Applying the histogram reweighting method, we investigate the critical behavior of the $XY$ model on growing scale-free networks with various degree exponents $\lambda$. For $\lambda ⩽3$, the critical temperature diverges as it does for the Ising model on scale-free networks. For $\lambda =8$, on the other hand, we observe a second-order phase transition at finite temperature. We obtain the critical temperature $T_c=3.08\left(2\right)$ and the critical exponents $\tilde{\nu }=2.62\left(3\right)$, $\gamma ∕\tilde{\nu }=0.127\left(4\right)$, and $\beta ∕\tilde{\nu }=0.442\left(2\right)$ from a finite-size scaling analysis.

One-dimensional directed driven stochastic flow with competing nonlocal and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion process. The nonlocal skids promote strong clustering in the stationary populated phase. Such clusters drive the dynamic phase transition and determine its scaling properties. We numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current and first order in the regime where the bulk is in control. The first-order transition originates from a turnabout of the cluster drift velocity. At the critical line, the current remains analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise. A self-consistent cluster dynamics analysis explains why these scaling properties remain that simple.

The effect of cementation processes on the acoustical properties of sands is studied via molecular dynamics simulation methods. We propose numerical methods where the initial uncemented sand is built by simulating the settling process of sediments. Uncemented samples of different porosity are considered by emulating natural mechanical compaction of sediments due to overburden. Cementation is considered through a particle-based model that captures the underlying physics behind the process. In our simulations, we consider samples with different degrees of compaction and cementing materials with distinct elastic properties. The microstructure of cemented sands is taken into account while adding cement at specific locations within the pores, such as grain-to-grain contacts. Results show that the acoustical properties of cemented sands are strongly dependent on the amount of cement, its stiffness relative to the hosting medium, and its location within the pores. Simulation results are in good correspondence with available experimental data and compare favorably with some theoretical predictions for the sound velocity within a range of cement saturation, porosity, and confining pressure.

We develop a methodology for the calculation of surface free energies based on the probability distribution of a wandering interface. Using a simple extension of the $NpT$ sampling, we allow the interface area to randomly probe the available space and evaluate the surface free energy from histogram analysis and the corresponding average. The method is suitable for studying systems with either continuous or discontinuous potentials, as it does not require explicit evaluation of the virial. The proposed algorithm is compared with known results for the surface tension of Lennard-Jones and square well fluids, as well as for the interface tension of a bead-spring polymer model, and good agreement is found. We also calculate the interfacial tensions of freely jointed tangent hard sphere chains on athermal walls for a wide range of chain lengths and densities. The results are compared with three different theoretical approaches: scaled particle theory (SPT), Yu-Wu density functional theory, and an analytical approximation based on the latter approach. Whereas SPT only yields qualitative results, the last two approaches are found to yield very good agreement with simulations.

Molecular-dynamics and Monte Carlo simulations have been used to compute the crystal-melt interface stress $\left(f\right)$ in a model Lennard-Jones (LJ) binary alloy system, as well as for elemental Si and Ni modeled by many-body Stillinger-Weber and embedded-atom-method (EAM) potentials, respectively. For the LJ alloys the interface stress in the (100) orientation was found to be negative and the $f$ vs composition behavior exhibits a slight negative deviation from linearity. For Stillinger-Weber Si, a positive interface stress was found for both (100) and (111) interfaces: $f_{100}=(380\pm 30)\mathrm{mJ}∕{\mathrm{m}}^2$ and $f_{111}=(300\pm 10)\mathrm{mJ}∕{\mathrm{m}}^2$. The Si (100) and (111) interface stresses are roughly 80 and 65% of the value of the interfacial free energy $\left(\gamma \right)$, respectively. In EAM Ni we obtained $f_{100}=(22\pm 74)\mathrm{mJ}∕{\mathrm{m}}^2$, which is an order of magnitude lower than $\gamma$. A qualitative explanation for the trends in $f$ is discussed.

