A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible nonideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to “model A,” characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.

We calculate the survival probability of an immobile target surrounded by a sea of uncorrelated diffusive or subdiffusive evanescent traps (i.e., traps that disappear in the course of their motion). Our calculation is based on a fractional reaction-subdiffusion equation derived from a continuous time random walk model of the system. Contrary to an earlier method valid only in one dimension ($d=1$), the equation is applicable in any Euclidean dimension $d$ and elucidates the interplay between anomalous subdiffusive transport, the irreversible evanescence reaction, and the dimension in which both the traps and the target are embedded. Explicit results for the survival probability of the target are obtained for a density $\rho \left(t\right)$ of traps which decays (i) exponentially and (ii) as a power law. In the former case, the target has a finite asymptotic survival probability in all integer dimensions, whereas in the latter case there are several regimes where the values of the decay exponent for $\rho \left(t\right)$ and the anomalous diffusion exponent of the traps determine whether or not the target has a chance of eternal survival in one, two, and three dimensions.

While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge, Heitzig, Petoukhov, and Kurths [Phys. Rev. Lett. 108, 258701 (2012)], it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of defining a meaningful coupling strength using information-theoretic measures and demonstrate the shortcomings of the well-known mutual information and transfer entropy. Instead, we propose a certain time-delayed conditional mutual information, the momentary information transfer (MIT), as a lag-specific measure of association that is general, causal, reflects a well interpretable notion of coupling strength, and is practically computable. Rooted in information theory, MIT is general in that it does not assume a certain model class underlying the process that generates the time series. As discussed in a previous paper [Runge, Heitzig, Petoukhov, and Kurths, Phys. Rev. Lett. 108, 258701 (2012)], the general framework of graphical models makes MIT causal in that it gives a nonzero value only to lagged components that are not independent conditional on the remaining process. Further, graphical models admit a low-dimensional formulation of conditions, which is important for a reliable estimation of conditional mutual information and, thus, makes MIT practically computable. MIT is based on the fundamental concept of source entropy, which we utilize to yield a notion of coupling strength that is, compared to mutual information and transfer entropy, well interpretable in that, for many cases, it solely depends on the interaction of the two components at a certain lag. In particular, MIT is, thus, in many cases able to exclude the misleading influence of autodependency within a process in an information-theoretic way. We formalize and prove this idea analytically and numerically for a general class of nonlinear stochastic processes and illustrate the potential of MIT on climatological data.

We investigate numerically the position- and momentum-space Shannon information entropies, $S_x^{\beta }$ and $S_p^{\beta }$, respectively, of energy eigenstates $|\beta \rangle$ for an electron in four kinds of one-dimensional (1D) nonuniform systems, i.e., the Harper model, the slowly varying potential ones, the complex quasiperiodic potential ones, and the random-dimer potential ones. In the former three models, electronic localization properties are well-defined. For them, we find it interesting that, $S_x^{\beta }$ is greater than, equal to, and less than $S_p^{\beta }$ for delocalized, critical, and localized states in position-space, respectively, which can be used as signatures of the transition from a delocalized phase to a localized ones. With the criterion, we analyze the random-dimer potential model. We give another perspective and propose a consistent interpretation of discrepancies about the random-dimer potential model. Therefore, all these provide us a simple method to discern the nature of states in these 1D nonuniform systems.

The jamming of particles under flow is of critical importance in a broad range of natural and industrial settings, such as the jamming of ice in rivers, or the plugging of suspended solids in pipeline transport. Relatively few studies have been carried out on jamming of suspended particles under flow, in comparison to the many studies on jamming in gravity-driven flows that have revealed various features of the jamming process. Fluid-driven particle flows differ in several aspects from gravity-driven flows, particularly in being compatible with a range of particle concentrations and velocities. Additionally, there are fluid-particle interactions and hydrodynamic effects. To investigate particle jamming in fluid-driven flows, we have performed both experiments and computer simulations on the flow of circular particles floating over water in an open channel with a restriction. We determined the flow-rate boundary for a dilute-to-dense flow transition, similar to that seen in gravity-driven flows. The maximum particle throughput increased for larger restriction sizes consistent with a Beverloo equation form over the entire range of particle mixtures and restriction sizes. The exponent of ∼3/2 in the Beverloo equation is consistent with approximately constant acceleration of grains due to fluid drag in the immediate region of the opening. We verified that the jamming probability from the dense flow gave a geometric distribution in the number of particles escaping before a jam. The probability of jamming in both experiments and simulations was found to be dependent on the ratio of channel opening to particle size, but only weakly dependent on the fluid flow velocity. Flow entrance effects were measured and observed to affect the jamming probability, and dependence on particle friction coefficient was determined from simulation. A comprehensive model for the jamming probability integrating these observations from the different flow regimes was shown to be in good agreement for experimental data on average times before jamming.

