In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed.

Small number dust particle clusters can be used as probes for plasma diagnostics. The number of dust particles as well as cluster size and shape can be easily controlled employing a glass box placed within a Gaseous Electronics Conference (GEC) rf reference chamber to provide confinement of the dust. The plasma parameters inside this box and within the larger plasma chamber have not yet been adequately defined. Adjusting the rf power alters the plasma conditions causing structural changes of the cluster. This effect can be used to probe the relationship between the rf power and other plasma parameters. This experiment employs the sloshing and breathing modes of small cluster oscillations to examine the relationship between system rf power and the particle charge and plasma screening length inside the glass box. The experimental results provided indicate that both the screening length and dust charge decrease as rf power inside the box increases. The decrease in dust charge as power increases may indicate that ion trapping plays a significant role in the sheath.

The properties of self-similar optical waves propagating in a tapered cubic-quintic nonlinear waveguide are investigated. Using a lens-type transformation we obtain the exact analytical self-similar solutions which describe the propagation of bright-shaped solitons, dark-shaped solitons, kink-shaped solitons, and antikink-shaped solitons. The stability of the solutions is examined by numerical simulations such that stable bright solitons are found. Beyond the exact analytical solutions, asymptotic optical waves are also found by employing a direct ansatz. These waves possess linear chirps and can propagate self-similarly. The possibility of controlling the shape of output asymptotic optical waves is demonstrated. The analytical results are confirmed by numerical simulations. Finally, we investigate the generation and propagation properties of self-similar optical waves in a quintic nonlinear medium.

The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ${\xi }_{i\alpha }\in \{-1,0,1\}$ for all $i$, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.

Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally treelike graph and factor graph ($p$-spin) ensembles. We present exact analytical expressions, which can be efficiently approximated numerically for many types of correlation functions and for the average free energies of open and closed finite chains. All the results achieved, with the exception of those involving closed chains, are then rigorously derived without replicas, using a probabilistic approach with the same flavor of cavity method.

Relativistic effect is important in many quantum systems but theoretically complicated from both fundamental and practical perspectives. Herein we introduce an efficient computational procedure to predict the structure and energetic properties of relativistic quantum systems by mapping the Pauli principle into an effective pairwise-additive potential such that the properties of relativistic nonquantum systems can be readily predicted from conventional liquid-state methods. We applied our theoretical procedure to relativistic uniform electron gases and compared the pair correlation functions with those for systems of nonrelativistic electrons. A simple analytical expression has been developed to correlate the exchange-correlation free energy of relativistic uniform electron systems.

Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits $1/f$ noise if Boltzmann's factor is extended to include local alignment entropy to all orders. We show that this nonlinear correction maintains maximum entropy during equilibrium fluctuations. Indeed, as with the usual way to resolve Gibbs' paradox that avoids entropy reduction during reversible processes, the correction yields the statistics of indistinguishable particles. The correction also ensures conservation of energy if an instantaneous contribution from local entropy is included. Thus, a common mechanism for $1/f$ noise comes from assuming that finite-size fluctuations strictly obey the laws of thermodynamics, even in small parts of a large system. Empirical evidence for the model comes from its ability to match the measured temperature dependence of the spectral-density exponents in several metals and to show non-Gaussian fluctuations characteristic of nanoscale systems.

Condensation of fluctuations is an interesting phenomenon conceptually distinct from condensation on average. One striking feature is that, contrary to what happens on average, condensation of fluctuations may occur even in the absence of interaction. The explanation emerges from the duality between large deviation events in the given system and typical events in a new and appropriately biased system. This phenomenon is investigated in the context of the Gaussian model, chosen as a paradigmatical noninteracting system, before and after an instantaneous temperature quench. It is shown that the bias induces a mean-field-like effective interaction responsible for the condensation on average. Phase diagrams, covering both the equilibrium and the off-equilibrium regimes, are derived for observables representative of generic behaviors.

Neural field theory insights are used to derive effective brain connectivity matrices from the functional connectivity matrix defined by activity covariances. The symmetric case is exactly solved for a resting state system driven by white noise, in which strengths of connections, often termed effective connectivities, are inferred from functional data; these include strengths of connections that are underestimated or not detected by anatomical imaging. Proximity to criticality is calculated and found to be consistent with estimates obtainable from other methods. Links between anatomical, effective, and functional connectivity and resting state activity are quantified, with applicability to other complex networks. Proof-of-principle results are illustrated using published experimental data on anatomical connectivity and resting state functional connectivity. In particular, it is shown that functional connection matrices can be used to uncover the existence and strength of connections that are missed from anatomical connection matrices, including interhemispheric connections that are difficult to track with techniques such as diffusion spectrum imaging.

The ability to understand the impact of adversarial processes on networks is crucial to various disciplines. The objects of study in this article are fitness-driven networks. Fitness-dependent networks are fully described by a probability distribution of fitness and an attachment kernel. Every node in the network is endowed with a fitness value and the attachment kernel translates the fitness of two nodes into the probability that these two nodes share an edge. This concept is also known as mutual attractiveness. In the present article, fitness does not only serve as a measure of attractiveness, but also as a measure of a node's robustness against failure. The probability that a node fails increases with the number of failures in its direct neighborhood and decreases with higher fitness. Both static and dynamic network models are considered. Analytical results for the percolation threshold and the occupied fraction are derived. One of the results is that the distinction between the dynamic and the static model has a profound impact on the way failures spread over the network. Additionally, we find that the introduction of mutual attractiveness stabilizes the network compared to a pure random attachment.

