurs but it is relatively moderate. The second transition seems to be governed by the so-called Weissenberg effect. These transitions are not sensitive to driving forces. By a scaling analysis, it is shown that the stress component is proportional to the Reynolds number on the boundary of the first transition in the Wi-Re space. This scaling coincides well with the numerical result.

A spatially randomized fractal interpolation algorithm to construct synthetic fields with statistical properties close to real turbulence is proposed. It improves the previous works on fractal interpolation so that the position mapping between large and small scales is chosen randomly and the stretching factors are drawn from any chosen random multiplier model. In particular, using different parameters of Log-Poisson model, synthetic fields with absolute scaling properties close to SL94 model (for fully developed turbulence), K41 model and MB2000 model (for magnetohydrodynamic turbulence) are obtained, respectively. To model real turbulence fields which do not obey absolute scaling laws but ESS scaling laws, a refined technique is added. It is shown that both the velocity structure functions and the moments of subgrid-scale stress can be precisely predicted when the scale invariance is broken.

We have calculated viscosity and mutual diffusion of deuterium-tritium (DT) in the warm, dense matter regime for densities from 5 to $20\text{g}/{\text{cm}}^3$ and temperatures from 2 to 10 eV, using both finite-temperature Kohn-Sham density-functional theory molecular dynamics (QMD) and orbital-free molecular dynamics (OFMD). The OFMD simulations are in generally good agreement with the benchmark QMD results, and we conclude that the simpler OFMD method can be used with confidence in this regime. For low temperatures (3 eV and below), one-component plasma (OCP) model simulations for diffusion agree with the QMD and OFMD calculations, but deviate by 30% at 10 eV. In comparison with the QMD and OFMD results, the OCP viscosities are not as good as for diffusion, especially for $5\text{g}/{\text{cm}}^3$ where the temperature dependence is significantly different. The QMD and OFMD reduced diffusion and viscosity coefficients are found to depend largely, though not completely, only on the Coulomb coupling parameter $\Gamma$, with a minimum in the reduced viscosity at $\Gamma \approx 25$, approximately the same position found in the OCP simulations. The QMD and OFMD equations of state (pressure) are also compared with the hydrogen two-component plasma model.