We propose a unified model to build planar graphs with diverse topological characteristics which are of relevance in real applications. Here convex regular polyhedra (Platonic solids) are used as the building blocks for the construction of a variety of complex planar networks. These networks are obtained by merging polyhedra face by face on a tree-structure leading to planar graphs. We investigate two different constructions: (1) a fully deterministic construction where a self-similar fractal structure is built by using a single kind of polyhedron which is iteratively attached to every face and (2) a stochastic construction where at each step a polyhedron is attached to a randomly chosen face. These networks are scale-free, small-world, clustered, and sparse, sharing several characteristics of real-world complex networks. We derive analytical expressions for the degree distribution, the clustering coefficient, and the mean degree of nearest neighbors showing that these networks have power-law degree distributions with tunable exponents associated with the building polyhedron, and they possess a hierarchical organization that is determined by planarity.

We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter $\beta =0.7$. In the limit of creeping flow, droplet breakup occurs at a critical capillary number $0.35<{\text{Ca}}_c<0.4$ for the viscosity ratio of unity, consistent with previous numerical simulations and experiments. Droplet breakup can also be promoted by increasing the Reynolds number. Finally, we numerically investigate a single bubble rising under buoyancy force in viscous fluids for a wide range of Eötvös and Morton numbers. Numerical results are compared with theoretical predictions and experimental results, and satisfactory agreement is shown.

The role of particle inertia and particle–free-surface collisions in periodic free-surface flows is evaluated in the framework of an analytical flow model for a thermocapillary liquid bridge. Inertia and particle–free-surface collisions lead to particle accumulation, but on different time scales, and can lead to different accumulation patterns. A comparison with experimental results provides strong evidence that the experimentally observed accumulation patterns are due to particle–free-surface collisions.

In this paper, we delineate the consequences of electrokinetic interactions on the “coffee stain” effect, induced by the deposition of particles during drop evaporation. We consider evaporation of an electrolytic drop in contact with a charged substrate and probe the effects of electrical double layer formation at the drop-substrate interface on the dynamics of particles suspended inside the drop. We show that the simultaneous considerations of streaming potential and flow-actuation-mechanism-independent description of the evaporation flux and the depth average velocities result in an enhanced induced radial pressure gradient. As a result, the deposition speed of the particles in the disordered packing regime, occurring at the end of the lifetime of the drop [Marin et al., Phys. Rev. Lett. 107, 085502 (2011)], is greatly enhanced. This, in turn, is likely to signify an augmented degree of disordering in the evaporation-induced particle deposition.

We report experimental and numerical studies of combined natural and magnetic convection of a paramagnetic fluid inside a cubical enclosure heated from below and cooled from above and subjected to a magnetic field gradient. Values of the magnetic field gradient are in the range $9\le \left|\mathrm{grad}\right|b_0{|}^2|\le 900$ T${}^2$/m for imposed magnetic field strengths in the center of the superconducting magnet bore of $1\le |b_0{|}_{\max }\le 10$ T. Very good agreement between experiments and simulation is obtained in predicting the integral heat transfer over the entire range of working parameters (i.e., thermal Rayleigh number $1.15\times {10}^5\le {\text{Ra}}_{\mathrm{T}}\le 8\times {10}^6$, Prandtl number $5\le \text{Pr}\le 700$, and magnetization number $0\le \gamma \le 58.5$). We present a stability diagram containing three characteristic states: steady, oscillatory (periodic), and turbulent regimes. The oscillatory states are identified for intermediate values of Pr ($40\le \text{Pr}\le 70$) and low magnetic field ($|b_0{|}_{\max }\le 2$ T). Turbulent states are generated from initially stable flow and heat transfer regimes in the range of $70\le \text{Pr}\le 500$ for sufficiently strong magnetic field ($|b_0{|}_{\max }\ge 4$ T).

We report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the generalized Gumbel (GG) distribution like many other equilibrium and nonequilibrium systems with high degree of correlations but do not obey the Gallavotti-Cohen steady-state fluctuation relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution.

A nematic liquid crystal with high, positive dielectric anisotropy (5CB) has been studied under the influence of the combined action of a dc and an ac electric field. Broad frequency, voltage, and cell thickness ranges were considered. Pattern morphologies were identified; the thresholds and critical wave numbers were measured and analyzed as a function of frequency, dc-to-ac voltage ratio, and thickness. The current-voltage characteristics were simultaneously detected.

A biophysical tool is introduced that seeks to provide a theoretical basis for helping drug design teams assess the most promising drug targets and design optimal treatment strategies. The tool is grounded in a previously validated computational model of the feedback that occurs between a growing tumor and the evolving vasculature. In this paper, the model is particularly used to explore the therapeutic effectiveness of two drugs that target the tumor vasculature: angiogenesis inhibitors (AIs) and vascular disrupting agents (VDAs). Using sensitivity analyses, the impact of VDA dosing parameters is explored, as is the effects of administering a VDA with an AI. Further, a stochastic optimization scheme is utilized to identify an optimal dosing schedule for treatment with an AI and a chemotherapeutic. The treatment regimen identified can successfully halt simulated tumor growth, even after the cessation of therapy.

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, which includes relaxation in the plates as a key ingredient. First, we make an analysis of the scaling of the largest events with system size and show that, when parameters are appropriately interpreted, the typical size of the largest events scale as the system size, without the necessity to tune any parameter. Second, we show that the temporal activity in the model is inherently nonstationary and obtain from here justification and support for the concept of a “seismic cycle” in the temporal evolution of seismic activity. Finally, we ask for the reasons that make the model display a realistic value of the decaying exponent $b$ in the Gutenberg-Richter law for the avalanche size distribution. We explain why relaxation induces a systematic increase in $b$ from its value $b\simeq 0.4$ observed in the absence of relaxation. However, we have not been able to justify the actual robustness of the model in displaying a consistent $b$ value around the experimentally observed value $b\simeq 1$.

Finding communities, or clusters or modules, in networks can be done by optimizing an objective function defined globally and/or by specifying conditions which must be satisfied by all communities. Radicchi et al. [Proc. Natl. Acad. Sci. USA 101, 2658 (2004)] define a susbset of vertices of a network to be a community in the strong sense if each vertex of that subset has a larger inner degree than its outer degree. A partition in the strong sense has only strong communities. In this paper we first define an enumerative algorithm to list all partitions in the strong sense of a network of moderate size. The results of this algorithm are given for the Zachary karate club data set, which is solved by hand, as well as for several well-known real-world problems of the literature. Moreover, this algorithm is slightly modified in order to apply it to larger networks, keeping only partitions with the largest number of communities. It is shown that some of the partitions obtained are informative, although they often have only a few communities, while they fail to give any information in other cases having only one community. It appears that degree 2 vertices play a big role in forcing large inhomogeneous communities. Therefore, a weakening of the strong condition is proposed and explored: we define a partition in the almost-strong sense by substituting a nonstrict inequality to a strict one in the definition of strong community for all vertices of degree 2. Results, for the same set of problems as before, then give partitions with a larger number of communities and are more informative.

We study the dynamics of a nonlinear one-dimensional disordered system obtained by coupling the Anderson model with the Gross-Pitaevskii equation. We introduce a single quantity globally characterizing the localization of the system. This quantity obeys a scaling law with respect to the width of the initial state, which can be used to characterize the dynamics independently of the initial state.

Improving the frequency precision by synchronizing a lattice of $N$ oscillators with disparate frequencies is studied in the phase reduction limit. In the general case where the coupling is not purely dissipative the synchronized state consists of targetlike waves radiating from a local source, which is a region of higher-frequency oscillators. In this state the improvement of the frequency precision is shown to be independent of $N$ for large $N$, but instead depends on the disorder and reflects the dependence of the frequency of the synchronized state on just those oscillators in the source region of the waves. These results are obtained by a mapping of the nonlinear phase dynamics onto the linear Anderson problem of the quantum mechanics of electrons on a random lattice in the tight-binding approximation.

The dynamics of a viscoelastic Maxwell fluid is studied in a partially filled cylinder rotating around a horizontal axis. At low rotational velocity, the fluid behaves in the same manner as a viscous fluid. A thin fluid film is pulled up from the edge of a fluid bump at the bottom of the cylinder, and it covers the inner wall of the cylinder completely. As a result, a steady state is the coexistence of the film and the bump of the fluid. When the rotational velocity of the cylinder is increased, the film formation fails and the bump of fluid rolls steadily at the bottom of the cylinder. This failure of film formation has never been observed in the case of a viscous fluid. At higher rotational velocity, the bump of the fluid starts to oscillate at the bottom of the cylinder. Then, the fluid bump again rolls steadily with a further increase in the rotational velocity. The failure of film formation is explained in terms of the elastic behavior of the viscoelastic fluid near the boundary between the film and the bump regions. The theoretical prediction shows good agreement with the experimental results. We further estimate the condition for which a viscoelastic fluid displays dynamically nonwetting behavior; i.e., the absence of fluid film at any value of rotational velocity.