We explore the networks that yield the largest mean consensus time of voter models under different update rules. By analytical and numerical means, we show that the so-called lollipop graph, barbell graph, and double-star graph maximize the mean consensus time under the update rules called the link dynamics, voter model, and invasion process, respectively. For each update rule, the largest mean consensus time scales as $O\left(N^3\right)$, where $N$ is the number of nodes in the network.

We study numerically joint mixing of salt and colloids by chaotic advection and how salt inhomogeneities accelerate or delay colloid mixing by inducing a velocity drift ${\mathbf{V}}_{\mathrm{dp}}$ between colloids and fluid particles as proposed in recent experiments [J. Deseigne et al., Soft Matter 10, 4795 (2014)]. We demonstrate that because the drift velocity is no longer divergence free, small variations to the total velocity field drastically affect the evolution of colloid variance ${\sigma }^2=\langle C^2\rangle -{\langle C\rangle }^2$. A consequence is that mixing strongly depends on the mutual coherence between colloid and salt concentration fields, the short time evolution of scalar variance being governed by a new variance production term $P=-\langle C^2\nabla ·{\mathbf{V}}_{\mathrm{dp}}\rangle /2$ when scalar gradients are not developed yet so that dissipation is weak. Depending on initial conditions, mixing is then delayed or enhanced, and it is possible to find examples for which the two regimes (fast mixing followed by slow mixing) are observed consecutively when the variance source term reverses its sign. This is indeed the case for localized patches modeled as Gaussian concentration profiles.

Immiscible displacement of viscous oil by water in a petroleum reservoir is often hydrodynamically unstable. Due to similarities between the physics of dielectric breakdown and immiscible flow in porous media, we extend the existing dielectric breakdown model to simulate viscous fingering patterns for a wide range of viscosity ratios (${\mu }_r$). At low values of power-law index η, the system behaves like a stable Eden growth model and as the value of η is increased to unity, diffusion limited aggregation–like fractals appear. This model is compared with our two-dimensional (2D) experiments to develop a correlation between the viscosity ratio and the power index, i.e., η = ${10}^{-5}{\mu }_r{}^{0.8775}$. The 2D and three-dimensional (3D) simulation data appear scalable. The fingering pattern in 3D simulations at finite viscosity ratios appear qualitatively similar to the few experimental results published in the literature.

The object of experimental study is a fluid flow generated by differential rotation of a free light spherical body in a rotating cylindrical cavity. The body stays near the axis under the action of centrifugal force. The body rotation is generated by a force field oscillating in the cavity reference system (vibrational hydrodynamic top). It was found that the Taylor-Proudman column that forms undergoes instability, which manifests itself in the formation of a two-dimensional azimuthal wave at the column boundary, in a Stewartson layer. The experimental results are summarized on a plane of dimensionless parameters, i.e., the dimensionless velocity of the cavity rotation and Rossby number. The bounds of the Stewartson layer stability were found and the supercritical structures and transition sequences were studied. Systematic research into that problem in its classical formulation—when a sphere is fixed on the axis and its differential rotation is imposed—was done for comparison. It was demonstrated that in conditions of vibratory differential rotation of a free sphere the stability threshold of the Stewartson layer was reduced by more than one order of magnitude, in comparison with the classical case. A qualitative change was also found in the wave phase velocity which for a free sphere exceeds the lagging differential rotation velocity of the body. It was concluded that the uncovered specifics are related to the difference in the mechanism of the Taylor-Proudman column formation and of the flow generation in it. For a vibrational hydrodynamic top, streams in the column will not be defined by Ekman pumping but by steady streaming, which is also responsible for the free-sphere differential rotation.

The kinetic Monte Carlo method is used to model the dynamic properties of proton diffusion in anhydrous proton conductors. The results have been discussed with reference to a two-step process called the Grotthuss mechanism. There is a widespread belief that this mechanism is responsible for fast proton mobility. We showed in detail that the relative frequency of reorientation and diffusion processes is crucial for the conductivity. Moreover, the current dependence on proton concentration has been analyzed. In order to test our microscopic model the proton transport in polymer electrolyte membranes based on benzimidazole ${\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{N}}_2$ molecules is studied.

In this paper we study the four-point correlation function ${\chi }_4$ of collective density fluctuations in a nonequilibrium liquid. The equilibration is controlled by a modified stretched exponential behavior $\{exp[-{(t_w/\tau )}^{\beta }]\}$ having the relaxation time $\tau$ dependent on the aging time $t_w$. Similar aging behavior has been seen experimentally in supercooled liquids. The basic equations of fluctuating nonlinear hydrodynamics are solved here numerically to obtain ${\chi }_4$ for equilibrium and non equilibrium states. We also identify a dynamic length scale $\xi$ from the equilibrated function. $\xi \left(T\right)$ grows with fall of temperature $T$. From a broader perspective, we demonstrate here that the characteristic signatures of dynamical heterogeneities in a supercooled liquid, observed previously in computer simulations of the dynamics of a small number of particles, are also present in the coarse grained equations of generalized hydrodynamics.

The spatial suppression of order parameter fluctuations in a critical media produces critical Casimir forces acting on confining surfaces. This scenario is realized in a critical binary mixture near the demixing transition point that corresponds to the second-order phase transition of the Ising universality class. Due to these critical interactions similar colloids, immersed in a critical binary mixture near the consolute point, exhibit attraction. The numerical method for computation of the interaction potential between two spherical particles using Monte Carlo simulations for the Ising model is proposed. This method is based on the integration of the local magnetization over the applied local magnetic field. For the stronger interaction the concentration of the component of the mixture that does not wet colloidal particles should be larger than the critical concentration. The strongest amplitude of the interactions is observed below the critical point.

We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent $z^{\prime }$ saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to ${70}^5$ sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions.