The dynamic shape relaxation of the two-layer vesicle is calculated. In addition to the undulation relaxation where the two bilayers move in the same direction, the squeezing mode appears when the gap between the two bilayers is small. At a large gap, the inner vesicle relaxes much faster, whereas the slow mode is mainly due to the outer-layer relaxation. We have calculated the viscoelasticity of the dilute two-layer-vesicle suspension. It is found that for a small gap, the applied shear drives the undulation mode strongly while the slow squeezing mode is not much excited. In this limit, the complex viscosity is dominated by the fast-mode contribution. On the other hand, the slow mode is strongly driven by shear for a larger gap. We have determined the crossover gap, which depends on the interaction between the two bilayers. For a series of samples where the gap is changed systematically, it is possible to observe the two amplitude switchings.

To probe the mechanical properties of cells, we investigate a technique to perform deformability-based cytometry that inherently induces normal antipodal surface forces using a single line-shaped optical trap. We show theoretically that these opposing forces are generated simultaneously over curved microscopic object surfaces with optimal magnitude at low numerical apertures, allowing the directed stretching of elastic cells with a single, weakly focused laser source. Matching these findings with concomitant experimental observations, we elongate red blood cells, effectively stretching them within the narrow confines of a steep, optically induced potential well.

It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and, hence, systemwide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e., the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture and, thus, enhance the level of protection of critical infrastructures.

PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the question of rank stability and choice of the damping factor (a parameter in the algorithm) is clearly important. We investigate PR as a function of the damping factor $d$ on a network obtained from a domain of the World Wide Web, finding that rank reversal happens frequently over a broad range of PR (and of $d$). We use three different correlation measures, Pearson, Spearman, and Kendall, to study rank reversal as $d$ changes, and we show that the correlation of PR vectors drops rapidly as $d$ changes from its frequently cited value, $d_0=0.85$. Rank reversal is also observed by measuring the Spearman and Kendall rank correlation, which evaluate relative ranks rather than absolute PR. Rank reversal happens not only in directed networks containing rank sinks but also in a single strongly connected component, which by definition does not contain any sinks. We relate rank reversals to rank pockets and bottlenecks in the directed network structure. For the network studied, the relative rank is more stable by our measures around $d=0.65$ than at $d=d_0$.

Orderliness, reflected via mathematical laws, is encountered in different frameworks involving social groups. Here we show that a thermodynamics can be constructed that macroscopically describes urban population flows. Microscopic dynamic equations and simulations with random walkers underlie the macroscopic approach. Our results might be regarded, via suitable analogies, as a step towards building an explicit social thermodynamics.

It is known that many-fermion systems, such as complex atoms and nuclei, reveal (at some level of excitation energy) local signatures of quantum chaos similar to the predictions of random matrix theory. Here, we study the gradual development of such signatures in a model system of up to 16 fermions interacting through short-range pairing-type forces in a two-dimensional harmonic trap. We proceed from the simplest characteristics of the level spacing distribution to the complexity of eigenstates, strength, and correlation functions. For increasing pairing strength, at first, chaotic signatures gradually appear. However, when the pairing force dominates the Hamiltonian, we see a regression towards regularity. We introduce a “phase correlator” that allows us to distinguish the complexity of a quantum state that originates from its collective nature, from the complexity originating from quantum chaos.

We present microwave experiments on the symmetry reduced five-disk billiard studying the transition from a closed to an open system. The measured microwave reflection signal is analyzed by means of the harmonic inversion and the counting function of the resulting resonances is studied. For the closed system this counting function shows the Weyl asymptotic with a leading exponent equal to 2. By opening the system successively this exponent decreases smoothly to a noninteger value. For the open systems the extraction of resonances by the harmonic inversion becomes more challenging and the arising difficulties are discussed. The results can be interpreted as a first experimental indication for the fractal Weyl conjecture for resonances.