The glass transition temperature and relaxation dynamics of the segmental motions of thin films of polystyrene labeled with a dye, 4-[$N$-ethyl-$N$-(hydroxyethyl)]amino-4-nitroazobenzene (Disperse Red 1, DR1) are investigated using dielectric measurements. The dielectric relaxation strength of the DR1-labeled polystyrene is approximately 65 times larger than that of the unlabeled polystyrene above the glass transition, while there is almost no difference between them below the glass transition. The glass transition temperature of the DR1-labeled polystyrene can be determined as a crossover temperature at which the temperature coefficient of the electric capacitance changes from the value of the glassy state to that of the liquid state. The glass transition temperature of the DR1-labeled polystyrene decreases with decreasing film thickness in a reasonably similar manner to that of the unlabeled polystyrene thin films. The dielectric relaxation spectrum of the DR1-labeled polystyrene is also investigated. As the thickness decreases, the $\alpha$-relaxation time becomes smaller, and the distribution of the $\alpha$-relaxation times becomes broader. These results show that thin films of DR1-labeled polystyrene are a suitable system for investigating confinement effects of the glass transition dynamics using dielectric relaxation spectroscopy.

We address the relation between long-range correlations and coherent charge transfer in substitutional DNA sequences using the transfer matrix approach. The substitutional sequences exhibit long-range correlations and show good transmittivity in comparison with uncorrelated random ones. It is found that the charge transfer efficiency varies for different substitutional sequences and many will present electronic delocalization in the system. Further, the resistivity for substitutional sequences may range from decreasing with the length, length independence, or increasing with the length. The conduction mechanisms of various behaviors observed for these sequences are analyzed.

We study a nonlinear quenching of turbulent magnetic diffusion and effective drift velocity of large-scale magnetic field in a developed two-dimensional MHD turbulence at large magnetic Reynolds numbers. We show that transport of the mean-square magnetic potential strongly changes quenching of turbulent magnetic diffusion. In particularly, the catastrophic quenching of turbulent magnetic diffusion does not occur for the large-scale magnetic fields $B\gg B_{\mathrm{eq}}∕\sqrt{\mathrm{Rm}}$ when a divergence of the flux of the mean-square magnetic potential is not zero, where $B_{\mathrm{eq}}$ is the equipartition mean magnetic field determined by the turbulent kinetic energy and $\mathrm{Rm}$ is the magnetic Reynolds number. In this case the quenching of turbulent magnetic diffusion is independent of magnetic Reynolds number. The situation is similar to three-dimensional MHD turbulence at large magnetic Reynolds numbers whereby the catastrophic quenching of the $\alpha$ effect does not occur when a divergence of the flux of the small-scale magnetic helicity is not zero.

Elementary processes in free-decaying two-dimensional (2D) turbulence are examined by extensive analyses of fine structures in the density distribution of a magnetized pure electron plasma that is linearly unstable with the initial ring-shaped profile, deforms nonlinearly into patches of vortices, and relaxes into a single-peaked stable distribution via successive mergers among the patches. The stochastic dynamics of the decreasing number of vortices in the real space correspond to the time evolution of energy spectra $E\left(k\right)$ in the wave number $\left(k\right)$ space that the energy transfers down to lower $k$ while the upward-spreading tails of the spectra fit to the power-law $(\propto k^{-\alpha })$ with $\alpha >3$. The transfer rates, $\epsilon \left(k\right)$ and $\eta \left(k\right)$ in energy and enstrophy spaces, evaluated from the time-resolved $k$-spectra demonstrate characteristic features of the 2D turbulence, i.e., $\epsilon \left(k\right)$ is negative and deepest below the $k_{\mathrm{i}\mathrm{n}\mathrm{j}}$ corresponding to the size of the first-generated patches, and $\eta \left(k\right)$ increases from zero to a constant value at $k>k_{\mathrm{inj}}$. By averaging the time-dependent spectra of $E\left(k\right)$, $\epsilon \left(k\right)$, and $\eta \left(k\right)$, constructions are carried out for the spectra in a stationary turbulence that is sustained by the continuous generation of vortices due to the instability and dissipation at high $k$. The spectra are qualitatively consistent with the 2D turbulence theory with discrepancies including that $\alpha \approx 4.4$ and that the enstrophy transfer rate is almost zero around $k=k_{\mathrm{inj}}$ reflecting the contribution from the coherent vortices.

