Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.

The distribution of human linguistic groups presents a number of interesting and nontrivial patterns. The distributions of the number of speakers per language and the area each group covers follow log-normal distributions, while population and area fulfill an allometric relationship. The topology of networks of spatial contacts between different linguistic groups has been recently characterized, showing atypical properties of the degree distribution and clustering, among others. Human demography, spatial conflicts, and the construction of networks of contacts between linguistic groups are mutually dependent processes. Here we introduce an adaptive network model that takes all of them into account and successfully reproduces, using only four model parameters, not only those features of linguistic groups already described in the literature, but also correlations between demographic and topological properties uncovered in this work. Besides their relevance when modeling and understanding processes related to human biogeography, our adaptive network model admits a number of generalizations that broaden its scope and make it suitable to represent interactions between agents based on population dynamics and competition for space.

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time $\left(\mathcal{PT}\right)$ symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the $\mathcal{PT}$-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and $\mathcal{PT}$-symmetric cases. Interactions and collisions between the conservative and $\mathcal{PT}$-symmetric solitons are briefly investigated, as well.

Squire's theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.

Quantifying the behavior of circulating tumor cells (CTCs) in the blood stream is of fundamental importance for understanding metastasis. Here, we investigate the flow mode and velocity of CTCs interacting with red blood cells (RBCs) in various sized microvessels. The flow of leukocytes in microvessels has been described previously; a leukocyte forms a train with RBCs in small microvessels and exhibits margination in large microvessels. Important differences in the physical properties of leukocytes and CTCs result from size. The dimensions of leukocytes are similar to those of RBCs, but CTCs are significantly larger. We investigate numerically the size effects on the flow mode and the cell velocity, and we identify similarities and differences between leukocytes and CTCs. We find that a transition from train formation to margination occurs when $(R-a)/t^R\approx 1$, where $R$ is the vessel radius, $a$ is the cell radius, and $t^R$ is the thickness of RBCs, but that the motion of RBCs differs from the case of leukocytes. Our results also show that the velocities of CTCs and leukocytes are larger than the average blood velocity, but only CTCs move faster than RBCs for microvessels of $R/a\approx 1.5$–$2.0$. These findings are expected to be useful not only for understanding metastasis, but also for developing microfluidic devices.

In a classical ideal plasma, a magnetic field is known to reduce the heat conductivity perpendicular to the field, whereas it does not alter the one along the field. Here we show that, in strongly correlated plasmas that are observed at high pressure and/or low temperature, a magnetic field reduces the perpendicular heat transport much less and even enhances the parallel transport. These surprising observations are explained by the competition of kinetic, potential, and collisional contributions to the heat conductivity. Our results are based on first-principle molecular dynamics simulations of a one-component plasma.

The dynamics of an incompressible, dissipationless Hall magnetohydrodynamic medium are investigated from Lagrangian mechanical viewpoint. The hybrid and magnetic helicities are shown to emerge, respectively, from the application of the particle relabeling symmetry for ion and electron flows to Noether's first theorem, while the constant of motion associated with the theorem is generally given by their arbitrary linear combination. Furthermore, integral path variation associated with the invariant action is expressed by the operation of an integrodifferential operator on the reference path. The eigenfunctions of this operator are double Beltrami flows, i.e., force-free stationary solutions to the equation of motion and provide a family of orthogonal function bases that yields the spectral representation of the equation of motion with a remarkably simple form. Among the double Beltrami flows, considering the influence of a uniform background magnetic field and the Hall term effect vanishing limit, the generalized Elsässer variables are found to be the most suitable for avoiding problems with singularities in the standard magnetohydrodynamic limit.

