We report a molecular-dynamics study of flow of Lennard-Jones fluid through a nanochannel where size effects predominate. The momentum and energy accommodation coefficients, which determine the amount of slip and temperature jumps, are calculated for a three-dimensional Poiseuille flow through a nano-sized channel. Accommodation coefficients are calculated by considering a “ gravity”- (acceleration field) driven Poiseuille flow between two infinite parallel walls that are maintained at a fixed temperature. The Knudsen number (Kn) dependency of the accommodation coefficients, slip length, and velocity profiles is investigated. The system is also studied by varying the strength of gravity. The accommodation coefficients are found to approach a limiting value with an increase in gravity and Kn. For low values of Kn (<0.15), the slip length obtained from the velocity profiles is found to match closely the results obtained from the linear slip model. Using the calculated values of accommodation coefficients, the first- and second-order slip models are validated in the early transition regime. The study demonstrates the applicability of the Navier-Stokes equation with the second-order slip model in the early transition regime.

An intriguing phenomenon displayed by granular flows and predicted by kinetic-theory-based models is the instability known as particle “clustering,” which refers to the tendency of dissipative grains to form transient, loose regions of relatively high concentration. In this work, we assess a modified-Sonine approximation recently proposed [Garzó, Santos, and Montanero, Physica A 376, 94 (2007)] for a granular gas via an examination of system stability. In particular, we determine the critical length scale associated with the onset of two types of instabilities—vortices and clusters—via stability analyses of the Navier-Stokes-order hydrodynamic equations by using the expressions of the transport coefficients obtained from both the standard and the modified-Sonine approximations. We examine the impact of both Sonine approximations over a range of solids fraction $\phi <0.2$ for small restitution coefficients $e$ $=$ 0.25–0.4, where the standard and modified theories exhibit discrepancies. The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations, of which a small percentage were not considered due to inelastic collapse. Results show excellent quantitative agreement between MD and the modified-Sonine theory, while the standard theory loses accuracy for this highly dissipative parameter space. The modified theory also remedies a high-dissipation qualitative mismatch between the standard theory and MD for the instability that forms more readily. Furthermore, the evolution of cluster size is briefly examined via MD, indicating that domain-size clusters may remain stable or halve in size, depending on system parameters.

Reorientation of the segregation pattern of a binary granular mixture on a two-dimensional horizontally oscillating tray is numerically realized. The mixture consists of large and heavy particles and small and light particles, and the segregation pattern shows a transition between a striped pattern perpendicular to the oscillation and one parallel to the oscillating direction according to the change of area fractions of the two types of particle. The transition mechanism is discussed on the basis of a simplified one-dimensional dynamics.

We investigate the nonlinear rheology of dilute, depletion-induced colloidal gels and report that these systems yield via a two-step process. We propose the two yield points to be associated with interparticle bond rotation and bond breakage, respectively. These distinct yielding mechanisms lead to remarkable creep profiles at intermediate values of the applied stress, highlighted by an anisotropic shear-induced strengthening and flow arrest at very large accumulated strains ($\gamma \sim$ 80). The possible microstructural origins of this behavior are discussed.

We present an extended Cahn-Hilliard model for simulating interfacial anisotropy in thin-film dynamics by incorporating high-order terms in the energy from an expansion of the energy about an equilibrium state, following earlier work by Abinandanan and Haider [Philos. Mag. Sect. A 81, 2457 (2001)]. For example, to simulate SiGe/Si thin films, where diamond cubic symmetry is needed, fourth order derivatives are included in the energy. This results in a sixth order evolution equation for the order parameter. For less symmetric crystals, one needs to add terms of higher order than fourth order. One advantage of this approach is its intrinsic regularized behavior. In particular, even for strongly anisotropic surface energy, sharp corners will not form and the extended anisotropic Cahn-Hilliard equations are well-posed. For this system we develop an energy-stable numerical scheme in which the energy decreases for any time step. We present two-dimensional (2D) and three-dimensional (3D) numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the computed equilibrium shapes using the new model and results from an analysis associated with a Wulff construction for energy minimization. The model predictions also compare well with experimental results for silicon voids. In the context of thin films, we observe the formation of interconnected ridges, wires, and fortresses similar to those observed in SiGe/Si thin films.