We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov chain strategy. Special attention is devoted to Hamiltonian cycles of (nonregular) random graphs of minimal connectivity equal to 3.

Efficiency of a Brownian particle moving along the axis of a three-dimensional asymmetric periodic channel is investigated in the presence of a symmetric unbiased force and a load. Reduction of the spatial dimensionality from two or three physical dimensions to an effective one-dimensional system entails the appearance of entropic barriers and an effective diffusion coefficient. The energetics in the presence of entropic barriers exhibits peculiar behavior which is different from that occurring through energy barriers. We found that even on the quasistatic limit there is a regime where the efficiency can be a peaked function of temperature, which indicates that thermal noise can facilitate energy transformation, contrary to the case of energy barriers. The appearance of entropic barriers may induce optimized efficiency at a finite temperature.

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately $0.02\mathrm{nl}$. Upon varying the gas pressure, a critical value is found where the size distribution becomes a pure power law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher’s model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent $\tau$ has a steep minimum, at criticality, as previously reported in nuclear multifragmentation studies. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is $\nu =1∕2$. The sizes of the largest and average fragments, on the other hand, do not go to zero abruptly but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian.

We present a detailed treatment of the nonequilibrium Green’s function method for thermal transport due to atomic vibrations in nanostructures. Some of the key equations, such as self-energy and conductance with nonlinear effect, are derived. A self-consistent mean-field theory is proposed. Computational procedures are discussed. The method is applied to a number of systems including one-dimensional chains, a benzene ring junction, and carbon nanotubes. Mean-field calculations of the Fermi-Pasta-Ulam model are compared with classical molecular dynamics simulations using a generalized Langevin heat bath. We find that nonlinearity suppresses thermal transport even at moderately high temperatures.

Experimental magnetization curves for a polydisperse ferrofluid at various concentrations are examined using analytical theories and computer simulations with the aim of establishing a robust method for obtaining the magnetic-core diameter distribution function $p\left(x\right)$. Theoretical expressions are fitted to the experimental data to yield the parameters of $p\left(x\right)$. It is shown that the majority of available theories yield results that depend strongly on the ferrofluid concentration, even though the magnetic composition should be fixed. The sole exception is the second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] which yields consistent results over the full experimental range of ferrofluid concentration. To check for consistency, extensive molecular dynamics and Monte Carlo simulations are performed on systems with discretized versions of $p\left(x\right)$ corresponding as closely as possible to that of the real ferrofluid. Essentially perfect agreement between experiment, theory, and computer simulation is demonstrated. In addition, the MMF2 theory provides excellent predictions for the initial susceptibility measured in simulations.

We study the effects of extreme confinement on the self assembly of the colloids found in magnetorheological (MR) fluids using Brownian dynamics simulations. The MR fluid is confined in a thin slit with a uniform external magnetic field directed normal to the slit. We find a crossover in the behavior of the system from two dimensions to three dimensions as the slit thickness is increased. A simple model is presented to describe this crossover as a function of the slit thickness and volume fraction of the MR fluid. The model is able to predict the salient features of the structure formation that has been observed in these systems. Furthermore, the model predicts the approximate time scales for structure formation under a variety of conditions. We present a quantitative analysis of the effect of volume fraction on the behavior of the system. Additionally, we show quantitatively how energy barriers to structure formation play a crucial role in determining the steady state structure of these systems. Our analysis explains the discrepancies between previous experimental and theoretical work on the self-assembly of MR fluids confined in thin slits.