Numerical simulations of the incompressible Euler equations are performed using the Taylor-Green vortex initial conditions and resolutions up to ${4096}^3$. The results are analyzed in terms of the classical analyticity-strip method and Beale, Kato, and Majda (BKM) theorem. A well-resolved acceleration of the time decay of the width of the analyticity strip $\delta \left(t\right)$ is observed at the highest resolution for $3.7<t<3.85$ while preliminary three-dimensional visualizations show the collision of vortex sheets. The BKM criterion on the power-law growth of the supremum of the vorticity, applied on the same time interval, is not inconsistent with the occurrence of a singularity around $t\simeq 4$. These findings lead us to investigate how fast the analyticity-strip width needs to decrease to zero in order to sustain a finite-time singularity consistent with the BKM theorem. A simple bound of the supremum norm of vorticity in terms of the energy spectrum is introduced and used to combine the BKM theorem with the analyticity-strip method. It is shown that a finite-time blowup can exist only if $\delta \left(t\right)$ vanishes sufficiently fast at the singularity time. In particular, if a power law is assumed for $\delta \left(t\right)$ then its exponent must be greater than some critical value, thus providing a new test that is applied to our ${4096}^3$ Taylor-Green numerical simulation. Our main conclusion is that the numerical results are not inconsistent with a singularity but that higher-resolution studies are needed to extend the time interval on which a well-resolved power-law behavior of $\delta \left(t\right)$ takes place and check whether the new regime is genuine and not simply a crossover to a faster exponential decay.

In this Brief Report, we show that balanced chemical reaction systems governed by the law of mass action have an elegant conservation-dissipation structure. From this structure a number of important conclusions can be easily deduced. In particular, with the help of this structure we can rigorously justify the classical partial equilibrium approximation in chemical kinetics.

We carry out a high-precision Monte Carlo study of the shortest-path fractal dimension $d_{\min }$ for percolation in two and three dimensions, using the Leath-Alexandrowicz method which grows a cluster from an active seed site. A variety of quantities are sampled as a function of the chemical distance, including the number of activated sites, a measure of the radius, and the survival probability. By finite-size scaling, we determine $d_{\min }=1.13077\left(2\right)$ and $1.3756\left(6\right)$ in two and three dimensions, respectively. The result in two dimensions rules out the recently conjectured value $d_{\min }=217/192$ [Deng et al., Phys. Rev. E 81, 020102(R) (2010)].

We investigate the problem of survival at the very low target-density limit and report on a second-order phase transition for one-dimensional random searches in which the energy cost of locomotion is a function of the distance traveled by the searcher. Surprisingly, from analytical calculations (also tested numerically) we find identical critical exponents for arbitrary energy cost functions. We conclude that there is a single universality class that describes this process.

The momentum relaxation of a relativistic Brownian particle immersed in a fluid is studied on the basis of the Fokker-Planck equation for the relativistic Ornstein-Uhlenbeck process. An analytical expression is derived for the short-time relaxation rate. The relaxation spectrum has both discrete and continuum components. It is shown that the Fokker-Planck equation under consideration is closely related to the Schrödinger equation for the hydrogen atom. Hence it follows that there is an infinite number of discrete states. The momentum autocorrelation function is calculated numerically for a strongly relativistic particle.

We study reaction fronts described by the Kuramoto-Sivashinsky equation subject to a Poiseuille flow. The fronts propagate with or against the flow located inside a two-dimensional slab. Steady front profiles can be flat, axisymmetric, or nonaxisymmetric, depending on the gap between the plates and the average flow speed. We first obtain the steady front solutions, later executing a linear stability analysis to determine the stability of the fronts. Applying fluid flow can turn initially unstable fronts into stable fronts. Stable steady fronts propagating in the adverse direction of the Poiseuille flow are axisymmetric for slow fluid flows. However, for higher speeds an adverse flow can lead to stable nonaxisymmetric fronts. We also show regions of bistability where stable nonaxisymmetric and axisymmetric fronts can coexist.

We study the problem of master-slave synchronization and control of totalistic cellular automata. The synchronization mechanism is that of setting a fraction of sites of the slave system equal to those of the master one (pinching synchronization). The synchronization observable is the distance between the two configurations. We present three control strategies that exploit local information (the number of nonzero first-order Boolean derivatives) in order to choose the sites to be synchronized. When no local information is used, we speak of simple pinching synchronization. We find the critical properties of control and discuss the best control strategy compared with simple synchronization.