We report experiments on the rapid contact-line motion present in the early stages of capillary-driven spreading of drops on dry solid substrates. The spreading data fail to follow a conventional viscous or inertial scaling. By integrating experiments and simulations, we quantify a contact-line friction ${\mu }_f$ which is seen to limit the speed of the rapid dynamic wetting. A scaling based on this contact-line friction is shown to yield a universal curve for the evolution of the contact-line radius as a function of time, for a range of fluid viscosities, drop sizes, and surface wettabilities.

Biological systems contain biochemical control networks that reside within a remarkable spatial structure. We present a theoretical study of a biological system in which two chemically coupled species, an activating species and an inhibiting species forming a negative feedback, are synthesized at unique sites and interact with each other through diffusion. The dynamical behaviors in these systems depend on the spatial locations of these synthetic sites. In a negative feedback system with two sites, we find two dynamical modes: fixed point and stable oscillations whose frequency can be tuned by varying the distance between the sites. When there are multiple synthetic sites, we find more diverse dynamics, including chaos, quasiperiodicity, and bistability. Based on this theoretical analysis, it should be possible to create in the laboratory synthetic circuits displaying these dynamics. This study illustrates the concept of “spatial switching,” in which bifurcations in the dynamics occur as a function of the geometry of the system.

We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system. We develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death. An important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix. Our results are fully supported by the detailed numerical analysis for different network topologies.

We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment $H_E$, consisting of $N$ noninteracting chaotic systems. The parameters are set so that when either particle is separately placed in contact with the environment, a dissipative behavior is observed. When both particles are simultaneously in contact with $H_E$ an indirect coupling between them is observed only if the particles are in near-resonance. We study the equilibrium properties of the system considering ensemble averages for the case $N=1$ and single trajectory dynamics for $N$ large. In both cases, the particles and the environment reach an equilibrium configuration at long times, but only for large $N$ can a temperature be assigned to the system.

Electro-oxidation of ethanol represents a key process in fuel-cell technology. We introduce a generalization of the random sequential adsorption model to study the long time scale and large length scale properties of the electro-oxidation process. We provide an analytical solution for one dimension and Monte Carlo results in two dimensions. We characterize the coverage and percolation properties of the jammed state and unveil the influence of quenched impurities in the selectivity of oxidation products.

The Yukawa model in the quenched approximation is expressed as a disordered statistical mechanics model on a four-dimensional Euclidean lattice. We study this model, giving particular attention to the singularities of the Dirac operator in the phase diagram. A careful analysis of a particular limiting case shows that finite volume effects can be huge and questions the quenched approximation. This is confirmed by numerical simulation performed in this limiting case and without the quenched approximation.

We have experimentally investigated the interactions between floating magnetic spheres which are submitted to a vertical magnetic field, ensuring a tunable repulsion, while capillary forces induce attraction. We emphasize the complex arrangements of floating bodies. The equilibrium distance between particles exhibits hysteresis when the applied magnetic field is modified. Irreversible processes are evidenced. Symmetry breaking is also found for three identical floating bodies when the strength of the magnetic repulsion is tuned. We propose a Dejarguin-Landau-Verwey-Overbeek (DLVO)–like potential, i.e., an interaction potential with a primary and a secondary minimum, capturing the main physical features of the magnetocapillary interaction, which is relevant for self-assembly.