A model is proposed for sputter roughening of inhomogeneous systems with slowly sputtered impurity particles randomly distributed in the bulk. Surface inhomogeneity, which develops as a result of coupling between the time evolution of the local surface impurity concentration and the local surface shape, is tuned by changing the dependence of the sputtering probability upon impurity concentration. In $1+1$dimensions, we find long-time scaling exponents that are consistent with Kardar—Parisi—Zhang (KPZ) values. However, for a range of surface inhomogeneity, impurity pinning results in a persistent growth regime where the surface roughens rapidly. We correlate this rapid roughening to fluctuations of the impurity concentration at the surface. Roughening in this regime leads to the formation of cones whose shape is determined by material property and sputtering flux, suggesting a unique method of nanostructure fabrication. In $2+1$ dimensions, a similar variation of the roughening behavior with surface inhomogeneity is observed. For small surface inhomogeneity, there is an initial exponential roughening followed by power-law roughening with an effective growth exponent much smaller than KPZ. For larger surface inhomogeneity two power-law roughening regimes are observed, with an initial rapid roughening that crosses over to slower roughening; the effective exponent in each of these regimes increases with surface inhomogeneity. The surface morphology observed in the simulations is considerably noisier than experimental data for InP and GaSb. Our model shows noisy nonlinear pattern formation in contrast to the marked long-range hexagonal ordering seen in experiments. However, the scaling behavior is robust enough that roughening kinetics similar to that observed experimentally can be obtained depending upon the values of inhomogeneity and the strength of the nonlinear term in the model.

We study roughness scaling of the outer surface and the internal porous structure of deposits generated with the three-dimensional bidisperse ballistic deposition (BBD), in which particles of two sizes are randomly deposited. Systematic extrapolation of roughness and dynamical exponents and the comparison of roughness distributions indicate that the top surface has Kardar-Parisi-Zhang (KPZ) scaling for any ratio $F$ of the flux between large and small particles. A scaling theory predicts the characteristic time of the crossover from random to correlated growth in BBD and provides relations between the amplitudes of roughness scaling and $F$ in the KPZ regime. The porosity of the deposits monotonically increases with $F$ and scales as $F^{1∕2}$ for small $F$, which is also explained by the scaling approach and illustrates the possibility of connecting surface growth rules and bulk properties. The suppression of relaxation mechanisms in BBD enhances the connectivity of the deposits when compared to other ballisticlike models, so that they percolate down to $F\approx 0.05$. The fractal dimension of the internal surface of the percolating deposits is $D_F\approx 2.9$, which is very close to the values in other ballistic-like models and suggests universality among these systems.

The behavior of a nematic liquid crystal at a surfactant-laden interface to an aqueous phase is studied under the condition of homeotropic anchoring. It is shown that with decreasing surfactant concentration the system shifts from surface-enhanced to surface-decreased order, i.e., the behavior changes from complete nematic wetting when the nematic–isotropic phase transition is approached from above to a different wetting behavior below the transition, characterized by a considerably decreased Maier-Saupe order parameter at the interface. The experimental behavior is analyzed within the framework of the Landau–de Gennes theory supplemented by a surface free energy, in which the wetting behavior is controlled by the magnitude of the anchoring strength and the preferred surface order parameter in comparison to the bulk order parameter. The theoretical modeling is able to account for all experimental observations.

Stochastic dynamics of a tethered membrane with a bond-fluctuating coarse-grained Monte Carlo simulation shows, in addition to diffusion, nondiffusive behavior sensitive to the type of membrane, its size, and quality of the solvent. Motion of the membrane’s center node is described by the variation of the mean-square displacement $\left(R_n^2\right)$ with time step $\left(t\right)$, i.e., $R_n^2\propto t^{2\nu }$ with the exponent $\nu \simeq 1∕8-1∕6$ in the short time followed by subdiffusive power laws (i.e., $\nu \sim 1∕5,1∕10$) in the intermediate time regimes before reaching diffusion $\nu =1$. The crossover between in-plane wrinkle modes is identified from the segmental (node) motion of the membrane.