Pseudopotential lattice Boltzmann (LB) models have been recognized as efficient numerical tools to simulate complex fluid systems, including those at thermodynamic equilibrium states and with phase transitions. However, when the equation of state (EOS) of real fluids is implemented, the existing pseudopotential LB models suffer from thermodynamic inconsistency. This study presents a multipseudopotential interparticle interaction (MPI) scheme, which is fully consistent with thermodynamics and applicable to engineering applications. In this framework, multiple pseudopotentials are employed to represent dominant interaction potentials at different extents of the mean free path of particles. By simulating van der Waals and Carnahan-Starling fluids, it is demonstrated that the MPI scheme can correctly simulate the physical nature of two-phase systems on the lattice including the continuum predictions of liquid-vapor coexistence states and the sound speeds in liquid and vapor phases. It is also shown that the lattice interactions of the MPI scheme represent underlying molecular interactions as they vary in a broad range from strong short-distance repulsions to weak long-distance attractions during phase transitions. Consequently, the MPI is proved to be a reliable LB scheme as it avoids generating unphysical potentials in implementing the EOSs of real fluids and limiting the spurious velocities at the interface of two-phase systems. Additionally, a straightforward procedure is suggested and discussed to preset the MPI system with the two-phase properties of a selected fluid.

By means of numerical simulations, we show that assemblies of frictionless rigid pentagons in slow shear flow possess an internal friction coefficient (equal to $0.183\pm 0.008$ with our choice of moderately polydisperse grains) but no macroscopic dilatancy. In other words, despite side-side contacts tending to hinder relative particle rotations, the solid fraction under quasistatic shear coincides with that of isotropic random close packings of pentagonal particles. Properties of polygonal grains are thus similar to those of disks in that respect. We argue that continuous reshuffling of the force-bearing network leads to frequent collapsing events at the microscale, thereby causing the macroscopic dilatancy to vanish. Despite such rearrangements, the shear flow favors an anisotropic structure that is at the origin of the ability of the system to sustain shear stress.

To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type $\text{RD}+X$ that mixes random deposition (RD) with a correlated-growth process $X$, we use a simplex decomposition of the height field. A distinction between growth processes $X$ that do and do not create voids in the bulk leads to the definition of the effective probability $p_{\mathrm{eff}}$ of the process $X$ that is a measurable property of the bulk morphology and depends on the activation probability $p$ of $X$ in the competitive process $\text{RD}+X$. The bulk morphology is reflected in the surface roughening via nonuniversal prefactors in the universal scaling of the surface width that scales in $p_{\mathrm{eff}}$. The equation and the resulting scaling are derived for $X$ in either a Kardar–Parisi–Zhang or Edwards–Wilkinson universality class in $(1+1)$ dimensions and are illustrated by an example of $X$ being a ballistic deposition. We obtain full data collapse on its corresponding universal scaling function for all $p\in (0;1]$. We outline the generalizations to $(1+n)$ dimensions and to many-component competitive growth processes.

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the effects of random initial conditions on the dynamical scaling behavior of an order parameter. In the FE Manna model, the density $\rho$ of total particles is conserved, and an absorbing phase transition occurs at ${\rho }_c$ as $\rho$ varies. In this work, we show that, for a given $\rho$, random initial distributions of particles lead to the domain structure in which domains with particle densities higher and lower than ${\rho }_c$ alternate with each other. In the domain structure, the dominant length scale is the average domain length, which increases via the coalescence of adjacent domains. At ${\rho }_c$, the domain structure slows down the decay of an order parameter and also causes anomalous finite-size effects, i.e., power-law decay followed by an exponential one before the quasisteady state. As a result, the interplay of particle conservation and random initial conditions causes the domain structure, which is the origin of the anomalous dynamical scaling behaviors for random initial conditions.

The formation of donut- and croissantlike buckles has been observed onto the free surface of gold thin films deposited on silicon substrates. Numerical simulations clearly evidence that the coupling effect between the atmospheric pressure acting on the free surface and the plastic folding of the ductile film is responsible for the circular blister destabilization and the formation of the donut- and croissantlike buckling patterns.

This study shows that the stability of solitary waves excited in a lipid monolayer near a phase transition requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the condition results in a threshold for excitation, saturation of the wave's amplitude, and the splitting of the wave at the phase boundaries. Splitting in particular confirms that a hydrated lipid interface can undergo condensation on adiabatic heating, thus showing retrograde behavior. Finally, using the theoretical insights and state dependence of conduction velocity in nerves, the curvature of the adiabatic state diagram is shown to be closely tied to the thermodynamic blockage of nerve pulse propagation.

Research collaboration occurs more frequently today than in the past. As a consequence, cooperation and competition are crucial determinants of academic success. In multiauthored publications, not all authors contribute evenly. Hence, some authors end up with less time or resources to work on parallel projects, decreasing their number of publications. Although detailed information on the contribution of each author in multiauthored publications is generally not available, the order of authors often discloses information on differential contributions. Here we analyze the full data set of Physical Review journals to show that, along with the increasingly number of multiauthored publications, first authors incur costs and last authors are bestowed benefits in terms of number of publications. In other words, authors publishing more often as first authors have fewer publications in the short-term than authors publishing more often as last authors. Using a simplified network representation where direct links represent the costly action of first authors towards last authors, we analyze the evolution of cooperation in multiauthored publications.

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called controllers. However, the real systems represented by networks contain unreliable components and modern robust control engineering has not addressed the problem of structural changes on complex networks including scale-free topologies. Here, we introduce the concept of structurally robust control of complex networks and provide a concrete example using an algorithmic framework that is widely applied in engineering. The developed analytical tools, computer simulations, and real network analyses lead herein to the discovery that robust control can be achieved in scale-free networks with exactly the same order of controllers required in a standard nonrobust configuration by adjusting only the minimum degree. The presented methodology also addresses the probabilistic failure of links in real systems, such as neural synaptic unreliability in Caenorhabditis elegans, and suggests a new direction to pursue in studies of complex networks in which control theory has a role.

The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent (exponential dynamical instability) is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov exponent, as a unified characterization of nonexponential and exponential dynamical instabilities in one-dimensional maps. Chaos is classified into three different types, i.e., superexponential, exponential, and subexponential chaos. Using one-dimensional maps, we demonstrate superexponential and subexponential chaos and quantify the dynamical instabilities by the Lyapunov pair. In subexponential chaos, we show superweak chaos, which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth. The scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process, which is related to infinite ergodic theory.

We establish sufficient criteria for the existence of a limit cycle in the Liénard system $\dot{x}=y-\varepsilon F\left(x\right),\dot{y}=-x$, where $F\left(x\right)$ is odd. In their simplest form the criteria lead to the result that, for all finite nonzero $\varepsilon$, the amplitude of the limit cycle is less than $\rho$ and $0\le a\le \rho \le u$, where $F\left(a\right)=0$ and ${\int }_0^{u}F\left(x\right)dx=0$. We take the van der Pol oscillator as a specific example and establish that for all finite, nonzero $\varepsilon$, the amplitude of its limit cycle is less than $2.0672$, a value whose precision is limited by the capacity of our symbolic computation software package. We show how the criterion for the upper bound can be extended to establish a bound on the amplitude of a limit cycle in systems where $F\left(x\right)$ contains both odd and even components. We also show how the criteria can be used to establish bounds for bifurcation sets.

We present an experimental study investigating the transition zone between a liquid-like unyielded region and a solid-like yielded region in a yield-stress fluid. The configuration consists of a rectangular closed-channel flow disturbed by the presence of a step. Upstream of the step, a solid-liquid interface between a dead zone and a flow zone appears. In this study, we use a model fluid, namely polymer micro-gel Carbopol, which exhibits Herschel-Bulkley viscoplastic rheology. Exploiting the fluid transparency, the flow is monitored by particle image velocimetry using an internal visualization technique. The main outcome of this study is to show that, except in a thin transition layer close to the solid-liquid interface, the flow behaves as an apparent Poiseuille flow with an apparent slip condition at the base. The slip frontier is found to be almost independent of the flow rate while the corresponding slip velocity increases with the flow rate.

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For $h\le -1$ or $h>h_c$, where $h$ is the D'yakov parameter and $h_c$ is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow—at first quadratically and later linearly—with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.