We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction. In this part, we develop analytical results when the problem can be cast as an equivalent continuum and described as a one-dimensional (1D) problem. This is always the case when gravity acts against drying by opposing corner flow, or when it enhances drying by increasing corner film flow but it is sufficiently small. We obtain results for all relevant variables, including drying rates, extent of the macroscopic film region, and the demarkation of the two different regimes of constant rate period and falling rate period, respectively. The effects of dimensionless variables, such as the bond number, the capillary number, and the Sherwood number for external mass transfer are investigated. When gravity acts to enhance drying, a 1D solution is still possible if an appropriately defined Rayleigh number is above a critical threshold. We derive a linear stability analysis of a model problem under this condition that verifies front stability. Further analysis of this problem, when the Rayleigh number is below critical, requires a pore-network simulator which will be the focus of future work.

An analytical study of the relativistic interaction of a linearly polarized laser field of $\omega$ frequency with highly overdense plasma is presented. In agreement with one-dimensional particle-in-cell simulations, the model self-consistently explains the transition between the sheath inverse bremsstrahlung absorption regime and the $\vec{J}\times \vec{B}$ heating (responsible for the $2\omega$ electron bunches), as well as the high harmonic radiations and the mean electron energy.

We revisit an approach to the replica-based analysis of the spherical spin-glass model that makes use of a mapping of the problem onto a one-dimensional interacting charge system. A saddle point approximation leads to the conclusion that the interaction between charges is irrelevant in the thermodynamic limit, and as a consequence, that there is no nontrivial correlation between replicas for this model. This allows us to show that quenched and annealed disorder averages agree for the spherical spin glass. We demonstrate this result within two different mathematical frameworks, and we also relate our analysis to the conclusions that follow from the replica symmetry ansatz.

In the energy landscape picture, the dynamics of glasses and crystals is usually decomposed into two separate contributions: interbasin and intrabasin dynamics. The intrabasin dynamics depends partially on the quadratic displacement distribution on a given metabasin. Here we show that such a distribution can be approximated by a Gamma function, with a mean that depends linearly on the temperature and on the inverse second moment of the density of vibrational states. The width of the distribution also depends on this last quantity, and thus the contribution of the boson peak in glasses is evident on the tail of the distribution function. It causes the distribution of the mean-square displacement to decay slower in glasses than in crystals. When a statistical analysis is performed under many energy basins, we obtain a Gaussian in which the width is regulated by the mean inverse second moment of the density of states. Simulations performed in binary glasses are in agreement with such a result.

We propose a simple cellular automaton model for the description of the evolution of a colony of Bacillus subtilis. The originality of our model lies in the fact that the bacteria can move in a pool of liquid. We assume that each migrating bacterium is surrounded by an individual pool, and the overlap of the latter gives rise to a collective pool with a higher water level. The bacteria migrate collectively when the level of water is high enough. When the bacteria are far enough from each other, the level of water becomes locally too low to allow migration, and the bacteria switch to a proliferating state. The proliferation-to-migration switch is triggered by high levels of a substance produced by proliferating bacteria. We show that it is possible to reproduce in a fairly satisfactory way the various forms that make up the experimentally observed morphological diagram of B. subtilis. We propose a phenomenological relation between the size of the water pool used in our model and the agar concentration of the substrate on which the bacteria migrate. We also compare experimental results from cutting the central part of the colony with the results of our simulations.

We propose a simple phenomenological model exhibiting on-off intermittency over an extended range of control parameter. We find that the distribution of the “off” periods has a power-law tail with an exponent varying continuously between $-1$ and $-2$, at odds with standard on-off intermittency which occurs at a specific value of the control parameter and leads to the exponent $-3/2$. This nontrivial behavior results from the competition between a strong slowing down of the dynamics at small values of the observable and a systematic drift toward large values.