We study the kinetics of phase separation of a binary (A,B) mixture confined in a thin film of thickness $D$ by numerical simulations of the corresponding Cahn-Hilliard-Cook (CHC) model. The initial state consisted of 50$\%$ A:50$\%$ B with a concentration gradient across the film, i.e., the average order parameter profile is ${\Psi }_{\mathrm{av}}(z,t=0)=(2z/D-1){\Psi }_g,0⩽z⩽D$, for various choices of ${\Psi }_g$ and $D$. The equilibrium state (for time $t\to \infty$) consists of coexisting A-rich and B-rich domains separated by interfaces oriented perpendicular to the surfaces. However, for sufficiently large ${\Psi }_g$, a (metastable) layered state is formed with a single interface parallel to the surfaces. This phenomenon is explained in terms of a competition between domain growth in the bulk and surface-directed spinodal decomposition (SDSD) that is caused by the gradient. Thus, gradients in the initial state can stabilize thin-film morphologies which are not stable in full equilibrium. This offers interesting possibilities as a method for preparing novel materials.

We study the structural and dynamical mechanisms of reinforcement of a polymer nanocomposite (PNC) via coarse-grained molecular dynamics simulations. In a regime of strong polymer-filler interactions, the stress at failure of the PNC is clearly correlated to structural quantities, such as the filler loading, the surface area of the polymer-filler interface, and the network structure. Additionally, we find that small fillers, of the size of the polymer monomers, are the most effective at reinforcing the matrix by surrounding the polymer chains and maximizing the number of strong polymer-filler interactions. Such a structural configuration is correlated to a dynamical feature, namely, the minimization of the relative mobility of the fillers with respect to the polymer matrix.

We study the internal nonlinear dynamics of an inhomogeneous short lattice DNA model by solving numerically the governing discrete perturbed sine-Gordon equations under the limits of a uniform and a nonuniform angular rotation of bases. The internal dynamics is expressed in terms of open-state configurations represented by kink and antikink solitons with fluctuations. The inhomogeneity in the strands and hydrogen bonds as well as nonuniformity in the rotation of bases introduce fluctuations in the profile of the solitons without affecting their robust nature and the propagation. These fluctuations spread into the tail regions of the soliton in the case of periodic inhomogeneity. However, the localized form of inhomogeneity generates amplified fluctuations in the profile of the soliton. The fluctuations are expected to enhance the denaturation process in the DNA molecule.

We consider voter dynamics on a directed adaptive network with fixed out-degree distribution. A transition between an active phase and a fragmented phase is observed. This transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out-degree distribution. However, if a significant number of nodes with low out degree is present, then fragmentation can occur even far below the estimated critical point due to the formation of self-stabilizing structures that nucleate fragmentation. This process may be relevant for fragmentation in current political opinion formation processes.

The advent of the Internet and World Wide Web has led to unprecedent growth of the information available. People usually face the information overload by following a limited number of sources which best fit their interests. It has thus become important to address issues like who gets followed and how to allow people to discover new and better information sources. In this paper we conduct an empirical analysis of different online social networking sites and draw inspiration from its results to present different source selection strategies in an adaptive model for social recommendation. We show that local search rules which enhance the typical topological features of real social communities give rise to network configurations that are globally optimal. These rules create networks which are effective in information diffusion and resemble structures resulting from real social systems.

We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding particles, thereby questioning their interpretation as a quantifier for complexity or correlations. We then propose a refined definition of these measures, investigate its properties, and discuss its numerical evaluation. As an example, we study coupled logistic maps and study the behavior of the different measures for that case. Finally, we investigate other local effects during the coarse graining of the complex system.

We have extended the classical hydrodynamics formalism to include nonlocal quantum behavior via the phenomenological Bohm potential. We have then solved the quantum hydrodynamics equations to derive an expression for the dynamical structure factor, which describes the density-density correlations in the system. This formalism can be applied to high density strongly coupled electron fluids in the long wavelength domain. We show that at densities above $7\times {10}^{25}$ cm${}^{-3}$ there are significant differences in the dispersion relation. Future experiments at large laser facilities could provide an experimental test of the theory.

It is shown numerically that kink-shaped and bell-shaped localized moving defects may coexist in a biatomic crystalline lattice. The shape and velocity of these waves are defined from a corresponding single wave exact traveling wave solution to the governing coupled nonlinear equations. The features of the initial conditions, or an external loading, are found that provide simultaneous propagation of these nonlinear moving defects, inputs, and their amplitudes.