Consistency of response in a system driven repeatedly by a complex signal has been observed in many nonlinear dynamical systems. We investigate the consistency of unidirectionally coupled semiconductor lasers with optical feedback and measure the complexity of the entire laser system by using the Lyapunov spectrum. The complexity strongly depends on the degree of consistency. It is found that the complexity of the coupled laser system can be classified into three regions. When the system shows consistency, the complexity of the entire laser system corresponds to that of the solitary drive laser. In the inconsistency region, the complexity of the entire laser system corresponds to the sum of the complexity of the uncoupled drive and response lasers. The complexity increases more than the sum of the two solitary lasers near the boundary of the consistency region, where new dynamical fluctuations appear due to the optical carrier interaction between the two lasers.

Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay valid when the effective Planck constant is increased? In this paper, we numerically study this problem, focusing on semiclassical predictions for the decay of the quantum Loschmidt echo in deep quantum regions. Our numerical simulations, carried out in the chaotic regime in the sawtooth model and in the kicked rotator model and also in the critical region of a one-dimensional Ising chain in transverse field, show that the semiclassical predictions may work even in deep quantum regions, particularly for perturbation strength in the so-called Fermi-Golden-Rule regime.

We report experimental evidence of an effect opposite to the “solidification” of small bubbles in liquid where the surface can become immobile. Namely, it is demonstrated that smooth solid spheres falling in a yield-stress fluid under the action of gravity can behave similar to drops. Particle tracking velocimetry was used to determine the shape of the yielded region around solid spherical particles undergoing slow stationary motion in 0.07$\%$ w/w Carbopol gel due to gravity under creeping flow conditions. The flow field inside the yielded region was determined by particle image velocimetry. It was found that the shape of the yielded region and the flow field around slow-moving rough particles is similar to the published results of numerical simulations, whereas those around smooth spheres resemble the experimental results obtained for viscous drops. The effect was explained by a slip of the gel on the smooth surface. Most likely, the slip originated from seepage of clean water from the gel, forming a thin lubricating layer near the solid surface.

We numerically study the effect of adding quenched disorder in the form of randomly placed pinning sites on jamming transitions in a disk packing that jams at a well-defined point $J$ in the clean limit. Quenched disorder decreases the jamming density and introduces a depinning threshold. The onset of a finite threshold coincides with point $J$ at the lowest pinning densities, but for higher pinning densities there is always a finite depinning threshold even well below jamming. We find that proximity to point $J$ strongly affects the transport curves and noise fluctuations, and we observe a change from plastic behavior below jamming, where the system is highly heterogeneous, to elastic depinning above jamming. Many of the general features we find are related to other systems containing quenched disorder, including the peak effect observed in vortex systems.

Large density fluctuations were observed by illuminating a cylindrical cell filled with sulfur hexafluoride (SF${}_6$), very near its liquid-gas critical point ($|T-T_c|<300\mu \mathrm{K}$) and recorded using a microscope with 3 μm spatial resolution. Using a dynamic structure factor algorithm, we determined from the recorded images the structure factor (SF), which measures the spatial distribution of fluctuations at different moments, and the correlation time of fluctuations. This method authorizes local measurements in contrast to the classical scattering techniques that average fluctuations over the illuminating beam. We found that during the very early stages of phase separation the SF scales with the wave vector $q$ according to the Lorentzian $q^{-2}$, which shows that the liquid and vapor domains are just emerging. The critical wave number, which is related to the characteristic length of fluctuations, steadily decreases over time, supporting a sustained increase in the spatial scale of the fluctuating domains. The scaled evolution of the critical wave number obeys the universal evolution for the interconnected domains at high volume fraction with an apparent power law exponent of −0.35 ± 0.02. We also determined the correlation time of the fluctuations and inferred values for thermal diffusivity coefficient very near the critical point, above and below. The values were used to pinpoint the crossing of $T_c$ within 13 μK.