Recent experiments reveal an unexpected dip of the shear stress as the shear rate increases, from the rate-independent regime to Bagnold flow. Employing granular solid hydrodynamics, it is shown that in uniform systems, such dips occur for given pressure or normal stress, but not for given density. If the shear rate is strongly nonuniform, enforcing a constant volume does not prevent the local density to vary, and a stress dip may still occur.

The fracture mechanics was usually employed to explain the crack propagation in the deposition produced by drying colloidal suspension. However, more complex than conventional fracture, those cracks periodically distribute and make up a unique pattern. Inspired by the concept of spinodal decomposition, here we develop the theory to illustrate the possible mechanism of the spatial arrangement of the cracks. It indicates that before the cracks develop and propagate in the deposition under the law of fracture mechanics, the periodically distributed flaws are generated by the phase separation of colloidal clusters and solvent. Then the cracks originate at the sites of those flaws in terms of fracture mechanics. It concludes that the crack spacing results from the wavelength of the concentration fluctuation during the phase separation, linearly growing with the increase of the deposition thickness and initial particle concentration, which is consistent with experimental results.

Despite their lack of thermodynamical stability, nanoemulsions can show a remarkable degree of kinetic stability. Among the various different preparation methods the phase-inversion concentration method is particularly interesting as it occurs spontaneously. Here we investigate such a system composed of a surfactant, cosurfactant, and oil that upon dilution with water forms long time metastable oil-in-water nanoemulsion droplets. The dynamics of the amphiphilic monolayers and its elastic properties is important for their stability and therefore the monolayer dynamics have been investigated by neutron spin echo (NSE). Despite the difficulties arising from the inherently polydisperse nature and the large number of different components necessarily contained in commercial nanoemulsion formulations, information concerning the membrane rigidity was extracted from the combination of small angle neutron scattering and NSE and several different formulations are compared. These results show that small amounts of different admixed ionic surfactants can modify the monolayer rigidity substantially and similarly effects of surface bound polyelectrolytes have been evaluated.

The traditional modeling framework for determining streaming potential, when taking into consideration finite size effects, suffers from an oversight in that while the model incorporates the size effects in the ion distribution profiles, it neglects these very same effects in the flux contributions, even though diffusivities are intrinsically linked with ionic friction, which again depends on the size of the ions. This oversight may lead to inconsistent quantitative estimates through ad hoc consideration of diffusivity values, apparently independent of the specific size of the ions, which nevertheless determines the ionic profiles. We remedy this theoretical inconsistency by expressing the diffusivity in terms of the ionic radius and investigate the consequences of such a description of the diffusivity-dependent flux, consistent with the ionic distribution profiles, on streaming potential mediated flow predictions. Additionally, we consider the effects of “charge induced thickening” so that both viscosity and diffusivity are expressed as spatially varying functions. As an unintuitive implication, we also show that calculation of nonzero values of streaming potential under the purview of classical Boltzmann distributions, which consider ions to be pointlike charges, is itself a theoretical inconsistency. We believe that the simple framework presented in this paper will pave the way for more sophisticated modeling efforts in the future.

A surprising feature of many bacterial motors is the apparently conserved form of their torque-frequency relation. Experiments indicate that the torque provided by the bacterial rotary motor is approximately constant over a large range of angular speeds. This is observed in both monotrichous and peritrichous bacteria, independently of whether they are propelled by a proton flux or by a Na${}^{+}$ ion flux. If the relation between angular speed $\omega$ and swimming speed is linear, a $\omega$-independent torque implies that the power spent in active motion is proportional to the instantaneous bacterial speed. Using realistic values of the relevant parameters, we show that a constant torque maximizes the volume of the region explored by a bacterium in a resource-depleted medium. Given that nutrients in the ocean are often concentrated in separate, ephemeral patches, we propose that the observed constancy of the torque may be a trait evolved to maximize bacterial survival in the ocean.

Spiral wave meander is a typical feature observed in cardiac tissue and in excitable media in general. Here, we show for a simple model of excitable cardiac tissue that a transition to alternans—a beat-to-beat temporal alternation in the duration of cardiac excitation—can also induce a transition in the spiral core motion that is related to the presence of synchronization defect lines (SDLs) or nodal lines. While this is similar to what has been predicted and indeed observed for complex-oscillatory media close to onset, we find important qualitative differences. For example, single straight SDLs rotate and induce an additional nonresonant frequency characterizing the core motion of the attached spiral. We analyze this behavior quantitatively as a function of the steepness of the restitution curve and show that the velocity and the directionality of the core motion vary monotonically with the control parameter. Our findings agree with recent observations in rat heart tissue cultures indicating that the described behavior is of rather general nature. In particular, it could play an important role in the context of potentially life-threatening cardiac arrhythmias such as fibrillation for which alternans and spiral waves are known precursors.

Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in a bacterial colony is investigated theoretically through a continuum model that considers chemotaxis. In the case of the gradient sensed by the bacterium is nearly uniform, the bacterial colony patterns are self-similar, which means they look the same at every scale. The scaling law of the bacterial colony growth has been revealed explicitly. Chemotaxis biases the movement of the bacterial population in colony to trend toward the chemical attractant. Moreover, the bacterial colonies evolve for a long time as the traveling wave with a sharp front.

Motivated by the idea that some characteristics are specific to the relations between individuals and not to the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have a link in one of the two states. We consider this link-dynamics model in fully connected networks, square lattices, and Erdös-Renyi random networks. In each case we find and characterize a number of nontrivial asymptotic configurations, as well as some of the mechanisms leading to them and the time evolution of the link heterogeneity index distribution. For a fully connected network and random networks there is a broad distribution of possible asymptotic configurations. Most asymptotic configurations that result from link dynamics have no counterpart under traditional node dynamics in the same topologies.

In three-dimensional excitable systems scroll waves may lose their originally straight shape through different instabilities. In experiments, the formation of zigzag-shaped or helical filaments is often observed. Such a deformation may be due to either a twist-induced instability or a 3D meandering instability. We performed a systematic study using a Belousov-Zhabotinsky (BZ) system with a vertical gradient of excitability and determined the necessary twist for the onset of undulation in the filament. Thus, we demonstrate that in the case of a BZ system with a gradient parallel to the filament, the deformation of the filament is induced by a twist-induced instability.

The effect of polymers on the bouncing behavior of droplets in a highly viscous, vertically shaken silicone oil bath was investigated in this study. Droplets of a sample liquid were carefully placed on a vibrating bath that was maintained well below the threshold of Faraday waves. The bouncing threshold of the plate acceleration depended on the acceleration frequency. For pure water droplets and droplets of aqueous polymer solutions, a minimum acceleration amplitude was observed in the acceleration threshold curves as a function of frequency. The bouncing acceleration amplitude for a droplet of a dilute aqueous polymer solution was higher than the acceleration amplitude for a pure water droplet. Measurements of the center of mass trajectory and the droplet deformations showed that the controlling parameter in the bouncing process was the oscillating elongational rate of the droplet. This parameter can be directly related to the elongational viscosity of the polymeric samples. The large elongational viscosity of the polymer solution droplets suppressed large droplet deformations, resulting in less chaotic bouncing.

The magnetohydrodynamic dynamo effect is considered to be the major cause of magnetic field generation in geo- and astrophysical systems. Recent experimental and numerical results show that turbulence constitutes an obstacle to dynamos; yet its role in this context is not totally clear. Via numerical simulations, we identify large-scale turbulent vortices with a detrimental effect on the amplification of the magnetic field in a geometry of experimental interest and propose a strategy for facilitating the dynamo instability by manipulating these detrimental “hidden” dynamics.

In this paper, we introduce a simple and practical method to generate Gaussian self-similar stochastic processes [fractional Gaussian noises (fGns) and fractional Brownian motions (fBms)] by interpolating between two known series of them. We apply the rotation algorithm to different cases including different pairs of fBms (fGns) and also different pairs each composed of an fBm and an fGn. Our results show that the sensitivity of our method for two fBms (fGns) is higher when approaching the series with a larger (smaller) Hurst exponent and, for the case with one fBm and one fGn by approaching the Hurst exponent of the selected fBm, the Hurst exponent of the produced series changes more. Surprisingly, by using this method, we can generate (positively and/or negatively) correlated series from two uncorrelated ones (one Brownian motion and one white Gaussian noise) or it is possible to generate uncorrelated signals (one or two depending on the choice of two input signals) from two correlated ones. For two fGns, using the rotation algorithm, the evolution starts from larger scales in the system, while for two fBms, the evolution starts from smaller scales in the system.

The graph layouts used for complex network studies have been mainly developed to improve visualization. If we interpret the layouts in metric spaces such as Euclidean ones, however, the embedded spatial information can be a valuable cue for various purposes. In this work, we focus on encoding useful navigational information to geometric coordinates of vertices of spatial graphs, which is a reverse problem of harnessing geometric information for better navigation. In other words, the coordinates of the vertices are a map of the topology, not the other way around. We use a recently developed user-centric navigation protocol to explore spatial layouts of complex networks that are optimal for navigation. These layouts are generated with a simple simulated annealing optimization technique. We compare these layouts to others targeted at better visualization and discuss the spatial statistical properties of the optimized layouts for better navigability and its implication.

We consider the physical limit of the directional sensing ability of living cells, as in chemotaxis, under a low concentration and shallow chemoattractant gradient. Elliptic cells sense the direction, which is a stochastic variable of a characteristic distribution with peaks at directions not necessarily to the gradient. The peak positions depend on the information of the gradient that cells use to infer the direction and also the shape and orientation of cells. Cells of different shapes may use different inference strategies to increase their directional sensing performance.