The head-on collision of two ion acoustic solitary waves is investigated in a magnetized plasma containing trapped electrons and dust grains. For completeness, the fluctuations in dust grain charge are taken into account. By using the extended Poincaré-Lighthill-Kuo (PLK) perturbation method, an analytical expression is obtained for the phase shift that takes place due to the collision of the waves. How the phase shift behaves under the combined effect of trapped electrons and dust grains along with the finite temperature of ions is examined. A focus is given to uncover the situations of fluctuating charge and fixed charge on the dust grains in the plasma. Interestingly, the solitary waves acquire a larger phase shift and are delayed more in the case of dust grains having a fluctuating charge.

We validate the application of our recent orbital-free density functional theory (DFT) approach [Phys. Rev. Lett. 113, 155006 (2014);] for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion coefficient, the viscosity coefficient, the electrical and thermal conductivities, and the reflectivity coefficient of hydrogen and aluminum plasmas. Very good agreement is found with orbital-based Kohn-Sham DFT calculations at lower temperatures. Because the computational costs of the method do not increase with temperature, we can produce results at much higher temperatures than is accessible by the Kohn-Sham method. Our results for warm dense aluminum at solid density are inconsistent with the recent experimental results reported by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)].

The topography of a reactive surface contains information about the reactions that form or modify the surface and, therefore, it should be possible to characterize reactivity using topography parameters such as surface area, roughness, or fractal dimension. As a test of this idea, we consider a two-dimensional (2D) lattice model for crystal dissolution and examine a suite of topography parameters to determine which may be useful for predicting rates and mechanisms of dissolution. The model is based on the assumption that the reactivity of a surface site decreases with the number of nearest neighbors. We show that the steady-state surface topography in our model system is a function of, at most, two variables: the ratio of the rate of loss of sites with two neighbors versus three neighbors $(d_2/d_3)$ and the ratio of the rate of loss of sites with one neighbor versus three neighbors $(d_1/d_3)$. This means that relative rates can be determined from two parameters characterizing the topography of a surface provided that the two parameters are independent of one another. It also means that absolute rates cannot be determined from measurements of surface topography alone. To identify independent sets of topography parameters, we simulated surfaces from a broad range of $d_1/d_3$ and $d_2/d_3$ and computed a suite of common topography parameters for each surface. Our results indicate that the fractal dimension $D$ and the average spacing between steps, $E\left[s\right]$, can serve to uniquely determine $d_1/d_3$ and $d_2/d_3$ provided that sufficiently strong correlations exist between the steps. Sufficiently strong correlations exist in our model system when $D>1.5$ (which corresponds to $D>2.5$ for real 3D reactive surfaces). When steps are uncorrelated, surface topography becomes independent of step retreat rate and $D$ is equal to 1.5. Under these conditions, measures of surface topography are not independent and any single topography parameter contains all of the available mechanistic information about the surface. Our results also indicate that root-mean-square roughness cannot be used to reliably characterize the surface topography of fractal surfaces because it is an inherently noisy parameter for such surfaces with the scale of the noise being independent of length scale.

We investigate the loading and unloading behavior of soft solids in adhesive contact with randomly rough profiles. The roughness is assumed to be described by a self-affine fractal on a limited range of wave vectors. A spectral method is exploited to generate such randomly rough surfaces. The results are statistically averaged, and the calculated contact area and applied load are shown as a function of the penetration, for loading and unloading conditions. We found that the combination of adhesion forces and roughness leads to a hysteresis loading-unloading loop. This shows that energy can be lost simply as a consequence of roughness and van der Waals forces, as in this case a large number of local energy minima exist and the system may be trapped in metastable states. We numerically quantify the hysteretic loss and assess the influence of the surface statistical properties and the energy of adhesion on the hysteresis process.

Motifs in RNA tertiary structures are important to their structural organizations and biological functions. Here we consider an H-H-type pseudoknot (HHpk) motif that consists of two hairpins connected by a junction loop and with kissing interactions between the two hairpin loops. Such a tertiary structural motif is recurrently found in RNA tertiary structures, but is difficult to predict computationally. So it is important to understand the mechanism of its formation and stability. Here we investigate the stability of the HHpk tertiary structure by using an all-atom molecular dynamics simulation. The results indicate that the HHpk tertiary structure is stable. However, it is found that this stability is not due to the helix-helix packing, as is usually expected, but is maintained by the combined action of the kissing hairpin loops and junctions, although the former plays the main role. Stable HHpk motifs may form structural platforms for the molecules to realize their biological functions. These results are useful for understanding the construction principle of RNA tertiary structures and structure prediction.

Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behavior, such as frequency synchronization (FS) as a paradigm, in real-world networks with a finite number of oscillators. A major current challenge is to obtain an analytical solution for the phase angles. Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, with arbitrary finite-variance distribution of the natural frequencies of the oscillators. The master solution embodies all particular solutions of the finite-size Kuramoto model for any frequency distribution and coupling strength larger than the critical one. Furthermore, we present a criterion to determine the stability of the FS solution. This allows one to analytically infer the relationship between the physical parameters and the stable behavior of networks.

We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number $N$. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects such as vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommensurable frequencies, our formulas are generically valid also in the free-field case of noninteracting bosons.

Using a quantum map version of the one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with the quantum standard map. Existence of critical phenomena, which depends on the number of frequency component $M$, is demonstrated. Diffusion exponents agree with theoretical prediction for the transition, but the critical exponent of the localization length deviates from it with increase in the $M$. The critical power ${\epsilon }_c$ of the normalized perturbation at the transition point remarkably decreases as ${\epsilon }_c\sim {(M-1)}^{-1}$.

Sedimentation behaviors of an oblate ellipsoidal particle inside narrow $[R/a\in (1.2,2.0\left)\right]$ infinitely long circular tubes are studied by the lattice Boltzmann method, where $R$ and $a$ are the radius of the tube and the length of the semimajor axis of the ellipsoid, respectively. The Archimedes numbers (Ar) up to 70 are considered. Four periodic and two steady sedimentation modes are identified. It is the first time that the anomalous mode has been found in a circular tube for an ellipsoidal particle. The phase diagram of the modes as a function of Ar and $R/a$ is obtained. The anomalous mode is observed in the larger $R/a$ and lower-Ar regime. Through comparisons between the anomalous and oscillatory modes, it is found that $\frac{R}{a}$ plays a critical role for the anomalous mode. Some constrained cases with two steady modes are simulated. It is found that the particle settles faster in the unconstrained modes than in the corresponding constrained modes. This might inspire further study on why the particle adopts a specific mode under a certain circumstance.

By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrödinger equation, the modulation instability (MI) of its $n=1$ Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked step with the $n=1$ mode. This fundamental insight, the enslavement of all higher modes to the $n=1$ mode, explains the formation of a triangular-shaped spectrum that generates the Akhmediev breather, predicts its formation time analytically from the initial modulation amplitude, and shows that the Fermi-Pasta-Ulam (FPU) recurrence is just a matter of energy conservation with a period twice the breather's formation time. For higher-order MI with more than one initial unstable mode, while most evolutions are expected to be chaotic, we show that it is possible to have isolated cases of “super-recurrence,” where the FPU period is much longer than that of a single unstable mode.

Dendrite sidebranch detachment is an important fragmentation mechanism during the solidification of alloys. The detachment occurs at the junction between a sidearm and its parent stem. While this pinching process is driven by capillarity, the presence of solidification opposes the instability. Using a simple numerical model of a single sidearm, we are able to capture the essential dynamics of dendrite sidebranch development and the resulting morphological transitions. While shortly before pinch-off the neck itself obeys well-known universal scaling relations, the overall evolution of the sidearm shape sensitively depends on its initial geometry and the rate of solidification. It is found that pinch-off only occurs over limited ranges of geometrical parameters and cooling rates and is generally bounded by sidearm retraction and coalescence regimes. Simple scaling relations are identified that provide the bounds for the pinch-off regime. Pinching at the branching point is shown to be faster than the Rayleigh-Plateau instability of an infinitely long cylinder.