In this paper we solve the inviscid inertial wave solutions in a circular pipe or annulus rotating constantly about its axis with moderate angular speed. The solutions are constructed by the so-called helical wave functions. We reveal that the mean velocity profiles must satisfy certain conditions to accommodate the inertial waves at the bulk region away from boundary. These conditions require the axial and azimuthal components of the mean velocity to take the shapes of the zeroth and first order Bessel functions of the first kind, respectively. The theory is then verified by data obtained from direct numerical simulations for both rotating pipe and circular annulus, and excellent agreement is found between theory and numerical results. Large scale vortex clusters are found in the bulk region where the mean velocity profiles match the theoretical predictions. The success of the theory in rotating pipe, circular annulus, and streamwise rotating channel suggests that such inertial waves are quite common in wall bounded flow with background rotation.

Experiments involving radial foils on a $1 \mathrm{M}\mathrm{A}$, $100 \mathrm{n}\mathrm{s}$ current driver can be used to study the ablation of thin foils and liners, produce extreme conditions relevant to laboratory astrophysics, and aid in computational code validation. This research focuses on the initial ablation phase of a $20 \mu \mathrm{m}$ Al foil (8111 alloy), in a radial configuration, driven by Cornell University's COBRA pulsed power generator. In these experiments ablated surface plasma (ASP) on the top side of the foil and a strongly collimated axial plasma jet are observed developing midway through the current rise. With experimental and computational results this work gives a detailed description of the role of the ASP in the formation of the plasma jet with and without an applied axial magnetic field. This $\sim 1$ $\mathrm{T}$ field is applied by a Helmholtz-coil pair driven by a slow, $150 \mu \mathrm{s}$ current pulse and penetrates the load hardware before arrival of the COBRA pulse. Several effects of the applied magnetic field are observed: (1) without the field extreme-ultraviolet emission from the ASP shows considerable azimuthal asymmetry while with the field the ASP develops azimuthal motion that reduces this asymmetry, (2) this azimuthal motion slows the development of the jet when the field is applied, and (3) with the magnetic field the jet becomes less collimated and has a density minimum (hollowing) on the axis. PERSEUS, an XMHD code, has qualitatively and quantitatively reproduced all these experimental observations. The differences between this XMHD and an MHD code without a Hall current and inertial effects are discussed. In addition the PERSEUS results describe effects we were not able to resolve experimentally and suggest a line of future experiments with better diagnostics.

Devising a statistical mechanics framework for jammed granular materials is a challenging task as those systems do not share some important properties required to characterize them with statistical thermodynamics tools. In a recent paper [Asenjo et al. Phys. Rev. Lett. 112, 098002 (2014)], a new definition of a granular entropy, which puts the protocol used to generate the packings at its roots, has been proposed. Following up these results, it is shown that the protocol used in Asenjo et al. can be recast as a canonical ensemble with a particular value of the temperature. Signature of gaussianity for large system sizes strongly suggests an asymptotic equivalence with a corresponding microcanonical ensemble where jammed states with certain basin volumes are sampled uniformly. We argue that this microcanonical ensemble is not Edwards's microcanonical ensemble and generalize this argument to other protocols.

A model for the probabilistic function followed in editing Wikipedia is presented and compared with simulations and real data. It is argued that the probability of editing is proportional to the editor's number of previous edits (preferential attachment), to the editor's fitness, and to an aging factor. Using these simple ingredients, it is possible to reproduce the results obtained for Wikipedia editing dynamics for a collection of single pages as well as the averaged results. Using a stochastic process framework, a recursive equation was obtained for the average of the number of edits per editor that seems to describe the editing behavior in Wikipedia.

The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.

We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady state, even in the limit of infinite coupling. An analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration and structural heterogeneity, both of which amplify erosion. The latter, however, can differ significantly from degree heterogeneity. Finally, we show that erosion is marked by the reorganization of oscillators according to their node degrees rather than their natural frequencies.

To bridge the gap between single and isolated pore systems to multipore systems, such as membranes and electrodes, we studied an array of nanochannels with varying interchannel spacing that controlled the degree of channel communication. Instead of treating them as individual channels connected in parallel or an assembly like a homogeneous membrane, this study resolves the pore-pore interaction. We found that increased channel isolation leads to current intensification, whereas at high voltages electroconvective effects control the degree of communication via suppression of the diffusion layer growth.